Pythagorean theorem please show work thank you

In ∆MNP, m∠N = 90º, NH – altitude, m∠P = 21º, PM = 4 cm. Find MH.

Sveta_85 [38]

Answer:

0.51 cm

Step-by-step explanation:

In right triangle MNP, MP = 4 cm, m∠N = 90°, m∠P = 21°

By the sine definition,

$\sin \angle P=\dfrac{\text{Opposite leg}}{\text{Hypotenuse}}=\dfrac{MN}{MP}\\ \\MN=MP\sin \angle P\\ \\MN=4\sin 21^{\circ}\approx 1.43\ cm$

Now, consider right triangle HMN (it is right because NH is an altitude). By the cosine definition,

$\cos \angle M=\dfrac{\text{Adjacent leg}}{\text{Hypotenuse}}=\dfrac{MH}{MN}\\ \\MH=MN\cos \angle M$

In the right triangle, two acute angles are always complementary, so

$m\angle M=90^{\circ}-m\angle P=90^{\circ}-21^{\circ}=69^{\circ}$

Thus,

$MH=1.43\cos 69^{\circ}\approx 0.51\ cm$

7 0

3 years ago

Use the given transformation to evaluate the integral.

GuDViN [60]

For the transformation

$\begin{cases}x=7u+v\\y=u+7v\end{cases}$

the Jacobian is

$\dfrac{\partial(x,y)}{\partial(u,v)}=\begin{bmatrix}7&1\\1&7\end{bmatrix}$

with determinant

$\det\left(\begin{bmatrix}7&1\\1&7\end{bmatrix}\right)=48$

The vertices of the triangle in the $u,v$ -plane are

$(x,y)=(0,0)\implies(u,v)=(0,0)$

$(x,y)=(7,1)\implies(u,v)=(1,0)$

$(x,y)=(1,7)\implies(u,v)=(0,1)$

Then the integral is

$\displaystyle\iint_R(x-8y)\,\mathrm dA=-48\int_0^1\int_0^{1-v}(u+55v)\,\mathrm du\,\mathrm dv=\boxed{-448}$

3 0

3 years ago

Jimmy purchased a package of jelly beans that contained 75 jellybeans. Out of the 75 jellybeans, 8 are pink, 17 are orange, 22 a

Luba_88 [7]

Find completion to question in comment section.

Answer:

D. One of the jellybeans that slipped out was orange and one was black

Step-by-step explanation:

We calculate the option with the highest probability of occurrence :

Total number of jellybean = 75

n(T) =75

n(Pink) = 8

n(red) = 22

n(Orange) = 17

n(green) = 8

n(white) = 6

n(black) = 4

We assume that the jelly beans must have slipped out one after the other.

Evaluating the options :

A.)

P(pink) and P(white)

8/75 * 6/74 = 0.0086486

B.)

P(green) and P(green)

8/75 * 7/74 = 0.0100900

C.)

P(white) and P(white)

6/75 * 5/74 = 0.0054054

D.)

P(orange) and P(black)

17/75 * 4/74 = 0.0122522

From the probability values obtained, the highest is D. Hence, the most likely to have occurred is One of the jellybeans that slipped out was orange and one was black

5 0

3 years ago

A blueprint for a house has a scale factor = 10. A wall in the blueprint is 8 in. What is the length of the actual wall?

oksian1 [2.3K]

Answer: 6.67 feet (check to see if you made a typo)

Step-by-step explanation:

if the scale factor is ten than we multiply 8 by 10

8 * 10 = 80

important to remember this is 80 INCHES not 80 FEET

to convert 80 inches into feet, we divide by 12 because there are 12 inches in a foot

80/12 = 6.67 feet

check to make sure that the first option is actually 6.67 inches because it would make more sense for it to be in feet

7 0

3 years ago

From the diagram, what can you conclude about triangle CAD?

Alex

I cant see the triangle so its kinda hard to know

7 0

3 years ago