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The graph when translated 5 units up is g(x) = 3x + 5.

Consider a parent function f(x),

When translating a function up or down by a value (say b), you let g(x) = f(x) + b

If b is positive your graph is translated up, if b is negative your graph is translated down.

When translating a function to the right or left by a value (say a) you let g(x) = f( x + a).

If a is positive your graph is translated to the left, if a is negative your graph is translated to the right.

Therefore, the function g(x) when the graph of the function f(c) = 3x is translated 5 units upwards will be:

g(x) = f(x) + 5

g(x) = 3x + 5

The function g(x) when the graph of f(x) is translated 5 units up is g(x) = 3x + 5.

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When the graph of f(x) is translated five units up, the function g(x) becomes g(x) = 3x + 5.

Given function is , f(x) = 3x

We can get,

f(1) = 3(1) =3

f(2) = 3(2) = 6

f(3) = 3(3) = 9

f(0) = 3(0) = 0

f(-1) = 3(-1) = -3

f(-2) = 3(-2) = -6

x             1           2            3           0            -1             -2

f(x)          3          6            9           0            -3             -6

Let us assume, new function is g(x)

Think about the parent function f. (x),

If you want to scale a function up or down by a certain amount, let g(x) = f(x) + b.

Your graph is translated upward if b is positive and downward if b is negative.

Let g(x) Equal f(x + a) when moving a function to the right or left by a certain amount (let's say a).

Your graph will be translated to the left if an is positive and to the right if an is negative.

As a result, when the graph of the function f(c) = 3x is translated 5 units upward, the function g(x) will be as follows:

g(x) = f(x) + 5     (because 5 units up)

We can substitute f(x) value,

g(x) = 3x + 5

Therefore,

The function g(x) when the graph of f(x) is translated 5 units up is g(x) = 3x + 5.

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A diameter of a circle is any straight line segment that passes through the center of the circle and has endpoints on the circle.

The diameter of the circle is 28 inches.

In geometry, a circle's diameter is any straight line segment that passes through the center of the circle and has endpoints on the circle. It is also referred to as the circle's longest chord. Both definitions apply to a sphere's diameter.

The diameter is twice the radius because the greatest distance between two points on a circle must be a line segment through the center of the circle.

Here, CF is a radius and the diameter is twice the radius.

Diameter of a circle = 2r

d = 2r

Where, r = 14

Diameter of a circle, d = 2r

Diameter of a circle = 2(14)

Diameter of a circle = 28

Therefore, the diameter of the circle is 28 inches.

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Answer:

x= 36 y= 67 and z=77

Step-by-step explanation:

The sum of the measures of the angles of a triangle is 180

can be written as x+y+z=180

The sum of the measures of the second and third angles is four times the measure of the first angle.  

It can be written by:  x+y=4z

The third angle is 10 more than the second

It can be written as z=y+10

By solving the equations systems the above values can be determined.

x+y+z=180

x+y=4z

z=y+10

Answer:

74/100

37/50 (this is the answer if 74/100 is simplified)

Hope this helps :)

Explanation right below.

Step-by-step explanation:

The 4 in 0.74 ends in the hundredths place, so 74 will be put over 100 in a fraction to get 74/100. If 74/100 needs to be simplified then divide the numerator and denominator by 2 to get 37/50.

The car comes to a complete stop when t = 14secs.

What is velocity  ?

Velocity is the rate and direction of an object's movement, whereas speed is the time rate at which an object is moving along a path. Put another way, speed is a scalar value, while velocity is a vector.

Given:

velocity v(t) = 0.5t^2 – 14t + 80

Differentiating the equation with respect to t to get the velocity,

we get ,

dv/dt = 2 x .05t - 14

when the car stops the velocity becomes 0.

Therefore,

2 x .05t - 14= 0

=> t = 14 secs

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Question:

A car's velocity is modeled by v(t) = 0.5t2 – 14t + 80 for 0 ≤ t ≤ 14, where the velocity is in feet per second and time is in seconds. When does the car come to a complete stop?

20 seconds

14 seconds

8 seconds

4 seconds

a) Each side of the square is 9 cm long. b) The perimeter of the shape is 18 cm.

Perimeter refers to the total length of the boundary or outer edge of a two-dimensional shape.

a) The perimeter of a square is the sum of the lengths of all its sides. Since all sides of a square are equal, we can divide the perimeter by the number of sides to find the length of one side:

Perimeter of square = 4 x Length of one side

36 cm = 4 x Length of one side

Divide both sides by 4:

Length of one side = 36 cm / 4 = 9 cm

Therefore, each side of the square is 9 cm long.

b) To find the perimeter of the shape made by cutting an equilateral triangle from a rectangle, we need to add up the lengths of all its sides.

The length of the rectangle is equal to the length of the base of the equilateral triangle plus the length of one of its sides. Since the equilateral triangle has all sides equal, we can find its length by dividing the length of the rectangle by 2:

Length of equilateral triangle = Length of rectangle / 2

Length of equilateral triangle = 7.2 cm / 2 = 3.6 cm

The perimeter of the equilateral triangle is three times its side length:

Perimeter of equilateral triangle = 3 x Length of one side

Perimeter of equilateral triangle = 3 x 3.6 cm = 10.8 cm

The perimeter of the shape is the sum of the length of all its sides, which is the sum of the length of the rectangle and the perimeter of the equilateral triangle:

Perimeter of shape = Length of rectangle + Perimeter of equilateral triangle

Perimeter of shape = 7.2 cm + 10.8 cm = 18 cm

Therefore, the perimeter of the shape is 18 cm.

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a) If a square has a perimeter of 36 cm, how long is each side of the square?

b) The following shape is made by cutting an equilateral triangle from a rectangle. Find its perimeter.

7.2 cm

13 cm

18 cm

23 cm

The required three ways of solutions are,
1 - Transposition left to right
2- Property of equality
3 - Transposition right to left

Here,
Given expression,

13=-2(y-4)+3y

Approach 1,
13 = -2 (y - 4) + 3y
13 = -2y + 8 + 3y
13 = y + 8
13 - 8 = y
5 = y

Approach 2
13 = -2 (y - 4) + 3y
13 - 3y = -2y + 8
Adding 3y both side
13 - y = +8
Subtracting 13 on both sides
-y = -5

Multiplying by -1 on both sides
y = 5

Approach 3
13 = -2 (y - 4) + 3y
transposition of the variable to the left and contents to the right
2(y - 4) - 3y = -13
2y - 8 -3y = -13
-y -8 = -13
-y = -13 + 8
-y = -5
y = 5

Thus, the required three ways of solutions are,
1 - Transposition left to right
2- Property of equality
3 - Transposition right to left

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There will be total 6 pathways to directly connect to every other building

It is given that,

There are four buildings on the Mansfield High School Campus with a condition that none of the three can stand in straight line.

We need to find,

The total number of ways through which all the four buildings can be directly connected with each other in such a way that none can stand in straight line

Firstly, Let us consider that the buildings are arranged on the corner points of an imaginary square.

Then the number of ways through which all four buildings can be directly connected is by going straight from one building to other by following the imaginary square boundary lines = 4

the number of ways through which all four buildings can be directly connected is by going diagonally from one building to other by following the diagonal of the imaginary square = 2

Hence, The total number of pathways to directly connect to every other building = 4 +2 = 6

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Answer:

C. The classmate was supposed to multiply the exponents.

Step-by-step explanation:

[tex] { ({2}^{3}) }^{2} = {2}^{6} = 64[/tex]

Answer:

C

Step-by-step explanation:

your classmate multiplied the exponenets

Answer: 10 tutors

Step-by-step explanation:

Make the proportion:

72 students - 6 tutors

120 students - x tutors

Hence,

[tex]\displaystyle\\x=\frac{(120)(6)}{72} \\\\x=\frac{720}{72} \\\\x=\frac{(72)(10)}{72}\\\\ x=10\ tutors[/tex]

The order number that conveys a different information between the two analytical reports presented in tabular form is Order 102

The report that accompanies a similar question consists of two tabular forms of (analytical) reports, as follows;

Report 1.

Order. Stock # Qty

101. 27–671. 1

102. 27–781. 2

103. 27–090. 3

Report 2.

Order. Stock # Qty

101. 27–671. 1

102. 27–783. 2

103. 27–090. 3

From the above reports, by examination, we have at order 102

Stock number (Stock #) for Order 102 in Report 1 = 27–781

Stock number (Stock #) for Order 102 in Report 2 = 27–783

Therefore;

The order(s) that have (has) a different information between the reports is; Order 102

The correct option is therefore;

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======================================================

Work Shown:

5a^2

5(2)^2

5(4)

20

Explanation:

I replaced 'a' with 2, since a = 2. Then use PEMDAS to simplify the expression into one single number at the end. The value b = 6 won't be used at all since b is not found anywhere in the original expression.

Answer:

5a² = 20

Step-by-step explanation:

Given expression,

→ 5a²

Now we have to,

→ Evaluate the given expression.

We have to use,

→ a = 2

→ b = 6

Let's evaluate the expression,

→ 5a²

→ 5 × (a)²

→ 5 × (2)²

→ 5 × 4

→ 20 => {solution}

Therefore, the answer is 20.

Answer:

(-9,4)

Step-by-step explanation:

(-4-5,2+2)

Answer: 2 1/2 as a decimal is 2.5

2 as a decimal is 0.02

Step-by-step explanation:

For each line,  an equation in slope-intercept form :

y = (-1/4)x - 2 .

Summary of the lesson. The slope-intercept form is just a means of stating a line's equation so that the slope (steepness), as well as y-intercept (where the line crosses the vertical y-axis), as well as y-intercept (where the line crosses the vertical y-axis), are obvious. This form is also known as the y = MX + b form.

The slope, m, of a line represents its steepness. The slope of something like the line is however termed a gradient, sometimes. A line's y-intercept, b, represents the y-coordinate of something like the point where the line's graph intersects the y-axis.

To begin, use the slope formula to determine the average slope here between two points.

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

= (-1 - (-4))/ (-4-8)

= 3/(-12)

= -1/4

So the slope is -1/4.

We must now determine the y-intercept. This will be accomplished by converting a single of the points and indeed the slope through into point-slope form of something like a linear equation, which is y2-y1 = m(x2-x1).

Let’s plug in the point (8,-4).

So we get y-(-4) = (-1/4)(x-8) ⇒  y+4

= (-1/4)x + 2  ⇒  y

= (-1/4)x - 2.  

So y = (-1/4)x - 2  

For each line, write an equation in slope-intercept form y = (-1/4)x - 2.

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Answer: 66 degrees for 1st angle

52 degrees for 2nd angle

62 degrees for 3rd angle

Step-by-step explanation:

3x+(x + 30)+(x + 40)=180

3x+x+30+x+40=180

3x+x+x+30+40=180

5x+70=180

5x=110

x=22

3x=

3(22)=66 degrees for 1st angle

x+30=

22+30=52 degrees for 2nd angle

x+40=

22+40=62 degrees for 3rd angle

Answer:

3x=66

x+30=52

x+40=62

66,42,62

Step-by-step explanation:

(3x)+(x+30)+(x+40)=180

5x+70=180

5x=110

x=22

3x=66

x+30=52

x+40=62

The simplification of each sum or difference of given expression [tex]\frac{m}{3m+6}- \frac{4m}{m+2}[/tex] is equal to (-11m)/ 3(m+2). Restriction on the variables is given by m ≠ -2.

As given in the question,

Given expression is [tex]\frac{m}{3m+6}- \frac{4m}{m+2}[/tex]

Simplify the expression by taking the least common multiple

[tex]\frac{m}{3m+6}- \frac{4m}{m+2}\\\\= \frac{m}{3(m+2)}- \frac{4m}{m+2}\\\\= \frac{m -12m}{3(m+2)}\\ \\= \frac{-11m}{3(m+2)}[/tex]

Restriction on the variables is given by m ≠ -2.

Therefore, the simplification of each sum or difference of given expression [tex]\frac{m}{3m+6}- \frac{4m}{m+2}[/tex] is equal to (-11m)/ 3(m+2). Restriction on the variables is given by m ≠ -2.

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Answer:

Hello,

1/37

Step-by-step explanation:

Explanation on the picture

The answer should be $2.16.

Explanation:

1.5 pounds is 24 ounces

24 divided by 4 = 6

So, 0.36 x 6 = $2.16

---------------------------------------------------------

Hope this helps!

Have a great day and God bless! :)

   A parabola having vertex at the origin and focus at (0, -1.5) is expressed by the following equation:

y = -x²/6

 A parabolic function is one that has a quadratic variable, its shape is defined by the intersection of an inclined plane whose angle of inclination with respect to the axis of revolution of the cone is equal to that presented by its generatrix.

Since the vertex and the focal axis are on the same axis, we analyze that:

(x - 0)² = 4p(y - 0)

Focus

f = (0, 0 + p)

0 + p = -1.5

p = 0 -1.5

p = -1.5

(x - 0)² = 4*(-1.5)(y - 0)

(x)² = -6(y)

y = -x²/6

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Answer:

inverse

In math, a reciprocal is also called an inverse.

Step-by-step explanation:

Answer:

A correlative is another name for a reciprocal.

Correlative:

A degree into which 2 or more values are associated.

Answer:

26.5

Step-by-step explanation:

Planteamiento:

a - 1 = 3b

a + b = 35

Desarrollo:

de la primer ecuación del planteamiento:

a = 3b + 1

sustituyendo este último valor en la segunda ecuación del planteamiento:

(3b+1) + b = 35

4b = 35 - 1

4b = 34

b = 34/4

b = 8.5

de la segunda ecuación del planteamiento:

a + 8.5 = 35

a = 35 - 8.5

a = 26.5

Comprobación:

de la primer ecuación del planteamiento:

a - 1 = 3b

26.5 - 1 = 3*8.5

25.5 = 25.5

Respuesta:

ya que:

26.5>8.5

El número mayor es:

26.5

The cost of the pizzas that Christina bought will be $4.30.

From the information, The cost of a large pizza is $0.90 and the cost of a small pizza is $0.70. Christina bought 4 large pizzas and 1 small pizza.

The number of pizzas will be:

= 4 + 1

= 5 pizzas

The cost will be:

= 4($0.90) + 1($0.70)

= $3.60 + $0.70

= $4.30

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The cost of a large pizza is $0.90 and the cost of a small pizza is $0.70. Christina bought 4 large pizzas and 1 small pizza. How much pizza did Christina buy how much did she pay?

The cost of 3 pens will be 27P and the cost of 2 rulers will be 30p.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given that the cost of 5 pens and 3 rulers is 90p the cost of 2 pens and 1 ruler is 33p. the cost of 3 pens and 2 rulers will be calculated as below:-

From the equations and solve:-

5p + 3r = 90p

2p + r = 33p

5p + 3r = 90p

-6p - 3r = -99p

Cost of one pen P = 9

The cost of the 1 ruler:-

2p + r = 33p

2 x 9 + r = 33

18 + r = 33

r = 33 - 18

r = 15

Cost of 3 pens = 3 x 9 = 27

Cost of 2 rulers = 2 x 15 = 30

Therefore, the cost of 3 pens will be 27P and the cost of 2 rulers will be 30p.

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72/6=12

that means every tutor would have 12 students. if the academy has 120 students then we divide 120 by 12 to get 10. That means the academy needs 10 tutors.

In fraction, June is 9/8 as old as David.

What is a fraction?

A fraction is a portion of a whole or, more broadly, any number of equal pieces. In ordinary English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters. A common, vulgar, or simple fraction has a numerator above a line and a non-zero denominator below (or after) that line. Numerators and denominators are also employed in uncommon fractions such as compound fractions, complex fractions, and mixed numerals.

The required fraction is (3/4) x (3/2) = 9/8

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The description of the transformation that occurs to any given point is a 4 unit left translation and 8 units up translation

The rule is given as

(x,y) --> (x-4, y+8)

The above rule represents a translation transformation

This is evident because it has the format

(x,y) --> (x + h, y + k)

By comparison, we have

h = -4

k = 8

This represents a 4 unit left translation and 8 units up translation

Hence, the description of the transformation that occurs to any given point is a 4 unit left translation and 8 units up translation

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Answer:

if the experiment continued under the same conditions.

Answer: if the experiment continued under the same conditions.

Step-by-step explanation:E2022

1:4 is the ratio of the pigeon's aorta radius to that of the goose.

So,

Canceling it to the simplest form:

So, the ratio is 1:4.

Therefore, 1:4 is the ratio of the pigeon's aorta radius to that of the goose.

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