What is the volume of this triangular pyramid?

Answer:

Measure of angle A = 55°.

Step-by-step explanation:

From the picture attached,

[tex]\frac{AC}{LN}=\frac{BC}{LM}[/tex]

[tex]\frac{10}{5}=\frac{8}{4}[/tex]

2 = 2

Corresponding sides of the given triangles ΔACB and ΔNLM are proportional.

Therefore, ΔACB ~ ΔNLM.

m∠A = 180° - (90° + 35°) [By triangle sum theorem]

         = 180° - 125°

         = 55°

Measure of angle A is 55°.

Answer:

1/20

Step-by-step explanation:

Karina ate 1/2 of the muffins. Ulysses ate 1/4 of the muffins. Zawanna ate 1/5 of the muffins. Juan ate the rest of the muffins. What fraction of the muffins did Juan eat?

Let the total number of muffins = 1

Hence:

The fraction of muffins Juan ate =

1 - (1/2 + 1/4 + 1/5)

Lowest common denominator is 20

1 - ( 10 + 5 + 4/20)

1 - 19/20

= 1/20

The Fraction of muffins Juan ate is 1/20

Answer:

Ratio=  7:9

Step-by-step explanation:

What is the ratio of angelfish to  seahorses?

14 angel fish : 18 seahorses

14:18 = 7:9

Answer:

6 hours and 25 minutes

Step-by-step explanation:

10:15 to 4:40 = 6 hours and 25 minutes

Answer:

[tex]\boxed{50cm^2}[/tex]

Step-by-step explanation:

Hello There!

The shown figure is a trapezoid

The formula for area of a trapezoid is

[tex]A=\frac{a+b}{2} h[/tex]

where a = base 1

b = base 2

h = height

the dimensions given are

13 & 7 - bases

5 - height

so all we have to do is plug in the values into the formula

[tex]A=\frac{7+13}{2} 5\\7+13=20\\\frac{20}{2} = 10\\10*5=50\\A=50[/tex]

So we can conclude that the area of the trapezoid is 50 cm²

Answer:

k =  -9

Step-by-step explanation:

f(x) = 2x²+kx-20

From remainder theorem,

x = 10 and f(10) = 90

f(10) = 90

Subsitute the value of x into the expression above.

f(10) = 2(10²)+10k-20 = 90

200+10k-20 = 90

Solve for k by collecting like terms

10 k = 90+20-200

10k = 110-200

10k = -90

k = -90/10

k = -9.

Hence the value of the constant is -9

Answer:

b

Step-by-step explanation:

Answer:

Perimeter: 18    Area: 18

Step-by-step explanation:

6 + 6 + 3 + 3 = 18

6 x 3 = 18

Answer:

In 2014, the population is of the United States was about 318,900,000 people. Choose the best approximation of the United States Population in 2014.

people

people

Answer:

people

Step-by-step explanation:

Given

US Population in 2014: About 318,900,000

Required

Approximate

From the given options, it's seen that the population of US is to be approximated to one significant digit and the result should be presented in standard form

So, the first step is to write out the population

318,900,000

As a general rule,

Category 1: Digit 0-4 are approximated to 0

Category 2: Digit 5-9 are approximated to 1

Since, we are approximating to one significant digit, only the first digit is needed, others are to be approximated.

The first digit is 3, meaning that approximation starts from the next digit which is 1

Approximating 318,900,000 will give 300,000,000 because "1" falls in category 1 as illustrated above.

The final step is to convert 300,000,000 to standard form.

There are 8 0s after 3.

Hence,

Conclusively, the approximation of 318,900,000 is  people

Step-by-step explanation:

Answer:

50% percent chance the ball will be yellow

Step-by-step explanation:

Find the amount of all the balls-24 and the amount of yellow balls-12

Then divide the number of yellow balls by the number of total balls.

12÷24=0.5

0.5=50%

Answer:

x=1, y=1

Step-by-step explanation:

Sub y=2x-1 into 3x+8y=11

3x+8(2x-1)=11

3x+16x-8=11

19x=11+8

19x=19

x=1

Sub x=1 into y=2x-1

y=2(1)-1

y=2-1

y=1

Answer:

5 is the answer

Step-by-step explanation:

2 4 6 8 10

1. 2 3 4 5

Juices

Answer:  $0.18

Step-by-step explanation:

Answer:

Im pretty sure its 114 m^2 sorry if im wrong

Answer:

The total surface area of the figure would be 114m.

