What are the values of each variable

The triangles below are similar. Triangle A B C. Side A C is 10 and side A B is 5. Angle C is 30 degrees. Triangle D E F. Side E

Gnoma [55]

Answer:

$\triangle ABC {\displaystyle \sim } \triangle DE\ F$

$\triangle CBA {\displaystyle \sim } \triangle FED$

$\triangle BAC {\displaystyle \sim } \triangle EDF$

Step-by-step explanation:

Given

$\triangle ABC {\displaystyle \sim } \triangle DE\ F$

$AC = 10$

$AB = 5$

$\angle C = 30^\circ$

$ED = 7.5$

$DF = 25$

$\angle F =30$

$\angle E =90$

Required

Which of the options is/are true:

$\triangle CBA {\displaystyle \sim } \triangle FED$ $\triangle CBA {\displaystyle \sim } \triangle FDE$ $\triangle BAC {\displaystyle \sim } \triangle EFD$

$\triangle BAC {\displaystyle \sim } \triangle EDF$ $\triangle ABC {\displaystyle \sim } \triangle DE\ F$ $\triangle ABC {\displaystyle \sim } \triangle DFE$

The given triangles, implies that:

$A {\displaystyle \sim } \ D$

$B {\displaystyle \sim } \ E$

$C {\displaystyle \sim } \ F$

By taking each sides of both triangle, one after the other; the possible similar triangles are:

$\triangle ABC {\displaystyle \sim } \triangle DE\ F$

$\triangle CBA {\displaystyle \sim } \triangle FED$

$\triangle BAC {\displaystyle \sim } \triangle EDF$

5 0

3 years ago

suppose a charity received a donation of $22.8 million. if this represents 58% of the charity's donated fund, what is the total

Mrac [35]

The total amount is "x", so, if 22.8 is 58%, "x" is the 100%,

$\bf \begin{array}{ccllll}
amount&\%\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
22.8&58\\
x&100
\end{array}\implies \cfrac{22.8}{x}=\cfrac{58}{100}\implies \cfrac{22.8\cdot 100}{58}=x$

6 0

3 years ago

Jenna wants to build 8 birdhouses. She needs 2 3/5 square feet of plywood for each birdhouse. If the plywood costs $0.56 per squ

goldenfox [79]

Answer:

$11.76

Step-by-step explanation:

We first need to find the amount of plywood for all birdhouses.

2 3/5 * 8 = 104/5 or 20.8 or 20 4/5

Now we can solve the cost for all the birdhouses by multiplying the total amount of plywood needed by the price per square foot.

20.8 * 0.56 = $11.648 or estimated $11.65

Remember, the question might be different, so don't submit anything yet. If the people who sell the plywood only sell in integer numbers (meaning you can't buy 4/5 of a square foot of wood but can only by amounts with no fractions), then Jenna must buy 21 square feet of plywood and will have a little bit of wood left over. Now solve just like before.

21 * 0.56 = $11.76

Therefore the answer is $11.76 if she can only buy an integer amount of plywood or estimated $11.65. I think the best answer is 11.76.

3 0

3 years ago

Calculate the factorization 16w^2+48w+36=(4w+[1])^2

stiv31 [10]

Answer:

[1] = 6

x = -3/2 is the root

Step-by-step explanation:

A perfect square trinomial is of the form ...

(a + b)² = a² +2ab +b²

You have ...

a²=16w² ⇒ a = 4w
b² = 36 ⇒ b = 6
2ab = 2(4w)(6) = 48w

Then the factorization is ...

16w² +48w +36 = (4w +6)²

This will be zero when x = -6/4 = -3/2.

3 0

3 years ago

2/3(3y+6)=0 Please help! One solution, No solution, or Many solutions? Please answer by 3:35, September 4, 2020

Serjik [45]

Answer:

one solution

Step-by-step explanation:

2/3(3y+6)=0

Multiply by 3/2

3/2 *2/3(3y+6)=0*3/2

3y+6 = 0

Subtract 6 from each side

3y = -6

Divide by 3

3y/3 = -6/3

y = -2

There is one solution

6 0

4 years ago