Figure ABCDE was reflected across the line y = x to
create figure A'B'C'D'E'. What are the coordinates of
the pre-image of E?

Answer:

The given equation is y=-x+3.

The equation for the table is y=-x-3.

The slopes are the same (both are -1) but the y-intercepts are different (the given equation has y-intercept 3 while the table has y-intercept -3). The two lines are parallel.

Also, if you plug a point from the table into the equation, the point renders the equation false.

Step-by-step explanation:

You can use your equation and plug in your points from the table.

So let's see if (-4,1) is a point on the graph of the line of y=-x+3.

1=-(-4)+3

1=4+3

1=7 is not true so the point isn't on the graph of the line y=-x+3.

Let's see if we can find the appropriate equation for the points in the table.

I'm going to first see if there is a constant slope.

In the first two points, the y's are going down by 2 while the second are going up by two.

So the slope of line going through the first two points is -2/2=-1.

So looking at the middle points...the y's are going down by 3 while the x's are going up by 3. So the slope is still retaining -1 since -3/3=-1.

Finally, lets see if the slope still remains the same for the last two points. The y's are going down by 2 while x's are going up by 2. So the set of points do represent a line since the points follow a constant slope per pair of points.

Slope-intercept form of a line is y=mx+b where m is the slope and b is the y-intercept.

We know m is -1 so our line is of the form

y=-x+b.

To find b I will use a point from the table such as (-4,1).

1=-(-4)+b

1=4+b

Subtract 4 on both sides:

1-4=b

-3=b

So the equation for the line in the table is

y=-x-3.

So the two are both lines with the same slope but different y-intercept. The lines are therefore parallel.

Answer:

The given equation is y=-x+3.

The equation for the table is y=-x-3.

The slopes are the same (both are -1) but the y-intercepts are different (the given equation has y-intercept 3 while the table has y-intercept -3). The two lines are parallel.

Also, if you plug a point from the table into the equation, the point renders the equation false.

Step-by-step explanation:

You can use your equation and plug in your points from the table.

So let's see if (-4,1) is a point on the graph of the line of y=-x+3.

1=-(-4)+3

1=4+3

1=7 is not true so the point isn't on the graph of the line y=-x+3.

Let's see if we can find the appropriate equation for the points in the table.

I'm going to first see if there is a constant slope.

In the first two points, the y's are going down by 2 while the second are going up by two.

So the slope of line going through the first two points is -2/2=-1.

So looking at the middle points...the y's are going down by 3 while the x's are going up by 3. So the slope is still retaining -1 since -3/3=-1.

Finally, lets see if the slope still remains the same for the last two points. The y's are going down by 2 while x's are going up by 2. So the set of points do represent a line since the points follow a constant slope per pair of points.

Slope-intercept form of a line is y=mx+b where m is the slope and b is the y-intercept.

We know m is -1 so our line is of the form

y=-x+b.

To find b I will use a point from the table such as (-4,1).

1=-(-4)+b

1=4+b

Subtract 4 on both sides:

1-4=b

-3=b

So the equation for the line in the table is

y=-x-3.

So the two are both lines with the same slope but different y-intercept. The lines are therefore parallel.

Answer:

Step-by-step explanation:

We can model a line with slope-intercept form:

[tex]y = mx + b[/tex]

where [tex]m[/tex] is the slope and [tex]b[/tex] is the Y-intercept.

We know that the new line is parallel to the given line, so the two lines have the same slope, or [tex]m = \frac{3}{2}[/tex]:

[tex]y = \frac{3}{2}x + b[/tex]

To determine [tex]b[/tex], we just need to plug in the given point that the line passes through, [tex](-2, 3)[/tex]:

[tex]y = \frac{3}{2}x + b[/tex]

[tex](3) = \frac{3}{2}(-2) + b[/tex]

[tex]3 = -3 + b[/tex]

[tex]b = 6[/tex]

This gives us the following equation:

[tex]y = \frac{3}{2}x + 6[/tex]

The equation of the line is y = (3/2)x + 6.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The equation of the line passes through the point (-2,3).

y = m(1)x + c

The equation of the line is parallel to the line whose equation is y=3/2x-4.

