The sum of two numbers is 24. Their difference is 15. What are the two numbers?

Answers

Answer 1

Answer: x+y = 24x-y = 15 Thus, x=15+y Substitute for x in first equation becomes 15 +y + y = 24. 2y=9; therefore y=4.5, and since x = 24-y, x= 19.5 Check answer: 4.5 + 19.5 = 24; 19.5-4.5 = 15

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What are the solutions to the system of equations?

Answers

Answer:

A. $(1,5)$ and $(5,13)$

Step-by-step explanation:

We have been given a system of equations. We are asked to find the solution of our given system.

$\left \{ {{y=x^2-4x+8}\atop {y=2x+3}} \right.$

Equate both equations:

$x^2-4x+8=2x+3$

$x^2-4x-2x+8-3=2x-2x+3-3$

$x^2-6x+5=0$

Split the middle term:

$x^2-5x-x+5=0$

$x(x-5)-1(x-5)=0$

$(x-5)(x-1)=0$

Use zero product property:

$(x-5)=0\text{ (or) }(x-1)=0$

$x=5\text{ (or) }x=1$

Now, we will substitute both values of x, in our given equation to solve for y.

$y=2x+3$

$y=2(1)+3$

$y=2+3$

$y=5$

One solution: $(1,5)$

$y=2x+3$

$y=2(5)+3$

$y=10+3$

$y=13$

2nd solution: $(5,13)$

Therefore, option A is the correct choice.

Answer:

Step-by-step explanation:

Given the 2 equations

y = x² - 4x + 8 → (1)

y = 2x + 3 → (2)

Since both express y in terms of x we can equate the left sides, that is

x² - 4x + 8 = 2x + 3 ( subtract 2x + 3 from both sides )

x² - 6x + 5 = 0 ← in standard form

(x - 1)(x - 5) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 5 = 0 ⇒ x = 5

Substitute these values into (2) for corresponding values of y

x = 1 : y = (2 × 1) + 3 = 2 + 3 = 5 ⇒ (1, 5)

x = 5 : y = (2 × 5) + 3 = 10 + 3 = 13 ⇒ (5, 13)

Solutions are (1, 5) and (5, 13)

X+2/8=1/2 what is x explain how you got the answer

Answers

x= 1/4

x+2/8 = 1/2
-2/8 -2/8

x=1/4

A box of 6 trophies costs $5. How much would it cost to buy 48 trophies?

Answers

Answer:

$40

Step-by-step explanation:

since 6 x 8 = 48

you need 8 boxes which each cost $5

8 x $5 =$40

What is the distance between the points M-1,5)
and Z(6,2)?

Answers

Answer:7.61577

Step-by-step explanation:

Explain how am estimate helps you to place the decimal point when multipling 3.7 X 5.1

Answers

well 3.7×5.1 put the decimals at the end so 37×51=1887 there is 2 decimals so it should be 18.87 you put it back 2 spaces since there's 2 decimals

Since 3*5=15, then the answer to 3.7*5.1 should be close to that same value. But if you were solving it by hand, and accidentally wrote the answer as 1.887 or 188.7. Estimating helps you know that you placed the decimal in the wrong area, Since the number isn't close to 15.3.7*5.1+18.87

75% of what number is 27?

Answers

So we want to know the number from which we take 75% and get 27. If the number we are looking for is x, then the equation to find that x would be: (75/100)*x=27 which says seventy five percent out of x is equal 27. So, x=(27*100)/75. And finally, x= 2700/75=36. So, 75% out of 36 is 27.

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