10) 18p³ - 6p² +3p-1

y -intercept #4 the starting value

(1 , 7.5) #3 the value after 1 year

because the x axis is the time (in years). When x = 0 (at the y-intercept) time = 0 or beginning time. When x = 1 one year has passed.

Answer: 18

Step-by-step explanation:   it is the smallest one in both tables.

1x6=6 2x6=12 3x6=18

1x9=9 2x9=18

hope this helped

36% of the shape is shaded in the given figure.

For the given question.

The shape of the boxes with some shaded part is given.

The total number of small parts in the figure is 25.

The total of shaded parts is 9.

Let 'x' be the percentage of shaded region.

Then,

x% of 25 = 9

25x/100 = 9

x = 900/25

x = 36%

Thus, the shaded percentage is found as 36%.

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Answer: The first one

Step-by-step explanation:

Answer:

x= −3/10

y= 3/7

Step-by-step explanation:

The dimensions of the deck would be increased by 1 feet.

Area of a rectangle = length x width

Initial area of the deck = 3 x 8 = 24 feet²

Area of the deck when it is increased = (1 + 0.50) x 24  = 36 feet²

Length of the deck after it is increased = 3 + x

Width of the deck after it is increased = 8+ x

Area of the new deck : (3 + x) + (8 + x) = 36

24 + 3x + 8x + x² = 36

x² + 8x + 3x + 24 - 36 = 0

x² + 11x - 12 = 0

The solutions of the quadratic equation are -1 and 12

-1 + x = 0

x = 1

or

12 + x = 0

x = -12

Thus, the dimension of the deck would be increase by 1 feet.

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By using the linear equation y=3x we draw the graph for proportional relationship.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

A proportional relationship graph between two variables is a relationship where the ratio between the two variables is always the same

the graph of any proportional relationship is characterized by a straight line with data points passing through the origin (0, 0).

By the definition of proportional relationship of graph, we can reduce relationship between the values on the x-coordinate and y-coordinate of the given graph

As they are  proportional and represented by euation

y = 3x

Where, x represent the time and y represent the number of sit-ups.

Hence by using the linear equation y=3x we draw the graph for proportional relationship.

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Answer: Femi is 14 years old

Step-by-step explanation: ten years ago ade was 2 and ade is half the age of Femi so that means Femi was 4 at that time since 2 is half of 4 and since he is 12 ten years later Femi is 14 ten years later.

Answer: The Pink one

Step-by-step explanation: Trapezoids have 2 parallel sides and 2 non-parallel sides.

A. The formula for h is h = V / πr².

B. The height of a container if the volume is 56.52 cubic inches and the radius is 1.5 inches is 8 inches.

The volume of a cylinder is calculated thus:

= πr²h.

where π = 3.142

r = radius

h = height

Therefore, the height will be:

V = πr²h

We have to make h the subject of the formula. This will be:

h = V / πr²

The height of a container if the volume is 56.52 cubic inches and the radius is 1.5 inches will be:

h = V / πr²

h = 56.52 / (3.142 × 1.5²)

h = 56.52 / 7.0695

h = 8

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By solving a linear equation, we will see that the points are vertical only if the value of x is -2.

We say that two points (x₁, y₁) and (x₂, y₂) are vertical if the points have the same x-component and different y-component, so we must have:

x₁ = x₂

y₁ ≠ y₂

In this case, the two points are:

F(3-2x, 12) and G(x+9, 7)

The y-component is different, so we only need to have:

3 - 2x = x + 9

This is a linear equation, below I will solve it:

3 - 2x = x + 9

3 - 9 = x + 2x

-6 = 3x

-6/3 = x

-2  =x

The points are vertical if x = -2.

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After simplification of the given expression -5w /9 =30 , value of w is equal to -54.

As given in the question,

Given expression is equal to :

-5w / 9 = 30

Simplification of the given expression to get the value of w is :

-5w / 9 = 30

Multiply both the side of the given expression by 9 we get ,

-5w = 30 × 9

Divide both the side of the given expression by -5 we get,

-5w /-5 = ( 30 × 9 ) / -5

⇒ w = -(6 × 9 )

⇒ w = -54

Therefore, after simplification of the given expression -5w /9 =30 , value of w is equal to -54.

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The function has the vertex value of (-1, -1)

From the question, the definition of the functuion is given as

y = 2x² + 4x + 1

Start by differentiating the function

This is done as follows

y' = 4x + 4

Next, we set the differentiated equation to 0

So, we have the following equation

4x + 4 = 0

This gives

4x = -4

Divide by 4

x = -1

Next, we substitute x = -1 in the given equation y = 2x² + 4x + 1

So, we have the following equation

y = 2(-1)² + 4(-1) + 1

Evaluate

y = -1

Recall that

x = -1 and y = -1

So, we have

(-1, -1)

Hence, the vertex of the function is (-1, -1)

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The vertex of the given function y = 2x² + 4x+1 is (-1, -1) which is the correct answer would be an option (B).

