emily and how are selling wrapping paper for a school fundraiser. customers can buy rolls of plain wrapping paper and rolls of holiday wrapping paper. emily sold 14 rolls of plain wrapping paper and 6 rolls of holiday wrapping paper for a total of $248. joe sold 10 rolls of plain wrapping paper and 12 rolls of holiday wrapping paper for a total of $316. find the cost each of one roll of plain wrapping paper and one roll of holiday wrapping paper.

Answer:

a. 53/82

b. 13 7/8

c. 12 16/23

d. 8 1/2

e. 5 8/15

f. 10 1/2

g.  3 13/18

h.   1 39/40

Step-by-step explanation:

Step-by-step explanation:

a. 13/41 + 27/82

[tex]\frac{13}{41}+\frac{27}{82}[/tex]

[tex]\frac{13\times 82+27\times 41}{82\times 41}=\frac{53}{82}[/tex]

b. [tex]3\frac{5}{24} + 6\frac{7}{24} + 4\frac{9}{24}[/tex]

[tex]\frac{77}{24}+\frac{151}{24}+\frac{105}{24}[/tex]

[tex]\frac{77+151+105}{24}=\frac{333}{24}[/tex]

c) [tex]5\frac{2}{3} + \frac{29}{69} + 6 \frac{21}{23}[/tex]

[tex]\frac{17}{3}+\frac{29}{69} +\frac{159}{23}[/tex]

[tex]\frac{17\times 23}{3\times 23}+\frac{29}{69} +\frac{159\times 3}{23\times 3}[/tex]

[tex]\frac{17\times 23+29+159\times 3}{69}=\frac{897}{69}=\frac{13}{1}[/tex]

d) [tex]3\frac{9}{10} + \frac{4}{9} + \frac{7}{45} + 4[/tex]

[tex]\frac{39}{10} + \frac{4}{9} + \frac{7}{45} + \frac{4}{1}[/tex]

[tex]\frac{39}{10} +\frac{4\times 10}{1\times 10}+\frac{4\times 5}{9\times 5} + \frac{7}{45}[/tex]

[tex]\frac{39+1\times 10}{10}+ +\frac{4\times 5+7}{45}[/tex]

[tex]\frac{49}{10}+\frac{27}{45}[/tex]

[tex]\frac{49\times 45+27\times 10}{10\times 45}=\frac{11}{2}[/tex]

e)[tex]6-\frac{7}{15}[/tex]

[tex]\frac{6}{1}--\frac{7}{15}[/tex]

[tex]\frac{6\times 15-7\times 1}{1\times 15}=\frac{83}{15}[/tex]

f)[tex]11\frac{3}{8} - \frac{7}{8}[/tex]

[tex]\frac{91}{8}- \frac{7}{8}[/tex]

[tex]\frac{91-7}{8}=\frac{84}{8}=\frac{21}{2}[/tex]

g)[tex]7 \frac{1}{6} - 3\frac{4}{9}[/tex]

[tex]\frac{43}{6}-\frac{41}{9}[/tex]

[tex]\frac{43\times 9-41\times 6}{54}[/tex]

[tex]=\frac{141}{54}=\frac{47}{18}[/tex]

h)[tex]5\frac{3}{8}-3\frac{2}{5}[/tex]

[tex]\frac{43}{8}-\frac{17}{5}[/tex]

[tex]\frac{43\times 5-17\times 8}{8\times 5}=\frac{79}{40}[/tex]

Hey!

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[tex]\boxed{ \bf A.~15,006.099~<~15,006.101}[/tex]

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

Explanation:

Since both numbers have 15,006 before the decimal we only need to see which number has a bigger decimal.

0.099 < 0.101

0.101 - 0.099 = 0.002

So, 15,006.101 is 0.002 bigger than 15,006.099!

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

Hope This Helped! Good Luck!

Answer:

x≤-17/9

Step-by-step explanation:

9x≤-17

1) Divide both sides by 9:

x≤-17/9

12×12 squared is = 12•144/=

1728

If you need a better explanation just ask in the comments.

Happy to help! Please mark as BRAINLIEST! Thanks

Answer:

-4 and 6

Step-by-step explanation:

sum means +

-4+6=2

difference means -4-6=10

The sum of two integers is 2 and their difference is 10 then the two integers will be -4 and 6 and this can be determined by using the arithmetic operations.

Given :

Let the two integers be 'a' and 'b'. Then the sum of the two integers will be:

a + b = 2   ---- (1)

The difference between the two integers will be:

a - b = 10  ----- (2)

Now, solve the equation (1) for 'a'.

a = 2 - b --- (3)

Now, put the value of 'a' in equation (2).

2 - b - b = 10

2 - 2b = 10

2b = -8

b = -4

Put the value of 'b' in equation (3).

a = 2 - (-4)

a = 2 + 4

a = 6

Therefore, the correct option is D) -4 and 6.

For more information, refer to the link given below:

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y=8(x^2 + 4x + 4) +17 + -32

Simplify:

y = 8(x^2 + 4x + 4) + 15

Use distributive property:

y = 8x^2 + 32x +32 - 15

Simplify:

y = 8x^2 + 32x +17

Complete the square using  form ax^2+bx+c:

a = 8, b = 32, c = 17

vertex form = a(x+d)^2+e

d = b/2a and e = c-b^2/4a

d = 32/2*8 = 32/16 = 2

e = 17 - 32^2/4*8 = 17-1024/32 = 17-32 = -15

Vertex form = y = 8(x+2)^2 + -15

Answer:

18/49 or 0.367

Step-by-step explanation:

1 (1/6)=7/6

now,

3/7 ÷ 1 (1/6)

=3/7 ÷ 7/6        [∵1 (1/6)=7/6]

=3/7 x 6/7          

=18/49

=0.367

Answer:

4x - 9y = 3

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

Given

4x - 8 = 9y - 5 ( subtract 9y from both sides )

4x - 9y - 8 = - 5 ( add 8 to both sides )

4x - 9y = 3 ← in standard form

The original equation 4x - 8 = 9y - 5 can be rearranged to the standard form by initially adding 8 to both sides and then subtracting 9y from both sides. The final equation in standard form is 4x - 9y = 3.

The given equation is in the form of 4x - 8 = 9y - 5. To convert the equation to standard form, we'll need to rearrange it so all variables and constants are on one side of the equation. Standard form is typically written as Ax + By = C. Here are the steps to do that:

So, the

standard form

of the given equation is 4x - 9y = 3.

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Answer:

See attached graph

Step-by-step explanation:

The graph of distance from home as a function of time starts at the origin of coordinates (0,0) since at time zero minutes Varun is at home.

Then we represent his driving at constant speed (although it has not been specified in the problem) as a line with positive slope equal to his speed, that goes on for the first five minutes. After that, he reaches the traffic light that keeps him at the same distance from home for three minutes (notice the line representing the distance covered is flat from minute 5 to minute 8, while he is not moving).

Then he starts moving again (we assume at the same speed as before - so the line representing his position is again a line with positive slope and with the SAME inclination as that which represents the first 5 minutes of his trip.

The line ends at minute 15 which is the time it took him to get to work.

Answer:

63/h - 3.14

Step-by-step explanation:

Quotient means divide.

So the answer to the division is a quotient. 63/h is the quotient of the division.

Less means subtract so the subtraction that is taking place is

63/h - 3.14 and that's your answer.

Often with these questions, you start backwards as in this question.

Step-by-step explanation:

The easiest thing to do here is:

4x + 2 = -2 and 4x + 2 = 26

Just know whaever you get for x is greater or less than the actual answer.

4x + 2 = -2

      - 2  - 2

 4x = -4

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

x = -1 <--- Because -2 is supposed to be greater than x, x equals any number less than -1 but not -1.

4x + 2 = 26

     - 2    - 2

  4x = 24

  [tex]\frac{4x}{4} = \frac{24}{4}[/tex]

x = 6 <--- Because 26 is supposed to be less than x, x equals any numbey greater than 6 but not 6

Answer:

-1 > x OR 6 < x

Step-by-step explanation:

4x + 2 > 26

- 2 - 2

___________

4x > 24

__ ___

4 4

x > 6

__________________________________________________________

4x + 2 < −2

- 2 - 2

___________

4x < -4

__ __

4 4

x < -1

The above answers are written in reverse, which are the exact same result.

I am joyous to assist you anytime.

Answer:

32,470

Step-by-step explanation:

since there is a 7 in the ones place it will chnage the 6 to a 7 to make it 32,470

In order to find the answer to this question you must find the tenth place value and look to the right of the tenth place value and if the value next to the tenths higher then five you round up.

[tex]32,467[/tex]

[tex]Tenths=67[/tex]

[tex]7>5[/tex]

[tex]32470[/tex]

[tex]=32,470[/tex]

Therefore the answer is "32,470."

Hope this helps.

Answer:

This quantity is already simplified.

Perhaps there was a typographical error?

Answer: This quantity is already simplified.

Perhaps there was a typographical error?

Step-by-step explanation:

Answer:

13 Miles

Step-by-step explanation:

All you need to do is divide 65 by 5.

65 / 5 = 13

Answer:

U.S.= 9

France= 2

Step-by-step explanation:

2×4=8 +1=9

9-7=2

Hope this helps!!!

Brady

  Number of Gold medals won by USA are 9 and gold medals won by France are 2.

   Let the gold medals won by USA = x

And the gold medals won by France = y

It's given in the question "gold medals won by USA are 1 more than 4 times the number of gold medals won by France"

Therefore, equation for this situation will be,

x = 4y + 1 --------(1)

Second statement of the question states "USA won 7 gold medals more than France"

Therefore, equation will be,

x = y + 7 -------(2)

By substituting the value of 'x' in equation (1) from equation (2),

y + 7 = 4y + 1

4y - y = 7 - 1

3y = 6

y = 2

By substituting the value of 'y' in equation (1),

x = 4(2) + 1

x = 9

      Therefore, USA won 9 gold and France won 2 gold medals in the Winter Olympic Games.

Learn more,

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[tex]\bf \boxed{-2}\rule[0.35em]{12em}{0.25pt}\stackrel{~\hfill -\sqrt{2}}{\approx -1.4}\rule[0.35em]{10em}{0.25pt}\boxed{-1}[/tex]

Final answer:

The negative square root of two, −√2, falls between the consecutive integers -2 and -1 on the number line.

Explanation:

The student is asking about the position of the square root of a negative number on the number line, specifically −√2 (negative square root of two). To answer this, we first need to understand that the square root of a positive number is a number that, when squared, gives the positive number in question. For √2, we know that it falls between 1 and 2 because 1 squared is 1 and 2 squared is 4, and 2 lies between these two values.

Since the student is asking for negative √2, we simply reflect the position of √2 across the origin (zero) on the number line to find where −√2 lies. Hence, −√2 will fall between the integers -2 and -1. If we were estimating, we might say it is just a bit closer to -2 than -1, because √2 is approximately 1.414.

The required line parallel to y = - 7x - 2 through (- 4, 6) is y = -7x - 22.

The slope is the rate of change of the y-axis with respect to the x-axis.

The equation of a line in slope-intercept form is y = mx + b, where

slope = m and y-intercept = b.

We know the greater the absolute value of a slope is the more steeper is it's graph or rate of change is large.

We know parallel lines have the same slope.

Given line is y = - 7x - 2, hence the required line will also have a slope of - 7

which is passing through the point (-4, 6).

∴ 6 = (-7)(-4) + b.

6 = 28 + b.

b = - 22.

Hence the required line is y = -7x - 22.

learn more about lines here :

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Answer:

x = 4

Step-by-step explanation:

look at the screenshots below, they'll explain the answer

Hope I helped :)

Answer:

I think it is 4.52 × 10^-4

Answer:

Step-by-step explanation:

students = x

non-students=y

x+y=410

y=410-x

3x+7y=1650

3x+7(410-x)=1650

3x+2870-7x=1650

-4x=-1220 (divide both sides by -4)

x=305 y=410-305=105

Hence, 305 students attended and 105 non-students attended

The problem can be represented by two linear equations, s + n = 323 and 2s + 3.5n = 790. After putting these equations into the format y = mx + b, they can be graphed to find the solution at the point where the two lines intersect.

First, let's define two variables, s for the number of students and n for the number of non-students. From the information we have:

To solve the problem by graphing, we need to convert these equations into y = mx + b format. Our first equation then becomes s = -n + 323 and the second becomes s = (790 - 3.5n) / 2. Plotting these equations on a graph and finding the point where the lines intersect will give us the value of s and n. The x-values corresponds to n (non-students) and y-values to s (students).

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See the attached picture for the answer.

Answer:

[tex]3 \frac{3}{4} \times 3 \frac{1}{3} = \frac{15}{4} \times \frac{10}{3} = \frac{25}{2} = 12 \frac{1}{2} [/tex]

The area of this room is 12 1/2 yd².

The area of the rectangular room is (12.5) square yards, calculated by multiplying length and width.

To find the area of a rectangular room, you multiply its length by its width. Given that the length is [tex]\(3 \frac{3}{4}\)[/tex] yards and the width is  [tex]\(3 \frac{1}{3}\)[/tex] yards, you can calculate:

[tex]\[ \text{Area} = \text{Length} \times \text{Width} \][/tex]

First, let's convert the mixed numbers to improper fractions:

[tex]\[ 3 \frac{3}{4} = \frac{4 \times 3 + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4} \text{ yards} \]\[ 3 \frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{9 + 1}{3} = \frac{10}{3} \text{ yards} \][/tex]

Now, plug these values into the formula:

[tex]\[ \text{Area} = \frac{15}{4} \times \frac{10}{3} \]\[ \text{Area} = \frac{15 \times 10}{4 \times 3} \]\[ \text{Area} = \frac{150}{12} \]\[ \text{Area} = 12.5 \text{ square yards} \][/tex]

So, the area of the rectangular room is [tex]\(12.5 \, \text{square yards}\).[/tex]

Answer:

32+q

Step-by-step explanation:

The complete question is

Jake has 32 quarters on his desk, molly has q quarters in her purse.  

Which algebraic expression represents the total number of quarters that Jake and Molly have?  

we know that

To find out the total number of quarters that Jake  and Molly have, sum the amount of quarters that Jake has plus the amount of quarters that Molly has

Let

x ----> the amount of quarters that Jake has

y ----> he amount of quarters that Molly has

so

x+y

we have

[tex]x=32\ quarters\\y=q\ quarters[/tex]

substitute

32+q

Hey!

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Steps To Solve:

~Coordinates of the line

(0, -1) and (-1, 0)

~Find slope

[tex]m = \frac{0 - (-1)}{-1 - 0} = \frac{1}{-1} = -1[/tex]

~Find the equation of the line

y = mx + b

m = slope

b = y-intercept

m = -1 or -x

b = -1

y = -x - 1

~Check using zero rule (substitute x and y for (0, 0))

y = 0 - 1

y = -1 (Correct)

0 = -x - 1

-x = 1 - 0

-x = 1 (Incorrect)

~Check

{x<−3y≤−x−1

0 < -3(0) ≤ 0 - 1

0 < 0 ≤ -1

*Note* Since the line isn't near the origin, the points (0, 0) don't satisfy the equation.

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Answer:

{x<−3y≤−x−1

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Hope This Helped! Good Luck!

Answer:

Perimeter = 89mm

area= 528 or 220

Step-by-step explanation:

hope this is useful

Answer:

Perimeter is 99 because 22+44+15+18=99

Area is 396 because 22+44=66÷2=33x12=396

The formula for the calculating the are of trapezium is a+b÷2xheight I hope this helped I gave you the formula to calculate the area of trapezium as well just to give extra help! Your welcome!

Answer: 6,300,000

Step-by-step explanation:

Answer:

6,003,000

You would place the six in the millions place, and the 3 in the thousands place!

Answer:

1,888 bags.

Step-by-step explanation:

Let x represent the the weight of container of peppercorns.

We have been given that the container of oregano is 17 pounds heavier than a container of peppercorns. So the weight of container of oregano would be [tex]x+17[/tex].

We are also told that the total weight of both containers is 253 pounds. We can represent this information in an equation as:

[tex]x+x+17=253[/tex]

Let us solve for x.

[tex]2x+17=253[/tex]

[tex]2x+17-17=253-17[/tex]

[tex]2x=236[/tex]

[tex]\frac{2x}{2}=\frac{236}{2}[/tex]

[tex]x=118[/tex]

Therefore, the weight of peppercorns is 118 pounds.

Now, we will convert 118 pounds to ounces.

1 pound equals 16 ounces.

118 pounds = 118*16 ounces = 1,888 ounces

Since the peppercorns will be sold in one-ounce bags, therefore, 1,888 bags of peppercorns can be made.

Answer:

D

Step-by-step explanation:

The absolute value always returns a positive value, that is

| - a | = | a | = a, thus

| 7 | = 7 → D

Answer:

Step-by-step explanation:

|7|=7 answer : D