What is 20% of 120?
Select one:

20

60

240

24

Percentile 15  

z-Score -1.036

The function f(x) = -4(x+2)² - 12 can be rewritten in the form

f(x) = -4x² - 16x - 28.

The concept used in this problem is expanding and simplifying an algebraic expression. We are given a quadratic function in a different form, and we need to rewrite it in standard form, which is in the form of f(x) = ax² + bx + c.

This involves expanding and simplifying the squared term and combining like terms. The process of expanding and simplifying an algebraic expression is a fundamental concept in algebra.

Here we have

f(x)= -4(x+2)²- 12      

To rewrite the function f(x) = -4(x+2)² - 12 in form f(x) = ax² + bx + c

Expand the squared term and simplify the expression.

The steps are as follows:

f(x) = -4(x+2)² - 12 (original function)

f(x) = -4(x² + 4x + 4) - 12 (expand the squared term)

f(x) = -4x² - 16x - 16 - 12 (distribute the -4)

f(x) = -4x² - 16x - 28 (combine like terms)

Therefore,

The function f(x) = -4(x+2)² - 12 can be rewritten in the form

f(x) = -4x² - 16x - 28.

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Answer:

48

Step-by-step explanation:

x/3 - 6 = 10

      +6   +6

x/3=16

16*3=48

Answer:

48

Step-by-step explanation:

Answer:

  81

Step-by-step explanation:

The relevant rules of exponents are ...

  (ab)^c = (a^c)(b^c)

  a^-b = 1/a^b

  (a^b)(a^c) = a^(b+c)

  (a^b)^c = a^(bc)

__

Applying these rules, we can simplify this expression as follows:

  \(\dfrac{(3x^{-4})^6}{9x^{-12}}=\dfrac{3^6}{9}x^{(-4)(6)-(-12)}=81x^0=\boxed{81}\)

_____

Additional comment

The rules of exponents derive from the fact that an exponent indicates repeated multiplication. That is, x·x·x = x³, where the exponent 3 indicates x is a factor 3 times. When this idea is used for division, we see the exponent is the difference between numerator and denominator exponents:

  (x·x·x)/(x·x) = x   or   x³/x² = x³⁻² = x¹ = x

This idea extends to cases where the denominator exponent is larger:

  (x·x)/(x·x·x) = 1/x   or   x²/x³ = x²⁻³ = x⁻¹ = 1/x

This can help you see that moving a factor from numerator to denominator (or vice versa) changes the sign of its exponent.

__

This idea of repeated multiplication also applies when exponents are layered:

  (x·x·x)(x·x·x) = (x³)² = x⁶ . . . . . the product exponent is the product of 3 and 2 as we indicated in the rules above

Answer:

The equation of the line in slope-intercept form is:

y = x + 4

Step-by-step explanation:

The slope-intercept form of the line equation

\(y = mx+b\)

where

Given the points on the line graph

Determining the slope between (0, 4) and (1, 5)

(x₁, y₁) = (0, 4)

(x₂, y₂) = (1, 5)

Using the formula

Slope = m =  [y₂ - y₁] /  [x₂ - x₁]

                =  [5 - 4] / [1 - 0]

                = 1 / 1  

               = 1

Thus, the slope of the line = m = 1

We know that the value of the y-intercept can be determined by setting x = 0 and determining the corresponding value of y.

From the graph, it is clear

at x = 0, y = 4

Thus, the y-intercept b = 4

now substituting b = 4 and m = 1 in the slope-intercept form

y = mx + b

y = (1)x + 4

y = x + 4

Therefore, the the equation of the line in slope-intercept form is:

y = x + 4

Answer:

c. Rational

because → whole numbers are positive and Starts from 0 so not whole number

Integers can be negative and positive

Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14, . 09, and 5,643.1.

Irrational number that cannot be written in p/q

but -2.4 written in p/q = -24/100

Step-by-step explanation:

c. Rational

-2.4 is a rational number

Answer:

The function g(x) is the derivative of the function sin(x). So, g(x) = cos(x).

Therefore, the instantaneous rate of change of g with respect to x at x = π/3 is cos(π/3), which is approximately equal to 0.5.

Step-by-step explanation:

np and pls mark brainlist:)

Answer:

656×1000

Step-by-step explanation:

Given the function, f(x) = 8x + 7:

Since it is a linear function, it doesn’t have any constraints or undefined points. Thus, the domain is all real numbers as x-values.

Domain:  interval notation: (-∞, ∞)

Set notation: {x | x ∈ R}

The same goes for the range: all real numbers are valid as outputs (y-values).

Range: interval notation: (-∞, ∞)

Set notation: {y | y ∈ R}

Please mark my answers as the Brainliest if you find my explanations helpful :)

Answer:

C and E

Step-by-step explanation:

23 > 16 and \(23\geq 16\) are both true statements since the quantity of 23 is greater than that of 16.

