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3 years ago

If (x+3) varies directly as y and x=3 when y=12, what is the value of x when y=8?

Mathematics

1 answer:

slavikrds [6]3 years ago

6 0

Answer:

x = 1.

Step-by-step explanation:

y = k(x + 3)

When x = 3 y = 12 so

12 = k(3 + 3)

6k = 12

k = 2.

So the relation is y = 2(x + 3)

When y is 8:

8 = 2(x + 3)

2x = 8 - 2*3 = 2

x = 1.

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Devide 840 in the ratio 3:4

tia_tia [17]

Answer:

360:480

We know the total (840) so add the ratio: 3 + 4 =7

Divide 840 by 7 = 120

Multiply each part of the ratio by 120

3 x 120 = 360

4 x 120 = 480

Step-by-step explanation:

6 0

3 years ago

I need help or the answer

loris [4]

Answer:

5x+4y = 52

Step-by-step explanation:

We can first write the equation in point slope form

y-y1 = m(x-x1) where m is the slope and (x1,y1) is the point

y - 8 = -5/4 ( x-4)

Multiply each side by 4 to get rid of the fraction

4(y - 8) = 4*(-5/4) ( x-4)

4(y - 8) = -5 ( x-4)

Distribute

4y - 32 = -5x+20

We want the equation in the form

Ax + By = C

Add 5x to each side

5x+4y -32 = -5x+5x+20

Add 32 to each side

5x+4y -32+32 =32+20

5x+4y = 52

4 0

3 years ago

If the slope and a point of a line are given, then the equation of the line can be written in point-slope form. True False

denis23 [38]

True, just plug the slope and points into the formula: y - y1 = m(x - x1), where y1 is the y number, m is the slope, and x1 is the x number.

6 0

3 years ago

8-35. Use your knowledge of polygons to answer the questions below, if possible.

Nataliya [291]

Answer:

(a)I. 13 Sides II. 7 Sides

(b) 4 Sides, Square

(c)x=52 degrees

(d)x=107 degrees

(e)1620 degrees

Step-by-step explanation:

(a)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

I. If the Interior angle is $1980^0$

Then:

$(n-2)180^0=1980^0\\$Divide both sides by 180^0 $ to isolate n$\\n-2=11\\$Add 2 to both sides of the equation\\n-2+2=11+2\\n=13$

The polygon has 13 sides.

II. If the Interior angle is $900^0$

Then:

$(n-2)180^0=900^0\\$Divide both sides by 180^0 $ to isolate n$\\n-2=5\\$Add 2 to both sides of the equation\\n-2+2=5+2\\n=7$

The polygon has 7 sides.

(b)The sum of the exterior angle of a polygon is 360 degrees,

Each exterior angle of a n-sided regular polygon is: $\frac{360^0}{n}$

If the exterior angle of a regular polygon is 90°

Then:

$90\°=\frac{360^0}{n}\\ 90n=360\\n=4$

The regular polygon has 4 sides and it is called a Square.

(c)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

Each Interior angle of a regular n-sided polygon is: $\frac{(n-2)180^0}{n}$

For a pentagon, n=5

Then:

$\frac{(5-2)180^0}{5}=2x+4\\108=2x+4\\108-4=2x\\104=2x\\x=52^0$

(d)The sum of the exterior angle of a polygon is 360 degrees.

If four of the exterior angles of a pentagon are 57, 74, 56, and 66.

Let the fifth angle=x

Then:

$57+74+56+66+x=360^0\\253+x=360\\x=107^0$

(e)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

In an 11-gon., n=11

Therefore, the sum of the interior angle=(11-2)180= $1620^0$

The sum of the interior angle does not change either in a regular or irregular polygon.

3 0

3 years ago

According to Masterfoods, the company that manufactures M&M's, 12% of peanut M&M's are brown, 15% are yellow, 12% are re

Luda [366]

Answer:

The questions asked are

If you randomly select 4 peanuts

1. Compute the probability that exactly three of the four M&M’s are brown

2. Compute the probability that two or three of the four M&M’s are brown.

3. Compute the probability that at most three of the four M&M’s are brown.

4. Compute the probability that at least three of the four M&M’s are brown.

Step-by-step explanation:

Given the following information

Brown=12%. P(B)=0.12

Yellow=15%. P(Y)=0.15

Red=12%. P(R), =0.12

Blue=23%. P(B) =0.23

Orange, =23%. P(O) =0.23

Green=15%. P(G)=0.15

Question 1.

They are independent events

If there are exactly three brown and the last is not brown

P(B n B n B n B')

P(B)×P(B)×P(B)×P(B')

0.12×0.12×0.12×(1-P(B))

0.001728×(1-0.12)

0.001728×0.88

0.00152.

0.152%

2. If two or three are brown

I.e we are going to two brown and two none brown or three brown and one not brown. (P(B)×P(B)×P(B')×P(B'))+ (P(B)×P(B)×P(B'))

(0.12×0.12×0.88×0.88)+(0.12×0.12×0.12×0.88)

0.0112+0.00152

0.0127

1.27%

3. At most three brown out of four then we are going to have

BBBB', BBB'B', BB'B'B', B'B'B'B'

These are the cases of at most three brown.

P(B)×P(B)×P(B)×P(B') + P(B)×P(B)×P(B')×P(B') + P(B)×P(B')×P(B')×PB')+ P(B')×P(B')×P(B')×P(B')=

0.12×0.12×0.12×0.88+ 0.12×0.12×0.88×0.88+ 0.12×0.88×0.88×0.88+ 0.88×0.88×0.88×0.88=0.694

0.694

69.4%

4. At least 3 brown out of four selection

I.e BBBB', BBBB

These are the two options

P(B)×P(B)×P(B)×P(B') + P(B)×P(B)×P(B)×P(B)=

0.12×0.12×0.12×0.88 + 0.12×0.12×0.12×0.12

0.001728

0.173%

4 0

3 years ago

Read 2 more answers