Each patron can borrow up to 6 books. If all the patrons are currently holding on to 6 books each, how many books are left in the library?

Answer:

-4 and -16

Step-by-step explanation:

Let x = first number

Let y = second number

Given:

⇒ xy = 64

Given:

⇒ x + y = -20

Rewrite  x + y = -20  to make x the subject:

⇒ x = -20 - y

Substitute into xy = 64 and solve for y:

⇒ (-20 - y)y = 64

⇒ -20y - y² = 64

⇒ y² + 20y + 64 = 0

⇒ (y + 4)(y + 16) = 0

⇒ y = -4, y = -16

As x + y = -20

If y = -4 then x = -16

If y = -16 then x = -4

Therefore, the two numbers are -4 and -16

Let they be a and b

So

[tex]\\ \rm\rightarrowtail (a-b)^2=(a+b)^2-4ab[/tex]

[tex]\\ \rm\rightarrowtail (a-b)^2=(-20)^2-4(64)=400-256=144[/tex]

[tex]\\ \rm\rightarrowtail a-b=12\dots(2)[/tex]

From both equations

The equation solved by the John to find w, the greatest width in centimeters he can use for the mosaic, is w(w + 2) = 48.

Area of a rectangle is the product of the length of the rectangle and the width of the rectangle. It can be given as,

[tex]A=a\times b[/tex]

Here, (a)is the length of the rectangle and (b) is the width of the rectangle

The area of the tile is 48 square cm. John wants to make the mosaic with this tile having the length 2 cm longer than the width.

Let the width of the rectangle mosaic is w cm. Thus, the length of it is,

[tex]l=w+2[/tex]

As the area of a rectangle is the product of its length and width and Tte area of the tile is 48 square cm. Thus,

[tex]A=l\times w\\48=(w + 2)\times w \\48=w(w+2)\\w(w+2)=48[/tex]

The equation which John solve to find w, the greatest width in centimeters he can use for the mosaic is

[tex]w(w+2)=48[/tex]

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Answer:

B. w(w + 2) = 48

Step-by-step explanation:

I just took the quiz.

Have the day you deserve :)

sin alpha= a/c

sin 23° = x/13

x= sin 23° ×13

x≈ 5.08

Answer:

3

Step-by-step explanation:

Hard to see but pretty sure thats it

x=37.5

if you need an explanation i can type it in the comments

The amount which Brandon have saved in interest by consolidating the two balances on the card with the lower interest rate is $256.12.

Monthly payment is the payment which has to paid against the loan amount or the borrowed money calculated with interest rate.

It can be calculated with the following formula.

[tex]M=P\left (\dfrac{r}{1-(1+r)^{-nt}}\right)[/tex]

Here, (P) is the principal amount, (r) is the interest rate and (t) is time.

Brandon has two credit cards and would like to consolidate the two balances into one balance on the card with the lower interest rate.

The table below shows the information about the two credit cards Brandon currently uses.    

Interest rate for the card a is,

[tex]r=\dfrac{13}{12\times100}=0.01083[/tex]

The time period is 8 years and there are 12 months in one year. Thus, the monthly payment of card A will be,

[tex]M=1157.98\left (\dfrac{0.01083}{1-(1+0.01083)^{-12(8)}}\right)\\M=19.47[/tex]

In the 8 years, there is total 96 monthly payments. Thus, the total payment by card A is,

[tex]P_a=19.47\times96=1869.12[/tex]

For the card B the monthly payment is $22.14. Thus the total payment by card B is,

[tex]P_b=22.14\times96=2125.44[/tex]

The difference in the payment is,

[tex]d=2125.44-1869.12\\d=256.12[/tex]

Hence, the amount which Brandon have saved in interest by consolidating the two balances on the card with the lower interest rate is $256.12.

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Answer:

C. 256.32

Step-by-step explanation:

Answer:

Diana works at a clothing store. She sold 1/5 of the total number of green shirts on Monday and 3/12 of the total number of green shirts on Tuesday.

Answer:

x=4

Step-by-step explanation:

6x+3 = 27

Subtract 3 from each side

6x+3-3=27-3

6x = 24

Divide each side by 6

6x/6 = 24/6

x = 4

Answer:

x=4

Step-by-step explanation:

6x+3=27

6x=24

x=4

Answer:

1 5/32

Step-by-step explanation:

this is the answer

Answer:

The correct answer is 1 5/32

Step-by-step explanation:

First,convert both of the mixed numbers into improper fractions.Next,do the KCF method.Keep,change,and flip.First,like up 4 5/8 and 2 1/2 next to eachother with a multiplication sign in the middle.(Must be in this order!!)Next,turn the multiplication sign into a division sign.After this,change the second mixed number,and flip the denominator and the numerator.Then simply multiply the top numerators and the denominators.That is where you get you answer, Simplifying may be needed. :)

Answer:

(-5,3) (-7,3) (-5,6)

Step-by-step explanation:

So the line x= -1 is also a vertical line but this time it passes through the point (-1,0).

I hope this helps!!

Answer:

im terreb.le at math

Step-by-step explanation:

Answer:

285 dancers

Step-by-step explanation:

[tex]\frac{acrobats}{dancers}[/tex] = [tex]\frac{13}{15}[/tex] = [tex]\frac{247}{x}[/tex]

After cross-multiplication:

13x = ( 15 )( 247 )

13x = 3705

x = 285 dancers

Answer:

$60 per ticket

Step-by-step explanation:

$215 is what it costs after the discount, so add the amount taken off, back on.

215+25

240

Then, divide by 4 to find the cost of each individual ticket.

240/4

60

Answer:

0.03×104=3.12

0.3×104=31.2

0.3×10=3

0.03×109=3.27

these are the products

hope it helps!

The scale factor when a triangle of 8cm side is enlarged to a triangle of 64cm side is 8.

Side of the first triangle = 8cm

Side of the second triangle = 64cm

A scale factor is a number by which the size or dimension of an object is enlarged or diminished.

For example, if an equilateral triangle with a side x is dilated by a scale factor of 2, the enlarged size of the side will be 2a.

So, scale factor = side of the second triangle/ corresponding side of the first triangle.

Scale factor = 64/8

Scale factor = 8

Therefore, The scale factor when a triangle of 8cm side is enlarged to a triangle of 64cm side is 8.

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Answer:

8 I did the assignment

Step-by-step explanation:

Answer:

C) 43.96

Step-by-step explanation:

1. Use the formula to find the circumference of a circle whic is C= πR

2. First multiply the radius (7 in) by 2

3. 7 x 2 = 14

4. Then multiply 14 by 3.14

5. 14 x 3.14 = 43.96

5. There's your answer :)

Hope this helps :)

The value of cos(x) that supports Steve's claim is 1/√10

Given the following trigonometry identity

tan(x) = 3

According to the theorem;

tan x = opposite/adjacent = 3/1

Opposite = 3

Adjacent = 1

Determine the hypotenuse

hyp = √3² + 1²
hyp = √10

Since cos(x) = adj/hyp

cos(x) = 1/√10

Hence the value of cos(x) that supports Steve's claim is 1/√10

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keeping in mind that a function does not have any X-Repeats, that is, the 1st coordinate in every pair never repeats, Check the picture below.

Answer:

y=x+1

Step-by-step explanation:

at each x you move up by 1

Answer:

70° and 20°

let the other 2 angles be 7x and 2x

90+7x+2x=180

9x=180-90

x=90/9

x=10

7x=7x10

70

2x=2×10

2p

The expressions are irrational 1/3 + √216 and √64+ √353 and the expressions √100 × √100, 13.5 + √81, √9 + √729, and 1/5 + 2.5 are rational number.

If the value of a numerical expression is terminating then they are the rational number then they are called the rational number and if the value of a numerical expression is non-terminating then they are called an irrational number.

1.  √100 × √100

→ √100 × √100

→ 10 × 10 = 100

This is a rational number.

2.  13.5 + √81

→ 13.5 + √81

→ 13.5 + 9 = 22.5

This is a rational number.

3.  √9 + √729

→ √9 + √729

→ 3 + 27 = 30

This is a rational number.

4.  √64+ √353

→ √64 + √353

→ 8 + √353

This is an irrational number.

5.  1/3 + √216

→ 1/3 + √216

→ 1/3 + √216

This is an irrational number.

6.  1/5 + 2.5

→ 1/5 + 2.5

→ 0.2 + 2.5 = 2.7

This is a rational number.

More about the rational number link is given below.

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Answer:

A, B, C, F

Step-by-step explanation:

edge

Answer:

i believe she spent $4.482 on clementines

Answer:

x ≈ 5.8 degrees

Step-by-step explanation:

the sum of all exterior of any polygon is 180 degrees

so:  7x+4 + 5x+4 + 4x+9 + 9x-6 + 4x+1 =  180

combine 'like terms':

29x + 12 = 180

29x = 168

x ≈ 5.8

Answer: $40000

Step-by-step explanation:

200000(0.2) = $40000

This is the best I could find

Some recommended apps for solving geometry and triangle problems are "Ge oGebra," "De smos Geometry," and "Ma thway."

Ge oGebra: Ge oGebra is a versatile mathematics app that covers various topics, including geometry and triangles. It provides interactive tools for constructing and analyzing geometric shapes, making it a valuable resource for visualizing and understanding different properties and theorems related to triangles.

De smos Geometry: While De smos is primarily known for its graphing capabilities, the De smos Geometry app also offers tools for creating and manipulating geometric shapes, including triangles. It can help users explore and solve various triangle-related problems.

M athway: M athway is a comprehensive math problem-solving app that covers a wide range of topics, including geometry and triangles. Users can input specific problems, and the app provides step-by-step solutions, making it a helpful tool for both learning and verifying answers to geometry and triangle problems.

To know more about geometry, click here.

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------------The given question is incomplete, the complete question is:

"What are some recommended apps for solving geometry and triangle problems?"-------------

A finite, nonzero area formed by the lines would have a fixed measurement

The number of separate region that have a finite, nonzero area is 64

The given parameters are:

The number (n) of separate region that have a finite, nonzero area is calculated as:

n = (h - 1) * (v - 1)

This gives

n = (9 - 1) * (9 - 1)

Evaluate the product

n = 64

Hence, the number of separate region that have a finite, nonzero area is 64

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Answer:

x=200

Step-by-step explanation:

4x-x=600

3x=600

divide by 3

x=200

to check your work:

4(200)-200=600

800-200=600

Answer:

a. 120 Degrees

b. 180-120=60 60 Degrees

Step-by-step explanation:

A straight line has a maximum of 180 degrees.

ABC is 120, so CBD is 60

a) The size of angle ABC is 120 degrees.

b) The size of reflex angle CBD is 240 degrees.

a) The size of angle ABC is 120 degrees by inspecting at the protractor and counting from 0° 1o 120°

Reflex angles are formed by extending one of the sides of an angle beyond the straight line, creating an angle greater than 180 degrees. They can be visualized as the "extra" portion of a rotation around a point, beyond the 180-degree mark

b) To determine the size of reflex angle CBD,  consider that a reflex angle measures more than 180 degrees but less than 360 degrees. Since angle ABC is 120 degrees, subtract this angle from 360 to find the remaining measure of the reflex angle CBD.

Reflex angle CBD = 360 degrees - 120 degrees

= 240 degrees.

Therefore, the size of reflex angle CBD is 240 degrees.

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