Answer:

the probability of rolling a 6 on one die is 1/6 or 16.7 %

the same could be said about rolling a 4 on a similar die.

Answer:

Explanation:

Here, we want to select ways of constructing a parallel line through a point

To do this, we can use the following methods:

a) We can construct two perpendicular lines to the given line, after which we can connect them using a straight line. The straight line would be parallel to the line passing through the original point

b) We can also create a perpendicular line to the original line, after which we can add a perpendicular line to the new perpendicular line created.

The new perpendicular line created will be parallel to the original line

Given parameters:

Terms of the sequence  = 7/8 , 3/4 , 9/14

From terms, we know that our first term is  \(\frac{7}{8}\)

We need find either of the common difference or the common ratio of this sequence.

For this, the common ratio is applicable.

  Common ratio  = \(\frac{3}{4} / \frac{7}{8}\)

 This is the factor by which when we multiply the subsequent terms with results into them;

     Solving the above gives \(\frac{6}{7}\)

The common ratio is 6/7.

To find the nth of this sequence we apply the formula below;

            A\(_{n}\)  = Arⁿ⁻¹

Aₙ is the term we are looking for

A is the first term of the sequence

r is the common ratio

n is the position of the term

  So for any nth term in this sequence;

         Aₙ   = \(\frac{7}{8}\) x \(\frac{6}{7}\) ⁿ⁻¹

We can use the above solution to find any term in the sequence.

The graph of g(x) is on the image at the end, and the correct option for the transformation is B.

We define a horizontal dilation of scale factor k as:

g(x) = f(k*x)

if k > 1, we have a stretch.

if  0 < k < 1, we have a shink of scale factor 1/k

Here we have:

g(x) = f (5x) = 5x - 4

We can notice that k = 5, then we have a stretch, thus, the correct option is B.

The graph of function g(x) can be seen in the image at the end.,

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Answer:

Equipamiento para 8 jugadores

Explanation:

Porque la diferencia de dinero no es muy grande ni muy pequeña, por lo que obtienes equipamiento para más jugadores a un buen precio.

Austin's rate of motion is (1/70)π Radians per second.

To determine Austin's rate of motion in radians per second, we need to use the formula for angular velocity:

ω = Δθ / Δt

Where:

ω = angular velocity (in radians per second)

Δθ = change in angular displacement (in radians)

Δt = change in time (in seconds)

We know that Austin runs three-quarters of a circular track, which means he covers an arc length that is equal to three-quarters of the circumference of the circle. Let's call the radius of the circle "r". Then, the arc length covered by Austin is given by:

s = (3/4) * 2πr

s = (3/2)πr

We also know that it takes Austin 1 minute and 45 seconds to cover this distance. This is the same as 105 seconds (since 1 minute = 60 seconds).

So, Δt = 105 seconds

Now, we can calculate the change in angular displacement (Δθ). The total angle around a circle is 2π radians, so the angle covered by Austin is given by:

Δθ = (3/4) * 2π

Δθ = (3/2)π

Therefore, Austin's rate of motion (ω) in radians per second is:

ω = Δθ / Δt

ω = [(3/2)π] / 105

ω = (3/210)π

ω = (1/70)π radians per second

So, Austin's rate of motion is (1/70)π radians per second.

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Answer:

x=4 and deviding by 8 by 2 and we get 4

Answer:

2.9

Step-by-step explanation:

You can find this answer two different ways.

First, you can turn the percent into a decimal, multiply the two numbers, and add them together. (0.16 * 2.5) and then (0.4 + 2.5)

Second, you could find the decimal and add it to 1.0 so you get 1.16 and multiply by 2.5. (1.16 * 2.5)

Answer:

sorry I dont know

Step-by-step explanation:

Answer:

J

Step-by-step explanation:

it is 6, 2 1/3(7/3), 2, 1/4, 0, -5

Answer:

J.

Step-by-step explanation:

Greatest to Least :

6 numbers, 3 different types.

We have negatives, positives, and fractions in this list.

So what would we need to do first is decrypt the fractions, so how many times does 7 go into 3? 2 times, and it would 1/3 left, making the improper fraction into 2 1/3

So we have the greatest, 6

Then with the next 2 1/3 (7/3)

Then with 2

Then with 1/4

Then with 0

And since negative number are below 0

-5 would be the least number

Answer:

9 laps takes 5 minutes 25 seconds.

Step-by-step explanation:

Here is given:

4 laps takes 6 minutes 12 seconds.

We have to find how long 1 lap takes.

4/4 6/4 12/4 --> 1 lap takes 2 minutes 33 seconds.

Now, multiply each by 9 because you want to find 9 laps, so:

1x9 2x9 33x9 --> 9 laps takes 5 minutes 25 seconds.

Hope this helps :)

Answer:

blue= x

pink=2x

green= 4x

orange=8

=

7x+8

Step-by-step explanation:

Answer:

20 blogs

Step-by-step explanation:

Step 1:  Determine the proportion of pop culture blogs:

First, we need to determine the proportion of pop culture blogs already written.  We can do this by dividing the number of pop culture blogs already written by the total number of blogs written:

The proportion of pop culture bloggers = Number of pop culture bloggers / Total number of bloggers

Proportion =  26 / (20 + 26 + 7 + 12)

Proportion = 26 / 65

Proportion = 0.4

Step 2:  Multiply the proportion of pop culture blogs by the number of upcoming blogs:

To determine the expected number of pop culture blogs that will be written given the data, we can multiply the proportion of pop culture blogs already written by the number of upcoming blogs:

Expected number of pop culture blogs = proportion of pop culture blogs *  number of upcoming blogs

Expected number = 0.4 * 50

Expected number = 20

Thus, you should expect 20 pop culture blogs to be written given the data.

The equation for w(width of rectangle) is: W = (P - 2L)/2

The correct answer is an option (c)

We know that the formula for the perimeter of the rectangle is:

P = 2L + 2W

where P is the perimeter of the rectangle,

L is the length of the rectangle,

and W is the width of the rectangle.

We need to rearrange this equation for w.

Consider equation,

P = 2L + 2W

P - 2L = 2L + 2W - 2L      ......(subtract 2L from each side of equation)

P - 2L = 2W

(P - 2L)/2 = 2W/2             .....(divide each side by 2)

W = (P - 2L)/2

Therefore, the correct answer is  W equals the quantity P minus 2 times L all over 2

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The complete question is:

Makayla is taking a math course and is working with the perimeter of rectangles. She knows the perimeter and length of her rectangle but wants to solve for the width. Rearrange the following equation for W, where P is the perimeter, L is the length, and W is the width of the rectangle. P = 2L + 2W.

a) W = 2P − 2L

b) W = P/ 2-2 times L

c) W equals the quantity P minus 2 times L all over 2

d) W = 2P + 2L

Answer:

c) W equals the quantity P minus 2 times L all over 2

Step-by-step explanation:i just took the test

Answer: -6a-15b+12y+6

Step-by-step explanation:

Answer:

It is 16

Step-by-step explanation:

Because 64÷4=16 80÷5=16 96÷6=16

So to find the constant of portionality you divide the second number by the first number.

Answer:its 16

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

r=10 and the angle bln 5√3 and -5 is 330 or 11π/6

Given statement solution is :- It takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

To determine the number of months it takes to pay off the credit card and the total amount paid, including interest, we can follow these steps:

Step 1: Calculate the monthly interest rate.

The APR (Annual Percentage Rate) is given as 9.5%. To find the monthly interest rate, we divide this by 12 (the number of months in a year):

Monthly interest rate = 9.5% / 12 = 0.0079167

Step 2: Determine the monthly payment.

The monthly payment is given as $400.

Step 3: Calculate the interest and principal paid each month.

The interest paid each month can be calculated by multiplying the monthly interest rate by the current balance.

Principal paid = Monthly payment - Interest paid

Step 4: Track the remaining balance each month.

Starting with the initial balance of $1,367.90, subtract the principal paid each month to determine the new balance.

Step 5: Repeat Steps 3 and 4 until the balance reaches zero.

Continue calculating the interest and principal paid each month, updating the balance, until the remaining balance becomes zero.

Step 6: Determine the total number of months and the total amount paid.

Count the number of months it takes to reach a balance of zero. Multiply the number of months by the monthly payment ($400) to find the total amount paid.

Let's calculate the number of months and the total amount paid, including interest:

Month 1:

Interest paid = 0.0079167 * $1,367.90 = $10.84

Principal paid = $400 - $10.84 = $389.16

New balance = $1,367.90 - $389.16 = $978.74

Month 2:

Interest paid = 0.0079167 * $978.74 = $7.75

Principal paid = $400 - $7.75 = $392.25

New balance = $978.74 - $392.25 = $586.49

Month 3:

Interest paid = 0.0079167 * $586.49 = $4.64

Principal paid = $400 - $4.64 = $395.36

New balance = $586.49 - $395.36 = $191.13

Month 4:

Interest paid = 0.0079167 * $191.13 = $1.51

Principal paid = $400 - $1.51 = $398.49

New balance = $191.13 - $398.49 = -$207.36 (Paid off)

It takes 4 months to pay off the credit card. Now, let's calculate the total amount paid, including interest:

Total amount paid = 4 * $400 = $1600

Therefore, it takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

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