Use properties of exponents to simplify the following expression.

Help!!!Math!! Please explain how you got your answer.

400%

Suppose sales in 1994 were 100 of some unit. Then in 1995, they were ...

... 100 - 80% × 100 = 100 × (1 - 0.80) = 100 × 0.20 = 20 . . . . units

Then the percent increase to sales of 100 units in 1996 can be found from ...

... percent change = ((new value) - (old value))/(old value) × 100%

... = (100 -20)/20 × 100%

... = 80/20 × 100%

... = 400%

The increase from 1995 to 1996 was 400%.

Answer:

36

Step-by-step explanation:

The length of 1 1/2 units is equivalent to 3/2 = 6/4 = 6×(1/4) = 6 cubes.

The width of 1/2 units is equivalent to 2/4 = 2×(1/4) = 2 cubes.

The height of 3/4 units is equivalent to 3×(1/4) = 3 cubes.

Then, in terms of cubes, the dimensions are 6 × 2 × 3. The volume is the product of these dimensions, so is ...

... 6 × 2 × 3 = 36 . . . . cubes

Answer:

Step-by-step explanation:

the answer is

1.  x=28

2. p=7

Answer:

21

Step-by-step explanation:

Simplify 5^2 to 25

25-2^2

Simplify 2^2 to 4

25-4

Answer

21

The value of the expression will be 21.

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The expression is given below.

⇒ 5²- 2²

Simplify the expression, then the value of the expression will be given as,

⇒ 5²- 2²

⇒ 25 - 4

⇒ 21

The value of the expression will be 21.

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Answer:

The answer is B. Step 2; 8x − 16 = 16 + 2x

Hope This Helps!

Answer:

Step-by-step explanation:

a) p(1) = 1³ -3·1² +2·1 -1 = 1 -3 +2 -1 = -1 . . . . not zero

b) Dividing p(x) by x-1 gives x² -2x +0 with a remainder of -1 (as found in part (a)). So the function can be written as ...

... p(x) = (x -1)(x² -2x +0) -1

_____

Polynomial division can be done using synthetic division or long division. The latter can be done by hand or by using any of several on-line calculators. Attached is output from one of them.

We know that :

✿  [tex]\mathsf{Cos\theta = \frac{Adjacent\;Side}{Hypotenuse}}[/tex]

✿  [tex]\mathsf{Sin\theta = \frac{Opposite\;Side}{Hypotenuse}}[/tex]

✿  [tex]\mathsf{Tan\theta = \frac{Opposite\;Side}{Adjacent\;Side}}[/tex]

From the Figure :

✿  [tex]\mathsf{Cosx = \frac{4}{5}}[/tex]

✿  [tex]\mathsf{Sinx = \frac{3}{5}}[/tex]

✿  [tex]\mathsf{Tanx = \frac{3}{4}}[/tex]

Only 1st Statement is True

1st Option is the Answer

Answer:

31.020

Step-by-step explanation:

Multiply the fraction by 4/4 to get the denominator to 1000. Simplify to a denominator of 100 if you like. Then use place value to write your number.

... 31 + 5/250 = 31 + 20/1000 . . . . thirty-one and twenty thousandths

... = 31 + 0.020 =  31.020 . . . or . . . 31.02

Let x represent the number of adults who swam at the pool. Then (262-x) is the number of children. Multiplying these numbers by the corresponding admission charge will give the associated receipts. We are given the total of receipts, so we can write the equation ...

