A triangle has coordinates F(−2, 3), G(−4, 1), and H(−2, −2). The triangle is translated and its image has coordinates F’(0, 0), G’(−2, −2), and H’(0, −5). What is the correct rule for the translation? (x, y) Right-arrow (x + 2, y + 3) (x, y) Right-arrow (x + 2, y – 3) (x, y) Right-arrow(x – 2, y + 3) (x, y) Right-arrow (x – 3, y+ 2) Use the figure to identify the correct rule for the translation. (x, y) Right-arrow (x – 3, y + 4) (x, y) Right-arrow (x + 3, y – 4) (x, y) Right-arrow (x – 4, y + 3) (x, y) Right-arrow (x + 4, y – 3)

Answer:

5 cookies and 4 brownies

Step-by-step explanation:

First, let's assign variable for cookies and brownies:

x= cookies

y= brownies

Now, let's create an equation with the information given to us:

[Note: "#of brownies + 8" equals the number of cookies because, in the question, we are told He bought 8 more cookies than brownies ]

cost of a brownie * #of brownies +  cost of a cookie * (#of brownies + 8 ) = $7.50

1.25y + 0.5x = 7.5

Since we want to solve the problem graphically, let's solve our equation for y, so it can be graphed:

1.25y + 0.5x = 7.5   [Subtract 0.5x from both sides]

1.25y = -0.5x + 7.5   [Divide both sides by 1.25 so we just get y]

y = -0.4x + 6

This equation will be used to determine what we can buy at the bakery with $7.50.

Now, we will graph the equation (see attached image). What we will see is that as x increases, y decreases. This makes sence, since the number of brownies (y) you can buy with your budget decreases as the number of cookies (x) you buy increases. Lastly, since we can't buy a fraction of a cookie, we want to find a coordinate on the line that has both a natural [see definition if confused] x and y value. To do this, we will look at the graph and see if a x value of 1 gives us a natural y value. If not, we go on to 2 and see if it gives us a natural y value. This continues until you find both a natural x and y value. This will happen at x=5 and y=4. This answer tells us that, with $7.50, Qasim and his children bought 5 cookies and 4 brownies.

*Natural number: Positive, whole numbers

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Answer:

The future value of the annuity is $14,170.

The total amount invested is $39,000.

The interest earned is $14,170 - $39,000 = -$24,830

Step-by-step explanation:

The future value of the annuity can be calculated using the formula:

FV = P * (1 + r)^n

where FV is the future value, P is the annual payment, r is the annual interest rate, and n is the number of years.

In this case, the annual payment is $13,000, the annual interest rate is 3%, and the number of years is 3. So, the calculation is:

FV = $13,000 * (1 + 0.03)^3

FV = $13,000 * 1.09

FV = $14,170

So, the future value of the annuity is $14,170.

How much was invested?

The annual payment is $13,000. We multiply that by the number of years of the investment, 3 years. The total amount invested is $39,000.

How much interest was earned?

We can calculate the interest earned by subtracting the total amount invested from the future value.

The interest earned is $14,170 - $39,000 = -$24,830

So, the future value of the annuity is $14,170, the total amount invested is $39,000 and the interest earned is -$24,830.

perpendicular means the opposite inverse of a slope

so the slope of the other line is -7/2

y = -7/2x + b

from the given point (-4,6)

6 = (-7 *4)/2 + b

6 = -14 +b

b = 20

y = -7/2x + 20

Answer:

x=$3059.00

Step-by-step explanation:

To solve this equation, we need to use the properties of exponential functions and perform some algebraic manipulations. First, we can simplify the right-hand side of the equation by combining the constant terms and the exponent on the x:

$4001.035 = $105 + x(1.03)3 + x(1.032)

Next, we can combine the x terms on the left-hand side by multiplying them out and combining the exponents:

x(1.03)3 + x(1.032) = x(1.03)3 + x(1.03)(1.03) = x(1.03)4

Now we have:

$4001.035 = $105 + x(1.03)4

To solve for x, we need to isolate it on one side of the equation. We can do this by subtracting 105 from both sides:

$3900.035 = x(1.03)4

Next, we divide both sides by 1.03^4

x = $3900.035 / (1.03)^4

x = $3,059.00

x= $3059.00 (rounded to the nearest cent)

Answer:

The dimensions of the garden are not provided in the question, so it is not possible to determine the area for which Jane needs to buy mulch. Without knowing the dimensions, there is not enough information to answer the question.

Step-by-step explanation:

Due to length restriction, we kindly invite to check the explanation for further details on profit and risk minimization.

