to slove the equation below, you would x - 62 = 123

Answer:

\({ \tt{h(x) = 3(x + 1)(x + 3)(x - 4)}} \\ \\ { \tt{h(x) = 3 \{( {x}^{2} + 4x + 3)(x - 4) \} }} \\ \\ { \tt{h(x) = 3 \{ {(x}^{3} - {4x}^{2} + {4x}^{2} - 8x + 3x - 12) \} }} \\ \\ { \tt{h(x) = 3( {x}^{3} - 5x - 12) }} \\ \\ { \tt{h(x) = 3 {x}^{3} - 15x - 36 }}\)

Third degree polynomial with a constant of -36

Answer:

\(3x^3-39x-36\)

Step-by-step explanation:

\(\mathrm{Expand\:}\left(x+1\right)\left(x+3\right) $ by applying the FOIL method: $\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd$\)

\(\left(x+1\right)\left(x+3\right)=x^2+x\cdot \:3+1\cdot \:x+1\cdot \:3\)

\(=x^2+4x+3\)

\(\mathrm $Thus $ 3\left(x+1\right)\left(x+3\right)\left(x-4\right)\\\\=3\left(x^2+4x+3\right)\left(x-4\right)\\\\\)

\(= (3x^2 + 12x + 9)(x - 4)\)

\(= x(3x^2 + 12x + 9) -4 (3x^2 + 12x + 9)\\\\= 3x^3 + 12x^2 + 3x - 12x^2 - 48x - 36)\\\\= 3x^3 + (12x^2 - 12x^2) + (9x - 48x) -36\\\\= 3x^3-39x-36\)

Equate the factors of the polynomial equation to 0, to obtain the zeros of the equation.

For (x-6),

In polynomial equation the power of factor (x - 6) is 3. So multiplicity is 3.

For (x + 5),

The power of factor (x + 5) is 2, so multiplicity is 2.

For (x + 10),

The power of factor (x + 10) is 1, so multiplicity is 1.

For (x-23),

The power of factor (x - 23) is 3, so multiplicity is 3.

Answer:B.

Step-by-step explanation:

-16 is the least. It is behind zero. 3 is near zero but it is still greater. 47 is way past zero.

GCF is the greatest factor that divides the polynomial completely.

The given polynomial is,

Expand the polynomial.

Take the common factor of the terms outside.

The common factor outside of the brackest is the GCF.

Therefore, the GCF is,

Answer:

conceptual

Step-by-step explanation:

\(2x^{6}\) is the Simplify of the expression   2x² x x³

\(2x^{2} xx^{3} = 2x^{6}\)

what is simplify?

To simplify means to make anything basic or simpler, for example. a: to reduce to the bare minimum. b: to become simpler or broader in scope: It was advised to streamline management processes.

The fundamental guidelines and procedures to simplify any algebraic statement are as follows:

When you describe a complex mathematical idea to a child in words they can easily understand, you are simplifying. When you eliminate many of the tasks that were keeping you occupied and stressed out, you have simplified.

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Answer: 45

Step-by-step explanation:

The total profit in all was \(1040-900=\$ 140\).

The total profit per pizza was \((0.50)(8)=\$4\).

This means they sold \(\frac{140}{4}=35\) pizzas.

Adding this to the 10 pizzas held back, there were \(35+10=45\) pizzas in the original order.

Answer:

\(5x^4-\frac{25x^4}{x+8}+\frac{5x^5}{(x+8)^2}\)

Step-by-step explanation:

\(f(x)=x^5\\f'(x)=5x^4\\g(x)=1-\frac{5}{x+8}\\g'(x)=\frac{5}{(x+8)^2}\\\\\frac{d}{dx}f(x)g(x)\\\\=f'(x)g(x)+f(x)g'(x)\\\\=5x^4(1-\frac{5}{x+8})+x^5(\frac{5}{(x+8)^2})\\\\=5x^4-\frac{25x^4}{x+8}+\frac{5x^5}{(x+8)^2}\)

Answer:

\(m \angle AEB = m \angle ADB\)

Step-by-step explanation:

By the Inscribed Angle Theorem, since both angles have the same intercepted arc, they are congruent.

The value of the missing length to the nearest tenth are;

a. x = 7.5

b. x = 7.8

Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

Therefore ;

c² = a²+b²

a. x² = 9²-5²

x² = 81-25

x² = 56

x = √56

x = 7.5 ( nearest tenth)

b. using Pythagoras theorem also!

x² = 6²+5²

x² = 36+25

x² = 61

x = √61

x = 7.8( nearest tenth).

Therefore the value of the missing values are 7.5 and 7.8

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Answer: They resold them for $30 more than the original price.

Answer: 37.5%

Step-by-step explanation:

$80 - $50 = $30,

$30/$80 = 0.375 > 37.5%

The percentage of the distance Dominic is on the path is his distance

travelled as a fraction of the total distance when equivalent to 100.

The distance he has travelled on the path is 8.75 miles.

The given parameter are;

Length of Dominic's path = 12.5 miles

The length of the way Dominic is to the end = 70%

Required:

The distance Dominic has travelled on the path

The distance Dominic has travelled, D is 70% of 12.5 miles.

70% of 12.5 miles = 70% × 12.5 miles = 8.75 miles

The distance Dominic has travelled on the path, D = 8.75 miles

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Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

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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If a sum of $500 were shared among a group of people in the following ratios,

a) 6:4 then, 6x = 300 and 4x = 200.

b) 1:4:5 then, x = 50 , 4x = 200 and 5x = 250.

c) 1 : 8 : 1 then, x =50 , 8x = 400 and x = 50

d) 10 : 5: 4: 1 then, 10x = 250 , 5x = 125, 4x = 100, x = 25.

What is ratio?

a) 6:4

Let it be 6x , 4x

6x + 4x = 500

10x = 500

x = 50

Then, 6x = 300 and 4x = 200.

b) 1:4:5

Let be x, 4x, 5x

x + 4x + 5x = 500

10x = 500

x = 50.

Then x = 50 , 4x = 200 and 5x = 250.

c) 1 : 8 : 1

x + 8x + x =500

10x = 500

x = 50

Then, x =50 , 8x = 400 and x = 50

d) 10 : 5: 4: 1

10x + 5x + 4x + x = 500

20x = 500

x = 25

Then, 10x = 250 , 5x = 125, 4x = 100, x = 25.

Hence, If a sum of $500 were shared among a group of people in the following ratios,

a) 6:4 then, 6x = 300 and 4x = 200.

b) 1:4:5 then, x = 50 , 4x = 200 and 5x = 250.

c) 1 : 8 : 1 then, x =50 , 8x = 400 and x = 50

d) 10 : 5: 4: 1 then, 10x = 250 , 5x = 125, 4x = 100, x = 25.

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The nominal return on an investment doesn’t consider the effect of inflation on purchasing power. If the inflation rate is positive, the real return will be less than the nominal return on an investment.

What is inflation?

In simple words continuing to rise in general price is regarded as inflation. There is a different kind of inflation, for example; The increase in price due to an increase in the aggregate of goods and services compared to aggregate supply is called demand-pull inflation.

If the inflation rate is positive, the actual return will be less than the nominal return on investment.

Therefore, In order to complete the statement, The nominal return on an investment doesn’t consider the effect of inflation on purchasing power. If the inflation rate is positive, the real return will be less than the nominal return on an investment.

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Answer:

The REAL RETURN on an investment considers the effect of inflation on purchasing power. If the inflation rate is positive, the nominal return will be

GREATER THAN the real return on an investment.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: The answer to your question is C. Brainliest?

Step-by-step explanation:

For the first square, we can multiply both the numerator and denominator by 5 to get an equivalent fraction with a denominator of 60:

2/12 = (2 x 5) / (12 x 5) = 10/60

For the second square, we can multiply both the numerator and denominator by 4 to get an equivalent fraction with a denominator of 60:

2/15 = (2 x 4) / (15 x 4) = 8/60

Now, we can add the two fractions:

10/60 + 8/60 = 18/60

Simplifying this fraction by dividing both numerator and denominator by 6, we get:

18/60 = 3/10

Therefore, the total shaded area in the diagram is 3/10 or 0.3 in decimal form.

The answer is C. 0.3.

Answer:

○ \(\displaystyle y = 2x + 2\)

Step-by-step explanation:

Starting from the y-intercept of \(\displaystyle [0, 2],\)travel south two units, then west one unit to the endpoint AND x-intercept of \(\displaystyle [-1, 0].\)Doing so will give you the rate of change of 2:

\(\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{-2 ± 0}{0 - 1} = m \hookrightarrow \frac{-2}{-1} = m \\ \\ 2 = m\)

With all the above information, you arrive at the equation of the line.

I am joyous to assist you at any time.

Answer:

  x = 25

Step-by-step explanation:

You want to know the value of x when the sides of an equilateral triangle are labeled (4x -3), (3x -5), (2x +20).

The angle markings indicate the angles of the triangle all have the same measure. That means the side lengths all have the same measure. We can use that fact to equate expressions for side length:

  4x -30 = 3x -5

  x = 25 . . . . . . . . . add 30-3x to both sides

The value of x is 25.

__

Check

The side lengths are ...

They are all the same, as expected.

Answer:

2 Percent or %

Step-by-step explanation:

The decimal 0.02 would be equivalent to 2 percent, or 2 per hundred.

Answer:

0.02 is 2 percent as a percent

Answer:

The independent variable is b. The dependent variable is p. The equation that represents the relationship between the variable is b = 6p.

Step-by-step explanation:

If you read it carefully, it says that b is equal to 6 times p. Since p is time with 6 it is dependent and b is independent. Hope this helps, thank you :) !!

Thus, from the all given expressions, the number of servings Riley will ve using is 15/2 ÷  3/4.

Once kids have a firm grasp on proper fractions, they are introduced to mixed numbers and incorrect fractions. A mixed number combines an integer (whole number) and a fraction. It is also sometimes referred to as a mixed fraction (part of a whole number).

The composite number's fractional component needs to be a legal fraction (less than one whole). The numerator (top number) of a correct fraction is less than its denominator (bottom number),

Given data:

Convert the mixed fraction 7 1/2 in the proper fraction:

= 7 1/2

= (7*2 + 1)/2

= 15/2

Number of serving cups =  Total amount of salsa / Serving cup size

Number of serving cups =  15/2 ÷  3/4

Thus, from the all given expressions, the number of servings Riley will ve using is 15/2 ÷  3/4.

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Complete question:

Riley is dividing a batch of 7 1/2 cups of salsa into equal servings that are 3/4 cup each. Select all of the expressions that can be used to find the number of servings Riley will have.