if f(x) = 2x-7 and g(x)= x2-5, find g[f(5)]

Let x equal the number of tiny book boxes and y equal the number of large book boxes.

Because John must pack at least 35 boxes:

(number of tiny book boxes) + (number of large book boxes) = (at least) 35

x + y ≥ 35

Since John needs to pack at least 350 books:

(number of small books packed) + (number of large books packed) (is at least) 350

(number of small books per box)(number of boxes of small books) + (number of large books per box)(number of boxes of small books) ≥ 350

15x + 8y ≥ 350

Your system of inequalities is:

x + y ≥ 35

15x + 8y ≥ 350

The smallest integer greater than 2000 for both the fractions [tex]\frac{17k}{66} \ and \ \frac{13k}{105}[/tex] to be terminating decimals is 2079.

K is greater than 2000.

[tex]k> 2000\\[/tex].

Given fractions are

[tex]\dfrac{17k}{66} \ and \ \dfrac{13k}{105}[/tex].

In order for the decimal equivalents to be terminating, the only factors that can remain in the denominators are 2 and 5.

Here, the given denominators are 66 and 105 respectively.

Now factors of 66 will be 2,3,11.

And the factors of 105 will be 3,5,7.

So, the value of k must be multiples of 3, 7, and 11. The LCM of these numbers will be,

[tex]3\times 7\times 11=231[/tex]

Now the value of K must be greater than 2000, so the multiple of 231 which is greater than 2000 is its [tex]9^{th}[/tex] multiple,

[tex]231\times9=2079[/tex]

Hence 2079 is the smallest integer greater than 2000 for both the fractions [tex]\frac{17k}{66} \ and \ \frac{13k}{105}[/tex] to be terminating decimals.

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Answer:

1

Step-by-step explanation:

x + 2y = 6, multiply by 2 = 2x + 4y = 12

2nd equation:                    2x - 3y = 26

It has one solution

Answer: One solution

Step-by-step explanation:

Convert both equations into slope-intercept form:

x+2y=6

2y=6-x

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

Slope = 6/2 = 3

2x-3y=26

y=2x-26/3

Slope = 2/3

Therefore, he system of equations have one solution because their slopes are not equal.  

The steps to construct a parallelogram using a ruler and a compass are;

1. Draw a starting line segment l linger than 8 cm.

2. Mark point K on the line segment.

3. Widen the compass to a radius of 8 cm using the ruler.

4. Place the compass at point K and with the 8 cm radius mark point L on the line l.

5. At point L construct a 45° angle as follows;

The above steps bisects the 90° angle of the perpendicular lines.

6. Adjust the radius of the compass to give an opening of 6 cm and from point L draw an arc to intersect XL at M.

7. At point M construct a line YM at 45° angle to the line l.

8. From point M draw an arc to intersect YM and label the point as point N.

9. Join point M and N to complete the construction of the parallelogram KLMN.

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Answer:

-25/1 or -25

Step-by-step explanation:

Answer:

-25/1 or -25

Step-by-step explanation:

there hope this will help a lot

9

Step-by-step explanation:

woody is 5

buzz is 3

mr potato head is 3

rex is 7

alien is 1

If -0.14 is changed to 2, the graph would become a positive graph, or it would be steeper, because it has a positive slope

The equation of the graph is given as:

[tex]y = -0.14x + 3[/tex]

The above equation is a linear equation, which is represented as:

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

Where m represents the slope of the linear equation.

By comparison, we have:

[tex]m = -0.14[/tex]

i.e. the slope of the equation [tex]y = -0.14x + 3[/tex] is -0.14

When -0.14 is replaced with 2, the equation becomes

[tex]y = 2x + 3[/tex]

And the slope of the new equation [tex]y = 2x + 3[/tex] is

[tex]m =2[/tex]

2 is greater than -0.14, and 2 is positive.

This means that the graph would become a positive graph, or it would be steeper, because it has a positive slope

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Answer:

2000 Meters

Step-by-step explanation:

First, DIvide 1250 by 5 and you get 250. Multiply by 8 and you get 2000.

Answer:Group of answer choices 2/5 x ? = 4/3 ? X 2/5 = 4/3 4/3 x ? = 2/5 ? ÷ 5/2 = 3/4 4/3 ÷ 2/3 = ?