In this problem we find the case of a person that invests a lot of money, distributed in two investments. We need to determine how much money must be invested in each plan to earn a desired return:

R = (C - c) · (r₁ / 100) + c · (r₂ / 100)

Where:

Part A - If we know that R = 9300, C = 91000, r₁ = 10 and r₂ = 11, then the amount invested in the most risky investment:

9300 = (91000 - c) · (10 / 100) + c · (11 / 100)

930000 = (91000 - c) · 10 + c · 11

930000 = 910000 - 10 · c + 11 · c

c = 20000

The person must invest $ 20000 in the least risky investment and $ 71000 in the most risky investment.

Part B - The use of two accounts gives a reasonable equilibrium between profit and risk minimization.

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The graph of the linear function y = -3x is attached below.

A linear function is a type of mathematical function that describes a straight line relationship between two variables. It is defined by an equation of the form:

y = mx + b

where y is the dependent variable (output), x is the independent variable (input), m is the slope of the line, and b is the y-intercept (the point where the line crosses the y-axis).

In a graph, a linear function will always be a straight line. The slope (m) tells you how steep the line is, and the y-intercept (b) tells you where the line crosses the y-axis. The slope-intercept form is y = mx + b

The linear function given is y = -3x

From the table of values;

f(x) = -3x

f(-1) = -3(-1)

f(-1) = 3

f(0) = -3(0)

f(0) = 0

f(1) = -3(1)

f(1) = -3

Plotting this on a graph, our slope is -3 and since it doesn't have a            y - intercept, the graph passes through the origin.

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According to the information, 11 boxes and 2 units are required to complete the order.

To find the number of boxes and units required to complete the order we must perform the following procedure:

If we know that each box can hold 8 units and the order is for 90 units, then we divide the total number of units by the number of units per box.

So we know that we are going to need 11 boxes to complete part of the order. Now, to know how many units we have left without storing we must multiply 8 * 11 and subtract the result from 90:

According to the above, the number of boxes would be 11 and the number of units would be 2.

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An Inequality for the statement is -4y ≤ -2/3.

Inequality refers to a relationship that makes a non-equal comparison between two numbers or other mathematical expressions.

Given statement,

Number y multiplied by -4 is no more than -2/3

which means

- 4 y is less or equal to -2/3 and can be written as inequality

-4y ≤ -2/3

Hence, -4y ≤ -2/3 is the Inequality for the given statement.

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Answer:

  No

Step-by-step explanation:

You want to know if -8 is irrational.

A number is irrational if it has a decimal fraction part that does not terminate and does not repeat.

If you can describe all of the digits of the number explicitly without resort to functions or symbols, the number is not irrational.

  -8 is not irrational

Given: f(x)=  4x 2 +1 / x

​When we differentiate both sides in relation to x, we obtain

f ′ (x)=  x(8x)−(4x² +1)/x² = 4x² −1 / x²

​(a) To improve function.

f  (x)≥0

⇒ 4x²-1/ ≥0

⇒ 4x²- 1 ≥ 0

⇒ (2x-1) (2x+1) ≥0

⇒ x ≥ 1/2 or x≤ -1/2

So, f(x) is increasing function on (-∞, -1/2] ∪ [1/2,∞)

(b) for decreasing function,

⇒ 4x²-1/x² ≤0

⇒ 4x²-1 ≤0

⇒(2x - 1) (2x+1)≤0

⇒ x ≤ 1/2 or x≥ -1/2

so, f(x) is decreasing on [-1/2, 1/2]

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​

Between the ages of 14 and 16, g(x) increases by a factor of 64/56 = 1.1429.

A defined range of values inside a piece of data is known as an interval. It measures the spread of the data and is defined as the difference between the maximum and minimum values of the data set. Intervals can be applied in many different contexts, from tracking the evolution of data distribution to spotting trends. Additionally, outliers and unusually high or low values in a data collection can be found using intervals. In statistics, interval data are frequently used to quantify data variability.

Divide the value of g(16) by the value of g to find the factor by which g(x) increases across the range of 14 to 16. (14).

G(14) has a value of 56, and G(16) has a value of 64.

Therefore, 64/56 = 1.1429 is the factor by which g(x) increases between 14 and 16.

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Using mathematical operations, since 1/3 of the sundaes Lisa is making are mint, and 1/2 of the remaining (or 1/3) are chocolate, the number of vanilla sundaes is 10.

The basic mathematical operations are addition, subtraction, division, and multiplication.

Mathematical operations can be applied to any mathematical problem to find their solutions.

The total number of Sundaes Lisa is making = 30

The proportion of the sundaes that are mint ice cream = 1/3

The proportion of the sundaes that are = 1/3 (1/2 of 2/3)

The vanilla proportion = 1/3 (1 - 1/3 - 1/3)

The number of sundaes that will be vanilla = 10 (30 x 1/3)

Thus, determining the fractional values using mathematical operations, Lisa is making an equal number of mint, chocolate, and vanilla ice cream.

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The equations of the tangent to the curve when x = 1 are;

[tex]y = 5\frac{1}{3}\cdot x - 1\frac{1}{3}[/tex]

[tex]y = 1\frac{1}{3} - \frac{1}{3} \cdot x[/tex]

The tangent to a curve at a point, is the line that best fits the rate of change of the curve at the specified point.

The equation to be differentiated in the question is; y² - 5·x·y + 4·x = 0

The derivative of the above equation using the differentiation of a product is as follows;

2·y·y' - (5·y + 5·x·y') + 4 = 0

2·y·y' - 5·y - 5·x·y' + 4 = 0

2·y·y' - 5·x·y' - 5·y + 4 = 0

y'·(2·y - 5·x) - 5·y + 4 = 0

The slope of the curve, therefore is; y' = (5·y - 4)/(2·y - 5·x)

At x = 1, we get;

y² - 5·y + 4 = 0

(y - 4)·(y - 1) = 0

At x = 1, y = 4 and y = 1

Therefore;

At (1, 4), y' = (5 × 4 - 4)/(2 × 4 - 5 × 1) = 16/3

The equation of the tangent is therefore;

y - 4 = (16/3)·(x - 1)

y = 16/3)·x - 16/3 + 4 = 16/3)·x - 4/3

The tangent at (1, 4) is; y = (16/3)·x - 4/3 = (5 1/3)·x - 1 1/3

At (1, 1), y' = (5 × 1 - 4)/(2 × 1 - 5 × 1) = 1/-3 = -1/3

The equation is therefore;

y - 1 = (-1/3)·(x - 1)

y = (-1/3)·x + 1/3 +  1 = 4/3 - (1/3)·x

The equation of a second tangent is; y = 4/3 - (1/3)·x = (1 1/3) - (1/3)·x

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16.25 percent the total number of students on the honor roll decreased.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, last year at a certain high school, there were 140 boys on the honor roll and 100 girls on the honor roll.

This year, the number of boys on the honor roll decreased by 25% and the number of girls on the honor roll decreased by 6%.

So, the number of boys = 140 - 25% of 140

= 140 - 0.25×140

= 140 - 35

= 105

The number of girls = 100 - 6% of 100

= 96

Total number of students last year = 140+100

= 240

Total number of students this year = 105+96

= 201

Difference = 240-201

= 39

Now, percentage decrease = 39/240 ×100

= 0.1625×100

= 16.25%

Hence, 16.25 percent the total number of students on the honor roll decreased.

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Answer:

B

Step-by-step explanation:

9x² - y² = 1

use the power rule to differentiate

[tex]\frac{d}{dx}[/tex] (a[tex]x^{n}[/tex] ) = an[tex]x^{n-1}[/tex]

[tex]\frac{d}{dx}[/tex] (y² ) = 2y [tex]\frac{dy}{dx}[/tex]

[tex]\frac{d}{dx}[/tex] ( constant ) = 0

differentiate both sides with respect to x

9 × 2x - 2y [tex]\frac{dy}{dx}[/tex] = 0 , that is

18x - 2y[tex]\frac{dy}{dx}[/tex] = 0

Answer:

4x - 7

Step-by-step explanation:

The x represents Bob's age since, we don't know what it is, I put it as a variable.

2x      This represents Jeff who is 2 times Bob's age.

x - 7    Peter is younger than Bob by 7 years so we need to take away 7                    from Bob's age

2x + x - 7 + x    This would be the expression

4x - 7                Now just combine the like terms. We don't have Bob's age so the expression will stay like this.

Answer:The missing length can be found using the formula for the area of a triangle, which is:

Area = (base * height) / 2.

We know the base is 18.7 inches and the area of the shaded region is 152.405 in^2.

So, the height can be found using the formula:

152.405 = (18.7 * height) / 2

Solving for height:

height = 2 * 152.405 / 18.7

height = approximately 12.67 inches.

$120.00 increased by 20% is $144.00

By the synthetic division method, the polynomial x³ - 2x - 8 dividing by x - 2 will get a remainder -4.

Given the polynomial,

x³ - 2x - 8

dividing a polynomial by x - 2

Solution will be :

Coefficients are required for Synthetic Division.

As a result, the coefficients are :

1, 0, -2, -8

as well as we have x-2

2   1   0  -2   8

          2   4    4              

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

      1    2   2   -4

By synthetic division, the remainder is now -4.

Substituting  the polynomial in x = 2 the Remainder theorem yields the required remainder.

  = 2³ -2 x 2 - 8

  = 8 -4 -8

  = -4

Which is equivalent to synthetic division. Therefore the correct division is option B.

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The role of the media in a democracy is essential for a free and informed society.

