Solve: 5^3 a 125 b 25 c 15 d 5

Answer:

33, 35, 37

Step-by-step explanation:

Consecutive: in a row

Odd: any number not evenly divisible by 2

Integers: Whole numbers

Sum: the answer to an addition problem

So, 100 is close to 30*3, so start there and move on. It has to be a little more, so start at 31, 33, and 35, but it's only 99, so you need something a little more. Check 33, 35, and 37 to be sure, and you've got your answer!

Answer:  see proof below

Step-by-step explanation:

Use the following Power Reducing Identities:

[tex]\cos^2 A = \dfrac{1}{2}(1 + \cos 2A)\\\\\sin^2 A = \dfrac{1}{2}(1 - \cos 2A)[/tex]

Use the following Product to Sum Identity:

[tex]\cos A\cdot \cos B=\dfrac{1}{2}\bigg[\cos(A+B)+\cos(A-B)\bigg][/tex]

Proof LHS → RHS

[tex]\text{LHS:}\qquad \qquad \qquad \cos^2\beta\cdot \sin^4\beta\\.\qquad \qquad \qquad =\cos^2\beta\cdot \sin^2\beta\cdot \sin^2 \beta[/tex]

[tex]\text{Power Reducing:}\qquad \dfrac{1}{2}\bigg(1+\cos 2\beta\bigg)\dfrac{1}{2}\bigg(1-\cos 2\beta\bigg)\dfrac{1}{2}\bigg(1-\cos 2\beta\bigg)\\\\\\.\qquad \qquad \qquad \quad =\dfrac{1}{8}(1+\cos 2\beta)(1-\cos 2\beta)(1-\cos 2\beta)[/tex]

[tex]\text{Expand:}\qquad \qquad \dfrac{1}{8}\bigg(1-\cos 2\beta-\cos^2 2\beta+\cos^3 2\beta\bigg)\\\\.\qquad \qquad \qquad =\dfrac{1}{8}\bigg(1-\cos 2\beta-\cos^2 2\beta+\cos^2 2\beta \cdot \cos \2\beta\bigg)[/tex]

[tex]\text{Power Reducing:}\qquad \dfrac{1}{8}\bigg(1-\cos 2\beta -\dfrac{1}{2}(1+\cos 4\beta)+\dfrac{1}{2}(1+\cos 4\beta)\cos 2\beta\bigg)\\\\.\qquad \qquad \qquad =\dfrac{1}{16}\bigg(2-2\cos 2\beta -1-\cos 4\beta +\cos 2\beta +\cos 4\beta \cdot \cos 2\beta \bigg)\\\\.\qquad \qquad \qquad =\dfrac{1}{16}\bigg(1-\cos 2\beta -\cos 4\beta+\cos 4\beta \cdot \cos 2\beta \bigg)[/tex]

[tex]\text{Product to Sum:}\quad \dfrac{1}{16}\bigg(1-\cos 2\beta -\cos 4\beta +\dfrac{1}{2}[\cos(4\beta+2\beta)+\cos (4\beta-2\beta)]\bigg)\\\\.\qquad \qquad \qquad =\dfrac{1}{32}\bigg(2-2\cos 2\beta -2\cos 4\beta +\cos 6\beta +\cos 2\beta\bigg)\\\\.\qquad \qquad \qquad =\dfrac{1}{32}\bigg(\cos 6\beta-2\cos 4\beta -\cos 2\beta +2 \bigg)[/tex]

[tex]\text{LHS=RHS:}\\ \dfrac{1}{32}\bigg(\cos 6\beta-2\cos 4\beta -\cos 2\beta +2 \bigg)=\dfrac{1}{32}\bigg(\cos 6\beta-2\cos 4\beta -\cos 2\beta +2 \bigg)[/tex]

Answer:

56740.15908m³

Approximately to the nearest whole number, the volume of 46 acre-ft of reservoir = 56740m³

Step-by-step explanation:

1 meter = 3.28084ft

1 acre = 43,560 ft²

Therefore, using our unit conversion, the volume in S.I units of a reservoir containing 46 acre- ft of water is calculated as :

46 acre - ft × (1 meter/3.28084ft) × (43,560ft²/1 acre) × (1 meter/3.28084ft)²

= 2003760/35.314670112

= 56740.15908m³

Approximately to the nearest whole number, the volume of 46 acre-ft of reservoir = 56740m³

Answer:

Step-by-step explanation:

1. isolate the variable   subtract both sides by 8                   (12x+8-8<116-8)  

2. Divide both sides by twelve                                               (12x/12<116-8/12)                                            

3. Simplify                                                                                 (x<108/12)      

=12x+8−8<116−8

=12x<108

[tex] \frac{12x}{12} < \frac{108}{12} [/tex]

x<9

Answer:

The polynomial form of the expression is: 25·X² + 2·X + 2.

Step-by-step explanation:

The expression that can be formed using the provided data is:

[tex](3X)^{2}+(4X-3)+(-4X)^{2}-(2X-4)[/tex]

Simplify the expression to get a result in polynomial form as follows:

[tex](3X)^{2}+(4X-3)+(-4X)^{2}-(2X-4)[/tex]

[tex]=9X^{2}+4X-3+16X^{2}-2X+5\\\\=(9+16)X^{2}+(4-2)X+(5-3)\\\\=25X^{2}+2X+2[/tex]

Thus, the polynomial form of the expression is: 25·X² + 2·X + 2.

Answer:

the answer is -6

Step-by-step explanation:

if you have -5 and you take away another number, you end up with -6

Answer:

-6

Step-by-step explanation:

-5 - 1 ISNT -4

-5 + 1 IS -4

Answer:

No, it is not a magic square.

Step-by-step explanation:

A magic square is when whatever way you add it from, it is always the same answer (the magic sum). As you can clearly tell, it doesn't add up to the same number.

Answer:

C

Step-by-step explanation:

Given

- [tex]\frac{1}{4}[/tex] (12x + 8) ≤ - 2x + 11 ← distribute parenthesis on left side

- 3x - 2 ≤ - 2x + 11 ( add 3x to both sides )

- 2 ≤ x + 11 ( subtract 11 from both sides )

- 13 ≤ x , thus

x ≥ - 13

Since x can equal - 13 then a solid circle at - 13 represents the solution

Since x greater than - 13 then the arrow is facing to the right of - 13 on the number line.

Then the graph representing the solution is C

Answer: 95 units.

Step-by-step explanation:

The cost of making x units is:

C(x) = x^2 + 10*x + 45.

Now, if the cost is $10,020, then we can solve this for x as:

C(x) = 10,020 = x^2 + 10*x + 45

x^2 + 10*x + 45 - 10,020 = 0

x^2 + 10*x - 9,975 = 0

Now, remember that for a quadratic equation:

a*x^2 + b*x + c = 0

the solutions are:

[tex]x = \frac{-b +-\sqrt{b^2 - 4*a*c} }{2*a}[/tex]

In this case the solutions are:

x = [tex]x = \frac{-10 +-\sqrt{10^2 - 4*1*(-9,975)} }{2*1} = \frac{-10 +- 200}{2}[/tex]

Then we have two solutions, one for each sign:

x = (-10 -200)/2 = -110

x = (-10 + 200)/2 = 95

Here we must choose the positive option, as x represents a positive quaintity.

Then the number of units manufactured is 95.

Answer:

[tex]\frac{PQ}{DE}[/tex] = [tex]\frac{4}{6}[/tex]

Step-by-step explanation:

Given

Δ PQR ~ Δ DEF

Then the ratio of corresponding sides are equal

The corresponding letters in the names of the triangles gives the corresponding sides.

Thus PQ/DE, QR/EF, PQ/DF

In this case

[tex]\frac{PQ}{DE}[/tex] = [tex]\frac{4}{6}[/tex]

Answer:

Step-by-step explanation:

n + q = 20

.05n + .25q = 3.00

5n + 25q = 300

 n + q = 20

5n + 25q = 300

-5n - 5q = -100

20q = 200

q = 10 quarters

n + 10 = 20

n = 10 nickels

(10 nickels, 10 quarters)

Answer:

Step-by-step explanation:

2z = 4a/m +3

 -3        -3

2z - 3 = 4a/m

 ×m        ×m

(2z -3)m = 4a

     ÷4      ÷4

[(2z -3)m]/4 = a

a = (2mz - 3m)/4

Answer:

0.5625

Step-by-step explanation:

Answer:

10 times.

Step-by-step explanation:

Since 1 liter = 1000 milliliters, we can say that 600 milliliters is equal to 0.6 liters because 600/1000 = 0.6

Since the gas can holds 6 liters, and the lawn mower holds 0.6 liters, 6/0.6 = 10.

So, he can fill his lawn mower 10 times with the gas can

Mr Green can fill his lawn 10 times

the first step is to convert the milliliters to liters

600 milliliters to liters

= 600/1000

= 0.6 liters

the number of times can be calculated as follows

= 6/0.6

= 10

hence it will take Mr. Green  10 times to fill his lawn mower

please see the link below for more information

https://brainly.com/question/632986?referrer=searchResults

Answer: m²-mn

Explanation: multiply the letter outside the brackets by everything inside the brackets, so, m×m = m² and m×n = mn, altogether it is m²-mn.

Answer:

what is the value of q?

Step-by-step explanation:

Answer:

n = 8

Step-by-step explanation:

:)

S is the answer

Step-by-step explanation:

Let 3+4+8+9+13+14+18+___ 40 terms=S

Answer:

58 miles per hour

Step-by-step explanation:

leave a heart please :D

Answer:

3.14 is the simplified version (approximate) to π

Answer:

261

I hope this helps!

A constant is any numbers in an equation that don't have any variable connected to it.

-9x^3 and 12p are not constants since they are connected to variables.

6 is a constant because its not connected to any variable.

Best of Luck!

Answer:

36. 58.34

37. 530.66

Step-by-step explanation:

36. 2x3.14x8=7.28x8=58.34

so 36=58.34

37.

3.14x26/2=3.14x13x13=530.66

please brainly

Answer:

2.4 miles.

Step-by-step explanation:

10sec = 4 miles.......what abt.....

6 sec =  ??

cross multiply:

6sec × 4miles ÷ 10 sec= 2.4miles

Answer:

Any real number will have only one real cube root. Hence the technicalities associated with the principal root do not apply.

Step-by-step explanation:

Answer:

I think it's -1, 4. But i'm not a 100% sure.

Step-by-step explanation:

Answer:

To find the range, first order the data from least to greatest. Then subtract the smallest value from the largest value in the set.

Step-by-step explanation:

This is how you solve for Range; I can't view the image on my chromebook.

Answer:

a²+b²=126

Step-by-step explanation:

(a+b)²=a²+b²+2ab

(12)²=a²+b²+2×9

144=a²+b²+18

a²+b²=144-18=126