Test Prep: Simplify −5 (7 + x) + 2 5/6x.

The graph that shows the horizontal compression is graph A.

For a function f(x), we define a horizontal compression of scale factor k as :

g(x) =f(x*k)

In this case, the function f(x) is graphed at the top, and we want to identify the graph of f(4*x).

So we have a compression of scale factor k = 4.

This only changes the values in the horizontal axis, and the vertical axis remains unchanged, so option D and C can be discarded.

Now, B is a dilation and A is a compression, so the correct option is graph A.

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Answer: To find the value of k(9), we need to substitute x=9 into the given function k(x):

k(9) = 2(9)² - 3√(9)

k(9) = 2(81) - 3(3)

k(9) = 162 - 9

k(9) = 153

Therefore, the value of k(9) is 153.

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Answer:

the answer to ur question is 6

Answer:

25

Step-by-step explanation:

Answer:

Step-by-step explanation:

In order to find a hole, you have to factor the denominator to see if it matches an expression in the numerator and can therefore be crossed out.

The factored form of the denominator is shown below:

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

Because the term x-1 is in both the numerator and the denominator, it is a hole, or removeable discontinuity. To find the hole, we plug in a 1 to the fraction that remains after we cancel the hole:

[tex]f(1)=\frac{1}{1-3}=-\frac{1}{2}[/tex]

The hole is found at (1, -1/2)

The option D "Both expressions should be evaluated by substituting any two values for x. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent." describes the correct method. So the option D is correct.

The substitution method is a method of solving a system of linear equations by expressing one variable in terms of the other and then substituting the expression into the other equation. This method can be used when the system of equations consists of two linear equations with two unknowns.

The elimination method is a technique used to solve systems of linear equations. It involves transforming the given system into an equivalent system of equations in which the coefficients of one of the variables are the same in each equation, and then eliminating that variable by addition or subtraction. So the option D is correct.

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Which describes the correct method?

A. Both expressions should be evaluated by substituting one value for x. If the final values of the expressions are both positive after the substitution, then the two expressions must be equivalent.

B. Both expressions should be evaluated by substituting with one value for x. If the final values of the expressions are the same, then the two expressions must be equivalent.

C. Both expressions should be evaluated by substituting any two values for x. If for each substituted value, the final values of the expressions are positive, then the two expressions must be equivalent.

D. Both expressions should be evaluated by substituting any two values for x. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent.

The value of h is 1.89. The solution involves setting up and solving an equation involving the probabilities of selecting a red or white present.

Santa Claus has a total of 3h+11 red presents and h+5 white presents in his stocking. If Ethan selects a present at random from the stocking, the probability of obtaining a red present is given as 19/26. Using this information, we can form an equation (3h+11)/(4h+16) = 19/26 and solve for h. Cross-multiplying and simplifying, we get 494h = 936, which leads to h = 1.89. Therefore, the value of h that satisfies the given conditions is approximately 1.89.

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Complete question:

Santa Claus has 3h+11 red presents and h+5 white presents in his stocking. Ethan selects a present at random from the stocking. Given that the probability that he obtains a red present is 19/26, find the value of h. ​

The complex zeros of the given polynomial function f(x) = x^4 + 170x^2 + 169 are [-i\sqrt{2}, i\sqrt{2}, -1, 1].

To find the complex zeros of the given polynomial function f(x) = x^4 + 170x^2 + 169, we can start by noting that this polynomial is a perfect square of a binomial. Specifically, we have:

f(x) = (x^2 + 13)^2

Therefore, the zeros of f(x) are the values of x that satisfy f(x) = 0. In other words, we need to solve the equation:

(x^2 + 13)^2 = 0

Taking the square root of both sides, we get:

x^2 + 13 = 0

Solving for x, we get:

x = ±i√13

However, we need to find the complex zeros of f(x), which are the roots of the equation f(x) = 0. Since f(x) = (x^2 + 13)^2, the zeros of f(x) are exactly the same as the zeros of x^2 + 13, namely ±i√13.

But this is not the end of the story. Since x^2 + 13 has only two distinct roots, namely ±i√13, each of these roots must occur with multiplicity 2 in f(x). This means that f(x) has a repeated root at each of the values ±i√13.

Finally, we note that x^2 + 13 can be factored as:

x^2 + 13 = (x + i√13)(x - i√13)

Therefore, we can write f(x) as:

f(x) = (x^2 + 13)^2 = (x + i√13)^2(x - i√13)^2

This gives us the factored form of f(x), and we can see that it has four roots, namely -i√13, i√13, -i√13, and i√13, which can be simplified to -i√2, i√2, -1, and 1.

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Answer:

Step-by-step explanation:

A. the rate of change is 50

Answer:

If 400 ml of squash is made by mixing 50 ml of cordial with water, then the remaining volume is water.

The volume of water used in making the squash = 400 ml - 50 ml = 350 ml

The fraction of the drink that is water is:

Water volume / Total volume = 350 ml / 400 ml = 7/8

Therefore, 7/8 of the drink is water.

Answer:

[tex]\frac{7}{8}[/tex]

Step-by-step explanation:

We know that 400ml squash = 50ml of Cordial With Water.

Therefore in 400ml of squash, amount of water will be 400ml - 50ml = 350ml of water.

In fraction form, this will be [tex]\frac{350}{400} =\frac{7}{8}[/tex]

Hope it helps

The trinomials that have (3x+2) as a factor are [tex]x^{2} 6x^2+19x+10, 6x^2-x-2\sqrt{x} \\\\[/tex]  , [tex]6x^2+7x-3, 6x^2-5x-6 and 12x^2-x-6.[/tex]

A trinomial is a polynomial with three terms. Each trinomial can be written in the form ax^2+bx+c, where a, b and c are constants, and x is a variable. If a trinomial has (3x+2) as a factor, then it can be written in the form (3x+2)(ax+b). By multiplying out this expression, we can obtain the trinomial ax^2+bx+c.

To find the trinomials that have (3x+2) as a factor, we need to solve the equation ax^2+bx+c = (3x+2)(ax+b). This can be done by equating coefficients of the same powers of x. For example, equating the coefficients of x^2 gives us the equation a = 3a. Since a cannot equal both 3a and 0, we must have a = 0. Similarly, equating the coefficients of x gives us the equation b = 3b+2a, so b = -2a. Finally, equating the constants gives us the equation c = 3b+2a, so c = 2a.

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The sale price of the laptop is $414 after the use of the coupon.

Answer:

$385.00

Step-by-step explanation:

Original Price - Discount = Sale price

Since the discount is 30%, we would multiply 0.30(550) to get the amount of the discount.

0.30(550) = 165

550 - 165 = $385

Answer:

The answer is D

Step-by-step explanation:

Answer: Let's start by representing the number of Blu-Ray discs sold as x.

According to the problem, the store sold 2/3 as many DVDs as Blu-Ray discs. So the number of DVDs sold is 2/3 of x, or (2/3)x.

We also know that the total number of DVDs and Blu-Ray discs sold was 280. So we can set up an equation:

(2/3)x + x = 280

To solve for x, we can simplify the equation by combining like terms:

(5/3)x = 280

Multiplying both sides by 3/5, we get:

x = 168

So the number of Blu-Ray discs sold was 168.

To find the number of DVDs sold, we can use the expression we derived earlier:

(2/3)x = (2/3) * 168 = 112

Therefore, the store sold 112 DVDs on that day.

Step-by-step explanation:

The polynomial function is V(x) = (30-2x)(20-2x)x and the volume of the pan is 864 cm^3.

The polynomial function

To find the volume of the pan, we first need to determine the dimensions of the base and height.

If we cut equal squares with sides of length x from the corners of a 30 cm by 20 cm piece of aluminum, then

Thus, the volume of the pan can be expressed as:

V(x) = (30-2x)(20-2x)x

The volume

Using the remainder theorem, we have

V(6) = (30 - 2 * 6)(20 - 2 * 6) * 6

Evaluate

V(6) = 864

Thus, when x = 6, the volume of the pan is:

V(6) = 864 cm^3.

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Answer:

The reduced answer is 1/4

The required form of a(x + b)² + c to rewrite the given expression y = 3x² − 4x + 2 is given by y = 3(x - (2/3))² + 4/3.

