Loretta is a single mom with two kids. In 2009 her gross income was $61,840. She filed
her taxes as Head of the Household and claimed herself and her 2 children. Using the tables
above find Loretta's taxable income.

Answer:

[tex]Z = \frac{37i }{113 } - \frac{23}{113} [/tex]

Step-by-step explanation:

We have the complex number relationship as:

E=IZ

Where E=(5+9i) and I=(8+7i)

We solve for Z to get;

Z=E/L

We then substitute the expressions to get:

[tex]Z = \frac{5 + 9i}{8 + 7i} [/tex]

We rationalize to get:

[tex]Z = \frac{5 + 9i}{8 + 7i} \times \frac{8 - 7i}{8 - 7i} [/tex]

We simplify to obtain:

[tex]Z = \frac{40 - 35i + 72i - 63}{ {8}^{2} + {7}^{2} } [/tex]

This gives

[tex]Z = \frac{37i - 23}{113 } [/tex]

Or

[tex]Z = \frac{37i }{113 } - \frac{23}{113} [/tex]

Final answer:

It would have taken Janet about 9.7536 pages to read..

Explanation:

To determine Janet's reading progress, her reading speed is multiplied by the duration she read. With a reading speed of 3.6 pages per minute, if Janet read for 2.71 minutes, the calculation is 3.6 multiplied by 2.71, resulting in 9.7536. Hence, Janet would have read approximately 9.7536 pages. This calculation showcases how the product of reading speed and time provides a quantitative measure of reading accomplishment. It's a straightforward way to estimate the amount of material covered within a specific timeframe, offering insights into reading efficiency and progress.

a) ASA congruency

b)SAS congruency

c)SSS congruency

d) Not congruent

Step-by-step explanation:

Step 1:

a)

Angle PRQ = Angle RQS

Angle PRQ = Angle QRS (since PQ is parallel to RS , these form corresponding angles and hence are equal.

QR is the common Side

Hence 2 angles are same and the side which is included are same.Hence the 2 given triangles are congruent.

Step 2 :

b)

Angle IGH = Angle EDF

Side IG = DF and Side GH = DE

Here 2 of the sides of the triangle are same and the Angle which is included are same.

Hence the given triangles are equal

Step 3:

c)

In the given triangles the three sides re equal. Hence as per the side Side Side postulate the triangles are equal.

Step 4:

d) 2 angles are equal but the equal Side is not included and hence the two triangles are not congruent

Answer:

Step-by-step explanation:

I don't have all the information, but all you need to do it convert 2 hours to minutes (which would be 120 minutes) and setup a proportion.

amount of calories burnt per minute           x (total amount of calories burnt)

____________________________    = ________________

1 minute                                                              120 minutes

Hope this helps!

They would burn 360 calories doing 2 hr of bowling.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

We are given that this energy is measured in calories. When you exercise, you use up or burn calories.

The information shows about how many calories a 125-pound person burns each minute bowling.

We need to do it convert 2 hours to minutes which would be 120 minutes and setup a proportion.

The amount of calories burnt per minute  x (total amount of calories burnt)

1 minute  =  120 minutes

Multiply 120 x 3 = 360.

Hence, they would burn 360 calories doing 2 hours of bowling.

More can be learned about proportions at;

brainly.com/question/24372153

#SPJ5

Answer:

$19.60

Step-by-step explanation:

$98 is made each week.

80% is saved, and the rest is spend on lunch, so 20% is spent on lunch.

20%=.20

98•.20=19.6

$19.60 is spend on lunches each week.

