Mr. Mateo ordered several copies of a book that weighs 3/5 of a pound each along with some other school supplies for his classroom. If the total weight of the box that contains the supplies was 10 pounds, what is the maximum number of copies of the bookthat Mr. Mateo could have ordered

Answer:

18

Step-by-step explanation:

[tex]\frac{3!6!}{5!2!}[/tex]

n! = n * (n-1)!

For example 7!  can be written as 7 * 6!

3! is 3* 2!

6! is 6 * 5!

[tex]\frac{3!6!}{5!2!}[/tex]

[tex]\frac{3*2!6*5!}{5!2!}[/tex]

Cancel out 5!  from the top and bottom . Also cancel out 2! from top and bottom.

[tex]\frac{3*2!6*5!}{5!2!}[/tex]

3*6= 18

Answer:

if there are 8 7th graders there are 32 6th graders. 4*8=32

Step-by-step explanation:

Answer:

[tex]AC=14\sqrt{2}m[/tex]

Step-by-step explanation:

we are given trapezoid ABCD

AC is a diagonal

∠ABC ≅ ∠ACD

we know that

BC and AD are parallel

so, <DAC = <ACB

so, ΔABC ≅ΔACD

Since, both triangles are similar

so, their ratios must be equal

we get

[tex]\frac{BC}{AC} =\frac{AC}{AD}[/tex]

now, we can plug values

[tex]\frac{14}{AC} =\frac{AC}{28}[/tex]

[tex]AC^2=14\times 28[/tex]

[tex]AC^2=14^2\times 2[/tex]

[tex]AC=14\sqrt{2}m[/tex]

To find the length of AC, the diagonal in trapezoid ABCD, we can use the fact that ∠ABC ≅ ∠ACD and the lengths of the bases BC and AD. By setting up a proportion using the corresponding sides of the similar triangles ABC and ACD, we can find that AB/AC = 1/2. Multiplying the length of AB by 2 gives us AC = 28m.

Given that ∠ABC ≅ ∠ACD and the lengths of the bases BC and AD are 14m and 28m respectively, we can find the length of AC, which is a diagonal in trapezoid ABCD.

Answer:

<1 = 30

<2= 41

<3 = 96

Step-by-step explanation:

 Angle 1  ,66 and 84 form a triangle and triangles add to 180 degrees

<1 + 66 + 84 = 180

Combine like terms

<1 +150 = 180

Subtract 150 from each side

<1 + 150 -150 = 180-150

<1 = 30

Angle 3 and 84 form a straight line.  A straight line is 180 degrees.

<3 + 84  =180

Subtract 84 from each side

<3 +84-84 = 180 - 84

<3 = 96

<2 , <3 and 43 form a triangle which adds to 180 degrees,

<2 + <3 + 43 = 180

We have already found <3 to equal 96 degrees

<2 + 96+43 = 180

Combine like terms

<2 +139=180

Subtract 139 from each side.

<2 +130-139 = 180-139

<2 = 41

NOTE: I ACCIDENTALLY clicked one star. That DOES NOT count as a real rating, and this DOES NOT mean my answer is bad!

Answer:

Commutative Property of Addition

Step-by-step explanation:

Step 2: -4 + (-37) + (-3) + (-47) + 7

Step 3: -4 + (-37) + (-47) + (-3) + 7

Because the order was changed, it is the Commutative Property.

Answer:

The answer is B

Step-by-step explanation:

3 and 6 are alternate exterior angles which make lines l and m parallel.

Answer: c

Step-by-step explanation:

Answer:Yes

Step-by-step explanation:

When the negative is on the outside of the bracket you distribute the negative to each term inside the parentheses.

Answer:

yes you would change the signs that are inside the parenthesis

Step-by-step explanation:

you do so because the negative outside the parenthesis mean you are distributing the negative to the terms.

Answer:

x = 29 1/3 degrees

Step-by-step explanation:

A triangle has 3 angle that total 180 degrees.

The three angles given are 82 degrees ,2x+10 degrees and x degrees.

So,  

82+ (2x+10) + x = 180

Combine like terms.

92 + 3x = 180

Subtract 92 from each side

3x = 180 -92

3x = 88

divide each side by 3

3x/3 = 88/3

Change 88/ 3 to a mixed number

3 goes in to 88 29 times  with 1 left over.

x = 29 1/3 degrees

Answer:

0.1111%

Step-by-step explanation:

2 dice, each with 6 sides. 36 possible outcomes.

Possible sums for 9 are 1,8 2,7 3,6 4,5

That means there is only 4 possible ways to get 9 out of 36 possible outcomes. 4/36 is your probability

Answer:

x=6

Step-by-step explanation:

We can find < PMN by using the law of triangles.

The sum of the angles of a triangle adds to 180

<M + <N + < PMN = 180

32 + 64+ < PMN = 180

96 + < PMN = 180

Subtract 96 from each side

96 -96 < PMN = 180-96

< PMN =84

<PMN + <NPQ forms a straight line so it equals 180

<PMN + <NPQ=180

84 + <NPQ=180

Subtract 84 from each side

84-84 + <NPQ=180-84

<NPQ=96

<NPQ = 6x

96 = 6x

Divide each side by 6

96/6 = 6x/6

16 =x

Answer:

The length of each piece of fabric is [tex]L=\frac{3}{5}[/tex]

Step-by-step explanation:

Given : Dai has 3 meters of fabric that he wants to cut into 5 equal sized pieces.

To find : What is true about the length of each piece of fabric ?

Solution :

Dai has 3 meters of fabric.

He cuts the fabric into 5 equal sized pieces.

So, The length of each piece is defined as

[tex]L=\frac{3}{5}[/tex]

Therefore, The length of each piece of fabric is [tex]L=\frac{3}{5}[/tex]

Answer:

x=-12 and -3

Step-by-step explanation:

The quadratic formula is

[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex].

It is important because while some quadratics are factorable and can be solved not all are. The formula will solve all quadratic equations and can also give both real and imaginary solutions. We will substitute a=1, b=15 and c=36.

[tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}\\x=\frac{-15+/-\sqrt{(15)^2-4(1)(36)} }{2(1)}\\x=\frac{-15+/-\sqrt{225-144} }{2}[/tex]

We will now simplify and solve.

[tex]x=\frac{-15+/-\sqrt{81}}{2}\\x=\frac{-15+/-9}{2}[/tex]

x=-12 and x=-3

Answer:

slope = 1 , y- intercept = - 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

y = x - 5 is in this form

with slope m = 1 and y- intercept c = - 5

The options are

a.) 5x - 9

b.) 6x + 20

c.) 6x²- 23x + 20

d.) 6x²-14x - 9

Answer:

c.) 6x²- 23x + 20

Step-by-step explanation:

Rectangle area can be computed as length × width . The garden is a rectangle so the area can be computed by multiplying the length and the width.

Area= L × W

Length = 3x - 4

width = 2x - 5

Area = (3x - 4)(2x - 5)

Area = 3x(2x) + 3x(-5) -4(2x) -4(-5)

Note : - × - = +

Area = 6x² -15x - 8x + 20

Area = 6x² - 23x + 20

Answer: Yes

Step-by-step explanation: 4x5 is 20 + 2 is 22 then when you multiply that by 9 you get 198

36x5 is 180 + 18 is 198

Both answers equal each other

The calculated fraction 21/6 to a mixed number is 3 1/2

From the question, we have the following parameters that can be used in our computation:

Number = 21/6

Divide 21 by 6

So, we have

Quotient = 3

Next, we have

Remainder = 21 - 6 * 3

Evaluate the products

Remainder = 3

So, we have

Fraction = 3 3/6

Simplify

Fraction = 3 1/2

Hence, the fraction to a mixed number is 3 1/2

Read more about fraction at

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Answer: 5/8

Step-by-step explanation:

Answer:

(5x-2) and (x+2)

Step-by-step explanation:

Answer:

the factors are (5x-2)  and (x+2)

Step-by-step explanation:

5x^2 + 8x – 4

first we multiply 5  and -4= -20

product is -20  and sum is +8

find out two factors whose product is -20 and add upto +8

10 * (-2) = 20

10 +(-2)= 8

5x^2 +10x-2x – 4

group the terms and factor out GCF

(5x^2 +10x)+(-2x – 4)

5(x+2) -2(x+2)

(5x-2)(x+2)

the factors are (5x-2)  and (x+2)

Answer:

Hello, the answer tho this question is C.) 70.7 feet.

Answer:

A. 3

Step-by-step explanation:

To find the midpoint  between two numbers, we add the two numbers and divide by 2

midpoint = (x1+x2)/2

midpoint = (-9+15)/2

midpoint = (6)/2

midpoint =3

Answer:

It will take 6 years

Step-by-step explanation:

Marshall starts at 36,000 dollars and Jim starts at 51,000, multiply the pay raises by 6 and for Jim you get $9,000 and Marshall gets $24,000 pay raise in 6 years.

Sorry If It Is a bit confusing, I'm not really good with words. :/

Both of them will get the same salary after 6 year.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, Marshall Earns a salary of $36,000, and each year he receives a $4,000 raise. Jim earns a salary of $51,000, and each year he receives a $1,500 raise.

Let x be the year in which they will get the same salary

Establishing the equation, we get

36000+4000x = 51000+1500x

Simplifying the equation,

36+4x = 51+1.5x

2.5x = 15

x = 6

Hence, Both of them will get the same salary after 6 year.

For more references on equations, click;

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Answer:

150

Step-by-step explanation:

The ratio of boys to girls is 3 to 7.

We don't know the number of boys or girls. The number of boys and the number of girls are multiples of 3 and 7, respectively. Since they are in the ratio of 3 to 7, then by multiplying both 3 and 7 by the same number, you will get the number of boys and the number of girls. We need to find that number. Call that number x.

The ratio of boys to girls is:

3x to 7x

There are 3x boys and 7x girls.

The number of girls is 200 more than the number of boys.

7x = 3x + 200

Subtract 3x from both sides.

4x = 200

Divide both sides by 4.

x = 50

The number of boys is 3x, so

3x = 3(50) = 150

150 boys and 350 girls were enrolled that year.

Since a college was previously an all girls college, and then it began to allow boys to enroll, and by 2012 the ratio of boys to girls was 3 to 7, to determine, if there were 200 more girls than boys in 2012, how many boys were enrolled that year, the following cross multiplication calculation must be performed:

Therefore, 150 boys and 350 girls were enrolled that year.

Learn more in https://brainly.com/question/13904768

Answer:

.513 is larger

Step-by-step explanation:

1st method is the thousandths place larger or smaller

.1 tenths

.01 hundredths

.001 thousandths

In this case the thousandths is larger for .513

2nd method

subtract the two number

.513 - .5129 = .0001

Since the number recieved is positive this means .513 is larger

Answer:

[tex]m\angle EFG=52^{o}[/tex]

Step-by-step explanation:

We have been given that line m is parallel to line p, [tex]m\angle HEF=39^{o}[/tex] and [tex]m\angle IGF=13^{o}[/tex].

Since line m is parallel to line p and EJ is a transversal, so measure of angle EJG will be 39 degrees as angle EJG is alternate interior angle of angle HEF. Both angles are inside parallel lines m and p and on opposite side of transversal EJ.

We can see that angle EFG is exterior angle of triangle GFJ. Since the measure of an exterior angle of a triangle equals to the sum of the opposite interior angles.

We can see that angle IGF and angle EJG are opposite interior angles of angle EFG.

[tex]m\angle EFG=m\angle IGF+m\angle EJG[/tex]

Upon substituting our given values we will get,

[tex]m\angle EFG=13^{o}+39^{o}[/tex]

[tex]m\angle EFG=52^{o}[/tex]

Therefore, measure of angle EFG is 52 degrees.

A negative divided by a positive gives a negative result

So the answer is -3.1

Hope this helps!

this was correct on my test, hope it helps! ;)

(Brainliest would help a lot btw)

X1 = -6

Y1= 1

X2= 4

Y2 = 8

8 - 1

____

4 + 6

7

_ is your answer

10

Answer:

6

Step-by-step explanation:

Jack would need 6 teaspoons of baking powder for 9 cups of flour to maintain the ratio given in the original recipe.

To determine how much baking powder is needed if Jack uses 9 cups of flour instead of 3, you can set up a proportional relationship because the quantity of baking powder required is directly proportional to the amount of flour used.

If the original recipe calls for 2 teaspoons of baking powder for every 3 cups of flour, for 9 cups of flour (which is 3 times as much), you would need 3 times as much baking powder. Hence, the calculation would be as follows:

2 teaspoons baking powder / 3 cups flour = x teaspoons baking powder / 9 cups flour

By cross-multiplication, we can find the value of x:

2/3 * 9 = x

x = 2 * 3 = 6 teaspoons of baking powder

Therefore, Jack would need 6 teaspoons of baking powder for 9 cups of flour to maintain the ratio given in the original recipe.

Answer:

The length for a rectangle with a perimeter of 34 units and a width of 6.5 units would be 10.5 units.

Step-by-step explanation:

To find the length, you can use the equation [34 - (6.5 x 2) ÷ 2 = the length]. So, 6.5 x 2 = 13, then 34 - 13 = 21, finally, 21 ÷ 2 = 10.5 . So the length of the rectangle is 10.5 . To double check, (6.5 x 2) + (10.5 x 2) (=) 34. So this answer is correct.

Answer:

( l + 4) * ( w + 3 ) * ( h + 7)

let l represent the length, w represent the width, and h represent the height of your cub-shaped gift.

Though, if your gift is in the shape of a cube, that would mean all the sides are the same length.

( 2 + 4 ) * ( 2 + 3 ) * ( 2 + 7 )

6 * 5 * 9 = 270

(I haven't done geometry in awhile though, so this may be incorrect unless it actually makes sense.)

Answer:

V = (x+ 4)(x + 3)(x + 7); V = x³ + 14x² + 61x + 84

Step-by-step explanation:

Let x = the side of the cube

Then the dimensions of the gift box are

l   = x + 4

w = x + 3

h = x+ 7

V = lwh

V = (x+ 4)(x + 3)(x + 7)     Multiply the first two terms

V = (x² + 7x + 12)(x+ 7)     Remove parentheses

V = x³ + 14x² + 61x + 84

Answer:

Option C is the correct option.

Step-by-step explanation:

In the given cosine graph we can draw some parameters of the equation as below

y = a cos(bx + c) + d

1) amplitude a = (1+3)/2=2

2) Period = π

3) phase shift = -π ( to the left)

4) Vertical shift = -1 ( downwards on y-axis)

Therefore the equation of the graph will be

y = -2cos[2(x + π)] - 1

Option C is the correct answer.