The solution of the expression 6 × [tex]\frac{1}{4}[/tex] × (12 - 3) using order of operations rule BODMAS/PEMDAS is 13.5.
What is BODMAS?
BODMAS is acronym for B is for Bracket, O is for Of, D is for Division, M is for Multiplication, A is for Addition, and S is for Subtraction. This rule is used to explain the order of operation of a mathematical expression and solve the expression in case it has more than one operational signs. BODMAS is same as PEDMAS which i acronym for P-Parentheses, E-Exponents, D-Division, M-Multiplication, A-Addition, and S-Subtraction.
Here the expression is:
6 × [tex]\frac{1}{4}[/tex] × (12 - 3)= 6 × [tex]\frac{1}{4}[/tex] × (9) {solving the brackets}
= 54 × [tex]\frac{1}{4}[/tex]
= 13.5
The value of given expression is 13.5
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The solution of the expression is using order of operations rule BODMAS/PEMDAS is 13.5.
What is BODMAS?BODMAS stands for Bracket, Of, D, Multiplication, Multiplication by One, Addition by One, and Subtraction by One. This rule is used to specify the order of operations in a mathematical equation as well as to solve expressions with multiple operational signs. P-Parentheses, E-Exponents, D-Division, M-Multiplication, A-Addition, & S-Subtraction are collectively referred to as PEDMAS. BODMAS stands for the same thing.
The abbreviation BODMAS was created to aid kids in remembering the right order to carry out mathematical operations when solving problems.
Here the expression is:
6 × 1/4 × (12 - 3)= 6 × 1/4 × (9) {solving the brackets}
= 54 × 1/4
= 13.5
The value of given expression is 13.5
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Which of the following expressions is equal to 9?
4 x (one-half x 6) ÷ 3
6 ÷ (one-fourth x 3 x one and one-fourth)
8 + (one-third x 6) ÷ 5
10 − (one-fifth x 10) + 1
can someone help out with these 2 questions please?
The values x and y that make the quadrilaterals parallelograms are:
a. x = 2 and y = 41
b. x = 4 and y = 3
How to find the values x and y that make the quadrilaterals parallelograms?
a. Since opposite sides of parallelograms are equal in length. We can say:
2x + 7 = x + 9
2x - x = 9 - 7
x = 2
Also, two adjacent angles of parallelograms adds up to 180 degrees. That is:
(2y - 5)° + (2y + 21)° = 180°
4y + 16 = 180
4y = 180 - 6
4y = 164
y = 164/4
y = 41
b. Since the diagonals divide each other equally. We can say:
x + 8 = 16 - x
x + x = 16 - 8
2x = 8
x = 8/2
x = 4
5y + 4 = 2y + 13
5y - 2y = 13 - 4
3y = 9
y = 9/3
y = 3
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The Area of a Rectangle is 75. The length is 3 times the
width. Find the Width.
04
06
0 5
08
Answer:
the width of the rectangle is 5.
Step-by-step explanation:
Let's assume that the width of the rectangle is x. Then, according to the problem statement, the length of the rectangle would be 3x.
The area of a rectangle is given by the formula:
Area = Length x Width
Substituting the values of length and width in the formula, we get:
75 = (3x) x (x)
Simplifying the right-hand side, we get:
75 = 3x^2
Dividing both sides by 3, we get:
25 = x^2
Taking the square root of both sides, we get:
x = ±5
Since the width cannot be negative, we take the positive value of x, which is 5.
Therefore, the width of the rectangle is 5
Erica runs at a constant speed of 3.5 meters per second for 1/2
hour. Then, she walks at a rate of 1.5 meters per second for
1/2
meters.How far did Erica run and walk for 60 minutes?
Erica covered a total distance of 4,500 meters in 60 minutes (1 hour).
Define distance travelledDistance traveled is the total length of the path covered by an object in motion over a given period of time. It is a scalar quantity.
Erica ran at a rate of 3.5 meters per second for 1/2 hour, which is 30/2 = 15 minutes.
During this time, she covered a distance of:
distance = rate x time
distance = 3.5 m/s x 900 s
distance = 3,150 meters
Next, Erica walked at a rate of 1.5 meters per second for 1/2 hour, which is also 15 minutes.
During this time, she covered a distance of:
distance = rate x time
distance = 1.5 m/s x 900 s
distance = 1,350 meters
Adding the distances Erica ran and walked, we get:
total distance = 3,150 meters + 1,350 meters
total distance = 4,500 meters
Therefore, Erica covered a total distance of 4,500 meters in 60 minutes (1 hour).
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Question
What is the measure of angle LEP?
Angle L E P. Ray E W is between rays E L and E P. Angle L E W is labeled 51 degrees. Angle P E W is labeled 27 degrees.
The measure of angle LEP can be found using the angle addition postulate, which states that the measure of an angle formed by two adjacent angles is equal to the sum of their measures. Given that angle, LEW is 51 degrees and angle PEW is 27 degrees, we can find the measure of angle LEP by adding these two angles. Thus, the angle LEP is 78 degrees (51 + 27).
L
/ \
/ \
/ \
E-------P
W
In mathematics, an angle is a geometric figure formed by two rays sharing a common endpoint, known as the vertex of the angle. There are two main ways to label angles: by giving the angle a name, usually a lowercase letter or a Greek letter, or by using the three letters that define the angle, with the middle letter being where the angle is located. Angles are typically measured in degrees using a protractor and are defined by their measure, which is not dependent upon the lengths of the sides of the angle. Coterminal angles share terminal sides but differ in size by an integer multiple of a turn.
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Caleb's annual salary is $45,000 per year. His employer matches 75% of his 401k
contributions up to 10% of his annual salary. Caleb contributes $250 from each
biweekly paycheck to his 401k account. What is the combined total of his annual
contribution and his employer's contribution?
The combined total of his annual contribution and his employer's contribution is $13,000.
What is the Combined total?The term "combined total" refers to the sum or aggregate of two or more individual quantities, values, or amounts. It represents the cumulative or total amount resulting from the combination or addition of multiple components.
According to the given information:
First, let's calculate Caleb's annual contribution to his 401k account.
Caleb contributes $250 from each biweekly paycheck, so his biweekly contribution is $250.
Since there are 26 biweekly pay periods in a year (52 weeks), his total biweekly contributions in a year would be 26 * $250 = $6,500.
Caleb's annual salary is $45,000 per year, and his employer matches 75% of his 401k contributions up to 10% of his annual salary. So, the maximum employer match would be 75% of 10% of $45,000, which is 0.75 * 0.10 * $45,000 = $3,375.
Since Caleb's annual contribution ($6,500) is less than the maximum employer match ($3,375), his employer will match his entire contribution.
Therefore, the combined total of Caleb's annual contribution and his employer's contribution would be $6,500 + $6,500 = $13,000.
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please help asap!!!!!
The equation that represents the proportional relationship is [tex]y=\frac{1}{4}x[/tex].
What is proportion?
Proportion is a mathematical concept that describes the equality of two ratios. In other words, it is a statement that two ratios or fractions are equal.
For example, if we have two fractions [tex]\frac{a}{b}[/tex] and [tex]\frac{c}{d}[/tex], we can say that they are in proportion if:
=> [tex]\frac{a}{b}=\frac{c}{d}[/tex]
Now the ratio between x and y = 4:1
Here x = 28 then y = [tex]\frac{1}{4}\times28 = 7[/tex]
Then, x = 12 then [tex]y=\frac{1}{4}\times12 = 3[/tex]
We can see that the ratio between X and Y is always 4:1, which means that Y is one-fourth of X. We can write this as:
=>[tex]y=\frac{1}{4}x[/tex]
Therefore, the equation that represents the proportional relationship is:[tex]y=\frac{1}{4}x[/tex].
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An outline of a city map is shown. The population of the city is 23,023 people. What is the population density of the city?
Answer:148.38
Step-by-step explanation:
Population Density=Population of country÷Area of country
Population of country=23,023
Area of country=(18*8)+(4*5)=164 m²
Population Density=23023÷164=148.38 people/m²
game 2: xenia wins if there are 2 heads and 1 tails. yolanda wins if there are 2 tails and 1 heads. zoe wins if there are 3 heads or 3 tails. is this a fair game?
