Final answer:
The gradient of the line perpendicular to a line with a gradient of 2/3 is -3/2 since perpendicular slopes are negative reciprocals of each other.
Explanation:
If the gradient of a line C is 2/3, we need to find the gradient of the line which is perpendicular to C. In mathematics, particularly in coordinate geometry, the slopes (or gradients) of two perpendicular lines are negative reciprocals of each other. This means that if the slope of the first line is m, the slope of the line perpendicular to it will be -1/m.
Therefore, the gradient of the line perpendicular to line C, which has a gradient of 2/3, will be the negative reciprocal of 2/3.
perpendicular = -1 / (2/3) = -3/2
So, the gradient of the line perpendicular to C is -3/2.
Triangle ABC was dilated using the rule
Point Y is the center of dilation. Triangle A B C is dilated to form triangle A prime B prime C prime.
If CA = 8, what is C'A'?
10 units
12 units
16 units
20 units
Answer:
A) 10.
Step-by-step explanation:
You divide 5/4 to get 1.25 and multiply that by 8 to get 10.
The length of C'A' is 10 units, the correct option is A.
What is Dilation?Dilation is the process of enlarging or compressing a figure. The factor by which this process happens is called the scale factor.
Triangle ABC is dilated by the rule Dy, 5/4
If measure of CA = 8
The length of C'A' will be determined by using the formula of scale factor
Scale factor = Dimensions of new figure/ Dimensions of original figure
Here,
Scale factor = C'A' / CA
(5/4) x CA = C'A'
C'A' = (5/ 4) x 8
C'A' = 10 units
Your question seems incomplete, the complete question is :
Triangle ABC was dilated using the rule Dy, 5/4
If CA = 8, what is C'A'?
10 units
12 units
16 units
20 units
To know more about Dilation
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Brian is a junior and is paid $18.42 per hour. Calculate
his weekly wage if he works 38 hours at the normal
rate and 6 hours overtime at time-and-a-half.
Answer:
$865.74
Step-by-step explanation:
Time-and-a-half wage means you multiply the regular hourly rate by 1.5.
Regular wage: 38 hours at $18.42/hour
Time-and-a-half: 6 hours at 1.5 * $18.42/hour
Total weekly wage:
38 hours at $18.42/hour + 6 hours at 1.5 * $18.42/hour =
= 38 * $18.42 + 6 * 1.5 * $18.42
= $699.96 + $345.78
= $865.74
Answer: His weekly wage is $865.74
how do you find the third side if a right triangle??
Answer:
use the pythagorean theorem
Step-by-step explanation:
I have no idea what the answers are pls help my math people
Answer:
(-2,-7) answer (-1,14)
3 questions answer (4,-11)
(5,10) answer ( 10,-15)
What are the dimensions of the poster at one-third its current size?
Answer:
you enter x 1/3 and will get the answer.
You haven't given the dimensions so an example is below.
Step-by-step explanation:
Ex 1
Poster current size 60inches
60 x 1/3 = 20 = 20inches
Ex 2
Poster current size 63 inches
60 x 1/3 = 21 = 21inches
Ex 3
Poster current size 67 inches
67 x 1/3 = 22.33 = 22.33 inches
Ex 4
Poster current size 81 x 47 inches
81 x 1/3 = 27 47 x 1/3 = 15.66
This means the poster at 1/3 size is 27in x 15.66in
1. Two 1 kg blocks are about to slide down frictionless inclined planes as shown below. Each block is 1 m high. Which statement is
correct?
Two 1 kg blocks sliding down frictionless inclined planes will take the same amount of time.
Explanation:The correct statement is that both blocks will take the same amount of time to slide down the inclined planes.
When the blocks slide down the inclined planes, their acceleration is determined by the force of gravity acting on them. Since the mass of both blocks is the same and the force of gravity is the same for both, their acceleration will be the same.
Additionally, the height of the inclined planes is the same for both blocks, so they will cover the same vertical distance. As a result, the time taken for both blocks to slide down will be the same.
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Sally gets paid $15.00 dollars per hour for a 40-hour work week and y dollars for each hour she works over 40 hours. What is the equation for how many sally will earn if she works 48 hours?
The equation x = 600 + 8y represents the earnings of Sally if she works 48 hours.
Step-by-step explanation:
Sally gets paid $15.00 dollars per hour for a 40-hour weekly work.She gets y dollars for each extra hour she works over 40 hours.The equation can be framed as :
Let,
x be the total pay she could get for 48 hours.The amount she earned for 40 hours = 40 × $15 ⇒ $600The amount she earned for extra hours = 8 × y ⇒ 8yThe equation is given as,
Total earnings = amount earned for 40 hours + amount for extra 8 hours.
⇒ x = 600 + 8y
Therefore, the equation x = 600 + 8y represents the earnings of Sally if she works 48 hours.
Aseem and Stana are building model cars. Stana's car is 5 less than 2 times the length of Aseem's car. The sum of the lengths of both cars is 20 inches. Write an equation to determine the lengths of Aseem's and Stana's cars.
2x − 5 + x = 20
5 − 2x + x = 20
2x − 5 = 20
5 − 2x = 20
Answer:
2x − 5 + x = 20
Step-by-step explanation:
Let Aseem's car length be x
Then, length of Stana's car is:
2x - 5
Sum of lengths:
2x - 5 + x = 20
Final answer:
The correct equation that represents the lengths of the model cars Aseem and Stana are building is '2x - 5 + x = 20,' where x represents the length of Aseem's car.
Explanation:
The equation to determine the lengths of Aseem's and Stana's model cars is 2x − 5 + x = 20.
We can define the variable x as the length of Aseem's car, and since Stana's car is 5 inches less than twice the length of Aseem's car, Stana's car length is represented as
2x - 5.
The sum of the lengths of both cars together is 20 inches.
Therefore, the equatio becomes:
(2x - 5) + x = 20
i.e. 2x - 5 -x = 20
Solve for x
2x - 5 = x + 5
Step-by-step explanation:
[tex]2x - 5 = x + 5 \\ 2x - x = 5 + 5 \\ x = 10[/tex]
Answer:
x=10
Step-by-step explanation:
The original price of a ski jacket was $290. It was on sale at a 25% discount. Arianna had a coupon for an additional 10% off sale price. What price did Arianna pay for the ski jacket?
Answer:
Step-by-step explanation:
If the jacket was discounted at 25%, that means that you get 25% off, right? What it also means is that you are still paying 75%. To get to the price of the jacket on sale, multiply the price of the jacket by 75% (as a decimal):
290(.75) = 217.50
That's the price of the jacket when it is 25% off the original price. If Arianna got an additional 10% off that price, that means she got 10% off but is still paying 90%. To get to the final price that she paid, multiply the sale price of the jacket by 90% (as a decimal):
217.50(.90) = 195.75
That's what she paid in the end for the jacket (i guess not counting tax...?)
To find the price Arianna paid for the ski jacket, multiply the original price by the discount and coupon percentages.
Explanation:To find the price Arianna paid for the ski jacket, we need to calculate the discounts. First, we find the sale price by multiplying the original price by the discount percentage: $290 * 0.75 (100% - 25%) = $217.50. Then, we apply the coupon discount by multiplying the sale price by the coupon percentage: $217.50 * 0.90 (100% - 10%) = $195.75. Therefore, Arianna paid $195.75 for the ski jacket.
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15. The number of girls varied directly as the number of boys and inversely as the number of teachers. When there were 50 girls, there were 20 teachers and 10 boys. How many boys were there when there were 10 girls and 100 teachers?
Final answer:
By establishing an equation G = k(B/T), where G is the number of girls, B is the number of boys, and T is the number of teachers, we determine the constant of proportionality (k) from the given values. Using this constant, we deduce that there are 10 boys when there are 10 girls and 100 teachers.
Explanation:
The number of girls varies directly as the number of boys (B) and inversely as the number of teachers (T). This can be written as an equation, G = k(B/T), where G is the number of girls, and k is a constant of proportionality. From the given information, when there were 50 girls, there were 20 teachers and 10 boys. Plugging these values into the equation gives us 50 = k(10/20), which simplifies to 50 = k/2. Solving for k gives us k = 100.
Now, to find out how many boys are there when there are 10 girls and 100 teachers, we use the equation with our value for k. We get 10 = 100(B/100). Simplifying this equation gives us 10 = B. Therefore, there are 10 boys when there are 10 girls and 100 teachers.
What is the value of this expression
3^2*2-4(3-1)
Answer:
10
Step-by-step explanation:
3^2*2-4(3-1)
3^2=9
9*2
9×2
18
4(3-1)
4(2)
8
18-8
=10
So the final answer is 10
(a+bz)/(a+b)=(c+dz)/(d+c) if bc=ad
We have proven that:
[tex]\[\frac{a + bz}{a + b} = \frac{c + dz}{d + c}\][/tex]
given that bc = ad.
To prove that
[tex]\[\frac{a + bz}{a + b} = \frac{c + dz}{d + c}\][/tex]
given that bc = ad, we'll start by manipulating one side of the equation to look like the other side.
Let's start with the left-hand side:
[tex]\[\frac{a + bz}{a + b}\][/tex]
To make it look like the right-hand side, we need to somehow introduce c and d into the expression.
From the given condition bc = ad, we can rearrange it to solve for d:
[tex]\[d = \frac{bc}{a}\]Now, let's substitute \( d \) into the expression:\[\frac{a + bz}{a + b} = \frac{c + \frac{bc}{a}z}{\frac{bc}{a} + c}\][/tex]
Now, to make it look like [tex]\( \frac{c + dz}{d + c} \), we need to factor \( c \)[/tex] out of the numerator:
[tex]\[= \frac{c\left(1 + \frac{bz}{a}\right)}{c\left(\frac{b}{a} + 1\right)}\]Notice that \( c \) cancels out in the fraction:\[= \frac{1 + \frac{bz}{a}}{\frac{b}{a} + 1}\]Now, we notice that \( \frac{b}{a} = \frac{c}{d} \), because \( bc = ad \). So, we can rewrite this as:\[= \frac{1 + \frac{bz}{a}}{\frac{c}{d} + 1}\][/tex]
This is now the same form as [tex]\( \frac{c + dz}{d + c} \), where \( d = \frac{bc}{a} \).[/tex]
So, we have proven that:
[tex]\[\frac{a + bz}{a + b} = \frac{c + dz}{d + c}\][/tex]
given that bc = ad.
Complete question:
Prove that (a+bz)/(a+b)=(c+dz)/(d+c) if bc=ad
We have proven that:
[tex]\[(a + bz)/(a + b) = (c + dz)/(d + c)\][/tex]
given that bc = ad.
To prove that
[tex]\[(a + bz)/(a + b) = (c + dz)/(d + c)\][/tex]
given that bc = ad, we'll start by manipulating one side of the equation to look like the other side.
Let's start with the left-hand side:
[tex]\[(a + bz)/(a + b)\][/tex]
To make it look like the right-hand side, we need to somehow introduce c and d into the expression.
From the given condition bc = ad, we can rearrange it to solve for d:
[tex]\[d = (bc)/(a)\]Now, let's substitute \( d \) into the expression:\[(a + bz)/(a + b) = (c + (bc)/(a)z)/((bc)/(a) + c)\][/tex]
Now, to make it look like [tex]\( (c + dz)/(d + c) \)[/tex], we need to factor \( c \) out of the numerator:
[tex]\[= (c\left(1 + (bz)/(a)\right))/(c\left((b)/(a) + 1\right))\]\\Notice that \( c \) cancels out in the fraction:\[= (1 + (bz)/(a))/((b)/(a) + 1)\][/tex]
Now, we notice that [tex]\( (b)/(a) = (c)/(d) \)[/tex], because [tex]\( bc = ad \)[/tex]. So, we can rewrite this as:[tex]\[= (1 + (bz)/(a))/((c)/(d) + 1)\][/tex]
This is now the same form as [tex]\( (c + dz)/(d + c) \), where \( d = (bc)/(a) \)[/tex].
So, we have proven that:
[tex]\[(a + bz)/(a + b) = (c + dz)/(d + c)\][/tex]
given that bc = ad.
Complete question:
Prove that (a+bz)/(a+b)=(c+dz)/(d+c) if bc=ad.
A girl of mass 25kg climbs up 8 steps
each of height 0.25m, in 20s. calculate
the power of the girl (s = 10ms]
The power of the girl is 24.5 Watts.
Given data:
The mass M = 25 kg, where the height of each step is 0.25m and the number of steps is 8.
To calculate the power of the girl:
Power = Work / Time
The work done is equal to the force applied multiplied by the distance covered.
Work = Force * Distance
The force applied is equal to the weight of the girl, which is given by:
Force = Mass * Gravity
Where gravity is approximately 9.8 m/s².
Force = 25 kg * 9.8 m/s² = 245 N
The distance covered is equal to the height of each step multiplied by the number of steps climbed.
Distance = Height * Number of Steps
Distance = 0.25 m/step * 8 steps = 2 m
Now, calculate the work:
Work = 245 N * 2 m = 490 J
Next, calculate the power by dividing the work by the time:
Power = 490 J / 20 s = 24.5 W
Hence, the power is 24.5 Watts.
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Which of the following best describes interval C on the graph shown? (4 points)
A coordinate plane is shown. The line decreases from x equals 0 to 2, then increases from 2 to 4, stays horizontal from 4 to 5, and decreases from 5 to 8.
Linear constant
Linear decreasing
Linear increasing
Nonlinear increasing
We can see that the y-value does not change on the interval C, so the correct option is "linear constant".
Working with linear equations:
A linear equation is of the form:
y = a*x + b
Where a is the slope and b is the y-intercept.
A horizontal line, also called a constant line, is of the form:
y = b
Where the slope is 0.
Here, you can see that on interval c we have a horizontal line, thus in interval c the graph is linear and constant, so the correct option is the first one.
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Select the sequence of transformations that will carry Triangle A onto triangle A’
To carry Triangle A onto Triangle A', one can use a sequence of geometric transformations such as translation, rotation, and reflection. An example sequence could include translating the triangle, rotating it, and then reflecting it across an axis.
Explanation:To answer the question on how to carry Triangle A onto Triangle A', we need to consider a sequence of geometric transformations. Without the specific diagram, we can only provide a general solution. Typically, transformations to carry one triangle onto another include translations, rotations, reflections, or a combination of these. For example, we may translate Triangle A horizontally or vertically, followed by a rotation around a point at a certain angle, and possibly apply a reflection across a line if the orientation of Triangle A' is opposite that of Triangle A. Example of a Sequence of Transformations: This sequence would successfully carry Triangle A onto Triangle A' given the right conditions.
Kiran shops for books during a 20% off sale. Write an equation that relates the sale price, s, to the original price p.
Answer:
s=p*.2
Step-by-step explanation:
.2 is 20 percent in decimal form
Final answer:
The equation that relates the sale price (s) to the original price (p) during a 20% off sale is s = 0.80p, showcasing the discounted price is 80% of the original price.
Explanation:
When a book is on sale for 20% off, the sale price, s, can be calculated from the original price, p, using the equation:
s = p - (0.20 × p)
This equation relies on the concept that a 20% discount reduces the original price by a factor of 20%. To express this as a mathematical operation, we multiply the original price by 20% (or 0.20) and subtract that value from the original price to obtain the sale price.
You can also simplify the equation:
s = p - 0.20p
s = (1 - 0.20)p
s = 0.80p
So the equation that relates the sale price to the original price is:
s = 0.80p
If in this picture, the biggest pyramid has a square base of 480ft by 480 ft, and it stands 450 ft tall, how many of the given groups (in the diagram) could fit inside of the pyramid?
Answer:
you didn't upload the picture. But I think you should find the volume of the given groups and also find the volume of the biggest pyramid then divide the volume of the biggest pyramid by the volume of the group
$1000 earning 5.25% interest compounded annually for 3 years.
