What is the volume of the shape in the picture?

Answer:

a^2+b^2=c^2

6^2+6^2=72

square root of 72

=8.49(3sf)

c^2-b^2=a^2

=3

x=3

answer : 3

step by step:

this may seem hard but it is easy.

the first thing to do is to look at the bottom of the shape it shows a right triangle that is missing the hypotenuse lets see how to solve for that:

name the hypotenuse  x

then write the equation

x^2= 6^2 + 6^2

x^2= 72

take both the square root of them

x = 8.5

next part is the rectangle and we see that it has been split into 2 right triangles which are the same but the cool part is that if we solve for one of the triangles we solve for the other we are going to do the same steps again notice now we are solving for the right angle that's not labeled if we solve that then that means we solve for the other triangle that is labelled x

first off we know that the hypotenuse is 9 and one angle is 8.5 so here is the equation:

x^2 = 9^2 - 8.5^2

x^2 = 8.75

take square root of both

x = 3

Answer:

58+-43=15

Step-by-step explanation:

Answer:C=10

Step-by-step explanation:

Follow along with the picture below

The formula for this type of problem is a^2+b^2=c^2

We know that 6=a and 8=b so we fill in the formula and square them

we then add the two values we got which get us to 100=c^2

we want to get rid of that square with we square root bothe sides and get c and the square root of 100 is 10.

So C=10

Answer:

$ 500 was the principal of the loan at 4%, and $ 2,500 was the principal of the loan at 3.5%.

Step-by-step explanation:

Given that Eric borrowed a total of $ 3000 from two student loans, and one loan charged 4% simple interest and the other charged 3.5% simple interest, both payable after graduation, if the interest he owed after 2 years was $ 215, to determine the amount of principal for each loan, the following calculation must be performed:

4 x 2 = 8

3.5 x 2 = 7

1500 x 0.08 + 1500 x 0.07 = 225

1400 x 0.08 + 1600 x 0.07 = 224

100 x 0.08 + 2900 x 0.07 = 211

500 x 0.08 + 2500 x 0.07 = 215

Therefore, $ 500 was the principal of the loan at 4%, and $ 2,500 was the principal of the loan at 3.5%.

Answer:

AnD = {8,10}

Step-by-step explanation:

A = {2, 4, 6, 8 ,10 ...}

B = {1, 3, 5, 7 ,9 ...}

C = {,2 ,3 ,4 ,5 ...}

D = { 8, 9 ,10 ,11 ...}

AnD = {8, 10}

Answer:

b=20 yards

Step-by-step explanation:

15^2+x^2=25^2

225+x^2=625

x^2=400

x=20

Answer:

x=20

Step-by-step explanation:

Answer:

Step-by-step explanation:

The matched statement to its corresponding reason for the given alternate interior angles as:

Given: Let points A, B, and C form a triangle.

definition: Let stackrel(harr)(DE) be a line passing through B, parallel to "bar(AC)", with angles labeled as shown.

Congruent angles: m∠1=m∠4, m∠3 = m∠5

Linear pair theorem: m∠4+m∠2+m∠5 = 180°

As per the shown figure,

Given:

Let points A, B, and C form a triangle.

Defining a parallel line and labeling angles:

Let stackrel(harr)(DE) be a line passing through B, parallel to "bar(AC)", with angles labeled as shown.

Alternate Interior Angles Theorem:

∠1=∠4

∠3 = ∠5

Congruent angles have equal measures:

m∠1=m∠4

m∠3 = m∠5

Definition of a straight angle and angle addition:

m∠4+m∠2+m∠5 = 180°

Substitution:

m∠1 + m∠2 +m ∠3 = 180°

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Solution :

Transforming given equations :

[tex]1)\ P = 600( 1 + \dfrac{12}{100})^t\\\\2)\ P = 1000( 1 + \dfrac{3}{100})^t\\\\3)\ P = 200( 1 + \dfrac{8}{100})^t\\\\4)\ P = 900( 1 - \dfrac{10}{100})^t[/tex]

From above equations we can see that equation 1) has largest percentage growth rate and the percent growth rate is 12% .

Hence, this is the required solution.

Answer: (i), 12%

Step-by-step explanation:

Given

The Population of four towns is given

(i) [tex]P=600(1.12)^t[/tex] i.e.

[tex]\Rightarrow P=600(1+0.12)^t\\\Rightarrow P=600(1+12\%)^t[/tex]

rate=12%

(ii) [tex]P=1000(1.03)^t[/tex]

[tex]\Rightarrow P=1000(1+0.03)^t\\\Rightarrow P=1000(1+3\%)^t[/tex]

rate=3%

(iii) [tex]P=200(1.08)^t[/tex]

[tex]\Rightarrow P=300(1+0.08)^t\\\Rightarrow P=300(1+8\%)^t[/tex]

rate=8%

(iv) [tex]P=900(0.90)^t[/tex]

[tex]\Rightarrow P=900(1-0.10)^t\\\Rightarrow P=900(1-10\%)^t[/tex]

rate=10% fall

So, the largest growth rate is for town (i)  i.e. 12%

Answer:

-11/2 = x

Step-by-step explanation:

5-2(3-x)=4x+10

Distribute

5 - 6 +2x = 4x+10

Combine like terms

-1 +2x = 4x+10

Subtract 2x from each side

-1 +2x-2x= 4x-2x+10

-1 = 2x+10

Subtract 10 from each side

-1-10 = 2x+10-10

-11 = 2x

Divide by 2

-11/2 = 2x/2

-11/2 = x

Answer:

See below

Step-by-step explanation:

5 - 2 * (3 - x) = 4x + 10

5 - 6 + 2x = 4x + 10

-2x = 11

x = -5.5

Answer:

Step-by-step explanation:

All three have blue eyes.

P(1 has blue eyes) = 16/100 = 4/25

P(3 have blue eyes) = 4/25 * 4/25 * 4/25

P(3 have blue eyes ) = 64/15625

If you need the decimal answer, it is .004096

No one has blue eyes out of three

The probability for this is very large.

P(no blues) = 1 - 64/15625

P(no blues) = 15561/15625  

If you need the decimal answer, it is 0.996

One has blue eyes (the other two do not).

P(1 has blue eyes) = 16/100 * 84/100*84/100

P(1 has blue eyes) = 112896/1000000

P(1 has blue eyes) = 0.112896

Answer:

PT = 12 units

Step-by-step explanation:

Given that,

PT=3x+3 and TQ=6x-6

T is the midpoint of PQ.

If T is mindpoint of PQ, it means,

PT = TQ

Substitute all the values,

3x+3 = 6x-6

Taking like terms together,

3x-6x = -6-3

-3x = -9

x = 3

So,

PT = 3x+3

= 3(3) + 3

= 9+3

= 12

So, the value of PT is equal to 12 units.

Answer:

The area of a given rectangle is 216 square inches.

Given that, the perimeter of the rectangle is 84 inches.

We need to find the area of a rectangle.

The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).

Let the width of a rectangle be x.

Given, that the length of a rectangle is six times its width. So, length=6x.

Now, 84=2(6x+x)

⇒14x=84

⇒x=6 inches

Then, length=6x=36 inches.

Area of a rectangle= Length×width=36×6=216 square inches

Therefore, the area of a given rectangle is 216 square inches.

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Answer:

A

Step-by-step explanation:

Did the quiz

Answer:

5.291 * 10^4

hhhhhhhhhhhhhhhhh

Answer:

The answer is B!!!!!!!!!!!!

Answer:

B. g(x)=x²-3 b is my answer

Answer:

3, 6, 12, 15

Step-by-step explanation:

3/12= 4

3/9= 3

I’m just gonna guess but I think 6

Answer:

For every 100-kilogram increase in mass, the fuel efficiency of car decreases by about 1.1 miles per gallon.

Step-by-step explanation:

Fuel efficiency after x kg in mass:

y = 43.28 -0.011x

Thus, the slope is of -0.011 per x kg.

Increase of 100:

When x = 100, as the slope is negative, the efficiency will decay by:

-0.011*100 = -1.1

Decay of 1.1 miles per gallon, so the answer is:

For every 100-kilogram increase in mass, the fuel efficiency of car decreases by about 1.1 miles per gallon.

Answer:

she is correct because there is not common factor of 3 and 8 so it cannot be factored

Step-by-step explanation:

Answer:

x=-3

Step-by-step explanation:

because f(x) is "y" now because y is 6 if you look properly where the coordinate of y is 6 x is -3

Answer:

a. For Asset 1, we have:

Total cost = $5,864

Total depreciation = $5,264

Annual depreciation = $877.33

b. For Asset 2, we have:

Total cost = $17,210

Total depreciation = $15,310

Annual depreciation = $3,827.50

Step-by-step explanation:

Note: The data in this question are merged together. They are therefore sorted before answering the question. See the attached pdf for the complete question with the sorted data.

Also note: See the attached excel file for the presentation of the data in the question with the answers (in bold red color).

The explanation of the answers is now given as follow:

Straight line method is a method of calculating depreciation and amortization of an asset by dividing the difference between the total cost and salvage value of an asset by its estimated useful life.

Therefore, wee have:

a. For Asset 1, we have:

Total cost = Cost + Shipping Charges + Setup Charge = $5,600 + $210 + $54 = $5,864

Total depreciation = Total cost - Salvage Value = $5,864.00 = $600 = $5,264

Annual depreciation = Total depreciation / Estimated Useful Life = $5,264 / 6 = $877.33

b. For Asset 2, we have:

Total cost = Cost + Shipping Charges + Setup Charge = $16,900 + $310 + $0 = $17,210

Total depreciation = Total cost - Salvage Value = $17,210 - $1,900 = $15,310

Annual depreciation = Total depreciation / Estimated Useful Life = $15,310 / 4 = $3,827.50