Which equation below represents a proportional relationship?



a. y = 5x – 9

b. y = 2x + 7

c. y = 8x

d. y = 3x – 2

Answers:

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Explanation:

We'll use the zero product property to solve.

[tex]3(x^2+5)^2(x^2-25)^3(x-8)^4 = 0\\\\(x^2+5)^2=0 \text{ or } (x^2-25)^3=0 \text{ or } (x-8)^4 = 0\\\\x^2+5=0 \text{ or } x^2-25=0 \text{ or } x-8 = 0\\\\x^2=-5 \text{ or } x^2=25 \text{ or } x = 8\\\\x=\pm\sqrt{-5} \text{ or } x=\pm\sqrt{25} \text{ or } x = 8\\\\x=\pm i\sqrt{5} \text{ or } x=\pm 5 \text{ or } x = 8\\\\[/tex]

where [tex]i = \sqrt{-1}[/tex]

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The notation [tex]x=\pm i\sqrt{5}[/tex] breaks up into [tex]x=i\sqrt{5} \text{ or } x=-i\sqrt{5}[/tex]. The multiplicity of these two roots is 2 as it's the exponent of the factor [tex](x^2+5)^2[/tex]. Focus on the outermost exponent.

The notation [tex]x = \pm 5[/tex] becomes [tex]x = 5 \text{ or } x = -5[/tex]. The multiplicity of these two roots is 3 since it's the outermost exponent of the factor [tex](x^2-25)^3[/tex]

And finally, the multiplicity of the root x = 8 is 4 because it is the outermost exponent of the factor [tex](x-8)^4[/tex]

Answer:

x = 1

Step-by-step explanation:

(4x/3) - 3x + 1 = 10

(4x/3) -3x = 9

4x - x = 3

3x = 3

x = 1

Answer:

D

Step-by-step explanation:

The rate at which the pool is filled is 1 gallon per 9 minutes. If you divide all the numbers of minutes in the left side of the table with the number of gallons on the right you get 9 minutes per gallon for each of them so they follow the rate.

Answer: p=x2−6x+8

Step-by-step explanation:

hope this answer helps

Answer:     x(x-4)(x-2)

Step-by-step explanation:

Answer:

y=19.6

Step-by-step explanation:

Answer:

to get y you subtract 12.4 from both side and that is your answer.

Step-by-step explanation:

19.6 hope it correct mark brainliest if so thank u have an nice day

9514 1404 393

Answer:

  4, 5, 6

Step-by-step explanation:

Let x represent the middle one. Then the sum of the first two is ...

  (x -1) +x

And we want that to be 3 more than the third:

  (x -1) +x = (x +1) +3

  2x = x +5 . . . . . . . . . add 1, simplify

  x = 5 . . . . . . . . . . . . . subtract x

Since 5 is the middle integer, the three integers are ...

  4, 5, 6

Answer:

18 students are making a B or higher

Step-by-step explanation:

24 * 75% = 18

Answer:

we are looking for the part

Answer:

11.3kg

Step-by-step explanation:

if 700=20

therefore 400=400*20÷700=11.3

Answer:

[tex]-15 + 6x[/tex]

Step-by-step explanation:

Given

[tex]Expression: 7 - 3(4 - 2x) - 10x[/tex]

Required

Determine Jon's error and make corrections.

Also, give the equivalent of the expression

The question has missing details because Jon's workings is not listed.

One mistake student's make during multiplications that involves minus (-) and plus (+) is in the signs.

So, watch out for the signs to know where the error is.

However, I'll give an equivalent of the given expression

[tex]7 - 3(4 - 2x) - 10x[/tex]

Open Bracket

[tex]7 - 12 + 6x - 10[/tex]

Collect Like Terms

[tex]7 - 12 - 10 + 6x[/tex]

[tex]-15 + 6x[/tex]

Hence, the given expression is equivalent to [tex]-15 + 6x[/tex]

Answer:

See below

Step-by-step explanation:

[tex]p = m + {x}^{2} \\ \\ p - m = {x}^{2} \\ \\ {x}^{2} = p - m \\ \\ x = \pm \sqrt{p - m} \\ [/tex]

Answer:

63.5

Step-by-step explanation:

248/4=62

the numbers are

60.5, 61.5, 62.5, 63.5

Answer:

The function of g(x) = 5x + 2

Step-by-step explanation:

Let us use the composite function to solve the question

∵ f(x) = 2x - 1

∵ f(g(x)) = 10x + 3

→ f(g(x)) means substitute x in f(x) by g(x)

∴ f(g(x)) = 2[g(x)] - 1

→ Equate the two right sides of f(g(x))

∴ 2[g(x)] - 1 = 10x + 3

→ Add 1 to both sides

∴ 2[g(x)] - 1 + 1 = 10x + 3 + 1

∴ 2[g(x)] = 10x + 4

→ Divide each term into both sides by 2

∵ [tex]\frac{2[g(x)]}{2}[/tex] = [tex]\frac{10x}{2}[/tex] + [tex]\frac{4}{2}[/tex]

∴ g(x) = 5x + 2

∴ The function of g(x) = 5x + 2

Answer:

y=7x

Step-by-step explanation:

When finding the slope intercept form using 2 points, we do the following.

y=mx+b (Slope intercept from)

y=7x+b (7 is slope)

Substitute the point

7=7(1)+b

7=7+b

b=0

y=7x

The slope intercept equation is y = 7x

Answer:

The answer is 36 adults and 88 children.

