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3 years ago

6

What polynomial will produce the sum 7x^2-x+3 when added to 3x^2-5x+4

1 answer:

Aleonysh [2.5K]3 years ago

5 0

Answer:

$4x^2 + 4x - 1$

Step-by-step explanation:

Let f(x) = $7x^2 - x + 3$ , g(x) = $3x^2 - 5x + 4$ , and let h(x) be the polynomial that we have to find.

From the question we know that,

f(x) = g(x) + h(x)

Subtract both sides by g(x),

f(x) - g(x) = h(x)

So h(x)

= f(x) - g(x)

= $7x^2 - x + 3 - 3x^2 + 5x - 4$

= $4x^2 + 4x - 1$

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The population of pets in Mr. Jones neighborhood in Bartlett has declined in the pass year by roughly 30%. Residents hypothesize

Shtirlitz [24]

Answer:

128 4/7

Step-by-step explanation:

100%-30%=70%

90=.7X

900=7X

128 4/7=X

6 0

10 months ago

<img src="https://tex.z-dn.net/?f=%20%5Csqrt%7Bx%20%5Csqrt%7Bx%20%5Csqrt%7Bx%20%5Csqrt%7Bx....%7D%20%7D%20%7D%20%7D%20%20%3D%20%

andrey2020 [161]

First observe that if $a+b>0$ ,

$(a + b)^2 = a^2 + 2ab + b^2 \\\\ \implies a + b = \sqrt{a^2 + 2ab + b^2} = \sqrt{a^2 + ab + b(a + b)} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{\cdots}}}}$

Let $a=0$ and $b=x$ . It follows that

$a+b = x = \sqrt{x \sqrt{x \sqrt{x \sqrt{\cdots}}}}$

Now let $b=1$ , so $a^2+a=4x$ . Solving for $a$ ,

$a^2 + a - 4x = 0 \implies a = \dfrac{-1 + \sqrt{1+16x}}2$

which means

$a+b = \dfrac{1 + \sqrt{1+16x}}2 = \sqrt{4x + \sqrt{4x + \sqrt{4x + \sqrt{\cdots}}}}$

Now solve for $x$ .

$x = \dfrac{1 + \sqrt{1 + 16x}}2 \\\\ 2x = 1 + \sqrt{1 + 16x} \\\\ 2x - 1 = \sqrt{1 + 16x} \\\\ (2x-1)^2 = \left(\sqrt{1 + 16x}\right)^2$

(note that we assume $2x-1\ge0$ )

$4x^2 - 4x + 1 = 1 + 16x \\\\ 4x^2 - 20x = 0 \\\\ 4x (x - 5) = 0 \\\\ 4x = 0 \text{ or } x - 5 = 0 \\\\ \implies x = 0 \text{ or } \boxed{x = 5}$

(we omit $x=0$ since $2\cdot0-1=-1\ge0$ is not true)

3 0

1 year ago

1) Determine if the side lengths given form a triangle

Margaret [11]

Using the triangle inequality theorem, we can figure this out.

2- Yes

3- No

4- No

5- Yes

6- Yes

6 0

2 years ago

Bob's mom is 3 times older than Bob. In 12 years, Bob's mom's age will be twice of

shusha [124]

I would use a chart to solve this problem.

This is a good wya to organize your information.

Down the left side, list the people involved.

I put Bob first and the mom second but the order doesn't matter.

Since Bob's mom is 3 times older than Bob, we can represent

Bob's age now as x and Bob's mom's age now as 3x.

Bob's age in 12 years will be x + 12 and Bob's mom's

age in 12 years will simply be 3x + 12.

Since the second sentence starts with in 12 years,

we will be using the information from our second column.

In 12 years, Bob's mom's age, 3x + 12, will be,

equals, twice of her son's age, 2(x + 12).

Solving from here, we find that x = 12.

This means that Bob's age now is 12 and his mom is 36.

The chart is attached below.

6 0

3 years ago

Read 2 more answers

The square root of a number x is always less than x

Gnom [1K]

Yes this is a correct statement.

8 0

3 years ago