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olchik [2.2K]
3 years ago
8

Help would really be appreciated with this one!

Mathematics
1 answer:
Marta_Voda [28]3 years ago
4 0
Point slope is nicer
y-y1=m(x-x1)
goes through the point (x1,y1) and has a slope of m

slope itnercept
y=mx+b
m=slope
b=y intercept




first find slope
slope between 2 points (x1,y1) and (x2,y2) is (y2-y1)/(x2-x1)
given
(7,82) and (4,18)
slope=(18-82)/(4-7)=-64/-3=64/3


point slope
point is (7,82) or you can do (4,18)
I'll do both
y-82=(64/3)(x-7) or
y-18=(64/3)(x-4)
those both work



slope intercept
slope is 64/3
y=64/3x+b
find b
input a point
(4,18)
18=64/3(4)+b
18=256/3+b
minus 256/3 from both sides
note: 18=54/3
-202/3=b
y=64/3x-202/3 is equation in slpe intercept
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A linear equation in two variables has infinitely many solution the set of all solutions to a linear equation in two variables f
Greeley [361]
<span>1, During a 1-hr television program, there were 22 commercials, Some commercials were 15 sec and some were 30 sec long. Find the number of 15- sec commercials and the number of 30 sec commercial if the total playing time for commercial was 9.5 minutes.

</span>a) <span>show how to formulate your system of equations for your problem,

Answer:
- state the variables: x number of 15 sec commercials, y number of 30 sec commercials
- translate the word statement into algebraic language

b) state the two equations:

- translate the word statement into algebraic equations:

</span><span>* there were 22 commercials => x + y = 22
* the total playing time for commercial was 9.5 minutes => 15x + 30y = 9.5*60 </span><span>

Answer:
Equation (1) x + y = 22
Equation (2) 15x + 30y =  570

c) state which method you will use to solve either addition or substitution

Answer:
adition: multiply the first equation times - 15 and add the two equations.

d) solve your system showing and explaining each step of the process

Answer:
- muliply eq (1) times - 15

-15x - 15y = - 330

- add that to the eq (2):

-15x + 15x - 15y + 30y = -330 + 570

- add like terms: 15y = 240

- divide both members by 15: 15y/15 = 240 / 15 => y = 16

- replace y = 16 in eq I(1) => x + 16 = 22 => x = 22 - 16 = 6

Solution: x = 6, y = 16

e) Be sure to check your solution!

x + y = 22
6 + 16 = 22
22 = 22 --> check

15x + 30y = 9.5*60
15(6) + 30(16) = 570
90 + 480 = 570
570 = 570 ---> check

f) Once a solution is found explain what this solution means in the context of the problem, write the answer to the word problem in words</span><span>

The solution means that d</span><span>uring a 1-hr television program, there were</span><span> 6 commercials of 15 sec and 16 commercials of 30 sec.

2, How many quarts of water should be mixed with a 30% vinegar solution to obtain 12 qt of a 25% vinegar solution. (Hint: water is 0% vinegar).</span>

a) variables:

- state the variables
x: number of quarters of water
y: number of quarters of vinegar

- translate the words into mathematical language

12 qt 25% vinegar solution

=> total number of quarts = 12 = x + y

balance in vinegar:

vinegar from water + vinegar from 30% vinegar solution = vinegar in the 25% vinegar solution

0 + 0.3y = 0.25 (x + y)

c) Equations

Eq (1) x + y = 12

Eq (2): 0.3y = 0.25x + 0.25y

=> 0.25x - 0.05y = 0

d) solve

- multiply eq (1) times 0.05 and add to eq (2)

0.05x + 0.05y = 0.6
0.25x - 0.05y = 0
------------------------
0.30x = 0.6

x = 0.6 / 0.3 = 2

x + y = 12 => y = 12 - y = 12 - 2 = 10

Solution: x = 2, y = 10

e) check:

x + y = 12
2 qt + 10qt = 12 qt
12 qt = 12 qt ---> check

vinegar:

10*0.3 = 12*0.25
3 = 3 -> check

f) Explanation of the solution

The solution means that you have to mix 2 qts of water with 10 qts of 30% vinegar solution to obtain 12 qt of 25% vinegar solution.

5 0
3 years ago
7.05, 5.07,7.5,0.57 least to greatest
Rudiy27

0.57 , 5.07 , 7.05 , 7.5

7 0
3 years ago
Read 2 more answers
What’s the correct answer for this question?
crimeas [40]

ANSWER

l

Or

Or

EXPLANATION

The given line has slope,

and

We can find the equation in the point slope form, which is given by,

We substitute the point and slope to get,

We can also simplify further to get,

We make y the subject to get,

This is called the slope intercept form.

We could also write in standard form to get

Or

5 0
3 years ago
5, 18, 6, 18, 13 WHATS THE INTERQUARTILE RANGE??
Harlamova29_29 [7]

Answer: 12.5

Step-by-step explanation:

25th Percentile: 5.5

50th Percentile: 13

75th Percentile: 18

Interquartile Range: 12.5

5 0
3 years ago
3 and 1/2 x 6 and 1/2
Lera25 [3.4K]

Answer:

91/4 or 22 3/4

Step-by-step explanation: i just know

5 0
3 years ago
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