Exponential Function: y = 6(1)²

The possible coordinates of point A such that the distance to point B is 10 units are:

(-5, -4) and (-5, 8)

We know that the distance between two points (a, b) and (c, d) is:

distance = √( (a - c)² + (b - d)²)

In this case, we know that:

B = (3, 2)

A = (-5, y)

And the distance is 10 units, then we can write:

10 = √( (3 + 5)² + (2 - y)²)

10² = 8² + (2 - y)²

100 - 64 =  (2 - y)²

36 =  (2 - y)²

±√36 = 2 - y

±6 = 2 - y

y = 2 ± 6

The two solutions are:

y = 2 + 6 = 8

y = 2 - 6 = -4

Then the possible coordinates are (-5, -4) and (-5, 8).

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Answer:

x = [tex]\frac{20}{7}[/tex]

Step-by-step explanation:

[tex]\frac{3}{4}[/tex] x - 5= [tex]\frac{1}{2}[/tex] x + 2x - 10

multiply through by 4 ( the LCM of 4 and 2 ) to clear the fractions

3x - 20 = 2x + 8x - 40

3x - 20 = 10x - 40 ( subtract 10x from both sides )

- 7x - 20 = - 40 ( add 20 to both sides )

- 7x = - 20 ( divide both sides by - 7 )

x = [tex]\frac{-20}{-7}[/tex] = [tex]\frac{20}{7}[/tex]

Answer:

[tex]x=\frac{20}{7}[/tex]

Step-by-step explanation:

Since x is on the right side of the equation, switch the sides so it is on the left side of the equation.

[tex]\frac{1}{2}x+2x-10=\frac{3}{4}x-5[/tex]

Simplify the left side of the equation by combing [tex]\frac{1}{2}[/tex] and [tex]x[/tex].

[tex]\frac{x}{2}+2x-10=\frac{3}{4}x-5[/tex]

To write [tex]2x[/tex] as a fraction with a common denominator, multiply by [tex]\frac{2}{2}[/tex].

[tex]\frac{x}{2}+2x*\frac{2}{2} -10=\frac{3}{4}x-5[/tex]

Simplify terms by combining [tex]2x[/tex] and [tex]\frac{2}{2}[/tex]. Combine the numerators over the common denominator.

[tex]\frac{x+2x*2}{2} -10=\frac{3}{4}x-5[/tex]

Raise x to the power of 1.

[tex]\frac{x^1+2x*2}{2} -10=\frac{3}{4}x-5[/tex]

Factor [tex]x[/tex] out of [tex]x^1[/tex].

[tex]\frac{x*1+2x*2}{2} -10=\frac{3}{4}x-5[/tex]

Factor [tex]x[/tex] out of [tex]x+2x*2[/tex].

[tex]\frac{x*1+x(2*2)}{2} -10=\frac{3}{4}x-5[/tex]

Factor [tex]x[/tex] out of [tex]x*1+x(2*2)[/tex]

[tex]\frac{x(1+2*2)}{2} -10=\frac{3}{4}x-5[/tex]

Multiply 2 by 2.

[tex]\frac{x(1+4)}{2} -10=\frac{3}{4}x-5[/tex]

Add 1 and 4.

[tex]\frac{5x}{2} -10=\frac{3}{4}x-5[/tex]

Combine [tex]\frac{3}{4}[/tex] and [tex]x[/tex].

[tex]\frac{5x}{2} -10=\frac{3x}{4}-5[/tex]

Move all terms containing [tex]x[/tex] to the left side of the equation.

[tex]\frac{7x}{4}-10=-5[/tex]

Move all terms not containing [tex]x[/tex] to the right side of the equation.

[tex]\frac{7x}{4}=5[/tex]

Multiply both sides of the equation by [tex]\frac{4}{7}[/tex]

[tex]\frac{7x}{4}*\frac{4}{7} =5*\frac{4}{7}[/tex]

Simplify both sides of the equation.

[tex]x=\frac{20}{7}[/tex]

Answer: 20

Step-by-step explanation: There are 2 ways to solve this problem. This is one way, it is a shortcut. So if you didn't know, 25% of 100 (the whole thing) is 1/4, so if you divide 80 by 1/4, you should get 20. The 2nd way is to set up a proportion, so it would be 25 over 100 = ? over 80. Now, you would cross multiply the 25 and 80 to get 2000. Then you take the 2000 and divide it by 100 to get 20. I hoped this explanation helped you.

Answer:

20

Step-by-step explanation:

Write 25% as 25/100

Since, finding the fraction of a number is same as multiplying the fraction with the number, we have

25/100 of 80 = 25/100 × 80

Therefore, the answer is 20

If you are using a calculator, simply enter 25÷100×80 which will give you 20 as the answer.

The algebraic expression is [tex]\frac{7}{10}m-\frac{1}{3}m+2m[/tex] = [tex]\frac{71m}{30}[/tex]

What do you mean by an algebraic expression?

Algebraic expression is the idea of ​​using letters or alphabets to represent numbers without specifying the actual values. Algebra Basics taught us how to use letters like x, y, and z to represent unknown values. These characters are called variables here. An algebraic expression can be a combination of variables and constants. Any multiplied value that is prefixed to a variable is a factor.

Given expression:

[tex]\frac{7}{10}m-\frac{1}{3}m+2m[/tex]

= [tex]\frac{21m-10m+60m}{30}[/tex]

= [tex]\frac{71m}{30}[/tex]

Therefore, [tex]\frac{7}{10}m-\frac{1}{3}m+2m[/tex] = [tex]\frac{71m}{30}[/tex]

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For a taxable income of $1,80,900, the effective tax rate is 21.11%.

Marginal tax is the tax rate applied to an individual’s last dollar of income. It is the additional tax that must be paid on any additional income earned. In other words, it is the tax rate that applies to an individual’s income after all deductions. For example, if an individual’s income is $50,000 and the marginal tax rate is 25%, then the individual must pay an additional $12,500 in taxes on top of the $25,000 in taxes already paid on their $50,000 income.

Marginal tax rates are progressive, meaning that as an individual’s income increases, the marginal tax rate will increase as well. The marginal tax rate is important to understand because it helps individuals determine how much additional income they will need to earn in order to make up for the taxes they will have to pay on that income. It is also important to understand how marginal tax rates can affect tax planning strategies.

To determine the effective tax rate for a taxable income of $180,900, calculate the sum of the marginal tax rates for each tax bracket that the $180,900 falls into. The taxable income of $180,900 is greater than $89,075 and less than $170,050. The marginal tax rates for these two tax brackets are 22% and 24%, respectively. The sum of the marginal tax rates is 46%. Divide the sum by the taxable income of $180,900 to get the effective tax rate of 21.11%. Round the final answer to the nearest hundredth to get 21.11%.

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The scale factor of the transformation is 2.25

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

Point H'(4.5, 6.75) is the result of dilating point H(2, 3)

This means that

The scale factor of the transformation = H'/H

Substitute the known values in the above equation, so, we have the following representation

Scale factor = (4.5, 6.75)/(2. 3)

Evaluate

Scale factor = 2.25

Hence, the scale factor is 2.25

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The equivalent expression is 1.5^24/0.7^18

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

one and five tenths raised to the fourth power divided by seven tenths raised to the third power, all raised to the sixth power

Rewrite properly

So, we have

(1.5^4/0.7^3)^6

Open the brackets

So, we have the following representation

(1.5^4/0.7^3)^6 = 1.5^(4 * 6)/0.7^(3*6)

Evaluate the products

(1.5^4/0.7^3)^6 = 1.5^24/0.7^18

Hence, the solution is 1.5^24/0.7^18

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The image after a dilation by a scale factor of 4 centered at the origin is (-132,-352).

Scale factor is a mathematical term that refers to the ratio of two corresponding sides of similar shapes. It is used to compare the size of objects or figures by determining the size of a model in relation to its actual size. For example, if two shapes are similar, then their scale factor will be the same. This is useful in engineering and architecture when building scaled models of structures and machines. Scale factors can also be used to determine the proportions and measurements of an object in relation to similar objects.

This is because a dilation by a scale factor of 4 is the same as multiplying the original coordinates by 4. So, if the original coordinates were (-3,-8), then the new coordinates would be (-12,-32). Then, the coordinates are shifted by the center (the origin), so the new coordinates are (-132,-352).

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Her commission rate is 7.44%.

What is commission rate?

