Any number besides 0 to the zero power evaluates to 0. True or false?

The number of standard version download and high-quality download is 870 and 490 respectively.

let

x + y = 1360

2.9x + 4.1y = 4532

From (1)

x = 1360 - y

Substitute x = 1360 - y into (2)

2.9x + 4.1y = 4532

2.9(1360 - y) + 4.1y = 4532

3944 - 2.9y + 4.1y = 4532

- 2.9y + 4.1y = 4532 - 3944

1.2y = 588

y = 588/1.2

y = 490

Substitute y = 490 into (1)

x + y = 1360

x + 490 = 1360

x = 1360 - 490

x = 870

So therefore, number of standard version download and high-quality download is 870 and 490 respectively.

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Using a system of equations, it is found that she invested 318.71 into Fund B.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are given as follows:

The amount she invested in Fund A was 3 times as much as the amount she invested in Fund B, hence:

x = 3y.

Fund A returned a 6% profit and Fund B returned a 15% profit, and the total profit was of 1380, hence:

1.06x + 1.15y = 1380.

We have that x = 3y, hence:

1.06(3y) + 1.15y = 1380.

4.33y = 1380

y = 1380/4.33

y = 318.71.

She invested 318.71 into Fund B.

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Answer:

its 63 you got it right

Step-by-step explanation:

Answer:-2,2.5,-7/3

Step-by-step explanation:

Applying the segment addition postulate:

x = 2.75

AB = 6x = 6(2.75) = 16.5 units

BC = 8x + 1/4 = 8(2.75) + 1/4 = 22.25 units.

Based on the segment addition postulate, since B lies between points A and C on a line segment, then:

AB + BC = AC

AC = 38 3/4

AB = 6x

BC = 8x + 1/4

Substitute

6x + 8x + 1/4 = 38 3/4 [segment addition postulate]

14x + 1/4 = 155/4

14x = 155/4 - 1/4

14x = (155 - 1)/4

14x = 154/4

14x × 4 = 154

56x = 154

x = 154/56

x = 2.75

AB = 6x = 6(2.75) = 16.5 units

BC = 8x + 1/4 = 8(2.75) + 1/4 = 22.25 units.

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Answer:

y = -2x + 10

Step-by-step explanation:

Answer:

I think it's a (16cm) ....

Answer:

Parker's unit rate is 5 miles per hour or 5mph.

Step-by-step explanation:

1 hour = 60 minutes

60/20 = 3 minutes

3 minutes for 1 lap

1 lap = 1/4 mile

1/4 mile (1 lap) x 4 laps = 1 mile

4 laps =  12 minutes

12 minutes per mile

60/12 = 5

5 miles per hour

Based on the given parameters, the value of y in the figure is 13

The measures of the angles are given as:

Angle 1 = 8y

Angle 2 = 6y - 2

The angles are supplementary angles

So. we have

8y + 6y - 2 = 180

Evaluate the like terms

14y =182

Divide both sides by 14

y = 13

Hence, the value of y in the figure is 13

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The correct option regarding the operations with scientific notation is given as follows:

B) Because numbers written in scientific notation have exponents, you can use the Laws of Exponents to multiply or divide the numbers.

A number in scientific notation is given by:

[tex]a \times 10^b[/tex]

With the base being [tex]a \in [1, 10)[/tex].

An example of a multiplication in scientific notation is:

[tex]2 \times 10^3 \times 3 \times 10^5 = 6 \times 10^{3 + 5} = 6 \times 10^8[/tex]

That is, we multiply the factors, and for the bases of 10, we keep the bases and add the exponents. In a division, we would divide the factors, and for the base of 10, we keep the base and subtract the exponents.

That is, since the numbers have exponents, rules of exponents are used for both multiplication and division, and option b is correct.

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Answer:

Yes

Step-by-step explanation:

8÷10+7÷100=

8/10 + 7/100=

80/100 + 7/100=     ==> make the denominators equal to each other

(80+7)/100=

87/100=0.87 √

Answer:

yes it does

Step-by-step explanation:

8÷10=0.8

7÷100=0.07

0.8+0.07=0.87

or the easy way ig

8÷10+7÷100=0.87

Answer:

10 for each

Step-by-step explanation:

1.90 x 10 = 19

2.10 x 10 = 21

so 19 + 21 = 30

Answer:

Step-by-step explanation:

You want the cost and the number of months of membership such that the cost of both gyms is the same.

The total cost of x months of membership at each gym will be the sum of its initial fee and the product of the monthly fee and the number of months.

The cost at Community Gym is ...

  c = 60 + 65x

The cost at Workout Gym is ...

  w = 190 +55x

These costs will be the same when ...

  c = w

  60 +65x = 190 +55x

Subtracting 60+55x from both sides of the equation leaves ...

  10x = 130

  x = 13 . . . . . . divide by 10

The cost will be the same after 13 months.

That cost will be ...

  60 +65(13) = 60 +845 = 905

The amount paid at each gym after 13 months will be $905.

[tex]\omega[/tex] is a 2020th root of unity, so [tex]\omega^{2020}=1[/tex] and we have a kind of reflection identity of [tex]\omega^{2020-n} = \omega^{-n}[/tex] for [tex]n\in\Bbb Z[/tex].

Let's evaluate the product first. Denote it by [tex]P_k[/tex]. We split the product where the [tex]j=k[/tex] factor would belong, and pull out powers of [tex]\omega^k[/tex].

[tex]\displaystyle P_k = \prod_{j=1, j\neq k} (\omega^k - \omega^j) \\\\ ~~~~ = \prod_{a=1}^{k-1} (\omega^k - \omega^a) \prod_{b=k+1}^{2019} (\omega^k - \omega^b) \\\\ ~~~~ = (\omega^k)^{k-1} \prod_{a=1}^{k-1} (1-\omega^{a-k}) \cdot (\omega^k)^{2019-k} \prod_{b=k+1}^{2019} (1 - \omega^{b-k}) \\\\ ~~~~ = (\omega^k)^{2018} \prod_{a=1}^{k-1} (1 - \omega^{-a}) \prod_{b=1}^{2019-k} (1 - \omega^b) \\\\ ~~~~ = \omega^{-2k} \prod_{a=1}^{k-1} (1-\omega^{-a}) \prod_{b=1}^{2019-k} (1-\omega^b)[/tex]

Now introduce some factors to "complete" the [tex]b[/tex]-product and have it contain 2019 factors.

[tex]\displaystyle P_k = \omega^{-2k} \prod_{a=1}^{k-1} (1-\omega^{-a}) \frac{\displaystyle \prod_{b=1}^{2019} (1 - \omega^b)}{\displaystyle \prod_{b=2020-k}^{2019} (1 - \omega^b)}[/tex]

It's relatively straightforward to show that if [tex]\zeta[/tex] is an [tex]n[/tex]-th root of unity, then

[tex]\displaystyle \sum_{m=1}^{n-1} (1-\zeta^m) = n[/tex]

which gives

[tex]\displaystyle P_k = 2020 \omega^{-2k} \frac{\displaystyle \prod_{a=1}^{k-1} (1-\omega^{-a})}{\displaystyle \prod_{b=2020-k}^{2019} (1 - \omega^b)}[/tex]

Shifting the index in the denominator and again using the reflection property eliminates all but one factor.

[tex]\displaystyle P_k = 2020 \omega^{-2k} \frac{\displaystyle \prod_{a=1}^{k-1} (1-\omega^{-a})}{\displaystyle \prod_{b=1}^k (1 - \omega^{-b})} \\\\ ~~~~ = \frac{2020 \omega^{-2k}}{1 - \omega^{-k}}[/tex]

Now evaluate the sum. We can exploit symmetry. Split the sum at the 1010th term, so that

[tex]\displaystyle - \sum_{k=1}^{2019} P_k = -2020 \left(\sum_{k=1}^{1009} \frac{\omega^{-2k}}{1 - \omega^{-k}} + \frac{\omega^{-2020}}{1-\omega^{-1010}} + \sum_{k=1011}^{2019} \frac{\omega^{-2k}}{1-\omega^{-k}}\right)[/tex]

The middle terms reduces to 1/2. Shifting the index in the second sum, we can condense it to

[tex]\displaystyle -\sum_{k=1}^{2019} P_k = -2020 \left(\frac12 + \sum_{k=1}^{1009} \left(\frac{\omega^{-2k}}{1-\omega^{-k}} + \frac{\omega^k}{1-\omega^k}\right)\right)[/tex]

Join the fractions.

