A solar panel has an area of x2 + 21x + 108. Find the possible dimensions of the solar panel.

Answer:

each of them need to save 24013813120321312331313131 cents

Step-by-step explanation:

The greatest common factor will be (x² – xy + y²).

This is a value or expression that can divide the given expressions without leaving a remainder.

Given the following expressions

x^3+^3 and x^2 - xy + y^2

Expand x^3+y^3

x^3+y^3 =(x + y)(x² – xy + y²).

Since (x² – xy + y²) is common to both expression, hence the greatest common factor will be (x² – xy + y²).

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Answer:

4x-8 = 4x+12

Step-by-step explanation:

you multiply everything in the parentheses by what is outside of it

4(x-2)                     = 2(2x+6)

4(x)=4x & 4(-2)=-8    2(2x)=4x & 2(6)=12 then write the numbers as an equation:

4x-8 = 4x+12

Answer:

Yes, since log(2) and log(5) both exist as valid values for the logarithm.

didnt check if ur equation is correct though

Answer:

\( f(x) = 4x^2 - 3x + 6 \)

Step-by-step explanation:

Quadratic function is given as \( f(x) = ax^2 + bx + c \)

Let's find a, b and c:

Substituting (0, 6):

\( 6 = a(0)^2 + b(0) + c \)

\( 6 = 0 + 0 + c \)

\( c = 6 \)

Now that we know the value of c, let's derive 2 system of equations we would use to solve for a and b simultaneously as follows.

Substituting (2, 16), and c = 6

\( f(x) = ax^2 + bx + c \)

\( 16 = a(2)^2 + b(2) + 6 \)

\( 16 = 4a + 2b + 6 \)

\( 16 - 6 = 4a + 2b + 6 - 6 \)

\( 10 = 4a + 2b \)

\( 10 = 2(2a + b) \)

\( \frac{10}{2} = \frac{2(2a + b)}{2} \)

\( 5 = 2a + b \)

\( 2a + b = 5 \) => (Equation 1)

Substituting (3, 33), and c = 6

\( f(x) = ax^2 + bx + x \)

\( 33 = a(3)^2 + b(3) + 6 \)

\( 33 = 9a + 3b + 6 \)

\( 33 - 6 = 9a + 3b + 6 - 6 \)

\( 27 = 9a + 3b \)

\( 27 = 3(3a + b) \)

\( \frac{27}{3} = \frac{3(3a + b)}{3} \)

\( 9 = 3a + b \)

\( 3a + b = 9 \) => (Equation 2)

Subtract equation 1 from equation 2 to solve simultaneously for a and b.

\( 3a + b = 9 \)

\( 2a + b = 5 \)

\( a = 4 \)

Replace a with 4 in equation 2.

\( 2a + b = 5 \)

\( 2(4) + b = 5 \)

\( 8 + b = 5 \)

\( 8 + b - 8 = 5 - 8 \)

\( b = -3 \)

The quadratic function that represents the given 3 points would be as follows:

\( f(x) = ax^2 + bx + c \)

\( f(x) = (4)x^2 + (-3)x + 6 \)

\( f(x) = 4x^2 - 3x + 6 \)

Answer:

finding the perimeter, you sumthe distance all round that is 7+7.5+17.8+6=38.3

38.3 is the perimeter

Answer:

The chances of drawing a heart are therefore 1352 (which reduces to 14 . If we draw another card without replacing the first card, what are the chances of drawing a second heart? There are now 12 hearts in the deck out of 51 cards total and so the odds are 1251 (which reduces to 417 ).

Step-by-step explanation:

So we know that in a 52 card deck, there are 13 hearts, so our probability of drawing a heart on the first try is 13/52.

Answer:

The second graph correctly displays the data shown in the frequency table. Hope this helps!

Answer:

\(\frac{x^3}{3}+2x^2 + K\\\\\)

Step-by-step explanation:

We can equate the expression x^2+4x to f(x) and specify the variable of integration , the integrand and the symbol simply like this ,

Let,

\(f(x)=x^2+4x\\\\F'(x)=f(x)\\\\\int f(x)\ dx=F(x) + K\)

Where the integrand is f(x) , x is the variable of integration , c is the constant of integration , and ∫ is the symbol of integration.

The derivate of what function is x^2 + 4x?

To find that out we integrate the function because Integrating a differentiate is the process of obtaining the original process because Integrals are also called as Anti-derivatives.

So,

\(\int\ x^2+4x \ dx\)

This is an indefinite integral which would result in an addition of a constant later on because it does not have limits. The variable of integration is x because there is only one variable present in this expression so naturally the variable of concern is x

so now we solve,

\(\int\ x^2+4x \ dx\\\\\frac{x^3}{3}+4(\frac{x^2}{2}) + K\\\\\frac{x^3}{3}+2x^2 + K\\\)

Where K is the constant of the indefinite integral.

Answer:

6

Step-by-step explanation:

You add 3 and 5 to get 8 and then you will subtract 2 from 8 to get 6

You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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Answer:

10.8°degrees

Step-by-step explanation:

please click the heart and rate excellent and brainleist to ❤☺️☻♨️♨️☻☺️❤

Collin's gross salary, after the 7% raise, for each 2-week pay period, will be approximately $1,159.17.

To calculate Collin's gross salary after the 7% raise for each 2-week pay period, we need to find the raise amount and add it to his current gross salary.

Collin's current gross salary is $1,083.34.

To find the raise amount, we multiply his current gross salary by 7% (or 0.07):

Raise amount = $1,083.34 \(\times\) 0.07

= $75.8338 (rounded to two decimal places)

Now, we add the raise amount to his current gross salary to find the new gross salary:

New gross salary = $1,083.34 + $75.8338 = $1,159.1738 (rounded to two decimal places)

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Answer:

Use Mathpapa to find your answer.

Step-by-step explanation:

It's a good, and powerful program.

Answer:

\(\frac{257357187500}{19683}\)

Step-by-step explanation:

We can convert these mixed fractions to ordinary fractions.

\(4(1/3)=\frac{(4*3)+1}{3}=\frac{13}{3}\)

\(3(1/3)=\frac{10}{3}\)

\(3(1/2)=\frac{7}{2}\)

\(9(3/4)=\frac{39}{4}\)

Then we have:

\(\frac{13}{3}*(\frac{10}{3}*\frac{7}{2})^{7}*\frac{4}{39}\)

\(\frac{257357187500}{19683}\)

I hope it helps you!

so lets start with making these equations

x + y = 43

x - y = 7

now we can rewrite the second equation in terms of x

x = 7 + y

now we plug that x value back into the first equation

7 + y + y = 43

7 + 2y = 43

2y = 36

y = 18

now we can plug the value of y into the rewritten second equation leaving us with

x = 7 + 18

x = 25

so y = 18 and x = 25

and the difference is 7

please give brainliest!

Answer: A=4800(.04)^14

Step-by-step explanation: solve

The Operating income is $172,500.

To calculate the margin of safety, contribution margin ratio, and operating income, we need to use the given information.

a. Margin of Safety:

Margin of Safety = Actual Sales - Break-even Sales

Given that the break-even point is at $750,000 in sales revenue and actual sales are $1,100,000, we can calculate the margin of safety:

Margin of Safety = $1,100,000 - $750,000 = $350,000

Therefore, the margin of safety is $350,000.

b. Margin of Safety as a Percentage of Sales:

Margin of Safety Percentage = (Margin of Safety / Actual Sales) * 100

Using the values from the previous calculations:

Margin of Safety Percentage = ($350,000 / $1,100,000) * 100 = 31.82%

Therefore, the margin of safety expressed as a percentage of sales is approximately 31.82%.

c. Contribution Margin Ratio:

Contribution Margin Ratio = (Contribution Margin / Sales) * 100

To calculate the contribution margin, we need to subtract variable costs from sales:

Contribution Margin = Sales - Variable Costs = $1,100,000 - $645,000 = $455,000

Using the values, we can calculate the contribution margin ratio:

Contribution Margin Ratio = ($455,000 / $1,100,000) * 100 = 41.36%

Therefore, the contribution margin ratio is approximately 41.36%.

d. Operating Income:

Operating Income = Sales - Variable Costs - Fixed Costs

Using the values provided:

Operating Income = $1,100,000 - $645,000 - $282,500 = $172,500

Therefore, the operating income is $172,500.

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Answer: See below

Step-by-step explanation:

The first is a beaker, it's used to measure liquid volume

The second is a ruler, it's used to measure length.

Last is a thermometer, it's used to measure temperature.

Answer:

$6.52

Step-by-step explanation:

Answer:

10 + 4i

Step-by-step explanation:

2 sqrt (25) + sqrt (-16) =

2 * 5     + 4i

10 + 4i

Answer:

\(10 + 4i\)

Step-by-step explanation:

Original Equation:

\(2\sqrt{25} + \sqrt{-16}\)

Simplify sqrt(25)

\(2*5+\sqrt{-16}\)

Simplify multiplication

\(10+\sqrt{-16}\)

Split the radical -16 into two, using the identity: \(\sqrt[n]{a} * \sqrt[n]{b} = \sqrt[n]{ab}\)

\(10 + \sqrt{-1}*\sqrt{16}\)

Simplify the sqrt(16) and sqrt(-1) using definition of an imaginary number

\(10 + 4i\)

Answer:

we are given A collector’s item is purchased for $150so, its value increases by 3% each yearso, t is time in yearsLet's assume cost of item after t years is C(t)so, we can use formula now, we can plug values so, equation is After doubling C(t)=2*150=300so, we can set C(t)=300and then we can solve for twe get so, doubling time is 23.44977 years

Answer:

B works ; it starts at 150, is positive, and slowly reaches 300

Step-by-step explanation:

Edge

Answer:

5 shipments had at least 10 broken tiles but less than 20 broken tiles.

Answer:

1,428 inches cubed

Step-by-step explanation:

This easy, to find a volume of a cube/rectangular prism you just do lengthxwidthxhight

12x7x17=1428

Answer:

\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)

Answer:

$67.50

Step by Step:

$45.00 divided by 6 = $7.50

$7.50 x 9 = $67.50

if the second number is lower than that's the answer. so in this case kayla

Answer:

P(A) = 0.57 (rounded to two decimal places).

Step-by-step explanation:

The probability of selecting a red marble from the hat can be found by dividing the number of red marbles by the total number of marbles:

P(red) = number of red marbles / total number of marbles

P(red) = 20/35

We can simplify this fraction by dividing both the numerator and denominator by 5:

P(red) = 4/7

So the probability of selecting a red marble from the hat is 4/7, or approximately 0.57 when rounded to two decimal places.

Therefore, P(A) = 0.57 (rounded to two decimal places).

The sets of angles one gets as one moves G are:

A triangle is known to be a kind of a polygon that is known to have three edges and also three vertices.

Note that the  it is said to be one of the main shapes in geometry as it is often shown as triangle ABC. Therefore, the  sets of angles one gets as one moves G are ∆EFD, GFD, GDE, etc.

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