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2 years ago

Write the equation of the line in slope- intercept and point-slope form.

Mathematics

1 answer:

AnnZ [28]2 years ago

3 0

Answer:

Step-by-step explanation:

As we move from the x-intercept (-2, 0) to the y-intercept (0, 4), x increases by 2 (this is the run) and y by 4 (this is the rise). Thus, the slope of this line is

m = rise/run = 4/2 = 2.

Given the y-intercept (0, 4) and the slope (2), the slope-intercept form of the equation of this line is y = 2x + 4.

From this we get the point-slope form:

y = 2x + 4 becomes y - 4 = 2(x - 0), or just y - 4 = 2x.

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Collin's retirement party costs $4 for every guest he invites. What is the maximum number of guests there can be if Collin can a

steposvetlana [31]

Answer:

Collin can invite maximum 6 guest to his retirement party.

Step-by-step explanation:

Total cost of retirement party = $24

Cost to be spend on each guest = $4

Number of guests to be invited in the retirement party= x

$x\times \$4=\$24$

$x=\frac{\$24}{\$4}$

x = 6

Collin can invite maximum 6 guest to his retirement party.

6 0

3 years ago

Help and show explanation please

Dennis_Churaev [7]

The picture can be divided into 2 same triangles and one rectangular.

The triangle areas is {1/2 *base * height}*2 (because 2 same triangles)

and you need to sum rectangular area (width * base).
The result will be area of 2 triangle +area of rectangular.
=2(1/2*base of triangle* height)+ (base of rectangular * height)
= (base of triangle* height)+(base of rectangular * height)
=(base of triangle +base of rectangular)*height

b1 is top length
b2 is bottom length, and so

Base of triangle =(b1-b2/2)
Base of rectangular =b2
Height =h
Thus A ={(b1-b2/2)+b2 }*h
A= [(b1+b2)/2]*h

8 0

2 years ago

The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the arch. The width of the roadway is 38 feet and

forsale [732]

Answer:

Only truck 1 can pass under the bridge.

Step-by-step explanation:

So, first of all, we must do a drawing of what the situation looks like (see attached picture).

Next, we can take the general equation of an ellipse that is centered at the origin, which is the following:

$\frac{x^2}{a^2}+\frac{y^2}{b^2}$

where:

a= wider side of the ellipse

b= shorter side of the ellipse

in this case:

$a=\frac{38}{2}=19ft$

and

b=12ft

so we can go ahead and plug this data into the ellipse formula:

$\frac{x^2}{(19)^2}+\frac{y^2}{(12)^2}$

and we can simplify the equation, so we get:

$\frac{x^2}{361}+\frac{y^2}{144}$

So, we need to know if either truk will pass under the bridge, so we will match the center of the bridge with the center of each truck and see if the height of the bridge is enough for either to pass.

in order to do this let's solve the equation for y:

$\frac{y^{2}}{144}=1-\frac{x^{2}}{361}$

$y^{2}=144(1-\frac{x^{2}}{361})$

we can add everything inside parenthesis so we get:

$y^{2}=144(\frac{361-x^{2}}{361})$

and take the square root on both sides, so we get:

$y=\sqrt{144(\frac{361-x^{2}}{361})}$

and we can simplify this so we get:

$y=\frac{12}{19}\sqrt{361-x^{2}}$

and now we can evaluate this equation for x=4 (half the width of the trucks) so:

$y=\frac{12}{19}\sqrt{361-(8)^{2}}$

y=11.73ft

this means that for the trucks to pass under the bridge they must have a maximum height of 11.73ft, therefore only truck 1 is able to pass under the bridge since truck 2 is too high.

5 0

3 years ago

Chris entered a hot dog eating contest. The table shows how many hot dogs remained in his tray at different times.

babymother [125]

The hot dogs remaining are decreasing by 11 as 2 minutes go by.

11 / 2 = 5.5

So he's eating 5.5 hot dogs per minute.

Minutes 2 4 6 8 9
Hot dogs remaining 49 38 27 16 5

5 0

3 years ago

Read 2 more answers

There are 14 tops you’d like to purchase, but you can only afford six. If you select tops at random, how many different groups o

Slav-nsk [51]

Answer:

3003 different groups of 6tops

Step-by-step explanation:

Using the combination formula, generally, when selecting r number of objects out of a pool of n numbers, this can be done in nCr number of ways.

nCr = n!/(n-r)!r!

If there are 14 tops I'd like to purchase and I can only afford six, the number of ways I can choose this six at random from the 14tops can be done in 14C6 number of ways.

14C6 = 14!/(14-6)!6!

14C6 = 14!/8!6!

14C6 = 14×13×12×11×10×9×8!/8!×6×5×4×3×2

14C6 = 14×13×12×11×10×9/6×5×4×3×2

14C6 = 14×13×12×11/8

14C6 = 3003ways

5 0

3 years ago

Write the equation of the line in slope- intercept and point-slope form.​

Write the equation of the line in slope- intercept and point-slope form.