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3 years ago

FAST PLEASE 50 POINTS :D

Mathematics

2 answers:

Ivenika [448]3 years ago

8 0

Answer:

20 units ^2

Step-by-step explanation:

The vertices are ( -8,-2) (-3,-2) (-3,-6) (-8,-6)

The sides are parallel

The lengths are *2- to -6 = 4 units

and -8 to -3 = 5 units

4*5 = 20 units ^2

Naddika [18.5K]3 years ago

3 0

Answer:

Area = 20 units²

Step-by-step explanation:

Let A(-8,-2), B(-3,-2), C(-3,-6) and D(-8,-6) so that the rectangle becomes ABCD.

=> Since it's a rectangle it will have two opposite sides equal.

So, let's find the length of any two sides (as length and width) by Distance Formula.

Distance Formula = $\sqrt{(x2-x1)^2+(y2-y1)^2}$

Side AB:

|AB| = $\sqrt{(-3+8)^2+(-2+2)^2}$

|AB| = $\sqrt{5^2}$

|AB| = 5

Side BC:

|BC| = $\sqrt{(-3+3)^2+(-6+2)^2}$

|BC| = $\sqrt{16}$

|BC| = 4

Now, Area:

Area of the rectangle = Length * Width

Area = 4 * 5

Area = 20 units²

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laila [671]

-1/4 + f/8 = 1/2.
The LCD is 8. Rewrite this equation as -8/4 + 8f/8 = 8(1/2) and then reduce the result:

-2 + f = =4

Then f = 6.

You should check this result.

8 0

2 years ago

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Serhud [2]

Answer:

152

Step-by-step explanation:

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3 0

2 years ago

The sum of Veronika's and Kate's weight is 118 pounds. Veronika weighs 26 pounds more than Kate. How much do they weigh individu

Ray Of Light [21]

Answer:

Veronika's weight = 92 pounds

Kate's weight = 46 pounds

Step-by-step explanation:

Let Veronika's weight = x

Let Kate's weight = y

The sum of Veronika's and Kate's weight is 118 pounds.

x + y = 118

Veronika weighs 26 pounds more than Kate.

x = y + 26

How much do they weigh individually?

We substitute y + 26 for x in Equation 1

x + y = 118

y + 26 + y = 118

26 + 2y = 118

2y = 118 - 26

2y = 92

y = 92/2

y = 46 pounds

x = y + 26

x = 46 + 26

x = 92 pounds

Hence,

Veronika's weight = 92 pounds

Kate's weight = 46 pounds

8 0

2 years ago

What degree of rotation is represented on this matrix

Korvikt [17]

Answer:

Option B is correct

the degree of rotation is, $-90^{\circ}$

Step-by-step explanation:

A rotation matrix is a matrix that is used to perform a rotation in Euclidean space.

To find the degree of rotation using a standard rotation matrix i.e,

$R = \begin{bmatrix}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}$

Given the matrix: $\begin{bmatrix}0 & 1 \\ -1 & 0\end{bmatrix}$

Now, equate the given matrix with standard matrix we have;

$\begin{bmatrix}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}$ = $\begin{bmatrix}0 & 1 \\ -1 & 0\end{bmatrix}$

On comparing we get;

$\cos \theta = 0$ and $-\sin \theta =1$

As,we know:

$\cos \theta = \cos(-\theta)$

$\sin(-\theta) = -\sin \theta$

$\cos \theta = \cos(90^{\circ}) = \cos( -90^{\circ})$

we get;

$\theta = -90^{\circ}$

and

$\sin \theta =- \sin (90^{\circ}) = \sin ( -90^{\circ})$

we get;

$\theta = -90^{\circ}$

Therefore, the degree of rotation is, $-90^{\circ}$

7 0

2 years ago

What is the value of a when we rewrite 8^x as a^-x/9

Andre45 [30]

Answer:

$a = \frac{1}{134217728}$

Step-by-step explanation:

Given

$8^x = a^{-x/9}$

Required

Find a

Take log of both sides

$log(8^x) = log(a^{-x/9})$

Apply law of logarithm

$x\ log(8) = (-x/9) log(a)$

Divide both sides by a

$log(8) = -\frac{1}{9} log(a)$

Multiply both sides by -9

$-9\ log(8) = log(a)$

Apply law of logarithm

$log(8^{-9}) = log(a)$

Cancel out log

$8^{-9} = a$

Rewrite as:

$a = 8^{-9}$

Apply law of indices

$a = \frac{1}{8^9}$

$a = \frac{1}{134217728}$

4 0

2 years ago