Step-by-step explanation:If 4/3 liters of water is enough to water 2/5 of the plants in the house, how much water is necessary to water all the plants in the house? Select all of the multiplication and division equations that represent this situation.

Answer:

3 1/3 liters of water

Step-by-step explanation:

4/3 is to 2/5

What 1 is to x

(4/3) / (2/5) = 10/3 = 3 1/3

Answer:

53

Step-by-step explanation:

248-195 is 53

you should take his weight and then subtract the amount he wants to weigh

Answer:

53 pounds

Step-by-step explanation:

248 minus 195 which gives you 53

He needs to lose 53 pounds.

Hope that helped!

Answer:

He had $210.1 after deductions.

Step-by-step explanation:

Add his regular pay and overtime pay together

$375.50 + $65.50 = $441

Now subtract his net pay from the total that he makes before deductions - with his overtime and regular pay.

$441 - $230.90 = $210.1

Answer:

below!

Step-by-step explanation:

Theoretical probability is used in mathematics to express the likelihood that a specific phenomenon will occur. Learn about the definition, formula, and real-world examples of theoretical probability like which flavor gumball a machine is most likely to dispense

Answer:

6x^2√x

Step-by-step explanation:

6 times 6 is 36

So you can take 6 out and leave x^5

However x^5 also have a power to square by:

x^4 which can turn into x^2

So we can take x^2 out

So the answer is 6x^2√x

Hope this helps!

I think its

the bottom left i might be wrong

What magic trick??

Are you gonna do a magic??

Sorry for a lot of questions.

Answer:

V = 14130 inches cubed

Step-by-step explanation:

the volume formula for a sphere is  [tex]V=\frac{4}{3} \pi r^{3}[/tex]. To solve plug in the values for each part of the equation. Pi will equal 3.14, and r will equal 15.

Step-by-step explanation:

There are other factors than Roberto coming that could have affected the outcome of the game. For example, maybe the night games were against better teams to generate better ratings in prime time. Moreover, maybe the Angels do better at home due to home-field advantage. There are many factors such as these that could explain why Roberto witnessed such a high win rate at the games he went to, so it cannot be concluded that Roberto's attendance caused the Angels to win.

Answer:

1960

Step-by-step explanation:

First, carry out the operation inside the parentheses: 495-475= 20. Next, follow the order of operations and do 87*20= 1740. Then, go from left to right, adding 1740 + 1084= 2824. Now, subtract all of that by 864. 2824-864= 1960.

Answer:

  multiply by (3-√7)/(3 -√7) and simplify

Step-by-step explanation:

When there are radicals or complex numbers in the denominator, you can rewrite the expression so it has a real, rational denominator. You do this by multiplying numerator and denominator by the conjugate of the denominator. That value is the denominator with its sign changed.

This takes advantage of the factoring of the difference of squares.

  (a -b)(a +b) = a² -b²

__

  [tex]\dfrac{2}{3+\sqrt{7}}=\dfrac{2}{3+\sqrt{7}}\times\dfrac{3-\sqrt{7}}{3-\sqrt{7}}=\dfrac{2(3-\sqrt{7})}{3^2-(\sqrt{7})^2}=\dfrac{2}{9-7}\times(3-\sqrt{7})\\\\=\boxed{3-\sqrt{7}}[/tex]

Answer:

Somewhat illegible but looks like the equation should be:

S = u t + 1/2 a t^2

100 = 20 + 1/2 * a * 4    where t = 2

a* 4 = 160

a = 40

Answer:

4i

Step-by-step explanation:

Distribute the 2, you get 4i.

It's imaginary because it has an i with it

Answer:

-4, real

Step-by-step explanation:

Hi there!

‘i’ is characterized as the sqrt of -1 or, alternatively, i^2= -1

If the problem is asking us to square i, then we know that it is going to equal -1. If we distribute the exponent, we would also square the 2, making it become 4. Now that we have done that, we multiply -1 and 4 to get a final answer of -4. This would be a real number as it is not imaginary.

I hope this can help!

4 its the correct answer do it

Step-by-step explanation:

its correct

Answer:

mx+b

Step-by-step explanation:

One way to express linear function rules is called slope-intercept form. Sometimes, f(x)=mx+b is used. In either case, m and b describe the general characteristics of the line. m indicates the slope, and b indicates the y-intercept.