The function is below given by,

y = 2x² + 4x + 1

Differentiate with respect to x to get the derivative of the above function,

y' = dy/dx = d/dx (2x² + 4x + 1)

y' = 4x + 4

Equating the derivative of the function to zero

y' = 0

4x + 4 = 0

4x = -4

Divide by 4 into both sides of the equation,

x = -1

Substitute x = -1 in the given function y = 2x² + 4x + 1

y = 2(-1)² + 4(-1) + 1

y = 2(1) - 4 + 1

y = -1

Therefore, the vertex of the given function is (-1, -1).

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The fraction of coefficient factor out is 3/8.

What is Fraction?
A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters. Numerators and denominators are also employed in uncommon fractions such as compound fractions, complex fractions, and mixed numerals. The numerator and denominator of positive common fractions are natural numbers.

The given expression is , 3/8d+3/4

From this, we have to eliminate the fraction for that we have to make common denominators like that,3/8 d + (3 * 2) / (4 * 2)=> 3/8 d + 6/8

Next, take out the common value i.e, 3/8=> 3/8 ( d + 2)

Therefore, the coefficient factor out is 3/8.

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Using proportions, the explanation for this is that a basketball game has four quarters, hence half-time is at the end of the second quarter.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using the basic arithmetic operations, especially multiplication and division with the unit rates in the problem.

The entirety of a basketball game is composed by:

4 quarters.

Hence the mid-point of the game is calculated as follows:

0.5 x 4 quarters = 2 quarters.

This means that the end of the second quarter is the mid-point of the game, which is why the halftime is positioned at the end of the second quarter.

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60 cents is 20% of $3.

In essence, percentages are fractions with 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). The value of a number out of 100 is the percentage of that number. The terms "percent" and "cent" combine to make the word "percentage." Having Latin and French roots, the term "cent" means "hundred," while the word "percent" means "per hundred."

Given Data

60 cents as a percent of $3

1 dollar = 100 cents

$3 dollar = 300 cents

Percentage:

[tex]\frac{Value}{Total value}[/tex] × 100

[tex]\frac{60}{300}[/tex] ×100

20%

60 cents in 20% of $3.

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The complete question is:
"60 cents is what percent of $3."

The number of centons between each Cylon attack are 21, 23 and 25.

An odd number is a number that is not perfectly divisible by 2. For example, 3 is an odd number because it is not perfectly divisible by 2.

A consecutive number is a number that follows each other on the number line. Consecutive odd numbers are odd numbers that follow each other on the number lines.

Let x represent the first odd number.

The next odd number : x + 2

The third odd number : x + 4

x + (x + 2) + (x + 4) = 75

Add similar numbers: 3x + 6 = 75

3x = 75 - 6

3x = 66

x = 21

The second numbers : 21+ 2 = 23

The third number = 21 + 4 = 25

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The value of p that will guarantee the continuity of the function is given as follows:

p = 6.5.

A function defined by f(x) is continuous at a point x = a if it is defined at x = a, and the lateral limits are equal, that is:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

In the context of this problem, the continuity of the function will be guaranteed if the lateral limits at x = -1 are equal.

To the left of x = -1, the function is less than -1, hence the lateral limit is:

lim x -> -1^- f(x) = lim x -> -1 (-2x² - 8x + 3) = -2(-1)² - 8(-1) + 3 = 9.

To the right of -1, the function is greater than -1, hence the lateram limit is:

lim x -> -1^+ f(x) = lim x -> -1 (4x + 2p) = 4(-1) + 2p = -4 + 2p.

The lateral limits have to be equal for the function to be continuous, hence:

-4 + 2p = 9

2p = 13

p = 13/2

p = 6.5.

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The differentiation of the given equations is [tex]\frac{d}{dx}x^{2}=2x[/tex].

Given that, [tex]\frac{d}{dx}x^{2}[/tex].

The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.

Differentiate using the Power Rule which states that [tex]\frac{d}{dx}x^{n}=nx^{n-1}[/tex].

1) [tex]\frac{d}{dx}x^{2}=2x[/tex]

2) [tex]\frac{d}{dx}(3x^{5})=15x^4[/tex]

3) [tex]\frac{d}{dx}(9x^{2})=18x[/tex]

4) [tex]\frac{d}{dx}(3x^{3})=9x^{2}[/tex]

5) [tex]\frac{d}{dx}(2x^{7})=14x^6[/tex]

6) [tex]\frac{d}{dx}(x^{7})=7x^6[/tex]

Therefore, the differentiation of the given equations is [tex]\frac{d}{dx}x^{2}=2x[/tex].