The payment that is either a fixed amount or a percentage of a sale is the commission rate. When they make a sale, people in commission-based professions like insurance brokers, real estate agents, and car salespeople are compensated.

The parameters given are;

The amount Mary earns annually = $28,000

The amount Mary grossed during a week = $658.00

The amount Mary had sold during the week to make the amount grossed during the week = $1673.19

Given that Mary makes $28,000 per year

Therefore;

The amount Mary earns per week = Amount earned per year/52

The amount Mary earns per week =  $28,000/52 = $538.46

The amount extra she made on commission = $658.00- $538.46= $119.54

The commission rate = Commission earned/(Amount of merchandise sold)×100

The commission rate = 119.54/1673.19 × 100 = 7.14%

Her commission rate = 7.44%

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Answer:

y = 1/9x + 5

Hope this helps!

Step-by-step explanation:

y = mx + b

m = slope

y = [tex]\frac{1}{9} x[/tex] + b

( x, y ) = ( 0, 5 )

(5) = [tex]\frac{1}{9} (0)[/tex] + b

5 = 0 + b

5 = b or b = 5

Putting it all together gets you y = [tex]\frac{1}{9} x[/tex] + 5

By using proportionality, it can be calculated that-

a) Constant of proportionality that relates the length of paver in the model and the actual length is k = [tex]\frac{4}{3}[/tex]

[tex]y = \frac{4}{3}x[/tex] is the required equation which relates the length of paver in the model and the actual length of the paver

b) Area of the rectangle = [tex]\frac{1}{3}[/tex] sq.feet

Constant of proportionality that relates the area of paver in the model and the actual area is k = [tex]\frac{9}{16}[/tex]

What is proportionality?

Suppose there are two quantities. Proportionality indicates that if there is a change in the value of one quantity, the value of other quantity also changes but maintaining a constant ratio

Proportionality can be direct or inverse

Direct proportion

Two quantities are said to be in direct proportion if on increasing the value of one quantity, the value of other quantity also increases and vice versa.

For example cost of a commodity and quantity of a commodity are in direct proportion

Inverse proportion

Two quantities are said to be in inverse proportion if on increasing the value of one quantity, the value of other quantity decreases and vice versa.

For example Number of men and number of days taken by those men to complete a job.

Length of paver in the model = [tex]\frac{2}{3}[/tex] ft

Actual length of paver = [tex]\frac{1}{2}[/tex] ft

Let the constant of proportionality be k

[tex]\frac{2}{3} = \frac{1}{2}k[/tex]

k = [tex]\frac{2}{3} \div \frac{1}{2}[/tex]

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

Let y be the length of paver in the model and x is the actual length

[tex]y = \frac{4}{3}x[/tex] is the required equation which relates the length of paver in the model and the actual length of the paver

b) Area of the model = [tex]\frac{1}{2}\times \frac{3}{8} = \frac{3}{16}[/tex] sq. feet

Actual area = [tex]\frac{2}{3} \times \frac{1}{2} = \frac{1}{3}[/tex] sq.feet

Let the constant of proportionality be l

[tex]\frac{3}{16} = \frac{1}{3}l[/tex]

l = [tex]\frac{3 \times 3}{16}\\[/tex]

l = [tex]\frac{9}{16}[/tex]

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Answer: 18/8 = 9/4

Step-by-step explanation:

6 can be write as 6/1

6/1 timed 3/8 = 18/8

Simplify by 2 = 9/4

The possible ways a basketball team could score 24 points, without making any free throws are given below.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Three types of points:

Free throws - 1 point

2 - points.

3 - points.

Now,

The different ways to have a score of 24 points without making any free throws.

Case 1:

2 x 12 = 24 points.

Case 2:

3 x 8 = 24 points.

Case 3:

2 x 6 = 12 and 3 x 4 = 12

12 + 12 = 24 points.

Case 4:

2 x 9 = 18 and 3 x 2 = 6

18 + 6 = 24 points

Case 5:

2 x 3 = 6 and 3 x 6 = 18

6 + 18 = 24 points

Similarly, we can have many possible ways.

We have to make sure that the points add to 24 points.

Thus,

The possible ways a basketball team could score 24 points, without making any free throws are given above.

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Answer:

The different ways to have a score of 24 points without making any free throws.

Case 1:

2 x 12 = 24 points.

Case 2:

3 x 8 = 24 points.

Case 3:

2 x 6 = 12 and 3 x 4 = 12

12 + 12 = 24 points.

Case 4:

2 x 9 = 18 and 3 x 2 = 6

18 + 6 = 24 points

Case 5:

2 x 3 = 6 and 3 x 6 = 18

6 + 18 = 24 points

Step-by-step explanation:

Because i know

By setting up the equation and solving and simplifying  the equation, the possible number of hours Frank can trim tree is 5.43 hours, round off the hour that will be 6 hours.

Algebraic simplification is the process of rewriting an algebraic expression in a simpler form, without changing its value.

An algebraic expression is a combination of numbers, variables, and arithmetic operations that can be evaluated to a specific numerical value.

let the required number of hours be h,

so setting up the equation,

7h + 9 = 47

Then we can subtract 9 from both sides to isolate h:

7h + 9 - 9 = 47 - 9

7h = 38

Dividing both sides by 7 gives us:

7h/7 = 38/7

h = 5.43

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The equation that can be used to determine the price, in dollars, of any watermelon based on the number of pounds is p = 0.7w

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Since the price of a watermelon that weights 9.3 pounds is $6.51, the cost per pound of watermelon will be:

= $6.51 / 9.3

= $0.7

Therefore, the equation is p = (0.7 × w) = 0.7w

where P = price

w = pound of watermelon

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Answer: line and line segment

Step-by-step explanation:

The least to greatest or increasing order of the given data set will be 0.1375,0.25,5/8,11/16 thus, option (C) is correct.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

As per the given data set,

The value of 5/8 = 0.625 and 11/16 = 0.6875

Thus, 0.1375 < 0.25 < 5/8 < 11/16

Hence "The least to greatest or increasing order of the given data set will be 0.1375,0.25,5/8,11/16".

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Answer:

the 4rd one

Step-by-step explanation:

The values of a and b in the expression x³ + ax³ + bx - 3 are a = 1 and b = -17

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

x^3+ax^3+bx-3

Rewrite properly

So, we have

x³ + ax³ + bx - 3

The expression has a factor of x - 3

This means that

(3)³ + a(3)³ + b(3) - 3 = 0

So, we have

27 + 27a + 3b - 3 = 0

Evaluate the like terms

27a + 3b = -24

Divide by 3

9a + b = -8

The expression has a remainder of 15 when divided by x + 2

This means that

(-2)³ + a(-2)³ + b(-2) - 3 = 15

So, we have

-8 - 8a - 2b - 3 = 15

Evaluate the like terms

-8a - 2b = 26

Divide by -2

4a + b = -13

So, we have

9a + b = -8

4a + b = -13

Subtract the equations

5a = 5

Divide

a = 1

Recall that 4a + b = -13

So, we have

4(1) + b = -13

So, we have

b = -13 - 4

Evaluate

b = -17

Hence, the values are 1 and -17

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The expression for the situation regarding the wedding singer is 15 + 60x.

The independent variable is the travel expense.

The dependent variable is the amount per hours.

It ie important to note that an expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

Let the number of hours be x

Since the wedding singer is paid $60 per hour plus $15 for travel expenses, the expression will be:

= 15 + (60 × x)

= 15 + 60x

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Answer:

Step-by-step explanation:

directly proportional means same

x=y

512=128

64=y

512/64=8

128/8=16

when x=64 then the value of y=16

Answer:

C

Step-by-step explanation:

given y is directly proportional to x then the equation relating them is

y = kx ← k is the constant of proportion

to find k use the condition when x = 512, y = 128

128 = 512k ( divide both sides by 512 )

[tex]\frac{128}{512}[/tex] = k , that is k = 0.25

y = 0.25x ← equation of proportion

when x = 64 , then

y = 0.25 × 64 = 16

Answer:

Step-by-step explanation:

[tex]2\sqrt{35[/tex]

Answer:

idek

Step-by-step explanation:

Answer:

Juliana uses 1/2 amount of sugar

Emiliano uses 3/2 amount of sugar

The experimental probability that the next man to walk by will have a beard is 2/3

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

Men with beard = 4

Men without beard = 2

This means that

P(Beard) = Beard/Total

Substitute the known values in the above equation, so, we have the following representation

P(Beard) = 4/6

Simplify

P(Beard) = 2/3

Hence the probability is 2/3

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1) The point of intersection is (1, 2) and (-1, 0).

2) The point of intersection is (4, 18).

3) The solutions are 0 and -2.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = x²(x + 1) and g(x) = x + 1

The point of intersection.

f(x) = g(x)

x²(x + 1) = (x + 1)

x² = 1

x = √1

x = ±1

x = 1, f(x) = 2.

(1, 2)

x = -1, f(x) = 0

(-1, 0)

x = 1, g(x) = 2

(1, 2)

x = -1, g(x) = 0

(-1, 0)

This means,

The point of intersection is (1, 2) and (-1, 0).

Now,

f(x) = (x + 5)(x - 2) and g(x) = (2x + 1)(x - 2).

The point of intersection:

f(x) = g(x)

(x + 5)(x - 2) = (2x + 1)(x - 2).

x + 5 = 2x + 1

5 - 1 = 2x - x

4 = x

x = 4

x = 4, f(4) = 9 x 2 = 18

x = 4, g(4) = 9 x 2 = 18

(4, 18)

The point of intersection is (4, 18).

Now,

(x - 3) (x + 5) = -15

The solutions to this equation.

x² + 5x - 3x - 15 = -15

x² + 2x - 15 + 15 = 0

x² + 2x = 0

x(x + 2) = 0

x = 0 and x + 2 = 0

x = 0 and x = -2

The solutions are 0 and -2.

Thus,

1) The point of intersection is (1, 2) and (-1, 0).

2) The point of intersection is (4, 18).

3) The solutions are 0 and -2.

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Answer:

[tex]\textsf{1.} \quad 4x \leq 25[/tex]

[tex]\textsf{2.} \quad x \leq 6.25[/tex]

3.  See attachment.

Step-by-step explanation:

Given information:

If the baseballs cost $4 each and x is the number of baseballs, then 4x represents the total cost of the baseballs.

The maximum amount of money available to spend on the baseballs is $25.

Therefore, the inequality to represent this is:

[tex]\large\boxed{4x \leq 25}[/tex]

Solve the inequality by dividing both sides by 4:

[tex]\implies \dfrac{4x}{4} \leq \dfrac{25}{4}[/tex]

[tex]\implies x \leq 6.25[/tex]

Note:  As x represents the number of baseballs you can buy, and as you cannot buy part of a baseball or negative baseballs, the real solution is 0 ≤ x ≤ 6.

To graph  x ≤ 6.25  on a number line:

To graph  0 ≤ x ≤ 6  on a number line:

Answer:

Average Rate of Change

Functions are relationships that exist between two variables. Graphing them allows us to observe and predict their behavior. The graph of a function is a line or curve where we can determine random values directly and identify a set of results through it.

The rate of change is one of the calculations we can determine from a graph. It is the change of the function per unit. It is deriving from the slope of the line formed in the interval. The formula for determining the rate of change is:

r

c

=

y

2

−

y

1

x

2

−

x

1

P

1

=

(

−

1

,

0

)

P

2

=

(

3

,

12

)

We use the average exchange rate formula:

r

c

=

y

2

−

y

1

x

2

−

x

1

We substitute the values, obtaining:

r

c

=

12

−

0

3

−

(

−

1

)

Solving, we obtain:

r

c

=

12

4

=

3

The average rate of change of

g

when

x

varies from

−

1

to

3

is:

R

c

=

3

The length of the rectangular garden is 28 feet.

Statement represents the mathematical solution to the given word problem.

The statement clearly explains the stated circumstance.

A rectangle is a part of a quadrilateral, whose sides are parallel to each other and equal.

Given that,

The area of the rectangular garden = 448 square feet.

Also, the length of the garden is 4 feet less than the twice of the width.

Let the width of garden is x feet

Then length of garden = 2x - 4

The area of rectangular garden = 448

x (2x - 4) = 448

x (x - 2) = 224

x = 16

The width of the garden is 16 feet.

The length of the garden = 2x - 4 = 2(16) - 4 = 32 - 4 = 28 feet

The required length of the garden is 28 feet.

The mathematical model to the given word problem is statement.

Statement clarify the given condition clearly.

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