Which statements are true regarding the expression below? Check all that apply. 8^-1×8^-3×8
○the last factor,8, with no exponent shown is equivalent to 8^0
○the sum of the exponents is -3
○ the value of the expression is -512
○the value of the expression is 1/512
○an equivalent expression is 8^7×8^-10
○ an equivalent expression is 8^-2×8^-2 ​

Answer:

42, 12)

Step-by-step explanation:

Let the present ages of the father and son be x years and y years respectively.

According to the question,

Condition I,

Three years ago the sum of the ages of the father and his son was 48 years.

or,(x−3)+(y−3)=48

or,x−3+y−3=48

or,x−6=48−y

or,x=54−y - (i)

Condition II,

Three years hence the father's age will be three times the son's age,

or,(x+3)=3(y+3)

or,x+3=3y+9 - (ii)

Put value of x from equation (i) in equation (ii), we get,

or,(54−y)+3=3y+9

or,54−y=3y+9−3

or,54−6=3y+y

or,48=4y

or,y=484

∴y=12

Put the value of y in equation (i), we get,

or,x=54−12

∴x=42

So, (x,y) = (42, 12)

Therefore, the required present ages of the father and the son are 42 years and 12 years respectively.

Answer:

a^2-b^2=(a + b) (a - b) is the formula

The Absolute Difference and the Relative Difference is  mathematically given as

Absolute Difference = $40;

Relative Difference = 19%. Option B

This is further explained below.

Generally, Divide the difference in values by the value that was used initially, and you will get the relative difference between the two values: difference original value

Perform the conversion to get a percentage out of this amount. If there was a rise in value, we would say there was an increase of x %.

We state there was an x % decline in the value if there was a decrease in the value. x represents the number that was arrived at by us.

In conclusion, since we are comparing A from be we have

Absolute Difference = 250-210

Absolute Difference = $40;

and

Relative Difference =  (Original-ref)/ref

Therefore

Relative Difference 250-210/210

Relative Difference=19%

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The domain and range of the function C(m) the equation for is  mathematically given as

Dc=[0,\infty)

This is further explained below.

Generally, The domain and the range of a function are as follows: The values that are assumed by an input are referred to as a function's domain, while the numbers that are assumed by the outputs are referred to as the function's range.

In this question:

C(m)=0.05m+20

The input, denoted by the letter m, is the number of phone calls, and this value might be anything between 0 to an unlimited amount. So

The domain is Dc=[0,\infty)

The value of C(0) is equal to 20 when the input m is set to 0. As m grows, so does C (m). What this indicates is that:

The range is: Rc=[20,\infty)

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CQ

Haley pays a monthly fee of $20 for her cell phone and then pays 5 cents per minute used. The total cost of Haley’s monthly cell phone bill can be expressed by the function C(m) = 0.05m + 20, where m is the number of minutes used. What are the domain and range of the function C(m)?

Based on the corresponding angles theorem, since lines m and n are parallel lines, the value of x = -3.

The corresponding angles that are formed when two parallel lines are intersected by a transversal are congruent, according to the corresponding angles theorem.

Given that lines m and n are parallel lines that are intersected by transversal t, therefore:

2x + 9 = 7x + 24

Solve for x

2x + 9 - 9 = 7x + 24 - 9 [subtraction property of equality]

2x = 7x + 15

2x - 7x = 7x + 15 - 7x [subtraction property of equality]

-5x = 15

-5x/-5 = 15/-5 [division property of equality]

x = -3

Therefore, based on the corresponding angles theorem, since lines m and n are parallel lines, the value of x = -3.

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Answer:

Interest = Rs. 1297.26

Step-by-step explanation:

To calculate the final amount, we can use the following formula:

[tex]\boxed{A = P(1 + \frac{r}{100})^n}[/tex],

where:

A = final amount

P = principal (initial) amount

r = rate

n = time in years,

and then we can subtract the initial amount from the final amount to find the interest.

We have been told in the question that the principal, P = Rs. 10,000; and the time is [tex]2\frac{1}{2}[/tex] years, therefore n = 2.5. The rate is 5%, therefore r = 5.

Using this information, and the formula above, we can calculate the final amount:

[tex]A = 10000(1 + \frac{5}{100})^{2.5}[/tex]

⇒ [tex]A = 10000(1.05)^{2.5}[/tex]

⇒ [tex]A = \bf 11297.26[/tex]

Now that we know what the final amount was, we can calculate the interest by subtracting the initial amount from it:

Interest = 11297.26 - 10000

             = 1297.26

Therefore the interest was Rs. 1297.26.

Answer:

Option 1

Step-by-step explanation:

Perpendicular lines form right angles

Parallel lines never intersect.

Answer:

option A

Step-by-step explanation:

Answer:

a= [tex]\frac{g-f}{n}[/tex]

Step-by-step explanation:

First, start off by subtracting f from both sides. This gives you "g - f" and you are left with "an." Now, to isolate the variable, we must divide "n" from both sides and you will get "a= g - f/n," which is the final answer.

Hope this helps! :D

Answer:

A) E

B) Shape A and E

(i think)

If the model is 3/5th of original plane then the length of the original plane is 41.6 feet.

It is given in the question that the model of an aircraft is 3/5th the length of the original plane.

So, Let the length of the original plane be x feet.

According to the question

3/5th of x is 24.96

[tex]x\times\frac{3}{5} =24.96[/tex]

Multiplying both sides by 5

3x=24.96*5

3x=124.8

Dividing both sides by 3

x=124.8/3

x=41.6

Hence , the value of x is 41.6 feet.

Therefore , if the model is 3/5th of original plane then the length of the original plane is 41.6 feet.

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Answer:

4

Step-by-step explanation:

56/4=14

72/4=18

100/4=25

4 has to be the biggest common factor.

The slope of the line is zero.

The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope or gradient. In the coordinate plane, it represents the slope of the line.

From the given figure we can see that the line is parallel to the x-axis.

Any line parallel to the x-axis is given by the general equation y = a .

This equation can also be written as:

y = 0 x + a.

Comparing the above equation with the general equation of a straight line  y = mx + c

we see m = 0 and c = a (a is a constant)

Hence the slope of the line is 0.

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Answer:

L: (4,0) and L': (2,0)

Step-by-step explanation:

Answer:

Step-by-step explanation:

I messed up on P'

I drew it as -3,3 but it should be -3,2

Which is what i wrote it as

Answer:

(- 2, 3 )

Step-by-step explanation:

6x + 2y = - 6 → (1)

3x - 4y = - 18 → (2)

multiplying (1) by 2 and adding to (2) will eliminate y

12x + 4y = - 12 → (3)

add (2) and (3( term by term to eliminate y

15x + 0 = - 30

15x = - 30 ( divide both sides by 15 )

x = - 2

substitute x = - 2 into either of the 2 equations and solve for y

substituting into (1)

6(- 2) + 2y = - 6

- 12 + 2y = - 6 ( add 12 to both sides )

2y = 6 ( divide both sides by 2 )

y = 3

solution is (- 2, 3 )

Answer:

(-2, 3)

Step-by-step explanation:

Answer:

26 i believe 66 - 40 = 26 hope this helps

Answer:

Hello,

Answer d

Step-by-step explanation:

Since x=y then 3v-1=2v+6 ==> v=7

Answer d

Answer:

z=3

Step-by-step explanation:

Answer:

Midpoint are 4,10

Step-by-step explanation:

x midpoint - 4

y midpoint - 10

midpoint formula (x1 + x2)/2 , (y1 + y2)/2

(2+8)/2, (7+13)/2

4,10

Full Explanation

[tex] M = (x_M, \; y_M) [/tex]

[tex] M = \left(\dfrac{x_1 + x_2}{2}, \; \dfrac{y_1 + y_2}{2}\right) [/tex]

[tex] M = \left(\dfrac{2 + 6}{2}, \; \dfrac{7 + 13}{2}\right)[/tex]

[tex] M = \left(\dfrac{8}{2}, \; \dfrac{20}{2}\right)[/tex]

[tex] M = (4, \; 10)[/tex]

The median of the data set given for the tips (in dollars) earned in the last hour by waiters in a Japanese restaurant is determined as: 28.

]The median of any given data set is the data value that lies at the center of the data set when ordered.

Given the data set, 30,17,47,47,26,17,36,31,21,17, order the data set from the least to the greatest:

17, 17, 17, 21, 26, 30, 31, 36, 47, 47

The center or middle of the data set is 28.

Thus, the median of the data set given for the tips (in dollars) earned in the last hour by waiters in a Japanese restaurant is determined as: 28.