The total probability of winning is 0.75, which is not equal to 1, indicating that the game is not fair.
To decide in case this is a fair game, we ought to calculate the likelihood of each player winning.
Let H speak to the result of flipping a head and Tail speak to the result of flipping a tail. At that point, the conceivable results of three coin flips are:
HHH, HHT, HTH, THH, TTH, THT, HTT, TTT
The likelihood of getting each result is 1/8, accepting the coin flips are reasonable and autonomous.
Xenia wins on the off chance that there are 2 heads and 1 tail. Three conceivable results fulfill this condition:
HHT, HTH, and THH. Hence, the likelihood of Xenia winning is 3/8.
Yolanda wins in case there are 2 tails and 1 head. There are moreover three conceivable outcomes that fulfill this condition:
TTH, THT, and HTT. Subsequently, the likelihood of Yolanda winning is additionally 3/8.
Zoe wins if there are 3 heads or 3 tails. Two conceivable results fulfill this condition:
HHH and TTT. In this manner, the likelihood of Zoe winning is 2/8 = 1/4.
To check in case the diversion is reasonable, we include the probabilities of each player winning:
3/8 + 3/8 + 1/4 = 0.75
The full probability of winning is 0.75, which isn't break even with 1, indicating that the game is not fair.
One way to form it a fair diversion would be to alter the payouts or the rules of the amusement to guarantee that the full likelihood of winning includes up to 1.
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An event where two or more things happen at the same time is called ______
A. Dependent event
B. Compound event
C. Independent event
D. Organized list
The event where two or more things happen at the same time is called a "compound event." the correct answer is B.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
A compound event refers to a situation where two or more events occur at the same time. In other words, it is an event that consists of multiple outcomes happening simultaneously.
For example, if you flip a coin and roll a dice at the same time, the resulting event would be a compound event because it involves the outcomes of both actions occurring simultaneously. It is important to distinguish between compound events and independent or dependent events, as they have different probabilities and methods of calculation. Compound events are often used in probability theory and statistics to analyze and predict the likelihood of multiple outcomes occurring at the same time.
The event where two or more things happen at the same time is called a "compound event." Therefore, the correct answer is B.
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Suki purchased $9,600 worth of stock and paid her broker a 2.5% broker
fee. She had an immediate need for cash and was forced to sell the stock
when it was worth $8,000. She used a discount broker who charged
$33.97 per trade transaction.
Compute Suki's net loss(-) after the broker fees were taken out.
The net loss is $1873.97.
What is the selling price?
The selling price formula is Selling Price = Cost Price + Profit Margin. Cost price is the price a retailer paid for the product. The profit margin is a percentage of the cost price.
Here, we have
Given: Suki purchased $9,600 worth of stock and paid her broker a 2.5% broker fee. She had an immediate need for cash and was forced to sell the stock when it was worth $8,000. She used a discount broker who charged $33.97 per trade transaction.
Purchase price: $9,600
Fee purchase: 2.5%
Selling price: $8,000
Fee scale: $33.97
The broker fee is the product of the broker fee rate of 2.5% and the purchase price:
Broker fee purchase = 2.5%× 9,600
= 240
The total purchase cost is the sum of the purchase price and the broker fee of the purchase:
Total purchase cost Purchase price = Broker fee purchase
= 9600 + 240
= 9840
The total selling cost is the selling price decreased by the broker fee of the sale (flat rate):
Total selling cost = Selling price - Broker fee sale
= 8,000 - 33.97
= 7966.03
The net loss is then the difference between the total purchase cost and the total selling cost:
Net loss = Total purchase cost - Total selling cost
= 9840 - 7966.03
= 1873.97
Hence, the net loss is $1873.97.
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A door has 3 meter height and 1 meter width. If a square piece of play wood has side length of 2.2 meter, can the play wood inter through the door? How do you know? Show your work with a figure.
No, the square piece of plywood cannot enter through the door because its diagonal is longer than the height of the door.
