Gracie, Mary, and Nancy each have a small collection of seashells. Gracie has 5 more than times the number of shells Mary has. Nancy has 1 more than times the number of shells Mary has. Gracie and Nancy have the same number of shells. If x is the number of shells Mary has, identify the equation that represents this situation and identify its solution.

Answers

Answer 1

Answer: First, let's name or variables. Let us name Gracie's number of seashells as G, Nancy's number of seashells as N and Mary's number of seashells is x. The first statement would give an algebraic expression of G = x + a5. The second statement gives N = x +b1. Also, G = N hence x +a5 = x + b1. Clearly, there are lacking values noted as a and b in the equation. Given a and b we can solve for x.

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Trying to translate word problems. Five times the sum of 3 and twice some number is 70. what is the number?

Answers

5(2x+3)=70
10x+15=70
10x=55
x=5.5

Write the slope-intercept form of the line with a slope of 2 and a y-intercept of -4. Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.

Answers

y=mx+b m=slope b=y intercept
y=2x-4

y = 2x -3
I think this is right

Social Security is supplemental retirement income and should not be the only thing a retiree relies on.

Answers

if its true or false the answer is true

The area of a rectangular wall of a barn is 55 square feet. It's length is 6 feet longer than the width. Find the length and width of the wall of the barn.

Answers

x - width
x+6 - length

$x(x+6)=55\n x^2+6x-55=0\n x^2+11x-5x-55=0\n x(x+11)-5(x+11)=0\n (x-5)(x+11)=0\n x=5 \vee x=-11$

x=5 feet
x+6=11 feet

Final answer:

The dimensions of the barn wall are found by setting up and solving a quadratic equation involving its area and the relationship between its length and width. Discarding the nonsensical negative solution, we find that the width of the wall is 5 feet and the length is 11 feet.

Explanation:

Given that the area of the rectangular wall is 55 sq. ft. and the length is 6 ft. longer than the width, we can assign the width as x and the length as x + 6. Therefore, length multiplies width equals to the area of the rectangle, we then have the equation: x * (x + 6) = 55.

After rearranging the equation, we obtain: x² + 6x - 55 = 0. This is a quadratic equation that we can solve using the quadratic formula or by factoring if possible. Factoring results in (x - 5)(x + 11) = 0. Setting each factor equal to zero gives the possible solutions x = 5 and x = -11.

However, since the dimensions of a physical object (in this case, width of the barn wall) cannot be negative, we discard x = -11. Therefore, the barn wall has a width of 5 feet and a length of 5 + 6 = 11 feet.

Learn more about Solving Quadratic Equations here:

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How many positive intergers less than 25 are divisible by 2, 3, and 5?

Answers

Hello,

All numbers divisible by 2,3,5 are multiple of 2*3*5=30.
The only positive integer multiple of 30 less than 25 is 0.
(I don't know if in US 0 is considerated as positive) in my country yes.

How many solutions are there to the system of equations? 4x-5y=5 -0.08x+0.10y=0.10

Answers

Using substitution method, the system of linear equations has no solution.

What is the solution to the system of equations?

To determine the solution to the system of equations, we can use substitution method;

4x - 5y = 5 ...eq(i)

-0.08x + 0.10y = 0.10 ...eq(ii)

From equation (i)

4x - 5y = 5

let's make x the subject of formula;

4x = 5 + 5y

x = (5 + 5y) / 4 ...eq(iii)

Put eq(iii) into equ(ii)

-0.08[(5 + 5y)/4] + 0.10y = 0.10

(-2/5 - 2/5y)/4 + 0.10y = 0.10

y = no solution

Since y has no solution, this implies that the system of linear equations has no solution.

Learn more on system of linear equations here;

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Simple..

you have:

4x-5y=5

-0.08+0.10y=0.10

Take....

4x-5y=5----> *1 -----> 4x-5y=5

-0.08+0.10y=0.10---> *50---->-4x+5y=5

Now....

4x-5y=5
-4x+5y=5

As you may be able to tell it has no solution.

Thus, your answer.

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a football player gained 2 yards on one play. on the next play, he gained 5 feet. was his gain greater on the play or the second play? explain.