Which of the following shows that polynomials are closed under subtraction when two polynomials, (4x^2 - 8x - 7) - (3x^2 - 5x + 16), are subtracted?

Answer:

Step-by-step explanation:

The ladder is the vertical leg and the slide is the hypotenuse of the triangle formed.

The angle opposite the ladder is 25°, slide has the length of x.

1st method:-

\( \frac{ - 40}{5} \) can also be written as\( - 40 \times \frac{1}{5} \)

We know that anything we multiply ( except 0 ) with a negative number , the product is also a negative number.

2nd method:-

\( \frac{ - 40}{5} = - 8\) We can write - 8 as \(8 \times ( - 1)\)

We know that anything we multiply ( except 0 ) with a negative number , the product is also a negative number.

Step-by-step explanation:

Since it's a right triangle, you can use Pythagoras

a^2 + b^2 = c^2

We have b and c, we just need a, so let's plug it in

\( {x}^{2} + {24}^{2} = {25}^{2} \)

\( {x}^{2} + 576 = 625\)

\( {x}^{2} = 49\)

\(x = 7\)

Answer: 7ft

Step-by-step explanation:

hypotenuse (h) = 25

perpendicular (p) = 24

base (b) = ?

We know by using Pythagoras theorem

b = √h² - p²

= √ 25² - 24²

= √ 49

= 7 ft

Answer:

75 words in 2.5 minutes

Step-by-step explanation:

30 words - 1 min

60 words - 2 min

30/2 = half a minute

=15

60+15=

75 words

Answer:

2sin^2(3x)

Step-by-step explanation:

The given expression is equivalent to \(2\sin^{2}{3x}\).

What is trigonometry identity?

When trigonometric functions are used in an expression or equation, trigonometric Identities come in handy.

One of the trigonometry identity is  \(\cos2x=2\cos^{2} x-1\).

What is the simplified expression for given expression?

In the given expression \(\cos6x\) can be break as \(\cos(2\cdot3x)\).

Now use the identity \(\cos2x=2\cos^{2} x-1\) in the given expression.

\(1-\cos6x=1-2\cos^{2}{3x}+1\)

\(=2(1-\cos^{2}{3x})\)

Now use the identity \(1-\cos^{2}x=\sin^{2}x\).

\(1-\cos6x=2\sin^{2}{3x}\).

Therefore, the given expression is equivalent to \(2\sin^{2}{3x}\).

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Answer:

D) 2.5

                                             Aaliyah- ツ

Answer:

Vertex: \((\frac{1}{2} ,16)\)

Zeros: \(\frac{3}{2}\)  and \(-\frac{1}{2}\)

Step-by-step explanation:

\(h(t)=-16t^2+16t+12\)

1) Find the x-coordinate of the vertex

\(x=\frac{-b}{2a}\) where the equation is \(f(x)=ax^2+bx+c\)

\(x=\frac{-16}{2(-16)} \\x=\frac{-16}{-32} \\x=\frac{16}{32} \\x=\frac{1}{2}\)

2) Find the y-coordinate of the vertex

Plug the x-coordinate \(\frac{1}{2}\) back into the original equation

\(h(\frac{1}{2} )=-16(\frac{1}{2}) ^2+16(\frac{1}{2})+12\\h(\frac{1}{2} )=-16(\frac{1}{4})+8+12\\h(\frac{1}{2} )=-4+20\\h(\frac{1}{2} )=16\)

Therefore, the vertex of the parabola is \((\frac{1}{2} ,16)\).

3) Find the zeros of the parabola

Rewrite the equation so that it equals 0

\(0=-16t^2+16t+12\)

Divide both sides by -16

\(0=t^2-t-\frac{12}{16}\)

Simplify the fraction

\(0=t^2-t-\frac{3}{4}\)

Complete the square; first isolate t²-t

\(t^2-t=\frac{3}{4}\)

Complete the square; Add \((\frac{1}{2} )^2\) to both sides

\(t^2-t+(\frac{1}{2})^2=\frac{3}{4}+(\frac{1}{2})^2\\(t-\frac{1}{2})^2 =\frac{3}{4}+\frac{1}{4} \\(t-\frac{1}{2})^2=1\\(t-\frac{1}{2})^2=1\)

Take the square root of both sides

\(t-\frac{1}{2} =\±\sqrt{1}\\t-\frac{1}{2} =\±1\)

Isolate t

\(t=\frac{1}{2}\±1\)

Find the zeros

\(t=\frac{1}{2}+1\\t=\frac{3}{2}\\or\\t=\frac{1}{2}-1\\t=-\frac{1}{2}\)

Therefore, the zeros of the parabola are \(\frac{3}{2}\) and \(-\frac{1}{2}\).

I hope this helps!

The value is 24 square units is parallel to the face of the right rectangular prism.

We can see that the face of the given rectangular prism shows a width 4 and a height of 6. If we cut the figure at any point along the length 20, such that the cross-section is parallel to the face, the cross-section, which occurs at x length, will always have the same dimensions, which are 4 and 6.

So the area of the cross-section which is parallel to the face of the given rectangular prism is given by:

A = 6 × 4

A = 24

Thus, the value is 24 square units is parallel to the face of the right rectangular prism.

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A = 6 × 4

A = 24

Thus, the value is 24 square units is parallel to the face of the right rectangular prism.

Answer:

Step-by-step explanation:

question 13:

the triangle with x is a 30-60-90 triangle which means

x= 17√3

then the traingle with y and z is a 45-45 triangle

z=34

y= 34√2

question 14:

x= 18√3

z=9

y= 18

Answer:

19

Step-by-step explanation:

First, you should arrange the data in ascending to descending to find the median.

12, 14, 15, 16, 17, 19, 21, 26, 26, 27, 28

Now let us use the given formula to find the median.

\(\sf \dfrac{n+1}{2} =--^t^h data\)

Here,

n → the number of elements

Let us find it now.

\(\sf Median= \dfrac{n+1}{2}\\\\\sf Median=\dfrac{11+1}{2} =6^t^h data\\\\Median=19\)

The model that represents the two equal expression for the value x is 2 is given by :

option C.  x  1  1 = 1   1   1   1

The correct model which represents the expression for the value x as 2 is given by :

A. x   x     x     x    = 1    1    1     1

On the left hand side substitute the value of x = 2 we get,

Left hand side

= 2    2    2    2

It is not equal to 1    1    1    1

Incorrect option.

B. x   x     x     x    = 1  

On the left hand side substitute the value of x = 2 we get,

2   2    2    2

which is not equal to 1

Incorrect option.

C. x   1   1  = 1      1     1     1

On the left hand side substitute the value of x = 2 we get,

2    1    1

= 1   1    1     1

= Right hand side.

Correct option.

D.  x      x    

On the left hand side substitute the value of x = 2 we get,

= 2      2

which is not equal to right hand side

Incorrect option.

Therefore, the correct model which represents the expression for the value of x = 2 is equal to option C.  x  1  1 = 1   1   1   1 .

The above question is incomplete , the complete question is:

Which model shows two equal expression when the value of x is 2 ?

Attached model.

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Answer:

D

Step-by-step explanation:

multiply the packs with the amount of bottles in each one. then subtract the number you got when you multiplied 4x8. I'm not good at explaining but hope this helps

The random variable X is defined only for the interval [0,1], and the pdf is 0 outside this interval. This is because the pdf is 0 for x outside the interval [0,1], and hence the integral from -infinity to 0 and from 1 to infinity will be 0.

The given probability density function (pdf) of X is as follows:

f(x) = {42.5(1-x), 0<=x<=1

= {0, otherwise

This pdf represents the probability distribution of the amount of space occupied by an article placed in a 1-ft packing container. To find the expected value of X, denoted by E(X), we can use the formula:

E(X) = integral from 0 to 1 of x*f(x) dx

Substituting the given pdf, we get:

E(X) = integral from 0 to 1 of x*42.5(1-x) dx

Simplifying the expression, we get:

E(X) = 42.5 * [integral from 0 to 1 of x dx - integral from 0 to 1 of x^2 dx]

E(X) = 42.5 * [(1/2) - (1/3)]

E(X) = 14.17

Therefore, the expected value of X is 14.17.

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Answer: $5

Step-by-step explanation:

Answer:

y = 2

Step-by-step explanation:

The line is horizontal and parallel to the x- axis with equation

y = c ( c is the value of the y- coordinates the line passes through )

The line passes through (0, 2 ) with y- coordinate 2 , then

y = 2 ← equation of line

Answer:

ok I really suck at math, but I think you may have to multiply the x/y to get the whole area of the circle. so maybe itd be 10x25. I'm sorry if this isnt correct

Bob continues his research because even though there is no linear equation relationship between the number of bedrooms and selling price, there could be another type of relationship.

Bob continues his research because even though the correlation value he calculated between the number of bedrooms and the selling price was only 0.05, this does not necessarily mean that there is no relationship of any kind between these two variables. It simply means that there is no linear relationship between the two. There could still be other types of relationships between the two variables, such as an exponential or quadratic relationship. It is possible that further analysis and exploration of the data set would reveal such a relationship and allow Bob to uncover the relationship between the two variables. Additionally, even if the correlation value is low, it does not necessarily mean that there is no relationship between the two variables. It simply means that the relationship is weak. Therefore, Bob should continue his research in order to uncover any potential relationships between the number of bedrooms and selling price.

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The 11th rating must be at least 85 in order for the store to have an average of at least 85 for the first 20 ratings. The least value the store can receive for the 11th rating and still be able to have an average of at least 85 for the first 20 ratings is 85.

To calculate this, we need to find the total of all the ratings so far, including the 11th rating, and then divide that by the number of ratings. We know that the first 10 ratings have an average of 75, so the total of all ratings is 750 (75 x 10).

To reach an average of 85, we need the total of the ratings to be 850 (85 x 10).

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Answer:

the value of x is 68

Step-by-step explanation:

because the line does change on either of the sides so that makes x the same value as the other side which is 68. forgive me if im wrong.

The correct null hypothesis for the given problem is \(H_0\) : μ = 8000.

To obtain the correct null hypothesis for the given problem, follow the given below steps:

Firstly, recall that the null hypothesis ( \(H_0\) ) is a statistical assumption used in hypothesis testing.

It is a statement that is assumed to be true until it is proven false by the alternative hypothesis.

Secondly, recall that the null hypothesis is the opposite of the alternative hypothesis (\(H_1\)), which is the statement that researchers want to prove to be true.

Thirdly, recall that the null hypothesis for a population mean is as follows:

 \(H_0\) : μ = \(\mu_o\)

where μ represents the population mean and

\(\mu_o\) represents the hypothesized population mean.

Therefore, for the given problem, the correct null hypothesis is:

 \(H_0\) : μ = 8000.

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Answer:

Option (2)

Step-by-step explanation:

In the graph of any function, x-values are the input values and y-values are represented by the output values.

From the graph of a function attached,

y-value of both the linear functions for same x-value will be the common output value.

In other words, y-coordinates of the ordered pair common to both the lines will be the output value for both the functions.

For x = -2, y = 1 will be common to both the functions.

Option (2) is the answer.

Answer:

The answer would be Y=10

The maximum profit is achieved when approximately 312.5 units of lab equipment are sold.

The revenue function R(x) represents the amount of money the company earns from selling x units of lab equipment. It is given by the equation:

R(x) = -0.32x^2 + 270x

The costs function C(x) represents the expenses incurred by the company for producing and selling x units of lab equipment. It is given by the equation:

C(x) = 70x + 52

To determine the company's profit, we subtract the costs from the revenue:

Profit = Revenue - Costs

P(x) = R(x) - C(x)

Substituting the given revenue and costs functions:

P(x) = (\(-0.32x^2 + 270x)\) - (70x + 52)

Simplifying the equation:

P(x) = -0.32x^2 + 270x - 70x - 52

P(x) = -\(0.32x^2\)+ 200x - 52

The profit function P(x) represents the amount of money the company makes from selling x units of lab equipment after deducting the costs. It is a quadratic function with a negative coefficient for the x^2 term, indicating a downward-opening parabola. The vertex of the parabola represents the maximum profit the company can achieve.

To find the maximum profit and the corresponding number of units sold, we can use the vertex formula:

x = -b / (2a)

For the profit function P(x) = -\(0.32x^2 + 200x\)- 52, a = -0.32 and b = 200.

x = -200 / (2 * -0.32)

x = 312.5

Therefore, the maximum profit is achieved when approximately 312.5 units of lab equipment are sold.

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Answer:

Part A

y =($50 - ($23 × 2 + $5)+ $22)

y = $21

Part B

Clay can get his balance to zero by withdrawing or writing another check for $21

Step-by-step explanation:

Last week, Clay had a beginning balance of $50 in his account. He wrote 2 checks for $23 each from his checking account , withdrew another $5, and finally made a deposit of $22.

Part A: Write an expression and your answer to show his final account balance at the end of the week 23 * 2 = 46

Let his final Account Balance = y

y =($50 - ($23 × 2 + $5)+ $22)

y =$72 - $51

y = $21

Part B: Explain in words, what Clay should do to get his account balance to zero?

Clay can get his balance to zero by withdrawing or writing another check for $21

= $21 - $21

= $0