... 2.00x +1.50(262-x) = 470.00

... 0.50x +393.00 = 470.00 . . . . . simplify

... 0.50x = 77.00 . . . . . . . . . . . . . . .subtract 393

... 77.00/0.50 = x = 154 . . . . . . . . . divide by the coefficient of x

... (262-x) = 108 . . . . . . . . . . . . . . . .find the number of children admitted

Answer:

Step-by-step explanation:

The question will look like (3b)/(a^-2)

To simplify, note the (a^-2). It is a negative, so flip the placement of the monomial. Note that the term is located in the decimal, so when it is flipped, it goes to the numerator (vice versa if it is opposite)

(3b)/(a^-2) = (3b)(a²)

3a²b, or (A) is your answer choice

~

Answer:

Option A) 3a2b

Step-by-step explanation:

Answer:

Number of girls in PE class is 20

D.  20 girls

Step-by-step explanation:

We are given

Number of girls in 6th grade =120

Number of boys in 6th grade =102

so, firstly we will find ratios of girls and boys

[tex]\frac{G}{B}=\frac{120}{102}[/tex]

now, we have

17 boys are in the first PE class

Let's assume number girls in PE class as 'x'

we know that

ratios of boys and girls must be equal

so, we get

[tex]\frac{G}{B}=\frac{120}{102}=\frac{x}{17}[/tex]

now, we can solve for x

[tex]\frac{120}{102}=\frac{x}{17}[/tex]

[tex]x=17\times \frac{120}{102}[/tex]

[tex]x=20[/tex]

So,

Number of girls in PE class is 20

2x + 10 can be simplified using the distributive property by factoring a 2 out of each term.

2(x + 5)

2(3x + 5) can be solved by applying the distributive property, by multiplying each term inside the parentheses by 2.

6x + 10

f(x) = 11.93·1.42^x

I entered the data into a graphing calculator and made use of its exponential regression function to find the coefficients of ...

... y = a·b^x

It told me ...

... a ≈ 11.9304, b ≈ 1.41885

In accordance with the problem statement, these values are rounded to hundredths to get the answer.

_____

Comment on the graph

The given points and two curves are show. The solid red curve is the exponential regression curve produced by the calculator. The dotted blue curve is the one you get when you round the numbers to the nearest hundredth.

Answer:

5400 mi²

Step-by-step explanation:

The area is half the absolute value of the sum of the determinants of the points taken pairwise in some consistent order around the polygon. For a triangle, this sum of determinants can also be written as the determinant of a 3×3 matrix of the coordinates with the third column being 1.

... Area = (1/2)|D|

where D = ...

[tex]\left|\begin{array}{ccc}0&-1&1\\-3&-9&1\\3&-2&1\end{array}\right|=\left|\begin{array}{cc}0&-1\\-3&-9\end{array}\right|+\left|\begin{array}{cc}-3&-9\\3&-2\end{array}\right|+\left|\begin{array}{cc}3&-2\\0&-1\end{array}\right|\\\\=-3+33-3=27[/tex]

Then the area is (in grid squares) ...

... Area = (1/2)|27| = 13.5 . . . . grid squares

Each grid square is (20 mi)² = 400 mi², so 13.5 grid squares is ...

... 13.5 × 400 mi² = 5400 mi²

Answer:

The difference is 18.7 degrees

Step-by-step explanation:

To find the difference in the temperature, we take the high temperature and subtract the low temperature.

Difference = high - low

                   = -3.6 - (-22.3)

                   = -3.6+22.3

                   = 18.7

The difference is 18.7 degrees

Answer:

3/√2

Step-by-step explanation:

find the details in the attachment (this is not the shortest way).

The shortest way is: to prove ED=AB, then to calculate x=AB/√2=3/√2.

Answer:

Step-by-step explanation:

∠1 is complementary to 15°, so is 90° -15° = 75°

∠2 completes the triangle with angles 49° and 75°, so is 180° -49° -75° = 56°

∠3 is supplementary to ∠2, so is 180° -56° = 124°

∠4 is complementary to 49°, so is 90° -49° = 41°

Answer:

-3367 1/9

Step-by-step explanation:

This is what calculators are for.

Perform the multiplication and division before the addition.

... = 10000/-9 -2256

... = -1111 1/9 -2256

... = -3367 1/9

_____

If you don't have a calculator, the Google and Bing search boxes can be relied upon to use the correct order of operations.

12 in

If the dilation is uniform, both height and width will be multiplied by 4.

New height = (1 in) × 4 = 4 in

New width = (3 in) × 4 = 12 in

34

KM is a transversal relative to parallel lines LM and KN. Thus ∠2 = ∠MKN ≅ ∠KML and ∠KML = ∠1. The two base angles of ΔKLM are equal, so that triangle is isosceles.

Then the ratios of all the sides are ...

... KL : LM : MN : KN = 8 : 8 : 8 : 9

The sum of these ratio units is 33, so each one stands for 132/33 = 4 perimeter length units. Then segment LM is 8×4 = 32 perimeter length units, and KN is 9×4 = 36 permeter length units.

The midsegment is the average of lengths LM and KN, so is ...

... (32 +36)/2 = 34 . . . . perimeter length units

The length of midsegment is 34 units.

Given data:

The trapezoid KLMN, Such that KL = MN.

And [tex]m\angle1 = m\angle2[/tex], LM/KN = 8/9

Also, perimeter of KLMN = 132 units.

To find:

The length of midsegment (KM).

In the given problem, we can observe that KM is a transversal relative to parallel lines LM and KN. Which means,

[tex]\angle MKN = \angle KML\\\angle 2=\angle 1\\[/tex]

Clearly, two base angles are equal. So, the triangles KLM and KMN are isosceles.

Taking the ratios of sides of two triangles as,

= KL : LM : MN : KN

= 8 : 8 : 8 : 9

The sum of ratio units is, 8 + 8 +8 +9 = 33. Then, the value of each ratio is,

[tex]= \dfrac{perimeter}{33} \\\\=\dfrac{132}{33} \\\\=4[/tex]

Then the length of segment LM is,

[tex]LM = 8 \times 4 = 32 \;\rm perimeter \;\rm length \;\rm units[/tex]

And, length of segment KN is,

[tex]KN = 9 \times 4 = 36 \;\rm perimeter \;\rm length \;\rm units[/tex]

Then, the length of midsegment KM is obtained by taking the average of LM and KN as,

[tex]KM = \dfrac{LM+KN}{2} \\\\KM = \dfrac{32+36}{2}\\KE = 34[/tex]

Thus, the length of midsegment is 34 units.

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Answer:

We are given:

[tex]SSx = 4[/tex]

[tex]SSy=25[/tex]

[tex]Sp=6[/tex]

We know that the Pearson's correlation coefficient is:

[tex]r=\frac{S_{p}}{\sqrt{SS_{x} \times SS_{y}} }[/tex]

     [tex]=\frac{6}{\sqrt{4 \times 25} }[/tex]

     [tex]=\frac{6}{\sqrt{100} }[/tex]

     [tex]=\frac{6}{10}[/tex]

Therefore, the option 6/10 is correct

Answer:

13

Step-by-step explanation:

65=5x(because number A is four times number B therefore, it is really B five times)

Then divide both sides by 5.

13=x

To find two numbers when their sum is 65 and one number is 4 times the other, the smaller number is 13, and the larger number is 52.

number, and 4x be the larger number.

Write an equation: x + 4x = 65.

Solve the equation: 5x = 65, x = 13.

The smaller number is 13, and the larger number is 4 times 13, which is 52.

f(x) = -(x -2)² +3

We can fill in the vertex (h, k) values immediately in the vertex form ...

... f(x) = a(x -h)² +k

To find the value of a, we solve the equation for a at some point other than the vertex. The given point is (0, -1), so we can use that:

... -1 = a(0 -2)² +3

... -4 = 4a . . . . . . . . . subtract 3, simplify

... -1 = a . . . . . . . . . . . divide by 4

Now, we know the function is ...

... f(x) = -(x -2)² +3

Answer:

Step-by-step explanation:

The simple answer is that logs cannot be negative and if you insert a 2 where the x is located you get a negative. Logs have to be >= 0

[text]log_5 (3x-10) = log_5 (-4)[tex]

It all has to do with logs being tied to exponents and exponents being tied to logs. Actually an inverse of an exponent is a log.

Answer:

0.471

Step-by-step explanation:

The mnemoic SOH CAH TOA reminds you that ...

... Sin = Opposite/Hypotenuse

... sin(S) = 32/68 ≈ 0.471

Answer:

Step-by-step explanation:

[tex](3m^2+2mn-n^2)+(m^2+4mn-n^2)\\\\=3m^2+2mn-n^2+m^2+4mn-n^2\qquad\text{combine like terms}\\\\=(3m^2+m^2)+(2mn+4mn)+(-n^2-n^2)\\\\=\boxed{4m^2+6mn-2n^2}[/tex]

Based on the available information, the expression (3m² + 2mn - n²) + (m² + 4mn - n²) is equivalent to 4m² + 6mn - 2n².

To simplify the expression (3m² + 2mn - n²) + (m² + 4mn - n²), we can combine like terms.

Like terms have the same variables and the same exponents.

Let's group the like terms together:

(3m² + m²) + (2mn + 4mn) + (-n²- n²)

Combining like terms within each group, we get:

4m² + 6mn - 2n²

Therefore, in this case, it is concluded that the expression (3m² + 2mn - n²) + (m² + 4mn - n²) is equivalent to 4m² + 6mn - 2n².

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Answer:

The solution for u is:

[tex]u = \frac{mpq}{q+p}[/tex]

Step-by-step explanation:

The first step to solve this problem is finding the least common multiplicator between p and q, that is pq, so:

[tex]\frac{u}{p} + \frac{u}{q} = m[/tex]

[tex]\frac{uq + up}{pq} = m[/tex]

[tex]uq + up = mpq[/tex]

[tex]u(q + p) = mpq[/tex]

[tex]u = \frac{mpq}{q+p}[/tex]

The required solution of the given equation for u is equal to

(m(p × q)) / (q + p).

Given that:

Equation: u/p + u/q = m, if p ≠ -q

To solve for u in the equation u/p + u/q = m, use the method of finding a common denominator and simplifying the expression.

First, need to find a common denominator for the fractions u/p and u/q. The common denominator in this case would be (p × q).

Multiplying the equation by (p × q) to get,

u(q) + u(p) = m(p × q)

Next, combine the terms with u as:

u × q + u × p = m(p × q)

Now, factor out u as:

u(q + p) = m(p × q)

To solve for u, divide both sides of the equation by (q + p):

u = (m(p × q)) / (q + p)

Therefore, the solution for u is u = (m(p × q)) / (q + p).

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Answer:

615

Step-by-step explanation:u make $20 a week and u worked 40 hours u jus do 40*20=$800

800-185=615 im pretty sure hope this helps

Answer:

Weekly net pay is $36790

Weekly gross pay is  $41600

Step-by-step explanation:

Net pay  is the gross pay minus taxes

Net pay = gross pay - taxes

Gross pay =  hours worked * hourly rate

Net pay = hours worked * hourly rate - taxes

We know the  

hours worked = 40

Hourly rate = 20

tax rate = 185 bi weekly  = 185/2 = 92.5 weekly

Net pay = 40 * 20 - 92.5

Net pay = 800-92.5

Net pay = 707.5

This is the weekly net pay

Assuming we work 52 weeks a year

Weekly net pay is 52* 707.5 = 36790

Weekly gross pay is  40*20 * 52 = 41600

Answer:

x ≈ 0, x ≈ 2.5

Step-by-step explanation:

The left point of intersection is very near the y-axis, where x=0.

The right point of intersection is somewhat below the midpoint between x=2 and x=4. It seems to be just about at the midpoint between that midpoint (x=3) and the line at x=2. We estimate the value at about x=2.5.

_____

If we knew the actual function definitions, we could solve for the points of intersection.