Can someone please help me complete the factoring of the polynomial

Answer:

8

Step-by-step explanation:

Substitute the values in the expression, we have:

\(\displaystyle{|-1-3|+4}\)

Evaluate:

\(\displaystyle{|-4|+4}\)

Any real numbers in the absolute sign will always be evaluated as positive values. Thus:

\(\displaystyle{|-4|+4 = 4+4}\\\\\displaystyle{=8}\)

Hence, the answer is 8. A quick note that z-value is not used due to lack of z-term in the expression.

Where the above relations are given, note that Options A,  D, and E are the relations that represents a function. The others are just relations.

To distinguish a function from a relation, look to see if any of the x values are repeated; if not, the relationship is a function. If some x values are repeated but the accompanying y values differ, we have a relation rather than a function.

Note that where you are given domain and range, only the range is represented on the x-axis.

Some of the x values may be seen repeated in B, and C.

How is this so?

B) In a coordinate system, values are represented as (x, y). so

In relations, B 2 is repeated twice to in connection with -5, and -6. That is:

(2, -5) , (2, -6)

Since two is x, then its repetition nullified the relation as a function.

C) On table indicated on C, it is much easier to identify the x and y values. As is seen, -3 is repeated twice in connection with 4 and 2. Thus, its repetition nullified the relation as a function.

As a result, Options A,  D, and E are the relations that represent a function.

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Answer:

442.96875 ft.

Step-by-step explanation:

Original Height (h) : 150 ft

Bounce 1 (h₁) : h/2 = 150/2 = 75 ft

Bounce 2 (h₂) : h₁/2 = 75/2 = 37.5 ft

Bounce 3 (h₃) : h₂/2 = 37.5/2 = 18.75 ft

Bounce 4 (h₄) : h₃/2 = 18.75/2 = 9.375 ft

Bounce 5 (h₅) : h₄/2 = 9.375/2 = 4.6875 ft

Bounce 6 (h₆) : h₅/2 = 4.6875/2 = 2.34375 ft

Finding the sum of bounces 1 - 5 :

Distance traveled :

Answer:

442.96875 ft

Step-by-step explanation:

We can model the height of each bounce as a geometric series.

General form of a geometric sequence: \(a_n=ar^{n-1}\)

(where \(a\) is the initial term and \(r\) is the common ratio)

If we let n be the number of bounces, then the initial term has to be:

\(a_1=\dfrac12(150)=75\)

since this is the height of the ball after the first bounce.

The common ratio r has already been given to us, as we have been told that the height of the bounce halves after each bounce.

\(\implies r=\dfrac12=0.5\)

Therefore, the geometric series to model the peak height of each bounce is:

\(a_n=75(0.5)^{n-1}\)

(where \(a_n\) is the height and n is the number of bounces)

Therefore, to calculate the total number of feet the ball travels until it reaches the peak height of the 6th bounce:

Total = 150 + (2 × sum of 1, 2, 3, 4 & 5th bounces) + 6th bounce

To find the sum, use the geometric sum formula:

\(S_n=\dfrac{a(1-r^n)}{1-r}\)

Therefore, the sum of the bounces 1 through 5 is:

\(\implies S_5=\dfrac{75(1-0.5^5)}{1-0.5}=145.3125\)

Height of the 6th bounce:

\(\implies a_6=75(0.5)^{6-1}=2.34375\)

\(\begin{aligned}\textsf{Total distance} & =150+2\left(\dfrac{75(1-0.5^5)}{1-0.5}\right)+75(0.5)^{6-1}\\ & = 150 + 2(145.3125)+2.34375\\ & = 150 + 290.625+2.34375\\ & =442.96875\: \sf ft \end{aligned}\)

The meaning of the statement is if you take n distinct numbers, x₁, ..., xₙ, and permute them in all possible ways, the number of different values that the function f(x₁, ..., xₙ) can take on will be a divisor of n!.

This assertion is a specific instance of a broader concept known as the Principle of Inclusion-Exclusion in the field of combinatorics. The Principle of Inclusion-Exclusion asserts that when dealing with a set comprising n elements and aiming to determine the number of possible subsets that can be selected, one can arrive at this figure by summing up the number of options for choosing 0, 1, 2, and up to n elements from the set.

Regarding the aforementioned assertion, the collection of components comprises every potential arrangement of the numerical values x₁, ..., xₙ. There is only one possible way to choose 0 elements, there are n options for choosing 1 element, selecting 2 elements can be done in n(n-1)/2 ways, and the pattern continues.

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Answer: The area is going to be 0.8

Step-by-step explanation:  The diameter is 1

You need the radius of the circle which is half the diameter. So the Radius(R) is 0.5.

After you find the radius of the circle to find the area of the circle you use the formula pie (R)^2. You are using 3.14

3.14(0.5)^2= 0.785

you then want to round your answer to the nearest tenth so the 8 turns the 7 into an 8.

So, the Area is 0.785 but after rounding it is 0.8.

Hope that helped :)

Answer:$1680

Step-by-step explanation:

48x$35=$1680

Answer:

The answer is D.21.

Step-by-step explanation:

You have to divide 14 by 2/3 and you get 21.

PLZ mark me Brainliest!

The scatterplot suggests the following types of data relationship: B. strong negative correlation.

In Mathematics and Statistics, a positive correlation is used to described a scenario in which two variables move in the same direction and are in tandem.

This ultimately implies that, a positive correlation exist when two variables have a linear relationship or are in direct proportion. Hence, when one variable increases, the other variable generally increases, as well.

By critically observing the scatterplot shown in the image attached above, we can reasonably infer and logically deduce that it represents a strong negative correlation because the data points increased from left to right and down to up respectively.

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Answer:

3x

Step-by-step explanation:

Answer:

$886.47

Step-by-step explanation:

The expected value for the amount of money made selling all of the candy in one bag is $15, and the standard deviation is approximately $24.33.

The standard deviation is a measurement of how widely apart a set of numbers or statistics are from their mean.

The expected value for the amount of money made selling all of the candy in one bag can be found by;

Expected value = mean number of candy bars per bag x price per candy bar

Expected value = 12 x $1.25 = $15

Formula for the standard deviation of a product of random variables:

\(SD (XY) = \sqrt{((SD(X)^2)(E(Y^2)) + (SD(Y)^2)(E(X^2)) + 2(Cov(X,Y))(E(X))(E(Y)))}\)

where X and Y are random variables, SD is the standard deviation, and Cov is the covariance.

X is the number of candy bars in a bag, which has a mean of 12 and a standard deviation of 2. Y is the price per candy bar, which is a constant $1.25. So we have:

E(Y²) = $1.25² = $1.5625

E(X²) = (SD(X)²) + (E(X)²) = 2² + 12² = 148

Cov (X,Y) = 0 (because X and Y are independent)

Using these values, we can calculate the standard deviation for the amount of money made selling all of the candy in one bag:

\(SD = sqrt((2^{2} )(148) + (0)(12)(1.25)^{2} + 2(0)(2)(12)(1.25))\)

SD = √(592)

SD ≈ $24.33

Therefore, the expected value for the amount of money made selling all of the candy in one bag is $15, and the standard deviation is approximately $24.33.

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Answer:

x=-3

Step-by-step explanation:

We move all terms to the left:

7+2x/3-(5)=0

We add all the numbers together, and all the variables

2x/3+2=0

We multiply all the terms by the denominator

2x+2*3=0

We add all the numbers together, and all the variables

2x+6=0

We move all terms containing x to the left, all other terms to the right

2x=-6

x=-6/2

x=-3

Answer:

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

10,-1

your welcome

thats the right answer

Answer:

  D, B, C; see attached

Step-by-step explanation:

You want to identify the transformations from Figure A to each of the other figures.

A translated figure has the same orientation (left-right, up-down) as the original figure. Figure D is a translation of Figure A. The arrow of translation joins corresponding points.

A figure reflected across a vertical line has left and right interchanged. Up and down remain unchanged. Figure B is a reflection of Figure A. The line of reflection is the perpendicular bisector of the segment joining corresponding points.

A rotated figure keeps the same clockwise/counterclockwise orientation, but has the angle of any line changed by the same amount relative to the axes. Figure C is a 180° rotation of Figure A. The center of rotation is the midpoint of the segment joining corresponding points. Unless the figures overlap, the center of rotation is always outside the figure.

__

Additional comment

The center of rotation is the coincident point of the perpendicular bisectors of the segments joining corresponding points on the figure. It will be an invariant point, so will only be on or in the figure of the figures touch or overlap. In the attachment, the center of rotation is shown as a purple dot.

Answer:

15 oz.

Step-by-step explanation:

Rounding to the nearest ounce:

14.853

Rounding notes:

If the number one place to the right of the rounding number is greater than 5, the number increases by 1.

If the number one place to the right of the rounding number is less than 5, the number stays the same and anything to the right of the rounding number changes to 0.

Work:

4 represents the 'ounces' place value.

To identify the rounding of 4, we need to determine if the value 8 is greater than 5, or less than 5.

8 > 5, meaning 4 increases to 5.

New rounded number = 15 oz.

Answer:

b

Step-by-step explanation:

IM DORA

Answer:

B      

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ur welcome ......

Step-by-step explanation:

Answer:

A. \(h(x)=\sqrt{x-3}\)

Step-by-step explanation:

The parent function of \(\sqrt{x}\) is translated to the left when \(h\) is positive in the transformation \(\sqrt{x+h}\).

If \(h\) is negative, the graph translates towards the left with the distance equal to the value of \(h\).

Here the graph moved 3 units towards the right. This means that \(h\) is negative and has the value of 3.

So, plugging that into the parent function for translation, the function becomes:

\(h(x)=\sqrt{x-3}\)

Answer:

2/15

Step-by-step explanation:

Answer:

2/15

Step-by-step explanation:

12 & 18 can be reduced to 2 & 3

25 & 5 can be reduced to 5 & 1

2/5 × 1/3 = 2/15

Answer:17

Step-by-step explanation:

DON'T TRUST ME

Answer:

B = 26.4

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp/ hyp

sin B = 4/9

Take the inverse sin of each side

sin ^-1 sin ( B) = sin ^-1 ( 4/9)

B = 26.38779996

B = 26.4

Answer:

\(26.4\º\)

Step-by-step explanation:

\(\theta=?\)

\($\sin(\theta)=\frac{opp}{hyp} = \frac{4}{9} $\)

\($\theta=\sin^{-1}\frac{4}{9} =\arcsin\frac{4}{9} \approx 26.4\º$\)

After 62.63 years Mr. Reihman's account outgrown Mr. Van Ausdall,

The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. A = P(1 + r/n)^nt, where P is the principal balance, r is the interest rate, n is the number of times interest is compounded annually, and t is the number of years, which is the formula for compound interest.

Given, Van Ausdall and Reihman both make the decision to start retirement funds.

Mr. Reihman contributes $10,000 at a constant rate of 7%, and

Mr. Van Ausdall contributes $35,000 at a continual rate of 5%.

Let "x" be the time when Mr. Reihman and Mr. Van Ausdall will have the same amount of money

From the general formula of continuous growth of the amount:

Amount = Principal amount*e^(rt)

Where r =rate of interest

t = time

At time x Mr. Reihman will have = 10,000*e^(7%*x)

At time x Mr. van will have =35,000* e^(5%*x)

Since at x, they both will have the same amount

thus,

10,000*e^(7%*x)  =3 5,000* e^(5%*x)

e^(7x/100 -5x/100) = 3.5

Taking natural logs on both the side

2x/100 = ln3.5

x = 50*ln 3.5

x = 62.63

Thus, after 62.63 years Mr. Reihman's account outgrown Mr. Van Ausdall,

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Complete question:

Reihman and Van Ausdall both decide to open retirement accounts. Mr. Van Ausdall puts in $35,000 with a continuous rate of 5% and Mr. Reihman puts in $10,000 with a continuous rate of 7%. After how much time will Mr. Reihman's account outgrow Mr. Van Ausdall? Solve algebraically and show all work.

Answer:

43.6 has 3 significant figures.

Answer:

Question 42

area of a triangle = 1/2 × base × height

Given:

Substituting given values into the formula:

⇒ 14 = 1/2 × x × (x + 3)

⇒ 28 = (x + 3)x

⇒ 28 = x² + 3x

⇒ x² + 3x - 28 = 0

⇒ (x - 4)(x + 7) = 0

⇒ x = 4, x = -7

As length is positive, x = 4 only.

⇒ height = 4 + 3 = 7 in

⇒ base = 4 in

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Question 43

volume of a cuboid = length x width x height

Given:

Substituting given values into the formula:

⇒ 72 = 6 × (2x - 5) × x

⇒ 12 = (2x - 5)x

⇒ 12 = 2x² - 5x

⇒ 2x² - 5x - 12 = 0

⇒ (x - 4)(2x + 3) = 0

⇒ x = 4, x = -1.5

As length is positive, x = 4 only.

⇒ height = 4 in

⇒ width = 2(4) - 5 = 3 in

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Question 44

Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

Substituting given values into the formula:

⇒ (x - 7)² + x² = 13²

⇒ x² - 14x + 49 + x² = 169

⇒ 2x² - 14x - 120 = 0

⇒ x² - 7x - 60 = 0

⇒ (x - 12)(x + 5) = 0

⇒ x = 12, x = -5

As length is positive, x = 12 only.

⇒ one leg = 12 m

⇒ other leg = 12 - 7 = 5 m

Answer:

x=18°

hope it helps.......

Answer:

x=15 degrees

hope it helps you

Answer:

divide 2320 by 1/2 and you will get your answer

Answer:

1160$

Step-by-step explanation:

1/2 of the regular price is the same as 1/2 of 2320. Since "of" means multiply, it's 1/2 x 2320, which is 1160.

Answer:

The correct function is

\(f(b) = {b}^{2} - 4\)

Step-by-step explanation:

√2x² + 7x +√2=0

2x + 7x + √ 2 =0

√2=9x

x = o.15713484