Use the Distributive Property to write an equivalent 2(9 + 5k)

Equation 1:

f(x) = t

Equation 2:

f(y) = (2t)/3

Answer: do you have a picture

Step-by-step explanation:

Answer:

1) 17/20 2)24 and  1/2 3)terminating 4) 0.8 5)1.8

Step-by-step explanation:

4) 4/5 times both sides by 2 then you get 8/10= 0.8

Answer:

first is 17/20, second is 24 1/2 , third is a terminating decimal, fourth is 0.8, and the fifth is 8.1.

Step-by-step explanation:

hope this helps :)

The solution of the graphed system of equations y = -x² + x + 2 and y = -x + 3 is (1,2)

The system of equations is given as:

y = -x² + x + 2

y = -x + 3

From the graph in the complete question, we have the following point of intersection between the equations

(x,y) = (1,2)

The point of intersection between the equations is the solution

Hence, the solution of the graphed system of equations is (1,2)

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Answer:

(1,2)

Step-by-step explanation:

:)

The pandemic has had a significant impact on the family economy in Honduras, as it has created a series of economic challenges for many families.

Below are some of the more common impacts of the pandemic on the Honduran household economy:

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Answer as a mixed number:   13   19/60

=========================================================

Explanation:

I'll be using this formula

a & b/c = (a*c+b)/c

to convert from a mixed number to an improper fraction

a & b/c = (a*c + b)/c

2 & 5/6 = (2*6 + 5)/6

2 & 5/6 = (12 + 5)/6

2 & 5/6 = 17/6

Use similar steps to find that

4 & 7/10 = 47/10

-------------------------

The picture is 17/6 inches tall. The length is 47/10 times this height value.

length = (47/10)*(height)

length = (47/10)*(17/6)

length = (47*17)/(10*6)

length = 799/60

------------------------

Then let's convert that to a mixed number.

Use a calculator to get 799/60 = 13.31667 approximately.

The stuff to the left of the decimal is the whole part 13, aka the quotient.

The remainder is calculated like so:

remainder = numerator - quotient*denominator

remainder = 799 - 13*60

remainder = 19

Therefore, 799/60 = 13 remainder 19

In other words, 799/60 = 13 & 19/60 which is equivalent to writing 13   19/60

Answer:

Option B

Step-by-step explanation:

Well, now that I found out the prices per ounce, it has to be option B. Here is my reasoning:

Option A, when you do 2.98÷15.5, you get 0.19225...

Option B, is a different story. When you do the same process, it amazingly comes out to 0.1785...(this means that Option B is 0.2 cents (rounded) cheaper per unit, then Option A.

So its option B

Your welcome.

Possible Answer:

"Let us Judge not, that we be not judged" I belive it means to not judge others by there Race, Relgion, or Color.

Recall that when adding polynomials you need to combine "like terms" (that is the terms that contain the SAME VAriable (letter) part.

Then in the addition:

(x + 2 y - 4 z) + ( x - 4 y + 6 z)

we combine:

x + x = 2 x

2 y - 4 y = - 2 y

and

- 4 z +6 z = 2 z

obtaining finally:

2 x - 2 y + 2 z

Answer:

x=-3

y=-4

Step-by-step explanation:

Given:

y=x-1

4x+8=y

Plug in the 1st equation into the 2nd equation

4x+8=x-1

subtract x from both sides

3x+8=-1

subtract 8 from both sides

3x=-9

divide both sides by 3

x=-3

Now that we have the x value, plug it into the first equation:

y=-3-1

simplify

y=-4

So, x=-3, and y=-4.

Hope this helps! :)

Answer:

D

Step-by-step explanation:

\(2x^2+2x+12=3x^2-x+2\\2x+12=x^2-x+2\\x^2-3x-10=0\\(x-5)(x+2)=0\\x=5, -2\)

The correct answer is choice D. Hope this helps!

Answer:

{-5, 2}

Step-by-step explanation:

  \(2x^{2} + 2x + 12 = 3x^{2} -x + 2\)    move everything to the right side

\(-2x^{2} -2x-12=-2x^{2} -2x-12\)  add line 1 and 2 to get the below equation

                      \(0 = x^{2} -3x -10\)   find multiples of -10 that add to give you -3

                                                    to get -10 we have to have (+)(-)

                                                           {-5, 2}

The average rate of change between 3 to 6 storms is 0.09.

Given

The price of bread has been increasing over the last month.

Brian believes there is a positive correlation between the number of predicted storms and the price of bread.

Number of Storms Predicted Bread Price;

1  $2.30

3  $2.41

4  $2.50

6  $2.68

7  $2.81

The formula to calculate the average rate of change between two values is as follows;

\(\rm Average \ rate = \dfrac{f(x_2) -f(x_1)}{x_2-x_1}\)

Therefore,

The average rate of change between 3 to 6 storms is;

\(\rm Average \ rate = \dfrac{f(x_2) -f(x_1)}{x_2-x_1}\\\\\rm Average \ rate = \dfarc{2.68-2.41}{6-3}\\\\\rm Average \ rate = \dfrac{0.27}{3}\\\\\rm Average \ rate = 0.09\)

Hence, the average rate of change between 3 to 6 storms is 0.09.

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Answer:

Area of room = 21 * 16

= 336 m²

Area of Carpet = (21 - 1)* (16-1)

= 20*15

= 300

Area of border = Area of room - Area of carpet

= 336 - 300

(a) To find the probability that 20 paperback books will fit on a 36 cm shelf, we need to calculate the probability that the total thickness of the books is less than or equal to 36 cm.

Let X be the total thickness of 20 paperback books. Since the thickness of each book is normally distributed with mean 1.9 cm and variance 0.90^2 cm, the sum of the thicknesses of 20 books will also follow a normal distribution. The mean of the sum is 20 * 1.9 cm and the variance is 20 * (0.90^2 cm)^2.

Using the properties of the normal distribution, we can standardize the problem by calculating the z-score:

z = (36 - 20 * 1.9) / sqrt(20 * (0.90^2))

We can then look up the probability associated with this z-score using a standard normal distribution table or calculator.

(b) Similarly, to find the probability that 8 paperback books and 8 hardback books will fit on a 36 cm shelf, we need to calculate the probability that the total thickness of these books is less than or equal to 36 cm.

Let X be the total thickness of 8 paperback books and Y be the total thickness of 8 hardback books. Since both X and Y follow normal distributions with their respective means, variances, and known quantities, we can calculate the sum of X and Y and use the z-score method to find the probability.

(c) To determine the smallest length of shelving so that 16 hardback books have at least a 99% chance to fit, we need to find the length that corresponds to the 99th percentile of the distribution of the total thickness of 16 hardback books. Using the mean and variance given for the hardback books, we can calculate the z-score associated with the 99th percentile and then convert it back to the length using the mean and standard deviation.

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Multiplying x by any positive number smaller than 1 will result in some smaller value.

For example, if the scale factor is k = 0.5, then we can think of this as the fraction k = 1/2. Multiplying by 1/2 will make any number smaller, namely, exactly half as much.

We are taking a fractional part of the original number, so its expected the result is smaller. It's like having a whole cake and we only take slices of that cake to end up with the new value. There's no way having one or more slice be larger than the original whole amount.

Because things are getting smaller, we call this type of dilation to be a reduction or we can call it shrinking. This is in contrast to an enlargement when k > 1.

-----------------------------------------

More info (optional section)

Claim:  For some positive number k such that k < 1, we have xk < x when x is positive.

The proof of this claim is fairly straight forward.

We multiply both sides of k < 1 by x to get

k < 1

x*k < x*1

xk < x

The inequality sign does not flip because we're multiplying both sides by a positive number x.

So because xk < x, this shows that the original value x gets smaller to xk when we apply the positive scale factor k such that k < 1. This is the same as saying 0 < k < 1. Furthermore, xk < x is the same as 0 < xk < x.

Answer:

D. Each segment of the electorate provides significant support to Mr Quintana

Step-by-step explanation:

From the question, we have the following logic statement;

If those segment that provide significant support to Ms Puerto also provide support to Mr. Quintana then no segment of the electorate that provides significant support to Mr. Quintana provides significant support to Mr. Ramirez

Counter to the If Then Logic structure

At least one segment of the lectorate provides significant support to Mr. Quintana and Mr. Ramirez

Therefore, there is at least one segment that provides support to Mr. Quintana but not to Ms. Puerta

The segments that provide support to Ms. Puerta do not provide support to Mr. Ramirez

Mr. Quintana's support includes those from the supporters of Ms. Puerta and those from the supporters of Mr. Ramirez

Therefore, each segment of the electorate provide significant support to Mr. Quintana.

The equation that models this scenario is: \(c(x) = -2x^2 + 16x + 168\).

Given:

Average number of students per session = 14

Fee per session = $12

For every $2 increase in the fee.

Let x be the number of $2 fee increases.

So, the fee for each session is $12 + ($2 x) as there is a $2 increase for each x.

and, the average reduces by 1 for each $2 increase then the average number of students per session is 14 - x.

Now, the revenue generated

\({\text} Revenue (c(x)) =\) \({\text} Fee per session * Average number of students per session\)

Substituting the values of fee per session = 12 + 2x and Average= 14- x into above formula as:

\(c(x) = (12 + (2 x)) * (14 - x)\)

Expanding and simplifying the equation:

\(c(x) = (12 + 2x) * (14 - x)\)

\(c(x) = 168 - 12x + 28x - 2x^2\)

\(c(x) = -2x^2 + 16x + 168\)

Therefore, the equation is: \(c(x) = -2x^2 + 16x + 168\)

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Th question attached here seems to be incomplete, the complete question is:

Type the correct answer in each blank. Use numerals instead of words. If necessary, use / for the fraction bar(s). John hosts an art workshop on the weekends. He has an average of 14 students in each session and charges a fee of $12 per session. He estimates that for every $2 increases in the fee, the average number of students reduces by 1. Complete the equation that models this scenario, where c(x) is the revenue generated and x is the number of $2 fee increases.

c(x) =_x^2 +_x+_

Answer:

Step-by-step explanation:

its correct [hope this helped]

Answer:

26 miles

Step-by-step explanation:

use pythagorean theorem to find that from post office to stevie's is 10 miles long( 6^2 + 8^2=100, and the square root of 100 is 10) then add the total distence together and get 8+8+10=26

The speed of the airplane in still air is 120 mph and the speed of the wind is 30 mph.

Let's assume the speed of the airplane in still air is represented by "A" and the speed of the wind is represented by "W."

On the trip from Thousand Oaks to Tijuana (against the headwind), the effective speed of the airplane will be reduced by the speed of the wind, so the equation can be written as:

180 miles = (A - W) * 2 hours

On the return trip from Tijuana to Thousand Oaks (with the tailwind), the effective speed of the airplane will be increased by the speed of the wind, so the equation can be written as:

180 miles = (A + W) * 1.2 hours

Now we have a system of two equations with two unknowns (A and W). Let's solve it:

From the first equation: 180 = 2(A - W)

Simplifying: A - W = 90    (Equation 1)

From the second equation: 180 = 1.2(A + W)

Simplifying: A + W = 150   (Equation 2)

Now, we can solve this system of equations by either substitution or addition/elimination method.

Using the addition/elimination method:

Add Equation 1 and Equation 2:

(A - W) + (A + W) = 90 + 150

2A = 240

A = 120

Substitute the value of A into Equation 1:

120 - W = 90

W = 120 - 90

W = 30

Therefore, the speed of the airplane in still air is 120 mph and the speed of the wind is 30 mph.

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the highest possible number of components that would manufacture them the most efficiently  =  33%

The correct option is C.

What is percentage?

a percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. percentage.

According to the given information:

the 50 electronics components that a factory must manufacture.

70 percent would be most efficiently manufactured by Machine A

30 percent would be most efficiently manufactured by Machine B,

If 36 percent of the components were manufactured by Machine A

the highest possible number of components that would manufacture them the most efficiently =

we know that :

A can manufacture:

50*70% = 35 components efficiently

B can manufacture:

50*30% = 15 components efficiently;

now :

A actually manufactured:

50*36% = 18 components (so all efficiently, since 35>18);

B actually manufactured:

50-18 = 32 components, out of which 15 were manufacture efficiently;

so,

the highest possible number of components that would manufacture them the most efficiently = 18 + 15

                                          =  33

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I understand that the question you are looking for is :

Of the 50 electronics components that a factory must manufacture, 70 percent would be most e¢ ciently manufactured by Machine A and the remaining 30 percent would be most efficiently manufactured by Machine B, though either machine could manufacture any of the 50 components. If 36 percent of the components were manufactured by Machine A and the remainder were manufactured by Machine B, what is thehighest possible number of components that were manufactured by the machine that would manufacture them the most efficiently?

(A) 30

(B) 32

(C) 33

(D) 35

(E) 36

Let it be:

• x: The larger number.

• y: The smaller number.

Then, we can write the following system of equations:

To solve the system of equations, we can use the elimination method.

Step 1: Multiply by -3 the Equation 1.

Step 2: We add both equations.

Step 3: We solve the resultant equation.

Step 4: We replace the value of y in any of the initial equations. For example, in Equation 1. Then, we solve for x.

Therefore, the larger number is 16, and the smaller number is -14.

Answer: C

Step-by-step explanation:

The solution is Option A.

The value of the equation is 6x³ - 12x² - 48x is A = 6x ( x + 2 ) ( x - 4 )

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = 6x³ - 12x² - 48x   be equation (1)

On simplifying the equation , we get

Taking 6x as the common factor , we get

A = 6x ( x² - 2x - 8 )

On simplifying the equation , we get

A = 6x ( x + 2 ) ( x - 4 )

Therefore , the value of A is 6x ( x + 2 ) ( x - 4 )

Hence , the equation is 6x ( x + 2 ) ( x - 4 )

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To find where the function f(x) = 3x^4 - 12x^3 - 108x^2 + 9 is increasing and decreasing, we need to determine the intervals for which the first derivative, f'(x), is positive or negative.

First, find the first derivative of f(x):
f'(x) = 12x^3 - 36x^2 - 216x

Now, to find the critical points, set f'(x) = 0 and solve for x:
12x^3 - 36x^2 - 216x = 0

Factor out the common factor, 12x:
12x(x^2 - 3x - 18) = 0

Solve the quadratic equation for x:
x^2 - 3x - 18 = 0
(x - 6)(x + 3) = 0

The critical points are x = 0, x = 6, and x = -3.

Now, test intervals around these critical points to determine where f'(x) is positive (increasing) or negative (decreasing).

Choose test points: x = -4, x = -2, x = 3, and x = 7.

f'(-4) = 12(-4)^3 - 36(-4)^2 - 216(-4) > 0 (positive, so increasing)

f'(-2) = 12(-2)^3 - 36(-2)^2 - 216(-2) < 0 (negative, so decreasing)

f'(3) = 12(3)^3 - 36(3)^2 - 216(3) > 0 (positive, so increasing)

f'(7) = 12(7)^3 - 36(7)^2 - 216(7) < 0 (negative, so decreasing)

So, the function is increasing on the intervals (-∞, -3) and (0, 6), and decreasing on the intervals (-3, 0) and (6, ∞).

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The average velocity from t = 2s to t = 4s would be - 48 ft/s.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that an object is thrown upward with initial velocity of 48 feet per second from a high of 120 feet. The height of the object t seconds after it is thrown is given by h(t) = - 16t² + 48t + 120.

Average rate of change of velocity with time is called average velocity. Mathematically -

v{avg.} = Δx/Δt                                                         .... Eq { 1 }

Δx = x(4) - x(2)

Δx = - 16(4)² + 48(4) + 120 - {- 16(2)² + 48(2) + 120}

Δx = - 96

Δt = 4 - 2 = 2

So -

v{avg.} = Δx/Δt = -96/2 = - 48 ft/s

Therefore, the average velocity from t = 2s to t = 4s would be - 48 ft/s.

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Bill has a total of 3 one-piece jumpsuits, 5 pairs of work pants, and 8 work shirts. To find the number of possible outfits he can wear to work, we can use the multiplication principle.

First, we need to determine how many choices Bill has for his top and bottom. He can either wear a jumpsuit or a combination of pants and a shirt. Therefore, he has 3 + (5 x 8) = 43 choices for his top and bottom.

Next, we can use the multiplication principle to determine the total number of possible outfits he can wear. Since he has 43 choices for his top and bottom, and each outfit combination is independent of the others, we can multiply the number of choices for his top and bottom by the number of one-piece jumpsuits he has.

Therefore, Bill has a total of 43 x 3 = 129 possible outfits he can wear to work.

In summary, Bill has 3 one-piece jumpsuits, 5 pairs of work pants, and 8 work shirts. He can wear either a jumpsuit or pants and a shirt to work. Using the multiplication principle, we determined that he has a total of 129 possible outfits he can wear.

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To prove the properties of the projection matrix, we'll assume that p is the projection matrix corresponding to a subspace S of \(R^{m}\).

(a) p² = p

To show that p² = p, we need to demonstrate that applying the projection matrix p twice is equivalent to applying it once.

Let's consider an arbitrary vector x in \(R^{m}\). Applying the projection matrix p to x yields its projection onto the subspace S:

p(x) = projection of x onto S

Now, if we apply the projection matrix p again to p(x), we have:

p(p(x)) = projection of p(x) onto S

Since p(x) is already the projection of x onto S, applying the projection matrix p once more won't change the result. Hence, we can write:

p(p(x)) = p(x)

This equation holds for any vector x in \(R^{m}\), meaning that p² = p.

(b) \(p^{T}\) = p

To prove that \(p^{T}\) = p, we need to show that the transpose of the projection matrix p is equal to p.

Let's consider an arbitrary vector x in \(R^{m}\). Applying the projection matrix p to x yields its projection onto the subspace S:

p(x) = projection of x onto S

Now, let's compute the transpose of p(x):

\((p(x))^{T}\) = \((projection of x onto S)^T\)

The transpose of a projection onto a subspace doesn't change the result because it only affects the column vectors of the projection matrix. The transpose of p(x) is still the projection of x onto S. Hence, we can write:

\((p(x))^T\) = p(x)

Since this equation holds for any vector x in \(R^{m}\), we can conclude that \(p^T\) = p.

Therefore, we have shown that (a) p² = p and (b) \(p^T\) = p, proving the properties of the projection matrix corresponding to a subspace S of \(R^{m}\).

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Answer:

9i + 2

Step-by-step explanation:

3 + 4i - 1 + 5i

=> 3 - 1 + 4i + 5i

=> 2 + 9i

=> 9i + 2

Answer:

9i + 2

Brainliest, please!

Step-by-step explanation:

(3 + 4i) - (1 - 5i)

3 + 4i - 1 + 5i

9i + 2

The description that accurately explains how a fair decision can be made in this situation is:

"If the product of the spins is 2, pale lilac will be used. If the product is 4, mellow sage will be used. If the product is 12, seafoam blue will be used. If the product is 1, 6, or 36, totally taupe will be used."

Decision-making based on random outcomes refers to a process where choices or actions are determined by the result of a random event or chance. This approach is often used in situations where there is uncertainty or when all available options are perceived to have similar values or consequences.

The decision on which paint color to use is based on the product of the outcomes from spinning the spinner twice. Each outcome corresponds to a specific number on the spinner. By multiplying the two outcomes together, we obtain the product.

According to the given description, specific products are associated with each paint color. For example, if the product of the spins is 2, the color pale lilac will be used. If the product is 4, mellow sage will be used. If the product is 12, seafoam blue will be used. And if the product is 1, 6, or 36, totally taupe will be used.

This approach ensures a fair decision-making process based on the random outcomes of spinning the spinner.

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