Step-by-step explanation:

The two equations are:

x+y=124 and 5x+3y=444

Using substitution method:

5x+3(124+x)=444

5x+372-3x=444

2x=72

x=36

5(36)+3y=444

180+3y=444

3y=264

y=88

Answer:

Step-by-step explanation:

sin A = [tex]\frac{a}{c}[/tex]

sin 9.4° = [tex]\frac{20.5}{c}[/tex] ⇒ c = (20.5) / (sin 9.4°) ≈ 125.52

tan A = [tex]\frac{a}{b}[/tex]

tan 9.4° = [tex]\frac{20.5}{b}[/tex] ⇒ b = (20.5) / (tan9.4°) ≈ 123.83

m∠B = 90° - 9.4° = 80.6°

m∠C = 90°

Answer:

Please check the explanation.

Step-by-step explanation:

Solving the expressions

7)

given the expression

[tex]\left(-7\right)+\:\left(-10\right)\:-\:5\:+2[/tex]

so

[tex]=\left(-7\right)-10-5+2[/tex]

[tex]=-17-5+2[/tex]

[tex]=-22+2[/tex]

[tex]=-20[/tex]

8)

[tex]\left(-9\right)+4+\left(-8\right)-\left(-7\right)[/tex]

so

[tex]=-5+\left(-8\right)-\left(-7\right)[/tex]

[tex]=-5-8-\left(-7\right)[/tex]

[tex]=-13-\left(-7\right)[/tex]

[tex]=-13+7[/tex]

[tex]=-6[/tex]

9)

[tex]\left(-6\right)\:-\:\left(2\:\times \:4\right)\:-\:\left(-1\right)\:[/tex]

so

[tex]\left(-6\right)-\left(2\times \:4\right)-\left(-1\right)[/tex]

Calculate within parentheses

[tex]=\left(-6\right)-8-\left(-1\right)[/tex]

[tex]=-14-\left(-1\right)[/tex]

[tex]=-14+1[/tex]

[tex]=-13[/tex]

10)

[tex]\left(-8\right)\:+\:\left(-4\:\div \:-4\right)\:-\:8[/tex]

solving

[tex]\left(-8\right)+\left(-\frac{4}{-4}\right)-8[/tex]

[tex]\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a[/tex]

[tex]=-8-\frac{4}{-4}-8[/tex]

[tex]=-8-\left(-1\right)-8[/tex]

[tex]\mathrm{Apply\:rule}\:-\left(-a\right)=a[/tex]

[tex]=-8+1-8[/tex]

[tex]\mathrm{Add/Subtract\:the\:numbers:}\:-8+1-8=-15[/tex]

[tex]=-15[/tex]

The value of the given expression 7) (-7) + (-10) – 5 +2 is -20, 8) (-9) + 4 + (-8) – (-7) is -6, 9) (-6) – (2 x 4) – (-1) is -11, 10) (-8) + (-4 ÷ -4) – 8 is -15.

BODMAS stands for B- bracket, O- order, D-division, M-multiplication, A- addition, S- subtraction. We use this rule when there is more than one operation are present in the mathematical expression.

7)  (-7) + (-10) – 5 +2

here, we will use the BODMAS rule, the addition and subtraction will go from left to right.

= -7 -10 -5 + 2

= -17 -5 + 2

= -22 + 2

= -20

8) (-9) + 4 + (-8) – (-7)

=  -9 +4 -8 +7

= -5 -8 +7

= -13 + 7

= -6

9) (-6) – (2 x 4) – (-1)

= -6 - 8 +1

= -12 + 1

= -11

10) (-8) + (-4 ÷ -4) – 8

= -8 -4/ (-4) - 8

= -8 +1 -8

= -7 -8

= -15

Therefore, the value of the given expression 7) (-7) + (-10) – 5 +2 is -20, 8) (-9) + 4 + (-8) – (-7) is -6, 9) (-6) – (2 x 4) – (-1) is -11, 10) (-8) + (-4 ÷ -4) – 8 is -15.

Learn more about the BODMAS rule here:

https://brainly.com/question/24383445

Answer:

-2

Step-by-step explanation:

First divide 18/-3 = -6

Then add 4 to -6

Answer is -2

Answer:

any line with the same slope but different y intercept

Step-by-step explanation:

Answer:

7x+6y=18

Step-by-step explanation:

Answer:

5 feet

mark above answer BRILLIANT

Answer:

D. (4, 0)

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define systems

-x + 5y = -4

4x + 3y = 16

Step 2: Rewrite systems

x = 5y + 4

4x + 3y = 16

Step 3: Solve for y

Step 4: Solve for x

And we have our final answer!

14 pennies and 8 nickles

i hope this helps

Answer:

0.01p + 0.05(22 – p) = 0.54

Answer:

-35 is the correct answer

Answer:

-35

Step-by-step explanation:

The answer is -35

-7 × 5 = -35