factor the expression
7x^2+12x+5

Jermaine's income tax was lowered by $640 as a result of the investment.

Assuming that the defined contribution account is a tax-deferred retirement account, Jermaine can lower his income taxes by the amount of his contribution multiplied by his marginal tax rate. The formula for this tax savings is:

Tax savings = Contribution × Marginal tax rate

Using the given values, Jermaine's contribution to the account is $3,200 and his marginal tax rate is 20%. Substituting these values into the formula, we get:

Tax savings = $3,200 × 0.20 = $640

Therefore, Jermaine can lower his income taxes by $640 by contributing $3,200 to the defined contribution account.

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The  required area of the rectangle is 8 sq. units

Any mathematical statement with numbers, variables, and an arithmetic operation between them is an expression or algebraic expression. For instance, the expression 4m + 5 is one in which the terms 4m and 5 and the variable m are separated by the arithmetic sign +.

From the diagram

Length = 4 units, width = 2 units

Area of rectangle = length×width

Area of rectangle = 4×2

Area of rectangle = 8 sq. units

Thus, required area of the rectangle is 8 sq. units

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Step-by-step explanation:

The 'x's '   ( the domain)  are mapped into two values of 'y' (the range)

Range =   1,6

The simple interest which has the least amount of interest is investment of $ 2000 at 10 % for 3 years

Given data ,

SI is the simple interest, P is the principal amount, r is the annual interest rate, and t is the time in years.

Given that P = 2000, r = 10% = 0.1, and t = 3 years, we can calculate the simple interest as:

SI = 2000 x 0.1 x 3 = 600

Hence , the simple interest earned on an investment of $2000 for 10% at SI for 3 years is $600

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Answer:

The graph should be increasing 2.25 each time

Step-by-step explanation:

Since Oscar buys his lunch in school cafeteria and the cost of 15 school lunches is 33.75

Divide them: 33.75 ÷ 15 =

and will represents the average cost of the lunches in dollar per lunch that is 2.25

Answer:

[tex] {(x - 1)}^{2} + {(y - 2)}^{2} = 5 [/tex]

The length of wire used for the square is 0.25 meters and the length of wire used for the circle is 1 meter. To maximize the total area, the wire should be cut in half, with each piece having a length of 1 meter.

To minimize the total area of both figures and minimize the length of wire used, the wire should be cut in half, giving each piece a length of 1 meter.

For the square frame, we know that each side of the square is equal to the length of wire used to make it, so we can divide the 1 meter of wire in half to get 0.5 meters for each side of the square.

The perimeter of the circle is the length of wire used to make it, so we can use the remaining 1 meter of wire to find the radius of the circle:

2πr = 1

r = 1/(2π)

Using this radius, we can find the circumference of the circle and the length of wire used:

C = 2πr = 1 meter

Therefore, the length of wire used for the square is 0.5 meters and the length of wire used for the circle is 1 meter.

To maximize the total area, we need to cut the wire into two equal pieces, each with a length of 1 meter.

For the square frame, each side will have a length of 0.25 meters, which will give us a total area of 0.0625 square meters.

For the circle, the radius will be 1/(4π) meters, which will give us a circumference of 1/(2π) meters and a total area of π/(16) square meters.

Therefore, to maximize the total area, the wire should be cut in half, with each piece having a length of 1 meter.

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Answer:Let's assume that the number of chewy toys for dogs purchased at Marco's Market is represented by x, and the number of cat collars purchased at Marco's Market is represented by y. Similarly, let's assume that the number of chewy toys for dogs purchased at Sonia's Superstore is represented by a, and the number of cat collars purchased at Sonia's Superstore is represented by b.

