Use the table below to find the indicated values:

The required coordinates of the vertices of △ABC after it has been rotated 90 degrees, reflected across the line y=0, and then translated according to the rule (x+3,y-3) are A''' = [8, 1], B''' = [-3, -6], and C''' = [-5, -4].

To determine the coordinates of the vertices of △ABC after it has been rotated 90 degrees, reflected across the line y=0, and then translated according to the rule (x+3,y-3), we need to apply these transformations to the coordinates of the original vertices in the order given.

First, we rotate the triangle 90 degrees counterclockwise around the origin. This transformation can be represented by the matrix:[cos(90) -sin(90)][sin(90) cos(90)]

Applying this matrix to the coordinates of the vertices of △ABC, we get:A' = [-5, 4]B' = [6, -3]C' = [8, -1]

Next, we reflect the triangle across the line y=0.

This transformation can be represented by the matrix:[-1 0][0 1]

Applying this matrix to the coordinates of the vertices of △ABC', we get:A'' = [5, 4]B'' = [-6, -3]C'' = [-8, -1]

Finally, we translate the triangle according to the rule (x+3,y-3).

This transformation can be represented by the matrix:[1 0][0 1]

Applying this matrix to the coordinates of the vertices of △ABC'', we get:A''' = [8, 1]B''' = [-3, -6]C''' = [-5, -4]

Therefore, the coordinates of the vertices of △ABC after given transformations are A''' = [8, 1], B''' = [-3, -6], and C''' = [-5, -4].

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The length of each side of the sign will be 14.81-inch approx.

It is assumed that an Octagon sign is created by cutting out triangles from a square's corners, and that the stop sign's overall length is 36 inches. Since we are aware that squares have right angles on all four sides, we can use Pythagoras' theorem to solve for the side of the sign in the image below.

           [tex]s^{2} =x^{2} +x^{2} \\s^{2}=2x^{2} ...................Eq.1[/tex]

Also, it is a square. So, the measurement of length from side to side

            [tex]2x+s=36....................Eq.2[/tex]

solving Eq.1 we get,

[tex]s=\sqrt{2} x[/tex]...putting this value in Eq.2,

            [tex]s=36-2x\\\\\sqrt{2} x=36-2x\\\\x=\frac{36}{2+\sqrt{2} }[/tex]

Putting this value of x in Eq.1,

          s = 14.8

Hence, The length of each side of the sign will be 14.81-inch approx.

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The slope of Line P Q is (v - z) divided by (w - x). The slope of Line P prime Q prime is

(v + b) - (z +b) divided by (w + a) - (x + a). Both lines have a slope that is (v - z) divided by (w - x). Therefore, the lines are parallel.

Slope of line :

Line slope is a measure of the slope and direction of a line. Finding the slope of a line in the coordinate plane helps predict whether the line is parallel or perpendicular without actually using a compass. The slope of a line is defined as the change in y-coordinate with respect to the change in x-coordinate of the line.

The formula for the slope is

m = (y₂ - y₁)/ (x₂ - x₁)

Where (x₁, y₁) and (x₂, y₂) are the points

We have given a line PQ passing through points (x,z ) and (w,v) then slope of line is

m = ( v- z)/(w-x) --(1)

that is line lie in XZ- plane .

The slope of line p prime and q prime

m' = (( v- b) - (z-b))/(w-a)- (x-a)

= (v -b -z + b) /(w-a -x + a)

= (v-z)/(w-x) --(2)

from (1) and (2) we get , m = m'

So, both lines are parallel lines .

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Complete question:

The slope of Line P Q is (v - z) divided by ________. The slope of Line P prime Q prime is _________ divided by (w + a) - (x + a). Both lines have a slope that is _______ divided by _______. Therefore, the lines are _______.

Answer: in the picture

Step-by-step explanation:

Answer:

a.) c(t)=44t+48

b.) the total initial cost of setting up a website and maintaining it for 6 months is $312

Step-by-step explanation:

h

The two equations that can be used to determine the number of hits that he had each year are given as follows:

His hits by team are divided as follows:

Then the total number of hits is obtained by the sum of the number of hits that he obtained with each of the three teams, as follows:

t = 2098 + 702 + 210 = 3010.

Then the amount of hits that he obtained each year is obtained applying the proportion, dividing t by 18, as follows:

a = t/18.

Hence the result is given as follows:

a = t/18 = 3010/18 = 167 hits per year.

The options are given by the image shown at the end of the answer.

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The possible values of k are -0.56, -3.56, -2, and -1.

We have the equation of the parabola, y=0.5(x-3)(x+k)

When we Substitute x=0, we get that y=0.5*(-3) * k  for instance y = -1.5k

So, the y-intercept is (0,-1.5k).

We will now substitute y=0, 0=0.5(x-3)(x+k) for instance  0=0.5(x-3)(x+k) x=3 and x=-k

So, the x-intercepts are (3,0) and (-k,0).

We can see that 'k' cannot be 0 or -3 since height = 0 if k=0, which is not conceivable. If k = -3, the base is also 0, which is not feasible.

We know that area of a triangle is 1/2*base*height

when we substitute we will get

1.5=1/2*(3+k) *(1.5k)

3=4.5k+1.5k^2

k=-0.56 and k=-3.56

or

1.5=1/2*(-3-k) *(1.5k)

3=-4.5k-1.5k^2

k=-2 and k=-1

hence the possible values of k will be -0.56, -3.56, -2, and -1.

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Your question is incomplete, most probably the full question was:

The area of the triangle formed by x− and y− intercepts of the parabola y=0.5(x−3)(x+k) is equal to 1.5 square units. Find all possible values of k.

Answer:x2 - 2x = 4x + 1" and "9x2 + 6x - 3 = 0

Step-by-step explanation: that will be your quadratic equation

The range of the data-set in this problem has a value given as follows:

7.7.

The range of a data-set is calculated as the difference between the largest value of the data-set and the smallest value of the data-set.

The data-set in this problem is defined as follows:

{6.2, 9.1. 2.9, 1.6, 9.3, 5.5, 8.3}

Hence to obtain it's range we have to obtain the smallest and the highest values from these values between the brackets.

The smallest value of the data-set and the highest value of the data-set are defined as follows:

Hence the range of the data-set is given by the difference of 9.3 and 1.6, as follows:

Range = 9.3 - 1.6 = 7.7.

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The  balloon's vertical distance above the ground is 300.19 feet.

What is angle of depression?

If the line of sight is directed downward from the horizontal line, then an angle is created with the horizontal line. The angle produced between the horizontal line and the observer's line of sight is known as the angle of depression if the object being observed is below the observer's level.

Given that a balloon make 22° angle with a fixed point. The horizontal distance of the balloon along the ground is 743 feet.

Here need to find the vertical distance.

To find the vertical distance, use tangent of 22°. The tangent of angle is the ratio of vertical distance to horizontal distance.

Therefore,

tan 22° = vertical distance/ horizontal distance

tan 22° = vertical distance/ 743

Multiply both sides by 743:

vertical distance = 743 × tan 22°

vertical distance = 300.191

vertical distance = 300.19 ( rounding to the nearest hundredth)

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Weight represents the top 10% of the zucchinis is 5.9

The formula for calculating a z-score is z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

We're looking for:

Weight is 10% of zucchinis at the top.

Top 10% = 90% of the population

90th percentile Z score is 1.282.

Hence

1.282 = x - 5 / 0.7

1.282 × 0.7 = x - 5

0.8974 = x - 5

x = 5 + 0.8974

x = 5.8974

5.9 ounces, roughly.

The top 10% of the zucchinis have a weight of 5.9 ounces.

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The teenager whom attended a football game will be 575 people.

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The cost per month is 39.96, the setup fee is 24.94, and the equations are x  = 39.96  and 6x + y = 264.70.

A formula known as an equation uses the equals sign to denote the equality of two expressions.

Given data:

A company offers premium cable for 39.96 per month plus a one-time set fee,

The total cost for setup and 6 months I'd 264.70

Write the equation as shown below,

The number of months × price per month + one-time setup fee = total cost

Calculate the equations,

x = number of months, y = setup fees

1 × x + y = 39.96 ⇒ x  = 39.96  (y = 0 for one month)

6 × x + y = 264.70 ⇒ 6x + y = 264.70

Solve the above equation by the elimination method

x = 39.96  and y = 24.94

Therefore, the cost per month is 39.96, the setup fee is 24.94, and the equations are x  = 39.96  and 6x + y = 264.70.

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The number of times to get a 3 will be 24 times.

It should be noted that the expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables

In this case, Jimm tossed a die several times and he got the number "3" on 8 of the tosses.

Therefore, when there are 64 tosses, the estimate will be:

= 3/8 × 64

= 3 × 8

= 24

The number of times is 24.

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Jimm tossed a die several times. He got the number "3" on 8 of the tosses. What is the best estimate of the total number of times he tossed the die 64 times?

Answer:

7) d (21)

6) a (102)

Step-by-step explanation:

For the first question, we should start with what we know first:

When angles are complementary then, their angles add up to 90.

So here we have 69 + something = 90.

We find out that the missing angle (angle B) is 21.

For this second question, we know that a straight line has an angle of 180. Here we have a straight line, but only part of the angle in which we only have 78.

Since we know 78 + x = 180

Then we can figure out that x = 102.

The point-slope form of the equation of Street D is; y = 0.8·(x - 5)

The point-slope of the equation of straight line can be expressed mathematically as (y - y₁) = m·(x - x₁)

The coordinates of the point

The x-intercept of the street D = 5

The y-intercept of the street D = -4

The x-intercept is the point the graph of the equation of the street intersects the x-axis.

At the x-intercept, the y-coordinate of the point of the graph is 0, therefore, the coordinate of the x-intercept is (5, 0)

The y-intercept is the point at which the graph of the function intersects the y-axis, therefore, the x-coordinate of the graph at the y-intercept is 0

The y-intercept of the street D is therefore; (0, -4)

The slope, m, of the equation of the street is therefore;

m = (-4 - 0)/(0 - 5) = 4/5 = 0.8

The point-slope form of the equation, using the x-intercept, (5, 0) is therefore;

y - 0 = 0.8·(x - 5)

y = 0.8·(x - 5)

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After solving the given fraction, the resultant fraction is (A) 1 15/21.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole.

A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

A fraction appears in the numerator or denominator of a complex fraction.

The numerator of a proper fraction is less than the denominator.

So, we have:

2 4/7 * 2/3

Now, solve the fraction as follows:

2 4/7 * 2/3

14+4/7 * 2/3

18/7 * 2/3

36/21

1 15/21

Therefore, after solving the given fraction, the resultant fraction is (A) 1 15/21.

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Answer:

Step-by-step explanation:

(x+4)(x+5) = 0

x = -4

x = -5

Population after 95 years is more than 28 billion.

What is a growth rate?

The growth rate of a value (such as GDP, turnover, earnings, etc.) gauges how much it has changed over time (month, quarter, year). The percentage is a fairly universal way to communicate it.

Here, we have

The present size of the population is 7 billion.

Assuming that the population starts growing from the age of "0"

The number of people after 30 years is equal to two times the present population i.e 14 billion

The number of people after 60 years is equal to two times the population after 40 years i.e 28 billion

Hence, the population after 95 years is more than 28 billion.

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The area of the rectangular park is 143360 square yards.

It is the conversion of one unit to another unit with its standard conversion.

Example:

1 hour = 60 minutes

1 minute = 60 second

1 km = 1000 m

We have,

Scale drawing of a rectangular park:

Wide = 5 inches

Length = 7 inches

Actual rectangular park:

Wide = 320 yards

Length = 448 yards

Now,

5 inches = 320 yards

7 inches = 7/5 x 320 yards

7 inches = 7 x 64 yards

7 inches = 448 yards

Now,

The area of the actual park.

= Length x Wide

=  448 x 320

= 143360 square yards.

Thus,

143360 square yards is the area of the actual park.

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The required linear model is y = 5800 + 324x.

What is a linear equation?

Equations whose variables have a power of one are called linear equations.

Given, a bakery sells 5800 muffins in 2010

the bakery sells 7420 muffins in 2015

So, the number of muffins sold after 2010 through 2015:

7,420 - 5,800 = 1,620

Then, the sales per year:

1,620 muffins sold since 2010 / 5 years = 324 muffins per year.

Then our linear model will be:

y = 5800 + 324x

Hence, the required linear model is y = 5800 + 324x.

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Answer:

Since there are no abcd options, I'll just give the answer here: 3/4 divided by 5/7 is 21/20

Step-by-step explanation:

First, we have to convert the division sign to a multiplication sign, so we do that by using the reciprocal of the second fraction:

3/4 divided by 5/7 will turn into 3/4 * 7/5

Here is how to solve that:

3           7

--     *    --

4           5

3*7 is 21, and 4*5 is 20, so the final fraction is 21/20, final answer.

Answer:

6

Step-by-step explanation:

The y intercept is when x=0

Answer:

1. 20 minutes (segment A)

2. 40 minutes (segment B)

3. 10 minutes (segment C)

4. 10 minutes (Segment D  minus Segment B)

5. Segments C & E (approaching x axis)

6. Segment A (greatest slope)

7. 115 minutes

Answer:

A 5 and -5

Step-by-step explanation:

You take the root of both sides to solve.

The gradient of the line in the given graph is 1/2.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

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

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

From the graph, let us consider two points from where the line is passing.

(-2, 3) and (2, 5).

Gradient is nothing but slope of the line.

m=5-3/2-(-2)

=2/4

=1/2

Hence, the gradient of line in the given graph is 1/2.

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By evaluating the exponential equation for the population:

P(x) = 200*(1.2)^x

We will get:

a) 240 badgers

b) 288 badgers

We know that the number of badgers increases by 20% each year, that increase after x years is given by the exponential equation:

P(x) = A*(1 + 20%/100%)^x

P(x) = A*(1.2)^x

Where A is the initial amount.

Here we know that the initial population of badgers is 200, then we have:

P(x) = 200*(1.2)^x

a) To find the population after one year, we need to evaluate the exponential equation in x = 1, we will get:

P(1) = 200*1.2^1 =240

b) The population after 2 years is:

P(2) = 200*1.2^2 = 288

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By reading the graph we can see that k(x) = 80 for x ∈ (5, 6]

Look at the graph and try to identify the line where y = 80, now move to the right until you hit the graph of k(x) (red graph).

Now, move downwards until you intercept the x-axis, that value in the x-axis is the input that gives k(x) = 80.

In this case, there is a set of values.

The open circle means taht the value does not belong to the set.

The closed circle means taht the value does belong to the set.

Then k(x) = 80 for all the values of x in the set:

(5, 6]

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Answer:

The right answer is C.

Step-by-step explanation:

The parent function is:

[tex]f(x)=x^3[/tex]

If something is subtracted from variable [tex]x[/tex] it means the graph shifted toward right and something is added to [tex]y[/tex] value then the graph is shifted up.

[tex]f(x)=(x-8)^3[/tex]

graph shifted toward right by [tex]8[/tex] units right

[tex]f(x)=(x-8)^3+3[/tex]

graph shifted toward right by [tex]3[/tex] units up

Thus the new function is:

[tex]g(x)=(x-8)^3+3[/tex]