Checking if the plywood would enter through the doorTo see if the plywood would enter through the door, we can use the Pythagorean theorem to find the length of the diagonal of the plywood:
diagonal^2 = side1^2 + side2^2
So, we have
diagonal^2 = 2.2^2 + 2.2^2
diagonal^2 = 4.84 + 4.84
diagonal^2 = 9.68
Take the square root
diagonal ≈ 3.11
Therefore, the diagonal of the plywood is approximately 3.11 meters.
Since the height of the door is only 3 meters, the plywood is too big to fit through the door. So we can conclude that the plywood cannot enter through the door.
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The following ordered pairs represent a function.
(-2,-1), (-1,0), (0,1), (1,2), (2,3)
Which two ordered pairs can be added to the given set and still have the set represent a function?
the two ordered pairs that can be added to the given set and still have it represent a function are (3,4) and (-3,-2).
In order for a set of ordered pairs to represent a function, each input (x-coordinate) must be paired with exactly one output (y-coordinate).
Looking at the given set of ordered pairs, we can see that this condition is met:
The input -2 is paired with the output -1.
The input -1 is paired with the output 0.
The input 0 is paired with the output 1.
The input 1 is paired with the output 2.
The input 2 is paired with the output 3.
To add two more ordered pairs to this set and still have it represent a function, we need to make sure that the new pairs each have a unique x-coordinate that is not already in the given set.
For example, we could add the pairs (3,4) and (-3,-2):
The input 3 is paired with the output 4, which is not already in the original set.
The input -3 is paired with the output -2, which is not already in the original set.
Therefore, the two ordered pairs that can be added to the given set and still have it represent a function are (3,4) and (-3,-2).
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The cone of the volcano has a height of 404 meters and a diameter of 430 meters. Find the volume of the cone. Round your answer to the nearest hundred thousand. Use 3.14 for π.
Answer:
Rounding to the nearest hundred thousand, the volume of the cone is approximately 19,400,000 cubic meters.
Which if the following graphs represents all values of x such that x > -3 and x < 2?
Step-by-step explanation:
The graph that represents all values of x such that x > -3 and x < 2 is the graph of a vertical line segment located between -3 and 2 on the x-axis, but excluding these two points. This can be represented graphically as:
|
|
|
---------x---------
|
|
|
-3 2
Here, the open circles indicate that the points -3 and 2 are not included in the range of values for x.
joy is giving ice cream cones to some children at a carnival. she has 8 chocolate ice cream cones, 10 vanilla ice cream cones, and 6 strawberry ice cream cones. if joy selects an ice cream cone randomly without looking, what is the probability that she will give a chocolate ice cream cone to the first child and then a vanilla ice cream cone to the second child?
The required probability that Joy will give a chocolate ice cream cone to the first child and then second child get a vanilla ice cream cone is equal to 3/16.
Number of chocolate ice cream cones = 8
Number of vanilla ice cream cones = 10
Number of strawberry ice cream cones = 6
Total number of ice cream cones = 8+10+6
= 24 cones,
The probability of Joy giving a chocolate ice cream cone to the first child is 8 cones,
P(chocolate) = 8/(8+10+6) = 8/24 = 1/3
Now,
Assuming that Joy gave away a chocolate ice cream cone to the first child,
There are 8-1=7 chocolate ice cream cones left.
Similarly, there are 10-1=9 vanilla ice cream cones left.
Probability of Joy giving a vanilla ice cream cone to the second child,
given that she gave a chocolate ice cream cone to the first child, is,
P(vanilla | chocolate)
= 9/(7+9)
= 9/16
Probability of Joy giving a chocolate ice cream cone to the first child and a vanilla ice cream cone to the second child is,
P(chocolate and vanilla)
= P(chocolate) × P(vanilla | chocolate)
= (1/3) × (9/16)
= 3/16
Therefore, the probability that Joy will give a chocolate ice cream cone to the first child and then a vanilla ice cream cone to the second child is 3/16.
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45,52,17,63,57,42,54,58 outlier
Answer: 31363022. or 17
Step-by-step explanation:
please help
Given POQ = 0 rad, the length of the arc PQ is twice the radius OP and OR = 4cm, find
a) the value of 0
b) the area of the shaded region if the length of the arc PQ is twice the length of the arc RS
As a result, the shaded region's area sector is **10.62 cm² cm.²
What is a sector?
A sector is a section of a circle in geometry that is bounded by two radii and an arc. It is a pie-shaped portion of a circle that touches the circle's center, has two straight edges (the two radius lines), and a curved edge created by the arc.
Arc Length = r is the formula for the arc length of a circle,
where is the radius of the circle and r is the radian measurement of the arc (or central angle).
The formula for arc length, L = r *, can be used to determine the value of zero. L is the length of the arc, r is the radius of the circle, and is the centre angle in radians. We can deduce from the facts provided that PQ equals 2 * OP.
Also obvious is that OR = 4 cm. We can claim that PQ = 2 * OR = 8cm because PQ is twice as long as OP. Now, we can calculate's value using the formula:
L = r * θ 8 = 4θ θ = 2
Consequently, = 2 radians.
We must know the length of arc RS in order to calculate the size of the shaded zone. PQ is twice RS, as we are aware. RS = PQ/2, which equals 4 cm. Now, we may apply the area of a formula.We may now apply the formula A = (1/2) * r² *, where A is the sector's area, r is the circle's radius, and is the centre angle in radians.
Sector PQR area equals (1/2) * OR2 * sector PQR area equals (1/2) * 16 * 2 sector PQR area equals (16)
Sector PSR area equals (1/2) * OR²2 * Sector PSR area equals (1/2) * 16 * π/3 Sector PSR area equals (8)/3
Sector PQR minus Sector PSR is equal to the area of the shaded region. Area of the shaded area is 16 - (8π)/3. Shaded area size: 10.62 cm²
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Find the value of x.
please answer
Answer:
x = 73°
Step-by-step explanation:
I added a photo of my notes
An inscribed angle is equal to half the arc on which it rests
So, according to the photo I've added (knowing that a full circle forms 360 degrees) we can write an equation:
2x + 214° = 360°
2x = 360° - 214°
2x = 146° / : 2
x = 73°
I not sure if this is the right answer, though...
the ratio of boys to girls in the class is 4:5. if there is a total of 27 students, how many more girls than boys are in the class?
Answer:
3 more girls than boys.
Step-by-step explanation:
Let's change 4:5 to 4x(boys) and 5x(girls).
Since there are 27 students, the equation would be:
4x+5x=27
Then, you simplify the equation:
9x=27
x=3
We are not finished yet!
Since there is 4x boys and 5x girls,
do 4 times 3 which gets you 12 boys
and 5 times 3 which gets you 15 girls.
15 girls minus 12 boys is 3 more girls than boys!
Hope this helps :)
The Area of a Rectangle is 40. The width is 2 less than 3
times the length. Find the width.
O 10
O 12
O 15
O 14
Therefore, the width of the rectangle is 10.
So, the answer is (O) 10.
How to find width of the rectangle?To find the width of a rectangle, you will need to have at least one of the following pieces of information:
Length and area: If you know the length and area of the rectangle, you can use the formula for area (A = length x width) and solve for the width (W = A/length).
Perimeter and length: If you know the perimeter and length of the rectangle, you can use the formula for perimeter (P = 2 x length + 2 x width) and solve for the width (W = (P - 2 x length)/2).
Diagonal and length: If you know the diagonal and length of the rectangle, you can use the Pythagorean theorem ([tex]a^2 + b^2 = c^2[/tex]) to solve for the width. [tex](W = \sqrt(c^2 - length^2)),[/tex] where c is the diagonal and a and b are the length and width (in some order).
Ratio of length to width: If you know the ratio of length to width, you can use this ratio to solve for the width. For example, if the ratio of length to width is 3:2, and the length is 15, then the width would be 10 (because 15/3 = 5 and 5 x 2 = 10).
Measurements: If you have physical access to the rectangle, you can measure the width directly using a ruler or tape measure.
Let's assume the length of the rectangle as "L" and the width as "W".