The total cost of chewy toys for dogs and cat collars at Marco's Market is given by:

2x + 8y

The total cost of chewy toys for dogs and cat collars at Sonia's Superstore is given by:

4a + 4b

We want to find values of x, y, a, and b such that:

2x + 8y = 4a + 4b

Simplifying the equation, we get:

x + 4y = 2a + b

We also know that the total amount set aside for the purchases is $96. Therefore, we have:

2x + 8y + 4a + 4b = 96

Simplifying the equation, we get:

x + 4y + 2a + b = 48

Now, we can plot the graph of the equation:

x + 4y = 2a + b

To plot the graph, we can rearrange the equation as follows:

4y - b = 2a - x

y = (2a - x + b)/4

We can choose values of x and b, and then calculate the corresponding values of y and a using the equation. For example, let's choose x = 0 and b = 8. Then, we have:

y = (2a - 0 + 8)/4 = (2a + 8)/4 = 0.5a + 2

Similarly, we can choose other values of x and b, and calculate the corresponding values of y and a. We can then plot the points on the graph and join them to get the line representing the equation.

Here is the graph:

Graph

To find the combination of chewy toys for dogs and cat collars for cats that adds up to the same amount and price at both stores, we need to find the point where the line intersects the line representing the equation of the total cost:

x + 4y + 2a + b = 48

We can find this point by solving the two equations simultaneously. However, we can also use the graph to estimate the point. From the graph, we can see that the point of intersection is approximately (12, 6). This means that we can purchase 12 chewy toys for dogs and 6 cat collars at Marco's Market, and 4 chewy toys for dogs and 10 cat collars at Sonia's Superstore, and the total cost would be $48 at both stores.

Step-by-step explanation:

The number of bacteria present at 5 hours is 148.413. The Option B is correct.

In exponential growth, a population's growth rate stays the same regardless of population size which makes the population grow faster and faster as it gets larger.

To get number of bacteria present at 5 hours, we need to evaluate the function [tex]f(5) = e^5.[/tex]

Using a calculator, we get:

[tex]f(5) = e^5\\f(5) = 148.413159103\\f(5) = 148.413.[/tex]

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Note tha given the above trigonometric expression, the solution is

x = 2π/3 or 4π/3

We will start by simplifing the equation by moving all the terms involving sin (x/2) to one side..

2sin (x  /2) = √(3)

Then, we can solve for sin(x/2) by dividing both sides by  two  

sin (x /2) = √(3)/2

This is true when x/2 is π /3 or 2π/3, since these are the values where

sin  (  π/3) = √(3)/2 and

sin  (2π/3) = √(3)/2.

To find the values of x, we multiply these solutions by two

x = 2pi/3 or 4pi/3

Since we need to make sure that these solutions are in the given interval (0, 2π)

 both solutions are in the interval, so our final answer is  

x = 2π/3 or 4 π/3

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Hence, the darkened sector covers an area of roughly [tex]10.55 km^2[/tex] as circle's radius is 7 km, and the shaded sector's central angle is 154 degrees .

The radii of a circle in geometry is the separation between any two points on the circle's circumference. It is frequently used to describe how far apart two points are. One of a circle's most crucial characteristics is its radius, which is taken into account when calculating a circle's circumference, area, and diameter. The distance around a circle that passes through its centre, or its diameter, is equal to half of its radius. Other shapes like spheres, cylindrical, and cones can also be described using the radius. The radius here means the distance from the shape's centre to any point on its perimeter.

given

The following formula must be used to determine a sector's area:

A = (θ/360)[tex]\pi r^2[/tex]

where r is the circle's radius, is pi, or roughly 3.14, and is the sector's centre angle, expressed in degrees.

The circle's radius is 7 km, and the shaded sector's central angle is 154 degrees, according to the provided figure. When these values are added to the formula, we obtain:

[tex]A = (154/360)\pi (7)^2[/tex]

[tex]= 10.55 km^2[/tex]

Hence, the darkened sector covers an area of roughly [tex]10.55 km^2[/tex] as circle's radius is 7 km, and the shaded sector's central angle is 154 degrees .

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The complete question is:-  

154 degree

7 km

Find the area of the shaded sector.

A = __ km2

Answer:

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

The number is basically a combination in the form of:

Hence the possible digits:

So possible telephone number combinations:

The value of the summation notation [tex]\sum\limits^{12}_{i=1} {-25x_i}[/tex] for the 12 measurements 69, -5, 47, -10, -80, 13, 64, -76, -95, 45, 9, 7 is 300

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

69, -5, 47, -10, -80, 13, 64, -76, -95, 45, 9, 7

The summation notation is given as

[tex]\sum\limits^{12}_{i=1} {-25x_i}[/tex]

The summation notation  [tex]\sum\limits^{12}_{i=1} {-25x_i}[/tex] means we multiply each value by -25 and add the results

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

Sum = -25 * (69 - 5 + 47 - 10 - 80 + 13 + 64 - 76 - 95 + 45 + 9 + 7)

Evaluate

Sum = 300

Hence, the value of the summation notation [tex]\sum\limits^{12}_{i=1} {-25x_i}[/tex] for the 12 measurements 69, -5, 47, -10, -80, 13, 64, -76, -95, 45, 9, 7 is 300

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The graph of the linear equation y = (1/2)*x + 3 can be seen in the image at the end.

Here we want to graph the linear equation:

y = (1/2)*x + 3

To graph it we need to find a few points on the line, graph them on a coordinate axis and then draw a line that connects them.

The first point that we can use is the y-intercept, it is what we get when we evaluate in x = 0.

y = (1/2)*0 + 3

The point is (0, 3)

Then we can get other points by evaluating in different values of x, for example, if x = 2

y = (1/2)*2 + 3 = 1+ 3 =4

If x = 4

y = (1/2)*4 + 3 = 2 + 3 = 5

So we have the points (2, 4) and (4, 5)

Now just graph all these points on a cordinate axis and connect them with a line, you will get a graph like the one in the image below.

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Answer:

9.6

Step-by-step explanation:

sin(angle)= opposite/hypotenuse

sin(42°)=6.4/X

X*SIN(42°)=6.4

X=6.4/SIN(42)

X=9.6

Answer:

Step-by-step explanation:

sin(42°)=6.4/X

X*SIN(42°)=6.4

X=6.4/SIN(42)

sin(42°)=6.4/X

X*SIN(42°)=6.4

X=6.4/SIN(42)

X=9.6

The expression of the matrix row operation is 1/4 Row 1 ⇒ Row 1

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

[tex]\left[\begin{array}{cccc}-24&-24&12&20\\-2&3&7&5\\-7&-3&3&-5\end{array}\right][/tex] into [tex]\left[\begin{array}{cccc}-6&-6&3&5\\-2&3&7&5\\-7&-3&3&-5\end{array}\right][/tex]

From the above matrices, we understand that

This means that

row 1 = 1/4(row 1)

This in other words means that

row 1 = (row 1)/4

When these values are evaluated, we have

[tex]\left[\begin{array}{cccc}-24&-24&12&20\\-2&3&7&5\\-7&-3&3&-5\end{array}\right][/tex] into [tex]\left[\begin{array}{cccc}-6&-6&3&5\\-2&3&7&5\\-7&-3&3&-5\end{array}\right][/tex]

This means that we replace -24, -24, 12, and 20 in row 1 with -6, -6, 3 and 5

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If a study of the consultants in a particular industry has determined that the standard deviation of the hourly fee of the consultants is $23.  the 99% confidence interval for the true mean hourly fee of all consultants in the industry is (107.1, 118.9).

The formula for a confidence interval for the population mean is:

CI = X- bar ± z* (σ/√n)

where:

X- bar  = sample mean

z* = z-score for the desired level of confidence (99% in this case)

σ = population standard deviation

n = sample size

Substituting the given values, we get:

CI = 113 ± 2.576 * (23/√100)

Calculating the standard error:

SE = σ/√n = 23/√100 = 2.3

Now we can substitute this value into the formula:

CI = 113 ± 2.576 * 2.3

CI = 113 ± 5.92

So,

Lower limit: 107.1

Upper limit: 118.9

Therefore, the 99% confidence interval for the true mean hourly fee of all consultants in the industry is (107.1, 118.9).

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Answer:

  a) 2:15 pm

  b) 240 km

Step-by-step explanation:

You want to know the time and place where a car leaving at 11:15 a.m. at 80 km/h catches up with a van leaving at 10:30 a.m. at 64 km/h.

The van travels for 11:15 -10:30 = :45, or 3/4 hour, before the car starts. This gives it a distance advantage of (3/4 h)(64 km/h) = 48 km.

The speed at which that distance is reduced is the difference between the car speed and the van speed:

  80 km/h -64 km/h = 16 km/h

The time it takes for the head-start distance to be reduced to zero is ...

  time = distance/speed

  time = (48 km)/(16 km/h) = 3 h

Three hours after the car leaves, it will catch up with the van. That time is ...   11:15 +3:00 = 14:15 = 2:15 p.m.

In 3 hours, the car travels (3 h)(80 km/h) = 240 km.

Note that the van has been traveling 3 3/4 hours, so will have also traveled (3 3/4 h)(64 km/h) = 240 km. The two vehicles need to be in the same place at the same time if they are to pass each other.

__

Additional comment

The attached graph shows the two vehicles will have traveled 240 km when they mean at 2:15 pm. The horizontal axis is hours after midnight. The vertical axis is kilometers from town X. The relation graphed is distance = speed × time.

The required value of y is 14 units for the given right triangle.

14. It is required to find the value of y.

According to the attached figure, we have a right triangle that has:

Length of AB = x units

Length of BC = 7 units

Length of AC = y units

∠ABC = 90°

∠BAC = 30°

As per the sine ratio, it can be written as follows:

sin 30° = BC/ AC

1/2 = 7/y

Apply the cross-multiplication, and we get

y = (7)(2)

y = 14 units

Therefore, the required value of y is 14 units for the given right triangle.

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The minimum value of the data set is 10.5.

Box plots are an effective graphical tool used to display a summary of a dataset. They provide a visual representation of the minimum and maximum values, quartiles, and outliers of the data. They are commonly used in statistics and can provide valuable insights into a dataset.

Now, let's consider the box plot in question. The box plot is labeled "Volunteer Service Hours" and it has four quartiles, each marked by a horizontal line. The first quartile (Q1) is marked at 13, the second quartile (Q2) is marked at 16.5, the third quartile (Q3) is marked at 20, and the fourth quartile (Q4) is marked at 23, with the end of the box extending to 27.

The minimum value of the data set can be found at the lower whisker of the box plot.

The lower whisker represents the minimum value that is not an outlier.

In this box plot, we do not see any outliers, so the minimum value of the dataset is represented by the lower end of the whisker, which is located at 10.5.

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The given ratio 1:0.2:0.75 can be expressed in its simplest form as 5:1:3/4.

To express 1:0.2:0.75 in its simplest form, we need to find the common factor that can divide all the numbers in the ratio without leaving a remainder.

First, we can convert 0.2 to a fraction by dividing 2 by 10, which gives us 1/5. Thus, the ratio can be rewritten as

1:0.2:0.75

= 1:2/10:0.75

= 1:1/5:0.75.

To find the common factor, we can convert all the numbers to fractions with a denominator of 5. We do this by multiplying the first number by 5/5, the second number by 1/1, and the third number by 5/4.

This gives us,

5/5:1/5:15/20.

Next, we can simplify the ratio by dividing all the numbers by their greatest common factor (GCF). In this case, the GCF is 1/5.

Dividing all the numbers in the ratio by 1/5 gives us,

5:1:15/4.

Finally, we can simplify 15/4 by dividing both the numerator and denominator by 5. This gives us 3/4. Thus, the final simplified ratio is 5:1:3/4.

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Answer:

37

Step-by-step explanation:

We are given the system of equations:

y = 4x^2 + 3x - 5

y = 2x^2 + x + 7

We can set the two equations equal to each other to get:

4x^2 + 3x - 5 = 2x^2 + x + 7

Simplifying, we get:

2x^2 + 2x - 12 = 0

Dividing both sides by 2, we get:

x^2 + x - 6 = 0

Factoring the left-hand side, we get:

(x + 3)(x - 2) = 0

Therefore, the solutions are x = -3 and x = 2.

To find the corresponding y-coordinates, we can plug these values of x into either of the original equations. Using the first equation, we get:

y = 4(-3)^2 + 3(-3) - 5 = 16

and

y = 4(2)^2 + 3(2) - 5 = 21

Therefore, the sum of the y-coordinates of the solutions is:

16 + 21 = 37

Answer: 37.

Answer:

C. (–3, –7)

Step-by-step explanation:

We can check each ordered pair by substituting the values of x and y into the equation y = x - 4 and see if the equation is true.

A. (-3, 7)

y = x - 4

7 = -3 - 4

7 = -7

This is not true, so (-3, 7) is not a solution.

B. (3, -7)

y = x - 4

-7 = 3 - 4

-7 = -1

This is not true, so (3, -7) is not a solution.

C. (-3, -7)

y = x - 4

-7 = -3 - 4

-7 = -7

This is true, so (-3, -7) is a solution.

D. (3, 7)

y = x - 4

7 = 3 - 4

7 = -1

This is not true, so (3, 7) is not a solution.

Therefore, the only ordered pair that is a solution of y = x - 4 is (–3, –7).

Using the relationship of distance, time and speed, the speed of the boat in still water is 8mi/hr

To determine the speed of the boat in still water, we can write an equation to represent this.

The speed as it travels upstream = x - 2

The speed as it travels downstream = x + 2

The total distance travelled by the boat = 15 + 15 = 30mi

Let's write an equation to represent this;

15/(x - 2) + 15/(x + 2) = 4

simplifying this;

15(x + 2) + 15(x - 2) = 4(x - 2)(x + 2)

15x + 30 + 15x - 30 = 4x² - 16

30x = 4x² - 16

4x² - 30x - 16 = 0

Solving for x;

x = -0.5, 8

But since the speed can't be negative, the speed is 8 mi/hr

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The values that fit in the solution are -4, -3, -2, -1 , 0

g > - 5

Inequalities are described as expressions that are used to represent an unequal relationship between numbers or variables.

They are represented with the symbols;

From the information given, we have that;

4 - 5g > 39

collect the like terms, we get;

-5g > 39 - 4

subtract the values

-5g > 35

Divide by the coefficient of g, we get;

g > -5

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Answer:

P = $1341.53

Step-by-step explanation:

A(t) = amount in t years

P = Principal (original investment)

r = annual interest rate (in decimal form)

n = number of times that interest is compounded each year

A(t) = P(1 + r/n)nt

Substitute in the given values:  2000 = P(1 + 0.04/12)12(10)

2000 = P(1.490832682)

P = $1341.53

Answer: 18 feet.

Step-by-step explanation:

Average of bases = (22 + 14.75) / 2

Average of bases = 18.375

18.375 to the nearest tenth is = 18ft

Therefore, the average of the two bases of the trapezoid is 18 feet.

Answer: IN ORDER FROM TOP LEFT OVER

Step-by-step explanation:

1. Example

2. Already correct

3. 43

4. 82

5. Supplementary

6. 68

7. 33

8. Adjacent (could be wrong)

9. 51

10. 128

11. 54

12. Complimentary

13. Parallel

14. 29

15. 117

HOPE THIS HELPS. I MAY HAVE GOTTEN 1 OR 2 WRONG.

Answer: C {m | m  > 2}

Step-by-step explanation:

write the number in exponential form with the base of 2

2^3m-4 > 2^2

compare the exponents = 3m-4 >2

move the constant to the right and then change the sign

3m> 2+4  add

3m>6 divide

m>2

The letters "L" and "X" both contain adjacent angles, as adjacent angles are angles that share a common vertex and side. In both letters, there are two angles that share a vertex and a side.

What is Acute angle ?

An acute angle is an angle that measures between 0 and 90 degrees. In other words, an acute angle is an angle that is smaller than a right angle, which measures exactly 90 degrees.

The letter "A" contains an acute angle, as the angle between the two lines that form the letter is less than 90 degrees.

None of the letters A, E, L, or X contain vertical angles, as vertical angles are formed by two intersecting lines and none of these letters contain intersecting lines.

Therefore, The letters "L" and "X" both contain adjacent angles, as adjacent angles are angles that share a common vertex and side. In both letters, there are two angles that share a vertex and a side.

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