What is the area of the shaded rectangle?

The measure of side BC is 30 units.

Given:

Points A, B, and C are collinear and B lies between A and C.

[tex]AC=48[/tex]

[tex]AB=2x+2[/tex]

[tex]BC=3x+6[/tex]

To find:

The value of BC.

Solution:

Points A, B, and C are collinear and B lies between A and C. So,

[tex]AB+BC=AC[/tex]              [Segment addition postulate]

[tex](2x+2)+(3x+6)=48[/tex]

[tex]5x+8=48[/tex]

Subtract 8 from both sides.

[tex]5x=48-8[/tex]

[tex]5x=40[/tex]

Divide both sides by 5.

[tex]\dfrac{5x}{5}=\dfrac{40}{5}[/tex]

[tex]x=8[/tex]

Now,

[tex]BC=3(8)+6[/tex]

[tex]BC=24+6[/tex]

[tex]BC=30[/tex]

Therefore, the value of BC is 30.

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The possible coordinates for G are -11 and 5.

Given:

On a number line, suppose point E has a coordinate of [tex]-3[/tex], and [tex]EG=8[/tex].

To find:

The possible coordinates of point G.

Solution:

Either point G lies 8 units left of point E or 8 units right of point E.

[tex]G=-3-8[/tex]

[tex]G=-11[/tex]

And

[tex]G=-3+8[/tex]

[tex]G=5[/tex]

Therefore, the possible coordinates for G are -11 and 5.

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9514 1404 393

Answer:

  (b)  domain: all reals; range: y ≤ 6

Step-by-step explanation:

The domain of any polynomial function is always "all real numbers." There are no values of the variable for which a polynomial is undefined.

The range of a polynomial will depend on its degree and the sign of the leading coefficient. Here, the degree is even, so the range has a limit. The leading coefficient is negative, so that limit is a maximum.

Only one answer choice has these characteristics:

  domain: all real numbers; range: y ≤ 6

__

The graph confirms this choice of range.

Answer:

The temperature was 80 degrees and it dropped 10 degrees. What is the temperature now?

80 - 10 = 70 degrees

Step-by-step explanation:

Answer:

16+21/8-6 simplifies to 13

Hope this helps!!

Answer:

D. 13

Step-by-step explanation:

Step 1:

16 + 24 / 8 - 6

Step 2:

16 + (24 / 8) - 6

Step 3:

16 + 3 - 6

Step 4:

(16 + 3) - 6

Step 5:

19 - 6

Answer = 13

Hope it helps :)

Answer:

Step-by-step explanation:

a) points not on the plane will be somewhere other than on the shaded area representing plane P. Z and W are two such points.

__

b) The name can consist of any three points not on the same line. That means names RVX, RSU, TUV are not allowed, but any other combination of these letters, along with the letter Q, can be used. A couple of possible names are ...

 QRS, STU

Answer:

[tex]94/99[/tex] Or [tex]0.94[/tex] as a repeating decimal

Step-by-step explanation:

Answer:

600,000+80,000+700+5

Answer:

answer is 6

Step-by-step explanation:

m^2 - 4m + 2

-2(2) - 4(-2) + 2

-4 + 8 + 2

-4 + 10

6

Step-by-step explanation:

Answer:

you would write it as -3.25 as a whole number

Answer:

0.4583

Hope it helps you!!

Matrix operations includes the addition, multiplication and subtraction of matrices

The correct option for the matrix that can be used to represent B is option D)

[tex]D) = \left[\begin{array}{rrr}6&-3&-6\\5&9&5\end{array}\right][/tex]

The reason the above option is correct is as follows:

From the graph, we have that the coordinates of the preimage are;

(-6, 5), (-3, 9), and (6, 5)

The coordinates of the preimage in matrix form is given as follows;

[tex]\left[\begin{array}{rrr}6&-3&-6\\5&9&5\end{array}\right][/tex]

The coordinates of the image are;

(-6, -5), (-3, -9), and (6, -5)

The coordinates of the image in matrix form is given as follows;

[tex]\left[\begin{array}{rrr}6&-3&-6\\-5&-9&-5\end{array}\right][/tex]

The above image matrix can be obtained from the primage matrix as follows:

[tex]\left[\begin{array}{rrr}1&0\\0&-1\end{array}\right]\left[\begin{array}{rrr}6&-3&-6\\5&9&5\end{array}\right] = \left[\begin{array}{rrr}6&-3&-6\\-5&-9&-5\end{array}\right][/tex]

Which is of the form AB = C

Where;

[tex]A = \left[\begin{array}{rrr}1&0\\0&-1\end{array}\right][/tex]

[tex]B = \left[\begin{array}{rrr}6&-3&-6\\5&9&5\end{array}\right][/tex]

[tex]C = \left[\begin{array}{rrr}6&-3&-6\\-5&-9&-5\end{array}\right][/tex]

Therefore, the matrix that could represent B is [tex]\left[\begin{array}{rrr}6&-3&-6\\5&9&5\end{array}\right][/tex] which is option D)

Learn more about matrix operations here:

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Answer:

$21 the minimum Bob has to may will be the amount payed regardless of the number of passengers in the taxi

Answer:

20x30xH=7000

11.6666 , depends on how much you need to round it. if 2 sig figs, round it to 12.

Answer:

Pyramid Height = 3 * Pyramid Volume / Base Area

Height = 3 * 7,000 / (30 * 20)

Height = 21,000 / 600

Height = 35 meters

Step-by-step explanation:

9514 1404 393

Answer:

  a) J(K(x)) = x; K(J(x)) = x; functions are inverses

  b) f(g(x)) = 8 -x; g(f(x)) = -x; functions are not inverses

  c) f(x) = 4 -x; f^-1(x) = 4 -x. g(x) = x -4; g^-1(x) = x +4

Step-by-step explanation:

a) Substitute for the function argument in the usual way. If the functions are inverses, their composite is the identity function.

  J(K(x)) = J(1/3x -2) = 3(1/3x -2) +6 = x -6 +6 = x . . . . functions are inverses

  K(J(x)) = K(3x +6) = 1/3(3x +6) -2 = x +2 -2 = x . . . . functions are inverses

__

b) f(g(x)) = f(x -4) = 4 -(x -4) = 4 -x +4 = 8 -x . . . . functions are not inverses

  g(f(x)) = g(4 -x) = (4 -x) -4 = -x . . . . functions are not inverses

__

c) To find the inverse function for y = f(x), solve x = f(y).

The inverse of f(x) = 4 -x is ...

  x = f(y) = 4 -y

  y = 4 -x . . . . . add y-x to both sides

  f^-1(x) = 4 -x

and for g(x) = x -4, the inverse is ...

  x = g(y) = y -4

  x +4 = y

  g^-1(x) = x +4

The entries for Row 3 in step 3 are : 0, -1, -2, 1

R_{1} = Row1

R_{2} = Row  2

R_{3} = Row  3

For the third step, STEP 3 :

THE VALUE OF Row 3 is obtained thus :

[tex]R_{3} = R_{3} - 3R_{1}[/tex]

[tex]From \: step \: 1 : R_{1} = [1 1 1 0][/tex]

[tex]R_{1} = [1 1 1 0] \\  \\

[tex]R_{3} = [3 2 1 1]  \\  

\\ 3R_{1} = 3(1 1 1 0) = [3 3 3 0][/tex]

[tex]R_{3} - 3R_{1} \:  =

(3 - 3), (2 - 3), (1 - 3), (1 - 0) = (0, -1, -2, 1)[/tex]

Hence, the entry for Row 3 in step 3 will be :

(0, - 1, - 2, 1)

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Answer:

[tex]x^2-6x+9[/tex]

Step-by-step explanation:

Say you have a function [tex]f(x)=x+1[/tex]. If you wanted to find f(3), you would replace the number in the parentheses, in this case 3, with x, to get [tex]f(3)=3+1=4.[/tex] When combining functions, you should do the same thing.

