What is the rule when multiplying by 10's?​

Answer:

a = 10 and b = 6

Step-by-step explanation:

I am having a little trouble reading the numbers, but I think that I see

\(\frac{7^{2} 7^{8} }{7^{4} }\)

If we wrote this in expanded form, it would look like:

\(\frac{7x7x7x7x7x7x7x7x7x7}{7x7x7x7}\)  How many 7s are on the top?  10  That is the answer to a.  The product of powers principle tells us that if we are multiplying powers with the same bases we add the exponents 2 + 8 = 10

\(\frac{^{10} }{7^{4} }\)

Now it looks like

\(\frac{7x7x7x7x7x7x7x7x7x7}{7x7x7x7}\)  if we cross the 7's out in the top and the bottom, we are left with 6 7's on the top.  That is the answer to b.

The quotient of powers principle tells us that if we are dividing powers with the same bases, we can subtract the exponents (10 -4 = 6)

By using the division property of equality we can divide both sides by -12 to get the solution x = -4

An equation:

A = B

Says that the number A is equal to the number B, so basically, are the same number.

So, if we divide both A and B by the same number C, we will get:

A/C and B/C

And A and B are the same numbers, then A/C and B/C also are the same numbers.

So in an equation, we can divide both sides by the same number (except 0) and the equation will not change.

In this case we have:

-12*x = 48

We could divide both sides by -12, so we will get:

-12*x/-12 = 48/-12

x*(-12/-12) = -4

x = -4

And thus we used the division property of equality to solve the equation.

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4. RSTU is a trapezoid because the opposite sides RS and UT are parallel.

5. RSTU is not an isosceles trapezoid because the diagonals are not congruent.

In order to verify that RSTU is a trapezoid, we would have to determine slope of the pair of opposite sides and check whether at least one pair of opposite sides are parallel;

RU ║ ST

Slope of side RU = Slope of side ST

Slope of RU = (y₂ - y₁)/(x₂ - x₁)

Slope of RU = (1 + 3)/(5 + 3)

Slope of RU = 4/8

Slope of RU = 0.5.

Slope of RS = (y₂ - y₁)/(x₂ - x₁)

Slope of RS = (-9 + 3)/(-4 + 3)

Slope of RS = -6/-1

Slope of RS = 6.

Slope of ST = (y₂ - y₁)/(x₂ - x₁)

Slope of ST = (-2 - 1)/(10 - 5)

Slope of ST = -3/5

Slope of ST = -0.6.

Slope of UT = (y₂ - y₁)/(x₂ - x₁)

Slope of UT = (-2 + 9)/(10 + 4)

Slope of UT = 7/14

Slope of UT = 0.5.

Therefore, RSTU is a trapezoid because the opposite sides RS and UT are parallel.

Question 5.

In order to determine whether RSTU is an isosceles trapezoid, we would have to determine length of the diagonals by using the distance formula and check whether they are congruent;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance RT = √[(-2 + 3)² + (10 + 3)²]

Distance RT = √170 units.

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance US = √[(5 + 4)² + (1 + 9)²]

Distance US = √181 units.

Therefore, RSTU is not an isosceles trapezoid because the diagonals RT and US are not congruent.

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Answer:

C i-statistic,ii) statistics III) statistics iv) statistics v) statistics

Answer:

Step-by-step explanation:

Answer:

2 adults, 8 children.

Step-by-step explanation:

just add the prices together.

If Group 1 trees produce 25 percent more coconuts than Group 2, proportionately, Group 2 trees produce 120 coconuts.

Proportion refers to the two ratios equated to each other.

Proportion shows how much quantity or value is contained in another.

We depict proportions using fractional values, such as fractions, decimals, and percentages.

The number of coconuts produced by Group 1 trees = 150

The percentage by which Group 1 trees produce more than Group 2 = 25%

Let Group 1's production compared to Group 2's = 1.25 (100% + 25%)

Let Group 2's production = 100% = 150/125 x 100

= 120 coconuts

Thus, Group 2 trees would produce 120 coconuts compared to Group 1 trees that produced 150, which was proportionately, 25% more.

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The graph of y=|x| is a v-shaped graph that starts at the origin and continues infinitely in both the positive and negative x-directions. The graph of y=|x|+2 is the same v-shaped graph, but it has been shifted up two units so that it no longer intersects the x-axis. Finally, the graph of y=|x|-1 is a v-shaped graph that has been shifted down one unit so that it intersects the x-axis at (1,0) and (-1,0). All three graphs are symmetric with respect to the y-axis.

Answer:

-2,0 0,-8 , 2,0 hope that helps

Answer:

The approximate user base of the social media site 10 months from now would be approximately 52,374.

Step-by-step explanation:

To calculate the approximate user base of the social media site 10 months from now, considering a 4% increase per month, we can use the following steps:

1. Calculate the monthly growth factor: 1 + (4% / 100) = 1 + 0.04 = 1.04

2. Apply the growth factor to the current user base for each month:

  Month 1: 35,930 * 1.04 = 37,387.2 (approx.)

  Month 2: 37,387.2 * 1.04 = 38,868.49 (approx.)

  ...

  Month 10: Previous Month * 1.04

By repeating this calculation for each month, we can determine the approximate user base 10 months from now.

Month 1: 37,387.2

Month 2: 38,868.49

Month 3: 40,391.33

Month 4: 41,957.61

Month 5: 43,569.34

Month 6: 45,228.24

Month 7: 46,936.32

Month 8: 48,695.44

Month 9: 50,507.45

Month 10: 52,374.40 (approx.)

Therefore, the approximate user base of the social media site 10 months from now would be approximately 52,374.

Answer:

- 8

Step-by-step explanation:

Substitute the values for a and b into the expression

(- 3 - 2(- \(\frac{1}{2}\) ) )³

= (- 3 + 1)³

= (- 2)³

= (- 2) × (- 2) × (- 2)

= 4 × - 2

= - 8

Step-by-step explanation:

y = 2/5 x - 9/5

when x = -1,

the value of y = 2/5(-1) - 9/5

= -2/5 - 9/5 = -11/5

when x = 0

=> y = 2/5(0) -9/5

= 0-9/5 = -9/5

when x=1

=> y = 2/5(1) - 9/5

= 2/5 - 9/5 = 7/5

Answer:

Let you be "x"

and your sister be "y"

when you are 2 your sister is twice your

x=2 y=4

so your sister is 2 year older than you

now you're 40 so your sister would be

Step-by-step explanation:

When I was 2 my sister was twice my ag Now I'm 40 then my sister age is 80.

\

Two or more expressions with an Equal sign is called as Equation.

Given,

When I was 2 years my sister was twice of my age.

Let us consider the ages by using a equation like this

x/y------>X represents my age/ y represents my sister age

x/y ----->2/4=40/a

a is the age of sister when i was 40.

Now let us solve 2/4=40/a

One by two equal to forty by a.

Apply cross multiplication

2a=160

Divide both sides by 2

a=80

Hence, if I'm 40, my sister is 80 years old.

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Answer:

1.) inverse proportion : 1kx = y

2) direct proportion. y = kx

Answer:

This is \(\frac{7}{100}\) of your money.

Step-by-step explanation:

We have a decimal number, and we want the answer to be a fraction. To transform a decimal number into a fraction, we multiply both the numerator and the denominator by 10 until none of them have decimal parts. So

\(0.07\times \frac{10}{10} = \frac{0.7}{10}\times \frac{10}{10} = \frac{7}{100}\)

This is \(\frac{7}{100}\) of your money.

Answer:

Below

Step-by-step explanation:

The two angles labeled are alternate angles of a pair of parallel lines crossed by a transversal ( the diagonal) ....so they are equal

x+ 18 = 4x+15    Solve for x

3 = 3x   ====>    x = 1    

Now....x+18  angle and angle ABD are complementary....the add to 90 °

   so   x+18    + ABD   = 90°        x = 1 from above....so

            1 + 18 + ABD = 90

               19  + ABD = 90

                        ABD = 71 °

A- none because they are parallel lines

Answer:

its A

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let h(x) = y

The exponentail function is of the form :

\(y = ab^x\)

We have :

\(y_{_1} = ab^{x_{_1}}\\y_{_2} = ab^{x_{_2}}\\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{ab^{x_{1}}}{ab^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{b^{x_{1}}}{b^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = b^{(x_1-x_2)}\)

Given points : (4, 9) and (5, 34.2)

We have:

\(\frac{34.2}{9} = b^{(5-4)}\\\\\implies 3.8 = b\)

Writing the equation with x, y and b:

\(y = ab^x\\\\\implies 9 = a(3.8^4)\\\\a = \frac{9}{3.8^4} \\\\a = 0.043\)

a = 0.043

b = 3.8

When x = 6, y will be:

\(y = (0.043)(3.8^6)\\\\y = 128.47\)

This is not the y value in the question y = 59.4

Therefore (6, 59.4) does not lie on the graph h(x)