​This means,

y = (3/2)x - 4

This is in the form of y = m(2)x + c

m(2) = (3/2)

So,

m(1) = m(2)

Now,

(-2, 3) = (x, y)

y = m(1)x + c

3 = (3/2) x (-2) + c

3 = -3 + c

c = 3 + 3

c = 6

Now,

y = m(1)x + c

y = (3/2)x + 6

Thus,

The equation of the line is y = (3/2)x + 6.

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Answer:

3875 feet above sea level

Answer:

[tex]3875[/tex]  [tex]feet[/tex]

Step-by-step explanation:

We first start at 7,000 feet above sea level, we then descend 4,500 feet closer to the sea level, therefore:

[tex]7,000 - 4,500[/tex]

[tex]==> 2,500[/tex]

Then we go up 1,375 feet farther from the sea level, so:

[tex]2,500 + 1,375[/tex]

[tex]==> 3,875[/tex]

Answer: 672 cars will have defective engine mounds

Step-by-step explanation: 25% of 2,688 is 672

Answer:

53

Equation:

y = -2(6) + 65

y = -12 + 65

y = 65 - 12

y = 53

Answer:

53

Stp-by-step explanation:

Answer:

GB is 15 units

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The Centroid is a point of triangle where all 3 medians intersect

In this problem point G is the centroid of the triangle FDE

FA, EB and DC are medians of the triangle FDE.

Remember that centroid divides the median in 2:1

FA is a is median so FG:GA=2:1.

Find the value of x

[tex]\frac{FG}{GA}=\frac{2}{1}\\\\\frac{5x}{x+9}=\frac{2}{1}\\\\5x=2x+18\\\\5x-2x=18\\\\3x=18\\\\x=6[/tex]

Find the value of GB

GB=2x+3

substitute the value of x

[tex]GB=2(6)+3=15\ units[/tex]

[tex]\bf \stackrel{5}{~~\begin{matrix} 20 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} \times \cfrac{3}{~~\begin{matrix} 4\\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies 5\times 3\implies 15[/tex]

The simplest form of the expression 20 x 3/4 is 15, which is achieved by first multiplying 20 by 3 to get 60, and then dividing 60 by 4.

The student has asked to find the simplest form of the mathematical expression 20 x 3/4.

To simplify this expression, you multiply 20 by 3 and then divide the result by 4.

First, calculate 20 times 3, which equals 60.

20×3 = 60

Next, divide 60 by 4, which gives you 15.

[tex]\frac{60}{4} = 15[/tex]

So, the simplest form of the expression 20 x 3/4 is 15.

Answer:

The mean will be increased by 5

Step-by-step explanation:

Suppose a set of data [tex](2, 4, 6, 8, 10, 12)[/tex]

Mean is defined as sum of all the values given set of data divided by total number of values.

Mean1 = [tex]\frac{2+4+6+8+10+12}{6} = \frac{42}{6} = 7[/tex]

Now if we add 5 toeach value, the new set becomes [tex](7, 9, 11, 13, 15, 17)[/tex]

for which,

Mean2 = [tex]\frac{7+9+11+13+15+17}{6} = \frac{72}{6} = 12[/tex]

Mean2 - Mean1 = 5

Answer:

Step-by-step explanation:

move x to the right making the equation 5y=-9x-1 then divide both sides by 5 to get y= -9/5x-1/5. the slope of a perpendicular line is the opposite reciprocal of the slope from the og eq. so the slope of the new line is 5/9x and the y-intercept stays the same so the equation should be y=5/9x-1/5

Answer:

75 and 552 =627

Step-by-step explanation:

First=x

Second 7x+27

x+ 7x+27= 627

8x+27=627

8x=600

x=75

75*7+27 =525

525+27 = 552

Answer:

22

Step-by-step explanation:

Answer:

Part a) The slope is [tex]m=-\frac{1}{3}[/tex]

Part b) The equation in point slope form is [tex]y-4=-\frac{1}{3}(x-3)[/tex]

Part c) The equation in slope-intercept form is [tex]y=-\frac{1}{3}x+5[/tex]

Step-by-step explanation:

we have the points (3,4) and (-3,6)

Part a) What is the slope of the line?

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute the given points

[tex]m=\frac{6-4}{-3-3}[/tex]

[tex]m=\frac{2}{-6}[/tex]

[tex]m=-\frac{1}{3}[/tex]

Part b) Write the equation of the line in point-slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=-\frac{1}{3}[/tex]

[tex]point\ (3,4)[/tex]

substitute

[tex]y-4=-\frac{1}{3}(x-3)[/tex]  ---> equation in point slope form

Part c) Write the equation of the line in slope-intercept form

[tex]y=mx+b[/tex]

we have

[tex]y-4=-\frac{1}{3}(x-3)[/tex]

Isolate the variable y

distribute right side

[tex]y-4=-\frac{1}{3}x+1[/tex]

Adds 4 both sides

[tex]y=-\frac{1}{3}x+1+4[/tex]

[tex]y=-\frac{1}{3}x+5[/tex] ---> equation in slope intercept form

Answer:

all work is pictured and shown

Final answer:

The equation of a line with a slope of 1 that passes through the point (2,5) in slope-intercept form is y = x + 3.

Explanation:

To write the equation of a line in slope-intercept form (y = mx + b), you need to know the slope (m) and the y-intercept (b). Since the slope is given as 1 and the line passes through the point (2,5), we can use the point-slope formula to find the y-intercept.

The point-slope formula is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through. Plugging in the values we have:

y - 5 = 1(x - 2) → y - 5 = x - 2 → y = x + 3

So, the equation of the line in slope-intercept form is y = x + 3.

Answer: [tex]2,412.74\ cm^2[/tex]

Step-by-step explanation:

You need to use the following formula for calculate the Total surface area of a solid hemisphere:

[tex]SA_{total}=3\pi r^2[/tex]

Where "r" is the radius.

 Since you cut a styrofoam ball in half, the total surface areas are equal.

The exercise gives you the diameter. Observe in the figure that this is:

[tex]d=32\ cm[/tex]

Since the radius is half the diameter, you know that:

[tex]r=\frac{d}{2}\\\\r=\frac{32\ cm}{2}\\\\r=16\ cm[/tex]

Finally, you can substitute the radius into the formula:

 [tex]SA_{total}=3\pi (16\ cm)^2=2,412.74\ cm^2[/tex] (Of each half of the styrofoam ball)

You can use the fact that along with the surface area of hemisphere, you need to add the surface area of the circle that's on the top of each hemisphere.(hemisphere means half of sphere)

The surface area of each half of the styrofoam ball is [tex]3\pi r^2 \: \rm unit^2[/tex]

Surface area of sphere = [tex]4 \pi r^2[/tex] sq. units where r is radius of sphere.

Since hemisphere is half of the sphere, thus,

Surface area of hemisphere = [tex]2\pi r^2[/tex] sq. units.

Since the foam ball is not hollow, if we slice it in half, each of the half piece is having surface = outer half sphere's surface + that circle which is formed due to slicing the ball

Thus, surface area of each half of the Styrofoam ball is calculated as

Surface area = Surface area of hemisphere + area of circle

Let the ball had radius r, then we have the needed surface area as:

[tex]S = 2\pi r^2 + \pi r^2 = 3\pi r^2 \: \rm unit^2[/tex]

S is surface area of each half of the styrofoam ball.

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The slope of the given line is:

                        [tex]\dfrac{4}{5}[/tex]

We know that if a line is represented in the slope intercept form i.e.

             [tex]y=mx+c[/tex]

then m represents the slope of the line and c represents the y-intercept of the line.

Here we are given a equation of a line as follows:

                [tex]y=\dfrac{4}{5}x-3[/tex]

i.e. on comparing the equation with  the slope-intercept form of the line we have the slope  of the line is:

             [tex]m=\dfrac{4}{5}[/tex]

Final answer:

The slope of the equation y=4/5x-3 is 4/5, which represents the consistent rise over run for the line.

Explanation:

The slope of the line is represented by the equation [tex]y = \frac{4}{5}x - 3 is \frac{4}{5}.[/tex] In the standard form y = mx + b, where m is the slope and b is the y-intercept, and the coefficient of x represents the slope of the line.

Therefore, by comparing the given equation to the standard form, the number 4/5 in front of x is the slope of the line. The slope indicates a rise of 4 units on the vertical axis for every increase of 5 units on the horizontal axis. The slope of a line remains constant along the entire length of the line.

Answer:

7 is rmthe correct answer as it's value is 3 the answer is on no 7.

Answer:

A

Step-by-step explanation:

Given

4 - t = 3(t - 1) - 5 ← distribute and simplify right side

4 - t = 3t - 3 - 5

4 - t = 3t - 8 ( subtract 3t from both sides )

4 - 4t = - 8 ( subtract 4 from both sides )

- 4t = - 12 ( divide both sides by - 4 )

t = 3

Answer: -39g + 9

Step-by-step explanation:

PEMDAS states that multiplication must be performed before addition & subtraction

  (6g × 7) - (3²g × 9) + 3³

=     42g   -     81g     + 9

=           -39g             + 9

Answer:

1.  0.8 cm

2.  1.6 cm

Step-by-step explanation:

1.

The scale for 2nd map is 1 cm to 50 km, that means "1 cm on map" is "50 km in real life".

We already know distance from Cleveland to Cincinnati is 40 km, which is less than 50, so we know the distance on map would be less than 1 cm.

So we set up ratio and figure out (let x be distance on map from Cleveland to Cincinnati):

[tex]\frac{1}{50}=\frac{x}{40}\\50x=40\\x=\frac{40}{50}\\x=0.8[/tex]

Hene, 0.8 centimeters would be the distance in 2nd map

2.

A scale of 1:50 means 1 cm equal 50 cm

So, 0.8m would be

0.8 * 100 = 80 cm

Hence, 80 cm would be represented by 80/50 on the map, that is:

[tex]\frac{80}{50}=1.6[/tex]

That is 1.6 centimeters

Answer:

a = -5

Step-by-step explanation:

(5 - 3)/(5 - a)

2/(5 - a)

perpendicular of 2/(5 - a) = -(5 - a)/2

(a - 0)/(1 - 0) = -(5 - a)/2

a/1 = -(5 - a)/2

2a = -5 + a

a = -5

Answer:

Step-by-step explanation:

Steps:

1. Let x = #

2. "Five less than six times a number" can be written as: 6x - 5

3. "is at least" is the same as "greater than or equal to" and can be written as: >=

4. "nine subtracted from two times that number" can be written as: 2x - 9

5. the equation is: 6x - 5 >= 2x - 9

6. solve for x by grouping the x variable terms on one side and the constants on the other side:

6x - 5 >= 2x - 9

-2x +5 -2X +5

4x >= -4

7. divide each side by 4, and you get: x = -1

The solution according to the given statement is "x = -1".

According to the question,

The equation will be:

By adding "5" both sides, we get

→ [tex]6x - 5+5 \geq 2x - 9+5[/tex]

→             [tex]6x \geq 2x-4[/tex]

By subtracting "2x" form both sides, we get

→     [tex]6x-2x \geq 2x-4-2x[/tex]

→             [tex]4x \geq -4[/tex]

→               [tex]x \geq -\frac{4}{4}[/tex]

→               [tex]x = -1[/tex]

Thus the above answer is appropriate.

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Answer:

d= -9                                       d=9  

Step-by-step explanation:

-2d = 18                                 -2d=-18

divide by -2

d= -9                                       d=9  

Answer:

d=(18-1)/-2l

Step-by-step explanation:

i-2dl=18

-l        

-2dl=18-l

/-2l        

d=(18-1)/-2l

The cost of a taxi ride can be calculated using the equation c = 1.75 + (m - 1/8) * 8 * 0.30, where c represents the total cost and m represents the total miles driven. Solving this equation for m when the total cost is $7.75 would yield the number of miles driven.

The subject of this question is the creation of an equation to calculate the cost of a taxi ride. According to the question, a taxi charges $1.75 for the first 1/8 mile and $0.30 for each additional 1/8 mile. First, we need to convert miles to 1/8 miles, since the pricing is based on this fraction. We know that each full mile is equal to 8 fractions of 1/8 mile. Therefore, to convert miles to 1/8 miles, we multiply the number of miles by 8.

