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iogann1982 [59]
3 years ago
10

Write the equation of the line given points (-4,6) and (-8,10)

Mathematics
1 answer:
Advocard [28]3 years ago
6 0

Answer:

the equation of the line in slope-intercept form is: y=-x+2

Step-by-step explanation:

First start by finding the slope of the segment that joins those two points using the general formula for the slope of the segments between two points (x_1,y_1) and (x_2,y_2) on the plane:

Slope=\frac{y_2-y_1}{x_2-x_1}

Then for our case, calling (-4, 6) = (x_1,y_1) and (-8, 10) = (x_2,y_2), we have:

Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{10-6}{-8-(-4)}\\Slope=\frac{4}{-8+4}\\Slope=\frac{4}{-4}\\Slope= -1

Now, knowing this, we can find the equation of the line by using the "point-slope" form of a line [of slope "m" and going through the point (x_0,y_0) that tells us:

y-y_0=m(x-x_0)

We will be then using the found slope (-1) and for example one of the given points: (-4 , 6), thus:

y-y_0=m(x-x_0)\\y-6=-1(x-(-4))\\y-6=-1(x+4)\\y-6=-x-4\\y=-x-4+6\\y=-x+2

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If a CONE has a DIAMETER of 10 centimeters and a Volume of 225 cubic centimeters, what is its approximate HEIGHT
ch4aika [34]

Answer:

The approximate height is 8.9 cm

Step-by-step explanation:

To find the height of a cone with a diameter of 10 cm and a volume of 225 cubic centimeter, we will follow the steps below;

first, write down the formula for finding the volume of a cone

v=πr²\frac{h}{3}

where v is the volume of the cone

r is the radius and h is the height of the cone

from the question given,

diameter = 10 cm   but       d=2r       this implies  that    r= \frac{d}{2}     r=   10/2   =    5cm

hence   r= 5cm

Also    v= 225 cm³

π  is a constant and is ≈ 3.14

We can now proceed to insert the values into formula and then solve for h

v=πr²\frac{h}{3}

225 ≈ 3.14 × 5² × \frac{h}{3}

225 ≈ 78.5 ×\frac{h}{3}

225 ≈ \frac{75.8 h}{3}

cross-multiply

675 = 75.8 h

divide both-side of the equation by 75.8

8.9 ≈ h

h≈ 8.9

Therefore, the approximate height is 8.9 cm

7 0
4 years ago
Layla wants to build a wooden box with a volume of 454545 cubic centimeters. She started with a width of 3\text{ cm}3 cm3, start
gogolik [260]

The correct question is;

Layla wants to build a wooden box with a volume of 45 cubic centimeters. She started with a width of 3 cm and a height of 3 cm. How long should Layla make the box?

Answer:

Box is 5 cm long.

Step-by-step explanation:

We are given;

Volume; V = 45 cm³

Width; w = 3 cm

Height;h = 3 cm

Now, this box has the shape of a cuboid and the volume of a cuboid is given as;

V = l × w × h

Where;

L is length

w is width

h is height

Making L the subject, we have;

V/wh = L

Plugging in the relevant values to obtain;

L = 45/(3 × 3)

L = 45/9

L = 5 cm

3 0
3 years ago
Factor completely 4p2 - 25q2 =
mel-nik [20]
Answer: 2(4p - 25q)


Explanation: 4p*2 = 8p - 25q*2 = 8p - 50q = 2(4p - 25q)
6 0
3 years ago
9. Mark is filling up crates with watermelons for the food drive. He has large watermelons that weigh 10 pounds each and smaller
abruzzese [7]
9. 10x + 5y is the equation for larger watermelons + smaller watermelons (you did not provide information about the medium watermelons, so we must assume given the options you miswrote one of them). We can hold NO MORE than 500 pounds, so 10x + 5y must be smaller than 500. The best answer is C assuming that "5y" represents your "Medium Watermelons"- because smaller watermelons are stated to be 5 and medium ones should therefore be between 5 and 10, the option provided by A wouldn't make since because 3 pounded watermelons are not "medium" in comparison to the "small ones" that are heavier/bigger. Your best option is C, 10x + 5y < 500, the exact answer technically would be 10x + 5y <= 500.
4 0
3 years ago
Forty students are In Science club. Of those 45% are girls. This percent increase 56% after new girls join the club. How many ne
stepan [7]
45% of 40 is 0.45×40=18 girls
if x girls join then 56% of 40+x is 0.56(40+x)=18+x
22.4+0.56x=18+x
put together like terms
4.4=0.44x
<span>x=10 girls joined</span>
8 0
4 years ago
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