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san4es73 [151]
3 years ago
5

Please help me! Write an equation in point-slope form of the line that passes through the given point and has the given slope.

Mathematics
1 answer:
andriy [413]3 years ago
8 0

9514 1404 393

Answer:

  1. y -3 = 5(x -1)
  2. y +1 = -3(x +2)
  3. y +7 = -1/4(x -4)

Step-by-step explanation:

When you are given a point and a slope, and asked for the equation in point-slope form, it is simply a matter of putting the given numbers into the appropriate places in the equation template.

  y -k = m(x -h) . . . . . . point (h, k), slope m

__

1. y -3 = 5(x -1) . . . . . . point (1, 3), slope 5

2. y +1 = -3(x +2) . . . . point (-2, -1), slope -3

  note that for k=-1, -k = -(-1) = +1; similarly the value of -h becomes +2

3. y +7 = -1/4(x -4) . . . point (4, -7), slope -1/4

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How do I solve these problems? ln(x) = 5.6 + ln(7.5) and log(x) = 5.6 - log(7.5)
SOVA2 [1]

Use the rules of logarithms and the rules of exponents.

... ln(ab) = ln(a) + ln(b)

... e^ln(a) = a

... (a^b)·(a^c) = a^(b+c)

_____

1) Use the second rule and take the antilog.

... e^ln(x) = x = e^(5.6 + ln(7.5))

... x = (e^5.6)·(e^ln(7.5)) . . . . . . use the rule of exponents

... x = 7.5·e^5.6 . . . . . . . . . . . . use the second rule of logarithms

... x ≈ 2028.2 . . . . . . . . . . . . . use your calculator (could do this after the 1st step)

2) Similar to the previous problem, except base-10 logs are involved.

... x = 10^(5.6 -log(7.5)) . . . . . take the antilog. Could evaluate now.

... = (1/7.5)·10^5.6 . . . . . . . . . . of course, 10^(-log(7.5)) = 7.5^-1 = 1/7.5

... x ≈ 53,080.96

8 0
3 years ago
Find the value of x.. is the answer 103? if not how do you figure it our
scoundrel [369]

The angle diagonal to 103° is equal to 103°.  So here's your equation:

(103+14x+7)°=180°

So now you can simplify:

110°+14x=180°

now subtract 110 on both sides

14x=70°

now divide by 14 on both sides

so the answer is x=5°

hope this helps


5 0
3 years ago
Which ordered pair is a solution of the equation y=x-4
Andreyy89
The answer would be y=-4 and x=4, so pick which ever number/letter has this answer.
5 0
4 years ago
Read 2 more answers
Write a 3-digit number that can be divided by 3 but not by 10.
NARA [144]

Answer:

Hi

999

Step-by-step explanation:

8 0
3 years ago
Simplify. -10m+2m^4-13m-20m^4
Ulleksa [173]
First one:

you can add -10m and -13m but you can't add -10m and 2m^4 becuase the powers aren't the same so

when adding the like terms
look at the:
powers, (x^3 adds with x^3)
placehloder letter (x adds with x and y adds with y and so on)

-10m+2m^4-13m-20m^4
powers: m^1 and M^4
placeholders: all m


add
-10m-13m+2m^4-20m^4
-23m-18m^4




second one:
when multiplying exponents, you add with like
so if you multipliy
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when multiply with coeficients
2x^2yz^3 times 4x^4y^2z^2=8x^6y^3z^5
so using associative property a(bc)=(ab)c
2/3 times p^4 times y^3 times y^4 times s^5 times 6 times p^2 times s^3
group like terms

(2/3 times 6) times (p^4 times p^2) times (y^3 times y^4) times (s^5 times s^3)
(4) times (p^6) times (y^7) times (s^8)
4p^6y^7s^8

8 0
3 years ago
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