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makkiz [27]
3 years ago
8

Each month Elizabeth budgets $760 for fixed expenses, $620 for living expenses, and $80 for annual expenses. Her annual net inco

me is $32,580. Which sentence best describes her monthly budget?
A. It shows a deficit of $1255
B. It shows a surplus of $1255
C. It shows a surplus of $1460
D. It is balanced
Mathematics
2 answers:
vichka [17]3 years ago
8 0

Answer: Option 'C' is correct.

Step-by-step explanation:

Since we have given that

Amount she spent on fixed expenses = $760

Amount she spent on living expenses = $620

Amount she spend for annual expenses = $80

Total expenditure will be

760+620+80\\\\=\$1460

Her annual net income = $32580

So, Her monthly net income will be

\frac{32580}{12}=\$2715

So, we can see that her income is more than her expenses.

So, she yield surplus.

Surplus = Revenue - Expenditure

=2715-1480\\\\=\$1255

Hence, It shows a surplus of $1255.

Hence, Option 'C' is correct.

Lostsunrise [7]3 years ago
6 0
760+620+80=1460 total monthly expenses.
$32,580 annually divided by 12 months = monthly income of $2,715
2,715-1460=1,255
Her budget shows a surplus of $1,255

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Line t passes through points (10, 1) and (2, 6). Line u is perpendicular to t. What is the slope of line u?
diamong [38]

Let's find the slope for line t first.

We can use the given points 2,6 and 10,1 to find the slope using the slope formula.

\frac{y.2 - y.1}{x.2 - x.1} = m

1 - 6 / 10 - 2

-5/8

The slope is -5/8.

Because we know the slope of this line, we can find the slope of the next line instantly, as they are perpendicular.

When a slope is perpendicular to another, it is equal to the negative reciprocal.

Negative reciprocal of -5/8 = 8/5

<h3>The slope of line u is 8/5</h3>
8 0
3 years ago
Which equations represent the line that is parallel to 3x − 4y = 7 and passes through the point (−4, −2)? Select two options.
Elanso [62]

Answer:

2 and 5

Step-by-step explanation:

The slope-intercept form of a line is y=mx-b where m is slope and b is y-intercept.

The point-slope form of a line is y-y1=m(x-x1) where m is the slope and (x1,y1) is a point on the line.

The standard form a line is ax+by=c.

So anyways parallel lines have the same slope.

So if we are looking for a line parallel to 3x-4y=7 then we need to know the slope of this line so we can find the slope of our parallel line.

3x-4y=7

Goal: Put into slope-intercept form

3x-4y=7

Subtract 3x on both sides:

  -4y=-3x+7

Divide both sides by -4:

   y=\frac{-3}{-4}x+\frac{7}{-4}

Simplify:

   y=\frac{3}{4}x+\frac{-7}{4}

So the slope of this line is 3/4.  So our line that is parallel to this one will have this same slope.

So we know our line should be in the form of y=\frac{3}{4}x+b.

To find b we will use the point that is suppose to be on our new line here which is (x,y)=(-4,-2).

So plugging this in to solve for b now:

-2=\frac{3}{4}(-4)+b

-2=-3+b

3-2=b

b=1

so the equation of our line in slope-intercept form is y=\frac{3}{4}x+1

So that isn't option 1 because the slope is different.  That was the only option that was in slope-intercept form.

The standard form of a line is ax+by=c and we have 2 options that look like that.

So let's rearrange the line that we just found into that form.

y=\frac{3}{4}x+1

Clear the fractions because we only want integer coefficients by multiplying both sides by 4.

This gives us:

4y=3x+4

Subtract 3x on both sides:

-3x+4y=4

I don't see this option either.

Multiply both sides by -1:

3x-4y=-4

I do see this as a option. So far the only option that works is 2.

Let's look at point slope form now.

We had the point that our line went through was (x1,y1)=(-4,-2) and the slope,m, was 3/4 (we found this earlier).

y-y1=m(x-x1)

Plug in like so:

y-(-2)=3/4(x-(-4))

y+2=3/4 (x+4)

So option 5 looks good too.

7 0
3 years ago
Read 2 more answers
Nicole and adam are each saving money for a car. the total amount of money nicole will save is represented by the function f (x)
Yakvenalex [24]
For this case we have the following functions:
 f (x) = 36 + 4x
 g (x) = x2 + 15
 By matching both functions we have:
 f (x) = g (x)
 36 + 4x = x2 + 15
 Rewriting we have:
 x2 + 15 - 4x - 36 = 0
 x2 - 4x - 21 = 0
 Solving the polynomial we have:
 (x-7) (x + 3) = 0
 x = -3
 x = 7
 Taking the positive root we have:
 x = 7
 Answer:
 
They will have the same amount of money saved after:
 
x = 7 weeks
8 0
3 years ago
Read 2 more answers
Find the sum of 10x^2-10x-6 and x+6.
Andre45 [30]

Answer:

10x²−9x

Step-by-step explanation:

10x²−10x−6+x+6

=10x²−10x−6+x+6

Combine Like Terms:

=10x²−10x−6+x+6

=(10x²)+(−10x+x)+(−6+6)

=10x²−9x

Hope this helps!

3 0
3 years ago
2 Points<br> A rational expression is undefined whenever its numerator is zero.
aev [14]
56 because you gotta multiply it
3 0
3 years ago
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