Three girls are selling cases of popcorn to earn money for a band trip. In their first week, emily sold 2 3/4 cases,brenda sold 4 1/4 cases, and shannon sold 31/2 cases. How many cases of popcorn have the girls dold in all?

Answer: 5 units down, 3 units up.

Step-by-step explanation: at the translation, the line is at 5, -3, putting the translation at 5 units right, 3 units up.

Answer:

[tex](-\infty,+\infty)[/tex]

Step-by-step explanation:

The given function is

[tex]y=\sqrt[3]{x+8}[/tex]

The range refers to the values of y for which  x is defined.

We solve for x to obtain;

[tex]y^3=x+8[/tex]

[tex]x=y^3-8[/tex]

This is a polynomial function in y.

x is defined for all values of y.

Therefore the range is all real numbers.

or

[tex](-\infty,+\infty)[/tex]

The first choice is correct.

Answer:

range is -∞<y<∞

Step-by-step explanation:

[tex]y=\sqrt[3]{x+8}[/tex]

Range of the given function is same as the domain of the inverse function

LEts find the inverse for the given equation

Swap the variables x and y . then solve for y

[tex]y=\sqrt[3]{x+8}[/tex]

[tex]x=\sqrt[3]{y+8}[/tex]

Take cube on both sides

[tex]x^3= y+8[/tex]

Subtract 8 from both sides

[tex]y=x^3-8[/tex]

Inverse function is a cubic function. For cubic function the domain is set of allr eal numbers. -∞<x<∞

Range of the given function is same as the domain of the inverse function

So range is -∞<y<∞

The first one is three

The second one is twelve

The last one is 2

Answer:

The slope will be 1 so one point down and one up.

The y-intercept is -2.

Step-by-step explanation:

s=slope

i=intercept

y=s*x+i

Answer:

Two more people.

Step-by-step explanation:

If 4 people can mow a lawn in 6 hours, then 4 people can mow 1/6 of a lawn in 1 hour.

If 4 people can mow 1/6 of a lawn in 1 hour, then 1 person can mow 1/24 of a lawn in 1 hour.

If 1 person can mow 1/24 of a lawn in 1 hour, then 6 people can mow 1/4 of a lawn in 1 hour.

If 6 people can mow 1/4 of a lawn in 1 hour, then 6 people can mow a lawn in 4 hours.

6 people minus 4 people is 2 people.

There are two more people will be needed to mow the lawn in 4 hours, It is assuming that each person mows at the same rate

The rate of work is defined as the number of units of work completed per unit time.

Let the number of the person are x,

Condition 1;

4 people in 6 hours complete the work, work done in one hour;

1 hour =(1/6) of the total work

Condition 2;

If four individuals can do one-sixth of the total work, one person can do one-quarter of the work in an hour.

1 person do = (1/4) of the total work;

Condition 3;

If one person can do 1/24 of total work

Six persons can do 1/4 of total work in the same amount of time.

If six individuals can mow a quarter of a lawn in an hour, The number of  people will be needed to mow the lawn in 4 hours;

n=6-4

n=2

Hence, there are two more people will be needed to mow the lawn in 4 hours,

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Answer:

It's ÷ (divide)

Step-by-step explanation:

Because 48+27 is 75, and 750÷10 is also 75.

Hope I helped :)

ANSWER

4.2kg

EXPLANATION

We want to convert the weight of Eliot's backpack, which weighs 4,200 grams into kilograms.

We know that:

1,000 grams =1kg

Therefore :

[tex] 4200g = \frac{4200}{1000} = 4.2kg[/tex]

Therefore the weight of Elliot backpack in kilograms is 4.2kg

Answer:

Circle Area: A=πr2

Square Area: Mulitply the Length by width

Triangle Are: A=hbb

2

Step-by-step explanation:

Hopes this helps!

Answer:

24

Step-by-step explanation:

Recall that in an equilateral triangle, all the interior angles are the same, that is, all are 60°.  If we look at the lower right 60° angle, we see that the side opposite this angle is the altitude (height) of the triangle.

In this problem the height is 4√3.  What is the hypotenuse?  We need to find the hypotenuse, because 3 times the length of this hypotenuse is the perimeter of the triangle.  

Consider the sine function.  Here, sin 60° = 4√3 / hyp, or:

√3        4√3

------- = -----------

    2        hyp

thus, the length of the hypotenuse is 8 and the perimeter of the triangle is 3 times that, or 24.

Answer:

4,1,2,3

Step-by-step explanation:

1.8+7=15

2.10/5=2

3.8+10=18

4.2(5)=10

Answer:

the answer is d

Step-by-step explanation:

To solve 2y - x = 3/4 (-y + 1) for y, distribute 3/4, combine like terms, and isolate y. The solution is y = (4x - 3)/11, which is answer D.

The student has asked to solve for y in the equation: 2y - x = 3/4 (-y + 1). To solve for y, we can follow these steps:

First, distribute the 3/4 across the parentheses: 2y - x = 3/4 (-y) + 3/4 (1).

This simplifies to: 2y - x = -3/4y + 3/4.

Add 3/4y to both sides to get: 2y + 3/4y - x = 3/4.

Combine like terms on the left: (2 + 3/4)y - x = 3/4. This is equivalent to (11/4)y - x = 3/4.

Add x to both sides: (11/4)y = x + 3/4.

Finally, multiply both sides by 4/11 to solve for y: y = (4/11)x + 3/11.

Therefore, the correct answer is D) y = (4x - 3)/11.

The function g(x) increases the slope of the line by a factor of 8.

We have,

Parent function f(x)=x.

We have to find the change will occur in the function when the parent function f(x) is replaced by 8f(x).

let g(x) be the function by replacing f(x) with 8f(x)

g(x)=8 f(x)

g(x) = 8x

Here, the slope of function is 8 and slope of g(x) is 1.

Thus, g(x) increases the slope of the line by a factor of 8.

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Replacing f(x) with 8f(x) scales up the output values of the function by 8 times. This results in the graph of the function stretching vertically i.e., it gets steeper.

The question is asking about the change in the parent function f(x)=x when we replace f(x) with 8f(x). This operation vertically stretches the graph of the parent function by a factor of 8. In mathematic terms, it scales up the output (or 'y' values) of the function by 8 times. To visualize this, if the original function produced a straight 45 degree line (for f(x)=x), this line will now become steeper, with all y-values multiplied by 8 i.e., the steepness or the slope of the line significantly increases. On a graph, instead of a point (1,1) on the line, you will see the point has moved up to (1, 8).

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1.   1.5x - 10 = 3 (2x - 4)

Step 1: Distribute 3 to the numbers in the parentheses

1.5x - 10 = (3 *2x) + (3* - 4)

1.5x - 10 = (6x) + (-12)

1.5x - 10 = 6x- 12

Step 2: Combine like terms (x's go with x's). Subtract 6x from both sides so that it is canceled out from the right side and brought to the left side.

(1.5x-6x) - 10 = - 12

-4.5x -10 = -12

Step 3: Continue combining like terms by adding 10 to both sides. This will cancel out -10 from the left side and move it to the right

-4.5x = -12 + 10

-4.5x = -2

Step 4: Divide -4.5 to both sides to isolate x

(-2/-4.5) = x

4/9 = x

2.  3 (-3x + 2) +4x = 1/2(5x - 30) - 9

Step 1: distribute 3 to the numbers in the parentheses.

(3*-3x) + (3*-2) +4x = 1/2 (5x - 30) -9

-9x + (-6) +4x = 1/2 (5x -30) -9

Step 2:

ANSWERS

A.

[tex] \frac{19}{20} [/tex]

EXPLANATION

It was given that triangle LMN is a right triangle and angle L and M are complementary.

This implies that:

[tex] \sin(L) = \cos(M) [/tex]

It was given in the question that:

[tex] \cos(M) = \frac{19}{20} [/tex]

This implies that:

[tex] \sin(L) = \frac{19}{20} [/tex]

Answer:

A. y = x^2 -6x + 13

Step-by-step explanation:

The parabola that opens up and has line of symmetry x=3 and a minimum at x=3  is

[tex]y=x^2-6x+13[/tex]

The reason is that, we can write this function in the vertex form to get;

[tex]y=x^2-6x+(-3)^2+13-(-3)^2[/tex]

[tex]y=(x-3)^2+13-9[/tex]

[tex]y=(x-3)^2+4[/tex]

Hence the line of symmetry is x=3 and the vertex is (3,4)

Answer:

option A

y = x² - 6x + 5

Step-by-step explanation:

step 1

Find out if a is positive or negative.

'a' is the coefficent of x

If the parabola is facing up , then a must be positive.

a = 1

Step 2

To find the minimum point

x = -b/2a

using the standard equation y = ax² + bx + c

x must be equal to 3

Equation 1

y = x² -6x + 13

x = -(-6)/2(1)

x =  3(ACCEPTED)

Equation 2

y = x² + 6x + 5

x = -6/2(1)

x = -3      

Equation 3

x² - 3x + 6

x =  3/2(1)

x =  3/2

Equation 4

x² + 8x + 19

x = -8/2(1)

x = -4

Step 3

At the minimum point there will be line of symmetry hence x = 3

Answer:

If you're asking for how many notebooks she bought, the answer is 16.

Step-by-step explanation:

Mrs. Lindy spends a total of 52$. If n represents the number of notebooks and each notebook costs $3.25, your equation will be 3.25n= 52. To solve for n, you have to get rid of 3.25 from both sides. Since you're multiplying 3.25 to n, divide by 3.25 to both sides to cancel it out. 52 divided by 3.25 equals 16, so n = 16. This means that Mrs. Lindy bought 16 notebooks.

I hope this helps!

Mrs Lindy  can buy at-most 16 books.

A statement of an order relationship-greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.

It is given that,

Number of notebooks = n

Cost of notebooks = $52

Cost of each notebook = $3.25

Now,As Mrs Lindy  can spend only $52 on books, this means cost of n books should be less than or equal to 52. We can represent this information in an equation as:

3.25n ≤ $52

⇒ n ≤ $52/3.25

⇒ n ≤ 16

Therefore, Mrs Lindy  can buy at-most 16 books.

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Answer:

39° and 51°

Step-by-step explanation:

The angle formed by 1 and 2 is a right angle = 90°, thus

∠1 + ∠2 = 90 ← substitute values

x + 22 + 3x = 90

4x + 22 = 90 ( subtract 22 from both sides )

4x = 68 ( divide both sides by 4 )

x = 17

Hence

∠1 = x + 22 = 17 + 22 = 39°

∠2 = 3x = 3 × 17 = 51°

Answer:

C

Step-by-step explanation:

[tex]m=\frac{y_2-y_1}{x_2-x_1} \\ \\ y_2-y_1=m(x_2-x_1) \\ \\ -y_1=-y_2+m(x_2-x_1) \\ \\ y_1=y_2-m(x_2-x_1)[/tex]

Answer:

C

Step-by-step explanation:

Given

m = [tex]\frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }[/tex] ( cross- multiply )

y₂ - y₁ = m(x₂ - x₁) ( subtract y₂ from both sides )

- y₁ = m(x₂ - x₁) - y₂

Multiply through by - 1

y₁ = - m(x₂ - x₁ ) + y₂, thus

y₁ = y₂ - m(x₂ - x₁ ) → C

Answer:

That number is 0.45

Step-by-step explanation:

3/5x = 2x - 63/100

0.63 = 2x - 3/5x

0.63 = 10/5x - 3/5x

0.63 = 7/5x

7x = 0.63*5 = 3.15

x = 3.15/7

Answer:

0.63Google

Step-by-step explanation:

Answer:

  (8, -1)

Step-by-step explanation:

We note that the coefficients of y are opposites, so when we add these equations, the y-terms will cancel:

  (3x -8y) +(-x +8y) = (32) +(-16)

  2x = 16 . . . . simplify

  x = 8 . . . . . . divide by 2

  -8 +8y = -16 . . . substitute into the second equation

  -1 +y = -2 . . . . . divide by 8

  y = -1 . . . . . . . . add 1

The solution is (x, y) = (8, -1).

_____

Comment on systems of equations

There are formulas for the solution of a system of equations like this. However, we are taught several methods that can be used instead of the formulas. One of my favorite is graphing, now that graphing calculators and apps are available on-line and on your local smart device. Other ad hoc methods include "elimination" or "addition", and "substitution." Using these methods can often save steps over using a formula, which is partly why they're taught.

Hey there! :)

Please keep in mind that slope-intercept form is : y=mx+b ; where m=slope, b=y-intercept

Using this, we can isolate y in our original given equation.

12x - y = 4

Start off by subtracting 12x from both sides.

-y = -12x + 4

Divide both sides by -1.

-y ÷ -1 = (-12x + 4) ÷ -1

Simplify!

y = 12x - 4

Therefore, using the slope-intercept form, we can come to the conclusion that because 12 is located in the "m" slot and "m=slope" then 12 is our slope. In addition, -4 is our y-intercept because it is located on the y position.

Slope = 12

Y-intercept = -4

Hope I helped! :)

Answer:

[tex]x<-2[/tex]

Step-by-step explanation:

Isolate the variable to find the solution set.

