5. Zach had a salary of $75,000 last year. He also received $4,500 in interest income from a CD he opened a few years ago. He contributed $4,000 to an IRA and had to move to another state for his new job. His moving expenses were $5,000. He is an unmarried man, with no dependents, and claims himself as an exemption. Standard deduction is $5700 for single, and exemption rate is $3,650 per exemption. What was Zach’s gross income?

⇒[tex]=(y+3)(y+7)\\=y(y+7)+3(y+7)\\=y^{2} +7y+3y+21\\=y^{2} +10y+21[/tex]

Attached is the solution in detail

The radical form of the expression  (5ab)[tex]^\frac{3}{2}[/tex]  is √(125 a³b³).

Simply put, simplifying a radical eliminates the need to find any more square roots, cube roots, fourth roots, etc. when expressing it in its simplest radical form. Additionally, it entails eliminating any radicals from the denominator of a fraction.

The sign used to represent the square root or nth root. Square-root-containing expressions are known as radical expressions.

Radical equation  = b[tex]\frac{m}{n}[/tex]  

= [tex]\sqrt[n]{b^m}[/tex]

So,

(5ab)[tex]^\frac{3}{2}[/tex] = [tex]\sqrt[2]{5^3}[/tex]

[tex]\sqrt[2]{5^3}[/tex] a³ b³

5³ = 125

√(125 a³b³)

The radical form of the expression  (5ab)[tex]^\frac{3}{2}[/tex]  is √(125 a³b³).

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The inequality that shows the least amount of money she needs to deposit to avoid a fee is 585.43 - 302.05 + x ≥ 300

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

Let x represent the least amount of money Keisha needs to deposit to avoid a fee. Keisha has $585.43 in her checking account and must maintain a balance of $300 to avoid a fee. She wrote a check for $302.05 today, Hence:

585.43 - 302.05 + x ≥ 300

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The equation for the line that is parallel to the given line and goes through the point (-8 2), is y = 3x + 26. See the explanation below.

Recall that the equation for the line is always given as:

y = mx + b

Where m is the slope.

Assuming that you have a line  y = 3x + 2

The line parallel to this line but intersecting the point (-8,2) is found by using y = mx + b and solving for b

m = 3; x = -8; and y = 2

b = y - mx

b = (2) - (3) (-8)

b = 26

Hence the equation for the line that is parallel to the given line going through point (-8, 2) is
y = 3x + 26

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Full Question:

Find the equation in slope-intercept form of the line y= 3x + 2 that passes through the point (-8,2) and is parallel to the line.

In the right triangle, the value of y is 3√2

The right triangle represents the given parameter

On the right angle, the value of y can be calculated using the following sine rule

This is represented as

sin(angle) = Opposite/Hypotenuse

So, we have

sin(45) = y/6

Make y the subject

y = 6 * sin(45)

Evaluate

y = 3√2

Hence, the value of y in the right triangle is 3√2

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Based on the length of the object in real life, and the scale factor used, the length of the object on the scale drawing in inches can be found to be 9.17 inches

The scale factor tells us how the measurement of an object on a drawing relates the measurement of the same object in reality.

For a scale factor of 1 inch to 6 feet, it means that every inch of an object on a drawing, would be 6 feet of the same object in real life.

For this object that is in a drawing with a scale factor of 1 inch to 6 feet, the length in real life of 55 feet tells us that the length in the drawing is:

= Number of feet in real life / Number of feet in scale factor per drawing

= 55 / 6

= 9.17 inches

Full question is:

A scale factor of 1 inch to 6 feet is used. An object in real life is 55 feet long. How many inches long should it be in the scale drawing?

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The equation of the line that passes through the graph is y + 2 = -3/2(x - 2)

The graph represents the given parameter

From the graph, the points are given as

(0, 1) and (2, -2)

Calculate the slope of the points using

Slope = (y₂ - y₁)/(x₂ - x₁)

Rewrite as

m = (y₂ - y₁)/(x₂ - x₁)

This means that

Slope = m

So, we have the following representation

m = (-2 - 1)/(2 - 0)

Evaluate

m = -3/2

The equation of the line is then calculated as

y = m(x - x₁) + y₁

Where

(x₁, y₁) = (2, -2)

m = -3/2

So, we have

y = -3/2(x - 2) - 2

Add 2 to both sides

y + 2 = -3/2(x - 2)

Hence, the equation of the line is y + 2 = -3/2(x - 2)

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The recursive formula of the arithmetic sequence is:

xₙ = n*4 + 13

With that we can see that x₁₁ = 57

Here we know that the first elements of the sequence are:

17, 21, 25, 29, ...

To find the common difference, d, we take the difference between any two consecutive elements, so we have:

c = 21 - 17 = 4

Then the recursive formula for the n-th term is:

xₙ = n*4 + d

The first element x₁ is 17, so we will have:

17 = 1*4 + d

17 - 4 = d = 13

The recursive formula is:

xₙ = n*4 + 13

b) the eleventh term of the sequence is given by replacing n in the above formula by 11.

x₁₁ = 4*11 + 13 = 44 + 13 = 57

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The area hexagon using Lin's and Andre's method is:

By Lin's method = 93.48inch^2

By Andre's method = 93.53 inch^2

What is Mensuration ?

The field of mathematics known as mensuration explores how to measure geometric objects and their attributes, such as length, volume, shape, surface area, lateral surface area, etc.

By Lin's method

He parted the hexagon into six equilateral triangle

So, area of equilateral triangle = √3/4 × (side)^2

Since the given side = 6inch

Therefore,

                area of equilateral triangle = √3/4 × (6)^2

                                                              =√3/4 × 36

                                                              = √3 x 9

                                                              = 1.732 x 9

                                                              = 15.58inch^2

The area of hexagon will be = 15.58 x 6

                                               = 93.48inch^2

Now, By Andre's method

he parted two triangle and one rectangle

The triangle has two equal side that means its an isosceles triangle

Area of isosceles triangle using only sides = ½[√(a^2 - b^2/4) × b]

given,

base = 10.4 inch

side = 6 inch

Area of isosceles triangle using only sides = ½[√(a^2 - b^2/4) × b]  

                                                                       = ½[√(6^2 - 10.4^2/4) × 10.4]

                                                                       = ½[√(36 - 108.16 /4) ×10.4]

                                                                       = ½[√(36 - 27.04) × 10.4]      

                                                                       = ½[√(8.96) × 10.4]

                                                                       = ½[2.99 × 10.4]  

                                                                       = 15.56inch^2

for two triangles the area will be =    15.56 x 2

                                                      = 31.13 inch^2

Now, area of rectangle = length x width

where,

Length = 10.4 inch

Width = 6 inch

So,

     area of rectangle = 10.4 x 6

                                   = 62.4 inch^2

Then, The area of hexagon will be = area of rectangle + area of two triangle

                                                          = 62.4 inch^2 + 31.13 inch^2

                                                          = 93.53 inch^2

Hence, by both methods the area from Lin's method = 93.49 inch^2

and by Andre's method = 93.53 inch^2

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Answer:

y = x in the slope intercept form

y - 2 = 1(x -2) in the point-slope form of a line

Step-by-step explanation:

Perpendicular slopes are opposite reciprocals of each other.  So the perpendicular slope would be 1.

We could write this in the point slope form of a line and the answer would be:

y - 2 = 1(x -2)  This would be the point slope form of a line.

If you want your answer in the slope intercept form

y -2 = 1(x-2)

y - 2 = x - 2  Add two to both sides

y = x

WHAT DO WE KNOW ABOUT PERPENDICULAR LINES ?

IS THAT WHEN THEIR GRADIENTS ARE MULTIPLIED THEY GIVE A PRODUCT OF -1.

TO FIND THE GRADIENT OF THE LINE PERPENDICULAR TO THE LINE WITH SLOPE/GRADIENT -1 WE CAN SAY

[tex]m1 \times m2 = - 1 \\ - 1 \times m2 = - 1 \\ m2 = 1[/tex]

THIS MEANS THAT THE GRADIENT OF THE NEW LINE IS 1

the general equation of the straight line is y=mx+c

[tex] - 2 = 1(2) + c \\ - 2 = 2 + c \\ c = - 2 - 2 \\ c = - 4[/tex]

This means that

[tex]y = 1x - 4 \\ simply \\ y = x - 4[/tex]

The probability of at least two purchasing an electric dryer is 0.572 and the probability of at least one type of purchase is 0.879.

What are examples and probability?

a dryer

           1 - 0.428  = 0.572

P(all 5 for purchasing gas) = 0.116

P(all 5 electrical purchases)  = 0.005

P(at least 1 of each type purchased) = 1 -(P(only 1 type is purchased))

= 1 - [ P(all 5 for purchasing gas) + P(all 5 electrical purchases)

= 1 - 0.116 - 0.005

= 1 - 0.121

= 0.879

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The length of the other parallel side = 7.5 cm

what is trapezium?

Trapezium is the quadrilateral whose only one pair of side is parallel.

as we know ;

       AREA OF TRAPEZIUM=1/2*(sum of parallel side)*(height)

       given:- one parallel side = 10 cm

                    height = 16 cm

                    Area= 140 cm

         Assume:-

                    other parallel side =x cm

   so,

           140=1/2*(10+x)*16

           140*2/16=10+x

           280/16=10+x

           35/2=10+x

           17.5-10=x

           x= 7.5cm

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When Walt mixes fruit punch for a party, the total liquid measure of the punch is 53 pints.

As given in the question,

Conversion factor as follows:

1 gallon = 8 pints.

1 quart = 2 pints.

Walt is mixing fruit punch for a party

Convert all the units to pints we get,

Walt combines 1 gallon 2 quarts 3 pints of orange juice, which is equivalent to 15 pints

He also combines 1 gallon 3 quarts 7 pints of pineapple juice, which is equivalent to 21 pints

He then combines 1 gallon 3 quarts 3 pints of ginger ale, which is equivalent to 17 pints.

Total measure of the punch = 15 + 21 + 17 = 53 pints.

Therefore, when Walt mixes fruit punch for a party, the total liquid measure of the punch is 53 pints.

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The chance that each number will occur when a randomly generated list of numbers, generates the number from 0 to 6 is 1/7.

Probability is a field of mathematics that focuses on determining the possibility that an event will occur. The proportion of favorable outcomes to all other outcomes determines an event's chances or probability.

Given:

A randomly generated list of numbers from 0 to 6.The total number are 7 (0,1,2,3,4,5,6).

The chance that each number will occur is,

P = 1/7

Therefore, the chance that each number will occur when a randomly generated list of numbers, generates the number from 0 to 6 is 1/7.

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Answer:

Step-by-step explanation:

The option that is most suitable for tabular data will be provided by-

Jasim's last week's total pay was £286.2.

Tabular data is data presented in the form of rows and columns.

Here,

Total time for which Jasim works last week = 30 hours

Time for which Jasim works at the weekend = 12 hours

Time for which Jasim works at the weekdays = (30 - 12) hours

                                                                           = 18 hours

Jasim's pay during weekdays = £8.70

Jasim's pay during weekends = £10.80 per hour

Jasim's pay during weekdays last week = £8.70 [tex]\times[/tex] 18

                                                                   = £156.6

Jasim's pay during weekends = £10.80

Jasim's pay during weekends = £10.80 per hour

Jasim's pay during weekdays last week = £10.80 [tex]\times[/tex] 12

                                                                   = £129.6

Total pay of Jasim for last week = £(156.6 + 129.6)

                                                     = £286.2

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A) W is a sub space of V

given that V =R^4 and W= [(x1, x2, x3, 0)|x1 ,x2, x3 E..R]

W is a subspace of V because of the following.

let  (x1, x2, x3, 0), (y1, y2, y3, 0)  ∈  W and a, b  ∈ V

now  

a(x1, x2, x3, 0)+b (y1, y2, y3, 0)= (a x1, a x2, a x3, 0)+(b y1, b y2,b y3, 0)

= (a x1+ b y1 , a x2+ b y2 , a x3+ b y3 ,0+0)=  

(a x1+ b y1 , a x2+ b y2 , a x3+ b y3 ,0+0)

LHS =RHS

∈W

since  (a x1+ b y1 , a x2+ b y2 , a x3+ b y3 ) are all elements of R

W is closed under vector addition and scalar multiplication.

Hence W is a sub space of V.

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Answer:

g(- 9) = - 43

Step-by-step explanation:

substitute x = - 9 into g(x) , that is

g(- 9) = 4(- 9) - 7 = - 36 - 7 = - 43

The function is decreasing because it is going down.

The domain is the set of x-values, which is [tex]x \leq 4[/tex] or [tex](-\infty, 4][/tex].

The range is the set of y-values, which is [tex]-6 \leq y < -1[/tex] or [tex][-6, -1)[/tex].

Answer:

24

Step-by-step explanation:

12 months in a year and Calvin gets 2 paychecks in one month

so 2 times 12 = 24 paycheck

No, because if he gets a paycheck every 2 weeks that would be about 4 paychecks in one month

so that would be about 48 paychecks in a year.

Answer:

Describe how anthropology challenges more commonly held notions of progress

Step-by-step explanation:

by using the unitary method, 11 inches of wire can be bought for 44 cents.

We are given that:

14 inches of wire costs 56 cents.

14 inches = 56 cents

Now, by using the unitary method, we get that:

1 cent = 14 / 56 inches.

1 cent = 1 / 4 inches.

Now, for 44 cents, by using the multiplication, we get that:

44 cents = 1 / 4 inches × 44

44 cents = 11 inches.

Therefore, we get that, by using the unitary method, 11 inches of wire can be bought for 44 cents.

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The counterexample of the statement "the difference of two numbers is greater than the greater number if the smaller number is greater than twice the additive inverse of the greater number"

"The difference of two numbers less than the greater number," is how the claim is expressed.

Give us x and y, where x is greater than y.

Thus, the statement can be interpreted as follows:

x - y < x

To both sides, add x.

-y < 2x

Replace with: y > -2x

This indicates that only when the smaller number is higher than twice the additive inverse of the larger number is the assertion true.

The smaller number must be bigger than twice the additive inverse of the larger number in order for the statement "the difference of two numbers is greater than the greater number" to be false.

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The $7,834.54 borrowed at 18.6% annual interest rate with the landscape architect's monthly payment of $500, gives the number of months it will take to repay the debt as approximately 19 months

Monthly payment on a loan, is the amount the person who takes the loan, pays each month in order to settle the loan in a given time period.

The monthly payment formula is presented as follows;

[tex] \displaystyle{M = \frac{P \cdot \left( \frac{r}{12} \right) \cdot \left( 1 + \frac{r}{12} \right)^{n} }{\left( 1 + \frac{r}{12} \right)^{n} - 1} }[/tex]

Where;

M = The amount the landscape architect paid monthly = $500

P = The amount loaned or borrowed = $7,834.54

r = The interest per annum = 18.6%

n = The number of monthly payment made

Therefore;

[tex] \displaystyle{500 = \frac{7834.54 \cdot \left( \frac{0.186}{12} \right) \cdot \left( 1 + \frac{0.186}{12} \right)^{n} }{\left( 1 + \frac{0.186}{12} \right)^{n} - 1} }[/tex]

Evaluating the above equation gives;

[tex] \displaystyle{500 = \frac{121.43537.1 \cdot 1.0155^{n} }{1.0155^{n} - 1} }[/tex]

[tex] \displaystyle{500 \times (1.0155^{n} - 1) = 121.43537.1 \cdot 1.0155^{n} }[/tex]

[tex] \displaystyle{500 \times 1.0155^{n} - 121.43537.1 \cdot 1.0155^{n} ) = 500 }[/tex]

Which by taking natural logarithms of both sides gives;

n•ln(1.0155) = ln(1.32077843609)

n = ln(1.32077843609) ÷ ln(1.0155) ≈ 18.09

Rounding up to the nearest month gives;

The number of months it will take the architect to pay the debt is approximately 19 months

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Answer: -44

have a good day

:/

The cost for 1.42 kg of this cheese will be $ 31.44 .

The process of translating measurements of a given quantity between different units, frequently using multiplicative conversion factors that change the value of the measured quantity without changing its effects, is known as unit conversion. The specific circumstances and the desired result dictate the conversion process. This may be governed by a regulation, contract, set of technical requirements, or other publicly available standards.

In its simplest form, the unitary procedure is used to determine the value of a single unit from a given multiple.

How to calculate the value of one pen, for example, if 40 cost Rs. 400. To finish it, using the unitary method. Additionally, after the value of a single unit has been established, we can multiply that value by the quantity of additional units required to establish the value of the additional units. This is typically how the concepts of ratio and proportion are used. The unitary method entails calculating the value of a single unit before calculating the value of the required number of units.

Given that 0.429 kg of cheese cost $9.50

As a result, the price of 1 kg of cheese is $9.50/0.429, which is $ 22.14.

As a result, 1.42 kg of cheese will cost you $22.14 * 1.42 = $31.44.

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The condition for the figure to be similar is that; DE = FD

Similar figure are zoomed in or zoomed out (or just no zoom) version of each other. They are scaled version of each other, and by scale, we mean that each of their dimension(like height, width etc linear quantities) are constant multiple of their similar figure.

In the problem, the ratio should be CD/DE = GD/DF

We can also write the ratios of the corresponding sides as:

CD/DE = GD/DF

Therefore, CE and GF are similar

Thus, the condition for the figure to be similar is that;

DE = FD

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The part of marketing copy that asks the audience to do something with the information you've just provided is known as call to action. Option B

Marketing copy can be defined as a content that is written to boost sales or to promote a product or service and also to persuade the readers to take a certain actions.

It is an important tool that is used to educate customers, and it provides the resources and contact details information to help various businesses increase the awareness of their products and services.

Call-to-action can be defined as the part of an advertisement or content that encourages the audience to do something.

In marketing, it help in converting a reader or visitor to a lead for the business sales team.

It also drives other marketing actions depending on the content's goal.

Hence, the marketing copy is call-to-action

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Answer:

Step-by-step explanation: B

Answer: 6391000 or 6.391 x 10^6

Step-by-step explanation:

**First, convert 7.7 x 10^2 to a number**

770

**Then multiply 8300 and 770**

6391000

**Convert to scientific notation**

6.391 x 10^6

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