The coordinates of the vertices for the image if the preimage is translated 3 units up is A′(−3, 6), B′(0, 10), C′(−3, 3) (option b).
In this particular question, we are given a triangle ABC with vertices at A(−3, 3), B(0, 7), and C(−3, 0). Our task is to determine the coordinates of the vertices for the image if the preimage is translated 3 units up.
When a figure is translated, it is moved to a new location without changing its shape or size.
Let's start by looking at vertex A(−3, 3). If we translate this vertex 3 units up along the y-axis, its new coordinates will be A′(−3, 6).
Similarly, if we translate vertex B(0, 7) 3 units up, its new coordinates will be B′(0, 10). Finally, if we translate vertex C(−3, 0) 3 units up, its new coordinates will be C′(−3, 3).
Therefore, the vertices of the image triangle are A′(−3, 6), B′(0, 10), and C′(−3, 3). This is option (B) from the given answer choices.
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What is the distance from (−18, −5) to (−18, 24)? −29 units −19 units 19 units 29 units
The distance from (-18, -5) and (-18, 24) is 29 units which is calculated with the formula of shortest distance between two coordinates.
Hence option d is the correct option.
The coordinates are given as, say P is (-18, -5) and Q is (-18, 24).
The distance between P and Q can be calculated with the formula of shortest distance between two coordinates as,
Shortest distance between P and Q, PQ = [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2 }[/tex] units
⇒ PQ = [tex]\sqrt{((-18) - (-18))^2 + ((24) - (-5))^2 }[/tex] units
⇒ PQ = [tex]\sqrt{(-18 +18)^2 + (24 +5)^2 }[/tex] units
⇒ PQ = [tex]\sqrt{(0)^2 + (29)^2 }[/tex] units
⇒ PQ = [tex]\sqrt{29^2}[/tex] units
⇒ PQ = 29 units
Hence option d 29 units is the correct option.
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3
A bag contains red and blue marbles, such that the probability of drawing a blue marble is . An experiment consists of
drawing a marble, replacing it, and drawing another marble. The two draws are independent. A random variable assigns
the number of blue marbles to each outcome.
What is the probability that the random variable has an outcome of 3?
a. 24%
C. 14%
96
b.
By 39%
d. 0
Answer:
We can use the binomial probability formula to find the probability of getting exactly 3 blue marbles in two draws:
P(X=3) = (2 choose 3) * (0.6)^3 * (0.4)^(-1) = 0.288
However, since we are asked for the probability of the random variable having an outcome of 3 (i.e. getting exactly 3 blue marbles), we can simply use this probability:
P(X=3) = 28.8%
Therefore, the answer is (a) 24%.
ind the area inside 2cos 3r
(tip: use6
and6
)
The area inside the polar curve R = 2cos(3θ) for three full rotations is 6π.
The polar curve R = 2cos(3θ) is symmetric about the x-axis, with three petals that extend from θ = 0 to θ = π/3, π to 4π/3, and 5π/3 to 2π. To find the area inside the curve, we need to integrate the expression for the area element in polar coordinates over the desired region:
dA = (1/2) [tex]R^{2}[/tex] dθ
The limits of integration for θ are from α = -6π to β = 6π, since we want to find the total area inside the curve for three full rotations. Thus, the integral for the area is:
A = ∫(β=6π, α=-6π) (1/2) [tex]R^{2}[/tex]dθ
= ∫(β=6π, α=-6π) (1/2) (2cos(3θ))^2 dθ
= 2∫(β=6π/3, α=-6π/3) cos^2(3θ) d(3θ) (using the identity cos^2(3θ) = (1 + cos(6θ))/2)
= ∫(β=6π/3, α=-6π/3) (1/2 + (1/2)cos(6θ)) d(3θ)
= (1/2)θ + (1/12)sin(6θ) ∣(β=6π/3, α=-6π/3)
= (1/2)(6π - (-6π)) + (1/12)(sin(36π) - sin(-36π))
= 6π
Correct Question :
Find The Area Inside R=2cos(3θ) (Tip: Use Α=−6π And Β=6π )
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please help! maths functions (find the equation of the line…)
Answer:
a) y = -2x + 3
b) y = -3x + 7
c) y = -1/2x + 4
d) y = 2
Step-by-step explanation:
Gradient is also known as slope
a) y = mx + b
3 = (-2)0 + b
b = 3
y = -2x + 3
b) y = mx + b
1 = (-3)(2) + b
1 = -6 + b
b = 7
y = -3x + 7
c) Slope m = (y2 - y1)/(x2 - x1)
m = (2 - 3)/(4 - 2) = -1/2
y = mx + b
3 = -1/2(2) + b
3 = -1 + b
b = 4
y = -1/2x + 4
d) The x‐axis or any line parallel to the x‐axis has a slope of 0.
y = mx + b
2 = -3(0) + b
b = 2
y = 2
Answer:
a) The equation of this line is y = -2x + 3
b) The equation of this line is y = -3x + 7
c) The equation of this line is y = -1/2x + 4 or y = -0.5x + 4
d) The equation of this line is y = 2
Step-by-step explanation:
The equation of a line can be written in the form y = mx + c, where m is the gradient and c is the y-intercept.
a) The equation of the line with a gradient of -2 and cutting the y-axis at 3 can be found using the point-slope form of a linear equation. The point-slope form is given by y - y1 = m(x - x1), where m is the gradient and (x1, y1) is a point on the line. Substituting m = -2 and (x1, y1) = (0, 3), we get:
y - 3 = -2(x - 0)
Simplifying the right-hand side gives:
y - 3 = -2x
Adding 3 to both sides gives the final equation:
y = -2x + 3
b) The equation of the line with a gradient of -3 and passing through the point (2, 1) can be found using the point-slope form again. Substituting m = -3 and (x1, y1) = (2, 1), we get:
y - 1 = -3(x - 2)
Simplifying the right-hand side gives:
y - 1 = -3x + 6
Adding 1 to both sides gives the final equation:
y = -3x + 7
c) To find the equation of the line passing through the points (2, 3) and (4, 2), we first need to find its gradient. The gradient is given by:
m = (y2 - y1)/(x2 - x1)
Substituting the coordinates of the two points, we get:
m = (2 - 3)/(4 - 2) = -1/2 or -0.5
Now, we can use the point-slope form again, this time with (x1, y1) = (2, 3) and m = -1/2:
y - 3 = (-1/2)(x - 2)
Simplifying the right-hand side gives:
y - 3 = (-1/2)x + 1
Adding 3 to both sides gives the final equation:
y = (-1/2)x + 4 or y = -0.5x + 4
d)The line is parallel to the x-axis and passes through the point (-3 ; 2). A line parallel to the x-axis has a gradient of 0. The general equation of a line is y = mx + c, where m is the gradient and c is the y-intercept. Since the gradient is 0, the equation becomes y = c. Since the line passes through the point (-3 ; 2), we can substitute y = 2 into the equation to find that c = 2. Therefore, the equation of this line is y = 2.
pls help me with this questions quick! right answer lol pls
The function given in the table is an exponential function.
The function given in the table is clearly not linear, since the y value is changing rapidly.
Here we can see that the function value is changing as the multiplication of 7.
y = 7⁰ = 1, when x = 1
y = 7¹ = 7, when x = 2
y = 7² = 49, when x = 3
y = 7³ = 343, when x = 4
y = 7⁴ = 2401, when x = 5
So here the equation of the function can be written as,
y = 7ˣ⁻¹
Here the variable x is in the exponent.
So it is an exponential function.
Hence the given function is an exponential function.
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Please answer all these questions by today
The statement that is not true on the cube - shaped box is C. The volume of the box is 1 square foot.
The possible dimensions for the bottom layer would be :
Length = 1 unit , Width = 12 unitsLength = 2 units , Width = 6 unitsLength = 3 units , Width = 4 unitsHow to find the possible dimensions ?In answer to the rectangular prism inquiry, we know that the prism is made of 36 cubic units and has a height of 3 units. To discover all potential bottom layer dimensions, divide the total number of cubic units (36) by the height (3 units):
36 / 3 = 12
The possible dimensions of the bottom layer:
1 x 12 = 12
2 x 6 = 12
3 x 4 = 12
This means that the possible dimensions would be:
Length = 1 unit , Width = 12 units
Length = 2 units , Width = 6 units
Length = 3 units , Width = 4 units
A square foot is a unit of area, not volume. The volume should be measured in cubic feet.
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work out the area of the shaded shape 5m 13m 9m 11m area
Answer:
To calculate the area of the shaded shape, we need to first find the area of the two rectangles and then subtract the overlap.
The area of the rectangle with dimensions 5m and 13m is:
Area = 5m x 13m = 65 square meters
The area of the rectangle with dimensions 9m and 11m is:
Area = 9m x 11m = 99 square meters
To find the overlap, we need to calculate the width of the shaded region. We can do this by subtracting the length of one rectangle from the other:
13m - 9m = 4m
So the width of the shaded region is 4m.
Now we can find the area of the shaded region by multiplying the width by the length:
Area = 4m x 5m = 20 square meters
Finally, we can find the total area by subtracting the overlap from the sum of the two rectangle areas:
Total Area = (65 + 99) - 20 = 144 square meters
Therefore, the area of the shaded shape is 144 square meters.
Answer: 61m^2 would be the answer
Find the value of c in the diagram below.
C-5 C-5 C-5 C-5 C-5 C-5=35
The value of c in the given diagram would be 10. 83.
How to find the value of C ?From the diagram we see that when C is subtracted by 5 and then multiplied with this value 6 times, we get the value of 35.
In other words:
6 ( C - 5 ) = 35
Showing that when C - 5 is multiplied by 6, we get the value of 35.
Therefore, solving gives:
6 C - 30 = 35
6 C = 35 + 30
6 C = 65
C = 65 / 6
C = 10. 83
In conclusion, the value of C is 10. 83.
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What is an equation of the line that passes through the points (-4, 8) and (6, 3)?
Answer:
y = - [tex]\frac{1}{2}[/tex] x + 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 4, 8 ) and (x₂, y₂ ) = (6, 3 )
m = [tex]\frac{3-8}{6-(-4)}[/tex] = [tex]\frac{-5}{6+4}[/tex] = [tex]\frac{-5}{10}[/tex] = - [tex]\frac{1}{2}[/tex] , then
y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (- 4, 8 )
8 = - [tex]\frac{1}{2}[/tex] (- 4) + c = 2 + c ( subtract 2 from both sides )
6 = c
y = - [tex]\frac{1}{2}[/tex] x + 6 ← equation of line
9. It is estimated that a certain model rocket will reach an altitude of 200 ft. A photographer is setting up a camera 50 ft away from the launch pad. At what angle should he set the tripod to get a picture at the maximum altitude?
The photographer should set the tripod at an angle of approximately 75.96 degrees to get a picture of the rocket at its maximum altitude.
We have,
We can use trigonometry to solve this problem.
C
/ \
/ \
/θ \
/ \
/ \
A-------------B
50 ft
In this diagram, A represents the launch pad, B represents the maximum altitude of the rocket, C represents the position of the photographer, and θ represents the angle at which the tripod should be set.
We want to find θ.
First, we can find the height of the triangle ABC using the Pythagorean theorem:
AB² = AC² + BC²
200² = AC² + 50²
AC² = 200² - 50²
AC = √(200² - 50²)
AC = 190.526 ft
Next, we can use the tangent function to find θ:
tan(θ) = opposite/adjacent = AB/BC = 200/50 = 4
Taking the arctangent of both sides, we get:
θ = [tex]tan^{-1}(4)[/tex]
θ = 75.96 degrees
Therefore,
The photographer should set the tripod at an angle of approximately 75.96 degrees to get a picture of the rocket at its maximum altitude.
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PLEASE HELP
Part A:
List the three different types of visuals we use to organize all the possible outcomes in a sample space
1
2
3.
Part B:
Leena is arranging 3 different books in a row on a shelf. A detective story (D), a mystery story (M), and a comic book (C)
1. Pick one of the three types of visuals you listed in Part A to create a sample space for the arrangement of all possible outcomes for arranging the 3 books on a shelf. (1 point)
Fill in the Blank I will choose to create a
for this scenario
2. Create your visual either by hand or using technology
There are 6 different possible arrangements as obtained using the factorial method and they are :
DMC, CMD, DCM, MDC, CDM, MCD
Given that:
DETECTIVE STORY = D
MYSTERY STORY = M
COMIC BOOK = C
Now, To use the factorial method, we find the factorial value of the number of books to be arranged
Number of different possible arrangements = (number of books)!
Number of books = 3
Hence,
3! = 3 x 2 x 1 = 6 ways
The sample space :
DMC
CMD
DCM
MDC
CDM
MCD
Therefore, there are 6 different samples on the SAMPLE SPACE.
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Complete question is,
Leena is arranging 3 different books in a row on a shelf. Create a sample space for the arrangement of a detective story (D), a mystery story (M), and a comic book (C).
Source
StylesNormal
What is 7/12x - y/6x^2 expressed in simplest form
The expression 7/12x - y/6x² in its simplest form is (7x - 2y)/(12x²).
We have,
To simplify the expression 7/12x - y/6x², we need to find a common denominator for the two terms.
The common denominator is 12x^2.
Multiplying the first term by x/x and the second term by 2/2, we get:
(7x)/(12x²) - (2y)/(12x²)
Combining the two terms, we get:
(7x - 2y)/(12x²)
Therefore,
7/12x - y/6x² in its simplest form is (7x - 2y)/(12x^2).
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It costs a car company $25,000,000 to develop and market the model of a new car. The company sells each car for $30,000 . Which of the following represents the number of cars, c , that the car company must sell to make over $5,000,000 in profit?
Answer:1,000
Step-by-step explanation:
So we add 25 million to 5 million which is 30 million. Then we divide 30 million to 30 thousand and get 1 thousand.
date:
go to 3. The tree harvester makes the same growth estimates for the trunk of a sequoia
tree that has a height of about 95 meters and a base diameter of about 12.2 meter.
Find the mass of the trunk.
Glant Sequola Facts
Height To 311 ft.
Age: To 3,200 years
Bark: To 31 in, thick
Base: To 40 ft. diameter
1 meter 3.28084
The wood of a sequoia tree has a density of about 450
kilograms per cubic meter.
mowans "rlod bnia Streishib el ribirW S
The mass of the trunk of the sequoia tree is 141443.1 kg.
The volume of a cylinder, using the formula:
V = πr²h
π is pi (approximately 3.14)
r is the radius of the trunk (which is half the diameter)
h is the height of the trunk
1 meter = 3.28084 feet
we can convert the given measurements from feet to meters to ensure consistent units.
The base diameter of the tree is 12.2 meters / 3.28084 = 3.719 meters,
so the radius is 3.719 / 2 = 1.8595 meters.
The height of the tree is 95 meters / 3.28084 = 28.9568 meters.
Therefore, the volume of the trunk is:
V = π(1.8595)²(28.9568) = 314.318 cubic meters
Now calculate the mass of the trunk by multiplying the volume by the density of the wood:
M = V × ρ
= 314.318 × 450
= 141443.1 kg
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What would happen if you put the wrong place value of a specific number
Writing the correct number relies on what our number system calls the place value system. The 9, the 3, and the 1 are all located in different spots in the larger number, and each of them is called a digit.
Putting the digits in the wrong locations could result in disaster when dealing with money and in many other situations.
The 10 passengers on a small airplane have paid a total of $1,580 for the flight.
If an economy ticket cost $135 and a first-class ticket costs $250 , how many economy tickets were bought?
Answer:
8 people bought economy and 2 bought first class
Step-by-step explanation:
there are 10 person and total is 1580 so 250+ 9(135)=1460 which is wrong so we gonna try adding 2(250) and 8(135) which got us 1580
What is the value of x? (6x+30) 2x
The value of x after solving the given equation (6x+30) = 2x is equal to -7.5.
To solve for x in the equation (6x+30) = 2x, we need to isolate x on one side of the equation.
First, we can simplify the equation by subtracting 2x from both sides:
(6x+30) - 2x = 0
Simplifying this further gives:
4x + 30 = 0
To isolate x, we can subtract 30 from both sides:
4x = -30
Finally, we can solve for x by dividing both sides by 4:
x = -7.5
Therefore, the value of x in the equation (6x+30) = 2x is -7.5.
In general, when solving linear equations such as this, we want to manipulate the equation in such a way that we can isolate the variable on one side of the equation.
This can involve adding or subtracting terms, multiplying or dividing by constants, or taking square roots, among other techniques. The goal is to get the equation into a form that allows us to solve for the variable by itself.
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Complete question is:
What is the value of x? (6x+30) = 2x
The table below lists the masses and volumes of several pieces of the same type of metal. There is a proportional relationship between the mass and the volume of the pieces of metal. Volume (cubic centimeters) (cubic centimeters) Volume Mass (grams) Mass (grams) 2.5 2.5 10.15 10.15 4.4 4.4 17.864 17.864 13.6 13.6 55.216 55.216 Determine the mass, in grams, of a piece of metal that has a volume of 12.4 12.4 cubic centimeters. Round your answer to the nearest tenth of a gram
The mass of a piece of metal that has a volume of 12.4 cubic centimeters.
We can set up a proportion with the given masses and volumes:
Mass ₁ / Volume ₁ = Mass ₂ / Volume ₂
We can choose any two sets of masses and volumes from the table to use in the proportion. Let's use the first set of masses and volumes:
2.5 / 2.5 = Mass₂ / 12.4
We can solve for Mass 2 by cross-multiplying and simplifying:
2.5 x 12.4 = 2.5 Mass ₂
31 = Mass ₂
Therefore, the mass of a piece of metal with a volume of 12.4 cubic centimeters is 31 grams. We can round this answer to the nearest tenth of a gram, which gives us 31.0 grams.
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The numbers 1, 2, 3 and 4 have weights 0.1, 0.2, 0.3 and 0.4 respectively.
What is the weighted mean?
2.5
2.8
3.0
3.2
Answer:
1(.1) + 2(.2) + 3(.3) + 4(.4)
= .1 + .4 + .9 + 1.6 = 3.0
Answer:
Step-by-step explanation:
To calculate the weighted mean, first multiply each number by its corresponding weight, then add-up the products and divide by the sum of the weights-
weighted mean = (1 x 0.1 + 2 x 0.2 + 3 x 0.3 + 4 x 0.4) / (0.1 + 0.2 + 0.3 + 0.4)
Then simplifying the numerator:-
weighted mean = (0.1 + 0.4 + 0.9 + 1.6) / (0.1 + 0.2 + 0.3 + 0.4)
Then adding up the numerator:-
weighted mean = 3 / 1So the weighted mean of the numbers 1, 2, 3, and 4 with weights 0.1, 0.2, 0.3, and 0.4 respectively is 3.
fill in the following table based on this function. show your work.
The table can be complete based on the function given by substituting as:
When s = 0, M(s) = -3
When s = 4, M(s) = 7
When s = 9, M(s) = 12
Given a function,
M(s) = 5√s - 3
Substitute each of the value of s to find the corresponding value of M(s).
When s = 0,
M(s) = 5√0 - 3 = 0 - 3 = -3
When s = 4,
M(s) = 5√4 - 3 = 10 - 3 = 7
When s = 9,
M(s) = 5√9 - 3 = 15 - 3 = 12
Hence the blank spaces are -3, 7 and 12.
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You want to purchase a new car
In 9 years and expected the car to cost $15,000. Your bank offers a plan a guaranteed APR of 6.5% .
If you make regular deposits.
How much should you deposit each month to end up $15,000 in 9 years ?
this needs to be done i dont know
Answer:
Step-by-step explanation:
I’m sorry but I don’t know how I can solve you question
The following information has been provided by Miller Company: Advertising expense $19,800 Interest expense $7,400 Rent expense for store $24,000 Loss on sale of property and equipment $11,400 Cost of goods sold $42,600 Depreciation expense $14,200 Prepaid insurance $2,000 What is the amount included in the Other Items section of Miller's income statement?
Answer:
To find the amount included in the Other Items section of Miller's income statement, we need to add up all the expenses and losses that are not related to advertising, interest, rent, cost of goods sold, depreciation, and prepaid insurance. These expenses and losses fall under the category of "Other Expenses" or "Other Items" in the income statement.
From the given information, the expenses and losses that are not included in the above categories are:
- Loss on sale of property and equipment = $11,400
Therefore, the amount included in the Other Items section of Miller's income statement is $11,400.
Step-by-step explanation:
AASAAAP. NEEDD HELLPPPPP
The coordinates of B'(6, 3) and C'(4, 4).
We have,
The point A (6, 8) is translated to A' (2, 5).
So, here the points are translated as
(x₁ - x₂ , y₁ - y₂)
= (6 -2, 8-5)
= (4, 3)
So, the coordinates of B'
= (8 -2, 8-5)
= (6, 3)
and, the coordinate of C'
= (6-2, 9-5)
= (4, 4)
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what numbers should replace a b c to make 9
Answer:
I did the math in my head but please please trust me
It’s below
Step-by-step explanation:
C = 1 1/2
B = 2
A = 5
I’m going to try to explain as best as I can
First solve for C by subtracting the other numbers in its line going up to down from 9:
9 - 3 1/2 + 4 = C
9 - 7 1/2 = C
1 1/2 = C
now that w have C we can solve for b doing same steps:
9 - 5 1/2 + 1 1/2 = b
9 - 7 = b
2 = b
now we do A:
9 - 2 + 2 = a
9 - 4 = a
5 = a
Answer
A should be 5
B should be 2
c should be
[tex] 1\frac{1}{2 \\ } [/tex]
all should add up to 9
2+A(5)+b(2)= 9
a(5)+3 1/2+ 1/2=9
5 1/2+ b(2)+ 1 1/2= 9
3 1/2+ 1 1/2+ 4= 9
PLEASE HELP ME!!!!!! I WILL APPRECIATE IT SO MUCH
please help me, here is schreenshot quick and right answers only. algebra
The linear function with the greatest rate of change is f(x) = 2x
Which linear function has the greatest rate of change?The general linear function can be written in the following way.
y = ax + b
a is the slope or rate of change, and b is the y-intercept.
From the given options, the line with the greatest rate of change is the one that grows the fastest, and we can see that the equation for that line is:
y = 2x
So that is the correct option.
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PLEASE ANSWER ASAP
Find the equation of the exponential function represented by the table below:
x y
0 2
1 6
2 18
3 54
what does y= ??
The value of Y is givan as y = 2 * 3^x
How to solve for yThe general form is of
y = ab^x
where we have to define the terms as
'a' is the initial value, 'b' is the base, and 'x' is the exponent
Point (0, 2):
y = ab^x
2 = a * b^0
Since any non-zero number raised to the power of 0 is 1, we have:
2 = a * 1
a = 2
Point (1, 6):
y = ab^x
6 = 2 * b^1
6 = 2 * b
b = 6 / 2
b = 3
From the values that we have solve we would have
y = 2 * 3^x
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Find the equation of the line joining the points (1,6) and (6,1)
Step-by-step explanation:
in what form do you need the equation ?
I assume it is the slope-intercept form :
y = ax + b
"a" being the slope of the line, "b" being the y-intercept of the line.
the slope of a line is the ratio
y-coordinate difference / x-coordinate difference
when going from one point on the line to another.
and the y-intercept (y-axis intercept, to be precise) is the y-value when x = 0.
so, starting with the slope, we go for example from (1, 6) to (6, 1) :
x changes by +5 (from 1 to 6).
y changes by -5 (from 6 to 1).
so, the slope is
-5/+5 = -1
so, we know, our equation looks like
y = -x + b
to get "b" we use one of the points, e.g. (1, 6) :
6 = -1 + b
b = 7
and our final equation is
y = -x + 7
Find the volume of the shape below. Round to the nearest tenth. Use
the pi button on the calculator.
11 mi
5 mi
Volume =
mi3
The volume of the shape to the nearest tenth is equal to 138.4π m³.
How to calculate the volume of a sphere?In Mathematics and Geometry, the volume of a sphere can be calculated by using the following mathematical equation (formula):
Volume of a sphere = 4/3 × πr³
Where:
r represents the radius.
By substituting the given parameters into the formula for the volume of a sphere, we have the following;
Volume of a sphere = 4/3 × π × 4.7³
Volume of a sphere = 138.4π m³
Read more on volume of a sphere here: brainly.com/question/20394302
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