Answers
Answer:
D
Step-by-step explanation:
y = x² - 4x - 5 → (1)
y = x - 9 → (2)
substitute y = x² - 4x - 5 into (2)
x² - 4x - 5 = x - 9 ( subtract x - 9 from both sides )
x² - 5x + 4 = 0 ← in standard form
(x - 1)(x - 4) = 0 ← in factored form
equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
x - 4 = 0 ⇒ x = 4
substitute these values into (2) for corresponding values of y
x = 1 : y = 1 - 9 = - 8 ⇒ (1, - 8 )
x = 4 : y = 4 - 9 = - 5 ⇒ (4, - 5 )
Related Questions
Please help solve this
Answers
Angles are measured in degrees and radians, and can be created by joining the extremities of two rays. The joint vertex is the common terminal of the two beams. Thus, ∠SRT = 38.16°.
What are angles?An angle is the result of the intersection of two lines.
An "angle" is the length of the "opening" between these two beams.
Angles are commonly measured in degrees and radians, a measurement of circularity or rotation.
In geometry, an angle can be created by joining the extremities of two rays. These rays are intended to represent the angle's sides or limbs.
The two primary components of an angle are the limbs and the vertex.
The joint vertex is the common terminal of the two beams.
According to our question,
6x-66°+5x-26°+70°+x+70°=360°
6x+5x+x+ 66°+140°=360°
12x+ 206°=360°
12x=360°-206°
12x= 154°
x= 154/12°
Hence, ∠SRT = 5x - 26°
= 5 * 154/12° - 26°
= 770/12° - 26°
= 64.16° - 26°
= 38.16°
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y=xto the power of 2+4x-12
Answers
The equation [tex]y = x^2 + 4x - 12[/tex] represents a parabolic curve in a 2D coordinate system.
What is graph?
A graph is a concept in mathematics and computer science that involves a set of nodes or vertices, linked together by edges to depict the interconnections between objects. Graphs are a powerful method for examining complex relationships within diverse systems, including communication networks, transportation systems, and social networks.
To graph this equation, you can follow these steps:
Choose a range of values for x that you want to plot. For example, you might choose x values from -6 to 2.
For each x value, calculate the corresponding y value by plugging it into the equation. For example, if x = -6, then y = [tex](-6)^2[/tex] + 4(-6) - 12 = 0.
Plot each (x, y) pair on the graph.
Connect the plotted points with a smooth curve to represent the parabolic shape of the equation.
Using these steps, you can graph the equation [tex]y = x^2 + 4x - 12[/tex] to visualize its shape and better understand its behavior.
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A customer purchased a book that had an original price for $38. The book is discounted 25%. The customer must pay a 6% sales tax on the discounted price of the book.
What is the total amount, in dollars, the customer pays for the discounted book?
Enter your answer in the box.
Answers
$30.21 is the total amount, in dollars, the customer pays for the discounted book.
If the original price of the book was $38, and it was discounted by 25%, then the discounted price of the book would be:
Discounted price = Original price - Discount
Discounted price = $38 - 0.25 x $38
Discounted price = $28.50
Now, the customer must pay a 6% sales tax on the discounted price of the book. The sales tax can be calculated as:
Sales tax = 0.06 x Discounted price
Sales tax = 0.06 x $28.50
Sales tax = $1.71
Therefore, the total amount the customer pays for the discounted book is the sum of the discounted price and the sales tax:
Total amount = Discounted price + Sales tax
Total amount = $28.50 + $1.71
Total amount = $30.21
So, the customer pays $30.21 for the discounted book
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In ΔMNO, the measure of ∠O=90°, MO = 8, ON = 15, and NM = 17. What ratio represents the sine of ∠M?
Answers
The ratio representing the sine of angle ∠M in triangle MNO, where ∠O = 90°, MO = 8, ON = 15, and NM = 17, is 17/8.
In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this problem, we are given a right triangle MNO, with a right angle at O. The side opposite angle M is MN, and the hypotenuse is MO.
To find the sine of angle M, we use the formula sin(M) = opposite/hypotenuse, where the opposite side is MN and the hypotenuse is MO.
Using the Pythagorean theorem, we can find the length of side MN:
[tex]MN^2 = MO^2 + ON^2[/tex]
[tex]MN^2 = 8^2 + 15^2[/tex]
[tex]MN^2[/tex] = 289
MN = 17
Therefore, the sine of angle M is:
sin(M) = MN/MO
sin(M) = 17/8
The ratio that represents the sine of angle M is 17/8.
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A
Samuel's specialty is fences. He has a standard fence he likes to build. It's
perimeter is 76 2/3 feet. If Samuel builds eight of these fences, how many feet of
material will he need? Explain how you found your answer.
Answers
Answer:
Samuel will need 614 2/3 feet of material to build eight of his standard fences. To find this answer, we simply need to multiply 76 2/3 feet (the perimeter of one fence) by 8 (the number of fences he wants to build). Thus, 76 2/3 feet x 8 = 614 2/3 feet.
a circle has an area of 78.5 units2 and a circumference of 31.4 units. if the radius is 5 units, what can be said about the relationship between the area and the circumference? (use 3.14 for .)
Answers
Step-by-step explanation:
give atleast 2 situations,in which you would store the data on cloud storage
Relationship between the area and the circumference of the circle is that they are proportional to each other.
The relationship between the area and the circumference of a circle with a radius of 5 units that has an area of 78.5 units² and a circumference of 31.4 units can be expressed as follows:
Area = πr²
where r is the radius of the circle.
Area = π(5)² = 78.5 units²
Therefore, the area of the circle is 78.5 units².
Circumference = 2πr,
where r is the radius of the circle.
2πr = 31.4 units
Therefore, 2π(5) = 31.4 units
Therefore, the circumference of the circle is 31.4 units.
Since the radius is the same, the relationship between the area and the circumference of the circle is that they are proportional to each other.
Area : Circumference
πr² : 2πr
r : 2
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1/4 divided by 3/2 as a fraction
Answers
Answer:
1/6
Step-by-step explanation:
1/4 divided by 3/2 as a fraction
1/4 : 3/2 = (flip 3/2 and change the sign from division to multiplication)
1/4 × 2/3 (semplify)
1/2 × 1/3 = (solve)
1/6
Answer:
= 1/6
Step-by-step explanation:
(1/4) ÷ (3/2) = (1*2) ÷ (4*3) = 2/12
= 1/6
Please help!! this is rizzcalc
Answers
The curve described by these parametric equations is the graph of the Cartesian equation: x = 2e^[(1 - y)/5]
What is the Cartesian equation?To eliminate the parameter t, we need to find a way to express t in terms of x and y, and then substitute that expression into one of the equations to eliminate t.
x(t) = 2e^t
y(t) = 1 - 5t
Let's start by solving the second equation for t:
y = 1 - 5t
Adding 5t to both sides, we get:
5t = 1 - y
Dividing both sides by 5, we get:
t = (1 - y)/5
Now we can substitute this expression for t into the first equation:
x = 2e^t
x = 2e^[(1 - y)/5]
This is the Cartesian equation in terms of x and y. We have eliminated the parameter t and expressed the equation solely in terms of x and y.
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you want to obtain a sample to estimate a population mean. based on previous evidence, you believe the population standard deviation is approximately . you would like to be 98% confident that your estimate is within 2 of the true population mean. how large of a sample size is required?
Answers
The required sample size is 108, to estimate the population mean with a 98% confidence level.
The following formula can be used to determine the required sample size.
n = ((z*σ) / E)^2
where:
n = sample size
z = z-score corresponding to desired confidence level (98% = 2.33 for two-sided test)
σ = population standard deviation (specified in the problem)
E = tolerance (2 for the problem)
After plugging in the values it looks like this:
n = ((2.33*) / 2)^2
n=107.13
Rounding up to the nearest integer, the required sample size is 108.
