Alex, an eighth grader, and Eric, a seventh grader, need to determine who came closer to their grade’s state record for the triple jump. Alex jumped 39.75 feet and Eric jumped 37 feet and inches. Who was closer to the state record if the eighth-grade record is 42.25 feet and the seventh-grade record is 39 feet 3 inches?

Answer:

X=(-1.5, 7.5)

Step-by-step explanation:

Simplifying

4x2 + -24x + -45 = 0

Reorder the terms:

-45 + -24x + 4x2 = 0

Solving

-45 + -24x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.

(-3 + -2x)(15 + -2x) = 0

Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying

-3 + -2x = 0

Solving

-3 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.

-3 + 3 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0

0 + -2x = 0 + 3

-2x = 0 + 3

Combine like terms: 0 + 3 = 3

-2x = 3

Divide each side by '-2'.

x = -1.5

Simplifying

x = -1.5  

Set the factor '(15 + -2x)' equal to zero and attempt to solve:

Simplifying

15 + -2x = 0

Solving

15 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-15' to each side of the equation.

15 + -15 + -2x = 0 + -15

Combine like terms: 15 + -15 = 0

0 + -2x = 0 + -15

-2x = 0 + -15

Combine like terms: 0 + -15 = -15

-2x = -15

Divide each side by '-2'.

x = 7.5

Simplifying

x = 7.5

Solution

x = {-1.5, 7.5}

Answer:

2/5

Step-by-step explanation:

Normally, percentage is expressed in 0 - 100 so for Randall to fill up 40% of his container, that means he'd fill out 40 out of a hundred. That's 40/100 which simplified will give you 2/5

Answer:

A picture provided would be better, but here's a picture to help you find an answer to your question.

Step-by-step explanation:

The two angles marked in red are corresponding angles on a pair of parallel lines. Corresponding angles are ALWAYS congruent to each other.

Step-by-step explanation:

She could take two science fiction, two biography, two thriller, one thriller and one science fiction, one thriller and one biography, one science fiction, and one biography

Answer: 3

Step-by-step explanation:

Science Fiction: SF

Biography: BI

Thriller: TH

SF:BI, TH

BI:TH

Answer:

When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable. We can eliminate the x-variable by addition of the two equations.

Answer:

y = 1/4 * x + 7

Step-by-step explanation:

We start with the equation for slope-intercept y = mx + b -

Y is any y point on the line. X is any x point on the line. M is the slope of the line. B is the y-intercept of the line.

We first find the slope by using this equation (y2 - y1) / (x2 - x1) -

(7 - 6) / (0 - (-4))

1 / (0 + 4)

Slope = 1/4

Now we insert the slope into the equation -

y = 1/4 * x + b

As said before, Y is any y point on the line and X is any x point on the line, so we can choose a random point and insert it in to find the y-intercept -

(The equation already tells you the y-intercept (0, 7) but for checking, we will insert the point in too)

7 = 1/4 * 0 + b

7 = b

b = 7

The y-intercept of the line is (0, 7)

We insert the y-intercept in the equation -

y = 1/4 * x + 7

y = 1/4 * x + b is our answer to the problem.

Answer:

Step-by-step explanation:

Answer:

96 cm or B

Step-by-step explanation:

Base-l*w, 6*6, 36

Side 1-(h*w)1/2, (30)1/2, 15

Side 2-Same as 1

Side 3-Same as 1

Side 4-Same as 1

15+15=30, 15+15=30, 30+30=60, 60+36=96

96 cm

Step-by-step explanation:

I assume the original expression is

2x² + 16x + 11

we need to get this into the form of a(x + b)² + c

let's do the generic multiplication and compare the result to the given expression :

a(x² + 2bx + b²) + c = ax² + 2abx + ab² + c

when we compare this with the original equation, we only need to look at terms with the same variable exponents.

2x² is the only term with "x²".

and ax² is the only term with "x²" in the generic form.

so ?

2x² = ax²

=>

a = 2

16x is the only term with "x" (exponent 1).

2abx is the only term with "x" in the generic form.

16x = 2abx

8x = abx = 2bx

4x = bx

=>

b = 4

11 is the only pure number (constant).

ab² + c is the only constant term in the genetic form.

11 = ab² + c = 2×4² + c = 2×16 + c = 32 + c

-21 = c

so, the solution is

2(x + 4)² - 21

The Eubanks Answer:

Step-by-step explanation:hehus

Answer:

m = 4

Step-by-step explanation:

The slope of two given points are:

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

We are given the points of (-11, -2) & (-15, -18).

[tex]m = \frac{-18+2}{-15+11} = \frac{-16}{-4}=\boxed{4}[/tex]

The slope of the line is 4.

Hope this helps.

Answer: ? What are you talking about?

Step-by-step explanation:

Answer:

Elise's number is 112/3.

Step-by-step explanation:

You can form the equation: [tex]\left(x-17\right)\cdot -3=-61[/tex]

Solution: [tex]\frac{\left(x-17\right)\left(-3\right)}{-3}=\frac{-61}{-3}[/tex]

[tex]x-17=\frac{61}{3}[/tex]

[tex]x-17+17=\frac{61}{3}+17[/tex]

x=112/3

Answer:

1/4 or .25

Explanation

As for this specific question algebra is something I do in my head and skip many steps for however if you want to proof my answer it would be this.

-0.25-16*.25=-0.25-4

-0.25-4=-0.25-4

-4.25=-4.25

For the function  f(x) = -x-4 the value of f(4) is -8.

The given function is f(x) = -x-4.

We need to find the value of f(4).

To find this we have to replace the x value with 4.

Substitute x=4 in the function:

f(4)=-4-4

f(4)=-8

Hence, the value of f(4) is -8.

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Answer:

b

Step-by-step explanation:

you add all of the expenses and then yeah

Answer:

I CANT SEE SRY

Step-by-step explanation:

Answer:

2 2/3

Step-by-step explanation:

Answer:

you have 41 quarters

Step-by-step explanation:

.....

Answer:

2.8625

This is 916 divided by 320

Answer:

Full Answer - 2.8625

Rounded - About 3

Nearest Tenth - 2.9

Nearest Hundredth - 2.86

Step by Step:

Shown Below  

Hope this Helps

Answer:

18-3n

Step-by-step explanation:

The nth term of this number sequence is,

⇒ a(n) = 15 - 3 (n - 1)

An arithmetic sequence is the sequence of numbers where each consecutive numbers have same difference.

Given that;

The sequence is,

15, 12, 9, 6..

Now, We can find the nth term as;

First term (a) = 15

Common difference (d) = 12 - 15 = - 3

We know that;

The nth term of the arithmetic sequence is,

⇒ a(n) = a + (n - 1) d

Hence, We get;

The nth term of this number sequence is,

⇒ a(n) = a + (n - 1) d

⇒ a(n) = 15 + (n - 1) (- 3)

⇒ a(n) = 15 - 3 (n - 1)

Thus, The nth term of this number sequence is,

⇒ a(n) = 15 - 3 (n - 1)

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Answer:

15.989

Step-by-step explanation:

i dont think you care

Answer:

D:  (-3, 0, 2, 9)

R: (4, 6, 7)

This relationship is a function as there are no two input that have the same output.

Step-by-step explanation:

This relationship is a function as there are no two input that have the same output.

The range is the second output (y-value) which is (4, 6, 7).

The domain is the first element (x-value) of a relation or function which is (-3, 0, 2, 9)

Hope this helps!

Answer:

y=3x+1

Step-by-step explanation:

The question is asking for an equation in slope-intercept form. This is y=mx+b, where m is slope and b is y-intercept. The slope is the change is y over the change in x. The y value changes 3 and the x value changes 1. So, the slope is 3/1 or just 3. The y-intercept is the value where the line intersects with the y-axis. Additionally, the y-intercept will have an x-value of 0. On the table, you can see that y=1 when x=0. Thus, the y-intercept is 1. Put the two values into the equation and you get y=3x+1.

Answer:

6

Step-by-step explanation:

you can find the mean by adding up all of the numbers, and then dividing that total by the amount of numbers in the sequence.

Answer:

y = 2(x - [tex]\frac{1}{2}[/tex] )² - [tex]\frac{11}{2}[/tex]

Step-by-step explanation:

y = 2x² - 2x - 5 ← factor out 2 from the first 2 terms

 = 2(x² - x) - 5

Using the method of completing the square

add/subtract (half the coefficient of the x- term)² to x² - x

y = 2(x² + 2(- [tex]\frac{1}{2}[/tex] ) x + [tex]\frac{1}{4}[/tex] - [tex]\frac{1}{4}[/tex] ) - 5

  = 2(x - [tex]\frac{1}{2}[/tex] )² + 2(- [tex]\frac{1}{4}[/tex] ) - 5

  = 2(x - [tex]\frac{1}{2}[/tex] )² - [tex]\frac{1}{2}[/tex] - 5

  = 2(x - [tex]\frac{1}{2}[/tex] )² - [tex]\frac{11}{2}[/tex] ← in vertex form

Answers:

[tex]\sqrt[c]{a^b}[/tex]

[tex](\sqrt[c]{a})^b[/tex]

Answer:

first 1 last 1 third 1 and forth 1

Step-by-step explanation:

Answer:

Step-by-step explanation:

The unit rate is the rate of the denominator of one unit. Unit rates are very common in our daily lives. For example, when we say we are traveling at 68 miles per hour, we mean we are traveling 68 miles in one hour. We'll write this rate as 68 miles/hour

Answer:

YESSIR

Step-by-step explanation: