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Alenkinab [10]
3 years ago
12

. Factorize a² +3ab - 5ab - 15b²

Mathematics
1 answer:
kipiarov [429]3 years ago
4 0

Answer:

a² +3ab - 5ab - 15b² = (a+3b) (a-5b)

Step-by-step explanation:

We need to factorize a² +3ab - 5ab - 15b². Firstly we need to rearrange the expression such that,

a^2-5ab+3ab-15b^2=(a^2-5ab)+(3ab-15b^2)

Now taking a common from the first two terms and 3b from last two terms, then :

(a^2-5ab)+(3ab-15b^2)=a(a-5b)+3b(a-5b)

In the above expression, a factor (a-5b) is in both the terms. It would mean that,

a(a-5b)+3b(a-5b)=(a+3b)(a-5b)

So, the factors of a² +3ab - 5ab - 15b² are (a+3b) (a-5b).

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3 years ago
A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a salesperso
serg [7]

Using variable concepts, of dependent and independent variables, it is found that the dependent variable is the amount of sales dollars earned.

<h3>What is the relation between a function and the dependent and independent variables?</h3>

  • A function has the following format: y = f(x).
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In this problem, the manager believes that the amount of sales dollars earned is a function of the number of contacts that the salesperson makes, hence:

  • The number of contacts is the independent variable.
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6 0
2 years ago
Cards are dealt, one at a time, from a standard 52-card deck. a if the first 2 cards are both spades, what is the probability th
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Then third card being spades would be 11 / 50

Now there are 10 spades and 49 cards left.
So the probability for fourth card would be 10 / 49

Fifth card would be 9 / 48.

So the probability of next three cards being spades would be
\dfrac{11}{50}\cdot\dfrac{10}{49}\cdot\dfrac9{48}=\dfrac{33}{3920}\approx\boxed{0.00842}

Hope this helps.
3 0
3 years ago
A brick is thrown upward from the top of a building at an angle of 250 above the horizontal, and with an initial speed of 15 m/s
mojhsa [17]

Answer:

(a) 25.08 m

(b) 2.05 m

Step-by-step explanation:

Let the height of the building be 'h'.

Given:

Angle of projection is, \theta=25°

Initial speed is, u=15\ m/s

Time of flight is, t=3.0\ s

(a)

Consider the vertical motion of the brick.

Vertical component of initial velocity is given as:

u_y=u\sin\theta\\\\u_y=15\sin(25)=6.34\ m/s

Vertical displacement of the brick is equal to the height of the building.

So, vertical displacement = -h (Negative sign implies downward motion)

Acceleration is due to gravity in the downward direction. So,

Acceleration is, g=-9.8\ m/s^2

Now, using the following equation of motion;

-h=u_yt+\frac{1}{2}gt^2\\-h=6.34(3)-\frac{9.8}{2}(3)^2\\\\-h=19.02-44.1\\\\-h=-25.08\\\\h=25.08\ m

Therefore, the building is 25.08 m tall.

(b)

Let the maximum height be 'H'.

At maximum height, the vertical component of velocity is 0 as the brick stops temporarily in the vertical direction.

So, v_y=0\ m/s

Now, using the following equation of motion, we have:

v_y^2=u_y^2+2gH\\\\0=(6.34)^2-2\times 9.8\times H\\\\19.6H=40.2\\\\H=\frac{40.2}{19.6}=2.05\ m

Therefore, the maximum height of the brick is 2.05 m.

5 0
3 years ago
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solniwko [45]

Answer:

Angle #4

Step-by-step explanation:

4 & 5 are equal, and opposite.

1 & 2 are also congruent by this standard.

6 0
3 years ago
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