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Slav-nsk [51]
2 years ago
7

Write the equation through (2,5) parallel to the line through (8,0) and (0,8)

Mathematics
1 answer:
klio [65]2 years ago
6 0

Answer:

y = -x + 7

Step-by-step explanation:

As we move from (8, 0) to (0, 8), we see x decreasing by 8 ('rise') and y increasing by 8 ('run').  Thus, the slope of this line is m = rise/run = 8/(-8) = -1.

Starting from y = mx + b and substituting 8 for x, 0 for y and -1 for m, we get:

0 = -1(8) + b, or b = 8

Then the equation of the line through the two given points is y = -x + 8.  Any line parallel to this one has the same slope:  m = -1.

Repeat the above work to find the y-intercept of the line parallel to y = -x + 8  that goes through (2, 5):

5 = -2 + b, or b = 7

Then the desired line (final answer) is y = -x + 7

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Which values are equivalent to the fraction below? 6^7/6^5
Helen [10]

Answer:

36

Step-by-step explanation:

Because the bases are the same we can just subtract the exponents to get us 6² or 36.

4 0
3 years ago
An angle of measure 120 degrees intersects the unit circle at point (-1/2,√3/2) What is the exact value of cos(120)
notka56 [123]

The exact value of cos120 if the measure 120 degrees intersects the unit circle at point (-1/2,√3/2) is 0.5

<h3>Solving trigonometry identity</h3>

If an angle of measure 120 degrees intersects the unit circle at point (-1/2,√3/2), the measure of cos(120) can be expressed as;

Cos120 = cos(90 + 30)

Using the cosine rule of addition

cos(90 + 30) = cos90cos30 - sin90sin30

cos(90 + 30) = 0(√3/2) - 1(0.5)

cos(90 + 30) = 0 - 0.5

cos(90 + 30) = 0.5

Hence the exact value of cos120 if the measure 120 degrees intersects the unit circle at point (-1/2,√3/2) is 0.5

Learn more on unit circle here: brainly.com/question/23989157

#SPJ1

7 0
1 year ago
What is the standard form of x/4 - y/3 =1 and 5/x - 2/y=7.
kompoz [17]
You can multiply both sides by a number that will get rid of the denominators. For ex. you can multiply the first equation by 12 because 4 and 3 both go into 12 evenly. MAKE SURE YOU MULTIPLY THE OTHER SIDE BY 12 AS WELL! Therefore, 12(x/4) - 12(y/3) = 12(1), or 3x - 4y = 12
5 0
3 years ago
A bag contains 8 purple marbles &amp; 12 green marbles. You choose one marble out of the bag without looking.
MrRissso [65]

Answer:

1. P(P) = 8/20 = 0.4

2. P(G) = 12/20 = 0.6

Step-by-step explanation:

Given;

Number of green marbles G = 12

Number of purple marbles P = 8

Total T = 12+8 = 20

The probability that you choose a purple marble P(P) is;

P(P) = number of purple marbles/total number of marbles

P(P) = P/T = 8/20 = 0.4

P(P) = 0.4

The probability that you choose a Green marble P(G) is;

P(G) = number of Green marbles/total number of marbles

P(G) = G/T = 12/20 = 0.6

P(G) = 0.6

6 0
3 years ago
In tests for intoxication, blood alcohol levels are expressed as percentages by volume. A blood alcohol level of 0.080% by volum
GaryK [48]

Answer:

The required volume is 5 ml.

Step-by-step explanation:

Given : In tests for intoxication, blood alcohol levels are expressed as percentages by volume. A blood alcohol level of 0.080% by volume means 0.080 mL of ethanol per 100 mL of blood and is considered proof of intoxication. If a person's total blood volume is 5.0 L.

To find : What volume of alcohol in the blood gives a blood alcohol level of 0.100 % by volume?

Solution :

According to question we use the formula,

\text{Present Volume}=\dfrac{\text{Vol}_{\text{Alcohol}}}{\text{Vol}_{\text{total}}}\times 100\%

The percentage of a blood alcohol level is 0.100%

The total volume of the blood is V=5L=5000 ml.

Substitute the value in the formula,

0.100=\dfrac{\text{Vol}_{\text{Alcohol}}}{5000}\times 100

\frac{0.100}{100}=\dfrac{\text{Vol}_{\text{Alcohol}}}{5000}

\text{Vol}_{\text{Alcohol}}=\frac{0.100\times 5000}{100}

\text{Vol}_{\text{Alcohol}}=5

Therefore, the required volume is 5 ml.

8 0
3 years ago
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