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3 years ago

Find the missing length. Give all answers in the simplest radical form.

Mathematics

1 answer:

Solnce55 [7]3 years ago

8 0

Answer:

x = 2 $\sqrt{74}$

Step-by-step explanation:

Since the triangle is right use Pythagoras' identity to solve for x

The square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

x² = 14² + 10² = 196 + 100 = 296

Take the square root of both sides

x = $\sqrt{296}$ = 2 $\sqrt{74}$

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Evaluate tan45/sin30 . In your final answer, include all calculations.

Maslowich

From the identity $\displaystyle{ \tan x= \frac{\sin x}{\cos x}$ , and from the values:

$\sin45^{\circ}=\cos45^{\circ}= \frac{ \sqrt{2}}{2}$ ,

we have: $\displaystyle{ \tan 45^{\circ}= \frac{\sin 45^{\circ}}{\cos 45^{\circ}}= \frac{ \frac{ \sqrt{2}}{2}}{\frac{ \sqrt{2}}{2}} =1$ .

We also know that $\sin30^{\circ}= \frac{1}{2}$ .

Thus, $\displaystyle{ \frac{\tan 45^{\circ}}{\sin30^{\circ}} = \frac{1}{\frac{1}{2}}=2.$

Answer: 2

8 0

3 years ago

On a loan of $1200 at 15% annual interest, Shirley had to pay $135 interest. For how many months did she have the loan?

natulia [17]

Answer:

9 months

Step-by-step explanation:

Principal= P= $1200

Rate=R= 15%

Interest= I= $135

Time= T= ?

I=P*R*T/100

135= 1200*15*T/100

135*100=18000*T

13500/18000=T

T= 0.75 years

T= 0.75*12= 9 months

3 0

3 years ago

Read 2 more answers

What’s 3/4 x 22/7 x 2

Zolol [24]

Answer:

$4\frac{5}{7}$

Step-by-step explanation:

we just multiply numerator by numerator and denominator by denominator

3/4x22/7

66/28x2/1

132/28

4 20/28

4 5/7

Hopes this helps,please mark brainliest

3 0

1 year ago

Read 2 more answers

What is the value of the x variable in the solution to the following system of equations? 4x − 3y = 3 5x − 4y = 3

andrew-mc [135]

Solve 4x − 3y = 3 and 5x − 4y = 3

Step 1: Solve for x in 4x-3y=3:
4x-3y=3
4x-3y+3y=3+3y [Add 3y to both sides]
4x=3y+3
 $\frac{4x}{4} = \frac{3x+3}{4}$ [Divide both sides by 4]
x= $\frac{3}{4}y+ \frac{3}{4}$

Step 2: Substitute $\frac{3}{4}y+ \frac{3}{4}$ for x in 5x-4y=3
5x-4y=3
5( $\frac{3}{4}y+ \frac{3}{4}$ )-4y=3
 $\frac{-1}{4}y+ \frac{15}{4} =3$
$\frac{-1}{4}y+ \frac{15}{4} - \frac{15}{4} =3- \frac{15}{4}$ [Subtract $\frac{15}{4}$ to both sides]
$\frac{-1}{4}y= \frac{-3}{4}$
$\frac{ \frac{-1}{4}y}{ \frac{-1}{4} }= \frac{\frac{-3}{4} }{ \frac{-1}{4}}$ [Divide both sides by $\frac{-1}{4}$ ]
y = 3

Step 3: Substitute 3 for y in x = $\frac{3}{4}y+ \frac{3}{4}$
$\frac{3}{4}y+ \frac{3}{4}$
$\frac{3}{4}(3)+ \frac{3}{4}$
x = 3

5 0

3 years ago

This graph represents x−4y=−8. Which ordered pair is in the solution set of x−4y≤−8? (3, 2) (2, 3) (−3, 1) (3, −2)

Zigmanuir [339]

Answer:

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Find the missing length. Give all answers in the simplest radical form.​

Find the missing length. Give all answers in the simplest radical form.