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Ivahew [28]
2 years ago
7

Write the equation of the line when m = 4 and the point (3, 15) lies on the line.

Mathematics
1 answer:
Nonamiya [84]2 years ago
6 0

Answer:

y=4x+3

Step-by-step explanation:

y=mx+b

15=4(3)+b

15=12+b

-12 -12

3=b

y=4x+3

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Please help me with these two questions, 10 points for each so in total 20!!
saul85 [17]

Answer:

\large\boxed{Q2.\qquad C.\ -2x+y=-2}\\\boxed{Q4.\qquad C.\ y=3x+12}

Step-by-step explanation:

Q2:

The point-slope form of an equation of a line:

y-y_1=m(x-x_1)

m - slope

The formula of a slope:

m=\dfrac{y_2-y_1}{x_2-x_1}

We have the points (4, 6) and (6, 10). Substitute:

m=\dfrac{10-6}{6-4}=\dfrac{4}{2}=2

y-6=2(x-4)           <em>use distributive property</em>

y-6=2x-8      <em>add 6 to both sides</em>

y=2x-2          <em>subteact 2 from both sides</em>

-2x+y=-2

Q4:

The slope-intercept form of an equation of a line:

y=mx+b

m - slope

b - y-intercept

Put the slope m = 3 and the coordinateso f the point (-2, 6) to the point-slope form of an equation of a line:

y-6=3(x-(-2))

y-6=3(x+2)         <em>use distributive property</em>

y-6=3x+6     <em>add 6 to both sides</em>

y=3x+12

4 0
3 years ago
Given the function f(x) = x^4 + 3x^3 - 2x^2 - 6x - 1, use intermediate theorem to decide which of the following intervals contai
marta [7]

f(x) = x^4 + 3x^3 - 2x^2 - 6x - 1

Lets check with every option

(a) [-4,-3]

We plug in -4  for x  and -3 for x

f(-4) = (-4)^4 + 3(-4)^3 - 2(-4)^2 - 6(-4) - 1= 55

f(-3) = (-3)^4 + 3(-3)^3 - 2(-3)^2 - 6(-3) - 1= -1

f(-4) is positive and f(-3) is negative. there is some value at x=c on the interval [-4,-3] where f(c)=0. so there exists atleast one zero on this interval.

(b) [-3,-2]

We plug in -3  for x  and -2 for x

f(-3) = (-3)^4 + 3(-3)^3 - 2(-3)^2 - 6(-3) - 1= -1

f(-2) = (-2)^4 + 3(-2)^3 - 2(-2)^2 - 6(-2) - 1= -5

f(-2) is negative and f(-3) is negative. there is no value at x=c on the interval [-3,-2] where f(c)=0.  

(c) [-2,-1]

We plug in -2  for x  and -1 for x

f(-2) = (-2)^4 + 3(-2)^3 - 2(-2)^2 - 6(-2) - 1= -5

f(-1) = (-1)^4 + 3(-1)^3 - 2(-1)^2 - 6(-1) - 1= 1

f(-2) is negative and f(-1) is positive. there is some value at x=c on the interval [-2,-1] where f(c)=0. so there exists atleast one zero on this interval.

(d) [-1,0]

We plug in -1  for x  and 0 for x

f(-1) = (-1)^4 + 3(-1)^3 - 2(-1)^2 - 6(-1) - 1= 1

f(0) = (0)^4 + 3(0)^3 - 2(0)^2 - 6(0) - 1= -1

f(-1) is positive and f(0) is negative. there is some value at x=c on the interval [-1,0] where f(c)=0. so there exists atleast one zero on this interval.

(e) [0,1]

We plug in 0  for x  and 1 for x

f(0) = (0)^4 + 3(0)^3 - 2(0)^2 - 6(0) - 1= -1

f(1) = (1)^4 + 3(1)^3 - 2(1)^2 - 6(1) - 1= -5

f(0) is negative and f(1) is negative. there is no value at x=c on the interval [0,1] where f(c)=0.  

(f) [1,2]

We plug in 1  for x  and 2 for x

f(1) = (1)^4 + 3(1)^3 - 2(1)^2 - 6(1) - 1= -5

f(2) = (2)^4 + 3(2)^3 - 2(2)^2 - 6(2) - 1= 19

f(-4) is positive and f(-3) is negative. there is some value at x=c on the interval [-4,-3] where f(c)=0. so there exists atleast one zero on this interval.

so answers are (a) [-4,-3], (c) [-2,-1],  (d) [-1,0], (f) [1,2]

8 0
3 years ago
Read 2 more answers
If the mass of the
DaniilM [7]

Answer:

the mass of liquid is 1,050 g

Step-by-step explanation:

subtract the total mass with the mass of the container

7 0
3 years ago
Find each missing length, will giv brainliest + 50 pts
kipiarov [429]

Step-by-step explanation:

1. 18^2 - 10^2 = 324 - 100 = 224

Sqt(224)=14.9666

Approximate = 14.97

2. 100 - 16 = 84

Sqrt 84 = 9.1652

Approximate = 9.17

3. 225 - 49 = 176

Sqrt 176 = 13.2665

Approximate = 13.27

4. 361 - 144 = 217

Sqrt 217 = 14.7309

Approximate = 14.73

4 0
2 years ago
Read 2 more answers
I need help please ASAP!! I'm in the middle of a quiz!
bixtya [17]

Answer:

2 is the correct answer

4 0
3 years ago
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