[tex]5>x+7 \\ \\ x<-2[/tex]

Answer:

see explanation

Step-by-step explanation:

Solve the inequality

5 > x + 7 ( subtract 7 from both sides )

- 2 > x ⇒ x < - 2

solution set {x | x ∈ R, x < - 2 }

Answer:

(x - 2)(x² + 2x + 4)

Step-by-step explanation:

A difference of cubes factors in general as

• a³ - b³ = (a - b)(a² + ab + b² )

note 8 = 2³ = 8 ⇒ b = 2 , with a = x

Hence

x³ - 8

= x³ - 2³

= (x - 2)(x² + 2x + 2²) = (x - 2)(x² + 2x + 4)

Answer: The rewritten expression would be [tex](x-2)(x^2+2x+4)[/tex]

Step-by-step explanation:

Since we have given that

[tex]x^3-8[/tex]

We need to use the difference of cubes:

As we know the formula of "Difference of cubes":

[tex]a^3-b^3=(a-b)(a^2+b^2+ab)[/tex]

So, it can be written as

[tex](x)^3-(2)^3=(x-2)(x^2+2x+4)[/tex]

Hence, the rewritten expression would be [tex](x-2)(x^2+2x+4)[/tex]

Answer:

There are 29760 possible ways

Step-by-step explanation:

Mrs. Pearson must elect a President, a Vice President and a Treasurer. Then you must choose 3 people. In this case the order matters, because there are three different positions (President, Vice President and Treasurer)

So this is a problem of perm

So this is a problem of permutations. The formula to calculate a permutation is:

[tex]P(n, r)=\frac{n!}{(n-r)!}[/tex]

Where n is the total number of people and you can choose r of them

So:

[tex]P(32, 3)=\frac{32!}{(32-3)!}[/tex]

[tex]P(32, 3)=\frac{32!}{29!}[/tex]

[tex]P(32, 3)=29760[/tex]

Final answer:

The roles of President, Vice President, and Treasurer need to be assigned to 32 students in a class. The total number of ways these roles can be assigned is 29760 ways.

Explanation:

The roles of President, Vice President, and Treasurer need to be assigned to 32 students in Mrs. Pearson's class.

To find the number of ways the roles can be assigned, we use the concept of permutations:

President can be selected from 32 students in 32 ways.

Vice President can be selected from the remaining 31 students in 31 ways.

Treasurer can be selected from the remaining 30 students in 30 ways.

Therefore, the total number of ways the roles can be assigned is 32 x 31 x 30 = 29760 ways.

Check the picture below.

make sure your calculator is in Degree mode.

Answer:

1: Permutation

2: 3080

Step-by-step explanation:

As order matters, (first place as opposed to second place) this must be a permutation.

For first place, there are 56 different contestants that could win it, while once first place is selected, there are only 55 to get second. This means that

56*55=3080

Answer:

it would be a rectangle

Step-by-step explanation:

it would be a rectangle because when you cut it in the cross section there will be four parell sides, so therefore it would have to make a rectangle because the side lengths would not be even.

Answer: it would be a rectangle

Answer:

16

Step-by-step explanation:

a/(1-r)

Use the infinite geometric series formula.

ANSWER

[tex]S_{\infty} = 16 [/tex]

EXPLANATION

Given the series:

8 + 4 + 2 + . . .

The first term of the series is

[tex]a_1 = 8[/tex]

The common ratio is

[tex]r = \frac{4}{8} = \frac{1}{2} [/tex]

The sum of this series is given by

[tex]S_{\infty} = \frac{a_1}{1 - r} [/tex]

[tex]S_{\infty} = \frac{8}{1 - \frac{1}{2} } [/tex]

Simplify:

[tex]S_{\infty} = \frac{8}{\frac{1}{2} } = 8 \times 2 = 16 [/tex]

Answer:

(x-3)^2

Step-by-step explanation:

Answer:

x = 3.391

Step-by-step explanation:

first you calculate.

7.9% - 0.25 = 3.22 + x

divide the numbers

[tex]\frac{7.9}{100}[/tex] - 0.25 = 3.22 + x

calculate again.

0.079 - 0.25 = 3.22 + x

move the terms

-0.171 = 3.22 + x

add the numbers

-x = 3.22 + 0.171

then change the signs

-x = 3.391

Final ans : x = -3.391

or some alternate answer's

x = -[tex]\frac{3391}{1000}[/tex] , x = -3[tex]\frac{391}{1000}[/tex]

Answer:x=−3.371

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

7.9

100

−0.25=3.2+x

0.079+−0.25=3.2+x

(0.079+−0.25)=x+3.2(Combine Like Terms)

−0.171=x+3.2

−0.171=x+3.2

Step 2: Flip the equation.

x+3.2=−0.171

Step 3: Subtract 3.2 from both sides.

x+3.2−3.2=−0.171−3.2

x=−3.371