Therefore, a sample size of at least 108 is required to estimate the population mean with a 98% confidence level and a margin of error of 2, taking the population standard deviation as approximate.
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reasons to include an interaction term in our model include which of the following? (1) to estimate context-specific effects of some predictor variable on the outcome (y). (2) if the joint effect of two variables on the outcome can be correctly modeled as the sum of the main effects associated with each variable. (3) looking at an anova table suggests that an interaction term noticeably improves the predictive power of the model.
Answers
Reasons to include an interaction term in our model include (1) to estimate context-specific effects of some predictor variable on the outcome (y) and (2) if the joint effect of two variables on the outcome cannot be correctly modeled as the sum of the main effects associated with each variable. So, the correct answers are (1) and (2).
Including an interaction term can be useful to estimate the context-specific effects of some predictor variable on the outcome (y) when the effect of that predictor on the outcome may depend on the value of another predictor variable.
Additionally, including an interaction term can be necessary if the joint effect of two predictor variables on the outcome cannot be correctly modeled as the sum of the main effects associated with each variable.
This is because the effect of one predictor variable on the outcome may depend on the value of the other predictor variable, and this dependency cannot be captured by the main effects alone.
So, the correct options are (1) and (2).
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5. A soccer team played 32 games. If they won 25% of
them, how many games did the team win?
Answers
To find out how many games the soccer team won, we need to multiply the total number of games they played by the percentage of games they won.
25% of 32 games can be calculated as:
0.25 x 32 = 8
Therefore, the soccer team won 8 games out of 32.
High Order Thinking Skills (HOTS) Q10. The amount of petrol in a tank is twice of that in another tank. If we draw out 25 litres from firs & add it the other, the amount of petrol in both the tanks will be the same. Find the amount o petrol in each tank now. ** Downloaded from www.studiestoday.com
Answers
Let the amount of petrol in the first tank be x liters.
Then, the amount of petrol in the second tank is 2x liters.
After taking out 25 liters of petrol from the first tank and adding it to the second tank, the total amount of petrol in both tanks becomes the same. Let y be this common amount of petrol in both tanks.
So, after the transfer of petrol:
Amount of petrol in the first tank = x - 25
Amount of petrol in the second tank = 2x + 25
As per the problem statement, these two amounts are equal. Therefore:
x - 25 = 2x + 25
Solving for x, we get:
x = 50
Substituting x = 50 in the expressions for the amounts of petrol in the two tanks, we get:
Amount of petrol in the first tank = x - 25 = 50 - 25 = 25 liters
Amount of petrol in the second tank = 2x + 25 = 2(50) + 25 = 125 liters
Therefore, the amount of petrol in the first tank is 25 liters and the amount of petrol in the second tank is 125 liters.
According to the problem, the amount of petrol in the second tank is twice that in the first tank, which means the amount of petrol in the second tank is 2x liters.
If we draw out 25 liters from the first tank and add it to the second tank, the amount of petrol in both tanks will be the same. Therefore, the total amount of petrol in both tanks after the transfer is (x - 25) + (2x + 25) = 3x.
Since the amount of petrol in both tanks is the same after the transfer, we can set up an equation:
x - 25 = (2x + 25) / 2
Simplifying this equation, we get:
2x - 50 = 2x + 25
2x - 2x = 25 + 50
x = 75
Therefore, the amount of petrol in the first tank is 75 liters, and the amount of petrol in the second tank is 2x = 2*75 = 150 liters.
[tex]\sqrt{2+-7+2=-3[/tex]
Answers
It has been proved from the given equation that (2 + -7 + 2 = -3)
How to solve Rational Equations?A rational equation is defined as an equation that containins at least one fraction whose numerator and denominator are polynomials. These fractions may be on one or both sides of the equation.
