What is Mary's net worth if her assets total $16000, her gross income is $45000, her student loan debt is $22000 (she has no other debts), and her annual expenses (including taxes) total $40000?

Answer:

[tex]\boxed{x^2=-8y}[/tex]

Step-by-step explanation:

[tex](a,b)\ is \ the\ focus\\y=k\ is \ the\ directrice\\\\Formula\ to\ use:\ y=\dfrac{(x-a)^2}{2(b-k)} +\dfrac{b+k}{2} \\\\Here: \ a=0,\ b=-2, \ k=2\\\\y=\dfrac{(x-0)^2}{2(-2-2)} +\dfrac{-2+2}{2} \\\\so\ y=-\dfrac{x^2}{8} \\\\or\ x^2=-8y[/tex]

The equation which represents the parabola is x^2 = 8y, the correct option is C.

If a quadratic equation is written in the form

y=a(x-h)^2 + k

then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)

First of all, i used this vertex formula thing since it is visible that there are quadratic functions. Otherwise, you had to use calculus to get critical points, then second derivative of functions to find the character of critical points as minima or maxima or saddle etc to get the location of vertex point.

This point (h,k) is called the vertex of the parabola that quadratic equation represents.

We are given that;

Focus of parabola= (0,–2)

Now,

The vertex is halfway between the focus and the directrix on a line perpendicular to them. Since the focus is at (0,-2) and the directrix is y = 2, we can find that:

The vertex is at (0,0), because it has an x-coordinate of 0 (same as the focus) and a y-coordinate of 0 (the average of -2 and 2).

p is equal to 2, because it is half of the distance between -2 and 2.

Now we can plug in these values into the formula:

(x - 0)^2 = 4(2)(y - 0)

Simplifying, we get:

x^2 = 8y

Therefore, the equation of the parabola will be x^2 = 8y.

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Answer:

3/25

Step-by-step explanation:

3/5 *3/15

9/75

Simplified 3/25

Answer:

3

Step-by-step explanation:

3/5 ÷ 3/15

=> 3/5 x 15/3

=> 3/5 x 5

=> 3

Answer: 4 8/10m

Explanation:

Total Ribbon = 24m

Total children = 5

Ribbon each student gets = 24÷5

= 4.8

Now 4.8 = 48/10

4 8/10m is the mixed fraction

So each child will get 4 8/10m ribbon

Must click thanks and mark brainliest

If five children share 24m of ribbon equally then each children gets [tex]4\frac{4}{5}[/tex] of ribbon.

A division is a process of splitting a specific amount into equal parts.

Given that five children share 24m of ribbon equally.

We have to find the amount of ribbon each children gets.

To find this we have to divide the length of the ribbon with the number of children.

Twenty four divided by five.

24 is the dividend and five will be the divisor

24/5

Now we have to write this in mixed fraction

[tex]4\frac{4}{5}[/tex]

Hence, if five children share 24m of ribbon equally then each children gets [tex]4\frac{4}{5}[/tex] of ribbon.

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Answer:

$54

Step-by-step explanation:

you just multiply 1 by 2 and get the answer 2 then multiply 27 dollars by 2 and get 54 dollars

Answer is: B

Step-by-step explanation: correct answer is B

b  

2

−a  

2

Given, acotθ+bcscθ=p

           bcotθ+acscθ=q

⇒p  

2

−q  

2

=(p−q)(p+q)

                   =[acotθ+bcscθ−bcotθ−acscθ][acotθ+bcscθ+bcotθ+acscθ]

                   =[cotθ(a−b)−cscθ(a−b)][cotθ(a+b)+cscθ(a+b)]

                   =(a−b)(cotθ−cscθ)(a+b)(cotθ+cscθ)

                   =(a  

2

−b  

2

)(cot  

2

θ−csc  

2

θ)

                   =(−1)(a  

2

−b  

2

)[∵csc  

2

θ−cot  

2

θ=1]

                   =(b  

2

−a  

2

)

Answer:

A 6.09

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

use formula for perimeter of rectangle but put X in place of length 50 m as breadth. so,

2(50+X)= 260

solve this and you will get X= 80

Answer:

80

Step-by-step explanation:

Perimeter area = 2(l × w)

Plug in:

2(x + 50) = 260

2x + 100 = 260

      -100    -100

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

2x = 160

----    -----

2       2

x = 80

So, x will be 80

Answer:

-4

Step-by-step explanation:

The average rate of change of the interval [a,b] is (f(b)−f(a)) / (b−a)

Replacing a=−5, b=4, f(x)=−x^2−5x+12.

 (f(b)−f(a))/(b−a) =12−5x4− 4^2 − (12−5 x(−5)−(−5)^2)/ (4−(−5))= −4.

Answer:

#1

The cost to produce 500 helmets:

#5

The break-even point is the price when profit is zero:

#6

There will be a profit as the selling price is greater than the break even point:

Find cost of x=500 helmets

Break even point

So

There is profit as its less than 18

Answer:

[tex]y=\displaystyle\frac{3}{2}x-3[/tex]

Step-by-step explanation:

Hi there!

Slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x=0)

We're given:

⇒ x-intercept = 2

⇒ y-intercept = -3

1) Determine the slope (m)

[tex]m=\displaystyle\frac{y_2-y_1}{x_2-x_1}[/tex] where two points that fall on the line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Given the x- and y-intercepts, we can rewrite them as points:

x-intercept = 2

⇒ (2,0)

y-intercept = -3

⇒ (0,-3)

Plug these points into the equation:

[tex]m=\displaystyle\frac{0-(-3)}{2-0}\\\\m=\displaystyle\frac{0+3}{2}\\\\m=\displaystyle\frac{3}{2}[/tex]

Therefore, the slope of the line is [tex]\displaystyle\frac{3}{2}[/tex]. Plug this into [tex]y=mx+b[/tex]:

[tex]y=\displaystyle\frac{3}{2}x+b[/tex]

2) Plug in the y-intercept (b)

[tex]y=\displaystyle\frac{3}{2}x+b[/tex]

We're given the y-intercept: -3. Plug this into [tex]y=\displaystyle\frac{3}{2}x+b[/tex]:

[tex]y=\displaystyle\frac{3}{2}x+(-3)\\\\y=\displaystyle\frac{3}{2}x-3[/tex]

I hope this helps!

Answer:

2pi*r(r+h)

Step-by-step explanation:

SEE IMAGE FOR SOLUTION

HAVE A GREAT DAY

Answer:

Solution given:

[tex]\sqrt{6-15x} =5x+d[/tex]......(1)

d=?

and

x=-2

Substituting value of x in equation 1.

[tex]\sqrt{6-15*-2} =5*-2+d[/tex].

Solve the like terms

[tex]\sqrt{6+30} =-10+d[/tex].

solve the like terms

[tex]\sqrt{36} =-10+d[/tex].

we have square root of 36 is 6.

6=-10+d

d=16

the value of constant term is 16.

The value of d for the expression [tex]\sqrt{6-15x} = 5x+d[/tex] is 16.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

The value of 'd' is calculated as,

[tex]\sqrt{6-15x} = 5x+d[/tex]

Put the value of x =-2,

[tex]\sqrt{6-(15\times -2)}=(5\times -2)+d[/tex]

√36 = -10 + d

6 = -10 + d

d = 16

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Answer:

540°

Step-by-step explanation:

90 revolutions = 360°×90 = 32400°

32400° in 60 sec or 1 min

so, in 1 sec 32400/60 = 540°

Answer:

540°

Step-by-step explanation:  

90 revolutions = 360°×90 = 32400°  

=> 32400° in 60 sec or 1 min  

=> In 1 sec,

=> 32400/60 = 540°

Answer:

A) both functions are linear

B) f(x) = 7446.4x + 178713.6 and f(x) = 11000x + 179000

C) House 2 will value $106894.4 more than house 1.

Step-by-step explanation:

A) Value Increase from year 1 to year 2:

House 1: 193,606.40 - 186,160 = 7446.4

House 2: 201,000 - 190,000 = 11000

Value Increase from year 2 to year 3:

House 1: 201,350.66 - 193,606.40 = 7744.26

House 2: 212,000 - 201,000 = 11000

This means that a constant increament in x variable gives a constant increament in both houses vales. Then, both functions are linear.

B) The slope is the same as the value increment from one year to the next one.

slope (m) of House 1: 7446.4

slope (m) of House 2: 11000

General formula of a line:

f(x) = mx+b

Replacing with a known point:

House 1

186,160 = 7446.4(1) + b

b = 186,160 - 7446.4 = 178713.6

equation: f(x) = 7446.4x + 178713.6

House 2

190,000 = 11000(1) + b

b = 190,000 - 11000 = 179000

equation: f(x) = 11000x + 179000

C) Replacing x = 30 into each equaiton:

Value of House 1 after 30 years

f(x) = 7446.4(30) + 178713.6 = 402105.6

Value of House 2 after 30 years

f(30) = 11000(30) + 179000 = 509000

Then, house 2 will value 509000 - 402105.6 = $106894.4 more than house 1.

Answer:

6 blocks have red faced

Step-by-step explanation:

54 blocks have 1 red face

Step-by-step explanation:

–17–12q=–17+10q

–17+17=10q+12q

0/22=22q/22

q=0

By some properties of logarithms, rewrite the equation as

[tex]2\log(a-2b) = \log(a) + \log(b) \\\\ \log(a-2b)^2 = \log(ab)[/tex]

so that

(a - 2b)² = ab

Expand the left side:

a ² - 4ab + 4b ² = ab

Rearrange terms to get a quadratic equation in a/b :

a ² - 5ab + 4b ² = 0

b must be greater than 0, otherwise log(b) doesn't exist, and the same goes for a. So we can divide by b ² to get

a ²/b ² - 5a/b + 4 = 0

Factorize and solve for a/b :

(a/b - 4) (a/b - 1) = 0

==>   a/b = 4   or   a/b = 1

However, if a/b = 1, then a = b makes a - 2b = -b. But we must have b > 0, so we omit the second solution and end up with

a/b = 4

Answer:

Step-by-step explanation:

A horizontal line is only concerned with the y value. The equation is y = 10 because that is the point that the line must go through.

The x value does not matter as long as the y value is given as 10. The domain is any real value. The range is 10

Answer:

Below!

Step-by-step explanation:

A straight line = 180 degrees, so all you need to do to find angle a is to subtract 156 from 180!

180 - 156 = 24 degrees

Hope this helped!

Answer:

Line segments A'B' and C'D' do not intersect and are the same distance apart as AB and CD.

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

48-15÷(3×5)+12

48-15÷15+12

48-1+12

59

Answer:

x=2,y=2

Step-by-step explanation:

3y-1 = 5

or, 3y = 5+1

or, y = 6/3

y = 2

2x+1 = 3y-1

or, 2x = 3×2-1-1

or, 2x = 4

or, x = 2

[tex]\\ \sf\longmapsto \left[{2x+1\atop 2x+x}\:\:\:{3y-1\atop 3}\right]=\left[{3y-1\atop 4}\:\:\;{5\atop 3}\right][/tex]

[tex]\\ \sf\longmapsto 3y-1=5[/tex]

[tex]\\ \sf\longmapsto 3y=5+1[/tex]

[tex]\\ \sf\longmapsto 3y=6[/tex]

[tex]\\ \sf\longmapsto y=2[/tex]

Put the value in 1st one

[tex]\\ \sf\longmapsto 2x+1=3y-1[/tex]

[tex]\\ \sf\longmapsto 2x+1=3(2)-1[/tex]

[tex]\\ \sf\longmapsto 2x+1=6-1[/tex]

[tex]\\ \sf\longmapsto 2x+1=5[/tex]

[tex]\\ \sf\longmapsto 2x=5-1[/tex]

[tex]\\ \sf\longmapsto 2x=4[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{4}{2}[/tex]

[tex]\\ \sf\longmapsto x=2[/tex]

Answer:

27/200

Step-by-step explanation:

To write 0.135 as a fraction you have to write 0.135 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number. 0.135 = 0.135/1 = 1.35/10 = 13.5/100 = 135/1000

Answer:

27/200

Step-by-step explanation:

your teacher tried to be tricky.

0.135 is simply 135/1000.

that is how you can express any finite decimal number.

anyway, now, we need to transform that fraction into one of the provided fractions. so, which one fits ?

with experience you see it right away. otherwise by simply trying.

in any case, the first option is the right one.

proof :

27/200 = 135/1000 ?

the denominator is our driver : what factor do I need to turn 200 into 1000 ? right, 5 ! 200×5 = 1000

so, we multiply numerator and denominator by 5 (it is important to do that for both, so that the value of the fraction does not change).

27/200 × 5/5 = (27×5) / (200×5) = 135/1000

and that is the proof. 27/200 is indeed 0.135

Answer:

its basically just rate of change or slope. with derivatoves you can find the slope of a tangent line which is a line that touches the curve at a point.

Answer:

considering it was simple interest,

We have the formula:

I = PRT ÷ 100

where,

for the first part of the question,

Thus, I = (2160 × 20 × 4)÷ 100

I = Rs. 1728

Now, for the second part,

T = 100×I÷PR

T = 100 × 1728÷(1800 × 12)

T = 8 Years

Answer:

So the amplitude is 7

The period is pi

The phase shift is negative pi/2

The midline is -3

Step-by-step explanation:

A trigonometric function is the same as

[tex]f(x) = a \cos(b(x + c)) - d[/tex]

Where a is the amplitude, 2 pi/ absolute value of b is the period, c is the phase shift, and d is the vertical shift or midline.

Given the function

[tex]7 \cos(2x + \pi) - 3[/tex]

The amplitude is 7, and the midline is -3. The period is

[tex] \frac{2\pi}{2} = \pi[/tex]

The phase shift is

[tex]2x + \pi = 0[/tex]

[tex]2x = - \pi[/tex]

[tex]x = - \frac{\pi}{2} [/tex]

So the amplitude is 7

The period is pi

The phase shift is negative pi/2

The midline is -3.

Answer: x= 42.3

Step-by-step explanation:

Sqrt a^2 + b^2 - (2ab)(cos 100)

Sqrt 25^2 + 30^2 - (2)(25)(30)(cos 100)

42.3

Analyzing the text, we find that the function is decreasing over the following intervals: (0, 1)

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

Going from maximum to minimum, meaning that between them the function decreases, thus, the first interval it is decreasing is between (0,1).

Going up, increases.

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

Thus, the function decreases over the following interval: (0, 1)

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Answer:

25/81 is already in the simplest form. It can be written as 0.308642 in decimal form (rounded to 6 decimal places).