Help please! How do I write an equation in standard form using the information on the graph?

From the exponential function, the average rate of change from year 1 to year 4 is 62.43, the average rate of change from year 5 to year 8 is 67.57 and the rate of change per year is 65

An exponential function is a type of function that involves a variable in an exponent. It is of the form f(x) = a⋅b^x where a and b are constants and b > 0, b ≠ 1. The input to the function, x, is the exponent that the base, b, is raised to. The output, f(x), is the result of raising the base to the exponent.

In this problem, we have to calculate the rate of increase per year.

Data;

rate = 2%

P = 3000

The exponential growth can be calculated by;

A = P(1 + r)ⁿ

In year 1

A = 3000(1 + 0.02)¹

A = 3060

In year 4

A = 3000(1 + 0.02)⁴

A = 3247.3

a)

The average rate of change from year 1 to year 4 will be

A = [3000(1 + 0.02)⁴ - 3000(1 + 0.02)¹] / 4 - 1

A = 62.43

The average rate of change from year 1 to year 4 is 62.43

b)

The average rate of change from year 5 to year 8 is calculated as

A = [3000(1 + 0.02)⁸ - 3000(1 + 0.02)⁵] / 8 - 5

A = 67.57

C)

The rate of change increase can be calculated as;

A = [3000(1 + 0.02)⁸ - 3000(1 + 0.02)¹] / 8 - 1

A =65

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Roller coaster B has greater top speed than roller coaster A.

Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor. The process may also require selection of the correct number of significant digits, and rounding. Different units of conversion are used to measure different parameters.

Given,

speed of roller coaster A = 110ft./s

speed of roller coaster B = 85mph

1 mile = 5280 feet

⇒ 85 mile = 5280 × 85 = 448800 feet

1 hour = 3600 seconds

speed of roller coaster  B = 448800/3600 ft/s = 124.67 ft/s

comparing speed of both

Speed of roller coaster B > speed of roller coaster A

Hence roller coaster B has greater top speed.

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Answer:

No, it is not a proportion

Step-by-step explanation:

10/12 and 40/64 is not a proportion since although the numerator is constant because when multiplied by 4, it gives us 40, however, when you multiply 4 by 12, you get 48, therefore, it is not a proportion since the changes in the value of a proportion must be constant in both the numerator and denominator.

Hope this helped!  :D

Answer:

The answer is C

Step-by-step explanation:

You have to divide both numerators then the denominater.

So, it would look like:  160 over 90 x 100 over 290

160x100=16   90x290=25     16/25

Answer:

9 = 1st number

21 = 2nd number

Step-by-step explanation:

given that :

1st number = x __eq_i

2nd number (in terms of the first number) = 2x + 3 __eq_ii

1st number + 2nd number = 30 __eq_iii

input eq_i and eq_ii in eq_iii

x + 2x + 3 = 30

3x + 3 = 30

3x = 30 - 3

x = 27 ÷ 3

x = 9

9 = 1st number

input the value of x in eq_ii

2x + 3

2(9) + 3

18 + 3

21 = 2nd number

hope that helps.

a) The longest time a borrower can take to pay off the new car loan of 2 - 6 years is 6 years.

b) Based on the above, the best interest rate the borrower could get is 8%.

Many factors are considered in determining the interest rate for a loan.

Some of the factors include:

We know that the longer the term of a loan, the higher the interest rate charged.  This higher rate is meant to compensate the lender for the time value of money, made variable by inflation and credit risks.

Thus, if a loan term varies between two and six years, the longest time to pay off the loan is 6 years while the best interest rate the borrower can be granted is 8%.

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The measurement of the hypotenuse is obtained as 9 units using the Pythagoras theorem.

What is Pythagoras Theorem?

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.

According to the graph -

The perpendicular measures 4 units.

The base measures 3 units.