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Answer:

Yes, it does.

Step-by-step explanation:

The most appropriate choice for function and graph of a function will be given by-

The graph passes through [tex](\frac{1}{3}, -0.3)[/tex]

What is function and graph of a function?

A function from A to B is a rule that maps to each elements of A, a unique element of B.

A is the domain of the function and B is the co-domain of the function.

A collection of all points of the form [tex](x, f(x))[/tex] is called graph of the function.

Here,

[tex]f(x) = 3x - 1.3[/tex]

Putting [tex]x = \frac{1}{3}[/tex]

[tex]f(\frac{1}{3}) = 3 \times \frac{1}{3} -1.3\\[/tex]

       [tex]= 1-1.3\\[/tex]

       [tex]= -0.3[/tex]

So, the graph passes through [tex](\frac{1}{3}, -0.3)[/tex]

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She make mistake in her first step. She plot a point at (3,2) instead of (3,−2).

Sandra is using the point-slope form [tex]y - y_{1} = m(x-x_{1})[/tex] to graph the equation [tex]y+2=(x-3)[/tex].

She completed the following steps.

1) Firstly she plot a point at (3,2)

2) Then she plot a point 5 units up and 4 units left from (3,2), at (−1,3).

3) Then she connect the points with a line.

She using the point slope for to graph the equation.

The point slope form is [tex]y - y_{1} = m(x-x_{1})[/tex].

The equation is [tex]y+2=(x-3)[/tex].

Now we compare the given equation to the point slope form.

After comparing we get

[tex]y_{1}[/tex] = -2 and [tex]x_{1}[/tex] = 3

So we have to plot a point at (3,-2) but she plot point at (3,2).

She make mistake in her first step.

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the graphs are attached herewith , where the label of the graph are :

  along X-axis: 1 square  division = 10 units

  along y-axis: 1  square division: 10 units

The problem we dealing with is related to manipulating graphs.For the question 7 to 10, the commonly given function is f(x)= √x, if the g(x) is nothing but the f(x-c) or f(x+c), so for the g(X) to be f(x-c), then a graph of that particular function turns to stretch downward whereas, for the f(x+c), it stretches upward.

So, for 7  g(x)=√x- 4 where -4  is c so the g(x) = f(x-c) so the  point for the graphs will stretch downward compare to the pint of the functions  f(x)= √x.

8. g(x)=√x +3

here g(x)= f(x+3), so the pints  stretched upward

9. g(x)=√x + 6 − 4=√x + 2

here additional number for the points ar 2, as it positive one,  so the  point of the function g(x), stretches upward

10. g(x)=√x - 7+3=√x -4

here the c is -4, so the point of the  g(x), stretches downward.

Same for the questions 11 to 14, the common function is f(x) = 1/x ,for which which g(x) = f(x-c) or f(x+c), for positive c , the graph stretches upward otherwise it moves downward

11. g(x) = 1/x +4

here the  c is positive, the graph stretches upward for the  g(x)

12. g(x) = 1/x - 6

here the  c is negative, the graph stretches downward for the  g(x)

13. g(x) = 1/x-6 + 8= 1/x+2

here the  c is positive, the graph stretches upward for the  g(x)

14. g(x) = 1/x+7 -4= 1/x+3

here the  c is positive, the graph stretches upward for the  g(x)

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The equation of the sequence is xₙ = 4n + 17 and the 11th term is 61

From the question, we have the sequence to be

17, 21, 25, 29, 21

The form of the sequence is given as

xₙ = cn + d

From the question, we have the first term to be 17

This means that

d = 17

So, we have

xₙ = cn + 17

When n = 1, we have x = 21

So, we have

21 = c + 17

Evaluate

c = 4

Substitute c = 4 in xₙ = cn + 17

xₙ = 4n + 17

This means that

n = 11

So, we have

x₁₁ = 4 * 11 + 17

Evaluate

x₁₁ = 61

Hence, the value is 61

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Answer:33 oz in march

Step-by-step explanation:

Answer: y=-1/2x+1

Step-by-step explanation: plug in numbers to find y intercept (b).

-1=-1/2(4)+b

-1=-2+b

b=1

y=-1/2x+1

Step 1

Let the length in minutes of Tika's class be m

His class had lasted already for 18 minutes

His class had 37 more minutes to end.

Step 2

Get the equation

Hence the answer is option B ------ ( m - 37 = 18)