Democracy is a form of government in which power is held by the people through their elected representatives. It is based on the principle of political equality and rule of law, where all citizens have an equal say in the decisions that affect their lives. It is a system of government in which citizens have the right to vote, stand for office, and participate in decision-making processes that shape their communities and the nation as a whole.

The media acts as a watchdog for the government, keeping them accountable and ensuring that the people are aware of the decisions being made. It also provides a platform for citizens to express their opinions and to discuss important issues. Additionally, the media can help to educate the public on important topics, such as politics, economics, and social issues. This helps to ensure that citizens are well informed and can make informed decisions when voting or engaging in other forms of political participation.

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The simplified form of the expression is 4x² - 3x + 2

Answer:

[tex]4x^{2} - 3x + 2[/tex]

Step-by-step explanation:

[tex](2x^{2} + x) - (-2x^{2} + 4x - 2)\\\\2x^{2} + x + 2x^{2} - 4x - 2\\\\\\4x^{2} -3x+2[/tex]

Answer:

80 months

Step-by-step explanation:

If the present monthly heating costs average $300, but the insulation is expected to reduce heating costs by 10%, then there will be a monthly saving of 10%:

[tex]\implies \rm Monthly\;saving=10\%\;of\;\$300 =\dfrac{10}{100} \times \$300=\$30[/tex]

To calculate how many months it will take to recover the cost of the insulation, divide the cost of installing the insulation by the monthly saving:

[tex]\implies \rm Number\;of\;months=\dfrac{\$2400}{\$30}=80[/tex]

Therefore, it will take 80 months to recover the cost of the insulation.

Answer:

80 months

Step-by-step explanation:

The expected monthly savings from the insulation are: $300 × 10% = $30.

So, the number of months required to recover the cost of the insulation, $2400, is $2400/$30 = 80 months.

From the given triangle, the value of sin Θ is 3/√34.

To find the value of sin Θ, we have to know the definition of sin Θ first. Sin Θ can be calculated using formula of:

sin Θ = the front side : the hypotenuse

Based on the given triangle, we need to find the lenght of hypotenuse first to be able to find the value of sin Θ. The hypotenuse of the given triangle is:

h = √(5² + 3²)

h = √(25 + 9)

h = √34

The exact value of sin Θ is:

sin Θ = 3 / √34

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Applying the exterior angle theorem, m<JKL = 22 degrees.

According to the exterior angle theorem, the following equation is created to find the value of x:

5x - 3 = x - 1 + 2x + 8

Combine like terms:

5x - 3 = 3x + 7

5x - 3 - 3x = 3x + 7 - 3x

2x - 3 = 7

Add 3 to both sides

2x = 10

x = 5

Find the measure of m<JKL (exterior angle):

m<JKL = 5x - 3

Plug in the value of x:

m<JKL = 5(5) - 3 = 22 degrees.

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The quadratic regression in this case is y = 126.01x2 - 312.04x + 888.88.

An analysis tool called quadratic regression is implemented to identify the parabola equation that perfectly matches a given collection of data. Finding the equation of the straight line that most closely matches a collection of data is the goal of this sort of regression, which is an expansion of simple linear regression.

Step 1:  Input the data sets into the graphing calculator.

Step 2: Choose "Scatter Plot" from the graphing calculator's interface.

Step 3: Choose "Quadratic Regression" from the graphing calculator's toolbar.

Step 4: The calculator will create the equation y=ax2+bx+c, where a, b, and c are constants.

Step 5: Round the constants to the hundredths place, and the best-suited quadratic model's equation will be: y = 0.06x2 - 3.12x + 4.00.

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10.44 Percent of increase in the price of a basketball .

A percentage is a number or ratio that is expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to denote it. A percentage is a dimensionless number; there is no specific unit of measurement for it.

By divided the number by the entire value and multiplying the outcome by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.

The price of basketball increased = $18.50 -$16.75 = 1.75$

Now the percent of increase in the price= 1.75/16.75×100

= 10.44%

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Answer:

  B.  y = 5x

Step-by-step explanation:

You want to find the proportional relationship among the answer choices.

The hint shows you the proportional relationship is expressed by an equation that has a multiplier for x, with no added constants, and no exponents.

You find the answer to this question by matching the answer choices to the given form. There is only one match:

  y = 5x

Answer: The answer is 6.75

Step-by-step explanation:

I did the math :b

The quantity of cells that will be in the culture on the 8 day assuming the number of cells is growing at an exponential rate would be = 128,000 cells.

An exponential rate of growth is defined as the increase in the population of an object under study over a period of time.

The number of cells the scientist started with = 1,000 cells

The number of cells in 4th day = 64,000

Therefore the rate of growth of cells per day;

= 64000/4

= 16,000

Therefore on the 8th day, the number of cells would be = 8×16000 = 128,000 cells.

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Answer:

Step-by-step explanation: