Three students are sitting on a school bus. Cassie is 5 feet directly behind Grayson and 5 feet
directly left of Deb. Cassie makes a paper airplane and throws it to Grayson. Grayson throws
the airplane to Deb, who throws it back to Cassie. How far has the paper airplane traveled? If
necessary, round to the nearest tenth.
feet

point-slope form: y-y₁ = m(x-x₁)

=============

[tex]\rightarrow \sf y - 5 = \dfrac{5}{3} (x-3)[/tex]

slope-intercept form: y = mx + b

============

[tex]\rightarrow \sf y - 5 = \dfrac{5}{3}(x)+ \dfrac{5}{3}(-3)[/tex]

[tex]\rightarrow \sf y - 5 = \dfrac{5}{3}(x)-5[/tex]

[tex]\rightarrow \sf y = \dfrac{5}{3}(x)-5+5[/tex]

[tex]\rightarrow \sf y = \dfrac{5}{3}(x)[/tex]

point slope form:-

Slope intercept form

y=mx+b

Answer:

Step-by-step explanation:

Complementary angles sum to 90 degrees.

< BAF and < BFA

<CDE and < CED.

Supplementary ( sum to 360):

< FBC and <BFE

<BCE and < FEC.

20 + 14 + 8 + 28 = 70

70/4(we're dividing by 4 cause the no.of characters is 4)

and = 17.5

hope it really helps...!!!

The percentage increase in the sales of hybrid cars from 2005 to 2012 is 10%.

Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred. Percentages are a measure of frequency.

Percentage increase = (number of cars sold in 2012 / number of cars sold in2005)^(1/n) - 1

(432,798/ 205,828)^(1/8) - 1 = 10%

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Answer:

[C] 1/3 of the pizza

Step-by-step explanation:

Given that:

Juan and two of his friends are going to share of a pizza.

Thus, we know that:
Juan + two of his friend = 3 people

Hence, each person gets

1/3 of the pizza

Check Answer

1/3 × 3 =1 whole {whole pizza}

or we can do

1/3 + 1/3 + 1/3 = 1 whole.

We can also do this:

Numerator = how many each person gets

Denominator = Total people

For more info about Numerator and Denominator:

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Kavinsky

Answer:

14

Step-by-step explanation:

Because I looked it up

The z-statistic for Brett's data is found to be as given by: Option A: -5.30 (approx).

Suppose we're specified that:

Then the z-statistic for this data is found as:

[tex]Z = \dfrac{\overline{x} - \mu}{\sigma/\sqrt{n}}[/tex]

For this case, we've got:

Thus, we get:

[tex]Z = \dfrac{\overline{x} - \mu}{\sigma/\sqrt{n}} = \dfrac{295 - 310}{20/\sqrt{50}} \approx -5.30[/tex]

Thus, the z-statistic for Brett's data is found to be as given by: Option A: -5.30 (approx).

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https://brainly.com/question/1640298

According to the given data and applying it's formula, the z-statistic is of z = -5.30.

It is given by:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

The parameters are:

In this problem, the values of the parameters are given by:

[tex]\overline{x} = 295, \mu = 310, \sigma = 20, n = 50[/tex]

Hence, the z-statistic is given by:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{295 - 310}{\frac{20}{\sqrt{50}}}[/tex]

z = -5.30.

The z-statistic is of z = -5.30.

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Answer:

I am unsure of the wording of this question, so I will answer both ways I see it.

When x = x + 3, the value of 2x³ + x² - x is 2x³ + 19x² + 59x + 66.

When x = 3, the value of 2x³ + x² - x is 60.

Step-by-step explanation:

x = x + 3 solution:

It is given that:
f(x) = 2x³ + x² - x

We are trying to find this when x = x+3. Substitute this value in for every x in the function.

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

Expand the first part.

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

Multiply pairs together.

f(x + 3) = 2(x + 3)(x² + 6x + 9) + (x + 3)² - (x + 3)

Multiply the remaining pairs together.

f(x + 3) = 2(x³ + 9x² + 27x + 27) + (x + 3)² - (x + 3)

Distribute the two inside the parenthesis.

f(x + 3) = 2x³ + 18x² + 54x + 54 + (x + 3)² - (x + 3)

Evaluate (x + 3)².

f(x + 3) = 2x³ + 18x² + 54x + 54 + (x² + 6x + 9) - (x + 3)

Remove all parenthesis and start simplifying.

f(x + 3) = 2x³ + 18x² + 54x + 54 + x² + 6x + 9 - x - 3

Combine all terms ending in x².

f(x + 3) = 2x³ + (18x² + x²) + 54x + 54 + 6x + 9 - x - 3

f(x + 3) = 2x³ + 19x² + 54x + 54 + 6x + 9 - x - 3

Combine all terms ending in x.

f(x + 3) = 2x³ + 19x² + (54x + 6x - x) + 54 + 9 - 3

f(x + 3) = 2x³ + 19x² + 59x + 54 + 9 - 3

Last, combine the final numbers to get:

f(x + 3) = 2x³ + 19x² + 59x + 60

x = 3 solution:

It is given that:
f(x) = 2x³ + x² - x

Substitute 3 in for every value of the function.

f(3) = 2(3)³ + (3)² - 3

Evaluate 3 cubed and then multiply it by 2.

f(3) = 2(27) + 3² - 3

f(3) = 54 + 3² - 3

Evalute 3 squared.

f(3) = 54 + 9 - 3

Add 54 and 9.

f(3) = 63 - 3

Subtract 3 from 63 to get:

f(3) = 60

Sum of the interior angles of any n-side shape must equals to :

[tex](n - 2) \times 180[/tex]

Thus ;

[tex](5 - 2) \times 180 = [/tex]

[tex] 3\times 180 = [/tex]

[tex]540 \: \: degrees[/tex]

So :

[tex]x + 122 + 100 + 90 + 144 = 540[/tex]

[tex]x +456 = 540[/tex]

Subtract both sides 456

[tex]x + 456 - 456 = 540 - 456[/tex]

[tex]x = 84[/tex]

There u go...

Answer:

18cm

if it takes 12cm to wrap 6 presents, it means it takes 2cm to wrap one present.

9 individual presents will take 2 wraps, so Dwayne needs 18cm of wrapping paper.

Answer:

Step-by-step explanation:

Part A, the system of equation is, presented here as follows;

(1) 2·y = 3·x + 2

(2) y = 2·x² - 3·x + 2

Part B; The graph of the system of equation is attached

The reason for the above answers is as follows;

Part A

A system of equations are a given number of equations from which a common solution of the system can be found

A linear equation is an algebraic equation in which the maximum exponent of the variables is one and the graph of the equation is a straight line which is of the form y = m·x + c

A maximum value of the exponents of the variable quadratic equation is 2, and the general form of the quadratic equation is y = a·x² + b·x + c, where a, b, and c are real numbers

Therefore, the system of equation that can be created is as follows;

(1) 2·y = 3·x + 2

(2) y = 2·x² - 3·x + 2

Method for solving;

Divide equation (1) by 2, and equate both values of y to find the common solution as follows;

2·y/2 = (3·x + 2)/2 = 1.5·x + 1

∴ y = 1.5·x + 1

Equating both values of y gives;

y = 1.5·x + 1

y = 2·x² - 3·x + 2

Therefore;

1.5·x + 1 = 2·x² - 3·x + 2

2·x² - 3·x - 1.5·x + 2 - 1 = 0

2·x² - 4.5·x + 1 = 0

Using the quadratic formula, we get;

x = (4.5 ± √((-4.5)² - 4×2×1))/(2 × 2)

x = 2, or x = 0.25

From which we get;

y = 1.5 × 2 + 1 = 4, or y = 1.5 × 0.25 + 1 = 1.375

The points where the line graph and the quadratic graph intersect are;

(2, 4), and (0.25, 1.375)

Part 2

Answer:

A i= 44. B i= 44. C i= 40.

Answer:

22%

Step-by-step explanation:

formula for percentage increase:
increase/original number x 100

increase is $66 (366-300)

66/300 x 100

= 22/100 x 100

= 22

hope this helped :)

The expression that can be used to represent Rebekah's age in years given Yvonne's age is 3y - 1.

Mathematical expressions are statements that contain a combination of numbers and variables.

Given that Yvonne's age is y.

Rebekah's age = one less than 3 times y. 'less' means subtraction and 'times' means multiplication.

(3 x y) - 1

3y - 1

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Answer:

3.09 per ft

Step-by-step explanation:

1 yd = 3ft

so 2 yd = 6ft

6ft = 18.54

18.54  /6ft

3.09 per ft

Add the prices together:

1.50 + 0.80 + 0.90 = 3.20

Answer: B. $3.20

Answer:

$  3.20  (Answer B)

Step-by-step explanation:

Add up the three prices given:

 $1.50

    0.80

     0.90

-------------

  $  3.20  (Answer B)

Answer:

y=8

Step-by-step explanation:

vertical lines parallel to x axis

Answer:

2^1/6

Step-by-step explanation:

either find the result of all equations or

times square root(2) by cube root (3) and put it over 1

... 1/6 and put this as the power to the number in the question

The true statement about the bank survey is (e) The bank does not need to use an inference procedure to determine the participant proportion

The population and the sample size are given as:

N = 60

This is so because the bank surveyed all her staff.

Since all the bank staffs participated in the survey, it means that the proportion of the study is 1 or 100%.

So, the bank do not need to determine the proportion that participates

Hence, the true statement is (e)

Read more about surveys at:

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The y-intercept is the b term in slope intercept form (y = mx + b) or in the form of a point (0, y).

Function 1 is in slope-intercept form, and the b term is 5.

Function 2 is given in a table, but it is easy to find the point (0, y) and y is 5.25.

5.25 > 5

Function 2 has the greater y-intercept.

Hope this helps!

Answer:

  $793

Step-by-step explanation:

The amount of money in an account earning simple interest is given by the formula ...

  A = P(1 +rt)

where P is the principal invested at rate r for t years.

__

Using the values given in the problem statement, the account balance can be found to be ...

  A = $650(1 +0.055×4) = $650×1.22 = $793

There will be $793 in the account after 4 years.

the question is not visible lol

P=80º

Start by doing 180-20 since N=20

M and P are congruent, so P = 160/2

P=80

Answer:

The area of T is equal to sum of area of R and Triangle

Step-by-step explanation:

[tex]area = 12 \times 2[/tex]

Area)= 24

[tex]area = \frac{1}{2} \times 12 \times 15[/tex]

Area= 90

Area of T = 90 PLUS 24

AREA == 114