Oliver works at a book store.He packed 20 identical paperbacks and 9 identical textbooks in a box .The total mass of the book was 44.4 pounds . After he put 1 more textbook and 5 more paperbacks in the box,the total mass of the books was 51 pounds.

Answers

Answer 1

Let x be the mass of the paperbacks and y be the mass of the textbook.

20x + 9y = 44.4 ----------- (1)
25x + 10y = 51 -------------(2)

(1) x 10:
200x + 90y = 444 --------(1a)

(2) x 9:
225x + 90y = 459 --------(2a)

(2a) - (1a):
25x = 15
x = 0.6 -------- sub into (1)

20 (0.6) + 9y = 44.4
12 + 9y = 44.4
9y = 44.4 - 12
9y = 32.4
y = 3.6

So the paperback's mass is 0.6 pounds and textbook is 3.6 pounds

Related Questions

The sum of the square of two negative numbers is 74. The difference is 24. determine the two numbers

Answers

The required negative numbers are -5 and -7.

What is a quadratic equation?

The quadratic equation is defined as a function containing the highest power of a variable is two.

Let the required negative numbers be x and y.

The sum of the square of two negative numbers is 74.

(x)² + (y )² = 74

x² + y² = 74

(x)² - (y)² = 24

y² - x² = 24

y² = x² + 24

Substitute the value of y² = x² + 24 in the equation x² + y² = 74,

x² + 24 + x² = 74

2x² = 74 - 24

2x² = 50

x² = 25

x = √25

x = ±5

x = 5, -5

Take the negative value as per the question.

Substitute the value of x = -5 in the equation y² = x² + 24,

y² = (-5)² + 24

y² = 25 + 24

y² = 49

y = √49

y = ±7

y = - 7

Therefore, the required negative numbers are -5 and -7.

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Final answer:

The problem is solved by converting the given conditions into a system of equations, which is then solved to find the two negative numbers. The numbers obtained, -3 and -27, satisfy both given conditions.

Explanation:

The question provided is a mathematical problem involving the determination of two negative numbers given that their squares sum to 74 and their difference is 24. Let's denote the smaller number as x and the larger number as y. The given conditions can be represented by two equations: [tex]x^2 + y^2 = 74[/tex] and y - x = 24.

To find the values of x and y, we solve these equations simultaneously. First, use the second equation to express y in terms of x:

y = x + 24

Then, substitute this expression for y into the first equation:

[tex]x^2 + (x + 24)^2 = 74[/tex]

This simplifies to a quadratic equation in x, which can be solved to find the value of x, and subsequently, y can be determined using the expression

y = x + 24.

After solving the quadratic equation, you find that the two negative numbers are -3 and -27, satisfying both the sum of their squares equaling 74 and their difference being 24.

Matthew made lasagna for dinner he gave equal portions of 2/3 of the lasagna 23 friends what diagram could Matthew use to find a fraction of the whole is lasagneach friend of got

Answers

the answer is 2/69 because if u divide 2/3 and 23 you get 2/69

Dana painted a wall in her bedroom that is 10.5 feet tall and 23.5 feet wide.she used exactly 3quarts of paint to cover the wall.How many square feet will 1quart of paint cover? Please explain

Answers

82.25 square feet

Start off by multiplying 10.5 by 23.5, to get the area of her wall - 246.75 square feet. This took up 3 quartz of paint, so divide both 246.75 by 3 to find out how many square feet were painted with only 1 quartz, 82.25 square feet! :D Hope I helped!

Solve the equation V - E + F = 2 for E

Answers

The given equation can be solved in terms of E as E = V + F - 2.

How to solve a linear equation?

A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.

The given equation is V - E + F = 2.

It can be solved as,

⇒ V - E + F = 2

⇒ V + F = 2 + E

⇒ E = V + F - 2

Hence, the solution for E can be obtained as E = V + F - 2.

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Final answer:

The equation V - E + F = 2 is solved for E by simple algebraic manipulation, resulting in the solved equation E = V + F - 2.

Explanation:

To solve the equation V - E + F = 2 for E, we need to isolate E on one side of the equation. This can be done through simple algebraic manipulation as follows:

Start with the original equation: V - E + F = 2.Add E to both sides: V + F = E + 2.Now, subtract 2 from both sides to solve for E: E = V + F - 2.

The solved equation for E is thus E = V + F - 2.

This equation shows the relationship between the vertices (V), edges (E), and faces (F) in a polyhedron, known as Euler's formula in the context of geometry.

A plot of land is a pentagon with vertices Q(-4, 4), R(2, 4), S(4, 1), T(2, -4), and U(-4, -4).

Each unit of the coordinate grid represents one meter.

Fencing costs $24.75 per meter. What is the cost of placing a fence around the plot of land?

Answers

The measure of QR is 6 units, which is 6 meters, since every unit on the coordinate grid is 1 meter.
The measure of UT is also 6 meters.
The measure of QU is 8 meters.
To find the measure of RS, we use the distance formula:
[tex]\sqrt{(x_{2}-x_{1})^2 + (y_{2}-y_{1})^2}[/tex]
We substitute the coordinates of R and S into the formula and have:
[tex]\sqrt{(2-4)^2+(4-1)^2} \\ =\sqrt{(-2)^2 + (3)^2} \\ =\sqrt{4+9} \\=\sqrt{13} \\=3.61[/tex]
To find the measure of ST we use the distance formula again, substituting the coordinates for S and T into the formula:
[tex]\sqrt{(4-2)^2+(1--4)^2} \\=\sqrt{(2)^2 + (1+4)^2} \\=\sqrt{4+5^2} \\=\sqrt{4+25} \\=\sqrt{29} = 5.39[/tex]
Now we find our perimeter by adding the sides together: 5.39 + 3.61 + 6 + 6 + 8 = 29 meters
Since fencing costs $24.75 per meter, we multiply this by our perimeter:
29(24.75) = $717.75

What is X the two numbers are 46 and 71

Answers

the answer would be 63 bc 46+71= 117 then a triangle usaually equals 180 so 180 -117=63!!

Abigail is redecorating her house. A scale drawing of 2 rooms can be seen below. If each 6 cm on the scale drawing equals 12 ft, what are the actual dimensions of Abigail’s house?

Room measurements:
A: 9 cm
B: 10 cm
C: 9 cm
D: 8 cm
E: 7 cm

Answers

the complete question in the attached figure

we know that

scale factor r=[dimension scale drawing]/[actual dimension]
r=6/12=0.5 cm/ft
[actual dimension]=[dimension scale]/r

for dimension scale=9 cm
[actual dimension]=[9]/0.5=18 ft

for dimension scale=10 cm
[actual dimension]=[10]/0.5=20 ft

answer
the actual dimensions of Abigail’s house are 18 ft x 20 ft
the area of Abigail’s house is (18*20)=360 ft²

Which completely describes the polygon
A: equilateral
B: equiangular
C: regular
D: congruent
the shape is Hexagon

Answers

A=equilateral hope that helped

Find the volume of this sphere.

Answers

The Volume of the sphere is 267.946 repeating, the rounded answer though, is ≈268

The formula I use is 4(3.14)(r^3)/3, I think it's easier, but that's just me. Hope this helps! ٩(ര̀ᴗര́)

A zookeeper asks,”How many animals were in the zoo each month of last year?”is this question statistical or not?Explain you reasoning.

Answers

um this is a random question um try google

History (from Greek ἱστορία, historia, meaning "inquiry, knowledge acquired by investigation")[2] is the study of the past as it is described in written documents.[3][4] Events occurring before written record are considered prehistory. It is an umbrella term that relates to past events as well as the memory, discovery, collection, organization, presentation, and interpretation of information about these events. Scholars who write about history are called historians.

help its easy i just have to much work! i need 4-8

Answers

4. Substituting for y:
.. 7x -(6 -2x) = 3
.. 9x = 9 . . . . . . . . . add 6, collect terms
.. x = 1
.. y = 6 -2*1 = 4
(x, y) = (1, 4)

5. Substituting for x:
.. 3(y -4) +y = 12
.. 4y = 24 . . . . . . . add 12, collect terms
.. y = 6
.. x = 6 -4 = 2
(x, y) = (2, 4)

6. Substituting for x:
.. 4(y -5) -y = 4
.. 3y = 24 . . . . . . . add 20, collect terms
.. y = 8
.. x = 8 -5 = 3
(x, y) = (3, 8)

7. y = 2x -6 . . . . . add 2x to the first equation
Substituting for y:
.. 5x -(2x -6) = 9
.. 3x = 3 . . . . . . . add -6, collect terms
.. x = 1
.. y = 2*1 -6 = -4
(x, y) = (1, -4)

8. x = 2 -3y . . . . . add -3y to the first equation
Substituting for x:
.. y -(2 -3y) = -6
.. 4y = -4 . . . . . . . add 2, collect terms
.. y = -1
.. x = 2 -3*(-1) = 5
(x, y) = (5, -1)

If 3p+4q=8 and 4p+3q=13, what is q equal to?

Answers

q= -1. I did this problem by elimination, by multiplying the first one by -4 and the second by 3, to cancel out the p. I ended up with -7q=7. I divided both sides by -7, and got q=-1.

Solve the system of equations.
4x-9y - 2=0
12x-5y+38=0
x equals?
y equals?

Answers

I: 4x-9y-2=0
II: 12x-5y+38=0

start by eliminating x by multiplying the first equation by 3 and subtracting II:

3*(4x-9y-2)-(12-5y+38)=3*(0)-0
12x-27y-6-12x+5y-38=0
-22y-44=0
-44=22y
-2=y

-> insert y=-2 in I:

4x-9*(-2)-2=0
4x+18-2=0
4x+16=0
4x=-16
x=-4

so the solution is y=-2 and x=-4

Answer:(-4,-2)

Step-by-step explanation:

Jim is 3 times as old as his cousin and the difference in their ages is 18. How old is Jim?

Answers

cousin is 9 , jim is 27

The Jim's age is 27.

It is required to find the age of Jim.

What is average?

Number that is calculated by adding quantities together and dividing the total by the number of quantities.

Given that:

Let cousin's age = x

Let Jim's age = 3x

Since the difference between their ages is 18,

3x - x = 18

Solving for x,

2x = 18

x = 9

Cousin's age is 9.

Jim's age is 27.

So, the Jim's age is 27.

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A recycling bin is in the shape of a right rectangular prism. The bin is 12 meters long, 512 meters wide, and 612 meters tall. What is the volume of the recycling bin? 3534 m³ 360 m³ 429 m³ 51834 m³

Answers

the answer is 3534 meters square

Answer:

3534

I just agree with the comment above me.

Marvin counts six $5 bills. write each value that he counts. what pattern do you see in the one digits of the values he counts?

Answers

Answer: If the number of bills counted is odd, the ones digit is 5; if the number of bills is even, the ones digit is 0.

Explanation

1) Simulate the counting of the bills:

number of bills counted          value            ones digit

1                                             5                         5

2                                             5 + 5 = 10       0

3                                             10 + 5 = 15         5

4                                             15 + 5 = 20         0

5                                              20 + 5 = 25        5

6                                              25 + 5 = 30        0

2) Pattern: you can see that the ones digit alreternate: 5, 0, 5, 0, 5, 0, ...

If the number of bills counted is odd the ones digit is 5, if the number of bills is even the ones digit is 0.

Final answer:

When counting $5 bills, the values are $5, $10, $15, $20, $25, $30 with a pattern in the one digits of 5, 0, 5, 0, 5, 0. This demonstrates the pattern of addition with multiples of five.

Explanation:

Marvin is counting $5 bills, hence each time he counts a bill the total value increases by $5. The values Marvin counts are $5, $10, $15, $20, $25, $30.

The one digits in these values form a pattern, specifically, they are 5, 0, 5, 0, 5, 0.

This pattern repeats every two counts: a 5 followed by a 0. This is because adding 5 to a multiple of 10 results in a number ending in 5, and adding another 5 results in another multiple of 10, which always ends in 0.

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If 200% of x is equal to 50% of y and x = 16, what is the value of y?

Answers

First, find what 200% of x is.
Multiply x by 2.
16 x 2 = 32
Since it is equal to 1/2 of y,
multiply it by 2 once more.
32 x 2 = 64
y = 64.
Hope this helps!

The geometric mean of 8 and 32

Answers

A geometric mean is the n-th root of the product of n numbers.

In this case, there are 2 numbers, which means you take the square root. If there were 3 numbers, you'd take the cube-root, and so on...

First, multiply 8 and 32 to get 256. Now, take the square root of 256, which is 16. This is the geometric mean.

The geometric mean of 8 and 32 is 16.

Given :

The two numbers 8 and 32

To find:

The geometric mean of given numbers.

Solution

The geometric mean is given by the formula:

[tex]G.M=\sqrt[n]{x_1\times x_2\times x_n}[/tex]

n = num ber of terms

According to question : n = 2

The geometric mean of given numbers:

[tex]G.M=\sqrt[2]{8\times 32}\\\\G.M=\sqrt[2]{256}\\\\G.M=16[/tex]

The geometric mean of 8 and 32 is 16.

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l4-8(3-12)l - l5-11l

Answers

The answer is -36 and you can also use the calculator to help!

Hope you have the correct answer

Final answer:

The given mathematical expression is solved by simplifying within parentheses, performing multiplication, and understanding the absolute value concept, leading to a final answer of 70.

Explanation:

The given mathematical expression is |4-8(3-12)| - |5-11|. To solve this, we first need to simplify the expressions within the absolute value bars, following the order of operations (PEMDAS/BODMAS).

Step 1: Simplify inside the parentheses

3-12 = -9. So, the expression now is |4-8(-9)| - |5-11|.

Step 2: Multiply

8 times -9 equals -72. Substituting this, we get |4 - (-72)| - |5-11|, which simplifies to |4 + 72| - |5-11|.

Step 3: Simplify the absolute values

4 + 72 equals 76, so |76| is just 76 because absolute values ensure a positive outcome. Next, 5-11 equals -6, so |5-11| is |-6|, which is 6. Therefore, you have 76 - 6.

Step 4: Subtract

Lastly, subtracting 6 from 76 gives 70. So, the final answer to the given expression is 70.

write 0.21 as a fraction in simplest form

Answers

Convert that to a decimal first
0.21 = 0.21
Now we do a fraction
21/100
That is in it's lowest terms
~Deceptiøn

0.21 as a fraction in simplest form is 21/100.

What is a fraction?

In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

In this exercise and scenario, we would convert the given decimal number 0.21 into a fraction by converting it into a percentage as follows;

0.21 = 21/100

Fraction: 21/100 = 0.21.

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Stella's friends got her a skydiving lesson for her birthday. Her helicopter took off from the skydiving center, ascending in an angle of 37 degree, and traveled a distance of 2.1 point, 1 kilometers before she fell in a straight line perpendicular to the ground. How far from the skydiving center did Stella land? Round your final answer to the nearest hundredth.

Answers

The situation is represented by a right triangle with 2.1km as the hypotenuse. The distance x from the center to the landing point divided by 2.1 is the cosine of 37 degrees. So x/2.1=cos37=0.7986 approx, x=2.1×0.7986=1.68 km.

1.68 km from the skydiving center did Stella land .

What is trigonometric ratio?

Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle.

The basic trigonometric ratios formulas are given below,

sin θ = Perpendicular/Hypotenusecos θ = Base/Hypotenusetan θ = Perpendicular/Basesec θ = Hypotenuse/Basecosec θ = Hypotenuse/Perpendicularcot θ = Base/Perpendicular

According to the question

Stella's friends got her a skydiving lesson .

Her helicopter took off from the skydiving center, ascending in an angle of 37 degree .

i.e angle of elevation = 37°

then traveled a distance of 2.1 kilometers , 1 kilometers before she fell in a straight line perpendicular to the ground.

i,e

Her helicopter is making a right angled triangle with respect to ground

in which

Hypotenuse of triangle = 2.1 km

Perpendicular of triangle = 1 km

with angle of elevation = 37°

now,

the distance from the skydiving center did Stella land

According to the Trigonometric ratios

cos θ = Base/Hypotenuse

substituting the value in formula

cos 37° = [tex]\frac{Base}{2.1}[/tex]

0.7986 * 2.1 = Base

Base = 1.68

Hence, 1.68 km from the skydiving center did Stella land .

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PLZZZZ HELP WILL MARK BRAINLIEST

Which statement is true about the distribution?

A line ranging from 10 to 45 with boxes between 15 and 25, and 25 and 40.

A.The IQR is the best measure of variability because the distribution has no outliers.

B.Either the IQR or the range are good measures of variability because the distribution has an outlier.

C.The range is the best measure of variability because the distribution has an outlier.

D.Either the IQR or the range are good measures of variability because the distribution has no outliers.

Answers

Hey there!

The correct answer is : D.Either the IQR or the range are good measures of variability because the distribution has no outliers.

Hopes this helps u :D

Answer:

answer is not that asnwer is iat the bottom

Step-by-step explanation:

Either the IQR or the range are good measures of variability because the distribution has no outliers.

Jane is planting flowers in her garden. She planted 8 flowers on Saturday and 10 on Sunday. So far she planted 2/5 of her flowers. How many flowers does she have total?

Answers

she has 45 flowers, 18/2=9, 9*5=45

the answer is 45. I hope this helped!!!

Can someone help me find the value of b? Thank you!

Answers

I think the value of b is 130 degrees. Hope this helps!

Line JM intersects line GK at point N. Which statements are true about the figure? Check all that apply.

GNJ is complementary to JNK.

MNL is complementary to KNL.

MNG is complementary to GNJ.

KNJ is supplementary to MNL.

GNM is supplementary to JNK.

Answers

See attached image

First, we must know this: Complementary angles are two angles whose sum is equal to 90°, while supplementary angles are two angles whose sum is equal to 180°. That been said, the only statement which is true is the second statement, MNL is complementary to KNL

Reasons why others are False
GNJ is supplementary to JNK, not complementary
MNG is supplementary to GNJ, not complementary
LNJ (not KNJ) is supplementary to MNL
GNM is equal to JNK, not supplementary

Answer:

its 2 and 5

Step-by-step explanation:

A computer program reduces the length of each side of an 8'' by 8'' square photograph by 25%. What is the area, in square inches, of the reduced photo?

Answers

36 in2 because it says reduce of each side by 25% not reduce the area by 25%

Jonah finished a race in 11.62 seconds. Marco finished the same race in 9.8 seconds. How many seconds faster did Marco finish the race than Jonah?

A. 1.82 seconds

B. 2.22 seconds

C. 10.64 seconds

D. 11.36 seconds

Answers

BBBBBBBBBBBBBBBBBBBbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

The answer is A. = 1.82 seconds

Marcus saves $13 each week.in how many weeks will he saved at least $100

Answers

13 x 8 = 104
So your answer is 8 weeks
Hope this helps:D
Have a great rest of a brainly day!

You can set up an equation.

13 × a = 100

divide both sides by 13 , and you get a = 7.7 (approximately)

So round it to the nearest whole number which is 8 .

it would take approximately 8 weeks to save $100

what is 3/10 in money form?

Answers

There are many different ways to teach or explain this. I'll try one way which may be different from what your daughter was taught, but it may help you understand better. 1. Common Denominators Before I get to your exact problem, I think it'll still be insightful to talk a little about fractions and common denominators. The denominator is the number on the bottom of the fraction. If the denominators of a bunch of fractions are the same, the problem is easier to handle. For instance, in your fractions above you have 3/10, 9/10, and 1/10. These have the same denominator, which makes them easier to compare directly. One way to think about fractions is in terms of a pie. The denominator tells you the total pieces of pie and the numerator (top number) is, say, how many pieces of pie you are going to eat out of the total. So, for 3/10, this is like saying there are 10 pieces of pie and you are going to have 3 of them. So, it should make sense if we rank these in order of smallest to largest, then the rank is 1/10, 3/10, and 9/10, because eating 1 out of 10 pieces of pie is a lot less than eating 9 out of 10 pieces of pie. You could summarize this and say: if you compare fractions with the same denominators (bottom numbers), then the fraction with the smallest numerator (top number) is the smallest fraction and the fraction with the largest numerator is the largest fraction. Again, this method is nice if you have fractions with the same denominator. In fact you can take fractions with different denominators and do some math to get them to all have common denominators and then still use this method. For what you're doing, I think there is a more concrete way to understand how to order the fractions from smallest to largest. Let's look at that now. 2. Change Fractions to Decimals What I explained above is nice if all your fractions have the same denominator, but unfortunately that's not the case with your problem. You have 12 fractions all having different combinations of numerators and denominators. One nice thing with fractions is that any fraction can be converted to an equivalent decimal by dividing the numerator by the denominator. For instance, take the fraction 1/10. In your calculator press 1, divided by, 10. 1/10 = 0.10 The part I like about this is to think of the decimals as money! So 1/10 (of a dollar) = 0.10 (this is a dime; 10 cents). Using our example from above, 1/10 = 0.10 3/10 = 0.30 9/10 = 0.90 10 cents is less than 30 cents, which is less than 90 cents. This rank order also confirms our answer from above. Now if we convert the 12 fractions from above into decimals and think of the decimals as money, we should have a more intuitive feel for ordering them. 1/10 = 0.10 (10 cents; smallest) 1/6 ~ 0.167 1/4 = 0.25 3/10 = 0.30 1/3 ~ 0.333 3/8 = 0.375 1/2 = 0.50 3/5 = 0.60 3/4 = 0.75 4/5 = 0.80 7/8 = 0.875 9/10 = 0.90 (90 cents; largest) Does this help? Please write back if you need anything else. :-) Also, I'd encourage you to search our archives for additional information on fractions or for any future problems you may have--our archives are a great resource!

3/10$ mind blown. lol. you cant delete this because this answer is actually right. all you had to do was add the money sign to make it in money form. just simplify it for your answer. i bet your teacher will give you an A. good luck kid.

Your cookie recipe calls for 34 cup of flour. You want to make 3 batches of cookies. Which diagram shows how much flour you need? ...

Answers

Im sorry but it seems like your picture still isnt showing

you will need 2 1/4 cups of flour

Hope this helps ;)

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