Find the lateral surface area of the triangular prism shown below.

Answer:

12=obtuse

13=right

14=not a triangle

16=acute

Step-by-step explanation:

Answer:

The length of side x in a 30-60-90 triangle is 2√3.

Step-by-step explanation:

The numbers 30-60-90 are angles, so we need to find the side x of a right triangle with the following information:

θ: is one angle of the right triangle = 30°

α: is the other angle of the right triangle = 60°

a: is one side of the right triangle = √3

b: is the other side of the right triangle =?

x: is the hypotenuse of the right triangle =?

The length of the hypotenuse can be found by Pitagoras:

[tex] x^{2} = a^{2} + b^{2} [/tex]    (1)

So, we need to find the side "b". We can calculate it with the given angles.

From the side "a" we have:

[tex] cos(\alpha) = \frac{a}{x} [/tex]

[tex] cos(60) = \frac{\sqrt{3}}{x} [/tex]    (2)

From the side "b":

[tex] sin(\alpha) = \frac{b}{x} [/tex]

[tex] sin(60) = \frac{b}{x} [/tex]   (3)

Now, we can calculate "b" by dividing equation (3) by equation (2).

[tex] tan(60) = \frac{\frac{b}{x}}{\frac{\sqrt{3}}{x}} [/tex]

[tex] b = tan(60)*\sqrt{3} = 3 [/tex]

Finally, we can find the length of the hypotenuse with equation (1):

[tex] x = \sqrt{a^{2} + b^{2}} = \sqrt{(\sqrt{3})^{2} + (3)^{2}} = 2\sqrt{3} [/tex]

Therefore, the length of side x in a 30-60-90 triangle is 2√3.

I hope it helps you!

Answer:

x ≤ 1/3

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

50.27

Step-by-step explanation:

Give me Brainllest

Answer:

Option B

Step-by-step explanation:

Set 1:

med: 76, Range: 50-65= 15IQR: 77-73= 4

find the median, range, and IQRfor each data set.

Set 2:

med: 60, Range: 68-55= 13,IQR: 63-59= 4

76- 60 =16

find the difference of the medians 16 is 4 times 4

so the difference of the medians is 4 times the IQR

----------------------------

hope it helps...

have a great day!!

Answer:9

Step-by-step explanation:

4 inches fits into 12 inches three times. Three rows multiplied by three columns equals 12.

Hope that helps!

Answer:

25

Step-by-step explanation:

rate of change =change of distance/ change of time

so if you look at the chart you can see these points: (2,50) and (6,150)

change of distance would be 150-50/ change of time which would be 6-2 which equals 100/4 which is 25, the rate of change.

Answer:

b = 12

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

b² + 5² = 13²

b² + 25 = 169 ( subtract 25 from both sides )

b² = 144 ( take the square root of both sides )

b = [tex]\sqrt{144}[/tex] = 12

Answer:

4.065

Step-by-step explanation:

40.6 divide by 5 so answer is 4.065

Answer:

Step-by-step explanation:

0.07/2.8 = 0.025

7/280 = 0.025

Yes they are same because their answer is same

Answer:

We now want to find the best approximation to a given function. This fundamental problem in Approximation Theory can be stated in very general terms. Let V be a Normed Linear Space and W a finite-dimensional subspace of V , then for a given v ∈ V , find w∗∈ W such that kv −w∗k ≤ kv −wk, for all w ∈ W.

Step-by-step explanation:

Answer:

yes, this quadrilateral is a parallelogram.

Step-by-step explanation:

Above quadrilateral ,

opposite angle 70=70

and there is also 180-70=110 (linear pair)

so, others opposite angle 110=110

This quadrilateral have opposite sides equal

so, this is parallelogram.

Answer:

4.5 > 4.420

0.67 < 0.8

0.82 = 0.820

62.4 > 6.24

0.13, 0.3, 0.303, 0.32

0.08, 0.8, 0.82, 8.2

24.54, 24.4, 24.304, 24.24

6.5, 6.25, 6.05, 6.007

Step-by-step explanation:

The most useful way to compare fractions is to add extra zeros at the end.

