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AVprozaik [17]
4 years ago
13

10. Write an equation in point-slope form for the line through the given point with the given slope.

Mathematics
1 answer:
Norma-Jean [14]4 years ago
6 0

Answer:

C

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = 5 and (a, b) = (8, 3), hence

y - 3 = 5(x - 8) → C


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Tina was asked to determine the possible dimensions of a given rectangle whose area is 12a4b3-18a6b3-72a7b3. Tina stated that th
Rufina [12.5K]

Answer:

Tina is correct

Step-by-step explanation:

Given

Area = 12a^4b^3 - 18a^6b^3 - 72a^7b^3

Required

State if 3a^4b^3(4-6a^2-24a^3) is a possible dimension

To do this, we simply expand 3a^4b^3(4-6a^2-24a^3)

3a^4b^3(4-6a^2-24a^3)

3a^4b^3 * 4-3a^4b^3 * 6a^2-3a^4b^3 * 24a^3

12a^4b^3 - 18a^{4+2}b^3 * -72a^{4+3}b^3

12a^4b^3 - 18a^{6}b^3 * -72a^{7}b^3

By comparison, the result of the expansion

12a^4b^3 - 18a^{6}b^3 * -72a^{7}b^3

and the given expression

Area = 12a^4b^3 - 18a^6b^3 - 72a^7b^3

are the same.

<em>Hence, Tina is correct</em>

7 0
3 years ago
A ball with mass m kg is thrown upward with initial velocity 28 m/s from the roof of a building 17 m high. Neglect air resistanc
lina2011 [118]

Answer:

The ball will take 6.3 seconds to reach the maximum height and hit the ground.

Step-by-step explanation:

a). When a ball was thrown upwards with an initial velocity u then maximum height achieved h will be represented by the equation

v² = u² - 2gh

where v = final velocity at the maximum height h

and g = gravitational force

Now we plug in the values in the equation

At maximum height final velocity v = 0

0 = (28)² - 2×(9.8)h

19.6h = (28)²

h = \frac{(28)^{2}}{19.6}

  = \frac{784}{19.6}

  = 40 meter

B). If the ball misses the building and hits the ground then we have to find the time after which the ball hits the ground that will be

= Time to reach the maximum height + time to hit the ground from the maximum height

Time taken by the ball to reach the maximum height.

Equation to find the time will be v = u - gt

Now we plug in the values in the equation

0 = 28 - 9.8t

t = \frac{28}{9.8}

 = 2.86 seconds

Now time taken by the ball to hit the ground from its maximum height.

H = ut + \frac{1}{2}\times g\times (t)^{2}

(17 + 40) = 0 + \frac{1}{2}\times g\times (t)^{2}

57 = 4.9(t)²

t² = \frac{57}{4.9}

t² = 11.63

t = √(11.63)

 = 3.41 seconds

Now total time taken by the ball = 2.86 + 3.41

                                                      = 6.27 seconds

                                                      ≈ 6.3 seconds

Therefore, the ball will take 6.3 seconds to reach the maximum height and hit the ground.

4 0
4 years ago
The amount of profit, p, you earn by selling knives, k, can be determined by: p=200k-500. a) Determine the constraints on profit
Lina20 [59]
Given: 

P = 200k - 500

A) To determine the constraints on profit and the value of the number of knives sold, k, let P = 0

P = 200k - 500
0 = 200k - 500

solve for k,

k = 2.5 knives or 3 knives


3 0
3 years ago
Use a number line to add the following: 14 + (-11)<br> Add.
harkovskaia [24]

Answer

try b

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Solve for x<br> 5(x + 1) = 6x+2
snow_tiger [21]

Answer:

X = 3

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
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