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AlekseyPX
3 years ago
8

In one month Kimberly earned $500 at her part-time job, and $50 was withheld for federal income tax. Suppose she earns $750 next

month. How much will be withheld for federal income
Mathematics
1 answer:
djverab [1.8K]3 years ago
8 0

Answer:

<em>It will be withheld $75 for federal income.</em>

Step-by-step explanation:

<u>Proportions</u>

Assuming the federal income tax is proportional to the earnings, we can establish the following relationship between the income tax (T) and the earnings (E):

T = k.E

Kimberly earned E=$500 and paid T=$50 for federal income tax, With this information, we can calculate the value of k:

50 = k ( 500)

k = 50 / 500

k = 0.1

The model is now:

T = 0.1*E

If Kimberl earns $750 next month, the tax will be:

T = 0.1*($750)

T = $75

It will be withheld $75 for federal income.

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Lucy is raising money for a school trip by selling lollipops and bags of
sukhopar [10]
<h3>16 lollipops and 9 bags of chips are sold</h3>

<em><u>Solution:</u></em>

Let "x" be the number of lollipops sold

Let "y" be the number of bags of chips sold

Cost of 1 lollipop = $ 1.50

Cost of 1 bag of chip = $ 1.75

<em><u>Yesterday Lucy made $39.75 from selling a total of 25  lollipops and bags of chips</u></em>

Therefore,

x + y = 25

y = 25 - x -------- eqn 1

<em><u>Yesterday Lucy made $39.75</u></em>

Therefore,

number of lollipops sold x Cost of 1 lollipop + number of bags of chips sold x Cost of 1 bag of chip = 39.75

x \times 1.50 + y \times 1.75 = 39.75

1.5x + 1.75y = 39.75 -------- eqn 2

<em><u>Substitute eqn 1 in eqn 2</u></em>

1.5x + 1.75(25 - x) = 39.75

1.5x + 43.75 - 1.75x = 39.75

0.25x = 4

<h3>x = 16</h3>

<em><u>Substitute x = 16 in eqn 1</u></em>

y = 25 - 16

<h3>y = 9</h3>

Thus 16 lollipops and 9 bags of chips are sold

7 0
3 years ago
Use ΔABC shown below to answer the question that follows:
topjm [15]

Answer:

The correct options are a and b.

Step-by-step explanation:

It is given that triangle ABC with segment AD drawn from vertex A and intersecting side BC.

Two triangle are called similar triangle if their corresponding sides are proportional or the corresponding interior angle are same.

To prove ΔABC and ΔDBA are similar, we have to prove that corresponding interior angles of both triangle as same.

If segment AD is an altitude of ΔABC, then angle ADB is a right angle.

\angle BDA=90^{\circ}

The opposite angle of hypotenuse is right angle. If segment CB is a hypotenuse, then angle ABC is a right angle.

\angle BAC=90^{\circ}

In triangle ΔABC and ΔDBA

\angle ABC\cong \angle DBA              (Reflexive property)

\angle BAC\cong \angle BDA              (Right angles)

By AA rule of similarity ΔABC and ΔDBA are similar.

Therefore correct options are a and b.

3 0
3 years ago
Read 2 more answers
Please help!!<br> Write a matrix representing the system of equations
frozen [14]

Answer:

(4, -1, 3)

Step-by-step explanation:

We have the system of equations:

\left\{        \begin{array}{ll}            x+2y+z =5 \\    2x-y+2z=15\\3x+y-z=8        \end{array}    \right.

We can convert this to a matrix. In order to convert a triple system of equations to matrix, we can use the following format:

\begin{bmatrix}x_1& y_1& z_1&c_1\\x_2 & y_2 & z_2&c_2\\x_3&y_2&z_3&c_3 \end{bmatrix}

Importantly, make sure the coefficients of each variable align vertically, and that each equation aligns horizontally.

In order to solve this matrix and the system, we will have to convert this to the reduced row-echelon form, namely:

\begin{bmatrix}1 & 0& 0&x\\0 & 1 & 0&y\\0&0&1&z \end{bmatrix}

Where the (x, y, z) is our solution set.

Reducing:

With our system, we will have the following matrix:

\begin{bmatrix}1 & 2& 1&5\\2 & -1 & 2&15\\3&1&-1&8 \end{bmatrix}

What we should begin by doing is too see how we can change each row to the reduced-form.

Notice that R₁ and R₂ are rather similar. In fact, we can cancel out the 1s in R₂. To do so, we can add R₂ to -2(R₁). This gives us:

\begin{bmatrix}1 & 2& 1&5\\2+(-2) & -1+(-4) & 2+(-2)&15+(-10) \\3&1&-1&8 \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\0 & -5 & 0&5 \\3&1&-1&8 \end{bmatrix}

Now, we can multiply R₂ by -1/5. This yields:

\begin{bmatrix}1 & 2& 1&5\\ -\frac{1}{5}(0) & -\frac{1}{5}(-5) & -\frac{1}{5}(0)& -\frac{1}{5}(5) \\3&1&-1&8 \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\3&1&-1&8 \end{bmatrix}

From here, we can eliminate the 3 in R₃ by adding it to -3(R₁). This yields:

\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\3+(-3)&1+(-6)&-1+(-3)&8+(-15) \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\0&-5&-4&-7 \end{bmatrix}

We can eliminate the -5 in R₃ by adding 5(R₂). This yields:

\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\0+(0)&-5+(5)&-4+(0)&-7+(-5) \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\0&0&-4&-12 \end{bmatrix}

We can now reduce R₃ by multiply it by -1/4:

\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\ -\frac{1}{4}(0)&-\frac{1}{4}(0)&-\frac{1}{4}(-4)&-\frac{1}{4}(-12) \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}

Finally, we just have to reduce R₁. Let's eliminate the 2 first. We can do that by adding -2(R₂). So:

\begin{bmatrix}1+(0) & 2+(-2)& 1+(0)&5+(-(-2))\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 0& 1&7\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}

And finally, we can eliminate the second 1 by adding -(R₃):

\begin{bmatrix}1 +(0)& 0+(0)& 1+(-1)&7+(-3)\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 0& 0&4\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}

Therefore, our solution set is (4, -1, 3)

And we're done!

3 0
3 years ago
Write a simplified polynomial expression in standard form to represent the area of the rectangle below. (2 points) A picture of
Jet001 [13]

Answer:

Area= 5x^2-18x -8

Step-by-step explanation:

If the rectangle show one side of length 5 x +2, and another side of length x - 4, then the area of this rectangle (given by the product of the sides' length) is:

Area = (5x+2)\,(x-4)\\Area = 5x^2-20x+2x-8\\Area= 5x^2-18x -8

which is already written in standard form.

4 0
3 years ago
Read 2 more answers
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The scale factor for math numbers are the numbers you multiply to get an anwser for its factor.
Ex: factor of 2 is 2,4,6,8 and so on with each number
4 0
3 years ago
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