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IgorC [24]
3 years ago
8

What is the equation of the line? Use y = mx+b

Mathematics
2 answers:
Olegator [25]3 years ago
8 0

Answer:

y = - \frac{1}{2} x + 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + b ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (2, 3) and (x₂, y₂ ) = (4, 2) ← 2 points on the line

m = \frac{2-3}{4-2} = - \frac{1}{2}

Note the line crosses the y- axis at (0, 4) ⇒ c = 4

y = - \frac{1}{2} x + 4 ← equation of line

rjkz [21]3 years ago
7 0

\text{Hello there!}\\\\\text{Find the slope of the line:}}\\\\\text{We are using the y= mx + b equation to answer the question}\\\\\text{We know that b is the "beginning point", or point on the y axis}\\\\\text{Therefore, our b variable would be 4}\\\\\text{You can use slope formula to find the slope of the line}\\\\\text{A quicker was is to look at the line and use the rise over run technique}\\\\\text{We see that the slope is negative, so it would be a negative}\\\\

\text{Go down once and go to the right twice}\\\\\text{This makes your slope -1/2}\\\\\boxed{\text{Answer: -1/2 + 4}}

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Write a ratio for the following word phrase. Write fractions in lowest terms.42 in. to 6 ft
ollegr [7]
42 feet to 6 feet can be written as both ratio and a fraction:

42:6
42/6

If we look at the fraction, we can clearly see that we can simplify it:

42/6 = 7/1 = 7

So we can write the ratio in its lowest terms as 7:1.
6 0
3 years ago
. A right cylindrical drum is to hold 7.35 cubic feet of liquid. Find the dimensions (radius of the base and height) of the drum
Drupady [299]

Answer:

r=1.05\ \text{ft}

h=2.12\ \text{ft}

20.91\ \text{ft}^3

Step-by-step explanation:

r = Radius

h = Height

Volume of cylinder = 7.35\ \text{ft}^3

V=\pi r^2h\\\Rightarrow h=\dfrac{V}{\pi r^2}\\\Rightarrow h=\dfrac{7.35}{\pi r^2}

Surface area is given by

A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi r^2+2\pi r\dfrac{7.35}{\pi r^2}\\\Rightarrow A=2\pi r^2+\dfrac{14.7}{r}

Differentiating with respect to radius we get

\dfrac{dA}{dr}=4\pi r-\dfrac{14.7}{r^2}

Equating with zero we get

0=4\pi r-\dfrac{14.7}{r^2}\\\Rightarrow 4\pi r=\dfrac{14.7}{r^2}\\\Rightarrow r^3=\dfrac{14.7}{4\pi}\\\Rightarrow r=(\dfrac{14.7}{4\pi})^{\dfrac{1}{3}}\\\Rightarrow r=1.05

\dfrac{d^2A}{dr^2}=4\pi-2\times \dfrac{14.7}{r^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=4\pi+2\times \dfrac{14.7}{1.05^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=37.96>0

So, the value of the function is minimum at r=1.05

h=\dfrac{7.35}{\pi r^2}=\dfrac{7.35}{\pi 1.05^2}\\\Rightarrow h=2.12

So, the radius and height which would minimize the surface area is 1.05 feet and 2.12 feet respectively.

Surface area

A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi \times 1.05^2+2\pi 1.05\times 2.12\\\Rightarrow A=20.91\ \text{ft}^3

The minimum surface area is 20.91\ \text{ft}^3.

8 0
3 years ago
Find a rational number that is between 9.5 and 9.7
Luba_88 [7]
9.5000032 is one such number
3 0
3 years ago
Read 2 more answers
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Artemon [7]

Answer:

a) 8

b) 2 1/4 hours

c) 4 7/8 hours

d) 4 1/8 hours

Step-by-step explanation:

a) LCD to be used to solve this problem is calculated as the Lowest common denominator of the above mixed fractions.

We have 1 1/2 hours and 1 1/8 hours

The lowest common denominator is the denominator calculated by

Multiplying the two denominators together and dividing by the common factor of the two denominators

Hence , we have

2 × 8 = 16

The common factor of 2 and 8 = 2

LCD = 16/2 = 8

b) How long did Matt drive?

We are told that Matt drove twice as long as John

John drove for 1 1/8 hours

Hence, the number of hours that Matt drove for =2 × 1 1/8

= 2 × 9/8 = 9/4 hours = 2 1/4 hours

c) How long the Sam, John and Matt drive ?

We are told in the question that

Sam drove for 1 1/2 hours

John drove for 1 1/8 hours

Matt drove for 2 1/4 hours

We would sum up the number of hours that each of them drove.

1 1/2 + 1 1/8 + 2 1/4

The Lowest common multiple of denominators is 8

= (1 + 1 + 2)( 4 + 1 +2/8)

= 4(7/8)

= 4 7/8 hours

d) How many hours is left for Bob to drive

We are told that the entire journey = 9 hours

The number of hours Sam, John and Matt drove for has been calculated in question c as 4 7/8 hours

The number of hours Bob will drive for is calculated as

9 hours - 4 7/8 hours

= 4 1/8 hours

6 0
3 years ago
Please help me do this i need it​
Darya [45]

Answer:

(x+1)(3x+2) is the answer

6 0
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