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2 years ago

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Mathematics

2 answers:

puteri [66]2 years ago

5 0

Answer:

$\huge{ \boxed{y = - \frac{1}{3} x + 1}}$

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

From the graph to find the equation of the line we must first find the slope

The slope of a line given two points can be found by using the formula

$m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\$

where

(x1 , y1) and (x2 , y2) are the points

Using the points (-6 , -3) and (6,-7) we have

$m = \frac{ - 7 - - 3}{6 - - 6} = - \frac{4}{12} = - \frac{1}{3} \\$

Next we use the slope that has been found and one of the points to find the equation of the line

To find an equation of a line when given the slope and a point we use the formula

y - y1 = m(x - x1)

where

m is the slope

( x1 , y1) is the point

From the question using slope -1/3 and point (-6,3) we have

$y - 3 = - \frac{1}{3} (x - - 6) \\ y - 3 = - \frac{1}{3} (x + 6) \\ y - 3 = - \frac{1}{3} x - 2 \: \: \: \\ y = - \frac{1}{3} x - 2 + 3 \: \:$

The equation of the line in slope-intercept form is

$y = - \frac{1}{3} x + 1 \\$

Hope this helps you

aleksklad [387]2 years ago

3 0

Answer:

y = - 1/3x - 5

Step-by-step explanation:

Use two given points (-6, -3) and (6, -7) to find equation of the line.

The slope:

m = (y₂ - y₁)/(x₂ - x₁) = (-7 - (-3)) / (6 - (-6)) = -4 / 12 = - 1/3

The y - intercept is also visible on the graph (0, -5):

b = -5

The line is:

y = - 1/3x - 5

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Samantha is using a 2-liter pitcher to serve lemonade to 10 of her friends. How many times will she need to fill the pitcher in

Mice21 [21]

Answer: 2 times

Step-by-step explanation:

Hi, since 1000 milliliters = 1 liter

We have to convert the 2 liters into milliliters:

2 x 1000 = 2000 milliliters, so she is using a 2,000 milliliters pincher.

Now we have to multiply the number of friends (10) by the amount of lemonade she serves to each one (400 ml)

400 x 10 = 4,000 milliliters

Finally, we have to divide the amount of lemonade she needs to serve (4,000 ml) by the capacity of the pitcher (2,000), to obtain the number of times that she will need to fill the pitcher.

4,000/2,000=2 times

Feel free to ask for more if needed or if you did not understand something.

4 0

3 years ago

Read 2 more answers

A triangular pyramid has a right triangle for its base. The perpendicular sides of the triangle are 10 inches and 18 inches long

igor_vitrenko [27]

The formula for a triangular pyramid is 1/3AH. A is the area of the base. H is the height of the pyramid. So to find the area of a right triangle, you would use the formula (a x b)/2. So (10 x18)/2 is 90 inches^2. Now you can fill in the first formula. 1/3(90 x 14), which equals 420 inches^3. I hope you find this helpful (if correct.)

6 0

3 years ago

Ally and Beck went fishing and caught a total of 75 fish. At home,

tigry1 [53]

Answer:

Beck actually caught 45 fish

Step-by-step explanation:

System of Equations

We call the following variables:

x = number of fish Ally caught

y = number of fish Beck caught

They caught a total of 75 fish, thus:

x + y = 75 [1]

If Ally had caught twice as much fish as she actually did, and Beck had caught three times as many fish as he actually did, then Ally would have caught 75 fewer fish than Beck, thus:

3y = 2x + 75 [2]

From [1]:

x = 75 - y [3]

Substituting in [2]:

3y = 2(75 - y) + 75

Operating:

3y = 150 - 2y + 75

Simplifying:

5y = 225

Dividing by 5:

y = 45

Beck actually caught 45 fish

3 0

3 years ago

Read 2 more answers

A softball has a diameter of 3.82 inches. How many square inches of material is necessary to cover a softball? Use 3.14 for π

lisabon 2012 [21]

Answer:

45.82 square inches

Step-by-step explanation:

Use the formula for the surface area of a sphere, A = 4 $\pi$ r²

If the diameter is 3.82 inches, the radius is 1.91 inches.

Plug in 3.14 as $\pi$ and 1.91 as r, and solve:

A = 4 $\pi$ r²

A = 4(3.14)(1.91²)

A = 45.82

So, approximately 45.82 square inches of material are needed.

6 0

2 years ago

Michael saves $423 dollars a month for college.

alexandr1967 [171]

Answer:

(a). $20,000

(b). The estimate will be lower than the actual amount.

Step-by-step explanation:

We have been given that Michael saves $423 dollars a month for college.

(a). We know that 1 year equals 12 months.

4 years = 4*12 months = 48 months.

$\text{Actual amount saved}=\$423\times 48$

Since we are asked to find the estimated amount of money Michael will save in 4 years, so we will estimate both quantities as:

$423\approx 400\\\\48\approx 50$

$\text{Actual amount saved}=\$400\times 50$

$\text{Actual amount saved}=\$20,000$

Therefore, Michael will save approximately $20,000 in 4 years.

(b).

The estimate will be lower than the actual amount as we rounded $423 down $23 to nearest hundred that is $400 and rounded 48 up 2 to nearest ten that is 40.

Therefore, the estimate will be lower than the actual amount.

5 0

3 years ago

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