MATHEMATICS MIDDLE SCHOOL

A school bought pens, each costing $1, and pencils, each costing $0.5. The cost of the whole purchase was $220. How many pens and pencils were purchased if there were 80 more pencils than pens?

Answers

Answer 1

Answer:

Answer:

120 pens and 200 pencils.

Explanation:

You can set a system of two equations.

1. Variables

x: number of pens
y: number of pencils

2. Cost

each pen costs $1, then x pens costs: x
each pencil costs $0.5, then y pencil costs: 0.5y

Then, the total cost is: x + 0.5y

The cost of the whole purchase was $ 220, then the first equation is:

x + 0.5y = 220 ↔ equation (1)

3. There were 80 more pencils than pens

Then:

pencils = 80 + pens

↓ ↓

y = 80 + x ↔ equation (2)

4. Solve the system

i) Substitute the equation (2) into the equation (1):

x + 0.5(80 + x) = 220

ii) Solve

x + 40 + 0.5x = 220

1.5x = 180

x = 180/1.5

x = 120 pens

iii) Substitute x = 120 into the equation (2)

y = 80 + 120

y = 200 pencils

Solution: 120 pens and 200 pencils ← answer

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Use the distributive property to write an equivalent expression for8(y-7)
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a paperweight is in the shape of a pyramid. The base is a square with sides of 1.5 centimeters. The height of the paperweight is 3 centimeters. Find the volume of the paperweight.

Answers

The answer is 1.5x3 which is 4.5 i am pretty sure.

Please Help Me !!!!!!

1. Polynomials Add or subtract

(4x2 + 15x – 3) – (–3x2 + 5) (1 point)

A.7x2 + 15x – 8

B.x2 + 12x + 2

C.x2 + 15x – 8

D.7x2 + 8 2.

2. Simplify the polynomial.

–3f2 + 4f – 3 + 8f2 + 7f + 1 (1 point)

A.5f2 – 11f + 2

B.11f2 + 11f + 2

C.5f2 + 11f – 2

D.–5f2 + 11f – 2

3. Add or subtract

(2x2 + 6x + 1) + (–7x2 + 2x – 3) (1 point)

A.5x2 – 4x – 2

B.–5x2 + 8x – 2

C.5x2 – 8x + 2

D.–9x2 – 8x + 2

4. Name the coefficients in the polynomial.

4x2 + 3x – 3 (1 point)

A.4, –3, –3

B.4, 3

C.4, 3, 3

D.–4, –3

5. How many terms are in the following polynomial?

6x4 + 3x3 – 2x2 + 15x – 14 (1 point) A. 5

B.4

C.3

D.2

6. In the expression –7x – 5x2 + 5, what is the coefficient of x? (1 point)

A.7

B.5

C.–5

D. -7

7. Write the expression using scientific notation.

(2.5 • 104)(4 • 103) (1 point)

A.10 • 107

B.10 • 108

C.1 • 108

D.10 • 1012

8. Write the expression using a single exponent.

22 • 28 (1 point)

A.410

B.210

C.416

D.216

Answers

Answer:

(1) A

(2) C

(3) B

(4) The coefficients are 4,3,-3.

(5) A

(6) D

(7) C

(8) B

Step-by-step explanation:

(1)

The given expression is

$(4x^2 + 15x - 3) - (-3x^2 + 5)$

Using distributive property.

$(4x^2 + 15x - 3) - (-3x^2) -( 5)$

$4x^2 + 15x - 3 + 3x^2 - 5$

On combining like terms.

$(4x^2+3x^2) + 15x +(- 3 - 5)$

$7x^2 + 15x-8$

Therefore, the correct option is A.

(2)

The given expression is

$-3f^2 + 4f - 3 + 8f^2 + 7f + 1$

On combining like terms.

$(-3f^2+ 8f^2) +( 4f + 7f )+(- 3 + 1)$

$5f^2 +11f -2$

Therefore, the correct option is C.

(3)

The given expression is

$(2x^2 + 6x + 1) + (-7x^2 + 2x - 3)$

Combined like terms.

$(2x^2-7x^2) + (6x+ 2x) + (1 - 3)$

$-5x^2 + 8x -2$

Therefore, the correct option is B.

(4)

The given expression is

$4x^2 + 3x - 3$

A number before variable terms are called coefficient of that term.

Therefore, the coefficients are 4,3,-3.

(5)

The given expression is

$6x^4 + 3x^3 - 2x^2 + 15x - 14$

It this polynomial, the number of terms is 5.

Therefore the correct option is A.

(6)

The given expression is

$-7x - 5x^2 + 5$

The coefficient to x is -7.

Therefore, the correct option is D.

(7)

The given expression is

$(2.5\cdot 10^4)(4\cdot 10^3)$

$(2.5\cdot 4)\cdot (10^4\cdot 10^3)$

Using product property of exponent.

$(10)\cdot 10^(4+3)$

$1\cdot 10^(1+4+3)$

$1\cdot 10^(8)$

Therefore, the correct option is C.

(8)

The given expression is

$2^2\cdot 2^8$

Using product property of exponent.

$2^(2+8)$

$2^(10)$

Therefore, the correct option is B.

$1.\n(4x^2+15x-3)-(-3x^2+5)\n=4x^2+15x-3+3x^2-5\n=7x^2+15x-8\leftarrow A.$

$2.\n-3f^2+4f-3+8f^2+7f+1\n=5f^2+11f-2\leftarrow C.$

$3.\n(2x^2+6x+1)+(-7x^2+2x-3)\n=2x^2+6x+1-7x^2+2x-3\n=-5x^2+8x-2\leftarrow B.$

$4.\n4x^2+3x-3\n\{4;\ 3;-3\}$

$5.\n6x^4+3x^3-2x^2+15x-14\n\{6;\ 3;-2;\ 15;-14\}\to5\leftarrow A.$

$6.\n-7x-5x^2+5\n\{-7\}\leftarrow D.$

$7.\n(2.5\cdot10^4)(4\cdot10^3)=2.5\cdot4\cdot10^(4+3)=10\cdot10^7\n=10^(1+7)=10^8=1\cdot10^8\leftarrow C.$

$8.\n2^2\cdot2^8=2^(2+8)=2^(10)\leftarrow B.$

What is the value of 10 rolls of quarters if there are 40 quarters in each roll?

Answers

(40 times 10) the answer is 400

1 roll __________ 40 quaters
10 rolls ________ x

x = 10 . 40
x = 400 quaters

fifty of the 80 students in the club were girls. what was the ratio of boys to girls in the club ? pls show workkk !! i will mark brainliest

Answers

Answer:

30:50

Step-by-step explanation:

80 Students.

50 Girls.

The Rest would be Boys so 80-50 equals to 30.

This would make the ratio 30:50 which simplifies to 3:5

3 Boys for Every 5 Girls.

Find the inverse f(x)= 3x-5/2

Answers

I hope it helps you get it right

Nathaniel writes the general form of the equation gm = cm + rg for when the equation is solved for m. He uses the general form to solve the equation –3m = 4m – 15 for m. Which expression shows what Nathaniel will actually evaluate?

Answers

Answer: C

Step-by-step explanation: i got it right on edg

Answer: -15/-3-4

Step-by-step explanation:

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