6(2x + 3) − 4(5x + 2)

Answer:

B

Step-by-step explanation:

The surface area (A) of a sphere is

A = 4πr² ← r is the radius which we require

Given A = 2500π, then

4πr² = 2500π ( divide both sides by 4π )

r² = 625 ( take the square root of both sides )

r = 25

The volume (V) of a sphere is

V = [tex]\frac{4}{3}[/tex]πr³, and

[tex]\frac{V}{\pi }[/tex] = [tex]\frac{4}{3}[/tex]r³ = [tex]\frac{4}{3}[/tex] × 25³ , thus

[tex]\frac{V}{\pi }[/tex] = [tex]\frac{4}{3}[/tex] × 15625 ≈ 20833.33.. → B

Answer:

10

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

17-7=10

Answer: 10

im not exactly sure what this question means but all you have to do is look at the number and u can see that is the answer. im not sure if your trying to do common sense or not but thats the answer?

Answer:

Square Root of 61

Step-by-step explanation:

Square root of 54

^u^

Answer:

Step-by-step explanation:

-5x - 3y= -7

+5x        +5x

-3y= 5x -7

------   ------

-3         -3

y=-5/3x + 7/3

Answer:

If it's 7 1/2 hours, then the answer is $11 dollars an hour.

Answer:

$11 dollars an hour.

Step-by-step explanation:

Answer:

-140 and -8.

Step-by-step explanation:

These are all of the steps to completely and correctly solve this question.

Hope this helps!!!

Kyle.

Answer:

-8 and -140

Step-by-step explanation:

Let the numbers be x and y.  Then xy = 1120, and x + y = -148.

Solving the first equation for y, we get 1120/x.

Substituting this into the second equation:  x + 1120/x = -148

Multiplying all terms by x removes x from the denominator(s):

x² + 1120 + 148x = 0.

Let's use the quadratic formula to find x.  Here a = 1, b = 148 and c = 1120.

Then the discriminant is b²-4ac, or, in this case, 148²-4(1)(1120) = 17424.  Because this discriminant is positive, we have two real, unequal roots.

They are:

       -148 ± √17424

x = ------------------------ = -8 and -140.

              2

Note that -8 and -140 add up to -148, so that's correct.

(-8)(-140) = 1120, so that also is correct.

Answer:

8861 : 9495

Step-by-step explanation:

Ratio of income in 2001 to 2003:

53,166 : 56,970

Then, you can simplify by dividing both sides by 6:

8,861 : 9,495

Can't simplify anymore, Therefore this is the answer!

8861 : 9495

Hope I helped! Have a good day :)

Answer:

[tex]\frac{8861}{9495}[/tex]

Step-by-step explanation:

Income of an individual in 2001 = [tex]\$ 53,166[/tex]

Income of an individual in 2003 = [tex]\$ 56,970[/tex]

Here, we need to find ratio of income in 2001 to the income in 2003 in simplest form .

i.e we need to convert [tex]\frac{\$53,166}{\$ 56,970}[/tex] in simplest form .

A fraction [tex]\frac{a}{b}[/tex] is said to be in simplest form if [tex]HCF(a,b)=1[/tex]

So, we will first find [tex]HCF(53166,56970)[/tex] then divide both numerator and denominator by the HCF .

Here,

[tex]53166=2\times 3\times 8861[/tex]

[tex]56970=2\times 3\times 3\times 3\times 5\times 211[/tex]

So, [tex]HCF(53166,56970)=2\times 3=6[/tex]

On dividing both numerator and denominator by 6 , we get

[tex]\frac{53166}{56970}=\frac{8861}{9495}[/tex]

Answer:

It's 24

Step-by-step explanation:

18 apps already installed

2/3 of 18 is 12

12+12=24

24 applications have been installed.

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

Given

18 apps already installed

2/3 of 18 = 12 are used

Additional 12 apps installed

Total = 12+12=24

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Answer:

k= 2/3 2 over 3.

or 0.60%

Step-by-step explanation:

Answer:

0.04 or 1/25

Step-by-step explanation:

Note that 25^3  = 15625.

Then 15625k = 625.

Solve for k using division:

k =  625 / 15625 = 0.04

Note that we could also do the problem in this manner:

25 = 5^2

625 = 5^4

Therefore, 5^4 * k = 5^2

Dividing both sides by 5^4, we get:

         5^2                                          1

k = ------------ = 5^(2-4) = 5^(-2) or ---------- = 1/25 = 0.04 (same as before)

          5^4                                        5^2

13-4=9 and 7-4=3

9+3=12

So the probability is 12/29

Answer:

the answer is B.  4/3 cubic ft.

Step-by-step explanation:

use the formula

V = LWH

using 1/3 for each calculation

length = 3 (1/3 ft)

width = 4 (1/3 ft)

height = 3 (1/3 ft)

then you substitute those dimension

V = (3/3 ft.) (4/3 ft.) (3/3 ft.)

V = (1 ft.) (4/3 ft.) (1 ft.)

V = 4/3 cubic ft

Solution: x ≥ -5

Domain Definition: The domain of a function is the set of input or argument values for which the function is real and defined

squareroot 2x + 10  ⇒  2x + 10 ≥ 0

Solve 2x + 10 ≥ 0:

Subtract 10 from both sides

2x + 10 - 10 ≥ 0 - 10

Simplify

2x ≥ -10

Divide both sides by 2

2x / 2  ≥  -10 / 2

Simplify

2x / 2

Divide the numbers: 2 / 2 = 1

= x

Note: x has the same value as 1

Divide the numbers: -10 / 2 = -5

= -5

The function domain is

x ≥ -5

Answer:

[tex]\boxed{\text{C. }x \geq -5}}[/tex]

Step-by-step explanation:

The domain is the set of all possible x-values that will make the function work.

The definition automatically eliminate options B and D.

Your function is

[tex]y = \sqrt{2x + 10}[/tex]

The number under the radical cannot be negative, because the square root of a negative number is imaginary.

Thus, we must have

[tex]\begin{array}{rcr}2x+ 10 & \geq & 0\\2x & \geq & -10\\x & \geq & -5\\\end{array}\\\\\text{The domain is }\boxed{\mathbf{x \geq -5}}[/tex]

The graph of your function shows that the range is x ≥ -5.

Answer:

D

Step-by-step explanation:

Note that 13 = 13[tex]x^{0}[/tex] since [tex]a^{0}[/tex] = 1

Then 13 is a monomial of degree 0 → D

Answer:

6.4

Step-by-step explanation:

5x = 32

Divide both sides by 5.

5x/5 = 32/5

x = 6.4

Divide by 5 on both sides.

5x divided by 5 leaves x alone.

32 divided by 5 is 6.4.

6.4 • 5 = 32

X = 6.4

Hope this helps!

Answer:

C.Use the distance formula to prove that all corresponding sides of the triangles have same lengths.Therefore, the two triangles are congruent by SSS.Then , corresponding angles of the triangles are congruent by CPCTC.

Step-by-step explanation:

We have to explain one way through which we can verify that the corresponding angles of the two triangles are congruent.

A. Use the slope formula to prove that the slopes of corresponding sides are opposite reciprocals . Therefore, the corresponding angles of the triangles are congruent.

In this option we are given that by slopes formula the slopes of corresponding sides are opposite reciprocals .It means sides are perpendicular but not give any information about congruency of two triangles through which we can say corresponding angles of two triangles are congruent.Hence, it is false.

B.Use the distance formula to prove that two corresponding sides of the triangles have same lengths. Therefore, corresponding angles of the triangles are congruent by CPCTC.

In this option we are given information about only two corresponding sides of two triangles . It is not sufficient to prove that corresponding angles of two triangles are congruent.Hence, it is false.

C.Use the distance formula to prove that all corresponding sides of the triangles have same lengths.Therefore,the two triangles are congruent by SSS. Then, corresponding angles of the triangles are congruent by CPCTC.

In this option we have complete information through which we can verify that corresponding angles of two triangles are congruent.Hence, it is correct.

D.Use the distance formula to prove that two corresponding sides of the triangles have same lengths.Therefore, the two triangles are congruent by SAS.Then, all corresponding angles of the triangles are congruent.

In this option we have no complete information through which we can two triangles are congruent by SAS. Therefore, In this option  explaination are not given properly.Hence , it is false.

Answer:

The answer to this is -5

Step-by-step explanation:

To do this, just do -125 to the 1/3 power. This is because you need to do the reverse of the order of operations.

Answer:

She did not buy enough border. She needs 34 ft not 30.

Step-by-step explanation:

Find the perimeter of her room in feet:

12 inches in a foot

96/12=8

3 feet in a yard

3(3)=9

8 ft + 8 ft + 9 ft + 9 ft = 34 ft

She bought 30 ft of border, which is not enough because she needs 34 ft

The given border of 30 feet is not enough.

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter.

Given:

Two walls are each 96 inches long, and two walls are each 3 yards long.

She pays $30 for border that costs $1 per foot.

First step is to convert inches to feet

1 inch = 1/12 feet

96 / 12 = 8 feet

and,  1 yard = 3 feet

3 x 3 = 9 feet

Now, the perimeter of the room

= 9 + 9 + 8 + 8

= 34 inches

The  feet of border bought

= $30 / $1

= 30

So, 34 > 30 thus the border is not enough

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Answer:

x is 38

Step-by-step explanation:

x=1.5

the full answer is in the photo

Answer:

[tex]10^{-p\left(t\right)}=t^{\left(0.5\right)}[/tex]

Step-by-step explanation:

Given equation is [tex]p\left(t\right)=-\log_{10}t^\left(0.5\right)[/tex]

Now question says to write that in exponential form.

So we can use the following conversion formula:

[tex]\log_ca=b\ \Rightarrow c^b=a[/tex]

[tex]p\left(t\right)=-\log_{10}t^\left(0.5\right)[/tex]

[tex]-p\left(t\right)=\log_{10}t^\left(0.5\right)[/tex]

[tex]\log_{10}t^\left(0.5\right)=-p\left(t\right)[/tex]

Apply conversion formula

[tex]p\left(t\right)=-\log_{10}t^\left(0.5\right)\ \Rightarrow 10^{-p\left(t\right)}=t^{\left(0.5\right)}[/tex]

[tex]10^{-p\left(t\right)}=t^{\left(0.5\right)}[/tex]

The required Paola needs to use 18 cups of water.

To determine the number of cups of water Paola needs to use, we need to know the ratio of water to iced tea mix. Typically, a common ratio for making iced tea is 1 tablespoon of iced tea mix per 1 cup of water.

A ratio is a comparison of two quantities or values, typically expressed in the form of a fraction or with a colon (:). It shows the relative sizes or amounts of two or more things in relation to each other.

Given that Paola uses 18 tablespoons of iced tea mix, she would need an equal amount of cups of water.

Therefore, Paola needs to use 18 cups of water.

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Answer:

A

Step-by-step explanation:

First, we know that angles 6 and 8 are supplementary.

Therefore m∠6 + m∠8 = 180°

123.5° + m∠8 = 180°

m∠8 = 56.5°

Then, using the alternating exterior angle theorem, we can find that...

m∠8 ≅ m∠1

So m∠1 = 56.5°

the answer to this question is A

Answer:

D

Step-by-step explanation:

(f+g)(x)   basically means to "ADD" f(x) and g(x).

We have

[tex]f(x)=\frac{x}{2}-3[/tex]

and

[tex]g(x)=3x^2+x-6[/tex]

Now we simply add these two, adding like terms as shown below (and simplify):

[tex](f+g)(x)=f(x)+g(x)\\=(\frac{x}{2}-3)+(3x^2+x-6)\\=3x^2+\frac{1}{2}x+x-3-6\\=3x^2+\frac{3}{2}x-9[/tex]

Correct answer is D

[tex]

n=14 \\

y=2\times n +3=2\times14+3 \\

y=24+3\Longrightarrow y=\boxed{27}

[/tex]

Check the picture below.

Answer: The difference between 82 and -40 is 122.

Step-by-step explanation:

To find out how much warmer 82 degrees is than -40 degrees, you add 40 to 82, which totals 122 degrees.

To determine how much warmer 82 degrees is compared to -40 degrees, we simply calculate the difference between the two temperatures. This is a simple calculation where we subtract the lower temperature from the higher temperature.

The calculation would be: 82 - (-40) = 82 + 40 = 122 degrees.

So, 82 degrees is 122 degrees warmer than -40 degrees. Note that this calculation assumes that the temperatures are measured on the same scale, which is typically Fahrenheit in the context of weather temperature changes in the United States.

Answer:

Answers May Vary

Step-by-step explanation:

Typically, Taratino's Car Garage will be the least expesive. The following equations for both auto shops:

Taratino's y=$30x

Cairo's y=$45+$24x

For x, that represents the total hours and y is total dollars

Answer:

the correct answer would be A

Step-by-step explanation:

100 is the independent variable and 240 is the dependent variable think about is like interest rate

Answer:

D

Step-by-step explanation:

sice the above mentioned congurency test is based on rhs axiom hence D is answer

Using the formula for compound interest, the total amount in the account after 10 years, with no further deposits and 3 percent interest compounded weekly, is approximately $1615.65.

This problem involves the concept of compound interest, specifically interest compounded weekly. To calculate the total amount in the account after 10 years, the formula for compound interest is used, which is A = P(1 + r/n)^(nt).

In this case, P, the principal amount, is $1200. The annual interest rate, r, is 3% or 0.03 when converted into decimal form. The number of times interest is compounded per year, n, is 52 weeks since interest is compounded weekly. Lastly, t stands for the number of years the money is invested or borrowed for, which is 10 in this instance. Plug these values into the formula to get the total amount after 10 years.

A = 1200(1 + 0.03/52)^(52*10) = $1615.65

So, if Hans makes no further deposits and the account earns 3 percent interest compounded weekly, the amount in the account after 10 years will be approximately $1615.65.

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Answer:

The answer is 80%.

Step-by-step explanation:

During a certain day, a worker made 81 parts.

He usually does 45 parts per day.

Number of extra parts made = [tex]81-45=36[/tex]

The percent by which he increased the number of parts he usually makes can be given as = [tex]\frac{36}{45}\times100[/tex] = 80%

Therefore, on that day, the percent increased by 80%.

Answer:

Increase by 80%

Step-by-step explanation:

45 : 100%

81 : y

[tex]\frac{81}{45} :\frac{y}{100}[/tex]

y × 45 = 81 × 100

45y = 8100

45y ÷ 45 = 8100 ÷ 45

y = 180

180% - 100% = 80%

Increase by 80%