To find the hypotenuse g apply the Pythagoras theorem -

(hypotenuse)^2=(base)^2+(perpendicular)^2

(g)^2=(3)^2+(4)^2

(g)^2=9+16

(g)^2=25

g=[tex]\sqrt{25}[/tex]

g=5

Therefore, line segment g measures 5 units.

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Answer:

Step-by-step explanation:

According to question, we know that

His Sister has "1/5*$25 which is equal to $5, and his father has "40%*$25 which is equal to 0.4 * $25 = $10". So, the money Hafiz, his sister and his father have in total

= $25+$5+$10 = $40

Hafiz = $25

Sister = [tex]\frac{1}{5}[/tex]

Father = 40%

Total money of Hafiz, Sister, and Father altogether.

[tex]\frac{1}{5} X[/tex] $25

= $5

40% (0.4) x $25

= $ 10

$ 25 + $ 5 + $ 10

The tax rate of an Item that costs $450 Before tax. and the sales tax is $31.50 is 7%

The tax rate is the percentage of an income or an amount of money that has to be paid as tax.

To find the tax rate of $31.50 from $450

The formula is

Amount taxed/Principal amount x 100

= $31.50/$450 x100

=$3150/450

=7%

Hence, the tax rate is 7%

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Answer:

27y - 45 + 7z

The length of segments TA and TB are both 4 cm.

To solve this problem, we can use the properties of circles and the relationship between the radius and the diameter.

Since the radius of the circle with center T is 4 cm, the diameter of this circle is 2 * 4 = 8 cm.

Since the length of segment ST is 9 cm, the diameter of the second circle is also 9 cm.

Since the radius of the circle with center T is 4 cm, the radius of the second circle is also 4 cm.

Since the two circles intersect at points A and B, the segments TA and TB are equal in length.The length of segment TA and TB is the radius of the second circle, which is 4 cm.

Therefore, the length of segments TA and TB are both 4 cm.

The figure is attached

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The number of times each number divides is 8 divides LCM into 11 times

11 divides into LCM 8 times and 22 divides into LCM 4 times .

What is LCM ?

The smallest positive integer that is divisible by both a and b is known as the least common multiple (lcm), lowest common multiple (lcm), or smallest common multiple of two numbers a and b in mathematics and number theory.

Least Common Multiple is a mathematical term. The smallest number that is a multiple of both of two numbers is called the least common multiple.

In mathematics, the least common multiple is sometimes referred to as LCM or the lowest common multiple. The smallest number among all the common multiples of the provided numbers is the least common multiple of two or more numbers.

The LCM of 8 , 11 and 22 is 88

∴ 8 divides into LCM 11 times

11 divides into LCM 8 times

22 divides into LCM 4 times

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The equations that are true for x = –2 and x = 2 are:

x^2-4=0 and 4x^2 = 16

We can determine the equations that are true for x = –2 and x = 2 by testing the given options:

After testing the options option  1 ; x^2-4=0 putting x = 2 or -2 into the equation will give zero.  

(2^)2-4=0

(-2)^2-4=0

Then option 4: 4x^2 = 16

4(2)^2 = 16

4(-2)^2 = 16

Therefore, option 1st and 4th are correct.

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Using place value along with division facts in a division equation, helps in dividing larger numbers easily. Place value counters and tape diagrams are often used to represent division using place value.

What is division?

With the arithmetic operation of division, we can divide a collection of items into equal pieces. Typically, it is represented by the symbol "÷".

The bigger amount that is divided into equal halves is called the dividend.

The number of groups that divide the payout is known as the divisor. Following division, the result is the quotient.

The value of a digit in a number is determined by its place in the number, or place value.

Divide larger numbers simply by applying place value and division facts in a division equation. Place value division is frequently shown using tape diagrams and place value counters.

Example - 4 ÷ 2 = 2

In the first equation, the digits are 4 and 2. We can write it as 4 ones ÷ 2 ones = 2 ones (using the division fact).

Example - 40 ÷ 20 = 2

For the second equation, the digits are the same, but a zero has been added after 4, and the quotient thus has one zero at the end. So, we can write it as 4 tens ÷ 2 ones = 2 tens (using place value and the division fact).

Example - 400 ÷ 200 = 2

Similarly, for the third division equation, the same digits are present, but the number of zeros has increased. We are dividing 4 hundreds ÷ 2 ones = 2 hundreds (using place value and the division fact).

Therefore, place value blocks help in division for making it simpler.

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Answer:

First, solve for two points as an equation instead of an inequality to find the boundary line for the inequality.

For:

x

=

0

(

3

⋅

0

)

+

2

y

=

6

0

+

2

y

=

6

2

y

=

6

2

y

2

=

6

2

y

=

3

or

(

0

,

3

)

For:

y

=

0

3

x

+

(

2

⋅

0

)

=

6

3

x

+

0

=

6

3

x

=

6

3

x

3

=

6

e

d

)

(

3

)

x

=

2

or

(

2

,

0

)

We can now graph the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality.

graph{(x^2+(y-3)^2-0.125)((x-2)^2+ y^2-0.125)(3x+2y-6)=0 [-20, 20, -10, 10]}

Now, we can shade the left side of the line. And we need to make the boundary line a dashed line because the inequality operator does not contain an "or equal to" clause.

graph{(3x+2y-6) < 0 [-20, 20, -10, 10]}

Step-by-step explanation:

Answer:

There is a root between x=3 and x=5.

Step-by-step explanation:

Not entirely sure what this question wants, but from this you can tell that the function crossed the x-axis in the interval (3, 5). When x is 3, y is 5, and then when x is 5, y is -2.

Answer:

1) 10/3

2) -1./3

3) -2/5

4) 1

5) undefined

6) 0

Step-by-step explanation:

Find two easy to read points. Go from one point to the other by going vertically first then horizontally. Moving up is positive and down is negative. Moving right is positive and left is negative.

slope = rise/run = (difference in y)/(difference in x)

1) slope = 10/3

2) slope = -1/3

3) slope = -2/5

4) slope = 1/1 = 1

5) slope = undefined (The slope of a vertical line is undefined.)

6) slope = 0 (The slope of a horizontal line is 0.)

Answer:

Step-by-step explanation:

Triangle JKL is a 51-51-78 triangle, since the angles in a triangle must add up to 180°. Since triangle PQR is similar to triangle JKL, it must also be a 51-51-78 triangle. Since corresponding sides in similar figures are in proportion, we can set up a proportion to find the length of PR:

(PR)/(JK) = (PQ)/(JL) = (36)/(18)

Cross multiplying and solving for PR, we find:

PR = (JK) * (PQ)/(JL) = 18 * 36/18 = 36

The price of a seven minute call direct to New York, in the evening, is given as follows:

$5.82.

The cost of the call is obtained considering the information given in the table, for which the proportions are applied.

We have a direct call, meaning that it is a person-to-person call, thus the flat rate is of $3.00 per minute.

Then the minute proportions, considering that the call happens in the evening, are given as follows:

A seven minute call is composed by six additional minutes after the first, hence the total cost is obtained as follows:

0.38 x 3 + 6 x 0.26 x 3 = $5.82.

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The blank spaces of the statement coefficient: The number in BLANK of the variable within the BLANK BLANK are, front, addition, subtraction.

A quantity or number that is combined with a variable is known as a coefficient. The variable is often multiplied by an integer, which is then printed next to it.

Terms that have the same variables raised to the same power are referred to as like terms. The only difference is in the numerical coefficients.

We know a coefficient is a constant value combined with a variable.

For example, In 7x the coefficient of x is 7.

Given, A fill-in-the-blank statement,

coefficient: The number in BLANK of the variable within the BLANK BLANK.

Therefore,

coefficient: The number in front of the variable within the addition subtraction.

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The coordinate of the point C is (0, a)

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

A = (0, a)

B = (b, 0)

As a general rule, the orthocenter of a triangle is a point located at the intersection of the lines containing the altitudes of the triangle.

This means that we start by calculating the equation of the altitude from B to line AC.

A linear equation is represented as

y = mx + c

Where

slope = m

y-intercept = c

Using the above as a guide, we have the following:

slope = (y₂ - y₁)/(x₂ - x₁)

This gives

m(BC) = (0 - 0)/(b - 0) = 0

y-intercept (c) = a

So the equation of the line BC is

y = 0 * x + a

y = a

For line AC, we have

m(AC) = (a - 0)/(0 - 0) = a/0 = undefined.

This means that the equation of the line AC is

x = 0

The equation x = 0 implies that the x-coordinate is always 0, irrespective of the y-coordinate e.g. (0, a)

At this stage, we have the coordinates of the points from lines AC and BC to be

(0, a) and (0, a)

Next, we calculate the C as follows

C = Midpoints of (0, a) and (0, a)

This gives

C = 1/2 * (0 + 0, a + a)

Evaluate

C = (0, a)

Hence, the coordinate of C is (0, a)

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[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill[/tex]

[tex](-6x^3 y^5 + 11x^3 y^2) \div (-2x^2 y^3)\implies \cfrac{-6x^3 y^5 + 11x^3 y^2}{-2x^2 y^3} \\\\\\ \cfrac{-6x^3 y^5}{-2x^2 y^3}+\cfrac{11x^3 y^2}{-2x^2 y^3}\implies \cfrac{-6}{-2}\cdot \cfrac{x^3 y^5}{x^2 y^3}+\cfrac{11}{-2}\cdot \cfrac{x^3 y^2}{x^2 y^3} \\\\\\ 3\cdot x^3 x^{-2}y^5 y^{-3}+\cfrac{11}{-2}\cdot \cfrac{x^3 x^{-2}}{y^3 y^{-2}}\implies 3x^{3-2}y^{5-3}-\cfrac{11}{2}\cdot \cfrac{x^{3-2}}{y^{3-2}} \\\\\\ ~\hfill {\Large \begin{array}{llll} 3x y^2 -\cfrac{11x}{2y} \end{array}}~\hfill[/tex]

There is a directly proportional relationship between the weight and total cost of bag of of lemons.

The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. The constant of proportionality may also be referred to as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.

When two variables are directly or indirectly proportional to one another, their relationship may be expressed using the formulas y = kx or y = k/x, where k specifies the degree of correspondence between the two variables. The proportionality constant, k, is often used.

As an illustration, we may write y = kx, where x is the amount of gas in gallons, y is the price in dollars, and k is the proportionality constant.

Given data :

One bag weighs 2.4 pounds and cost $5.28.

Another bag weighs 2.7 pounds and cost $5.94

2.4k = 5.28

k= 2.2

2.7k = 5.94

k = 2.2

k > 1

The weight and total cost of bag of of lemons is directly proportional, so when weight of lemon increases, the cost of lemon also increases.

Therefore, there is a directly proportional relationship between the weight and total cost of bag of of lemons.

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Check the picture below.

Answer:

both are right

Step-by-step explanation:

2/5x = 14

multiply both sides by 5/2:

(5/2)(2/5)x = 14(5/2)

x = 70/2 = 35

However, dividing by 2/5 is the same as multiplying by 5/2, so you are BOTH right.  Dividing by a fraction is the same as multiplying by the reciprocal of the fraction.

Answer:

It is in its simplest form

Step-by-step explanation:

Answer: 130

Step-by-step explanation:

The original price of the sweater is $303.

A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.

Given that, June is buying a sweater using a coupon offering a 30% discount on items over $99.

The discounted price is $91

Let the original price of the sweater be x.

So, 30% of x=91

30/100 ×x=91

0.3x=91

x=91/0.3

x=$303

Therefore, the original price of the sweater is $303.

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