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Answer: 124 degrees ==> Option 3

Step-by-step explanation:

ABC=ABX+XBC

ABX=XBC     ==> bisected angles are equal since when an angle is bisected, it is divided into two equal angles. Hence:

ABC=XBC*2

ABC=62*2

ABC=124 degrees ==> Option 3

Answer:

[tex]\sf x = -1 + \sqrt{5}\:i,\: -1 - \sqrt{5}\:i[/tex]

Explanation:

[tex]\sf \rightarrow x^2 + 2x +6 = 0[/tex]

[tex]\sf use\:quadratic\:formula: x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \quad when \: \: ax^2 + bx + c = 0[/tex]

comparing identify:

Substitute inside the formula:

[tex]\rightarrow \sf x = \dfrac{ -2 \pm \sqrt{2^2 - 4(1)(6)}}{2(1)}[/tex]

evaluate:

[tex]\rightarrow \sf x = \dfrac{ -2 \pm \sqrt{4 - 24}}{2}[/tex]

[tex]\rightarrow \sf x = \dfrac{ -2 \pm \sqrt{- 20}}{2}[/tex]

[tex]\rightarrow \sf x = \dfrac{ -2 \pm 2\sqrt{5}\:i}{2}[/tex]

[tex]\rightarrow \sf x =-1 \pm \sqrt{5}\:i[/tex]

[tex]\rightarrow \sf x = -1 + \sqrt{5}\:i,\: -1 - \sqrt{5}\:i[/tex]

It should be noted that y=x+8 is not an inverse variation.

The relationships between variables that are expressed in the form of y = k/x, where x and y are two variables and k is a constant number, are known as inverse variations. According to this statement, if the value of one item rises, the value of the other quantity falls.

Ab example is when a constant of variation is k = xy = 5(2) = 10 if y changes inversely as x and x = 5 when y = 2. Consequently, xy = 10 is the equation that describes this inverse variation.

Therefore, it should be noted that y=x+8 is not an inverse variation.

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[tex]9.6\times 10^9~~ = ~~(2\times 10^5)(4.8\times 10^n)\implies \cfrac{9.6\times 10^9}{2\times 10^5}~~ = ~~4.8\times 10^n \\\\\\ \cfrac{9.6}{2}\times \cfrac{10^9}{10^5}~~ = ~~4.8\times 10^n\implies 4.8\times 10^{9-5}~~ = ~~4.8\times 10^n \\\\\\ 4.8\times 10^4~~ = ~~4.8\times 10^n\implies \cfrac{4.8\times 10^4}{4.8}=10^n\implies \cfrac{4.8}{4.8}\times 10^4=10^n \\\\\\ 1\times 10^4=10^n\implies 10^4=10^n\implies 4 = n[/tex]

Answer:

y=5.6

Step-by-step explanation:

1 + 2y = 11.08 +0.2y

Move the values w/ y all to one side and the ones without to the other side

1+ 2y = 11.08 + 0.2y

-0.2y             - 0.2y

-1        -1

1.8y=10.08

Divide by 1.8

y=5.6

Exponent rules are those laws that are applied to exponent-based expressions to make them simpler. The principles of exponents make it simple and rapid to execute numerous arithmetic operations like addition, subtraction, multiplication, and division. These guidelines are also useful for reducing the complexity of numbers that have complex powers incorporating fractions, decimals, and roots.

Exponent rules, commonly referred to as the "laws of exponents" or "properties of exponents," facilitate the task of simplifying exponent-based statements. These guidelines are useful for reducing the complexity of expressions whose exponents are decimals, fractions, irrational numbers, or negative integers.

When an exponent is a negative number, we apply the negative law of exponents. This rule states, "The reciprocal should be taken to convert any negative exponent into a positive exponent." The change in sign of the exponent values moves the expression from the numerator to the denominator.

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The number line that represents the solution set for the inequality 3(8 – 4x) < 6(x – 5) will be D. A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.

It should be noted that a number line is used to illustrate the intervals between the numbers given.

Therefore, the number line that represents the solution set for the inequality 3(8 – 4x) < 6(x – 5) will be a number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right

In conclusion, the correct option is D.

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The experimental research has two key advantages over correlational studies.

1. The possibility of random assignment

2. Causal connections can be assumed.

Correlational studies merely examine the data that already exists, whereas experimental studies give the researcher the opportunity to influence the study's factors. Researchers can make inferences about how changes in one variable affect changes in another through the use of experimental investigations.

The factors in a correlation study are out of the control of the researcher or research team. The researcher merely measures the information she discovers in the outside world. She can then determine whether changes in one are related to changes in the other, or if the two variables are correlated. In such a study, experimenters gather existing data and use statistical methods to examine it, such as economic statistics from governments. The findings of correlation studies can lead to hypotheses that can be verified through a more focused experimental one.

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