109.06 in scientific notation is

Calculate the quotient. If needed, draw a model. 3/4 divided by 1/5

a_sh-v [17]

Answer:

15/4, or 3.75

Step-by-step explanation:

all i really did was plug it into the calculator like so: (3/4)/(1/5) and thats what came out

6 0

2 years ago

brooke found the equation of the line passing through the points (-7,25) and (-4,13) in slope-intercept form as follows

Goryan [66]

Answer:

The equation of the line passing through the points (-7,25) and (-4,13) in slope-intercept form is $\mathbf{y=-4x-3}$

Step-by-step explanation:

Equation of line passing through the points (-7,25) and (-4,13) in slope-intercept form.

The general equation of slope-intercept form is: $y=mx+b$

First we need to find slope

The formula used for finding slope is: $Slope=\frac{y_2-y_1}{x_2-x_1}$

We are given: $x_1=-7, y_1=25, x_2=-4, y_2=13$

Putting values in formula and finding slope

$Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{13-25}{-4-(-7)}\\Slope=\frac{13-25}{-4+7}\\Slope=\frac{-12}{3}\\Slope=-4$

So, slope m= -4

Now finding y-intercept

Using slope m=-4 and point (-7,25) we can find y-intercept

$y=mx+b\\25=-4(-7)+b\\25=28+b\\b=25-28\\b=-3$

So, y-intercept b =-3

Now, the equation of required line having slope m=-4 and y-intercept b=-3 is:

$y=mx+b\\y=-4x-3$

So, the equation of the line passing through the points (-7,25) and (-4,13) in slope-intercept form is $\mathbf{y=-4x-3}$

3 0

2 years ago

Ben needs 1 3/8 feet of fabric to make one banner. How many banners can he make from 4 1/2 yards of fabric?

skelet666 [1.2K]

Answer:

x = 9.818

x≈10

The number of banners that can be made are 10

Step-by-step explanation:

We can use the knowledge of proportion to solve this.

First we need to convert yard to feet.

1 yard = 3 foot

4 1/2 yard = y

cross-multiply

y = 4 1/2 × 3

=9/2 × 3

y = $\frac{27}{2}$ feet

This implies 4 1/2 yards = $\frac{27}{2}$ feet

Let x be the numbers of banners needed to make from 4 1/2 yards of fabric.

1 3/8 feet = 1 banner

$\frac{27}{2}$ feets = x

cross multiply

1 3/8 × x = $\frac{27}{2}$

$\frac{11x}{8}$ = $\frac{27}{2}$

cross-multiply

22x = 216

Divide both-side of the equation by 22

22x/22 = 216/22

x = 9.818

x≈10

The number of banners that can be made are 10

3 0

3 years ago

Matlab a farmer wishes to build a rectangular pen for his animals out of 40 feet of fencing what should be the length and width

ASHA 777 [7]

Width=w
length=(40-2w)/2=20-w
A=w(40-w)
A=40w-w²
A'=40-2w=0
2w=40
w=20

20x20 is the size of the pen having the greatest area. this tells us the largest rectangle for a given perimeter is a square

8 0

2 years ago

Find the coordinates of the orthocenter for XYZ with X(-5,-1) Y(-2,4), Z(3,-1)

V125BC [204]

9514 1404 393

Answer:

(-2, 2)

Step-by-step explanation:

The orthocenter is the intersection of the altitudes. The altitude lines are not difficult to find here. Each is a line through the vertex that is perpendicular to the opposite side.

Side XZ is horizontal, so the altitude to that side is the vertical line through Y. The x-coordinate of Y is -2, so that altitude has equation ...

x = -2

__

Side YZ has a rise/run of -1/1 = -1, so the altitude to that side will be the line through X with a slope of -1/(-1) = 1. In point-slope form, the equation is ...

y -(-1) +(1)(x -(-5))

y = x +4 . . . . . . . . subtract 1 and simplify

The orthocenter is the point that satisfies both these equations. Using the first equation to substitute for x in the second, we have ...

y = (-2) +4 = 2

The orthocenter is (x, y) = (-2, 2).

4 0

3 years ago