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qwelly [4]
2 years ago
9

Write an equation in point-slope form and slope-intercept form for each line.

Mathematics
1 answer:
Trava [24]2 years ago
8 0

Step-by-step explanation:

Point slope-form of a line passing through the point (x_0, y_0) and having m is y-y_0=m(x-x_0)\cdots(i)

The slope-intercept form of a line having slope m and y-intercept c is

y=mx+c\cdots(ii)

(1). The line is passing through (x_0, y_0)=(-5,6) and having the slope m=3.

So, by using equation (i), the point-slope form of the line is

y-6=3(x-(-5))

\Rightarrow y-6=3(x+5)

By using equation (ii), the slope-intercept form of the line is

y=3x+c\cdots(iii)

as the line is passing through the point (-5,6), so pout this point in the equation (iii) to get the value of c.

6=3\times(-5)+c

\Rightarrow 6=-15+c

\Rightarrow c=6+15=21

From equation (iii), the slope-intercept form of the line is y=3x+21.

(2). The line is passing through the points (–5, 9) and (1, 3).

As two points are given, so the slope of the line is

m=\frac{3-9}{1-(-5)}=-1.

Now, proceeding in the same way as in part (1),

By using equation (i), the point-slope form of the line is

y-3=-1(x-1) [taking point (1,3) and m=-1]

By using equation (ii), the slope-intercept form of the line is

y=(-1)x+c\cdots(iv)

as the line is passing through the point (1,3), so pout this point in the equation (iv) to get the value of c.

3=-1\times1+c

\Rightarrow 3=-1+c

\Rightarrow c=3+1=4

From equation (iv), the slope-intercept form of the line is y=-x+4.

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39=1 3/10b what will be the answer show work
Lubov Fominskaja [6]
1 3/10·b=39
(1·10+3)·b/10=39
13b/10=39
13b=39·10
13b=390|:13
<u>b=30</u>

<em>Answer: 30</em>
4 0
3 years ago
Two terms of a geometric sequence are given. Find the first five terms. Please help asap
Zepler [3.9K]

Answer:

4, 8, 16, 32, 64

Step-by-step explanation:

The nth term of a geometric sequence is

a_{n} = a₁(r)^{n-1}

Given

a₇ = 256 and a₁₀ = 2048 , then

a₁ r^{6} = 256 → (1)

a₁ r^{9} = 2048 → (2)

Divide (2) by (1)

\frac{a_{1}r^{9}  }{a_{1}r^{6}  } = \frac{2048}{256}

r³ = 8 ( take the cube root of both sides )

r = \sqrt[3]{8} = 2

Substitute r = 2 into (1)

a₁ × 2^{6} = 256

a₁ × 64 = 256 ( divide both sides by 64 )

a₁ = 4

Then

a₁ = 4

a₂ = 2a₁ = 2 × 4 = 8

a₃ = 2a₂ = 2 × 8 = 16

a₄ = 2a₃ = 2 × 16 = 32

a₅ = 2a₄ = 2 × 32 = 64

7 0
3 years ago
Greg runs 3 miles in 28 minutes. At the same rate, how many miles would he run in 42 minutes?
Paladinen [302]

Answer:

4.5

 miles

Step-by-step explanation:

Well, he runs

3

miles in

28

minutes. Also, see that

42

=

28

⋅

1.5

.

So, his journey would just be running

1.5

times, with each time running

28

minutes.

So, he runs a total of

1.5

⋅

3

=

4.5

miles

7 0
3 years ago
Read 2 more answers
Andrea has a goal of running at least 50 miles this month. She has already run 7 miles. How many miles does Andrea need to run e
Nuetrik [128]

Answer:

At least 1.72 miles per day.

Step-by-step explanation:

Given: Goal of running is at least 50 miles in a month.

           Andrea have already run 7 miles.

           Days left in the month is 25.

As given, Andrea have already run 7 miles.

∴ Andrea need to run this month= 50\ miles - 7\ miles= 43\ miles

Days remaining this month is 25.

Now, finding miles need to run each day to meet her goal.

Miles need to run each day= \frac{remaining\ miles}{remaining\ days}

⇒ Miles need to run each day= \frac{43}{25} = 1.72\ miles

∴ Andrea need to run at least 1.72 miles to meet her goal this month.

           

8 0
3 years ago
PLEASE help with these questions??<br> there are 7 of them!<br> Thank you!!
svetlana [45]
We know in these kind of triangles that have a 90 degrees angle, we can do:

{a}^{2} + {b}^{2} = {c}^{2}

so the first question:

\sqrt{ {99}^{2} + {20}^{2} } = 101

and then:

b = \sqrt{ {17}^{2} - {15}^{2} } = 8

so , when you want to rationalize , usually you must multiply the irrational factor as 1:

\frac{ \sqrt{15} }{ \sqrt{15} } = 1

so , now multiply:

\frac{3}{ \sqrt{15} } \times \frac{ \sqrt{15} }{ \sqrt{15} } = \frac{3 \sqrt{15} }{15} = \frac{ \sqrt{15} }{5}

in the next question,we know negative numbers in radical don't have any solution so 2 is correct,

4 0
3 years ago
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