Complete the empty table from the provided information.

Transform the graph of f(x) by dilating it by a factor of 3.

Write the equation of the resulting line in slope intercept form.

Answer:

The y intercept is 0

Step-by-step explanation:

Where the line crosses the y axis that is your y intercept

Check the picture below.

The area of the rectangle is  [tex]b^2[/tex] +9b square feet

The rectangle is the quadrilateral whose opposite sides are parallel and equal. The rectangle is a four sided shape that all the angles are 90 degrees

The area is defined as the total space occupied by the two dimensional shape like rectangle, triangle, circle etc..

The length of the rectangle = (5/3)b+15 feet

The width of the rectangle = (3/5)b feet

The area of the rectangle = The length of the rectangle × The width of the rectangle

Substitute the values in the equation

The area of the rectangle  = [(5/3)b+15] ×(3/5)b

Apply the distributive property in the equation

[(5/3)b+15] ×(3/5)b = [tex]b^2[/tex] +9b square feet

Hence, the area of the rectangle is  [tex]b^2[/tex] +9b square feet

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I think its 57 meters.

Answer:

52 centimeters

Step-by-step explanation:

A square has 4 sides

Side of square = 13 cm

Perimeter of square = sum of all sides of square

Perimeter of square = 4 x 13 = 52 cm

Answer:

volume=length×width×depth

Step-by-step explanation:

The percentage is calculated by dividing the required value by the total value and multiplying it by 100.

The monthly net income to keep housing a 30% of his budget is $7000.

The percentage is calculated by dividing the required value by the total value and multiplying it by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

Cost of monthly housing per month = $2100

$2100 = 30%

Monthly income = 100%

30% = 2100

Multiply 100/30 on both sides.

100/30 x 30% = 100/30 x 2100

100% = 7000

Thus,

The monthly net income to keep housing a 30% of his budget is $7000.

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Answer:

(3×6)÷5

Step-by-step explanation:

We are given the following expression:

(3/5)*6

The 6 can also be written as a fraction(6/1).

So we have a multiplication of fractions, is which we multiply the numerators and denominators.

So

(3*6)/5

The fraction sign means division

So the answer is:

(3×6)÷5

When Jennie drew a scale drawing of her family's game room. If the pool table is 4 feet wide in real life and using a scale of 1 inches: 2 feet, then the width of the pool table in her drawing is 2 inches

The width of the pool table in real life =  4 feet

The scale of width in drawing to real life = 1 inch : 2 feet

Therefore the equivalent ratio is

1 inch : 2 feet :: x inches : 4 feet

1 / 2 = x / 4

x = (1/2) × 4

= 2 inches

Hence, when Jennie drew a scale drawing of her family's game room. If the pool table is 4 feet wide in real life and using a scale of 1 inches: 2 feet, then the width of the pool table in her drawing is 2 inches

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The area of half circle is 14.13 sq.unit

The total area of the figure is 86.13 sq.unit

Given,

The figure is combined by a triangle, rectangle and a half circle.

The area of triangle = 18 sq.units

The area of rectangle = 54 sq.units

We have to find the area of half circle to get the total area of the figure;

Here,

Area of circle = π r²

Then,

Area of half circle =  π r² / 2

Here,

r = 6/2 = 3 units

Now,

Area = π r² / 2 = π × 3² / 2 = 28.27/2 = 14.13 sq.units

That is,

The area of half circle is 14.13 sq.unit

Then,

The total area of figure = Area of [triangle + rectangle + half circle]

The total area of figure = 18 + 54 + 14.13 = 86.13 sq.units

Therefore,

The total area of the figure is 86.13 sq.unit

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Considering the given triangle ABC that has vertices A(-4, 0), B(-4, 5) and C(1, 5). The option that has same slope with similar interval is B. D(-3, 0), E(-3, 1) F(-2, 1)

Slope refers to the gradient and is the ratio of the difference in the ordinate to the difference in the abscissa of in a given coordinate plane.

