Answer:
Step-by-step explanation:
To calculate the amount Aditi needs to pay, we need to apply the discounts step by step based on the given offer.
Step 1: 20% discount on all products
The marked price of the goods is Rs 2400. Applying a 20% discount means she will get a reduction of 20% of the marked price.
20% of Rs 2400 = (20/100) * Rs 2400 = Rs 480
After the first discount, the new bill amount is Rs 2400 - Rs 480 = Rs 1920.
Step 2: Additional 20% discount on the bill amount if it exceeds Rs 1000
The new bill amount after the first discount is Rs 1920. If this amount exceeds Rs 1000, Aditi will get a further discount of 20% on this bill amount.
Since Rs 1920 is greater than Rs 1000, we can apply a 20% discount to it.
20% of Rs 1920 = (20/100) * Rs 1920 = Rs 384
The final amount Aditi needs to pay after both discounts is Rs 1920 - Rs 384 = Rs 1536.
Therefore, Aditi needs to pay Rs 1536.
NO LINKS!! URGENT HELP PLEASE!!
Answer:
[tex]\text{a.} \quad m\angle NLM=93^{\circ}[/tex]
[tex]\text{c.} \quad m\angle FHG=31^{\circ}[/tex]
Step-by-step explanation:
The inscribed angle in the given circle is ∠NLM.
The intercepted arc in the given circle is arc NM = 186°.
According to the Inscribed Angle Theorem, the measure of an inscribed angle is half the measure of the intercepted arc.
Therefore:
[tex]m\angle NLM=\dfrac{1}{2}\overset{\frown}{NM}[/tex]
[tex]m\angle NLM=\dfrac{1}{2} \cdot 186^{\circ}[/tex]
[tex]\boxed{m\angle NLM=93^{\circ}}[/tex]
[tex]\hrulefill[/tex]
According to the Inscribed Angle Theorem, the measure of an inscribed angle is half the measure of the intercepted arc. Therefore:
[tex]m\angle HFG=\dfrac{1}{2}\overset{\frown}{HG}[/tex]
[tex]m\angle HFG=\dfrac{1}{2}\cdot 118^{\circ}[/tex]
[tex]m\angle HFG=59^{\circ}[/tex]
As line segment FH passes through the center of the circle, FH is the diameter of the circle. Since the angle at the circumference in a semicircle is a right angle, then:
[tex]m\angle FGH = 90^{\circ}[/tex]
The interior angles of a triangle sum to 180°. Therefore:
[tex]m\angle FHG + m\angle HFG + m\angle FGH =180^{\circ}[/tex]
[tex]m\angle FHG + 59^{\circ} + 90^{\circ} =180^{\circ}[/tex]
[tex]m\angle FHG +149^{\circ} =180^{\circ}[/tex]
[tex]\boxed{m\angle FHG =31^{\circ}}[/tex]
Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
The number line that represents the solution set for the inequality 3(8 – 4x) < 6(x – 5) is option C: A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3, and a bold line starts at negative 3 and is pointing to the left.
To determine the solution set for the inequality 3(8 – 4x) < 6(x – 5), we need to solve it step by step:
Simplify the inequality:
24 - 12x < 6x - 30
Combine like terms:
-12x - 6x < -30 - 24
-18x < -54
Divide both sides of the inequality by -18, remembering to flip the inequality sign:
x > (-54) / (-18)
x > 3
The inequality tells us that x must be greater than 3. To represent this on a number line, we place an open circle at the value 3 and draw a bold line pointing to the right to indicate that the solution set includes all values greater than 3.
Therefore, option C accurately represent the solution set for the inequality 3(8 – 4x) < 6(x – 5).
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Please answer ASAP I will brainlist
Answer:
There is one solution. The solution is 2, 18, 19.
Step-by-step explanation:
If you want me to show working tell me in the comments and I'll edit the answer
Answer:
A. (2, 18, -19)
Step-by-step explanation:
To solve:
Z is the most suitable variable to remove first
Add the first equation to the second equation: (this conveniently removes both y and z)
(x+y-z) + (4x-y+z) = 1+9
Simplify
5x = 10
Solve
x = 2
Multiply the second equation by 2 and minus it to the third equation: (Solve for y)
2(4x-y+z) - (x-3y+2z) = 2(9) - (-14)
Simplify
8x-2y+2z-x+3y-2z=18+14
7x+y=32
Substitute using x=2
7(2) + y = 32
y = 32 - 14
y = 18
Now substitute x and y for their respective values into Equation 1
2 + (-18) - z = 1
Simplify
-z = 19
z = -19
So :
x = 2, y = 18 , z = -19
If all the values in the series are same, then
Select one:
a. A.M = G.M = H.M
b. A.M > G.M > H.M
c. A.M < G.M < H.M
d. None of these
e. A.M ? G.M ? H.M
Note: A.M means Arithmetic mean, H.M means Harmonic mean, while G.M means Geometric mean.
Any answer without justification will be rejected automatically.
If all the values in the series are the same, the A.M, G.M, and H.M are all equal and can be represented as A.M = G.M = H.M = x.
If all the values in the series are the same, the arithmetic mean (A.M), geometric mean (G.M), and harmonic mean (H.M) will all be equal.
Let's consider a series with the same value repeated n times, denoted as x:
Series: x, x, x, ..., x (n times)
Arithmetic Mean (A.M):
The arithmetic mean is calculated by summing all the values in the series and dividing by the total number of values. In this case, the sum of all the values is nx, and since there are n values, the arithmetic mean is (nx) / n = x. So, A.M = x.
Geometric Mean (G.M):
The geometric mean is calculated by taking the nth root of the product of all the values in the series. In this case, the product of all the values is x^n, and since there are n values, the nth root of x^n is x. So, G.M = x.
Harmonic Mean (H.M):
The harmonic mean is calculated by taking the reciprocal of the arithmetic mean of the reciprocals of all the values in the series. Since all the values are the same, the reciprocal of each value is 1/x. The arithmetic mean of the reciprocals is (1/x + 1/x + ... + 1/x) / n = (n/x) / n = 1/x. Taking the reciprocal of 1/x gives x. So, H.M = x.
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(03.01 MC)
Explain how the Quotient of Powers Property was used to simplify this expression. (1 point)
three to the fourth power all over nine equals three squared
By simplifying 9 to 32 to make both powers base three and adding the exponents
By simplifying 9 to 32 to make both powers base three and subtracting the exponents
By finding the quotient of the bases to be one third and simplifying the expression
By finding the quotient of the bases to be one third and cancelling common factors
The correct answer is By finding the quotient of the bases to be one third and canceling common factors. Option D.
The Quotient of Powers Property states that when dividing two powers with the same base, you can subtract the exponents. In the given expression, we have three to the fourth power divided by nine.
To simplify this expression using the Quotient of Powers Property, we first need to recognize that nine can be written as three squared, since 3 multiplied by itself gives 9.
So, we have (3^4) / (3^2). According to the Quotient of Powers Property, we subtract the exponents: 4 - 2.
This gives us 3^(4-2), which simplifies to 3^2. Therefore, the expression three to the fourth power all over nine equals three squared.
It states that we find the quotient of the bases to be one third and cancel common factors. In this case, the bases are 3 and 3, and their quotient is indeed one third. Additionally, there are no common factors that can be canceled, as the expression does not contain any variables or additional terms.
Therefore, By finding the quotient of the bases to be one third and canceling common factors. accurately describes the steps involved in simplifying the expression using the Quotient of Powers Property.
We find the quotient of the bases (one third) and cancel common factors (which is not applicable in this case). Option D is correct.
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Note the complete question is
Explain how the Quotient of Powers Property was used to simplify this expression. (1 point)
Three to the fourth power all over nine equals three squared
A.) By simplifying 9 to 32 to make both powers base three and adding the exponents
B.) By simplifying 9 to 32 to make both powers base three and subtracting the exponents
C.) By finding the quotient of the bases to be one third and simplifying the expression
D.) By finding the quotient of the bases to be one third and cancelling common factors
Find the measurement of each angle in a triangle. You need to provide me 3 different measurement of angles. please help !!