From the given information, we know that:
The area of the rectangle is 40, so we have the equation:
[tex]L x W = 40[/tex]
The width is 2 less than 3 times the length, so we have the equation:
[tex]W = 3L - 2[/tex]
Now we can substitute the second equation into the first equation and get:
[tex]L x (3L - 2) = 40[/tex]
Expanding the left-hand side, we have:
3L^2 - 2L - 40 = 0
Dividing both sides by 1, we get:
[tex]3L^2 - 2L - 40 = 0[/tex]
Using the quadratic formula, we get:
[tex]L = 4 or L = -10/3[/tex]
Since the length of a rectangle cannot be negative, we take L = 4.
Then, we can use the equation W = 3L - 2 to find the width:
[tex]W = 3 x 4 - 2 = 10[/tex]
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What is the size of angle a?
Answer:
60 degrees
Step-by-step explanation:
The total angles of a circle add up to 360 so to find a missing angle, subtract the figures already given from 60. The angles given total to (140+125+35) = 300. To find angle a, you subtract the 300 from 360. 360-300 = 60 degrees. Therefore, angle a is 60 degrees
HELP PLS!
SHOW ALL STEPS FOR SURFACE AREA AND VOLUME AND I WILL MAKE U BRAINLIST!
Answer:
V = 4,423.4
SA = 1,508.0
Step-by-step explanation:
r = d/2
V = πr²h
(3.14)(8)²(22) = 4,423.362456
SA = 2πr(h + r)
2(3.14)(8)(22 + 8) = 1,507.964474
Geometry Please hurry
How do you see it? The diagram shows part of the Wheel of Theodorus.
Answer:
it is given that diagram shows part of the Wheel of Theodorus. graphics for exercise 20 page 428 geometry part (a). It is required to identify which ...
Step-by-step explanation:
In the circle below, suppose m VUX = 228° and mZUVW=121°. Find the following.
U
X
(a) m/VUX = °
(b) m LUXW =
0.
Assume that m arc VUX = 228° and m ∠UVW = 121° in the circle below.
m∠VUX = 66° and m m∠UXW = 59° respectively.
1) The given information is;
The angle of arc m∠VUX = 228°, the measured angle of ∠UVW = 121°
Given that m∠VUX = 228°, therefore, arc ∠XWV = 360 - 228 = 132°
Therefore, the angle subtended by arc ∠XWV at the centre = 88°
The angle subtended by arc ∠XWV at the circumference = m∠VUX
∴ m∠VUX = 132°/2 = 66° (Angle subtended at the center = 2×angle subtended at the circumference)
m∠VUX = 66°
2) Similarly, m∠XWV is subtended by arc m∠VUX, therefore, m∠XWV = (arc m VUX)/2 = 228°/2 = 114°
A quadrilateral's angles add up to 360°.
Therefore;
m∠VUX + m∠XWV + m∠UVW + m∠UXW = 360° (The sum of angles in a quadrilateral XWVU)
m∠UXW = 360° - (m∠VUX + m∠XWV + m∠UVW)
m∠UXW = 360° - (66 + 114 + 121)
m∠UXW = 360° - 301
m∠UXW = 59°.
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in classical variables sampling, the evidence supports the conclusion that the account is not materially misstated if both the upper and lower limits are within the bounds of
The evidence supports the conclusion that the account is not materially misstated if both the upper and lower limits are within the bounds of tolerable misstatement.
The preimage shown above is dilated by a scale factor of 4 about the center (-2,-2). What is the coordinate location of the point C'.
Type your answer as an ordered pair, (x,y) with no spaces.
The coordinate location of point C' after the dilation is (-10, 2).
What is coordinate location?
To find the coordinate location of point C' after the dilation by a scale factor of 4 about the center (-2,-2), we can use the following formula:
(x', y') = (k * (x - h) + h, k * (y - k) + k)
where (x, y) are the coordinates of the original point, (h, k) are the coordinates of the center of dilation, k is the scale factor, and (x', y') are the coordinates of the corresponding point after dilation.
For point C, the coordinates are (x, y) = (-2, -1) and the center of dilation is (h, k) = (-2, -2) with a scale factor of k = 4.
Plugging in these values, we get:
(x', y') = (4 * (-2 - (-2)) - 2, 4 * (-1 - (-2)) - 2)
= (-10, 2)
Therefore, the coordinate location of point C' after the dilation is (-10, 2).
