MATHEMATICS HIGH SCHOOL

What is the value of a for the equation below?15 + 2a = 35
a = 10
a = 5
a = 20
a = 25

Answers

Answer 1
Answer:

Steps to solve:

15 + 2a = 35

~Subtract 15 to both sides

2a = 20

~Divide 2 to both sides

a = 10

Best of Luck!

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Kendra has a bowl containing 10 blue marbles, 15 yellow marbles, 5 green marbles, and red marbles of the same size. She will randomly put out a marble, keep it outside the bowl, then pull out another marble.What is the probability she will draw a red marble and then a yellow marble?

1/14
5/72
1/18
3/20

Answers

The answer is 1/14.

There are in total 36 marbles:
10 blue + 15 yellow + 5 green + 6 red.

The probability to put out a red marble in the first draw is 6 out of 36 marbles because there are 6 red marbles of total 36:
P(r) = 6/36 = 1/6.

After that 1 red marble is outside the bowl, there are now 35 marbles in total.
The probability to put out a yellow marble in the second draw is 15 out of 35 because there are 15 yellow marbles of total 35 marbles:
P(y) = 15/35 = 3/7.

If we want both these events to occur (1. to draw the red marble and 2. to draw the yellow marble), we will use a multiplication rule. The multiplication rule calculates the probability that both of two events will occur:
P(r) × P(y) = 1/6 × 3/7 = 3/42 = 1/14.

Therefore, the probability Kendra will draw a red marble and then a yellow marble is 1/14.

Triangle XYZ is translated 4 units up and 3 units left to yield triangle X'Y'Z'. What is the distance between any two corresponding points on triangle XYZ and triangle X'Y'Z'?

Answers

Answer

5 units


Explanation

The translation of the points X<Y and Z makes a right triangle with legs 3 units and 4 units.

The distance between the correspong is the hypotenuse of the triangle.

Using the Pythagoras theorem;

c² = a² + b²

Where a and b are the legs and c is the hypotenuse.

c²   = 3² + 4²

      = 9 + 16

       = 25

c    = √25

      = 5 units

The sum of two numbers is 30 & their difference is 12.

Answers

x+y=30
x-y=12
add them together

x+y=30
x-y=12+
2x+0y=42

2x=42
divide 2
x=21

subsitute
x+y=30
21+y=30
subtrat 21
y=9


number sare 21 and 9
The answer is 21 and 9. You can use guess and check to solve this. If you add 21 and 9, the sum is 30, and if you subtract 9 from 21, the difference is 12. 

14. A polygon ABCD is inscribed in a circle. Find angle ABC15. A polygon GHIJ is inscribed in a circle if GHI=76 and HIJ=66 what is IJG

Answers

Answer:

m<ABC = 100degrees

m<IJG = 104degrees

Step-by-step explanation:

14. The sum of the opposite angle of the quadrilateral is 180degrees. Hence;

m<ADC + m<ABC = 180

3y+8+4y+4 = 180

7y + 12 = 180

7y = 180 - 12

7y = 168

y = 168/7

y = 24

Get <ABC

m<ABC  = 4y+4

m<ABC = 4(24) + 4

m<ABC = 96 + 4

m<ABC = 100degrees

15. Similarly for this;

GHI + IJG = 180

76 + m<IJG = 180

m<IJG = 180 - 76

m<IJG = 104degrees

Steve bought 2 plain and 1/4 of a pepperoni pizza. In all how much pizza did he buy?

Answers

In all he brought

Plain pizza + pepperoni pizza

= 2 + ¼
= 2¼

A quantity m varies jointly with p and r. If m is 1, p is 2, and r is 4. What is the constant of variation?1/8
1/2
2
8

Answers

m vaires jointly as with p and r
m=kpr
m=1
p=2
r=4
sub
1=k*2*4
1=k*8
divide both sides by 8
1/8=k

answer is contatnt is 8

Answer:

A) 1/8

Step-by-step explanation:

Given:

A quantity "m" varies jointly with "p" and "r".

Now we have to form the equation.

m = kpr, where "k" is the constant.

Now we have to plug in the given values; m =1, p = 2 and r = 4 and find the value of k.

1 = k.2.4

1 = 8k

Divide both sides by 8, we get

8k/8 = 1/8

k = 1/8.
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