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Neko [114]
3 years ago
7

A line crosses through the point (3,10) and another point can be found on the line by going right 2 and down 7. find slope and y

intercept
Mathematics
1 answer:
DerKrebs [107]3 years ago
3 0

Answer:

y =  \frac{-7x}{2}+\frac{41}{2}

Step-by-step explanation:

We are given the point (3, 10).

The second point is 2 on the x-axis and -7 on the y-axis. So our second point is: (3 + 2, 10 - 7) which is (5, 3).

Our formula for slope is m = \frac{rise}{run} = \frac{y2-y1}{x2-x1}

So, our equation would be \frac{3-10}{5-3} = \frac{-7}{2}

Using the standard formula of a line, y = mx + b, we can substitute for the slope, m.

y = \frac{-7x}{2} + b

Now, we can substitute a point on the line to determine the y-intercept:

Using the point (3, 10),

10 = \frac{-7(3)}{2} + b

b = 10 + \frac{21}{2}

b = \frac{41}{2}

So our full equation is: y =  \frac{-7x}{2}+\frac{41}{2}

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The base of a triangle is 3 more than 2 times of height. Determine the dimensions that give total area of 10 square feet.
Alona [7]

Answer:

height = 2.5 ft , base = 8 ft

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = \frac{1}{2} bh ( b is the base and h the height )

height = h then base = 2h + 3 and A = 10 , then

\frac{1}{2} h(h + 3) = 10 ( multiply both sides by 2 to clear the fraction )

h(h + 3) = 20 , that is

h² + 3h = 20 ( subtract 20 from both sides )

h² + 3h - 20 = 0 ← in standard form

(h + 4)(2h - 5) = 0 ← in factored form

equate each factor to zero and solve for h

h + 4 = 0 ⇒ h = - 4

2h - 5 = 0 ⇒ 2h = 5 ⇒ h = 2.5

but h > 0 , then h = 2.5

and 2h + 3 = 2(2.5) + 3 = 5 + 3 = 8

that is height = 2.5 ft and base = 8 ft

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2 years ago
What is two to the fourth power multiplied by four to the second power?
lutik1710 [3]
2 to the fourth power is technically
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4 years ago
Martha will build a pool in her backyard. She wants the pool to have a rectangular shape
Ivan

9514 1404 393

Answer:

  C.  161.459 square feet

Step-by-step explanation:

In feet, the dimensions of the pool are ...

  (5 m)(3.28084 ft/m) = 16.4042 ft

  (3 m)(3.28084 ft/m) = 9.84252 ft

Then the area of the pool is ...

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  about 161.459 square feet

_____

<em>Additional comment</em>

If you consider that a square meter is slightly less than 11 square feet, the pool area can be estimated to be (5 m)(3 m)(11 ft²/m²) = 165 ft². This is close enough to point you to the correct answer choice.

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3 years ago
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Answer:

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Step-by-step explanation:

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