what's the numerator for the following rational expression?
2/f + 5/f = ?/f

To make five loaves of bread, Alani will use 3 3/4 cups of pineapple juice, calculated by multiplying the amount required for one loaf, which is 3/4 cup, by five.

To solve this, you multiply the amount of pineapple juice needed for one bread by the total number of breads.

Multiply the amount of juice for one bread by the number of breads: 3/4 cup × 5 = 15/4 cups.

Convert the improper fraction to a mixed number: 15/4 cups is equal to 3 3/4 cups.

Therefore, Alani will use 3 3/4 cups of pineapple juice to make five loaves of bread.

Answer:

I believe the answer is "A circle is a set of all points in a plane that are the same distance from a fixed point called the center." I am 95% sure but please correct me if I am wrong. Hope this possibly helps someone!

Step-by-step explanation:

The volume of a prism is calculated by multiplying the area of the base with the height of the prism. The correct answer is D. The area of the base times the height of the prism.

The volume of a prism is calculated by multiplying the area of the base with the height of the prism. This means that out of the four options provided, the correct choice would be: D. The area of the base times the height of the prism.

For instance, if the area of the base of a rectangular prism is 30 square units and the height of that prism is 10 units, then the volume would be calculated as 30 (area of the base) * 10 (height of the prism) = 300 cubic units. Always remember that the volume of a 3D solid is expressed in cubic units.

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The solution is 2 glasses

The number of 1/4 quart-sized glasses to fill the lemonade is given by the equation A = 2 glasses

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 number of 1/4 quart-sized glasses to fill the lemonade be A

Now , the equation will be

The amount of lemonades = 1/2 quart of lemonade

The size of the glasses = 1/4 quart-sized glasses

So , the equation will be

A x 1/4 quart-sized glasses =  1/2 quart of lemonade  

On simplifying the equation , we get

A / 4 = 1/2

Multiply by 4 on both sides of the equation , we get

A = ( 1/2 ) x 4

A = 2 glasses

Therefore , the value of A is 2 glasses

Hence , the number of glasses is 2

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To express the integral from 0 to 3 of the function  as the limit of a Riemann sum, divide the interval into [tex]f(x) = x^3 - 6x[/tex] subintervals of equal width, find a Riemann sum, and then take the limit as n approaches infinity.

To express the given integral as the limit of a Riemann sum without evaluating, we represent the integral of the function [tex]f(x) = x^3 - 6x[/tex]split the interval [0,3] into n equal subintervals, each of width Δx = 3/n. Then we choose sample points x_i in each subinterval [x_{i-1}, x_i]. The Riemann sum is thus [tex]R = Σ(x_i^3 - 6x_i)Δx[/tex]en from i=1 to n and x_i is any point in the ith subinterval.

As n approaches infinity, which is equivalent to Δx approaching zero, the Riemann sums converge to the integral. The limit of the Riemann sum is then represented as lim_{n to ∞} R, which gives the exact area under the curve f(x) between 0 and 3, but we are not evaluating this limit.

Expression used represents the given paid installment for [tex]12[/tex] months is equal to [tex]S_{12} =\frac{ 75(1-1.06^{12}) }{1-1.06}[/tex].

" Expression is defined as the equation representing the relation between the numbers or the variables using mathematical operation."

Formula used

Geometric progression,

[tex]S_{n} = \frac{a(1-r^{n}) }{1-r}[/tex]

[tex]a=[/tex] first term

[tex]r=[/tex] common ratio

[tex]n=[/tex] number of terms

According to the question,

Given,

Amount to be paid first month [tex]'a' = \$75[/tex]

Increases by [tex]6\%[/tex] each month

Therefore,

Common ratio [tex]'r' = 1 + \frac{6}{100}[/tex]

                             [tex]= 1.06[/tex]

Number of months [tex]'n'= 12[/tex]

Substitute the value in the formula to get the expression for the given condition,

Required expression,

[tex]S_{12} =\frac{ 75(1-1.06^{12}) }{1-1.06}[/tex]

Hence, expression used represents the given paid installment for [tex]12[/tex] months is equal to [tex]S_{12} =\frac{ 75(1-1.06^{12}) }{1-1.06}[/tex].

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Final answer:

Gabriela's current age is found by setting up algebraic equations based on the information that Kevin is twice as old as Gabriela now, and was six times as old 12 years ago. Solving the equations, we find that Gabriela is 15 years old.

Explanation:

Finding Gabriela's Current Age:

The problem statement tells us that Kevin is currently 2 times as old as Gabriela and that 12 years ago, Kevin was 6 times as old as Gabriela. To solve for Gabriela's current age, let us use algebra. Let's denote Gabriela's current age as G and Kevin's current age as K. The given information can be translated into the following two equations:

Substituting the first equation into the second, we get:

2G - 12 = 6(G - 12)

Expanding both sides:

2G - 12 = 6G - 72

Moving all terms involving G to one side and constant terms to the other side, we get:

2G - 6G = -72 + 12

-4G = -60

Dividing both sides by -4 to solve for G:

G = 15

So, Gabriela is currently 15 years old.

The total dollar amount he must sell to make that in commission each month is $150000.

In mathematics →

Given is that a car salesman earns 2% commission on all of his sales. He needs to make $3,000 a month for his living expenses,

Assume that the total dollar amount he must sell to make that in commission each month is ${x}. Then, we can write -

3000 = 2% of {x}

3000 = (2/100) × {x}

{x} = (3000 x 100)/2

{x] = 300000/2

{x} = 150000

Therefore, the total dollar amount he must sell to make that in commission each month is $150000.

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Answer:

14.75

Step-by-step explanation:

65.5/2 = 32.75.

32.75 - 18 = 14.75

thats your answer. hope it helps

Answer:

Hello! The correct answer is 298.7 [tex]cm^{2}[/tex]

Step-by-step explanation:

I am just confirming!

Final answer:

Using the formula for a fixed-rate mortgage payment, the monthly mortgage payment for Nick's parents, who bought a home for $125,000 with a 30-year mortgage at 19.5%, is calculated to be $2,037.40, making the answer A. $2,037.40.

Explanation:

To calculate the monthly mortgage payment for Nick's parents, who purchased their first home with a 30-year mortgage at 19.5% interest, we need to use the formula for a fixed-rate mortgage payment. The formula is:

M = P[r(1+r)ⁿ]/[(1+r)ⁿ⁻¹]

Where:

For this calculation:

We insert these numbers into our formula:

M = $125,000[0.195/12(1+0.195/12)³⁶⁰]/[(1+0.195/12)³⁶⁰⁻¹]

After calculating, we find that the monthly mortgage payment (rounded to two decimal places) would be $2,037.40.

Therefore, the answer is A. $2,037.40.

Answer:

system 2 and system 3 have the same solution.

Step-by-step explanation:

system 1:

[tex]4x-5y=2[/tex]

[tex]3x-y=4[/tex]

we'll solve the two equation by the method of elimintaion to get the value of x and y.

on solving we get [tex]x=\frac{18}{11} ,y=\frac{10}{11}[/tex].

system 2:

[tex]4x-5y=2\\10x-21y=10[/tex]

on solving the above two equation by the method of elimination we get the value of x and y.

on solving we get [tex]x=\frac{-4}{17},y=\frac{-10}{17}[/tex].

system 3:

[tex]4x-5y=2\\24x-47y=22[/tex]

on solving the above two equation by the method of elimination we get the value of x and y.

on solving we get [tex]x=\frac{-4}{17} ,y=\frac{-10}{17}[/tex].

system 4:

[tex]4x-5y=2\\10x+3y=15[/tex]

on solving the above two equation by the method of elimination we get the value of x and y.

on solving we get [tex]x=\frac{81}{62} ,y=\frac{20}{31}[/tex].

on looking for the solution of all the four system we see that system 2 and system 3 have the same value for x and y.

Hence, system 2 and system 3 have the same solution.