Mathematics, 16.10.2020 07:01 marbo1

The total of every point I counted is going to be a point for this. Q1: The ratio of the number of cups of red paint to the number of cups of yellow paint that Garcia mixed to make a shade of orange paint is 4:1.

Part A: Write a sentence to describe the number of cups of red paint that Garcia mixed with each cup of yellow paint. (4 points)

Part B: How many cups of yellow paint should Garcia add to each cup of red paint to make the shade of orange? Explain your reasoning. (4 points)

Part C: If Garcia purchased 6 cups of red paint for $42, what is the unit price per cup of red paint? (2 points)

Q2: Collins has a part-time job as a dog walker. The table below shows the amount of money Collins earned for different numbers of hours of work:

Collins' Earnings from Dog Walking
Number of Hours Worked Money Earned (dollars)
5 30
6 36
8
66

Part A: What are the missing numbers in the table? Show your work. (4 points)

Part B: Collins also does part-time yard work. The ratio of the number of hours Collins works to the money he earns in dollars is 1:7. Create a table to show the money earned by Collins for 5, 6, and 8 hours of doing yard work. (3 points)

Part C: How many more dollars does Collins earn doing yard work for 5 hours than working as a dog walker for 5 hours? Show your work. (3 points)

Q3: Polly surveyed 850 teenagers to find out their favorite type of music. She found that 32% of the teenagers surveyed like hard rock.

Part A: How many teenagers surveyed like hard rock? Show your work. (4 points)

Part B: In another survey, Damian found that 75% of the total number of teenagers surveyed like pop music. If 150 teenagers like pop music, what is the total number of teenagers that Damian surveyed? Show your work. (4 points)

Part C: Give an example of a situation in which a percentage is greater than 100%. (2 points)

Q4: Part A: Wilson bought fruit that weighs 2 and 1 over 2 pounds. How many ounces does the fruit weigh? Show your work. (5 points)

[16 ounces = 1 pound]

Part B: A running tap dispenses 0.14 gallons of water every second. How many pints of water is dispensed after 50 seconds? Show your work. (5 points)

[1 gallon = 4 quarts, 1 quart = 2 pints]

(By the way, if you are wondering if this is FLVS, it is.)

Answers: 1

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Answers

Answer from: gunnatvinson

Step-by-step explanation:

Answer from: tobi15

I personally think the answer is A.

Answer from: Quest

2x^2 -2x -12 = 02(x -3)(x +2) = 0see below for explanation

step-by-step explanation:

equation

you are asked to write the equation

expression = 0

using the given expression. when you do that, you have

2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

(x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

-6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

x - 3 = 0

x = 3 . . . add 3 to both sides of the equation

x +2 = 0

x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

Answer from: Quest

x= -3 and $x=\frac{-3+/-3i\sqrt{3} }{2}$

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

$(x^3-a^3)=$ $(x-a)(x^2+ax+a^2)$

where a is the cube root of $a^3$ .

here this is 27 and the cube root of 27 is 3. so we write using the form:

$(x-3)(x^2+(3)x+3^2)\\(x-3)(x^2+3x+9)$ .

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

$x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}$

where a = 1, b=3, and c=9

$x=\frac{-3+/-\sqrt{3^2-4(1)(9)} }{2(1)} \\x=\frac{-3+/-\sqrt{9-36)} }{2} \\x=\frac{-3+/-\sqrt{-27)} }{2}\\x=\frac{-3+/-3i\sqrt{3} }{2}$

this cubic has two complex roots.

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