Mathematics, 21.07.2019 23:10 cxttiemsp021

One number is seven less than another. their sum is thirteen. find the numbers.
(smaller value)
(larger value)
isn't there more than 1 possible combination here? how do i know which one it wants?

Answers: 1

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Answer from: nbug2121

The numbers are 10 and 3.

Step-by-step explanation:

Set up equations relating the two numbers to each other.Solve for the two variables.

STEP 1: Based on the problem, two equations can be set up:

First, "one number is seven less than another." This can be expressed mathematically:

Let x = first number

y = second number

$x \ - 7 = \ y$

The second equation is based on "their sum is thirteen."

$x \ + \ y \ = 13$

STEP 2: Solve for the variables.

In this step, substitute the value of y from Equation 1 into Equation 2:

$x \ + \ (x \ - \ 7) \ = \ 13\\2x \ - \ 7 \ = 13\\$

Next, solve for x by manipulating the equation:

$2x \ = \ 13 \ + \ 7\\2x \ = \ 20\\\boxed {x \ = \ 10}$

Now that the value of x is known, it can be used to determine the value of y.

To do this, use the calculated value for x and plug it into Equation 1:

$y \ = \ x \ - 7\\y \ = 10 \ - 7\\\boxed {y = \ 3}$

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Keywords: two equations, two variables

Answer from: Quest

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

What is the length of the unknown leg in the right triangle ?

Answer from: Quest

b. 1.25 hr

step-by-step explanation:

if you have a constant speed of 60 mph, then you have a ratio between 60 mi. to 1 hr. dividing both sides by 60 we get the ratio

1 mi. to $\frac{1}{60} hr\\$

then mult. both sides by 75 we get the ratio

75 mi. to $\frac{75}{60} hr\\$

simplifying we get

75 mi. to $\frac{5}{4} hr$

or 1.25 hr.

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One number is seven less than another. their sum is thirteen. find the numbers.
(smaller value)...

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