So first you would have to find the slope using the two points and the equation: y2-y1/x2-x1, which in this case means you take 6+4/3+1, which would be a slope of 10/4 or 5/2, or 2.5. Using this, we can take a point, use point slope form, and rearrange it. So:

y-6=2.5(x-3)

y-6=2.5x-7.5

-2.5x+y=1.5

Answer:

$117.6

Step-by-step explanation:

Formula:

I = Prt

Given:

P = 210

r = 8% = 0.08

t = 7

Work:

I = Prt

I = (210)(0.08)(7)

I = 117.6

Answer:

Step-by-step explanation:

So with 8% interest, Jim will have to pay 8% more each year. For the first year we need to multiply 210 with 1.08 to find the amount that Jim would have had to pay to his sister if he had gotten an 8% interest for 1 year. Every time the year increases we need to multiply the previous number with 1.08 because we are looking for the 8% increased value of the previous one, therefore our equation is:

P(t) = 210*(1.08)^t --> (t=time in years, P(t)=amount of money Jim need to pay back with respect to time)

Since Jim gets an 8% interest for 7 years we have to put in 7 for t.

P(7)=210*(1.08)^7

which is approximately $359.903

440 bevause 154 is 35 percent of 440

The 154 mocha cupcakes represents a proportion of the total cupcakes sold in the bakery. The total number of cupcakes sold in the bakery on that day is 440.

Given that:

[tex]Mocha = 154[/tex]

From the question, we understand that the bakery sells other cupcakes too.

And Mocha only represents 35% of the total.

This means that:

[tex]Mocha = 35\% \times Total[/tex]

So, we have:

[tex]154 = 35\% \times Total[/tex]

Make Total the subject

[tex]Total = 154 \div 35\%[/tex]

[tex]Total = 440[/tex]

Hence, 440 cupcakes were sold on that day.

Read more about proportions at:

https://brainly.com/question/11654319

Answer:

a. 120 degrees

b. 2.0944 radians

Step-by-step explanation:

From 12:00 to 12:15 there forms a 90 degree angle. If we divide this by 3 we get that every 5 minutes the hand moves 30 degrees. Since in this scenario, the minute hand moved from 12:10 to 12:30 it, therefore, moved a total of 20 minutes so we can do the following math

20 / 5min = 4 times

4 * 30 degrees = 120 degrees

We can see that in this time it moved a total of 120 degrees. Now we can use this value to turn it into radians using the degree to radians formula

degrees * [tex]\pi /180[/tex] = radians

120 * [tex]\pi / 180[/tex] = radians

2.0944 = radians

Answer:

-3k + 10

Step-by-step explanation:

-3k-(-8)+2 = -3k + 8 + 2 = -3k +10

Answer:

-3k + 10

Step-by-step explanation:

-3k + 8 + 2 =

-3k + 10

Hope that helps!

Answer:

-9g

Step-by-step explanation:

Move -9 to the left of g

I think this is right, sorry if it is wrong, have a great day

Answer:

trigonometry

Step-by-step explanation:

hope this helps lovely

Answer:

trigonometry

Step-by-step explanation:

Have a great day!

Answer:

4x + 8

-45 - 5x

7x - 21

Step-by-step explanation:

For the first one

4(x + 2)

for distributive property you multiply the number or symbol next to the outside of the parenthesis, by everything inside the parenthesis.

4(x+2)

4*x = 4x

4*2 = 8

So, this is 4x + 8

-5(9+x)

-5*9= -45

-5*x=-5x

So, this is -45 - 5x

7(x-3)

7*x= 7x

7*-3= -21

This will be 7x - 21

Hope this helps!!

-Ketifa

Answer:

24

Step-by-step explanation:

3 * 2 = 6 * 4 = 24

Answer: 48

Step-by-step explanation:

3 x 2^4 =3 x 16 = 48