[tex]\displaystyle \frac{\omega^{-2k}}{1-\omega^{-k}} + \frac{\omega^k}{1-\omega^k} = 1 - \frac{2-\omega^{2k}-\omega^{-2k}}{2-\omega^k-\omega^{-k}} = -(1+\omega^k + \omega^{-k})[/tex]

The remaining sums are trivial.

[tex]-\displaystyle \sum_{k=1}^{2019} P_k = -2020 \left(\frac12 - 1009 - \frac{1-\omega^{1010}}{1-\omega} - \frac{1-(-\omega)^{1010}}{1+\omega}\right) \\\\ ~~~~ = 2020\cdot1009 - 1010 \\\\ ~~~~ = (2000+20)(1000+9) - 1000 - 10 \\\\ ~~~~ = 2\cdot1000^2 + 37\cdot1000 + 170[/tex]

Taking this last result mod 1000, we find the last 3 digits to be 170.

The  three equations with solution x=-5 Are as follows:

25 + x = 15 ............... equation 1.

7x = -35 .......................equation 2.

15 + x = 10 ..................equation 3

There is not more then one or two variables in a linear equation. In a linear equation, no variable is raised to a power larger than one or utilized as the denominator of a fraction. When you locate two values that satisfy a linear equation and display them on a coordinate grid, every one of the points falls on the same line.

A linear equation in one variable seems to be an equation that has just one solution and is stated in the form ax+b = 0, where a but instead b are two integers and x is a variable. 2x+3=8, for example, is a mathematical expression with a single variable.

x=-5 Given

This also can be written as :

25 + x = 15 ............... equation 1.

7x = -35 .......................equation 2.

15 + x = 10 ..................equation 3

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Answer:

Step-by-step explanation: C

Answer:

35.90%

Step-by-step explanation:

First, subtract the new no with that of 1990

318-234= 84

percentage of increase will be given by;

84/234×100= 35.8974%

Answer:

Q1 = 8

Hope this helps with your question :)

The line at the start of the "box" is Q1, the middle line in the "box" is the median also called Q2, and the last line of the "box" is Q3.

Cary's and Dan's present ages are 44 and 35 years respectively.

Let the Dan's present age be x years.

According to the given question.

Cary is 9 years older then Dan.

And, after seven years the sum of their ages will be 93.

So, from the given conditon we can say that

cary's age = 9 + x

And after seven years, sum of the ages of Cary and Dan

9 + x + 7 + x + 7 = 93

⇒ 23 + 2x = 93

⇒ 2x = 93 - 23

⇒ 2x = 70

⇒ x = 70/2

⇒ x = 35

⇒ Dan's present age is 35 years.

Therefore, Cary's age = 35 + 9 = 44 years.

Hence, Cary's and Dan's present ages are 44 and 35 years respectively.

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Answer

.9780

Step-by-step explanation:

Probability, not all 3 people are from Arizona

Arizona Equals 1-   2/91 =    89/91  = .9780

Probability is .9780

The slope of the side connecting (-4,1) and (-6,5) = -2

The slope of the side connecting (1,2) and (-1,6) = -2

The slope of the segment joining two points (x₁, y₁) and (x₂, y₂) = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

We have to find the slope of the side joining the points (x₁, y₁) = (-4,1) and (x₂, y₂) = (-6,5)

Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

          = [tex]\frac{5-1}{-6--4}[/tex]

          = 4/ -2

          = -2

We have to find the slope of the side joining the points (x₁, y₁) = (1, 2) and (x₂, y₂) = (-1,6)

Slope =  [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

          = [tex]\frac{6-2}{-1-1}[/tex]

          = 4/-2

          = -2

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If Ethan got his first job and is making $8.50 an hour. He really wants to buy a couple of video games, so he is trying to estimate how much his paycheck will be. The amount he can expect to bring home in his first paycheck is: $321.64.

Total hours=18 hours+25 hours

Total hours=43 hours

Income tax=Federal income tax+ State income tax

Income tax=10%+2%

Income tax=12%

Hence,
First paycheck:

First paycheck=$8.50×43 hours×(1-12%)

First paycheck=$8.50×43 hours×0.88

First paycheck=$321.64

Therefore if Ethan got his first job and is making $8.50 an hour. He really wants to buy a couple of video games, so he is trying to estimate how much his paycheck will be. The amount he can expect to bring home in his first paycheck is: $321.64.

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Answer:

y=3x+13

Step-by-step explanation:

Simply add the 3x to the other side.

Answer: y = 13 + 3x

Step-by-step explanation:

you just add 3x to both sides of the equation !! sorry if it doesn’t help but you basically put it the other way around and put 3x on both sides

The nonlinear- function which represents b(9)=4 is given by b(x)=72/x - 4 .

In mathematics and physics, a nonlinear system is one in which the change in the output is not proportional to the change in the input. Engineers, biologists, physicists, mathematicians, and many other scientists are interested in nonlinear problems since the majority of systems are inherently nonlinear.

Nonlinear function graphs don't resemble lines at all. It contains the formula f(x) = ax + b. Its equation can take any form, with the exception of f(x) = ax + b. The slope of the curve is the same between any two points. The point pairs on the graph do not all have equal slopes.

Of all the given options: the only equations which imply that b(9)=4  are :

i) b(x)=72/x - 4 and  (iv) b(x)=4

Of this two options only the first option is non-linear.

Hence the required option is  b(x)=72/x - 4 .

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The missing options are:

i)   b(x) = 72/x - 4

ii) b(x) = √x + 7

iii)b(x)  = 2x+1

iv) b(x) = 4

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Thomas bought 6 glass cups and 6 plastic cups

Thomas bought 12 glass and plastic cups from the store

Glass cups costs $3.25

Plastic cups cost $2.75

He spent a total of $36

Let g represent the number of glass cups and p represent the number of plastic cups

g + p= 12.........equation 1

3.25g + 2.75p= 36..........equation 2

From equation 1

g+p= 12

g= 12-p2

Substitute 12-p for g in equation 2

3.25(12-p)+2.75p = 36

39-3.25p+2.75p= 36

39-0.5p= 36

-0.5p= 36-39

-0.5p= -3

p= -3/-0.5

p= 6

Substitute 6 for p in equation 1

g + 6= 12

g= 12-6

g= 6

Hence there are 6 glass cups and 6 plastic cups

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Answer:

3x+5y=15

Step-by-step explanation:

3x+5y=15

5y=-3x-15

y=-3/5x-3

Because it has the same slope and a different y-intercept, it is parallel because the lines won't ever touch.

According to the solving the simplified value of the equation 1/(x^4)^-2 is

= x⁸.

PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction and is the main rule for simplifying expressions.

Simplification seems to be the process of substituting a mathematical expression with a simpler, usually shorter counterpart.

Designers employ simplification to make designs more memorable and instantly recognizable in logos, emblems, posters, computer icons, as well as other design applications.

Given :[tex]\frac{1}{\left(x^4\right)^{-2}}[/tex]

On simplifying we get:

Use  (aⁿ)ˣ  = aⁿˣ

so we get:

[tex]\frac{1}{X^{(4)(-2)}}[/tex]

=[tex]\frac{1}{x^{-8}}[/tex]

Use a⁻ⁿ = 1/aⁿ

Now:

= [tex]\frac{1}{\frac{1}{x^8}}\\=x^8[/tex]

According to the solving the simplified value of the equation 1/(x^4)^-2 is

= x⁸

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