Answer:
$1165.92
Step-by-step explanation:
1000*5.25%=52.5
1000+52.5=1052.5
1052.5*5.25%=55.26
1052.5+55.26=1107.76
1107.76*5.25%=58.16
1107.76+58.16=1165.92
I could b very wrong here tho XD
Adding and subtracting fractions
Answer:
Is possible
Step-by-step explanation:
It is possible to add and subtract fractions
Answer:
it is possible to add and subtract fractions
Step-by-step explanation:
Which set of measurements forms a right triangle? Use the Pythagorean theorem: a2 + b2 = c2.
A) 5, 12, 14
B) 5, 11, 13
C) 4, 11, 13
D) 5, 12, 13
Answer:
b
Step-by-step explanation:
Yesterday, 4/7 of the 210 students in a contest gave their speeches. How many students gave their speeches?
Answer:
120.
Step-by-step explanation:
210 * 4/7
= 30 * 4
= 120.
need helo figuring this out
Answer:
2/5
Step-by-step explanation:
Parallel lines have the same slope.
Find the area of a circle with a radius of 4 m
Answer
16 pi
Step-by-step explanation:
Area= pi times radius squared
4 squared=16
A=16 pi
Find the volume of the sphere. Either enter an exact answer in terms of π or use 3.14, for π and round your final answer to the nearest hundredth.
Radius 7
Answer: 1436.76
Step-by-step explanation:
formula:
[tex]volume=\frac{4}{3} \pi r^{3}[/tex]
input values into calculator:
[tex]\frac{4}{3} \pi 7^{3}[/tex]
7 because radius=7
rounded to 2 decimal places to become
1436.76
THIS IS ON E D E N U I T Y HELP PLEASE
This square pyramid has a surface area of 16 m2.
A square pyramid. The square base has side lengths of 2 meters. The triangular sides have a height of 3 meters.
Consider the square pyramid shown. If each dimension is doubled, how does the surface area change?
The surface area doubles.
The surface area triples.
The surface area increases by 4 times.
The surface area increases by 8 times.
2^2 = 4, so SA would be multiplied by 4
Answer: The surface area increases by 4 times
Step-by-step explanation: i did the assignment and got it correct hope it helps!! :)
how many ways can 12 swimmers finish in first , second, and third place?
Answer:
1320
Step-by-step explanation:
This can be solved using something called a permutation. There are 12 possible swimmers that can be in first place. After that, there are 11 swimmers left to be in second place. Finally there are 10 swimmers left for third place. Multiplying these together, you get 12*11*10=1320 ways. Hope this helps!
Answer:
1728
Step-by-step explanation:twelve swimmers can go in each place at any given time. Multiply the possibilities for first, second, and third place to get the answer.
State the Pythagorean Theorem and tell how you can use it to solve problems.
Answer:
Pythagorean Theorem: [tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex] OR [tex]c^{2}[/tex] - [tex]a^{2}[/tex] = [tex]b^{2}[/tex]
Step-by-step explanation:
You can use it to solve a side of a triangle when you have 2 of the sides of the triangle. I hope this helps! Please mark me brainliest!
The pythagorean theorem is [tex]a^2 + b^2 = c^2[/tex] .
It is used to solve problems by finding the hypotenuse of a right triangle using the two known lengths of the sides squared.
Hope this helps : )
The figure is made up of a cylinder and a sphere which has been cut in half. The radius of each half sphere is 5 mm. What is the volume of the composite figure? Use 3.14 for Pi. Round to the nearest hundredth. A cylinder and 2 half spheres. All have a radius of 5 millimeters. The cylinder has a height of 10 millimeters. Recall the formulas V = B h and V = four-thirds pi r cubed 376.80 cubic millimeters 847.80 cubic millimeters 1,177.50 cubic millimeters 1,308.33 cubic millimeters
Answer:
the answer is c
Step-by-step explanation:
I just took the test
Write an equation of the line that passes through the given points. (-4,7) and (1,2)
Answer:
-1x + 3
Step-by-step explanation: