Using the similar triangles which equation could be used to find the slope of line AB
Answers
The equation that could be used to find the slope of line AB is m = p/q.
What are similar triangles?Two triangles are said to be similar if they have congruent corresponding angles and their corresponding sides are in equal proportion.
Given that, is a graph showing two similar triangles, we need find the equation of the slope of the line AB.
So,
The slope = rise / run = Δy / Δx
Here, Δy / Δx = m/n
Since, the triangles are similar so, m/n = p/q
Therefore,
Δy / Δx = p/q
Hence, the equation that could be used to find the slope of line AB is m = p/q.
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Related Questions
PLEASE HELP ASAP!! WILL GIVE BRAINLIEST
Answers
And it's obvious that it's d
If the public debt of the United States in 2002 was $6,228,235,965,597.16 and the budget deficit in 2003 was $554,995,097,146.46, what was the public debt in 2003?
A. $11,778,186,937,061.76
B. $5,673,240,868,450.70
C. $5,549,950,971,464.60
D. $6,783,231,062,743.62
Answers
i am taking the test as well
Based on the public debt in 2002 and the budget deficit incurred in 2003, the public debt in 2003 was D. $6,783,231,062,743.62.
The budget deficit refers to the amount that the government had to borrow in order to fund the budget of the country.
To find the public debt in 2003 therefore, you need to add the debt of the previous year to the deficit of the current year.
= 2002 Public debt + Budget deficit
= 6,228,235,965,597.16 + 554,995,097,146.46
= $6,783,231,062,743.62
In conclusion, the public debt in 2003 was $6,783,231,062,743.62.
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A circular pool is surrounded by a circular walkway. The radius of the pool is y − 4 and the radius of the full circle formed by the walkway is y + 4. Write a polynomial that represents the area of just the walkway itself, not including the space covered by the pool. (The area of a circle is given by A = πr ^2, where r represents the radius of the circle.)
Answers
The polynomial representing the area of the walkway is the difference between the area of the large circle (π(y + 4)²) and the small circle (π(y − 4)²).
Explanation:To find the polynomial that represents the area of the walkway surrounding a circular pool, we need to calculate the difference between the area of the larger circle (walkway plus pool) and the area of the smaller circle (just the pool).
The radius of the pool is y − 4, and the radius of the walkway plus the pool is y + 4. The area of a circle is given by A = πr².
First, calculate the area of the large circle:
Area of the large circle = π(y + 4)²
Then, calculate the area of the small circle:
Area of the small circle = π(y − 4)²
Finally, the polynomial for the area of the walkway is found by subtracting the area of the small circle from the area of the large circle:
Area of the walkway = π(y + 4)² − π(y − 4)²
The polynomial that represents the area of just the walkway (not including the pool) is π(8y + 32).
Explanation:To find the area of just the walkway, we need to subtract the area of the pool from the area of the full circle formed by the walkway. The area of the pool is given by A = πr ^2, where r is the radius of the pool (y - 4). The area of the full circle is given by A = πr ^2, where r is the radius of the walkway (y + 4). Therefore, the area of the walkway is (π(y + 4) ^2) - (π(y - 4) ^2). Simplifying this expression, we get the polynomial: π(8y + 32).
Please HELP.. MEDAL/ FAN
The ages of students in a school are normally distributed with a mean of 15 years and a standard deviation of 2 years. Approximately what percent of the students are between 14 and 18 years old?
24.17%
62.47%
30.85%
93.32%,
Answers
So the solution for this is that P(students between 14 and 18 years) = 0.9332 - 0.3085 = 0.6247.
To get the percentage, just multiply it by 100 and you will get the answer.
A. 11 cm^3
B. 14 cm^3
C. 15 cm^3
D. 25 cm^3
Answers
We need to find the radius of the larger cylinder
V = [tex] \pi [/tex]r²h
960 = [tex] \pi [/tex]r²(16)
[tex] \frac{960}{16} = \pi r^2[/tex]
60 = [tex] \pi r^2[/tex]
[tex] \frac{60}{ \pi } = r^2 [/tex]
r = [tex] \sqrt{ \frac{60}{ \pi } } [/tex]
r ≈ 4.27 cm
The ratio of the bigger cylinder to smaller is:
16 : 4
Therefore, the big cylinder is 4 times bigger than the small cylinder
[tex] \frac{4.37}{4} [/tex] = r
r = 1.09 cm (radius of small cyclinder)
V (small cylinder) = [tex] \pi [/tex](1.09)²(4)
= 15 cm³
Your answer will be C. 15 cm³
while the base area = [tex] \pi r^{2}[/tex]
since the two cylinders are similar then the ratio between the two radii= the ratio between the two heights =16/4 =4
then the volume of the large cylinder with respect to the smaller dimensions= [tex] \pi * (4r)^{2} *(4*4)=(\pi r^{2} *4)*4*16[/tex]
but [tex] the volume of the smaller one = \pi r^{2} *4[/tex]
then the volume of the large cylinder = the volume of the smaller cylinder*4*16=960
then the smaller's volume= [tex] \frac{960}{4*16}=15[/tex]
You are standing 40 feet away from a building that is 115 feet tall. What is the angle from the ground to the top of the building to the nearest degree?
Answers
A knife is 3 times the cost of the spoon 9 spoons and 12 knives costs £82.80 work out the cost of 1 knife
Answers
Hope this helped!
The cost of spoon is £1.84 and therefore the cost of one knife is £5.52.
Given :
A knife is 3 times the cost of the spoon.9 spoons and 12 knives costs £82.80.Solution :
This question is solve by creating a linear equation and linear equations are nothing but yet another subset of "equations". Linear calculations that requires more than one variable can be done with the help of linear equations.The standard form of a linear equation in one variable is ax + b = 0.Now let x be the cost of spoon. Than the cost knife is 3x. It is given that 9 spoons and 12 knives costs £82.80.
[tex]9x + 12\times(3x)= 82.80[/tex]
[tex]9x + 36x = 82.80[/tex]
[tex]45x =82.80[/tex]
[tex]x = 1.84[/tex]
Therefore the cost of 1 knife = [tex]1.84\times 3 = 5.52[/tex].
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Y= v^2/2a solve for v
Answers
Y = (a v^2)/2
Y = (a v^2)/2 is equivalent to (a v^2)/2 = Y:
(a v^2)/2 = Y
Divide both sides by a/2:
v^2 = (2 Y)/a
Take the square root of both sides:
Answer: v = sqrt(2) sqrt(Y/a) or v = -sqrt(2) sqrt(Y/a)
Final answer:
To solve for v in the equation y = v²/2a, multiply both sides by 2a and then take the square root of both sides which gives v = √(2ay).
Explanation:
The question requires us to solve the equation y = v²/2a for the velocity v. To isolate v, we multiply both sides of the equation by 2a, then take the square root of both sides.
Multiply both sides of the equation by 2a: 2ay = v²Take the square root of both sides to solve for v: v = √(2ay)This mathematical process makes v the subject of the equation based on the given formula from kinematics. It's important to note that v will have two values, one positive and one negative, since taking the square root of a number yields both a positive and negative result.
What is the domain of the given function? {(3, –2), (6, 1), (–1, 4), (5, 9), (–4, 0)}
{x | x = –4, –1, 3, 5, 6} {y | y = –2, 0, 1, 4, 9} {x | x = –4, –2, –1, 0, 1, 3, 4, 5, 6, 9} {y | y = –4, –2, –1, 0, 1, 3, 4, 5, 6, 9}
Answers
{(3, –2), (6, 1), (–1, 4), (5, 9), (–4, 0)}
The domain is formed by the values of x, the first value of the ordered pairs (x,y), in this case 3, 6, -1, 5, and -4. Ordering the values:
Domain of the function={x | x = –4, –1, 3, 5, 6}
Answer: First option {x | x = –4, –1, 3, 5, 6}
1. A sine function has the following key features:
Frequency = 16π
Amplitude = 2
Midline: y = 3
y-intercept: (0, 3)
The function is not a reflection of its parent function over the x-axis.
Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.
2. A sine function has the following key features:
Period = 12
Amplitude = 4
Midline: y = 1
y-intercept: (0, 1)
The function is not a reflection of its parent function over the x-axis.
Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.
3. A sine function has the following key features:
Period = 4π
Amplitude = 2
Midline: y = 3
y-intercept: (0, 3)
The function is a reflection of its parent function over the x-axis.
Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.
4. picture
5. picture
Answers
See the attached image (figure 1)
16pi seems like a typo. I'm going to assume that it's a fraction and it is 1/(6pi)
f = 1/(6pi) = frequency
T = 1/f = 1/(1/(6pi)) = 6pi
Amplitude = 2
a = 2
b = 2pi/T = 2pi/(6pi) = 1/3
Midline: y = 3
d = 3
The function is
y = a*sin(bx-c)+d
y = 2*sin(1/3*x-0)+3
y = 2*sin(x/3)+3
===============================================
Problem 2
See the attached image (figure 2)
T = 12 is the period
a = 4 is the amplitude
b = 2pi/T = 2pi/12 = pi/6
y = 1 is the midline so d = 1
The y intercept is (0,1) which is the midline, which indicates no phase shifts have occurred so c = 0
The function is
y = a*sin(bx-c)+d
y = 4*sin((pi/6)x-0)+1
y = 4*sin((pi/6)x)+1
===============================================
Problem 3
See the attached image (figure 3)
Period = 4pi
T = 4pi
b = 2pi/T = 2pi/(4pi) = 1/2 = 0.5
Amplitude = 2
a = 2
Midline: y = 3
d = 3
y-intercept: (0,3)
The function is a reflection of its parent function over the x-axis, so 'a' is negative meaning a = -2 instead of a = 2
The function is
y = a*sin(bx-c)+d
y = -2*sin(0.5x-0)+3
y = -2*sin(0.5x)+3
===============================================
Problem 4
See the attached image (figure 4)
a = 10 which is half of the distance between the highest and lowest points
T = 8 is the period
b = 2pi/T = 2pi/8 = pi/4
c = -pi/2 is the phase shift since its really a cosine graph
d = 0 is the midline
The function is
y = a*sin(bx-c)+d
y = 10*sin((pi/4)*x+(-pi/2))+0
y = 10*sin((pi/4)*x+pi/2)
===============================================
Problem 5
See the attached image (figure 5)
a = 2 is the amplitude since it bobs up and down this distance from the midline
T = 8 seconds is the period (double that of the time it takes for it to go from the highest to the lowest point)
b = 2pi/T = 2pi/8 = pi/4
c = 0 is the phase shift as the buoy starts at normal depth of 20 meters
d = 20 is the midline
The function is
y = a*sin(bx-c)+d
y = 2*sin((pi/4)x-0)+20
y = 2*sin((pi/4)x)+20
===============================================
Answer:
1. Picture Below
2. Ordered Pair : (0,1) (3,5) (6,1) - Function: f(x)=4sin(pi/6x)+1
3. Ordered Pair : (0,3) (3.14,5) (6.27,3) - Function: f(x)= 2sin(1/2x)+3
4. I have no idea.
5. Plot the first point at (0, 20) and the second point at (2, 22)
Step-by-step explanation:
What is the probability that a point chosen at random in the rectangle is also in the blue triangle
Answers
Answer:
The probability that a point chosen at random in the rectangle is also in the blue triangle is:
1/2
Step-by-step explanation:
We are given a figure
We have to find the probability that a point chosen at random in the rectangle is also in the blue triangle.
Area of rectangle= 4×5 sq. in.
= 20 sq. in.
The area of blue triangle=[tex]\dfrac{1}{2}\times 4\times 5[/tex]
= 10 sq. in.
P(that a point chosen at random in the rectangle is also in the blue triangle)
= area of blue triangle/whole area of the rectangle
= 10/20
= 1/2
Answer: the answer is 1/2
Step-by-step explanation:
What is the measure of
A. Cannot be determined
B. 74
C. 16
D. 32
Answers
Why? The triangle in the problem is an isosceles triangle. That means the two legs of the triangle are equal and the angle opposite to the equal legs are also equal.
Therefore, angle C is also 74°.
The sum of the interior angles of a triangle is equal to 180°.
Thus,
180° = ∡A + ∡B + ∡C
180° = 74° + ∡B + 74°
180° = 148° + ∡B
∡B = 180° - 148°
∡B = 32°
The height of a tree was 4.8m .After one year the height of the tree was increased by 12.5%.find its new height
Answers
The new height of the tree after it has increased by 12.5% is 5.4 meters
To find the new height of the tree after it has increased by 12.5%, we start by calculating the increase in height using the following equation
Increase = 12.5% of the original height
The original height is given as 4.8m. So, the formula can be expressed as follows
Increase = 12.5% * 4.8
Increase = 0.125 * 4.8
Increase = 0.6 meters
Add the increase to the original height
New height = Original height + Increase
The above equation can then be expressed as follows
New height = 4.8 + 0.6
New height = 5.4 meters
Which of the following is equal to (2x/3 - 7) + 7
A. (2x - 7) + 21
B. 2x - 21/3
C. 3x/2
D. 2x/3
@texaschic101
Answers
The order of the mathematical operations is PEMDAS.
Therefor the first step you will take is to solve the operation inside the parenthesis.
(2x/3 - 7) =(2x/3 - 7)* 3/3 = 2x/3 - 21/3 = (2x - 21)/3
While adding or subtracting fractions, dont forget to check that each term have the same denominator.
Then the operation outside the parenthesis,
(2x - 21)/3 + 7 = (2x-21)/3 + 7 * 3/3 = (2x - 21)/3 + 21/3 =
(2x - 21 + 21) / 3 = 2x/3
The final answer is D. 2x/3
evaluate the principal square root of 36 .
answer ??? help plz thank u :)),
Answers
6.
Evaluate cot 290º. Round your answer to the nearest hundredth.
–1.06
–0.36
2.92
–2.75,
Answers
The solution this is the following:
cot(110°) = -cot(70°)
cot(70°) = -1/tan(70°)
tan(70°) ≈ 2.75
-1/tan(70°) ≈ -0.36
The table shows different geologic time periods: Period Number of Years Ago Jurassic 2.08 ⋅ 108 Silurian 4.38 ⋅ 108 Tertiary 6.64 ⋅ 107 Triassic 2.45 ⋅ 108
Order the time periods from oldest to youngest. (4 points)
1. Tertiary, Jurassic, Triassic, Silurian
2.Jurassic, Triassic, Silurian, Tertiary
3.Silurian, Triassic, Jurassic, Tertiary
4.Triassic, Silurian, Jurassic, Tertiary
Answers
A prism with a volume of 3125 ft³ is scaled down to a volume of 200 ft³.
What is the scale factor?
Enter your answer, as a decimal or a fraction in simplest form, in the box.
I think it's 2/5 or 0.4
Answers
Answer:
The scale factor is equal to [tex]0.4[/tex] or [tex]\frac{2}{5}[/tex]
Step-by-step explanation:
we know that
If two figures are similar. then the ratio of its volumes is equal to the scale factor elevated to the cube
Let
z------> the scale factor
x------> the volume of the dilated prism
y------> the volume of the original prism
so
[tex]z^{3}=\frac{x}{y}[/tex]
we have
[tex]x=200\ ft^{3}[/tex]
[tex]y=3,125\ ft^{3}[/tex]
substitute
[tex]z^{3}=\frac{200}{3,125}[/tex]
[tex]z=\sqrt[3]{\frac{200}{3,125}}[/tex]
[tex]z=0.4[/tex] or [tex]z=\frac{2}{5}[/tex]
The owners want to hire a contractor to build a porch along side the parlor. The parlor is rectangular with width Of 32 feet and length of 50 feet. The porch will have the same width that on each side of the house. See design plans.
Answers
a) Basically, you are adding the length of porch to the original length of the parlor.
Let's say that the newly added porch is x.
(50 + x)(32 + x)
1600 + 50x + 32x + x²
x² + 82x + 1600
b) Just make the polynomial x² + 82x + 1600 equal to 2320.
x² + 82x + 1600 = 2320
subtract 2320 on both sides to make the polynomial equal to 0.
x² + 82x - 720 = 0
factor this
(x - 8)(x + 90) = 0
(x - 8) =0 (x + 90) = 0
x = 8 x = - 90
(-90ft doesn't make sense. So don't mind about this.)
So the porch should be 8ft.
Hope this helped!
The width of the porch will be 32 feet, the same as the parlor. However, to calculate the amount of building materials needed, additional specifics are required such as the porch's length, location of posts, and number of boards.
Explanation:To answer the question related to designing a porch that matches the width of the parlor, we first understand that the parlor is of a rectangular shape with a width of 32 feet. Considering that the porch will have the same width, it means the porch will also have a width of 32 feet.
From this point, specifics such as the desired length of the porch, location of posts, number of boards or rails, and other related factors would come into play in the calculating of building materials needed for the construction. There may also be the need to consider factors like the ratio of width to length in the design, akin to the mathematical relation mentioned in the statement 'X = Y x 2 + 1'.
So, while we know the width of the porch because it matches the parlor, the exact amount of materials that will be required would depend on further specifics of the porch design, similar to the steps in a stoichiometry problem in chemistry where one calculates the amount of reactants or products in a chemical reaction based on known ratios.
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What is 8.3x10^-9 in standard form?
Answers
( eight zeros.)
The number of members f(x) in a local swimming club increased by 30% every year over a period of x years. The function below shows the relationship between f(x) and x:
f(x) = 10(1.3)x
Which of the following graphs best represents the function?
Graph of f of x equals 1.3 multiplied by 10 to the power of x
Graph of exponential function going up from left to right in quadrant 1 through the point 0, 0 and continuing towards infinity
Graph of f of x equals 10 multiplied by 1.3 to the power of x
Graph of f of x equals 1.3 to the power of x
Answers
f(x) = 10(1.3)^x
The graphs that best represents the function is:
Graph of f(x) equals 10 multiplied by 1.3 to the power of x.
Step-by-step explanation:The function that shows the relationship between f(x) and x: is:
[tex]f(x)=10\times (1.3)^x[/tex]
a)
Graph of f(x) equals 1.3 multiplied by 10 to the power of x.
This means that the expression is given by:
[tex]f(x)=1.3\times (10)^x[/tex]
Hence, option: a is incorrect since it is not equal to the given function f(x).
b)
Graph of exponential function going up from left to right in quadrant 1 through the point (0, 0) and continuing towards infinity.
In the given function f(x) when x=0 we have:
[tex]f(x)=10\times (1.3)^0\\\\\\f(x)=10\neq 0[/tex]
Hence, option: b is incorrect.
c)
Graph of f(x) equals 10 multiplied by 1.3 to the power of x.
This means that the function f(x) is given by:
[tex]f(x)=10\times (1.3)^x[/tex]
which is obviously true.
Hence, option: c is correct.
d)
Graph of (x) equals 1.3 to the power of x.
This means that the function f(x) is given by:
[tex]f(x)=(1.3)^x[/tex]
which does not m,atches the actual expression.
Hence, option: d is incorrect.
Three brothers have ages that are consecutive even integers. the product of the first and third boys' ages is 20 more than wice the second boy's age. find the age of each of the three boys.