Given this pricing structure, the costs associated with additional miles driven beyond the first 1/8 mile (which are already accounted for by the initial $1.75), can be represented by (m-1/8)*8*0.30. Here, (m-1/8) represents the additional miles traveled beyond the first 1/8 mile, and multiplying this by 8 converts these miles into 1/8 miles.

The total cost, c, can thus be represented by the equation c = 1.75 + (m - 1/8) * 8 * 0.30. If a ride cost $7.75, we can substitute this cost into the equation and solve for m to find the number of miles driven. This would give us the equation: 7.75 = 1.75 + (m - 1/8) * 8 * 0.30.

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Answer:

[tex]\large\boxed{14:2=20:\dfrac{20}{7}}[/tex]

Step-by-step explanation:

[tex]14:2=20:x\\\\\dfrac{14\!\!\!\!\!\diagup^7}{2\!\!\!\!\diagup_1}=\dfrac{20}{x}\\\\\dfrac{7}{1}=\dfrac{20}{x}\qquad\text{cross multiply}\\\\7x=(20)(1)\\\\7x=20\qquad\text{divide both sides by 7}\\\\x=\dfrac{20}{7}[/tex]

Answer:

A, C, and D are correct

Step-by-step explanation:

A. (0.32)(-2)

(0.32)(-2) = -0.64

Correct.

B. 1.6(-4)

1.6(-4) = -6.4

Wrong.

Divide by 10.

[tex]\dfrac{-6.4}{10} = \mathbf{-0.64}[/tex]

C. 0.64(-1)

0.64(-1) = -0.64

Correct.

D. (1.28)(-0.5)

(1.28)(-0.5) = 0.64

Correct.

E. (-4)(-0.16)

(-4)(-0.16) = 0.64

Wrong.

Multiply by -1.

(0.64)(-1)= -0.64

Answer:

A. [tex]R=1,500+6x,\ x\le 800[/tex]

B. 584

Step-by-step explanation:

A band is performing at an auditorium for a fee of $1500.

In addition to this fee, the band receives 30% of each $20 ticket sold. Let x be the number of tickets sold, then these x tickets cost $20x. Calculate 30% of 20x:

[tex]20x\cdot 0.3=6x[/tex]

A. The total cost is

[tex]R=1,500+6x[/tex]

The maximum capacity of the auditorium is 800 people, so x≤800.

B. The band needs $5,000 for new equipment so

[tex]1,500x+6x\ge 5,000\\ \\6x\ge 3,500\\ \\x\ge \dfrac{3500}{6}\\ \\x\ge 583.333...[/tex]

So, it is enough 584 tickets to be sold.

The band's revenue equation is R = 1500 + 0.30 * 20 * x. To earn $5000 for new equipment, the band needs to sell at least 584 tickets, considering their fixed fee and the additional revenue from ticket sales.

Calculating Revenue for a Band's Performance

The band's total revenue (R) when x tickets are sold can be calculated using the equation: R = 1500 + 0.30 *20* x. This equation includes their fixed fee of $1500 plus the variable amount obtained from ticket sales, which is 30% of the ticket price ($20). For every ticket sold, the band adds $6 (30% of $20) to their revenue.

For the band to afford new equipment costing $5000, we need to determine how many tickets need to be sold. The equation becomes:

R = 1500 + 0.30 * 20 * x

$5000 = 1500 + 6 * x

$5000 - 1500 = 6 * x

$3500 = 6x

x = $3500 / 6

x = 583.33

Since the band cannot sell a fraction of a ticket, they would need to sell at least 584 tickets to meet their goal of $5000.

Final answer:

A cube with a 5-inch edge has square-shaped faces, an area per face of 25 square inches, a total surface area of 150 square inches, and a volume of 125 cubic inches.

Explanation:

The question relates to the properties of a cube with an edge length of 5 inches. Here are the answers to each part:

b. Each face of the cube is a square shape.

c. The area of each face is 5 inches × 5 inches = 25 square inches.

d. The surface area of the cube is 6 × (area of one face) = 6 × 25 square inches = 150 square inches.

e. The volume of the cube is the cube of the side length, so 5 inches × 5 inches × 5 inches = 125 cubic inches.