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2 years ago

Find the value of x.

Mathematics

1 answer:

Dmitry [639]2 years ago

5 0

Answer:

Step-by-step explanation:

x+7 = 32 (similar triangles)

x = 25

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Find the missing value<br> 8<br> 14<br> 45 <br> 15

alekssr [168]

Answer:

The correct option is B.

Step-by-step explanation:

From the given figure it is nices that the length of sides AB, BC and AC are 20, 22 and 35. The line AD is angle bisector.

Let the missing value be x.

The Triangle Angle Bisector Theorem states that the angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.

Since AD is angle bisector, therefore

$\frac{AB}{AC}=\frac{BD}{CD}$

$\frac{20}{35}=\frac{22-x}{x}$

$20x=35(22-x)$

$20x=770-35x$

Add 35x both sides.

$55x=770$

Divide both sides by 55.

$x=\frac{770}{55}$

$x=14$

Therefore, second option is correct.

6 0

3 years ago

Financial planners recommend that families save about 5% of their take-home pay. Ed and Sherrie save $90 each pay period from th

Ratling [72]

Answer:

Ed and Sheerie save 7.5%.

Step-by-step explanation:

This question can be solved using a rule of three.

Ed and Sherrie save $90 each pay period from their combined paychecks, which total $1200. What percent do Ed and Sherrie save?

How much of $1200 is $90? $1200 is 100% = 1, $90 = x. So

$1200 - 1

$90 - x

$1200x = 90$

$x = \frac{90}{1200}$

$x = 0.075$

Ed and Sheerie save 7.5%.

7 0

3 years ago

The perimeter of Stephanie’s triangle is half the perimeter of Juan’s triangle. Juan’s triangle is shown. Write a numerical expr

denpristay [2]

The perimeter of a triangle is the sum of all side lengths of the triangle. The numerical expression for the perimeter of Stephanie's triangle is: $\frac 12 \times 25$

Let the sides of Juan's triangle be x, y and z. So:

$x = 5 \\ y = 8\\ z = 12$

The perimeter (J) of Juan's triangle is calculated by adding all sides.

So:

$J =x +y +z$

This gives:

$J =5 + 8 + 12$

$J =25$

From the question, we understand that:

The perimeter (S) of Stephanie's triangle is half that of Juan.

This means that:

$S = \frac 12J$

Substitute 25 for J

$S = \frac 12 \times 25$

Hence, the numerical expression for the perimeter of Stephanie's triangle is: $\frac 12 \times 25$

Read more about perimeters at:

brainly.com/question/11957651

4 0

3 years ago

Read 2 more answers

Answer??? please please

SCORPION-xisa [38]

Answer:

58 = <1

Step-by-step explanation:

The sum of the opposite interior angles of a triangle is equal to the exterior angle

101 = 43+ <1

Subtract 43 from each side

101- 43 = <1

58 = <1

4 0

3 years ago

Read 2 more answers

Use the given information to find the exact value of the trigonometric function

eimsori [14]

$\begin{gathered} \csc \theta=-\frac{6}{5} \\ \tan \theta>0 \\ \cos \frac{\theta}{2}=\text{?} \end{gathered}$

Half Angle Formula

$\cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}}$ $\tan \theta>0\text{ and csc}\theta\text{ is negative in the third quadrant}$ $\begin{gathered} \csc \theta=-\frac{6}{5}=\frac{r}{y} \\ x^2+y^2=r^2 \\ x=\pm\sqrt[\square]{r^2-y^2} \\ x=\pm\sqrt[\square]{6^2-(-5)^2} \\ x=\pm\sqrt[\square]{36-25} \\ x=\pm\sqrt[\square]{11} \\ \text{x is negative since the angle is on the 3rd quadrant} \end{gathered}$ $\begin{gathered} \cos \theta=\frac{x}{r}=\frac{-\sqrt[\square]{11}}{6} \\ \cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}} \\ \cos \frac{\theta}{2}is\text{ also negative in the 3rd quadrant} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{1+\frac{-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{\frac{6-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}} \\ \\ \end{gathered}$

Answer:

$\cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}$

Checking:

$\begin{gathered} \frac{\theta}{2}=\cos ^{-1}(-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}) \\ \frac{\theta}{2}=118.22^{\circ} \\ \theta=236.44^{\circ}\text{ (3rd quadrant)} \end{gathered}$

Also,

$\csc \theta=\frac{1}{\sin\theta}=\frac{1}{\sin (236.44)}=-\frac{6}{5}\text{ QED}$

The answer is none of the choices

7 0

1 year ago