Here, we have [tex]f(x)=x^2.[/tex] We want to find f(g(x)). So, you should replace x in the function f(x) with the function g(x). [tex]g(x)=x-3.[/tex] So, f(g(x)) would equal [tex](x-3)^2[/tex], which equals [tex]x^2-6x+9[/tex].

Hope this helps!

Answer:

44

Step-by-step explanation:

Let S = strawberry count

Chocolate = 1/4 * 80 = 20

Vanilla = 1/5 * 80 = 16

Total = C + V + S

80 = 20 + 16 + S

80 - 20 - 16 = S = 44

Answer:

Step-by-step explanation:

m+np

Now

Answer:

the fraction of 6/7 divided by 2 is 3/7

Answer:

A. Sequence 2 is arithmetic and Sequence 1 is geometric

Step-by-step explanation:

Hello,

Answer A

-10,20,-40,80,.... is geometric= Sequence 1

15,-5,-25,-45.... is arithmetic= Sequence 2

Answer:

$1,856.25

Explanation:

To find the square yards, multiply length and width

7.5 * 5 = 37.5

Then, since each square yard costs $49.50, multiply the square yards and the cost

37.5 * 49.50 = 1,856.25

Thus the answer is $1,856.25

The carpet for the room will cost $1,856.25.

This is the product of the unit cost per square yard multiplied by the area of the room.

The area of the room is = 37.5 square yards (Length x Width)

Length of the room = 7.5 yards

Width of the room = 5 yards

Therefore, the total area of the room = 37.5 square yards (7.5 x 5)

Thus, the total area of the room is 37.5 square yards and since each square yard costs $49.50, the total cost for buying the carpet will cost $1,856.25 ($49.50 x 37.5).

Learn more about area of a space at https://brainly.com/question/16758524

Step-by-step explanation:

$1660-$580= $1,080

Answer:

1660 minus 580

Step-by-step explanation:

they have already raised 580. so get 1660 is to subtract 1660 to 580

Answer:

2x^2 +16x=0

=>2 x(x+8)=0

=>2x=0 or x+8=0

=>x= 0 or x=-8

Step-by-step explanation:

Answer:

1980

Step-by-step explanation:

Answer:

The least possible amount of saving they could each have is 36$

Step-by-step explanation:

12+12+12 = 36

9+9+9+9=36

The equivalent expression of the given value is 4.1 m/s in two significant figures

Your question is incomplete, i believe the following is the intended question.

[tex]\frac{450 \ m}{ 110 \ s}[/tex] equals which of the following values to the correct number of significant figures ?

The express the given value in the correct significant figures we will simplify it as follows:

450 m has 2 significant figures ( 4 and 5)

110 s has 2 significant figures (1 and 1)

Thus, the resultant ratio of the two numbers will be expressed in two significant figures.

[tex]\frac{450 \ m}{110 \ s} = 4.0909 \ m/s\\\\in \ two \ significant \ figures = 4.1 \ m/s[/tex]

Therefore, the equivalent expression of the given value is 4.1 m/s

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my guess is "15m" is it correct ?

Explanation:

Apply the pythagorean theorem to find the missing side.

[tex]a^2 + b^2 = c^2\\\\x^2 + 20^2 = 25^2\\\\x^2 + 400 = 625\\\\x^2 = 625-400\\\\x^2 = 225\\\\x = \sqrt{225}\\\\x = 15[/tex]

The horizontal leg of the right triangle is 15 meters long. This is the distance from the base of the tree to the base of the building.

Side note: This right triangle is based off the 3-4-5 right triangle. It has been scaled up by a factor of 5.