Answer:

Multiply by 5

-250, 1250

Step-by-step explanation:

2 x -5 = -10

-10 x -5 = 50

50 x -5 = -250

-250 x -5 = 1250

Answer:

[tex]4\frac{1}{12}[/tex]

Step-by-step explanation:

7/12 * 7

7 = 7/1

7/12 * 7/1

49/12

12 goes into 49 four times, with a remainder of 1

[tex]4\frac{1}{12}[/tex]

Hope this helps :)

Answer:

4 1/12

Step-by-step explanation:

7/12 X 7

7/12 which is 7/12

do 7/12 times 7 which is 49/12

12 goes 4 times into 49 (up to 48)

there's one remaining

and its over 12

4 1/12

Answer:

5 Packages

Step-by-step explanation:

40 / 8 = 5

Answer:

Step-by-step explanation:

Answer:

£518

Step-by-step explanation:

Asking price = original cost × markup%

A = 280(1.85) = 518

Brian May needs to price his Antique Cherry Special guitar at £518. This price is determined by the original cost, £280, and a 85% markup, £238, on this cost.

Brian May needs to define a price for his signature Antique Cherry Special guitar that was costed at £280 and he wants an 85% markup on this cost. Markup is calculated by multiplying the cost by the markup percentage. In this case, the markup is £280 * 85/100 = £238. Therefore, to determine the final price Brian needs to add the original cost and the markup, which is £280 + £238 = £518. So the price Brian should ask for the guitar is £518.

https://brainly.com/question/31843661

#SPJ2

Answer:

9%

Step-by-step explanation:

It is simple because you just count to get to 24 and that is the percentage.

Answer:

Step-by-step explanation:

94 dollars

Answer:

The discount would be $94.50 but the final price would be $220.25.

Hope this helps!

Answer:

x=-4/5

Step-by-step explanation:

So first, since it says find f(-3) put -3 in the place of x in F(x)

So, f(-3)=5x+1

-3=5x+1

-4=5x

x=-4/5

or

x=-.8

Answer:

Well no cheating not from me

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

well plug it in: y=6x -> y=6(3/9) and solve, yes if theres a slope of 1

Answer:

c

Step-by-step explanation:

4*-8=-2

If a number is decreased by 79%, we are left with 21%.

so let's devide by 21 to get down to 1%, then multiply by 100 to get to the origininal number:

13 / 21 * 100 = 61.9047619048

To the nearest tenth it's 61.9

Final answer:

To find the original number when decreased by 79% to result in 13, we solve the equation 0.21x = 13, which gives us 61.9047619. Rounding this to the nearest tenth gives us 61.9.

Explanation:

To find the original number, we need to translate the percentage decrease back into the original number. Here's the step-by-step calculation:

So the original number to the nearest tenth is 61.9.

Answer:

a) $30

b) $8

Step-by-step explanation:

Wayne's savings to Stef's savings were in the ratio 5:6.

Let, Wayne's saving is 5x and Stef's saving is 6x.

Now, given that after spending $28 each the ratio became 1:4.

So, we can write the equation as

[tex]\frac{5x - 28}{6x - 28} = \frac{1}{4}[/tex]

⇒ 20x - 112 = 6x - 28

⇒ 14x = 84

⇒ x = 6

a) Therefore, Wayne's savings before he spends $28 is $(5 × 6) = $30

b) And, Stef's savings after she spends $28 will be $(6x - 28) = $(6 × 6 - 28) = $8 (Answer)

Answer:

You can determine if a polygon is a convex, by which way the edges points out

Convex is when all the points are facing out, so a polygon is a convex if all the edges are pointing out.

Answer:

  No side of the polygon crosses any other, even when extended indefinitely.

Step-by-step explanation:

If no sides of the polygon cross each other, it is convex when it has no internal reflex angles (angles measuring more than 180°). If sides of the polygon cross each other, it is not convex.

Another way to describe a convex polygon is that extending any one side indefinitely will not cause it to cross any other side.

Answer:

The total number of fliers they gave out is 1368.

Step-by-step explanation:

Given:

Volunteers for a political campaign gave out 21/38 of their fliers. They gave out the remaining 612 fliers in another neighborhood.

Now, to find the total number of fliers they gave out.

Let the total number of fliers be [tex]x.[/tex]

Number of fliers they gave out for a political campaign:

[tex]\frac{21}{38}\ of\ x[/tex]

[tex]=\frac{21}{38} \times x[/tex]

[tex]=\frac{21x}{38}[/tex]

Number of fliers remaining they gave out in another neighborhood = 612.

Now, to get the total number of fliers by putting an equation:

[tex]x-\frac{21x}{38} =612[/tex]

[tex]\frac{38x-21x}{38} =612[/tex]

[tex]\frac{17x}{38} =612[/tex]

Multiplying both sides by 38 we get:

[tex]17x=23256[/tex]

Dividing both sides by 17 we get:

[tex]x=1368.[/tex]

Therefore, the total number of fliers they gave out is 1368.

Answer: it would be 390

Just keep counting how many times one number goes into the other, start with the smallest

Answer:

[tex]68 \: {cm}^{2} [/tex]

Step-by-step explanation:

You can use 1 cm = 10 mm very well to help you with this.

The small two at the end of the unit (cm^2) refers, that the shape of an object is two dimensional. If we make 1 cm two dimensional by multiplying it with the original 1 cm, we get a total area of

[tex]1 \: {cm} \times 1 \: {cm} \: = 1 \: {cm}^{2} [/tex]

We have created an equation. Since we know 1 cm = 10 mm, we can replace the centimetres in the equation with the millimetres, like so:

[tex]10 \: mm \times 10 \: mm = 1 \: {cm}^{2} \\ 100 \: {mm}^{2} = 1 \: {cm}^{2} [/tex]

From there, its just a simple matter of calculation:

[tex]6800 \: {mm}^{2} \times \frac{1 \: {cm}^{2} }{100 \: {mm}^{2} } = 68 \: \: {cm}^{2} [/tex]

Answer:

c is the answer i am preety sure

Step-by-step explanation:

Gallery = g

Balcony = 2g (twice as many gallery)

Main floor = 2g + 225 ( 225 more than balcony)

The answer would be D.

The blank is -8

Step-by-step explanation:

Let us revise some rules of indices:

∵ [tex]4^{3}[/tex] × [tex]4^{-6}[/tex] = [tex]4^{5}[/tex] × [tex]4^{x}[/tex]

∵ All bases are equal

∴ Use the first and third rule above to find x

∵  [tex]4^{3}[/tex] × [tex]4^{-6}[/tex] = [tex]4^{3+-6}[/tex]

∴  [tex]4^{3}[/tex] × [tex]4^{-6}[/tex] = [tex]4^{-3}[/tex] ⇒ L.H.S

∵  [tex]4^{5}[/tex] × [tex]4^{x}[/tex] = [tex]4^{5+x}[/tex] ⇒ R.H.S

Equate L.H.S and R.H.S

∴  [tex]4^{-3}[/tex] =  [tex]4^{5+x}[/tex]

Equate the indices of the two sides

∴ -3 = 5 + x

- Subtract 5 from both sides

∴ -8 = x

∵ x represents the blank

∴ The blank = -8

The blank is -8

Learn more:

You can learn more about the indices in brainly.com/question/4419221

#LearnwithBrainly

Four to the power of three times four to the power of negative six is equal to four to the power of five times four to the power of negative eight.

To solve for the missing exponent, we can use the following properties of exponents:

Multiplying exponents with the same base: When multiplying powers with the same base, we add their exponents.

Negative exponents: A number raised to a negative exponent is equal to its reciprocal raised to the positive exponent.

Applying these properties:

4^3 * 4^-6 = 4^(3 - 6) = 4^-3 (since 4^-6 = 1/4^6)

4^5 * 4^x = 4^(5 + x)

Setting these equal to find x:

4^-3 = 4^(5 + x)

Therefore, x = -3 - 5 = -8.

Kate and Will meet at 1 : 09 pm

Solution:

The distance between Quebec City and New York City is 520 miles.

At the point where Kate and Will meet, they would have traveled 520 miles.

Let "t" represent the time it takes Kate to travel a certain distance before they met.

[tex]Distance = speed \times time[/tex]

If Kate drives at 55 mph, the distance covered would be

[tex]Distance = 55 \times t = 55t[/tex]

If Will drives at 75 miles per hour, then the distance covered will be

[tex]Distance = 75 \times t = 75t[/tex]

Since the total distance covered is 520 miles

Which means,

[tex]55t + 75t = 520\\\\130t = 520\\\\t = \frac{520}{130}\\\\t = 4[/tex]

Given that in question,

If Kate leaves Quebec and will leaves New York at 9:09 a.m

4 hours after 9: 09 am, Kate and Will will meet

9: 09 am + 4 hours = 1: 09 pm

Thus they would meet at 1 : 09 pm

Answer:

Therefore, equation of the line that passes through (-1,5) and is parallel to the line

[tex]2y+4x=-8[/tex]  

is

[tex]y=-2x+3[/tex]

Step-by-step explanation:

Given:

[tex]2y+4x=-8[/tex]        .Equation of line

can be written as

[tex]y=-2x-8[/tex]     ...which is in Slope intercept form

To Find:

Equation of line passing through ( -1, 5) and is parallel to the line 2y+4x=-8

Solution:

[tex]y=-2x-8[/tex] ...........Given

Comparing with,  

[tex]y=mx+c[/tex]    ....general form in slope intercept

Where m =slope  

We get

[tex]Slope = m = -2[/tex]

We know that parallel lines have Equal slopes.

Therefore the slope of the required line passing through (-1 , 5) will also have the slope = m = -2.

Now the equation of line in slope point form given by

[tex](y-y_{1})=m(x-x_{1})[/tex]

Substituting the points and so we will get the required equation of the line,

[tex](y-5)=-2(x-(-1))=-2(x+1)\\\\y-5=-2x-2\\y=-2x+3......Equation\ of\ line[/tex]

Therefore, equation of the line that passes through (-1,5) and is parallel to the line

[tex]2y+4x=-8[/tex]  

is

[tex]y=-2x+3[/tex]

Answer:

4+ x/2 =6

Step-by-step explanation:

Let  the number be X

half of the number is 1/2 multiply X= X/2

Four increased by half the number is 4+X/2

Therefore, Four increased by half of anumber is equal to six is written as

4+ x/2 =6

Answer:

2x-5

remainder of 0

Step-by-step explanation:

Check the image

Answer: 20%

Step-by-step explanation:

25 = 100%

25/5 = 5

100/5 = 20

That means 80% passed and 20% didnt.

Answer:

20%

Step-by-step explanation:

If 20 kids passed, that means 5 did not. 5/20 is 0.2. Write that in percentage is 20%.

Answer:

Akira needs 45 square inches of  gold foil to cover the chair free including the bottom​

Step-by-step explanation:

Total surface  =  surface area of the base square + area of 4 triangles

Step 1: The surface area of the base square

surface area of the base = surface area of the square =  [tex]s^2[/tex]

where s is the side length

The the surface area of the base  = [tex]3^2[/tex] = 9 square inches

Step 2: The surface area of the side triangles

The area of the triangle = [tex]\frac{1}{2}\times \text{side length} \times \text{slant height}[/tex]

On substituting the values,

The area of the triangle =[tex]\frac{1}{2} \times 3 \times 6[/tex]

The area of the triangle = [tex]\frac{18}{2}[/tex]

The area of the triangle = 9 square inches

Now the area of 4 triangles  =  4 x 9  = 36 square inches

Thus the total surface area  =  9 + 36 = 45 square inches

The amount of gold foil needed to cover a trophy in the shape of a square pyramid can be calculated using the surface area formula for square pyramids, which considers the base area and the slant height.

To calculate the amount of gold foil needed to cover the trophy, we need to find the surface area of the square pyramid trophy. The surface area of a square pyramid is calculated by the formula: Surface Area = base area + 1/2 * Perimeter of base * slant height. If we know the length of the base (which is a square here), the slant height, we can substitute them into this formula to get the surface area. This is the amount of gold foil Akira used to cover her trophy, assuming the gold foil perfectly fits the trophy shape with no overlap.

https://brainly.com/question/31800864

#SPJ