All categories

2 years ago

Helwp please thank uuu!

Mathematics

1 answer:

Minchanka [31]2 years ago

7 0

Step-by-step explanation:

<h3>Given,</h3>

GRAM is a parallelogram
m<GMA = 66°
m<GRP = 32°
m<PAM = 41°

<h3>Solutions:</h3>

i) Since,

Angles on the same side of a transversal in a parallelogram, there sum is 180° so,

<RGM + <GMA = 180°

=> <RGM = 180° - <GMA

=> <RGM = 180° - 66°

=> <RGM = 114° (Ans)

ii) Since,

Opposite angles of a diagonal as a transversal (here RM) are equal so,

<GRP = <PMA = 32°

As we have <GMA = 66° so,

=> <GMP = <GMA - <PMA

= 66° - 32°

=> <GMP = 34° (Ans)

iii) Since,

Opposite angles of a parallelogram are equal so,

<RGM = <RAM = 114°

As we have <PAM = 41° so,

=> <GAR = <RAM - <PAM

= 114° - 41°

=> <GAR = 73° (Ans)

iv) Since,

We got <PMA = 32° and <PAM = 41°, so by angle sum property of a triangle PMA,

=> <MPA = 180° - 32° - 41°

=> <MPA = 107° (Ans)

You might be interested in

Kevin will attend college where tuition is $11,000 a year. Books and supplies cost $900, housing and food are $8500, transportat

nignag [31]

C is the correct answer

8 0

3 years ago

Estimate the square root to the nearest integer.

nexus9112 [7]

Answer:
3
Explanation:
3^2 is equal to 9, and 4^2 is equal to 16, so sqrt(10) must be in between 9 and 16. Since 10 is closer to 9 than to 16, sqrt(10) is closer to 3 than 4, which means that to the nearest integer sqrt(10)=3

3 0

3 years ago

This composite shape is a rectangle with a semicircle attached on one end. The diameter of the semicircle is 6 feet.

Ugo [173]

As we can see on the picture we have a rectangle and half of circle.

The areas for half circle and rectangle are:

$A_{rectangle}=a\cdot b \\A_{halfcircle}=\frac{A_{circle}}{2}=\frac{\pi r^2}{2}$

The area of the figure is the sum of the area of half circle and rectangle. Also the height of a rectangle (6ft) is a diameter of a half circle therefore the radius of half circle is 6ft ÷ 2 = 3ft.

Now we calculate the areas.

$A_{rectangle}=10\cdot 6=\underline{60} \\A_{halfcircle}=\frac{3.14\cdot3^2}{2}=\underline{14.13} \\A_{total}=A_{rectangle}+A_{halfcircle} =60+14.13=\boxed{74.13\approx74}$

The area of the figure is approximately 74ft squared.

Hope this helps.

r3t40

3 0

3 years ago

Read 2 more answers

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

3 years ago

Is 4,4 on the graph of 3x-y=8

Alexxx [7]

When you put the equation given in slope-intercept form it becomes y=3x+8
After graphing this you find that the point (4,4) is not part of the equation.

3 0

3 years ago

Read 2 more answers