The given information from the question include

A(-4, 0), B(-4, 5) and C(1, 5)

The slope of the given triangle is calculated as follows

slope = ( 0 - 5 ) / ( -4 - 1 )

slope = -5 / -5

slope = 1

The domain of the line is -4 ≤ x ≤ 1

The range of the line is 0 ≤ y ≤ 5

options C and D values do not satisfy the domain and range conditions

Options B and A satisfies the the domain and range conditions however the slope of option B is what is equal to the slope of the sloping part of the given triangle and hence the correct option.

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Samuel's average speed during his morning training is 0.41 miles/minute.

Here we have to find the average speed of Samuel. We can solve this problem by following a few steps.

According to the problem, Samuel was preparing for the triathlon. He did 3 activities every morning; ran for 30 minutes, covered 4.5 miles; swam for 20 minutes, covered 2.3 miles biked for 45 minutes, and covered 9 miles.

We have to recall the formula of average speed as,

average speed = total covered distance/ total time

The total distance which has been covered is,  

The total covered distance is, ( 4.5 + 2.3 + 9 ) = 36.5 miles.

The total time which has been spent is,

The total spent time is, (30+ 20+ 40) = 90 minutes.

Now, we can easily calculate the average speed. Which is (36.5/90) = .41 miles/minute.

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The area of a triangle is 1/2bh. We know the area, a, the base, b, and we are attempting to find the height, h. So, we simplify the area formula with the value of b and solve for h, given a.

1/2(6)h = 30
3h = 30

Isolate h.

3h/3 = 30/3
h = 10

The total surface area of the cylinder is equal to 117.8 in^2

The total surface area of a cylinder can be calculated using the formula

[tex]TSA = 2\pi rh + 2\pi r^2[/tex]

Let's substitute the values and proceed to solve.

[tex]TSA = 2\pi rh + 2\pi r^2\\TSA = 2\pi * 2.5 * 5 + 2\pi * 2.5^2\\TSA = 117.8in^2[/tex]

The total surface area of the cylinder is 117.8 squared inch.

The area of each circle is

[tex]A = \pi r^2 \\A = 19.6in^2[/tex]

And there are two identical circle in the diagram and this will have a total area of

[tex]A = 2 * 19.6\\A = 39.2in^2[/tex]

The area of the sum of the two circles is 39.2in^2 and the total surface area of the cylinder is 117.8in^2

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The probability that the events (a) they both picked Limca = 0.04, (b) Ademola only picked Pepsi = 0.32, (c) They both picked the same brand = 0.33 (d) They picked different brand=0.67.

Probability is the fraction of the required outcome event divided by the number of possible outcomes of events.

Total possible outcome of the event of picking drinks contained in the crate = 19

Hence, we can compute the following as follows;

(a) The probability they both picked Limca = (4/19)×(3/18)

Limca = 12/342

Limca = 0.04

(b) The probability Ademola only picked pepsi = 6/19

pepsi = 0.32

(c) The probability they both picked the same brand = (9/19)×(8/18)+(6/19)×(5/18)+(4/19)×(3/18)

=(72+29+12)/342

= 114/342

= 0.33

(d) The probability they picked different brand = (9/19)×(6/18)+(9/19)×(4/18)+(6/19)×(9/18)+(6/19)×(4/18)+(4/19)×(9/18)+(4/19)×(6/18)

The probability they picked different brand = (54+36+54+24+36+24)/342

The probability they picked different brand = 228/332

The probability they picked different brand = 0.67

Therefore, the probability for events (a) is 0.04, (b) is 0.32, (c) is 0.33 and (d) is 0.67.

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Answer:

There are two pairs:

1 and 3

2 and 4

Step-by-step explanation:

Verticle angles are angles opposite to each other when two lines intersect.

The value of x is 43.

As per the property of exterior angles, the exterior angle is equal to sum of opposite interior angles. Also, the rightmost interior angle of triangle will be 35°. This will be according to the property that opposite angles are equal. Now, forming the equation for sum of exterior angles.

109 = x + 31 + 35

Performing addition on Right Hand Side of the equation

109 = x + 66

Rearranging the equation

x = 109 - 66

Performing subtraction on Right Hand Side of the equation

x = 43

Therefore, as per the angles of triangle, the value of x is 43.

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The null and alternative hypothesis is H₀ : p = 0.30 and Hₐ : p ≠ 0.30 respectively.

A hypothesis is a theory put up to explain a phenomenon. A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis.

Two alternatives being the same is the null hypothesis. The underlying assumption is that the observed difference is just the result of chance.

One of the ideas put out in the hypothesis test is the alternate hypothesis.

Mild depression affects about 30% of adults in the 50 to 60 age range.

500 people between the ages of 50 and 60 are chosen at random by the researcher, and they are instructed to take a vitamin D pill for six months.

The psychologist classifies 158 people as depressed.

The null hypothesis will be:

H₀ : p = 0.30 and;

The alternative hypothesis is,

Hₐ : p ≠ 0.30

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Answer:

a= one mile in 4 minutes

b =48 minutes

Step-by-step explanation:

A

t = 20 minutes

d = 5 miles

Average speed = distance ÷ time

5 miles÷ 20 minutes

= 1 mile in 4 minutes

= 0.25 miles in 1 minute

B

0.25 miles in 1 minute

12 miles in g minutes

12 miles in 48 minutes

we get this answer because 0.25 in one minute is 1 ÷4

12÷ 12 × 4

12÷ 48

= 12 miles In 48 minutes

Answer:

about 2 hours

Step-by-step explanation:

it is the reported average

17.54% is the probability that 5 messages are received in 1 hour.

The chance that X reflects the number of successes of a random variable in a Poisson distribution is provided by the following formula:

P(X = x) = ([tex]e^{-u}[/tex] × [tex]u^{x}[/tex]) ÷ x!

In where x is the number of successes, e is the Euler number, and u is the mean in the specified time frame.

In this case, the average message rate is 5 messages per hour.

The probability of receiving 5 texts in one hour.

Determine the value of P for x = 5 and u = 6.

P(X = x) = ([tex]e^{-5}[/tex] × [tex](5)^{5}[/tex]) ÷ 5!

P(X = x) = 21.0560 ÷ 5!

P(X = x) = 0.1754

There is a 17.54% chance that 5 messages will be received in 1 hour.

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Answer: B - 4.75 + 0.75 is greater than 25

Step-by-step explanation:

so, first you have 4.75 and she want to play video games that cost 0.75 each but we don't know how many video games she played.

Answer:

[tex]\begin{cases}y \geq -\dfrac{1}{2}x+2\\\\y > 2x-3\end{cases}[/tex]

Step-by-step explanation:

Find the equations of the two lines by substituting two points on each line into the slope formula to find the slope, then substituting the found slope and one of the points into the point-slope formula.

Equation of Line 1

Points on the line:  (0, 2) and (2, 1).

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-2}{2-0}=-\dfrac{1}{2}[/tex]

Substitute the found slope and one of the points into the point-slope formula:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-2=-\dfrac{1}{2}(x-0)[/tex]

[tex]\implies y=-\dfrac{1}{2}x+2[/tex]

Equation of Line 2

Points on the line:  (0, -3) and (2, 1).

