Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(2, 1)B(5, 1),C(5, 6), and D(2, 6). Given these coordinates, what is the length of side AB of this rectangle?

Answer:

x = 12

Step-by-step explanation:

(whole secant) x (external part) =  (whole secant) x (external part)

(6+x) *6 = (4+23) * 4

(6+x) *6 = 27*4

6(6+x) = 108

Divide each side by 6

6+x =18

Subtract 6 from each side

6+x-6 =18-6

x = 12

Answer:

[tex]\mathbf{g^{-1} (t) = log _2 \ 20 \ t}[/tex]

Step-by-step explanation:

Here is the full question

A standard piece of paper is 0.05 mm thick. Let's imagine taking a piece of paper and folding the paper in half multiple times. We'll assume we can make "perfect folds," where each fold makes the folded paper exactly twice as thick as before - and we can make as many folds as we want.

Write a function g that determines the thickness of the folded paper (in mm) in terms of the number folds made, n. (Notice that g(0) 0.05,)

[tex]g(n )= (05)2^n[/tex]

The function g has an inverse. The function g⁻¹ determines the number of folds needed to give the folded paper a thickness of t mm. Write a function formula for g⁻¹).

SOLUTION:

If we represent g(n) with  t;

Then

[tex]\mathbf{t = (0.05)2^n} \\ \\ \mathbf{\dfrac{t}{0.05} = 2^n} \\ \\ \mathbf{\dfrac {100 \ t }{ 5} = 2^n} \\ \\ \mathbf{20 t = 2^n}[/tex]

Taking logarithm of both sides; we have :

[tex]\mathbf{log (20 t) = n log 2} \ \ \ \mathbf{(since \ , log \ a^b = b \ log \ a) } \\ \\ \mathbf{n = \dfrac{log \ 20 t }{log \ 2 }} \\ \\ \mathbf{g^{-1} (t) = \dfrac{log \ 20 t }{log \ 2 }} \\ \\ \mathbf{g^{-1} (t) = log _2 \ 20 \ t}[/tex]

Answer:

A. y = 5/4(x - 1)

Step-by-step explanation:

The equation of a line can be written in the form:

[tex]\frac{y - y_1}{x - x_1} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

From the points given,

y1 = 0

y2 = 5

x1 = 1

x2 = 5

Therefore:

[tex]\frac{y - 0}{x - 1}= \frac{5 - 0}{5 - 1} \\\\\frac{y}{x - 1} = \frac{5}{4}[/tex]

Cross multiply:

4y = 5(x - 1)

y = 5/4(x - 1)

A. y = 5/4(x - 1)

Step-by-step explanation:

The equation of a line can be written in the form:

From the points given,

y1 = 0

y2 = 5

x1 = 1

x2 = 5

Therefore:

Cross multiply:

4y = 5(x - 1)

y = 5/4(x - 1)

Answer:

one slice of pizza: $1

one cookie: $2

Step-by-step explanation:

Emily: two pizzas (1+1)+three cookies (2+2+2)= 8

Rachel: one pizza (1)+four cookies (2+2+2+2)= 9

can i plz get brainilest? :)

Answer:

piza 1 buck

cooky 2 bucks

Step-by-step explanation:

i did not look at the other answer...

lol i copied the other answer

Answer:

y = 5

Step-by-step explanation:

y + 6 = –3y + 26

Add 3y to each side

y+3y + 6 = –3y+3y + 26

4y +6 = 26

Subtract 6 from each side

4y+6-6 = 26-6

4y = 20

Divide by 4

4y/4 = 20/4

y = 5

The solution of y in the equation y + 6 = - 3y + 26 is,

⇒ y = 5

We have to given that;

Expression is,

⇒ y + 6 = - 3y + 26

Now, We can simplify as;

y + 6 = - 3y + 26

Add 3y to each side

y + 3y + 6 = - 3y + 3y + 26

4y + 6 = 26

Subtract 6 from each side

4y + 6 - 6 = 26 - 6

4y = 20

Divide by 4

4y/4 = 20/4

y = 5

Thus, The solution of y in the equation y + 6 = - 3y + 26 is,

⇒ y = 5

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13 years

Step-by-step explanation:

17 + 15 + 23 + 23 + 23 =101 / 5 = 20.2

Mean before was 20.2

In order for the mean to be 19, all those numbers would have to add up 114 to be divided by 6 and have a mean of 19

114 / 6 = 19

114-101 = 13 is that number

17 + 15 + 23 + 23 + 23 + 13 = 114 / 6 = 19

Answer:

see below

Step-by-step explanation:

Let's call the width w. The length would then be 2w - 6. Since the area of a rectangle = length * width the answer is 208 = (2w - 6) * w.

Answer:

0.1875 as a decimal and 18.75% as a percent

Step-by-step explanation:

0.1875 is the decimal. Move point over 2 spots right to get percent.

===========================================================

Work Shown:

1/500 = 0.002 is the probability of winning $390

3/500 = 0.006 is the probability of winning $230

16/500 = 0.032 is the probability of winning $170

Multiply the probabilities with their respective winnings

0.002*390 = 0.78

0.006*230 = 1.38

0.032*170 = 5.44

Then add up those results

0.78+1.38+5.44 = 7.60

which is the expected value.

Side note: This game is not a fair game because mathematically a "fair game" is defined as such where the expected value is 0; ie, neither the player nor the dealer win and things break even.

Answer:

y = 5(2)ˣ

Step-by-step explanation:

numbers are doubled for y as x is changing by 1

it indicates exponential growth with y intercept 5 and rate 2:  y = 5(2)ˣ

Answer:

x=22.5

Step-by-step explanation:

We are given the proportion:

5/x=2/9

Cross multiply. Multiply the numerator (top number) of the first fraction by the denominator (bottom number) of the second. Then multiply the denominator of the first by the numerator of the second.

5*9=2*x

45=2x

2 and x are being multiplied. The opposite of multiplication is division. Divide both sides by 2. This will cancel out the 2 being multiplied by x, and leave x by itself.

45/2=2x/2

45/2=x

22.5=x

If we substitute 22.5 in for x, the final proportion will be:

5/22.5=2/9

Answer: 22.5 = x

Step-by-step explanation: First, write the problem, 5/x = 2/9. Next, cross multiply. Write the equation, 5 x 9 = 2x. After, write the equation in a multiplying fraction sentence. 45/2 = 2x/2. Lastly, solve for x by dividing 45 by 2. You should end up with a result of 22.5 = x.

Answer:

5 ounces

Step-by-step explanation:

Mr. Landry prepares 30 pounds of cake batter each morning and he uses half of the cake batter to make large cupcakes.

This means that he uses 15 pounds of cake batter.

He makes 48 cupcakes with the batter.

Therefore, the number of pounds of batter he uses per cake is:

15 / 48 = 0.3125 pounds

We have to convert it to ounces.

1 pound = 16 ounces

=> 0.3125 pounds = 16 * 0.3125 = 5 ounces

He uses 5 ounces of cake batter for each cake.

Answer:

5 ONCES

Step-by-step explanation:

sry i had caps on but i did the math

Answer.

x=156

How to solve

x /6 +6=32

1 /6 x+6=32

1 /6 x+6−6=32−6

1 /6 x=26

6*( 1/ 6 x)=(6)*(26)

x=156

Answer:

The true statements are

The domain for f(x) is the set {-5, -3, 0, 2, 6, 7, 9, 10, 13}

f(-3) = 2

Extra:

x -5 -3 0 2 6 7 9 10 13

f(x) 1 2 3 0 1 2 3 0 1

Answer:

8a^3.

Step-by-step explanation:

(a+b)^3=a^3+b^3+3a^2b+3ab^2

(a-b)^3=a^3-b^3-3a^2b+3ab^2

(a+b)^3+(a-b)^3=2a^3+6ab^2

According to the question

(a+b)^3+(a-b)^3+6a(a^2-b^2)

Put in the value

=2a^3+6ab^2 +6a^3–6ab^2

=8a^3

In the simplest form expression (a + b)³ + (a - b)³ + 6a(a² - b²) can be written as,  8a³

Algebraic identities are algebraic equations that are true regardless of the value of each variable. Additionally, they are employed in the factorization of polynomials. Algebraic identities are employed in this manner for the computation of algebraic expressions and the solution of various polynomials.

Given that,

A algebraic identity,

(a + b)³ + (a - b)³ + 6a(a² - b²)

It is known that,

(a + b)³  = a³ + b³ + 3ab(a + b)

(a - b)³  =  a³ - b³ - 3ab(a - b)

So, now we can substitute expressions

(a + b)³ + (a - b)³ + 6a(a² - b²)

a³ + b³ + 3ab(a + b) + a³ - b³ - 3ab(a - b) +  6a(a² - b²)

a³ + b³ +  3a²b + 3ab² + a³ - b³ -3a²b + 3ab² + 6a³ - 6ab²

8a³

Hence, the simplest form is 8a³

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Answer:

AA similarity

Step-by-step explanation:

Respective angles of both triangles are 40°, 50° and 90°

AA similarity is the case:

Answer:

The system of equations does not have a solution.

Step-by-step explanation:

For example, imagine these two equations y = x + 7 and y = x + 9

Now substitute y in the second equation with the value from the first equation:

x + 7 = x + 9

x - x + 7 = 9

0 + 7 = 9

7 = 9.

That happens because the equations represent parallel lines, which do not have a common pair of points.

Answer:

Step-by-step explanation:

49 is a perfect square, since it equals 7*7; 56 is not. If you have 35.2 and 37T, 36 is the perfect square between the two integers. Take the square root of the perfect square. If you have your square roots for memory, you know that the square root of 36 is equal to 6.

Answer:

-3

Step-by-step explanation:

[tex]f(x)=-2x^3+x^2-2 \\\\f(1)=-2(1)^3+(1)^2-2= \\\\-2+1-2=\\\\-3[/tex]

Hope this helps!

Answer:

A= 61

B=119

Step by step:

a; interior angle

180-(27+92)

=180(119)

=61

b; exterior angle

180-61

=119

Answer: 61 and 119

Step-by-step explanation:

Answer:

21.66666667

Step-by-step explanation:

3x-4(0)=65

3x=65

x=21.66666667

You replace y wil 0 when you are sovling for x

Answer:

72

Step-by-step explanation:

The sum of exterior angles is 360

360-57-68-32-59-72 =. 72

Answer:

Step-by-step explanation:

So basically, what you have to do is first find the area of the floor. The area can be split into 3 shapes, a quarter of a circle, a square, and a rectangle.

Quarter of circle: (3.14r^2)/4

3.14(100)/4

314/4

78.5

Square: s^2

100

Rectangle: lw

600

Total: 78.5+100+600

778.5

Cost: $2335.50

Answer:

5^18 in index form is the answer :)

Step-by-step explanation:

(5^3)^6

In a polynomial like this the rule is that,

(a^m)^n

= a^m*n (multiply the exponents)

So let a be 5

m be 3 and n be 6

5^3^6

= 5^3*6

= 5^18

Answer:

Step-by-step explanation:

If the two cone are similar then the heights are the same

let us find the height of the bigger cone

[tex]volume of cone= \frac{1}{3} \pi r^2h[/tex]

For the bigger cone

r= 3cm

v= 66cm^3

[tex]66=\frac{1}{3}*3.142*3^2*h\\ 66=\frac{28.278}{3} *h\\h*28.278=198\\h=\frac{198}{28.278} =7cm[/tex]

For the smaller cone

r=2cm

v=?

h=7cm

[tex]v=\frac{1}{3}*3.142*2^2*7\\\v=\frac{87.976}{3} \\\\\v=29.30cm^3[/tex]

Answer:

19.6

Step-by-step explanation:

[tex]66=(\frac{3}{2} )^{3} =\frac{27}{8}[/tex]

[tex]\frac{66 x8}{27} = 19.5555555556=19.6[/tex]

[tex]x=[/tex] · [tex]( multiplication symbol )[/tex]

Answer:

Step-by-step explanation:

The equation modeling the situation is ;

y = 25x + 80

We want to know what the y-intercept mean in this question

Mathematically, the equation of a straight line is ;

y = mx + c

where c is the y intercept and m is the slope

What we should understand is that at the y intercept which is 80 here, the value of x is 0

Now since y means the amount of money spent and x is number of chairs bought, the value 80 means that the amount spent when he bought 0 number of chairs is 80

Now going by the question, since he bought 0 chairs here and we still have some cost, definitely he spent the money on other things which of course might be the amount spent in purchasing some tables

Answer: 8

Step-by-step explanation:

(-11/2x + 3) -2(-11/4x - 5/2)

Distribute

-11/2x + 3 + 22/4x + 10/2

Simplify 22/4x and 10/2

-11/2x + 3 + 11/2x + 5

Cancel out 11/2x and -11/2x

3 + 5

Add 3 and 5

8

Answer:

8

Step-by-step explanation:

(-11/2 x + 3) -2(-11/4 x - 5/2)

Distribute

-11/2 x + 3 +11/2 x + 5

Combine like terms

-11/2 x +11/2 x + 5+3

8