A parent increases a child’s monthly allowance by 20% each year. If the allowance is $8 per month now, in about how many years will it take to reach $20 per month? Use the equation 20 = 8(1.2)x to solve the problem. Round to the nearest year.

Answer: I say 13

Step-by-step explanation:

Answer: To find the value of g(2+h)-g(2) divided by h, we can use the definition of the derivative. The derivative of a function at a point is a measure of the slope of the function at that point, and it can be calculated by taking the limit of the difference quotient as h approaches 0.

The difference quotient is defined as:

[g(2+h) - g(2)] / h

So, to find the derivative of g at x=2, we can substitute the value of x in the function g(x) and take the limit as h approaches 0:

lim h→0 [g(2+h) - g(2)] / h

Substituting the value of x in the function g(x), we get:

lim h→0 [(2+h)³ - 2(2+h) - (2² - 2*2)] / h

This simplifies to:

lim h→0 [8+6h+h²-2h - 4] / h

Which simplifies to:

lim h→0 [h²+6h+4] / h

And, finally:

lim h→0 [h(h+6)] / h

The limit of a quotient is equal to the quotient of the limits, as long as the limit of the denominator is not 0. In this case, the limit of the denominator (h) is 0, but the limit of the numerator (h(h+6)) is not. Therefore, we can safely take the limit:

h+6

So, the derivative of g at x=2 is h+6. When h=0, the derivative is equal to the function's value at that point, so the value of g(2) is 6.

Therefore, the value of g(2+h)-g(2) divided by h is:

(h+6) - 6 / h

Which simplifies to:

h / h

Which is equal to:

1

So, the final answer is 1.

Step-by-step explanation:

Luca's average trip will be 58 miles per hour.

Speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed. It's a scalar quantity.

In this case, it took Luca 8 hours to drive 464 miles from Richmond VA to Cleveland, OH. In miles per hour, Luca's average trip will be:

= Distance / Time

= 464 / 8

= 58 miles per hour.

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Answer:
Here is a sequence of numbers using the rule "x+8":

x+8=9 (x=1)

x+8=10 (x=2)

x+8=11 (x=3)

x+8=12 (x=4)

x+8=13 (x=5)

x+8=14 (x=6)

Here is the sequence of ordered pairs:

(1, 9)

(2, 10)

(3, 11)

(4, 12)

(5, 13)

(6, 14)

Answer:

It is the first answer,

Step-by-step explanation:

The hypotenuse is always the longest side and opposite of the right angel.  Side b is the adjacent side to J and c is the opposite side of J.

Total cost is the sum of all expenses incurred to produce a particular type of product. The answer is $1.50.

Total cost is the sum of all expenses incurred to produce a specific kind of output. Financial reporting, when overhead costs must be allocated to specific assets, is where the total cost approach is more useful from an accounting standpoint.

$8 was spent in total.

Xavier bought four $1.25 snacks.

4 x 1.25 = $5

The 2 cans cost $3 because 5 + 3 = 8, and we know how much the snacks cost ($5), making the total cost ($8).

Each can cost $1.50 because, if the price of the two cans was $3, we would have to divide it by two to get the price of the second can, which comes out to be $1.50. As a result, each can was $1.50.

Therefore, the answer is $1.50.

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Greatest common factor (GCF) of 50 and 65 is 5.

We will first find the prime factorization of 50 and 65. After we will calculate the factors of 50 and 65 and find the biggest common factor number .

Step-1: Prime Factorization of 50

Prime factors of 50 are 2, 5. Prime factorization of 50 in exponential form is:

50 = 21 × 52

Step-2: Prime Factorization of 65

Prime factors of 65 are 5, 13. Prime factorization of 65 in exponential form is:

65 = 51 × 131

Step-3: Factors of 50

1, 2, 5, 10, 25

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 50 and 65. The biggest common factor number is the GCF number.

So the greatest common factor 50 and 65 is 5.

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Answer:

245 miles

Step-by-step explanation:

210 = 6 gallons

210/6 = how far you can travel with one gallon

210/6 = 35

7*35 = how far you can travel with 7 gallons

7*35 = 245

Answer:

Ann drove 245 miles during her drive last weekend.

Step-by-step explanation:

If Ann used 7 gallons of gas during her drive last weekend, we can use the car's MPG to find out how far she drove by multiplying the number of gallons used by the MPG:

7 gallons * 35 miles/gallon = 245 miles

Answer:

1809/27=67 is your answer........

Answer:

- 2x +29

Step-by-step explanation:

Open up the parenthesis, then simplify

14 + 5x + 15 - 7x

5x - 7x + 14 + 15

-2x + 29

[tex]14+5(x+3) - 7x[/tex]

Distribute:

[tex]14+(5)(x)+(5)(3)-7x[/tex]

[tex]14+5x+15-7x[/tex]

Combine Like Terms:

[tex](5x-7x)+(14+15)[/tex]

[tex]\fbox{-2x + 29}[/tex]

Answer:316.8

Step-by-step explanation:

Answer:316.8

Step-by-step explanation:

Answer:

y = [tex]\frac{3}{4}[/tex]x + 3

Step-by-step explanation:

find the slope m

m = [tex]\frac{y2 - y1}{x2 - 21}[/tex]

m = [tex]\frac{3 - 0}{0 - - 4}[/tex]

m = [tex]\frac{3}{4}[/tex]

y = mx + b

find b

insert y1 and x1 into the equation

0 = [tex]\frac{3}{4}[/tex](-4) + b

0 = -3 + b

b = 3

y = [tex]\frac{3}{4}[/tex]x + 3

Step-by-step explanation:

the area of a trapezoid is

(a + b)/2 × x

a and b being the 2 bases. and x, as requested, is the height.

A

it does not matter which base is which, as long as we keep using them consistently.

so, let's assume a is the first base :

a = x + 5

and then for the second base

b = 2x - 1

now we use that in the main formula :

(x + 5 + 2x - 1)/2 × x = (3x + 4)/2 × x = (3x² + 4x)/2

A = (3/2)x² + (4/2)x = (3/2)x² + 2x ft²

B

now the height is increased by 4 ft.

that means we need to replace x by x + 4.

(3/2)(x+4)² + 2(x+4) = (3/2)(x² + 8x + 16) + 2x + 8 =

= (3/2)x² + (24/2)x + (48/2) + 2x + 8 =

= (3/2)x² + 12x + 24 + 2x + 8 =

= (3/2)x² + 14x + 32 ft²

with x being the original height, of course.

The value of s that makes the inequality true is 6

An inequality can simply be defined as a mathematical relation that makes a non-equal comparison between two variables, numbers, ratios or other mathematical expressions.

It is used in comparing two numbers on the number line on the basis of their size.

The inequality signs are;

From the expression given, we have;

7s < 42

Make 's' the subject by dividing both sides by 7, we have;

s > 42/7

s> 6

Hence, the value is greater than 6

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The elevation at which the race ends is given by the equation A = 195 feet

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the elevation at which the race ends be A

Now , the equation will be

The bike road race starts at an elevation of 500 feet

So , the initial elevation = 500 feet

The number of stages = 5 stages

The elevation at first stage = -139 feet

The elevation at second stage = -63 feet

The elevation at third stage = 197 feet

The elevation at fourth stage = 27 feet

The elevation at fifth stage = -327feet

So , the total elevation of all the stages during the bike race = initial elevation + elevation at first stage + elevation at second stage + elevation at third stage + elevation at fourth stage + elevation at fifth stage

Substituting the values in the equation , we get

The total elevation of all the stages during the bike race = elevation at which the race ends A

So ,

Elevation at which the race ends A = 500 + (-139) + (-63) + (197) + (27) + (-327)

On simplifying the equation , we get

Elevation at which the race ends A = 500 - 305

Elevation at which the race ends A = 195 feet

Therefore , the value of A is 195 feet

Hence , the race ends at an elevation of 195 feet

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The difference between the expansions of (A + B)^2 and (A - B)^2 is the sign of the middle term. In the second case it is negative, due to the negative sign on B.

Here we have two perfect square trinomials, these are:

(A + B)^2

(A - B)^2

Notice that the only difference between these is the sign of the second element.

Now we can expand these two expressions as:

(A + B)^2 = (A + B)*(A + B) = A^2 + 2AB + B^2

The second expression gives:

(A - B)^2 = (A - B)*(A - B) = A^2 + 2*A*(-B) + (-B)^2

                                       = A^2 - 2AB + B^2

There we can see that the only difference between these two expansions is the sign of the middle term. Where in the second case it is negative, due to the negative sign on B.

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Answer:

X > -20

Step-by-step explanation:

-10 - 9/2 x < 80

Move 10 to the other side

- 9/2 x < 80 + 10

Simplify

-9/2 x < 90

-9 x < 180

x > -20

(We switch the inequality sign if we are dividing with negatives)

Answer:

3.4 seconds

Step-by-step explanation:

Given function:

[tex]h(t)=-4.9t^2+2.45t+48.314[/tex]

where

The ball will strike the ground when its height is zero.

Therefore, to calculate when the ball strikes the ground, substitute h(t) = 0 and solve for t using the quadratic formula.

[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}[/tex]

Therefore:

Substitute these values into the quadratic formula:

[tex]\implies t=\dfrac{-2.45 \pm \sqrt{(2.45)^2-4(-4.9)(48.314)}}{2(-4.9)}[/tex]

[tex]\implies t=\dfrac{-2.45 \pm \sqrt{6.0025+946.9544}}{-9.8}[/tex]

[tex]\implies t=\dfrac{-2.45 \pm \sqrt{952.9569}}{-9.8}[/tex]

[tex]\implies t=\dfrac{-2.45 \pm 30.87}{-9.8}[/tex]

[tex]\implies t=\dfrac{-2.45 + 30.87}{-9.8}=-2.9[/tex]

[tex]\implies t=\dfrac{-2.45 -30.87}{-9.8}=3.4[/tex]

As time cannot be negative, t = 3.4 s only.

Therefore, the ball strikes the ground 3.4 seconds after it is launched.

Answer:

Step-by-step explanation:

So the person talked for 6 minutes.

The unitary approach involves calculating the value of a single unit, from which we may calculate the values of the necessary number of units.

Two quantities are compared to form a ratio. An equality of two ratios is a percentage. How to format a ratio Analyze the ratio to see whether it is part to part or part to whole. Calculate the whole and the pieces as necessary.

To solve this problem, we can use the following equation:

Cost = (Number of minutes x $0.31) + $0.89 + $1.23

We know that cost is $6.15 and the call lasted 6 hours. Since there are 60 minutes in an hour, we can convert the time in hours to minutes by multiplying 6 hours by 60 minutes/hour

So the number of minutes is 6 hours * 60 minutes/hour = 360 minutes

Now we can substitute the values into the equation:

Cost = (360 minutes x $0.31) + $0.89 + $1.23

Cost = $111.6 + $0.89 + $1.23

Cost = $113.72

The equation does not match the $6.15 cost, which means that the person talked for 6 minutes

So the person talked for 6 minutes.

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Answer: Set of integers

Integers are positive and negative whole numbers, with 0 included.

Answer: Set of Integers

Step-by-step explanation:

{...,-2,-1,0,1,2...}

since we can see that here is a zero as well as positive and negative numbers, therefore, we call this set, a set of integers.

hope that helps...

An example of limit in polynomial will be the polynomial function f(x) = x³ + 2x² - 5. As x approaches 2, the value of the function approaches 11. So, the limit of f(x) as x approaches 2 is 11.

A polynomial simply means an expression which is composed of variables, constants and exponents, which are combined using mathematical operations such as addition, subtraction, multiplication and division

In mathematical notation, we can write it as: Here, lim x->2 (x³ + 2x² - 5)

= x³ + 2x² - 5

= 2³ + 2(2²) - 5

= 8 + 8 - 5

= 11

This means that as x gets arbitrarily close to 2, the values of the function gets arbitrarily close to 11.

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Therefore , the solution to the given problem of equation comes out to be quotient : x² +x+6+ [tex]\frac{2}{x+2}[/tex] and remainder is 2

A mathematical depiction of two equal variables, one on either side of a "equals" sign, is called an equation. Equations can be used to solve common problems. To solve challenges in real life, we frequently turn for pre algebra assistance. Lessons in pre-algebra cover the foundational ideas of mathematics.

Here,

Given : synthetic division for

x³ + 3x² + 8x + 14

------------------------

x + 2

Write the problem in synthetic division format

-2  | 1 3 8 14

         -2 -2  

------------------------

     1   1  6

Carry down the leading coefficient, unchanged, to below the division symbol

-2  |    1 3 8 14

           -2 -2

---------------------------

         1  1   6

Multiply the carry - down value by the zero of the denominator, and carry the result up into the next column:

1(-2)=-2

-2 |  1 3 8 14

        -2 - 2

------------------

     1    1   6

=> We get:

As

x² +x+6+ [tex]\frac{2}{x+2}[/tex]

and remainder is 2

Therefore , the solution to the given problem of equation comes out to be quotient : x² +x+6+ [tex]\frac{2}{x+2}[/tex] and remainder is 2.

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Five vectors in Span (V₁ V₂) where V₁ = (8 2 7 ) and V₂ = (-6 4 0 ) is.

n(V₁ + V₂), n ∈ I, I = 1, 2, 3, 4, 5.

In mathematics, the set of all linear combinations of the vectors in S is referred to as the linear span, Denoted span(S), Either the intersection of all linear subspaces containing S, or the smallest subspace containing S, can be used to describe it. A vector space is therefore nothing more than the linear range of a set of vectors.

The vectors that are in the same span should be a multiple of the vectors

V₁ = (8 2 7 ), V₂ = (-6 4 0 )

Now, V₁ + V₂ = (2 6 7).

So, The five vectors in the span of V₁ and V₂ is,

2×(2 6 7).

= (4 12 14).

- 2×(2 6 7).

= (- 4 - 12 - 14).

3×(2 6 7).

= (6 18 21)

- 3×(2 6 7)

= (- 6 - 18 - 21).

5×(2 6 7).

= (10 30 35).

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Answer: jump off a cliff and shatter your bones

Step-by-step explanation:

Answer:

The first chart.

Step-by-step explanation:

The first table. The chart gives a ratio of 1:4, which is the same as the amount the teenager made.

Answer:

Step-by-step explanation:

One side of a square field is 92m. Find the cost of raising lawn on the field at the rate of 1.50 per sq.m

Square area = l²

Square area = 92²

Square area = 8466 m²

Cost = Area × rate of 1.50 per sq.m

Cost = 8466 × 1.50

Cost = 12696