Answer:
x=30 degrees, 2x=60 degrees, 3x=90 degrees
Step-by-step explanation:
in a triangle the sum of angles is 180 so
x+2x+3x=180
6x=180
x=180/6
x=30
so the angle x is 30 degrees, the angle that is 2x is 60 degrees and the angle the angle 3x is 90
Pls help I beg thank you
Answer:
8cm
Step-by-step explanation:
perimiter A = 11+11+4+4=30
perimiter B = 4+4+8+8=24
24+30=54
perimeter c =4+8+8+4+11+7+4=46
so perimiter of c is 8cm shorter than A and B total
hope this helps
how to distribute x(3-x)
Answer:
3x - x²
Step-by-step explanation:
x(3 - x)
each term in the parenthesis is multiplied by the x outside. This is called the Distributive law
= (x × 3) + (x× - x)
= 3x + (- x²)
= 3x - x²
The answer is:
3x - x²Work/explanation:
To simplify this expression, we will use the distributive property:
[tex]\sf{x(3-x)}[/tex]
Distribute the x:
[tex]\sf{x\cdot3-x\cdot x}[/tex]
[tex]\sf{3x-x^2}[/tex]
Therefore, the answer is 3x - x².What is the slope of the line shown below?
-6
10
(-3,-7) 5
-10
AY
(9, 1)
10
15
X
O A.-²2/
3
OB.
NIM
O c. 3
2
O D.
3
MIN
Answer:
[tex]m = \frac{1 - ( - 7)}{9 - ( - 3)} = \frac{8}{12} = \frac{2}{3} [/tex]
B is the correct answer.
Pls help I need this answer
Answer:
B , D , A
Step-by-step explanation:
(4x³ - 4 + 7x) - (2x³ - x - 8)
distribute the first parenthesis by 1 and the second by - 1
= 4x³ - 4 + 7x - 2x³ + x + 8 ← collect like terms
= 2x³ + 8x + 4 ← equivalent to expression B
---------------------------------------------------------------
(- 3x² + [tex]x^{4}[/tex] + x) + (2[tex]x^{4}[/tex] - 7 + 4x) ← remove parenthesis
= - 3x² + [tex]x^{4}[/tex] + x + 2[tex]x^{4}[/tex] - 7 + 4x ← collect like terms
= 3[tex]x^{4}[/tex] - 3x² + 5x - 7 ← equivalent to expression D
------------------------------------------------------------------
(x² - 2x)(2x + 3)
each term in the second factor is multiplied by each term in the first factor, that is
x²(2x + 3) - 2x(2x + 3) ← distribute parenthesis
= 2x³ + 3x² - 4x² - 6x ← collect like terms
= 2x³ - x² - 6x ← equivalent to expression A
what is the value of m
The value of m<RQS as required to be determined in the task content is; 70°.
What is the value of m<RQS as required to be determined?It follows from the task content that the measure of angle RQS is to be determined as required.
Recall, the measure of the central angle subtended by an arc is twice that which it subtends at any point on the circumference.
Therefore, m<RPS = 2 • m<RQS.
m<RQS = 140°/2
m<RQS = 70°.
Ultimately, the measure of angle RQS are; 70°.
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The veterinarian has prescribed carprofen 2.2 mg/kg BID x30d. Weight of patient is 34kg. Concentration is 75mg tablet. What is the amount of medication needed for 30 days?
The amount of medication needed for 30 days is approximately 59.84 tablets of carprofen.
To calculate the amount of carprofen medication needed for 30 days, we need to consider the prescribed dosage, the weight of the patient, and the concentration of the tablets.
The prescribed dosage is 2.2 mg/kg BID x 30d. This means that the patient should take 2.2 milligrams of carprofen per kilogram of body weight, twice a day, for 30 days.
