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beks73 [17]
2 years ago
11

Write an equation that passes through a pair of points

Mathematics
1 answer:
Phoenix [80]2 years ago
3 0

Answer:

C. y = -x + 2

Step-by-step explanation:

First, find the slope, m, of the line that passes through the two given points.

Slope = \frac{rise}{run} = \frac{-2}{2} = -\frac{1}{1} = -1

Next, determine the y-intercept, b.

The y-intercept is where the line intercepts the y-axis. The line intercepts the y-axis at y = 2. Therefore, b = 2.

Now, to get an equation of the line, substitute m = -1, and b = 2 in y = mx + b.

✅The equation would be:

y = -1x + 2

y = -x + 2

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What is 1/3 equal to
Grace [21]

Answer:

0.3

33.3%

Step-by-step explanation:

6 0
2 years ago
A rectangular box without a lid is to be made from 48 m2 of cardboard. Find the maximum volume of such a box. SOLUTION We let x,
tatiyna

Answer:

The maximum volume of such box is 32m^3

V = x×y×z = 32 m^3

Step-by-step explanation:

Given;

Total surface area S = 48m^2

Volume of a rectangular box V = length×width×height

V = xyz ......1

Total surface area of a rectangular box without a lid is

S = xy + 2xz + 2yz = 48 .....2

To be able to maximize the volume, we need to reduce the number of variables.

Let assume the rectangular box has a square base,that means; length = width

x = y

Substituting y with x in equation 1 and 2;

V = x^2(z) ....3

x^2 + 4xz = 48 .....4

Making z the subject of formula in equation 4

4xz = 48 - x^2

z = (48 - x^2)/4x .......5

To be able to maximize V, we need to reduce the number of variables to 1, by substituting equation 5 into equation 3

V = x^2 × (48 - x^2)/4x

V = (48x - x^3)/4

differentiating V with respect to x;

V' = (48 - 3x^2)/4

At the maximum point V' = 0

V' = (48 - 3x^2)/4 = 0

Solving for x;

3x^2 = 48

x = √(48/3)

x = √(16)

x = 4

Since x = y

y = 4

From equation 5;

z = (48 - x^2)/4x

z = (48 - 4^2)/4(4)

z = 32/16

z = 2

The maximum volume can be derived by substituting x,y,z into equation 1;

V = xyz = 4×4×2 = 32 m^3

7 0
3 years ago
On a recent trip to a local orchard, the Morgan family picked four different kinds of apples - Braeburn, Cortland, Fuji, and Rom
ivanzaharov [21]

Answer:

Morgan family picked 144 Braeburn apples, 96 Cortland apples, 72 Fuji apples and 48 Rome apples.

Step-by-step explanation:

Let B, C, F and R represent Braeburn apples, Cortland apples, Fuji apples, and Rome apples respectively.

We have been given that Morgan family picked a total of 360 apples. We can represent this information in an equation as:

B+C+F+R=360...(1)

We are told that Morgan family picked twice as many Braeburn as Fuji. We can represent this information in an equation as:

B=2F...(2)

We are told that Morgan family picked twice as many Cortland as Rome, that is:

C=2R...(3)

We are told that Morgan family picked 50% more Fuji than Rome, that is:

F=1.5R...(4)

Upon substituting equation (4) in equation (2), we will get:

B=2(1.5)R

B=3R

Now, each apple in in terms of Rome apples, so we will get:

3R+2R+1.5R+R=360

Let us solve for R.

7.5R=360

\frac{7.5R}{7.5}=\frac{360}{7.5}

R=48

Therefore, Morgan family picked 48 Rome apples.

Upon substituting R=48 in (3), we will get:

C=2R\Rightarrow 2(48)=96

Therefore, Morgan family picked 96 Cortland apples.

Upon substituting R=48 in (4), we will get:

F=1.5R\Rightarrow 1.5(48)=72

Therefore, Morgan family picked 72 Fuji apples.

Upon substituting F=72 in (2), we will get:

B=2F\Rightarrow 2(72)=144

Therefore, Morgan family picked 144 Braeburn apples.

3 0
3 years ago
A car manufacturer has a failure rate in their oil gasket of 2%. What is the probability that , of 1200 cars built, 50 will deve
Keith_Richards [23]

Answer:

4%

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
How many miles can a car travel on 15 gallons of gas if it travels 28 miles on 1 gallon of gas?
WITCHER [35]
What is 15 times 28? 
5 0
3 years ago
Read 2 more answers
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