MATHEMATICS HIGH SCHOOL

Which of the following is a monomial? A. 3x2 + 2x − 1
B. 4
C. 3x + 4
D. 2x − 1

Answers

Answer 1
Answer: "mono" means 1 or single. In algebra, a monomial is any number that is alone or by itself. For this question, among the choices, the monomial is the number 4. Therefore the answer to this question is letter B. 4.

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A pet shelter houses 32 cats and 45 dogs. What is the ratio of dogs to total number of cats and dogs? (Write your answer using the a:b format. For example, 1:1.)

Answers

Answer: 32:45

Step-by-step explanation: They share no common factors so it would just be 32:45

the answer is 45:77 . the question says “ ratio of dogs ( 45 ) “ to “ the total number of cats AND dogs “ which means cats and dogs combined which is 77/

Given the equation p=2w+2l solve for w

Answers

P= 2w + 21
-21 -21
P - 21 = 2w P -21
—————— —> ——- = w
2 2

Kathy lives directly east of the park. The football field is directly south of the park. The library sits on the line formed between Kathy's home and the football field at the exact point where an altitude to the right triangle formed by her home, the park, and the football field could be drawn. The library is 9 miles from her home. The football field is 12 miles from the library.a. How far is the library from the park?
b. How far is the park from the football field?

Answers

see the attached figure to better understand the problem

Let

z---------> distance from the library to the park in miles

x-------> distance from the park to the to the football field in miles

y-------> distance from the park to Kathy's home in miles

we know that

In the right triangle ABC

Applying the Pythagorean Theorem

x^(2) +y^(2) =(12+9)^(2) \n x^(2) +y^(2)=441 -----> equation 1

In the right triangle ABD

Applying the Pythagorean Theorem

12^(2) +z^(2) =x^(2) \n 144 +z^(2)=x^(2) -----> equation 2

In the right triangle BCD

Applying the Pythagorean Theorem

9^(2) +z^(2) =y^(2) \n 81 +z^(2)=y^(2) -----> equation 3

Add equation 2 and equation 3

144 +z^(2)=x^(2)

81 +z^(2)=y^(2)\n ------

144+81+2z^(2) =x^(2) +y^(2) -----> equation 4

Substitute equation 1 in equation 4

144+81+2z^(2)=441\n 2z^(2) =441-225\n 2z^(2)=216\n z^(2)=108\n z=√(108) miles\n z=10.39 miles

Find the value of x

144 +z^(2)=x^(2)\n 144 +√(108)^(2)=x^(2) \n x^(2) =144+108\n x^(2) =252\n x=√(252) miles\n x=15.87 miles

therefore

the answer is

Part a) The distance from the library to the park is equal to 10.39 miles

Part b) The distance from the park to the to the football field is equal to 15.87 miles
Look at the picture in the attachment.

Using the Pythagorean theorem, set up a system of three equations:
x^2+y^2=(12+9)^2 \n12^2+z^2=x^2 \n9^2+z^2=y^2 \n \nx^2+y^2=441 \n144+z^2=x^2 \n81+z^2=y^2

\hbox{substitute } 144+z^2 \hbox{ for } x^2 \hbox{ and } 81+z^2 \hbox{ for } y^2 \hbox{ in the first equation:} \n144+z^2+81+z^2=441 \n225+2z^2=441 \n2z^2=441-225 \n2z^2=216 \nz^2=(216)/(2) \nz^2=108 \nz=√(108) \nz=√(36 * 3) \nz=6√(3) \n z \approx 10.39

81+z^2=y^2 \n81+108=y^2 \n189=y^2 \n√(189)=y \n√(9 * 21)=y \ny=3√(21) \n y \approx 13.75

a. The library is approximately 10.39 miles (exactly: 6√3 miles) from the park.
b. The park is approximately 13.75 miles (exactly: 3√21 miles) from the football field.

Justin weighs 15 pounds less than Greg weighs. Half of Greg’s weight is 75 pounds less than Justin’s weight. How much does each of them weigh? Greg weighs 200 pounds, and Justin weighs 185 pounds. Greg weighs 190 pounds, and Justin weighs 175 pounds. Greg weighs 180 pounds, and Justin weighs 165 pounds. Greg weighs 170 pounds, and Justin weighs 155 pounds.

Answers

J=G-15
(G/2)=J-75

Substitute
(G/2)=G-15-75
G/2 =G-90
G-G/2= 90
G/2=90
G=180

J=G-15=180-15=165

Greg weighs 180 pounds, and Justin weighs 165 pounds.

Answer:

180 and 165

gg

A square has a perimeter of 100cm What is the length of each side?

Answers

Answer:

each side of the square is 25cm

Step-by-step explanation:

this is because of two things:

1. a square has equal sides

2. the perimeter is all the sides added together.

so if you call the length of one side x, you can make this equation:

x + x + x + x = 100

combine like terms

4x = 100

divide both sides by 4

x = 100/4

x = 25

Answer:

25 cm

I hope this helps!

Need help please
-3x + 5x -2 > 8x - 7 -9x

Answers

-3x + 5x -2 \geq 8x - 7 -9x\n 3x\geq-5\n x\geq-(5)/(3)
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COMPLETE THE EXERCISE BELOW TO DECOMPOSE 930