Answer:
1 : 15
2: 12
3: 52
4: 27.3
Step-by-step explanation:
For #1:
if line m and n are perpendicular then they will create right angles
Right angles have a measure of 90 degrees
That being said we can find the measure of the missing angle by subtracting the measure of the known angle (75) from 90
so k = 90 - 75
90 - 75 = 15
Hence k = 15.
For #3 ( very similar to #1, only difference is the values of the angles )
so R = 90 - 38
90 - 38 = 52
Hence, R = 52
For #2 and #4
Complementary angles have a sum of 90°
So like the previous questions we can find the measure of the missing angle by subtract the measure of the given angle from 90
∠V = 90 - 78
90 - 78 = 12
Hence ∠V = 12
∠Y = 90 - 62.7
90 - 62.7 = 27.3
Hence ∠Y = 27.3
Answer:
See Attachment.
Step-by-step explanation:
To create the new figure, we must multiply each coordinate by the scale factor, which is 1/2 in this case.
So j(-2,2) becomes j'(-1,1)
K(4,2) becomes K'(2,1)
L(4,-2) becomes L'(2,-1)
and M (-2,-2) becomes M'(-1,-1)
The scale factor is between 1 and 0 which means that this dilation is a reduction that will shrink the original figure to a smaller one.
Answer:
- 12 gallons 84%
- 8 gallons 4%
Step-by-step explanation:
I like to use an "X-diagram" to solve mixture problems. On the left side are the constituents of the mix; in the middle is the result of the mix; and on the right side are the differences between the numbers on each diagonal. These differences are the ratio numbers for the mix.
Here, that means the ratio of 84% solution to 4% solution is ...
48 : 32 = 12 : 8
Note that the last two "ratio numbers" were chosen so their sum is 20, hence they represent the number of gallons of the corresponding constituent in the mix. (The sum of the first two ratio numbers is 48+32=80, so to get a sum of 20, we divide each by 4.)
Mary must use ...
- 12 gallons of 84% acid solution
- 8 gallons of 4% acid solution
You may note that this solution takes much longer to explain than to do. The math here can all be done without a calculator.
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<em>Check</em>
12 × 84% + 8 × 4% = 10.40 = 20 × 52%
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<em>Usual Solution</em>
A more conventional approach would be to assign x to the amount of 84% solution needed. Then the number of gallons of acid in the mix is ...
0.84x + 0.04(20 -x) = 0.52(20)
0.80x + 0.8 = 10.4 . . . . simplify
0.80x = 9.6 . . . . . . . . . . subtract 0.8; next, divide by 0.8
x = 9.6/0.8 = 12 . . . . gallons of 84% acid
20-x = 8 . . . . . . . . . . gallons of 4% acid