Expression is equal to,

y = 3x² − 4x + 2

Required form to express 'y' is equal to,

a(x + b)² + c

Complete the square by adding and subtracting the square of half the coefficient of the x-term we get,

y = 3x² - 4x + 2

⇒ y = 3(x² - (4/3)x) + 2

⇒ y = 3(x² - 2(2/3)x) + 2

⇒ y = 3(x² - (4/3)x + (2/3)² - (2/3)²) + 2

⇒ y = 3(x - (2/3))² - 3(2/3)² + 2

Simplify the constant terms we have,

⇒ y = 3(x - (2/3))² - 2/3 + 2

⇒ y = 3(x - (2/3))² + 4/3

Therefore, the expression y = 3x² − 4x + 2  written in the form a(x + b)² + c is equal to y = 3(x - (2/3))² + 4/3.

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The above question is incomplete, the complete question is :

Let the expression y = 3x² − 4x + 2. Write expression y in the form

a(x + b)² + c.

Answer:

B

Step-by-step explanation:

The answer is B because for the slope of the first part of the equation, it's 2/3 up 2 over 3. The starting point for that part of the equation is -2, so that's where your starting point is. For the second part of the equation, your starting point is on 1, and the slope is -5, so moving to the right 1 and down 5.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 6000\\ P=\textit{original amount deposited}\\ r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &10 \end{cases}[/tex]

[tex]6000 = P\left(1+\frac{0.12}{4}\right)^{4\cdot 10} \implies 6000=P1.03^{40} \\\\\\ \cfrac{6000}{1.03^{40}}=P\implies 1839.34\approx P[/tex]

The statement that is true about the boxplot is option (E) I, III, and IV

I. It is a left skewed distribution which has outliers.

True. The boxplot is skewed to the left, as the median line is closer to the bottom whisker than to the top whisker. Additionally, there are circles (outliers) on the left-hand side of the plot.

II. It is a symmetrical distribution which has outliers.

False. The plot is not symmetrical because the median line is not in the middle of the box.

III. The interquartile range is less than 1.

True. The box covers the range from the first quartile (Q1) to the third quartile (Q3), and the length of the box is less than 1.

IV. Approximately 75% of the observations have a GPA of less than 3.

True. The top of the box represents the 75th percentile, which is approximately 3.

Therefore, the correct option is (E) I, III, and IV

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The given question is incomplete, the complete question is:

Which statement is true about the boxplot below?

I. It is a left skewed distribution which has outliers.

II. It is a symmetrical distribution which has outliers.

III. The interquartile range is less than 1.

IV. Approximately 75% of the observations have a GPA of less than 3.

(A) I only

(B) II only

(C) II and III

(D) III and IV only

(E) I, III, and IV

Calvin's average score per game is 198.To find Calvin's average score per game, we need to divide the total points by the number of games played. Therefore, we can use the formula:

Average score per game = Total points / Number of games

Substituting the given values, we get:

Average score per game = 2,178 / 11

Simplifying the expression, we get:

Average score per game = 198

Therefore, Calvin's average score per game is 198. This means that over the course of 11 games, he scored an average of 198 points per game.

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The sample that has a greater mass is given as follows:

The sample of rock.

The sample of rock has a mass that is 5000 times the mass of the sample of dry sponge.

A number in scientific notation is given by the notation presented as follows:

[tex]a \times 10^b[/tex]

With the base being [tex]a \in [1, 10)[/tex], meaning that it can assume values from 1 to 10, with an open interval at 10 meaning that for 10 the number is written as 10 = 1 x 10¹, meaning that the base is 1, justifying the open interval at 10.

To obtain which amount is greater, we must verify the bases when the exponent is the same, hence:

Hence the rock has the greater mass, and the ratio is given as follows:

10/0.002 = 5000.

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Therefore , the solution of the given problem of area comes out to be the force of 60 kN applies 5 kN/m2 of pressure to a 12 m² is 5 kN/m².

Calculating how much room is needed to fully cover the outside will reveal its overall size. When calculating a trapezoidal shape's surface, the immediate environs are taken into account. The surface area of something determines its overall measurements. The internal water capability of a cuboid is given by the total of the borders connected to each of its six rectangular edges.

Here,

The following method determines the pressure P that a force F exerts on an area A:

=> P = F/A

Inputting the numbers provided yields:

=> P = 60 kN / 12 m²

If we simplify, we get:

=> P = 5 kN/m²

As a result, the force of 60 kN applies 5 kN/m2 of pressure to a 12 m² is 5 kN/m².

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The value 8 is the common difference of the given sequence.

A sequence is a list of objects where repeats are allowed and the order is important. It includes members, much like a set. The length of the sequence is measured by the total number of elements.

Given the sequence below

12, 20, 28, 36...

The nth term of an arithmetic sequence is given as Tn = a + (n-1)d

The common difference is the difference between the preceding and the succeeding term.

First term = 12

Second term = 20

Common difference = 20 -12 = 28 - 20

Common difference = 8

Hence the common difference of the sequence is 8

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Answer:

y=-27+3/5   or 138 or 5 if need as a fraction

Step-by-step explanation:

5(y+25)-(-13)=0

add all the numbers together and all the variables

5(y+25)+13=0

multiply parentheses to get

5y+125+13=0

add all the numbers together n all the variables together to

5y+138=0

Then  move all terms hat have  y to the left and terms to the right

so 125  basiclly

5y=-138

y=-138/5

y=-27+3/5  aslo could be known as  - 138 over 5 (fraction )

Answer:

m = - 6.5

Step-by-step explanation:

the remainder theorem states

if a function f(x) is divide by (x - a) then the remainder is equal to f(a)

given

p(x) is divided by (x - 2) then p(2) = 2 ( the remainder )

then

2[tex](2)^{4}[/tex] - 5(2)² + 2m + 3 = 2

2(16) - 5(4) + 2m + 3 = 2

32 - 20 + 2m + 3 = 2

15 + 2m = 2 ( subtract 15 from both sides )

2m = - 13 ( divide both sides by 2 )

m = - 6.5

Answer:

Step-by-step explanation:

The initial height is the beginning of the graph, or in this case, x=0. So the initial height is 1.5.

The 95% of the babies born to 22-year-old mothers will weigh between 3308.4 grams and 5665.6 grams.The correct answer is option C) (3051.25, 5408.49).

To get started, let's put the mother's age into the given equation to determine the mean birth weight. Then, we'll use the RMS value to calculate the standard deviation.The equation for predicting baby birth weight in grams given the mother's age is: Y = -1163.45 + 245.15XWhere X is the mother's age, and Y is the baby's birth weight. We are given X=22, so let's use that to find the predicted mean birth weight:Y = -1163.45 + 245.15(22) = 4486.95 gramsThe RMS is given to be 589.3 grams. Because we're told that the distribution is approximately normal, we can use the 68-95-99.7 rule to find the 95% prediction interval. Here are the steps:Subtract the RMS from the mean to find the lower endpoint of the interval:4486.95 - (2 x 589.3) = 3308.35Add the RMS to the mean to find the upper endpoint of the interval:4486.95 + (2 x 589.3) = 5665.55Round both values to four decimal places, as instructed in the problem:3308.35 rounds to 3308.4 grams5665.55 rounds to 5665.6 gramsTherefore, about 95% of the babies born to 22-year-old mothers will weigh between 3308.4 grams and 5665.6 grams.The correct answer is option C) (3051.25, 5408.49).

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Answer:

Step-by-step explanation:

56+ 66 = 122

12-16 = -4

80 + 42 + 32 = 154

36 - 46 = -10

96 - 86 - 42 = -32

74 - 92- 84 = -102

(In case you need the total answer of everything added up the answer is : 128 )

The probability of Jones being the author is 0.0275.

The new evidence updates the probability of Jones being the author from 1 in 4 to 0.0084. The probability of Smith being the author is 0.4.

To calculate the new probability, we need to use Bayes' theorem.

P(Jones|that) = P(that|Jones) x P(Jones) / (P(that|Jones) x P(Jones) + P(that|Smith) x P(Smith))

P(Jones|that) = 0.0084 x 0.25 / (0.0084 x 0.25 + 0.4 x 0.75)

P(Jones|that) = 0.0084 / (0.0084 + 0.3)

P(Jones|that) = 0.0084 / 0.3084

P(Jones|that) = 0.0275

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