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-(-3)}{2-0}=-\dfrac{4}{2}=2[/tex]

Substitute the found slope and one of the points into the point-slope formula:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-(-3)=2(x-0)[/tex]

[tex]\implies y=2x-3[/tex]

When graphing inequalities:

As the line for equation 1 is solid and there is shading above the line, the line is represented by the inequality:

[tex]\boxed{y \geq -\dfrac{1}{2}x+2}[/tex]

As the line for equation 2 is dashed and there is shading above the line, the line is represented by the inequality:

[tex]\boxed{y > 2x-3}[/tex]

Therefore, the system of linear inequalities shown in the graph is:

[tex]\begin{cases}y \geq -\dfrac{1}{2}x+2\\\\y > 2x-3\end{cases}[/tex]

Answer:

D. Undefined

Step-by-step explanation:

[tex]m=[/tex] ∞

Hope this helps

The trapezoid's area can be understood as triangle a + triangle b. So, we write these triangles as an expression, and, since we cannot solve with no values, we simplify to prove the area of the trapezoid.

A triangle's area is 1/2bh. In their case, b is represented as b or a depending on the triangle.

t = 1/2ah + 1/2bh

Now, since both expressions use the terms 1/2 and h, distributed onto a second variable, it can be rewritten as a single expression where both are distributed onto both variables at the same time. This is because both terms being multiplied by something separately is the same as combining both terms and multiplying them both at the same time.

t = 1/2(a)h + 1/2(b)h
t = 1/2(a + b)h

Answer: arrow shaded to the left number line with closed circle on point negative 7 over 22 and arrow shaded to the left

Step-by-step explanation:

Answer:

for easier explanation.... it's D

Step-by-step explanation:

It is possible to have a series of true conditional statements that lead to a false conclusion.

Making decisions based on particular situations is made easier with conditional statements.

A conditional statement's truth value can be either true or false. Simply demonstrate that the conclusion is true whenever the hypothesis is true to establish the truth of a conditional.

Simply demonstrating that the conclusion is wrong each time the hypothesis is true suffices to demonstrate that a conditional is untrue.

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Answer: k = 13

Step-by-step explanation:

The table has a constant of proportionality of 25

The table represents the given parameter

On the table, we have the following points

(x, y) = (1, 25)

The constant of proportionality of the points is then calculated as

k = y/x

Substitute the known values in the above equation

So, we have

k = 25/1

Evaluate the quotient

So, we have

k = 25

Hence, the constant of proportionality of the table is 25

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The table shows the total cost to be a member of the gym for different numbers of months.



Number of months. total costs

3. $53.97

6. $77.94

12. $125.88



Create a function that gives the total cost C, in dollars to be a member of the gym given the number of months M of membership.

_____________________________________

Total cost = M* (factor per month ) + b

_____________________________________

The expression for a linear equation is

*The slope-intercept form.

y = mx + b

m= (y2-y1)/ (x2-x1) (I)

y-intercept is (0, b)

*and the point-slope form

y- y1 = m(x-x1) (II)

________________________

Point 1 (3, 53.97)

Point 2 (12, 125.88)

Replacing in (II)

The slope m = (y2- y1)/ (x2-x1) = (125.88- 53.97)/(12-3) = 7.99

y - 53.97 = 7.99* (x- 3)

y = 7.99 x - 7.99* 3 + 53.97

y = 7.99x + 30

____________________

Verifying

y = 7.99x + 30

x= 3

y = 7.99*3 + 30

y= 53.97

x= 6

y = 7.99*6 + 30

y= 77.94

x= 12

y = 7.99*12 + 30

y= 125.88

_________________________

Answer

The linear function is y = 7.99x + 30

The angle at which the projectile should be launched to hit the target which is 129 feet away is 7/100π.

The projectile fires with a velocity V₀ and angle of elevation θ, then the horizontal distance is given by the R(θ),

R(θ) = V₀²sin2θ/32

The given function in dependent on theta θ,

The angle at which the projectile must be fired so that it reaches the horizontal distance of 129 feet in front of the cannon,

R(θ) = V₀²sin2θ/32

putting R(θ) equal to 129,  V₀ = 80ft/s,

129 = (80)²sin2θ/32

sin2θ = (129 x 32)/(80 x 80)

sin2θ = 0.645

Hence,

θ = 7/100π

so, the projectile should be launched at angle of 7/100π.

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