What is coordinate?
A coordinate is a set of numbers or values that indicate the position or location of a point or object in a given space or system. Coordinates are often used in mathematics, geometry, physics, and other fields to describe the location of objects or points in a two- or three-dimensional space. The most common type of coordinates are Cartesian coordinates, which are represented by an ordered pair of numbers (x,y) that describe the location of a point on a two-dimensional plane, or an ordered triplet of numbers (x,y,z) that describe the location of a point in a three-dimensional space.
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Complete question is: The preimage shown above is dilated by a scale factor of 4 about the center (-2,-2). the coordinate location of the point C'after the dilation is (-10, 2).
9.8 Rahul and Rajesh were asked to subtract 4x - 5 from x² + 3x - 5. Their solutions are given below Rahul: (x² + 3x - 5)-(4x-5)=x² + 3x-5-4x+5=x²-x Rajesh: (x² + 3x - 5) - (4x - 5) = x² + 3x-5-4x-5=x²-x-10 Who solved the problem correctly and what was the mistake made by the other?
Answer:
Step-by-step explanation:
Rahul correctly solved the problem, because it changed the sign in places when there was a "-" in front of the bracket.
( x² + 3x - 5) - (4x - 5) = x² + 3x - 5 - 4x + 5 = x²-x
-(a+b) = -a-b
-(a-b+c-a+c)= -a+b-c+a-c
PLEASE HELP ILL GIVE BRAINLIEST
Hence, the response is (iv) 85 as the exterior angle is equal to the sum of the two opposite interior angles.
what is angle ?The apex of the angle is the intersection of two rays that together form the geometric shape known as an angle. Angles, which are commonly measured in degrees or radians, are employed in a variety of mathematical and scientific contexts, including engineering, physics, geometry, and trigonometry.
given
We can utilise the above details to construct an equation because the exterior angle is equal to the sum of the two opposite interior angles:
x + 35 = 120
35 is subtracted from both sides to yield:
x = 85
Hence, the response is (iv) 85 as the exterior angle is equal to the sum of the two opposite interior angles.
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The complete question is :-
Use the Exterior Angle Theorem to solve for x.
Exterior angle = 120°
60
120
O 155
85
35°
PLEASE HELP I NEED THIS CODE TO PASS!!!! PLEASE PLEASE HELP
For part A the length of the perpendicular is approximately 156.18. Length of GH, the area of the rectangle is approximately 12336.22 square units.
FOR Part B the length of the perpendicular is approximately 182.48.
the area of the triangle is approximately 8954.96 square units.
How to solve the question?
To find the perpendicular of a right triangle, we need to use the Pythagorean theorem, which states that the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Let the length of the perpendicular be h, and the length of the other leg of the triangle be b. Then, we can set up the equation:
175²= h²+ 79²
Simplifying, we get:
30,625 = h²+ 6,241
Subtracting 6,241 from both sides, we get:
24,384 = h²
Taking the square root of both sides, we get:
h ≈ 156.18
Therefore, the length of the perpendicular is approximately 156.18.
The area of a rectangle is given by the formula:
Area = length × width
Substituting the given values, we get:
Area = 156.18 × 79
Area = 12336.22 square units
Therefore, the area of the rectangle is approximately 12336.22 square units.
To find the perpendicular, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, we know the length of the hypotenuse and one of the other sides, so we can solve for the length of the perpendicular.
Using the Pythagorean theorem:
h²= b²+ p²
where h is the length of the hypotenuse, b is the length of the base, and p is the length of the perpendicular.
Substituting the given values:
207²= 98²+ p²
Simplifying:
42849 = 9604 + p²
Subtracting 9604 from both sides:
33245 = p²
Taking the square root of both sides (since p is a length, we only take the positive square root):
p = sqrt(33245)
p ≈ 182.48
Therefore, the length of the perpendicular is approximately 182.48.
To find the area of the triangle, we can use the formula:
Area = (1/2) x base x height
Substituting the given values:
Area = (1/2) x 98 x 182.48
Simplifying:
Area = 0.5 x 98 x 182.48
Area ≈ 8954.96
Therefore, the area of the triangle is approximately 8954.96 square units.
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