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3 years ago

If a(x) and b(x) are linear functions with one variable, which of the following expressions produces a quadratic function?

Mathematics

2 answers:

svp [43]3 years ago

7 0

Answer:

Option (a) is correct.

a(x)b(x) = (ab)(x)

To produce a quadratic equation the two linear equation must be multiply.

Step-by-step explanation:

Given : a(x) and b(x) are linear functions with one variable.

We have to choose from the given option the correct expression that will produce a quadratic equation.

Quadratic equation is an equation which is in the form of $ax^2+bx+c$ where $a\neq0$

Since given a(x) and b(x) are linear equation in one variables so to get square term we must multiply the two linear equations.

Let a(x)=3x+1

and b(x)= 8x+1

then when we multiply we get,

$a(x)\times b(x)=(3x+1)\times (8x+1)=24x^2+11x+1$

Thus, To produce a quadratic equation the two linear equation must be multiply.

Thus, a(x)b(x) = (ab)(x) is correct.

Option (a) is correct.

Novosadov [1.4K]3 years ago

6 0

I hope this helps you

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One pipe can empty a tank 5 times faster than another pipe can fill the tank. Starting with a full tank, if both pipes are turne

xxTIMURxx [149]

Answer:

40 hours

Step-by-step explanation:

Let's say that the slower pipe can fill x amount of the tank in one hour. It adds x amount to the tank every hour. Therefore, we can say, for the slower pipe,

1 hour = x amount

Then, the faster pipe empties the tank 5 times faster than the slower pipe fills it, so it removes 5 times the amount that the smaller pipe puts in, so for the faster pipe,

1 hour = -5x amount (negative to symbolize removing).

For the problem at hand, the tank starts at full, or 100%=1. It ends empty, or at 0% = 0. After 10 hours, if we only account for the slower pipe, we add x amount to the tank every hour, so we add 10 times that total, resulting in

1 + 10 * x as the ending result if we don't include the faster pipe. Then, the faster pipe removes 5x every hour, so in 10 hours, it removes 50x, so we have

1+10 * x - 50 * x as the final amount of stuff in the tank, which is equal to 0. Therefore, we have

1 + 10 * x - 50 * x = 0

1 - 40 * x = 0

add 40*x to both sides to isolate the x and its coefficient

1 = 40 * x

divide both sides by 40 to isolate x

x= 0.025

Therefore, the slower pipe adds 0.025, or 1/40 = 2.5% to the tank every hour. We want to figure out how long it would take for the slower pipe to fill up an empty tank, or turn it from 0% to 100% full.

Because the slower pipe adds 2.5% of the tank every hour, we can say that over y hours, it fills up

2.5% * y amount of the tank. We want to figure out how many hours it would take to make it 100% (we need to add 100% of the tank in the problem), so we can say

2.5% * y = 100%

divide both sides by 2.5% to isolate y

100%/2.5% = y = 40

5 0

3 years ago

The larger number is 18 more than twice the smaller. If the sum of the two numbers is 93, find

Zigmanuir [339]

Answer:

The smaller is 25

the larger is 68

8 0

2 years ago