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VMariaS [17]
3 years ago
13

This year, Carmen watched 70 movies. She thought that 21 of them were very good. Of the movies she watched, what percentage did

she think were very good?
Mathematics
1 answer:
spin [16.1K]3 years ago
8 0

Carmen thought 30% of the movies were good.

I found the percent by dividing 21 by 70

21/70= .3

.3= 30%

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A 22-foot ladder is leaning up against the side of a house. The ladder makes an angle of 77o with the ground. How far up the sid
Crank

Answer:

21.44 ft

Step-by-step explanation:

(sketch to understand)

use SOH/CAH/TOA rules to solve

sin rule is used

solve for x

(working in the picture attached)

8 0
2 years ago
Find the equation of the directrix of the parabola x2=+/- 12y and y2=+/- 12x
PIT_PIT [208]

Answer:

  1. x^2 = 12 y equation of the directrix y=-3
  2. x^2 = -12 y equation of directrix y= 3
  3. y^2 = 12 x   equation of directrix x=-3
  4. y^2 = -12 x equation of directrix x= 3

Step-by-step explanation:

To find the equation of directrix of the parabola, we need to identify the axis of the parabola i.e, parabola lies in x-axis or y-axis.

We have 4 parts in this question i.e.

  1. x^2 = 12 y
  2. x^2 = -12 y
  3. y^2 = 12 x
  4. y^2 = -12 x

For each part the value of directrix will be different.

For x²  = 12 y

The above equation involves x² , the axis will be y-axis

The formula used to find directrix will be: y = -a

So, we need to find the value of a.

The general form of equation for y-axis parabola having positive co-efficient is:

x² = 4ay  eq(i)

and our equation in question is: x² = 12y eq(ii)

By putting value of x² of eq(i) into eq(ii) and solving:

4ay = 12y

a= 12y/4y

a= 3

Putting value of a in equation of directrix: y = -a => y= -3

The equation of the directrix of the parabola x²= 12y is y = -3

For x²  = -12 y

The above equation involves x² , the axis will be y-axis

The formula used to find directrix will be: y = a

So, we need to find the value of a.

The general form of equation for y-axis parabola having negative co-efficient is:

x² = -4ay  eq(i)

and our equation in question is: x² = -12y eq(ii)

By putting value of x² of eq(i) into eq(ii) and solving:

-4ay = -12y

a= -12y/-4y

a= 3

Putting value of a in equation of directrix: y = a => y= 3

The equation of the directrix of the parabola x²= -12y is y = 3

For y²  = 12 x

The above equation involves y² , the axis will be x-axis

The formula used to find directrix will be: x = -a

So, we need to find the value of a.

The general form of equation for x-axis parabola having positive co-efficient is:

y² = 4ax  eq(i)

and our equation in question is: y² = 12x eq(ii)

By putting value of y² of eq(i) into eq(ii) and solving:

4ax = 12x

a= 12x/4x

a= 3

Putting value of a in equation of directrix: x = -a => x= -3

The equation of the directrix of the parabola y²= 12x is x = -3

For y²  = -12 x

The above equation involves y² , the axis will be x-axis

The formula used to find directrix will be: x = a

So, we need to find the value of a.

The general form of equation for x-axis parabola having negative co-efficient is:

y² = -4ax  eq(i)

and our equation in question is: y² = -12x eq(ii)

By putting value of y² of eq(i) into eq(ii) and solving:

-4ax = -12x

a= -12x/-4x

a= 3

Putting value of a in equation of directrix: x = a => x= 3

The equation of the directrix of the parabola y²= -12x is x = 3

5 0
3 years ago
The total number of students in the seventh grade is 9 more than 4 times as many students as are in the art class. If there are
mariarad [96]

Answer:

I think there are 23 students in the art class.

Step-by-step explanation:

You first subtract 9 from 101. Then, you divide by four to get 23.

4 0
3 years ago
Just before her party starts, Jane fills a cooler with 80 cups of ice. She also starts filling glasses with ice, 0.8 cups each.
Fofino [41]

The equation that shows how the total number of cups of ice used, y, depends on the number of glasses filled, x, is y = 0.8x + 80

<h3>Linear function</h3>

Filling the cooler is an illustration of a linear function

A linear function is represented as: y = mx + b

Where

  • m represents the slope/rate
  • b represents the y-intercept/the initial value
  • x and y are the variables

<h3>The equations</h3>

By comparison, we have the following parameters

  • m =0.8 --- the amount of cups per ice
  • b = 80 ---- the initial amount of cup

So, the equation that represents this scenario is

y = 0.8x + 80

Read more about linear functions at:

brainly.com/question/14323743

5 0
2 years ago
What is the reason that supports the statement made on line 5?​
creativ13 [48]

Answer:

V is given to be midpoint of WZ and XY

=> WV = VZ and XV = VY (1)

As opposite angles,

=> WVX = ZVY (2)

From (1) and (2), then

Triangle WXV = Triangle ZYV (SAS)

=> Option SAS is correct.

Hope this helps!

:)

8 0
3 years ago
Read 2 more answers
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