Answers
second brother = x + 2
third brother = x + 4
The product of the first and third boys' ages is 20 more than twice the second boy's age:
x(x+4) = 2(x+2) + 20
x² + 4x = 2x + 4 + 20
x² + 4x - 2x - 24 = 0
x² + 2x - 24 = 0
(x - 4)(x + 6) = 0
x = 4 or -6 (rejected, age cannot be negative)
First brother = 4
Second brother = 4 + 2 = 6
Third brother = 4 + 4 = 8
The three boys are 4, 6, and 8 years old.
Let x be the age of the first boy, snce they are consecutive even integers, they will be 2 way from each other.
1st boy= x
2nd boy= x+2
3rd boy = x+4
"product means the answer to a multiplication problem;
x(x+4)=20+2(x+2)
x%5E2+4x=20+2x+4
x%5E2+4x-2x=20+4
x%5E2+2x=24
x%5E2+2x-24=0
(x+6)(x-4)=0
x+6=0
x=-6
x-4=0
x=4
SInce we know they are even integers, the answerhas to be;
x=4
so the first boys age = 4
2nd boy= 4+2=6
3rd boy= 4+4=8
Hope this helps you
Find the measure of “rst”
Answers
Answer: it is 110 bcs each section in 10° and there are 11 sections
Eighty percent of the dogs have completed obedience classes. How many of the dogs have completed obedience classes? Five dogs of different breeds 4 dogs 3 dogs 2 dogs 1 dog
Answers
x--------> number of dogs that completed the obedience class
we know that
total number of dogs=5
Eighty percent of the dogs have completed obedience classes
so
x=0.80*5------> x=4
the answer is
4 dogs have completed obedience classes
4 dogs have completed the obedience classes
Explanation:
We are given that 80% of the dogs completed the obedience classes and that the total number of dogs who attended the class was 5
This means that 80% of the 5 dogs have completed the class
Therefore:
number of dogs that completed the class = 80% * 5
= 0.8 * 5
= 4 dogs
Hope this helps :)
Which value(s) of x would result in Set B being a function of the values in Set A? Select Function or Not a Function for each value of x. Are the following numbers a function or not a function
Answers
To determine if Set B is a function of the values in Set A, we need to ensure that each value of x in Set A has only one corresponding value in Set B:
-2: Function5: Function0: Not a Function1: Function-3: FunctionFor each value of x, we can determine if Set B is a function or not by checking if there is only one corresponding value in Set B.
For x = -2, there is only one corresponding value in Set B, so it is a function.
For x = 5, there is only one corresponding value in Set B, so it is a function.
For x = 0, there are multiple corresponding values in Set B, so it is not a function.
For x = 1, there is only one corresponding value in Set B, so it is a function.
For x = -3, there is only one corresponding value in Set B, so it is a function.
Therefore, Set B is a function of the values in Set A for all values of x except for x = 0.
Two numbers are in the ratio of 2 to 3. If the smaller number is 18, the larger number is _____. 21 27 36 54
Answers
the answer is 27
Answer: If two numbers are in a ratio of 2 to 3, this means that two times one number is equal to 3 times the other, or:
2*X = 3*Y, where X and Y are any numbers, and X is the bigger one and Y is the smaller one.
If Y=18, then:
2*X = 3*18 = 54
X=54/2 = 27
So the answer is 27.
o valor da expressão a=1,67 . 10 + 3,95 . 10
Answers
First we rewrite the expression:
a = (1.67 * 10) + (3.95 * 10)
We multiply each member of the parenthesis by 10:
a = 16.7 + 39.5
We add both values:
a = 56.2
Answer:
We note that the value of the expression for a is:
a = 56.2
How to solve
187=1/2*17(6+X)
Answers
The measure of angle x is 25 more than 4 times the measure of its complement. find the measure of x. x= degrees
Answers
x = 385 -4x . . . . . . . . . eliminate parentheses
5x = 385 . . . . . . . . . . . .add 4x
x = 77 . . . . . . . . . . . . . . divide by 5
The measue of angle x is 77°.
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