Now, we are given the rational expression as:
√(2 + -7 + 2 = -3)
In order words, we want to prove that:
(2 + -7 + 2 = -3)
The left hand side, when we multiply + and - sign, we have negative sign and as such we will have:
2 - 7 + 2
= 4 - 7
= -3
This is same as the right hand side of the original equation
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The boiling point of water is 212°F at sea level. Andres lives at an elevation of
7,500 ft and finds that water boils at 198°F. What is the percent decrease in
the boiling point of water from sea level to 7,500 ft? Give your answer to the
nearest tenth of a percent. Show your work.
Answers
Step-by-step explanation:
The decrease from 212 to 198 is 14 degrees
14 degrees is what percent of 212 degrees?
14 / 212 x 100% = 6.6 % decrease
true or false: to calculate the value of the 50th term, you could assume 5 is g(1). then, using the growth factor of 3, use g(n)
Answers
The given statement " to calculate the value of the 50th term, you could assume 5 is g(1). then, using the growth factor of 3, use g(n) = 5*3^n-1 with n = 50 to find g(50)" is true. Assuming that 5 is g(1), we can use the growth factor of 3 to find the value of g(50) using the formula g(n) = 5*3^(n-1).
Assuming that 5 is the first term of the sequence g(n), we can use the formula g(n) = 53^(n-1) to find any term of the sequence. This formula gives us the value of the nth term in the sequence, where n is any positive integer.
For example, if we want to find the 50th term of the sequence, we simply substitute n = 50 into the formula and calculate g(50) = 53^(50-1) = 5*3^49. Therefore, we can use this formula to find any term of the sequence, given the first term and the growth factor. so, the given statement is true.
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--The given question is incomplete, the complete question is given
" true or false: to calculate the value of the 50th term, you could assume 5 is g(1). then, using the growth factor of 3, use g(n) = 5*3^n-1 with n = 50 to find g(50)."--
If f varies inversely as g, find f when g= -6
f= 15 when g= 9
Answers
The value of f is -10.
What is an inverse function?
An inverse in mathematics is a function that "undoes" another part. In other words, if f(x) produces y, y entered into the inverse of f producing x. An invertible function has an inverse, and the inverse is represented by the symbol f1.
Here, we have
Given: If f varies inversely as g, and when g = -6, f = 15.
We have to find the value of f.
f ∝ 1/g
f₁ ×g₁ = f₂ ×g₂
Let the required value of f = x
Inserting in equation (1) and we get
15 × (-6) = x × 9
-90/9 = x
x = -10
Hence, the value of f is -10.
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The LIDAR camera displays a beam of light to determine the speed of the car is going. Light travels at 9.84 x 10^8 ft/sec. If it takes the beam 4.5 x 10^-7 to reach the car and return. How far away is the car? (remember divide by 2)
Answers
distance = (speed of light x time) / 2
where time is the time it takes for the beam of light to travel from the LIDAR camera to the car and back.
Plugging in the given values, we get:
distance = (9.84 x 10^8 ft/sec x 4.5 x 10^-7 sec) / 2
Simplifying the expression, we get:
distance = 2.205 ft
Therefore, the car is approximately 2.205 feet away from the LIDAR camera.
A yoga studio offers one option for a monthly membership of $120 for unlimited classes. A second option is to pay a monthly fee of $30 plus $5 per class. A new customer is deciding between the two options. If the customer chooses the second option, which
best describes how many classes they can take to spend less than the unlimited membership fee?
Answers
Answer: 17
Step-by-step explanation:
First, you would subtract 30 from 120 to see how much money is left over for the classes, which is 90. Now you would divide 90 by 5 to see how many classes you can go to with the leftover money, which is 18. But since this is the same as the 120, just take away one lesson so it's sum would be less than 120, which would be 17. Hope this helps
Factor the polynomial
HELPPP I NEED THIS DUE ASAP
Answers
Answer:
Tony is not correct because 3(x^2-25) can be factored further. The final answer is 3(x+5)(x-5)
Step-by-step explanation:
finally answer
What expression is equivalent to ^3sqrt27x + ^3sqrtx if x=0??
