Give a button and a bookmark
to each student who visited the fair. The buttons came in
packages of 30. The bookmarks came in packages of 50.
The committee needed the same number of each left
over for another fair. The committee estimated that
400 students would visit the fair. How many
packages of buttons and packages of bookmarks
did they need?

Answer:

Option A.

[tex]f(x)\leq 3x+4[/tex]

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

Step-by-step explanation:

we know that

If point C is a solution of the system of inequalities, then point C must satisfy both inequalities

Point C is located below the solid line f(x) and below the solid line g(x)

so

The shaded region of the solution set of the system must be below of the inequality f(x) and must be below of the inequality g(x)

therefore

The system is

[tex]f(x)\leq 3x+4[/tex]

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

Answer:

B

Step-by-step explanation:

Grace is 9 years old. We found this by setting up a system of equations with the information given and solving for Grace's age.

We are given two pieces of information about Ava and Grace's ages:

To find Grace’s age, we can set up a system of equations based on the information provided:

The first equation can be written as:

A + G = 35

From the second piece of information, we can write:

A = 3G - 1

Now, we can substitute the expression for A into the first equation:

3G - 1 + G = 35

Combine like terms:

4G - 1 = 35

Add 1 to both sides:

4G = 36

Divide by 4:

G = 9

So, Grace is 9 years old.

Final answer:

Using the properties of isosceles triangles, the acute base angle of the isosceles trapezoid, which is part of an isosceles triangle with a 46° vertex angle, is found to be 67°.

Explanation:

To find the measure of an acute base angle of the isosceles trapezoid that is part of an isosceles triangle with a 46° vertex angle, we can apply the properties of isosceles triangles. By the Isosceles Triangle Theorem, we know that the angles opposite the equal sides are equal.

Since the given triangle is isosceles, the two base angles must also be equal. Additionally, we know that the sum of all angles in any triangle is 180°.

Let's call each of the base angles B. Then, the sum of all angles in the triangle is:

46° + B + B = 180°

Now we solve for B:

2B = 180° - 46° = 134°

B = 134° / 2 = 67°

Thus, each base angle of the isosceles triangle is 67°. Next, considering the isosceles trapezoid, we know the adjacent angles must be supplementary because they are on the same line. This means that one base angle of the isosceles trapezoid equals:

180° - 67° = 113°

However, since the student is looking for the measure of an acute base angle of the trapezoid and 113° is an obtuse angle, the acute base angle is the original 67° angle that we found. This is because the acute and obtuse angles in the trapezoid are adjacent angles around the same vertex, and the acute angle is the angle that's interior to the triangle.

Therefore, the measure of an acute base angle of the trapezoid is 67°.

Answer:

Fraction of jokes of Brandon that are funny = [tex]\frac{3}{10}[/tex]

Step-by-step explanation:

We are given that, 30% of the Brandon's jokes are funny.

Now, to convert percent into fraction, we will multiply it by [tex]\frac{1}{100}[/tex]

Now,

[tex]30\%=30\times\frac{1}{100}=\frac{30}{100} = \frac{3}{10}[/tex]

∴ [tex]\frac{3}{10}[/tex] of the Brandon's jokes were funny.

Answer:

Infinitely many solutions.

Step-by-step explanation:

-t=9(t-10)-t=9(t-10)

-t=9t-90-t=9t-90

-t=8t-90=9t-90

8t-(-t)-90=9t-90

8t+t-90=9t-90

9t-90=9t-90

Answer:

If you mean −t=9(t−10), then the answer is 9, if you mean −t=9(t−10)−t=9(t−10) then infinite solutions.

Step-by-step explanation:

Here is the answer if you mean −t=9(t−10):

−t = 9 (t−10)

Simplify the equation.

-t = (9)(t) + (9)(-10)

-t = 9t + -90 (Add the opposite)

-t = 9t - 90

Subtract -9t

-t -9t = 9t - 90 - 9t

-10t = - 90

Divide -10 on both sides to make sure the equation is balanced on both sides. And to isolate t to get the final answer.

-10t  =  -90

-10t  =  -10

Therefore,

Is the final answer.

I Hope this helps! Have a great rest of your morning, afternoon, or evening! :D

Answer:

160/x = 4/3

x = (160/4)(3) = 40(3) = 120

Apples: 160 pounds

Grapes: 120 pounds

Blackberries: 160 pounds

The total weight of this truckload of fruit is 160 + 120 + 160 = 440 pounds.

To find the total weight of the truckload of fruit with apples weighing 160 pounds in a ratio of 4:3:4, calculate the total ratio parts and apply it to the weight of apples. The total weight of the fruit is 440 pounds.

The truck carries apples, grapes, and blackberries in the ratio of 4:3:4.

To find the total weight, you need to calculate the total ratio parts, which is 4 + 3 + 4 = 11 parts. Then, for apples alone, 4 parts represent 160 pounds, so each part is 160/4 = 40 pounds. The total weight of the truckload of fruit would be 11 parts * 40 pounds = 440 pounds.

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Final answer:

To raise the fraction 1/5 to 15ths, multiply both the numerator and the denominator by 3 to get the equivalent fraction 3/15.

Explanation:

To raise the fraction 1/5 to 15ths, we need to find an equivalent fraction that has a denominator of 15. To do this, we need to find a number that we can multiply both the numerator and the denominator of 1/5 by to get a new fraction with a denominator of 15. Since 5 multiplied by 3 equals 15, we multiply both the numerator and the denominator of 1/5 by 3.

Thus, we have:

1/5 × 3/3 = 3/15

To raise the fraction 1/5 to 15ths, multiply both the numerator and the denominator by 3 to get the equivalent fraction 3/15.

The fraction 1/5 is equivalent to 3/15 when raised to 15ths.

Answer:

18 miles in 1.5 hours

Step-by-step explanation:

2 miles = 10 minutes

90 minutes (1.5 hours) / 10 minutes = 9

Multiply

2 miles (9) = 10 minutes (9)

18 miles = 90 minutes

18 miles in 1.5 hours

Hope this helps :)

Answer:

Brook is faster.

Step-by-step explanation:

1 hour=60 minutes

2 hours=2*60=120 minutes

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

7 miles in 30 minutes vs 25 miles in 120 minutes

7/30=0.233...mile per minute

25/120=0.20833...mile per minute

Brook is faster than Joshua.

To determine which person is faster, we can compare their average speeds.

Average speed is calculated by dividing the total distance traveled by the total time taken.

For Brook, she traveled 7 miles in 30 minutes, so her average speed is:

7 miles ÷ 30 minutes = 0.2333 miles per minute.

For Joshua, he traveled 25 miles in 2 hours, which is equivalent to 120 minutes. So his average speed is:

25 miles ÷ 120 minutes = 0.2083 miles per minute.

Therefore, Brook is faster than Joshua as her average speed is higher.

Answer: Neither

Step-by-step explanation:

Answer:

Option c) is correct.

That is x-5y=12 and 3x+2y=-15 are the system of linear equations satisfies the point (-3,3) so this is the  solution.

Step-by-step explanation:

To verify that which system of linear equations having the solution (-3,-3)

Let  [tex]x-5y=12\hfill (1)[/tex]

and [tex]3x+2y=-15\hfill (2)[/tex]

To solve it we have to use elimination method

First multiply the equation(1) into 3 we get

[tex]3x-15y=36\hfill (3)[/tex]

Now subtracting the equations (2)and (3) the signs may vary in the second equation we get

[tex]3x-15y=36[/tex]

[tex]-3x-2y=+15[/tex]

________________

[tex]-17y=51[/tex]

_______________

[tex]y=-\frac{51}{17}[/tex]

[tex]y=-3[/tex]

Now substitue the value y=-3 in equation (1) we get

[tex]x-5y=12[/tex]

[tex]x-5(-3)=12[/tex]

[tex]x=12-15[/tex]

Therefore x=-3

Therefore the solution is (-3,-3)

Therefore Option c) is correct.

That is x-5y=12 and 3x+2y=-15 are the system of linear equations satisfies the point (-3,3) so  the solution is (-3,-3).

Answer:

is it 8 apples to her mother or 10 since I had this exact problem?

Step-by-step explanation:

Ashe started with 32 apples in the basket initially.

To find the half of something just multiply 1/2 with the given value.

According to the given question Linda picked a basket of apples.

Assuming she had x apples initially.

She gave half of the apples to the neighbour,Therefore she now has            (x - 1/2x) apples which is = 1/2x apples.

Then she gave 10 to her mother,So the remaining apples she has now is

= ( 1/2x - 10 ) apples

= (x - 20)/2.

Then she gave half of the apples to her best friend so the no. of apples she has now is (x - 20)/2×1/2 which is = (x - 20)/4 and she kept the remaining 3.

∴ (x - 20)/4 = 3

x - 20 = 12

x =32.

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The solution is price of 1 slice of pizza is $ 1.542 and price of 1 bottle of water is $ 2.083

Solution:

Let "p" be the price of 1 slice of pizza

Let "b" be the price of 1 bottle of water

Given that Abby bought two slices of pizza and two bottles of water for $7.25

So we can frame a equation as:

two slices of pizza x price of 1 slice of pizza + two bottles of water x price of 1 bottle of water = $ 7.25

[tex]2 \times p + 2 \times b = 7.25[/tex]

2p + 2b = 7.25 ---- eqn 1

Also given that Cameron bought four slices of pizza and one bottle of water for $8.25

So we can frame a equation as:

four slices of pizza x price of 1 slice of pizza + one bottles of water x price of 1 bottle of water = $ 8.25

[tex]4 \times p + 1 \times b = 8.25[/tex]

4p + b = 8.25 ---- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "p" and "b"

Multiply eqn 2 by 2

8p + 2b = 16.5 --- eqn 3

Subtract eqn 1 from eqn 3

8p + 2b = 16.5

2p + 2b = 7.25

(-) ----------------------

6p = 9.25

From eqn 1,

2p + 2b = 7.25

2(1.542) + 2b = 7.25

2b = 4.166

Thus price of 1 slice of pizza is $ 1.542 and price of 1 bottle of water is $ 2.083

Answer:

C. there is no solution since 4=7 is a false statement

Linear equations are equations with a leading degree of 1. This shows that there is no solution since 4 =7 is a false statement

Linear equations are equations with a leading degree of 1. Given the linear equation

Given

13+4x-9=7x+7-3x

Simplify

4 + 4x = 4x + 7

Collect the like terms

4x - 4x = 7 - 4
0x = 3

This shows that there is no solution since 4 =7 is a false statement

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Answer:

20

-

3

Step-by-step explanation:

Answer:

11k^3 (4k^2 - 6k +7)

Step-by-step explanation:

Take out the obvious GCF of 11

11 (4k^5 - 6k^4 + 7k^3)

Take out the GCF of k^3 (from the terms in the parentheses)

11k^3  (4k^2 - 6k + 7)

.

Factor the polynomial by its greatest common monomial factor of 44k^5-66k^4+77k^3 is:

Take out the obvious GCF of 11

11 (4k^5 - 6k^4 + 7k^3)

Take out the GCF of k^3 (from the terms in the parentheses)

11k^3  (4k^2 - 6k + 7)

To find the greatest common factor (GCF) among monomials, take each monomial and write it as high factorization. Then, identify the factors commonplace to each monomial and multiply the commonplace elements collectively.

Steps to Factoring a Monomial from a Polynomial

Conclusion: factoring trivial factors greatest common factor high polynomials whole factorization big concept common monomial factoring is the procedure of writing a polynomial as a made from two polynomials, considered one of that's a monomial that elements each term of the polynomial.

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Answer:

the remainder is 10

Step-by-step explanation:

Answer:

R=10

Step-by-step explanation:

1. 428/19=22

2. R=10

Steps for checking your work:

1. Multiply the divisor by the answer (aka quotient)

2. After that, add the remainder to the answer you got from doing step 1 for checking your work (aka proudct, since you multiplied)

Answer:

6.7√2 in ≈ 9.48 in

Step-by-step explanation:

First, use the area of the square to find the side length.

A = s²

44.89 in² = s²

s = 6.7 in

The diagonal of a square divides it into 45-45-90 triangles.  You can use Pythagorean theorem to find the length of the diagonal.

c² = a² + b²

c² = (6.7 in)² + (6.7 in)²

c = 6.7√2 in

c ≈ 9.48 in

Answer: 6.7√2

Step-by-step explanation: Let's start this problem by drawing a picture of a square with a diagonal of length x.

Now to find the length of the diagonal, let's first find the length of a side of the square. To find the length of a side, remember that the formula for the area of a square is S² and since we know that the area of the given square is 44.89 inches, we can set up the equation 44.89 = S².

Square rooting both sides, we have 6.7 = S so we can give the side of our square a length of 6.7. Now to find the value of x, it's important to understand that the diagonal of a square creates 45° 45° 90° triangles and in a 45° 45° 90° triangle, the hypotenuse = √2 × leg.

So we have x = 6.7√2.

So the length of the diagonal of the square is 6.7√2 inches.

Image provided.

Answer:

Linear

Explanation:

The first image attached below is the problem graphed. That is a linear line.

The second image is an example of a quadratic line.

This is how you can tell the line is linear.

Answer:

x = 5

Step-by-step explanation:

7x is a secant- secant angle and has measure equal to half the difference of the intercepted arcs, that is

7x = 0.5(22x + 10 - 50)

7x = 0.5(22x - 40) ← distribute

7x = 11x - 20 ( subtract 11x from both sides )

- 4x = - 20 ( divide both sides by - 4 )

x = 5

Answer:

x = 100°

y = 125°

z = 55°

Step-by-step explanation:

A straight line is 180°

A triangle is 180°

Solve in this order:

X: 180 - 80 = 100

Z: 180 - 80 - 45 = 55

Y: 180 - 55 = 125

Answer:

-4,-1,3,5,6

Step-by-step explanation:

The first set because domain is the set of elements giving values of x

Approximately $ 31419 profit is earned from selling books in entire month

Solution:

Given that Jodie had sold 885 copies of her new book

At the end of the month, she had sold 1,364 copies of her book

We have to determine the profit earned in the entire month

From given information,

Start of month sale = 885 copies

End of month sale = 1364 copies

Total copies of books sold = Start of month sold + end of month sold

Total copies of books sold = 885 + 1364 = 2249

Also given that each book profit is $ 13.97

Profit of 1 book = $ 13.97

Therefore for 2249 books, profit earned is given as:

Profit of 2249 books = $ 13.97 x 2249 = 31418.53

Therefore approximately $ 31419 profit is earned from selling books in entire month

Answer:

Step-by-step explanation:

4x - 2y = -5

-2y = -4x - 5

y = 2x + 5/2.....slope here is 2

-2x + 3y = -3

3y = 2x - 3

y = 2/3x - 1.....slope here is 2/3

NONE OF THE ABOVE.....they are not the same line....they are not parallel because they dont have the same slope....they are not perpendicular because they do not have negative reciprocal slopes

Answer:

this would be none of the above.

Step-by-step explanation:

its not equal because when solving, x and y isnt the same for both equations.

i cant explain the rest, my apologies but if u use a website called *desmos* you can put up equations and itll graph them for you. :3

Answer:

I think it's $1,349.86

Answer:

It's $1,349.86

Step-by-step explanation:

(trust me bro)

Answer:

The first is a solution, but the second is not

Step-by-step explanation:

we know that

If a ordered pair is a solution of a linear equation, then the ordered pair must satisfy the linear equation (makes the equation true)

we have

[tex]5x-\frac{y}{3}=13[/tex]

Verify the first ordered pair

Part a) we have (2,-9)

For x=2, y=-9

substitute in the linear equation

[tex]5(2)-\frac{(-9)}{3}=13[/tex]

[tex]10-(-3)=13[/tex]

[tex]10+3=13[/tex]

[tex]13=13[/tex] ----> is true

so

The ordered pair satisfy the equation

The ordered pair is a solution of the equation

Verify the second ordered pair

Part b) we have (3,-6)

For x=3, y=-6

substitute in the linear equation

[tex]5(3)-\frac{(-6)}{3}=13[/tex]

[tex]15-(-2)=13[/tex]

[tex]15+2=13[/tex]

[tex]17=13[/tex] ----> is not true

so

The ordered pair not satisfy the equation

The ordered pair is not a solution of the equation

Answer:

11/147

Step-by-step explanation:

11 + 7 + 3 = 21

chances of red = 11/21

and chances of yellow = 3/21

3/21 = 1/7

11/21 x 1/7 = 11/147

Answer:

14:30

Step-by-step explanation:

Okay so your looking for the probability of red or yellow roses so you would combine the numbers of red and yellow roses then add all the roses up together, all the red and yellow are 14 and there are 30 roses in the shop so the answer would be 14:30

Answer:

1.  A

2.  (6, 0.7)

3.

[tex]10.99D \leq 90.01[/tex]

and

[tex]10.99D + 9.99 \leq 100[/tex]

Step-by-step explanation:

1.

The equation to solve is:

[tex]Ax+4Ax=51+2Ax[/tex]

The variable is "x", so we take all the terms with x's and take the number to one side. Then we add up the like terms of x's and solve for x. Shown below:

[tex]Ax+4Ax=51+2Ax\\Ax+4Ax-2Ax=51\\x(A+4A-2A)=51\\x(3A)=51\\x=\frac{51}{3A}\\x=\frac{17}{A}[/tex]

x = 17/A

Correct answer is A

2.

The equation is:

[tex]10y=3x-11[/tex]

The point that would lie on the graph is the point when put, makes the equation true. So we check each point and see if the equation holds:

[tex]10y=3x-11\\10(0.5)=3(2)-11\\5\neq -5[/tex]

first point doesn't lie on the graph.

[tex]10y=3x-11\\10(1)=3(4)-11\\10 \neq 1[/tex]

second point doesn't lie on the graph.

[tex]10y=3x-11\\10(0.7)=3(6)-11\\7=7[/tex]

This point lies on the graph. So, this is the answer.

Correct answer is (6, 0.7)

3.

Let Miguel buy D DVDs. Each costing 10.99, that would make the cost:

10.99D

Shipping cost entire order is 9.99, so this would be added to DVD cost. Total cost:

10.99D + 9.99

This total cost can be NO MORE THAN 100, so this expression would be equal to or less than 100, so we can write:

[tex]10.99D + 9.99 \leq 100[/tex]

If we take 9.99 to the right side and subtract, it becomes:

[tex]10.99D \leq 90.01[/tex]

First choice is correct.

Second choice, clearly, isn't correct.

Third choice, similarly, isn't correct as well.

Fourth choice, because of "+" sign on right side (of 9.99) is also incorrect.

Fifth choice is what we initially got, so this is correct.

First and Fifth Choice is right.

Answer:

Step-by-step explanation:

Just do the long division and you'll find out.