The value of x with the given condition is 10

From the question, we have the following parameters that can be used in our computation:

D(7,2), E(1, 9), F(4,8), and G(x, 1),

Also, we have

DE || FG

This means that the lines DE and FG are parallel lines and they have equal slope

The slope is then calculated as

slope = (y₂ - y₁)/(x₂ - x₁)

So, we have

(9 - 2)/(1 - 7) = (1 - 8)/(x - 4)

Evaluate the difference

-7/6 = -7/(x - 4)

So. we have

x - 4 = 6

Evaluate

x = 10

Hence. the value of x is 10

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The efficiency of the motor rated at 2.0 hp and delivering only 1.6 hp to a transmission system is 75%

Efficiency of the machine is the ratio of the work input to the machine to the work output of the machine\

This represented mathematically as

= work input / work output * 100 / 1

Form the problem we have that

work input = motor rated at 1.5 hp

work output = motor rated at 2.0 hp

Efficiency = 1.5 / 2.0 * 100 / 1

Efficiency = 0.75 * 100 / 1

Efficiency = 75%

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The sum of angles of a triangle formed in a spherical geometry exists equivalent to 180∘.

The sum of angles of a triangle formed in a spherical geometry exists equivalent to 180∘.

A category of non-Euclidean geometry, spherical geometry is a subset of elliptical geometry. Any type of geometry that is not founded on conventional planes is known as non-Euclidean geometry. Lines in non-Euclidean geometry are not always the usual straight lines found in Euclidean geometry (i.e., plane geometry).

We require opposing sides and angles in order to use the sine rule. We can utilise this knowledge to locate the side that is opposite the other angle if we know two angles and one of the sides opposite. Accuracy points may be lost because of this.

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Answer:

the probability of rolling a sum of 6 with these dice is 1/6.

Step-by-step explanation:

To find the probability of rolling a sum of 6 with the given pair of dice, we can first list all possible pairs of outcomes that add up to 6:

(2,4)

(3,3)

(4,2)

For each of these pairs, we need to find the probability of rolling each number on its respective die and then multiply those probabilities together. The probability of rolling a particular number on one die is the number of times that number appears on that die divided by the total number of outcomes on that die.

For the first pair (2,4), the probability is:

(2 appears twice on one die out of six possible outcomes) × (4 appears once on the other die out of six possible outcomes) = (2/6) × (1/6) = 1/18

For the second pair (3,3), the probability is:

(3 appears twice on one die out of six possible outcomes) × (3 appears twice on the other die out of six possible outcomes) = (2/6) × (2/6) = 4/36

For the third pair (4,2), the probability is:

(4 appears twice on one die out of six possible outcomes) × (2 appears twice on the other die out of six possible outcomes) = (2/6) × (2/6) = 4/36

The total probability of rolling a sum of 6 is the sum of the probabilities of each possible pair:

1/18 + 4/36 + 4/36 = 1/6

Therefore, the probability of rolling a sum of 6 with these dice is 1/6.

Answer:

Step-by-step explanation:

Given the sample space

20 red marbles and

10 blue marbles

the sample size is

S= 20+10= 30

The probability that both are red if two marbles are pulled at once is

\(\frac{20}{30} *\frac{10}{30} \\\\=\frac{2}{3}*\frac{1}{3} = \frac{2}{9}\)

Answer: c

Step-by-step explanation:

i got it right

Answer:

C) Yes, because substituting these values into both equations forms two true statements.

Step-by-step explanation:

Answer:

502

Step-by-step explanation:

100 * 5 + 2 = 505

Answer:

To find the 100th term of the sequence, we need to use the recursive rule and iterate it 99 times, since we are starting at the first term and need to get to the 100th term.

The recursive rule is given as 5, which means each term in the sequence is equal to the previous term times 5. Therefore:

The first term is 2.

The second term is 2 * 5 = 10.

The third term is 10 * 5 = 50.

The fourth term is 50 * 5 = 250.

And so on...

Iterating this rule 99 times gives us:

The 100th term is 2 * 5^99, which is approximately equal to 6.33825300114 × 10^66.

Therefore, the 100th term of the sequence starting with 2 and with a recursive rule of 5 is approximately 6.33825300114 × 10^66.

Answer:

A,B, and C are all correct

Step-by-step explanation:

Rigid transformations do not change figures except for where they are at.

The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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Answer:

Step-by-step explanation

Divide    1/7    by    1/5    by multiplying   1/7 by the reciprocal of    1/5

​ 1/7 x 5=5/7

​