Answers
The expression [tex]^3\sqrt {27x} + ^3\sqrt{x}[/tex] is equivalent to 0 when x=0.
What is the equivalent expression?
Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.
If x=0, then the expression [tex]^3\sqrt {27x} + ^3\sqrt{x}[/tex] becomes:
And we are given that x=0. So, we can substitute x=0 into the expression:
[tex]^3\sqrt{ 27 * 0} + ^3\sqrt{0}[/tex]
= 0 + 0 = 0
The first term simplifies to ∛(0), which is 0, because any number raised to the 1/3 power and multiplied by 0 is equal to 0.
The second term also simplifies to ∛(0), which is 0, because any number raised to the 1/3 power and multiplied by 0 is equal to 0.
Therefore, the sum of the two terms is 0.
Hence, the expression [tex]^3\sqrt {27x} + ^3\sqrt{x}[/tex] is equivalent to 0 when x=0.
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Which one of the following is not equal reast
A 2 of 15
B 3/2 of 400
C 5% of60
D 6 of 50%
Answers
a train, an hour after starting, meets with an accident which detains it a half hour, after which it proceeds at of its former rate and arrives hours late. had the accident happened miles farther along the line, it would have arrived only hours late. the length of the trip in miles was:
Answers
The total distance of the trip is 600 km if a train meet with an accident and then proceed further with its former speed.
Normal time be x for remaining distance, but time taken = 4x/3
Difference in time = (1+1/2+4x/3)−(1+x)=72
x=9
2nd case of going further 90 km which lessens the difference by 1/2
If it loses 90 km in 1/2 hr.
Total difference was 3 + 1/2 out of which 1/2 was for repair
Difference in travelling is 3+1/2-1/2=3 hrs
It will lose 3 hrs in 90 x 6=540 km
Now it travelled for 10 hr hours, which is 1 hr + 540 km
So 540 in 9hr
So 60 km per hour
Total distance = 540+60=600km
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-- The given question is incomplete, the complete question is
"A train, an hour after starting, meet with an accident which delays it for half an hour and after this, it proceeds at 3/4th of its former rate and arrives 3.5 hrs late. Had the accident happened 90 km farther along the line, it would have arrived only 3 hour late. What is the length of trip in km?" --
Which equations represent the line that is parallel to 3x − 4y = 7 and passes through the point (−4, −2)? select two options. y = â€"three-fourthsx 1 3x − 4y = −4 4x − 3y = −3 y â€" 2 = â€"three-fourths(x â€" 4) y 2 = three-fourths(x 4)
Answers
Two equations that represent the line that is parallel to 3x - 4y = 7 and passes through the point (-4,-2) are [tex]y + 2 = (\frac{3}{4})(x + 4)[/tex] and [tex]y = (\frac{3}{4})x - 5[/tex]. So, option A and D are correct.
We know that a line parallel to 3x - 4y = 7 will have the same slope as the given line. So, we can rearrange the equation 3x - 4y = 7 into slope-intercept form y = mx + b to find the slope:
3x - 4y = 7
-4y = -3x + 7
[tex]y = (\frac{3}{4}) x - \frac{7}{4}[/tex]
Therefore, the slope of the line is 3/4.
Now, we can use the point-slope form of the equation of a line to write the equations of the line that is parallel to 3x - 4y = 7 and passes through the point (-4,-2):
[tex]y - (-2) = \frac{3}{4} *(x - (-4))[/tex] or [tex]y - (-2) = \frac{3}{4} x - 3[/tex]
Simplifying these equations, we get:
[tex]y + 2 = (\frac{3}{4})(x + 4)[/tex] or [tex]y = (\frac{3}{4})x - 5[/tex].
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Hey could someone help me with this?
Answers
Step-by-step explanation:
30% of 500 voted for Sycamore
30% x 500 = .30 * 500 = 150 votes
Fox Glen got the most votes
Solve.
3/4 + (1/3 divided by 1/6) - (-1/2) =
Answers
3/4+(1/3x6)-(1/2)
3/4+2-1/2
3/4+8/4-2/4
=9/4
For exercises 5 and 6, find the measures and length of each arc. Express the answer in terms of pi
Answers
5) The measure of arc BC is 1.14π radians and the length of arc BC is 2.86π units.
6) The measure of arc ABC is 1.99π radians and the length of arc ABC is 3.14π units.
What is an arc?An arc is a curved line that is a portion of a circle.
It is formed by connecting two points on the circumference of the circle with a curve.
5) BC: To find the measure of arc BC, we need to find the measure of angle BAC.
angle BAC = angle AOC
angle BAC = 129 degrees
Therefore, the measure of arc BC is:
arc BC = (129/360) x (2π x 4)
arc BC = 1.14π radians
To find the length of arc BC, we need to find the measure of angle BAC.
angle BAC = angle AOC
angle BAC = 129 degrees
Therefore, the length of arc BC is:
arc BC = (129/360) x (2π x 4)
arc BC = 2.86π
6) ABC: To find the measure of arc ABC, we need to find the measure of angle BOC.
angle BOC = 360 - angle AOB - angle AOC
angle BOC = 360 - 51 - 83
angle BOC = 226 degrees
Therefore, the measure of arc ABC is:
arc ABC = (226/360) x (2π x 4)
arc ABC = 1.99π radians
To find the length of arc ABC, we need to find the measure of angle BOC.
angle BOC = 360 - angle AOB - angle AOC
angle BOC = 360 - 51 - 83
angle BOC = 226 degrees
Therefore, the length of arc ABC is:
arc ABC = (226/360) x (2π x 4)
arc ABC = 3.14π
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The complete question is -
Type the correct answer in the box. Spell all words correctly.
Why is Net WPM a better formula than Gross WPM to calculate typing speed?
Net WPM is a better formula than Gross WPM to calculate typing speed because it includes
Reset
Next
Answers
Net WPM is a better formula than Gross WPM to calculate typing speed because it provides a more comprehensive and accurate measure of a person's typing abilities
What is the speed?Speed is a measure of how fast an object or person is moving. It is usually expressed in units of distance per unit of time, such as miles per hour (mph), kilometers per hour (km/h), or meters per second (m/s).
Net WPM is a better formula than Gross WPM to calculate typing speed because it takes into account the number of errors made during typing.
Gross WPM (Words Per Minute) is calculated by dividing the total number of characters typed by 5 (the average number of characters in a word) and then dividing the result by the time taken to type those characters in minutes.
However, Gross WPM does not account for any mistakes made during typing.
On the other hand, Net WPM calculates the typing speed by subtracting the number of errors made during typing from the total number of words typed and then dividing the result by the time taken to type.
This formula provides a more accurate measure of the typing speed, as it takes into account the accuracy of typing as well as the speed.
Therefore, Net WPM is a better formula than Gross WPM to calculate typing speed because it provides a more comprehensive and accurate measure of a person's typing abilities
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please help will give brainliest
Answers
The area of the space devoted to paintings is: 600 ft²
How to find the area of the triangle?The formula for the area of a triangle is expressed as:
A = ¹/₂ * b * h
where:
A is area
b is base
h is height
From the 7th grade painting, we see that each box of 1 unit represents 10 ft actually.
Thus, area of space devoted to paintings is:
Area = ¹/₂ * 40 * 30
= 600 ft²
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Trisha and her three sisters to
decide to purchase their mom a
Christmas gift. They decide that
everyone will contribute an equal
amount, up to $60 per person.
How much money will the sisters
spend on their mom for
Christmas?
Answers
Answer:
The sisters will spend a total of $240 on their mom for Christmas.
Step-by-step explanation:
$60 x 4 (sisters) = $240
In a green house basil is grown in planters that have a base of 3 1/2 by 1 3/4. If there is a 3x3 array of these planters with no space between them, what is the are covered by the planters?
Answers
1 3/4. (i could be wrong)