The required function of the line would be y = 2x + 1 which is shown in the given graph.

The slope-intercept form is one rule to represent linear function rules. f(x)=mx+b is sometimes used. In any scenario, m and b describe the line's overall features. The slope is denoted by m, while the y-intercept is denoted by b.

According to the given figure,

We clearly see that the coordinates of the y-intercept would be (0, 1).

The value of the x-coordinate is 1 when y-coordinate is 3.

Here the line passes through points (0, 1) and (1, 3).

Let the required linear function would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x₂ -x]

x₁ = 0, y₁ = 1

x₂ = 1, y₂ = 3

⇒ y - y₂ = (y₂ - y₁)/(x₂ -x₁ )[x -x₂]

⇒ y - 3 = (3 - 1)/(1 - 0 )[x -1]

⇒ y - 3 = (2)[x -1]

⇒ y - 3 = 2x - 2

⇒ y = 2x - 2 + 3

⇒ y = 2x + 1

Therefore, the required function of the line would be y = 2x + 1 which is shown in the given graph.

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In the given equation, as the value of y increase, the value of x also

increases.

Reasons:

A direct variation is a relationship that exists between two variables. It is

also known as a direct proportion which can be expressed as; y = k·x

Where k is a number

The given equation is 4·y = 16·x

Dividing both sides by 4 gives;

[tex]\displaystyle \frac{4 \cdot y}{4} = \frac{16 \cdot x}{4} = \frac{4 \times 4 \cdot x}{4}[/tex]

Which gives;

y = 4·x

Comparing the above equation with the equation for a direct variation gives;

y = 4·x

y = k·x

Therefore;

k = 4

The equation, y = 4·x, and therefore, the equation from which it is derived, 4·y = 16·x, is a direct variation.

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The relationship between sides DY, PY and DP is that they form a right-angled triangle.

The value of side length DY is 8 units

Side length DY can be calculated using the following Pythagoras theorem.

So, we have:

[tex]DP^2 =DY^2 + PY^2[/tex]

Substitute values for DP, DY and PY

[tex]10^2 =DY^2 + 6^2[/tex]

Evaluate the squares

[tex]100 =DY^2 + 36[/tex]

Subtract 36 from both sides

[tex]64 =DY^2[/tex]

Take square roots of both sides

[tex]8 =DY[/tex]

Rewrite as:

[tex]DY = 8[/tex]

Hence, the value of side length DY is 8 units

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Answer:

A

Step-by-step explanation:

Answer:

graph b

Step-by-step explanation:

The inverse of a function may or may not be a function

The function g(x) is given as:

[tex]g(x) = 2(x - 1)^2 - 3[/tex]

(a) Inverse function g^-1(x)

We have:

[tex]g(x) = 2(x - 1)^2 - 3[/tex]

Replace g(x) with y

[tex]y = 2(x - 1)^2 - 3[/tex]

Swap the positions of x and y

[tex]x = 2(y - 1)^2 - 3[/tex]

Add 3 to both sides

[tex]x + 3 = 2(y - 1)^2[/tex]

Divide both sides by 2

[tex]\frac{x + 3}2 = (y - 1)^2[/tex]

Take square roots of both sides

[tex]\sqrt{\frac{x + 3}2} = y - 1[/tex]

Add 1 to both sides

[tex]1 + \sqrt{\frac{x + 3}2} = y[/tex]

Rewrite as:

[tex]y = 1 + \sqrt{\frac{x + 3}2}[/tex]

Express as inverse function of g

[tex]g^{-1}(x) = 1 + \sqrt{\frac{x + 3}2}[/tex]

Hence, the inverse function of g is [tex]g^{-1}(x) = 1 + \sqrt{\frac{x + 3}2}[/tex]

(b) The domain, and the range of g(x) and g^-1(x)

Function g(x)

The function g(x) is a quadratic function.

So, the domain is:

The range is:

Function g^-1(x)

The function g^-1(x) is a square root function.

So, the domain is:

The range is:

The domain of g(x) is the range of g^-1(x), while the range of g(x) is the domain of g^-1(x).

(c) The graph

See attachment for the graph

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