What is the the y coordinate of the solution to this system of equations

The equation y+6=1/3(x-9) is written in point- slope form. What is the equation written in slope-intercept form?

kvv77 [185]

Your answer would be option three, y = 1/3 x -9 :)

6 0

3 years ago

A superhero is trying to leap over a tall building. The function f(x)=-16x^2+200x gives the superhero's height in feet as a func

Gemiola [76]

Answer:

Since $\bigtriangleup \geq 0$ , the superhero makes it over the building.

Step-by-step explanation:

The height is given by the following function:

$f(x) = -16x^{2} + 200x$

Will the superhero make it over the building?

We have to find if there is values of x for which f(x) = 612.

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

If $\bigtriangleup < 0$ , the polynomial has no solutions.

In this question:

$f(x) = -16x^{2} + 200x$

$-16x^{2} + 200x = 612$

$16x^{2} - 200x + 612 = 0$

We have to find $\bigtriangleup$

We have that $a = 16, b = -200, c = 612$ . So

$\bigtriangleup = (-200)^{2} - 4*16*612 = 832$

Since $\bigtriangleup \geq 0$ , the superhero makes it over the building.

7 0

3 years ago

What percentage of the mile times range from 7.25 to 9.375?

Step2247 [10]

1. We assume, that the number 9.375 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 9.375 is 100%, so we can write it down as 9.375=100%.

4. We know, that x is 7.25% of the output value, so we can write it down as x=7.25%.

5. Now we have two simple equations:

1) 9.375=100%

2) x=7.25%

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

9.375/x=100%/7.25%

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for what is 7.25% of 9.375

9.375/x=100/7.25

(9.375/x)*x=(100/7.25)*x - we multiply both sides of the equation by x

9.375=13.793103448276*x - we divide both sides of the equation by (13.793103448276) to get x

9.375/13.793103448276=x

0.6796875=x

x=0.6796875

now we have:

7.25% of 9.375=0.6796875

8 0

3 years ago

Ghost, Inc., has no debt outstanding and a total market value of $369,600. Earnings before interest and taxes, EBIT, are project

arlik [135]

Answer:

Ghost Inc.

A1.

Earnings Per share (EPS)

EPS in normal projection is $4.61 per share

EPS in an expansion is $5.31 Per share

EPS in a recession is $3.51 Per share

A2.

Changes to EPS in an expansion is +15.18%

Changes to EPS in a recession is -23.86%

B1.

Earnings Per share (EPS)

EPS in normal projection is $7.23 per share

EPS in an expansion is $8.62 Per share

EPS in a recession is $5.01 Per share

B2.

Changes to EPS in an expansion is +19.23%

Changes to EPS in a recession is -30.71%

Step-by-step explanation:

Underlying Information:

Earnings before interest and taxes, EBIT projections = $51,000

Expansionary EBIT projections = $51,000 x (100% + 15%) = $58,650

Recessionary EBIT projections = $51,000 x (100% -24%) = $38,760

Tax Rate = 24%

Market to Book Ratio = 1.0

Stock Price is constant.

Solution to A1.

Scenario 1 (Projected Earnings)

Earnings Per Share (EPS) = Net Income (Earnings after Tax) divided by Outstanding Shares in Issue

Net Income = EBIT minus tax = $51,000 - ($51,000 x 24%)

= $51,000 - $12240

= $38,760

Outstanding shares in issue = 8,400 ordinary Shares

EPS = $38,760 divided by 8,400 shares = $4.61 Per share

Scenario 2 (Projected Earnings in a strong expansion)

Earnings Per Share (EPS) = Net Income (Earnings after Tax) divided by Outstanding Shares in Issue

Net Income = EBIT minus tax = $58,650 - ($58,650 x 24%)

= $58,650 - $14,076

= $44,574

Outstanding shares in issue = 8,400 ordinary Shares

EPS = $44,574 divided by 8,400 shares = $5.31 Per share

Scenario 3 (Projected Earnings in a Recession)

Earnings Per Share (EPS) = Net Income (Earnings after Tax) divided by Outstanding Shares in Issue

Net Income = EBIT minus tax = $38,760 - ($38,760 x 24%)

= $38,760 - $9,302.4

= $29,457.6

Outstanding shares in issue = 8,400 ordinary Shares

EPS = $44,574 divided by 8,400 shares = $3.51 Per share

Solution to A2.

1.Changes to EPS in an expansion = EPS (Expansion) minus EPS (normal projection), all divided by EPS (normal projection)

= (5.31 - 4.61) / 4.61

= +15.18% change during an expansion

2.Changes to EPS in a recession = EPS (Recession) minus EPS (normal projection), all divided by EPS (normal projection)

= (3.51 - 4.61) / 4.61

= -23.86% change during a recession

Underlying Information:

Debt issue = $185,000

Interest on debt issued = 6% = $11,100

Market to Book Ratio = 1.0

Stock Price is constant.

Therefore Share Price = Market Value divided by Outstanding shares in issue = 369,600 / 8400 = $44

This implies our proceeds of $185,000 from debt issue would have repurchased $185,000 divided by $44 = 4,205 ordinary shares

This decision to repurchase its shares indicates the shares outstanding will reduce by 4,205. New outstanding shares will now be 4,195 shares

*Earnings before interest and taxes, EBIT normal projections = $51,000 & Earnings Before Tax (EBT) = $51,000 minus $11,100 (debt interest) = $39,900

*Expansionary EBIT projections = $51,000 x (100% + 15%) = $58,650 & Earnings Before Tax = $58,650 minus $11,100 (debt interest) = $47,550

*Recessionary EBIT projections = $51,000 x (100% -24%) = $38,760 & Earnings Before Tax = $38,760 minus $11,100 (debt interest) = $27,660

Tax Rate = 24%

Solution to B1.

Scenario 1 (Projected Earnings)

Earnings Per Share (EPS) = Net Income (Earnings after Tax) divided by Outstanding Shares in Issue

Net Income = EBT minus tax = $39,900 - ($39,900 x 24%)

= $39,900 - $9,576

= $30,324

Outstanding shares in issue = 4,195 ordinary Shares

EPS = $30,324 divided by 4,195 shares = $7.23 Per share

Scenario 2 (Projected Earnings in a strong expansion)

Earnings Per Share (EPS) = Net Income (Earnings after Tax) divided by Outstanding Shares in Issue

Net Income = EBT minus tax = $47,550 - ($47,550 x 24%)

= $47,550 - $11,412

= $36,138

Outstanding shares in issue = 4,195 ordinary Shares

EPS = $36,138 divided by 4,195 shares = $8.62 Per share

Scenario 3 (Projected Earnings in a Recession)

Earnings Per Share (EPS) = Net Income (Earnings after Tax) divided by Outstanding Shares in Issue

Net Income = EBT minus tax = $27,660 - ($27,660 x 24%)

= $27,660 - $6,638.40

= $21,021.60

Outstanding shares in issue = 4,195 ordinary Shares

EPS = $21,021.60 divided by 4,195 shares = $5.01 Per share

Solution to B2.

1.Changes to EPS in an expansion = EPS (Expansion) minus EPS (normal projection), all divided by EPS (normal projection)

= (8.62 - 7.23) / 7.23

= +19.23% change during an expansion

2.Changes to EPS in a recession = EPS (Recession) minus EPS (normal projection), all divided by EPS (normal projection)

= (5.01 - 7.23) / 7.23

= -30.71% change during a recession

6 0

3 years ago

A machine fills 75 bottles of water each minute. Write an equation to represent the number of bottles b of water the machine can

Len [333]

Answer:

b = 75m

Step-by-step explanation:

8 0

3 years ago

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