The weight of the patient is 34 kilograms. So, we need to calculate the total amount of carprofen needed for the entire treatment period.
First, we calculate the daily dosage by multiplying the weight of the patient (34 kg) by the prescribed dosage (2.2 mg/kg).
Daily dosage = 34 kg * 2.2 mg/kg = 74.8 mg/day.
Since the medication is prescribed twice a day, we multiply the daily dosage by 2 to get the total dosage per day.
Total dosage per day = 74.8 mg/day * 2 = 149.6 mg/day.
Finally, to find the total amount of medication needed for 30 days, we multiply the total dosage per day by the number of days.
Total medication needed = 149.6 mg/day * 30 days = 4488 mg.
Since the concentration of the tablets is 75 mg, we divide the total medication needed by the tablet concentration to find the number of tablets required.
Number of tablets needed = 4488 mg / 75 mg = 59.84.
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Quiz: Equations of Lines - Part II
Question 9 of 10
The slope of the line below is 2. Which of the following is the point-slope form
of the line?
OA. y-1 -2(x+1)
B. y-1=2(x+1)
OC. y+1 -2(x-1)
D. y+1=2(x-1)
-10
10-
(1,-1)
10
Answer:
We have the slope of the line, which is 2 and a point that is (1, -1).
To find the point-slope form of the line, we use the equation:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is the given point.
Substituting in the values we have, we get:
y - (-1) = 2(x - 1)
Simplifying this equation, we get:
y + 1 = 2(x - 1)
Therefore, the answer is option C: y + 1 - 2(x - 1).
a) Write a linear system to model the situation:
For the school play, the cost of one adult ticket is $6 and the cost of one student ticket is $4. Twice as many student tickets as adult tickets were sold. The total receipts were $2016.
b) Use substitution to solve the related problem:
How many of each type of ticket were sold?
Answer:
There were 126 student tickets sold and 252 adult ticket sold.
Step-by-step explanation:
Let x be the number of adult tickets sold
y be the number of students tickets sold
Twice as many student tickets as adult tickets were sold
a.
x = 2y ---equation 1
6x + 4y = 2016 ---equation 2
b.
Substitute equation 1 to equation 2
6(2y) + 4y = 2016
12y + 4y = 2016
16y = 2016
Divide both sides of the equation by 16
16y/16 = 2016/16
y = 126
Substitute y = 126 to equation 1
x = 2y
x = 2(126)
x = 252
Algebra Question
Jasmine played outside today. She asked her mother if she could play outside tomorrow. Her mother said she could play outside only if the difference between today’s temperature and tomorrow’s temperature is less than 10 degrees. If today’s temperature was 93, what is the range of temperatures that would allow Jasmine to play outside tomorrow?
Address each of these parts:
a. Define the variable for the situation.
b. Write an absolute value inequality to represent the situation (tolerance).
c. Solve the inequality.
Referring back to the last question, using words, write the interpretation of the solution in terms of the range of temperatures that will allow Jasmine to play outside. Then, graph the solution.
Answer:
a. Let tomorrow's temperature be x
b.
[tex] |93 - x | < 10[/tex]
c.
[tex] - 10 < 93 - x < 10 \\ - 103 < - x < - 83 \\ 103 > x > 83[/tex]
Identify the algebraic rule that would translate a figure 3 units left and 2 units up.
The algebraic rule for translating the figure 3 units left and 2 units up is (x-3, y+2). Option B.
To translate a figure 3 units to the left and 2 units up, we need to adjust the coordinates of the figure accordingly. The algebraic rule that represents this translation can be determined by examining the changes in the x and y coordinates.
When we move a figure to the left, we subtract a certain value from the x coordinates. In this case, we want to move the figure 3 units to the left, so we subtract 3 from the x coordinates.
Similarly, when we move a figure up, we add a certain value to the y coordinates. In this case, we want to move the figure 2 units up, so we add 2 to the y coordinates.
Taking these changes into account, we can conclude that the algebraic rule for translating the figure 3 units left and 2 units up is (x-3, y+2). The x coordinates are shifted by subtracting 3, and the y coordinates are shifted by adding 2. SO Option B is correct.
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PLSS HELP HURRYYY
ILL GIVE BRAINLIST
Answer:
hope you understand it and please follow me
Select all the correct answers.
Third
B.
90 feet
A. 16, 200 feet
√180 feet
C. √16, 200 feet
180 feet
D.
The area of a baseball field bounded by home plate, first base, second base, and third base is a square. If a player at first base throws the ball to a
player at third base, what is the distance the player has to throw?
First
90 feet
Home
Reset
Next
The diagonal distance from home plate to third base is approximately √16,200 feet.
The correct answers are:
B. 90 feet
C. √16,200 feet
D. 180 feet.
In baseball, the bases are arranged in a square shape.
The distance between each base is 90 feet.
Therefore, the correct answer for the distance a player at first base has to throw to a player at third base is 90 feet (option B).
To find the diagonal distance from home plate to third base, we can use the Pythagorean theorem.
Since the area of the baseball field is a square, the diagonal distance represents the hypotenuse of a right triangles.
The two legs of the right triangle are the sides of the square, which are 90 feet each.
Using the Pythagorean theorem [tex](a^2 + b^2 = c^2),[/tex] we can calculate the diagonal distance:
a = b = 90 feet
[tex]c^2 = 90^2 + 90^2[/tex]
[tex]c^2 = 8,100 + 8,100[/tex]
[tex]c^2 = 16,200[/tex]
c = √16,200 feet (option C)
Therefore, the diagonal distance from home plate to third base is approximately √16,200 feet.
The options A, √180 feet, and 180 feet are incorrect because they do not represent the correct distances in the given scenario.
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Roger can run one mile in 9 minutes. Jeff can run one mile in 6 minutes. If Jeff gives Roger a 1 minute head start, how
long will it take before Jeff catches up to Roger? How far will each have run?
They each will have run of a mile.
It will take approximately 5.33 minutes for Jeff to catch up to Roger. Both Jeff and Roger will have run a distance of 1 mile.
Let's calculate the time it takes for Jeff to catch up to Roger and the distance each will have run.
First, we need to determine how much distance Roger covers during the 1-minute head start. Since Roger runs one mile in 9 minutes, in 1 minute, he would cover 1/9 of a mile.
Now, let's set up an equation to represent the time it takes for Jeff to catch up to Roger:
Distance covered by Jeff = Distance covered by Roger + Distance covered during the head start
Let's denote the time it takes for Jeff to catch up as t minutes. During this time, Jeff runs a distance of 1 mile, while Roger runs a distance of 1/9 of a mile (from the head start).
Distance covered by Jeff = Distance covered by Roger + Distance covered during the head start
1 mile = (1/9) mile + (6 minutes) × t × (1 mile/6 minutes)
Now, let's solve this equation to find the time it takes for Jeff to catch up:
1 = (1/9) + (1/6)t
Multiplying the equation by the least common multiple (LCM) of 9 and 6, which is 18, to clear the fractions:
18 = 2 + 3t
Subtracting 2 from both sides:
16 = 3t
Dividing by 3:
t = 16/3 = 5.33 minutes (rounded to two decimal places)
Therefore, it will take approximately 5.33 minutes for Jeff to catch up to Roger. Both Jeff and Roger will have run a distance of 1 mile.
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A total of 90 groom's guests and 85 bride's guests attended a wedding. The bride's guests used 100 tissues. The groom's guests used 180 tissues. Calculate approximately how many tissues each groom's guest used.
Approximately 2 tissues were used by each groom's guest at the wedding.
The calculation is as follows:
180 tissues ÷ 90 guests = 2 tissues per guest.
To determine how many tissues each groom's guest used, we need to find the average number of tissues per guest. We start by adding up the number of tissues used by the groom's guests, which is 180.
Then, we divide this total by the number of groom's guests, which is 90. This division gives us an average of 2 tissues per guest.
By dividing the total number of tissues used by the total number of guests, we can find the average number of tissues per guest. In this case, each groom's guest used approximately 2 tissues.
It's important to note that this calculation assumes an equal distribution of tissues among all the groom's guests.
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Question #4
Find the measure of the indicated angle.
20°
161°
61°
73°
H
G
F
73° E
195°
The measure of the outside angle F indicated in the figure is 61 degrees,
What is the measure of angle GFE?The external angle theorem states that "the measure of an angle formed by two secant lines, two tangent lines, or a secant line and a tangent line from a point outside the circle is half the difference of the measures of the intercepted arcs.
Expressed as:
Outside angle = 1/2 × ( major arc - minor arc )
From the figure:
Major arc = 195 degrees
Minor arc = 73 degrees
Outside angle F = ?
Plug the value of the minor and major arc into the above formula and solve for the outside angle F:
Outside angle = 1/2 × ( major arc - minor arc )
Outside angle = 1/2 × ( 195 - 73 )
Outside angle = 1/2 × ( 122 )
Outside angle = 122/2
Outside angle = 61°
Therefore, the outside angle measures 61 degrees.
Option C) 61° is the correct answer.
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find surface area and volume
The surface area and volume of the composite solid is are 1720ft² and 3563.33 ft³ respectively.
What is volume and surface area of composite solid?The area occupied by a three-dimensional object by its outer surface is called the surface area.
The surface area of the solid = lateral area of pyramid + surface area of cuboid
lateral area of pyramid = 4 × 1/2 bh
= 4 × 1/2 × 10× 12
= 120×2 = 240 ft²
Surface area of the cuboid = 2( 100+ 320+ 320)
= 2( 740)
= 1480 ft²
Surface area of the composite solid = 240 + 1480
= 1720 ft²
Volume of the composite solid = volume of cuboid + volume of pyramid
volume of cuboid = 10×10×32 = 3200ft²
volume of pyramid = 1/3base area × height
height of the pyramid is calculated as;
diagonal of base = √ 10²+10²
= √200
= 14.14
h² = 13²-7.07²
h² = 169 - 49.98
h² = 119.02
h = 10.9 ft
Volume of pyramid = 1/3 × 100 × 10.9
= 363.33 ft³
Volume of the composite solid = 3200+363.33
= 3563.33 ft³
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if you apply the changes below to the quadratic pareent function, F(x)=x^2 what is the equation of the new function? shift 6 units right. shift 4 units down.
The equation of the new function after shifting 6 units right and 4 units down is f(x) = (x + 6)² - 4.
If we are to apply the changes below to the quadratic parent function, F(x) = x², what is the equation of the new function, given that we are to shift 6 units to the right and 4 units down? We will approach this question by following the steps outlined below.
Step 1: Identify the parent function F(x) = x² and its transformations
Step 2: Write the equation of the new function
Step 3: Simplify the new equation of the function.Step 1: Identify the parent function F(x) = x² and its transformations
Here, we are given the quadratic parent function F(x) = x² and two transformations: shift 6 units right and shift 4 units down.
The general equation for the horizontal and vertical shifts of a quadratic function is given by:f(x) = a(x - h)² + k, where a, h, and k are constants.
The value of a determines the direction of opening of the parabola, while (h, k) represents the vertex of the parabola.
If a > 0, the parabola opens upwards, while a < 0, the parabola opens downwards. If the values of (h, k) are positive, the parabola is shifted right and up, respectively. On the other hand, if the values of (h, k) are negative, the parabola is shifted left and down, respectively.
Therefore, given the quadratic parent function F(x) = x² and two transformations: shift 6 units right and shift 4 units down, we can represent these changes by the following:
a = 1 (since the parabola opens upwards)h = -6 (since we are shifting the parabola 6 units to the right)k = -4 (since we are shifting the parabola 4 units down)
Step 2: Write the equation of the new function Now that we have identified the constants a, h, and k, we can write the equation of the new function as follows:f(x) = a(x - h)² + kf(x) = 1(x - (-6))² + (-4)Replacing the constants a, h, and k in the equation, we have:f(x) = (x + 6)² - 4
Step 3: Simplify the new equation of the function.f(x) = (x + 6)² - 4= (x + 6)(x + 6) - 4= x² + 12x + 36 - 4= x² + 12x + 32Therefore, the equation of the new function after shifting 6 units right and 4 units down is f(x) = x² + 12x + 32.
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9497 ÷ 16 _R_ please
The diagram shows the curve y = √8x + 1 and the tangent at the point P(3, 5) on the curve. The tangent meets the y-axis at A. Find:
(i) The equation of the tangent at P.
(ii) The coordinates of A.
(iii) The equation of the normal at P.
The tangent and normal lines of the curve:
Case (i): y = (4 / 5) · x + 13 / 5
Case (ii): (x, y) = (0, 13 / 5)
Case (iii): y = - (5 / 4) · x + 35 / 4
How to determine the equations of the tangent and normal lines
In this problem we have the representation of a curve whose equations for tangent and normal lines must be found. Lines are expressions of the form:
y = m · x + b
Where:
m - Slopeb - Interceptx - Independent variable.y - Dependent variable.Both tangent and normal lines are perpendicular, the relationship between the slopes of the two perpendicular lines is:
m · m' = - 1
Where:
m - Slope of the tangent line.m' - Slope of the normal line.The slope of the tangent line is found by evaluating the first derivative of the curve at intersection point.
Case (i) - First, determine the slope of the tangent line:
y = √(8 · x + 1)
y' = 4 / √(8 · x + 1)
y' = 4 / √25
y' = 4 / 5
Second, determine the intercept of the tangent line:
b = y - m · x
b = 5 - (4 / 5) · 3
b = 5 - 12 / 5
b = 13 / 5
Third, write the equation of the tangent line:
y = (4 / 5) · x + 13 / 5
Case (ii) - Find the coordinates of the intercept of the tangent line:
(x, y) = (0, 13 / 5)
Case (iii) - First, find the slope of the normal line:
m' = - 1 / (4 / 5)
m' = - 5 / 4
Second, determine the intercept of the normal line:
b = y - m' · x
b = 5 - (- 5 / 4) · 3
b = 5 + 15 / 4
b = 35 / 4
Third, write the equation of the normal line:
y = - (5 / 4) · x + 35 / 4
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Evaluate |x - y| + 4 if x = -1, y = 3, and z = -4.
Answer:
8
Step-by-step explanation:
Substitute the values in the expression, we have:
[tex]\displaystyle{|-1-3|+4}[/tex]
Evaluate:
[tex]\displaystyle{|-4|+4}[/tex]
Any real numbers in the absolute sign will always be evaluated as positive values. Thus:
[tex]\displaystyle{|-4|+4 = 4+4}\\\\\displaystyle{=8}[/tex]
Hence, the answer is 8. A quick note that z-value is not used due to lack of z-term in the expression.
You flip a coin twice. The first flip lands tails up and the second flip also lands tails up. It is independent or dependent?
Answer:
Independent
Step-by-step explanation:
Flipping a coin is independent of each flip.
Answer:
Independent
Step-by-step explanation:
The flipping of two coins are an independent event. The reason for this is that one coin flip does not affect the outcome of the other flip. An example of a dependent event would be coat sales and weather, as cold weather would affect the amount of coats sold.
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A total of 60% of the customers of a fast food chain order a hamburger, french fries, and a drink. if a random sample of 15 cash register receipts is selected, what is the probability that less than 10 will show that the above three food items were ordered?
The probability that less than 10 out of 15 cash register receipts will show the three food items ordered is approximately 0.166.
To calculate the probability that less than 10 out of 15 cash register receipts show that the hamburger, french fries, and a drink were ordered, we can use the binomial probability formula. The formula for the probability of obtaining exactly k successes in n trials is:
P(X = k) = (nCk) * p^k * (1 - p)^(n - k)
where:
P(X = k) is the probability of obtaining k successes,
n is the number of trials,
p is the probability of success in a single trial, and
(nCk) is the binomial coefficient, which represents the number of ways to choose k successes out of n trials.
In this case, we want to find the probability of less than 10 out of 15 receipts showing the three food items ordered. We need to calculate the probabilities for k = 0, 1, 2, ..., 9, and sum them up.
Let's calculate the probabilities using the formula:
P(X < 10) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 9)
where:
n = 15 (number of trials),
p = 0.60 (probability of success, i.e., ordering hamburger, french fries, and a drink).
Using a binomial calculator or a statistical software, we can calculate each individual probability and then sum them up. The result will be the probability that less than 10 out of 15 receipts show the three food items ordered.
The probability that less than 10 out of 15 cash register receipts will show the three food items ordered is approximately 0.166.
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Suppose we have two equations and they are both equal to each other. Equation A is "y = x^2 - 9" and Equation B is "y = x + 3". If we had to solve this system of equations, what quadratic equation do we have to solve in order to get our x values?
a. x^2 - x - 12 = 0
b. x^2 + x + 3 = 0
c. x^2 - x - 6 = 0
Answer:
a) x² - x - 12 = 0
Step-by-step explanation:
We have equation A = equation B
⇒ x² - 9 = x + 3
⇒ x² - 9 - x - 3 = 0
⇒ x² - x - 12 = 0
Find the area of quadrilateral QUAD, whose vertices are:
Q (-4, 3), U (3, 6), 1 (6, 3), and D (1, -4).
The area of quadrilateral QUAD is 2.5 square units.
To find the area of quadrilateral QUAD with vertices Q (-4, 3), U (3, 6), 1 (6, 3), and D (1, -4), we can use the Shoelace formula (also known as Gauss's area formula or the surveyor's formula).
The Shoelace formula states that the area of a polygon with vertices (x1, y1), (x2, y2), ..., (xn, yn) can be calculated as:
[tex]Area = 1/2 * |(x1y2 + x2y3 + ... + xny1) - (x2y1 + x3y2 + ... + x1yn)|[/tex]
Using this formula, we can calculate the area of quadrilateral QUAD as follows:
Area = [tex]1/2 * |(-46 + 33 + 6*(-4) + 13) - (33 + 6*(-4) + 1*(-4) + (-4)*3)|[/tex]
Simplifying the expression, we get:
[tex]Area = 1/2 * |(-24 + 9 - 24 + 3) - (9 - 24 - 4 - 12)|Area = 1/2 * |(-36) - (-31)|Area = 1/2 * |-36 + 31|Area = 1/2 * |-5|Area = 1/2 * 5Area = 5/2[/tex]
The area of quadrilateral QUAD is 2.5 square units.
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The area of quadrilateral QUAD is 17.5 square units.
The area of quadrilateral QUAD, we can use the Shoelace Formula, also known as the Gauss's Area Formula.
The formula states that if the coordinates of the vertices of a polygon are given in order, then the area of the polygon can be calculated using the following formula:
Area = 1/2 × |(x1y2 + x2y3 + ... + xn-1yn + xny1) - (y1x2 + y2x3 + ... + yn-1xn + ynx1)|
Let's apply this formula to find the area of quadrilateral QUAD:
Q (-4, 3)
U (3, 6)
A (6, 3)
D (1, -4)
Area = 1/2 × |(-4 × 6 + 3 × 3 + 6 × (-4) + 3 × (-1)) - (3 × 3 + 6 × (-4) + (-4) × (-1) + (-1) × (-4))|
Area = 1/2 × |(-24 + 9 - 24 - 3) - (9 - 24 + 4 + 4)|
Area = 1/2 × |(-42) - (-7)|
Area = 1/2 × |-42 + 7|
Area = 1/2 × |-35|
Area = 1/2 × 35
Area = 17.5
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