For example, 0.67 ___ 0.80.

0.80 is obviously bigger than 0.67.

In 24.4, 24.54, 24.304, 24.24, you can add extra zeros as well.

24.400, 24.540, 24.304, 24.240 (This makes it much easier to group the numbers, whether from largest to smallest or smallest to larger).

**REMEMBER TO REMOVE THOSE ZEROS AFTER FINDING YOUR FINAL ANSWER**

Answer:

k=0 or k=9/10

Step-by-step explanation:

10k^2 - 10k- (-k) = - k- (-k)

10k^2-9k=0

k(10k-9)=0

k=0 or 10k-9=0

k=0 or k=9/10

Answer:k=(1/2,2/5)

Step-by-step explanation:

Step-by-step explanation:

hope it is helpful to you

Answer: 343.75

Step-by-step explanation:

There are multiple ways to do this

1) Use decimals

25% is equal to 0.25

To find 25% of 1375, multiply 0.25x1375.

0.25x1375

=343.75

Or you can use fractions!

25%=0.25

0.25=1/4

Divide 1375 by 4

=343.75

25% of 1375 is equal to 343.75

Answer:

Step-by-step explanation:

Answer:

2, 5, 8

Step-by-step explanation:

For starters, let us assume that the numbers are x-d, x, and x+d.

Where d is the common difference between terms.

This mean that we can say, from the question

x-d + x + x+d = 15

3x = 15,

x = 5,

This means that the terms are 5, 5-d and 5+d.

On the other hand,

(5-d) * 5 * (5+d) = 80

(5-d) * (5+d) = 80/5

(5-d) * (5+d) = 16

25 - d² = 16

d² = 9

d = + or - 3.

Finally, the three numbers will be 2, 5, and 8. On the flipside, their sum and product are 15 and 80.

Answer:

7

Step-by-step explanation:

Answer:

angle 5 = 149°

angle 7 = 149°

Answer:

Step-by-step explanation:

1.Given Information :

Distance (d) = 1/4 miles

Time (t) = 36 seconds

Speed = ?

[tex]Speed = \frac{Distance (d)}{Time (t)}\\\\Speed= \frac{\frac{1}{4} mile }{36 seconds} \\\\Speed =\frac{1}{44}m/hr[/tex]

2.The unit rates are equal

Answer:

1. 142

2. 38

3. 142

5. 142

6. 38

7. 142

8. 38

Step-by-step explanation:

Angles across from another angle in an x have the same value

A line has an angle of 180º so the angle on the other side of a split line is whatever angle would make it add up to 180

180º - 38º = 142º

Answer:

259200 seconds

How: 60×60×24 = 86400

That is for one full day, so multiply that by 3

Answer: 259200

Answer:

The airplane would starts its descent from an altitude 500 feet lower.

Step-by-step explanation:

The x-axis is horizontal and the y-axis is vertical (altitude). It would be 500 feet lower because they took 500 away from the 30,000.

Answer:

amy made 5.775 while vickie made 17.325

Step-by-step explanation:

i dunno

Answer:

Step-by-step explanation:

Answer:

solution given:

[tex] \sqrt{144 {x}^{6} {y}^{8} {z}^{7} } = \sqrt{(12 {)}^{2}( {x}^{6} ) {y}^{8} ( { {z}^{1} })^{6} } = 12 {x}^{3} {y}^{4} {z}^{3} \sqrt{z} [/tex]

is your answer.

Answer:

28%

Step-by-step explanation:

12+34+7=2856

Then, 2856/100 to get the percentage.

Answer:

C

Step-by-step explanation:

Start from left to right

Answer:

Step-by-step explanation: it is jedn

Step-by-step explanation:

4 pounds is 4÷1=8

2

5 pounds is 5÷1=10

2

Answer:

they would continue to make a profit because the decrease in price is 5%

Step-by-step explanation: