Consider the equation

ASAP PLEASE (this is like five questions in one) GIVING 15 POINTS!!!

valentinak56 [21]

Answer:

D

21√2/2

C

Step-by-step explanation:

For all problems, the ratios of the lengths of the sides are:

30-60-90 triangle 1 : √3 : 2

45-45-90 triangle 1 : √2 : √2

Problem 3:

30-60-90 triangle at left

Hypotenuse = 11

Short leg = 11/2

Long leg = 11/2 × √3

45-45-90 triangle at right

x = 11/2 × √3 × √2 = 11√6/2

Answer: D

Problem 4:

30-60-90 triangle at top

Hypotenuse = 7√3

Short leg = 7√3/2

Long leg = 7√3/2 × √3 = 7 × 3/2 = 21/2

45-45-90 triangle at right

x = 21/2 × √2 = 21√2/2

Answer: 21√2/2

Problem 7:

30-60-90 triangle

Long leg = 4√3

Short leg = y = 4√2/2 = 2√2

Answer: C.

Problem 6:

30-60-90 triangle at left

Hypotenuse = 12√6

Short leg = 12√6/2 = 6√6

Long leg = 6√6 × √3 = 6√2√3√3 = 18√2

45-45-90 triangle at right

x = 18√2/√2 = 18

Answer: C.

Problem 8:

45-45-90 triangle

Hypotenuse = 2

Leg = y = 2/√2 = 2√2/(√2√2) = √2

Answer: C.

5 0

2 years ago

A new factory is growing fast and hiring a lot of new workers. Every week, the total number of workers doubles in size. If it ta

MAXImum [283]

We know that the number of workers doubles every week.

This implies that the number of workers of the previous week is exactly half of the current one's.

So, it took 11 weeks for the factory to be at half capacity.

3 0

4 years ago

A school group is helping plant a new city garden. Today they used 12 1/2 pounds of potting soil and planted 2/5 of the garden.

Len [333]

Answer:

$18\frac{3}{4}$ pounds.

Step-by-step explanation:

Let x be the total amount of potting soil needed to complete the planting in new garden.

We are told that a school group is helping plant a new city garden. Today they used 12 1/2 pounds of potting soil and planted 2/5 of the garden. This means 2/5 of x equals to 12 1/2.

$\frac{2}{5} x=12\frac{1}{2}$

$\frac{2}{5} x=\frac{25}{2}$

$x=\frac{25}{2}\times\frac{5}{2}$

$x=\frac{125}{4}$

To find the amount of soil needed for the next of planting we will subtract the amount of potting soil used on the first day $(\frac{25}{2})$ from amount of total potting soil $(\frac{125}{4})$ .

$\text{Amount of potting soil needed for second day}=\frac{125}{4}-\frac{25}{2}$

$\text{Amount of potting soil needed for second day}=\frac{125}{4}-\frac{25\times 2}{2\times2}$

$\text{Amount of potting soil needed for second day}=\frac{125}{4}-\frac{50}{4}$

$\text{Amount of potting soil needed for second day}=\frac{75}{4}$

$\text{Amount of potting soil needed for second day}=\frac{75}{4}=18\frac{3}{4}$

Therefore, the group will need $18\frac{3}{4}$ pounds of potting soil to finish their work.

7 0

3 years ago

Factor 10m^5 n^3+5m^4 n^2-25m^2 n ??

Pavlova-9 [17]

I am not sure how the answer is coming up as an "m+1+ or "m-1" I am a ... Factor: : 4m^2 -18m + 14. We can simplify this, factor out 2 2(2m^2 - 9m + 7) ... FOIL (5m+3)(m+1) : 15m^2 - 10m - 25. Factor out 5 5(3m^2 - 2m - 5) Factors to 3(3m - 5)(m + 1) FOIL this to confirm it : 50m^3 - 2m. Simplify, factor out 2m 2m(25m^2 - 1)

3 0

4 years ago

Read 2 more answers

X^4 + 4x^3 + 3x^2 + 4x + 2 x²+1

dalvyx [7]

Answer:

${x}^{4} + 4 {x}^{3} + 4 {x}^{2} + 4x + 3$

Step-by-step explanation:

You can get it by adding numbers with same power of x. A like will be appreciated if you understand the explanation

6 0

3 years ago