MATHEMATICS MIDDLE SCHOOL

The sum of two numbers is 38. The greater number is 5 more than twice the lesser number. What is the greater of the two numbers?

Answers

Answer 1
Answer:

Have the first number be x and the other number be y.

Write the first equation: The sum is 38:

x+y=38

Then the second equation: x is 5 more than than 2y:

x=2y+5

Take the first equation and make it y=38-x

Then substitute it in for the 2nd equation to find x:

x=2(38-x)+5

x=76-2x+5

3x=81

x=27

Then substitute that into the 1st equation to find y:

(27)+y=38

y=11

The first number (x) is greater than the second number (y) because 27 is greater than 11

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A $1500 loan has an annual interest rate of 4 1/4% on the amount borrowed. How much time has elapsed if the interest is now $127.50?

Really need this please explain some work too. Thx!

Answers

127.50 = 1,500(0.0425) * x

127.50 = 63.75 * x

x= 127.50/63.75

x=2 

60 peoples will be attending a dinner party. each people at the party can seat 8 people. how many tables are needed? Write and solve the number fact you used to find the answer, and explain your reasoning

Answers

The answer is 7.5
But u need 8 tables because you cant cut a table in half. The number facts that i used was 60 divided by 8.

PS. Please like this answer or i wont answer anymore of your questions
the answer is 480 because u need to multiply 60 and 8 together

Elena and Marcus jog after school each day. Oneday, Elena and Marcus jogged a total of 15 miles.
Elena jogged 1 mile more than Marcus. Use a graph
to find the number of miles each person jogged.

Answers

Answer:Marcus jogged 7 miles while Elena jogged 8 miles.

Step-by-step explanation:

x + (x+1) = 15

2x+1=15

putting like terms together we get:

2x=15-1

2x=14

hence

x=14/2 = 7miles

therefore we conclude that Marcus jogged 7 miles while Elena jogged 8 miles.

Multiply and reduce to lowest terms. Convert into a mixed number if necessary. 4x5/9=

Answers

2 and 1/5 is your answer.

decimal form=2.2

WILL GET BRAINLIEST IF EXPLAINED AND CORRECT Give the equation for a circle with the given center and radius.
Center at (-1, 3), radius = 4
A. (x+3)2+(y−1)2=4
B. (x−3)2+(y+1)2=4
C. (x−1)2+(y+3)2=16
D. (x+1)2+(y−3)2=16

Answers

Answer:

D. (x+1)^2+(y-3)^2=16

Step-by-step explanation:

We are asked to write equation of a circle whose center is at point (-1,3) and whose radius is 4 units.

We know that equation of a circle is standard form is in format (x-h)^2+(y-k)^2=r^2, where (h,k) is the center of circle.

Upon substituting h=-1, k=3 and r=4 in the standard form of circle, we will get:

(x-(-1))^2+(y-3)^2=4^2

(x+1)^2+(y-3)^2=16

Therefore, our required equation would be (x+1)^2+(y-3)^2=16 and option D is the correct choice.

Answer:

It is D. (x + 1)^2 + (y - 3)^2 = 16.

Step-by-step explanation:

The general equation of a circle is

(x - h)^2 + (y - k)^2 = r^2  where  the center is (h, k) and the radius is r.

So substituting the given values the required equation is:

(x + 1)^2 + (y - 3)^2 = 4^2.

How do I work out the following simultaneous equations?x+3y=11 and 2x-y=11

Thank you, this is part of my half term homework and I really need to understand how to do this as soon as possible , thank you!

Answers

I'll show you two ways.

By substitution:

x+3y=11\n2x-y=1\n\nx=11-3y\n2x-y=1\n\n2(11-3y)-y=1\n22-6y-y=1\n-7y=-21\ny=3\n\nx=11-3\cdot3\nx=11-9\nx=2\n\n\boxed{(x,y)=\left(2,3\right)}

By elimination:

x+3y=11\n 2x-y=1|\cdot 3\n\nx+3y=11\n\underline{6x-3y=3}\n7x=14\nx=2\n\n 2+3y=11\n3y=9\n y=3\n\n\boxed{(x,y)=\left(2,3\right)}
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