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2 years ago

3. Which one doesn't belong? Give a reason why each square does not belong.

Mathematics

1 answer:

defon2 years ago

6 0

Answer:

C. 8%

Step-by-step explanation:

Because everyone can get divided by 5 equally besides 8

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Solve the equation 4x^3 + 4x^2-x-1 = 0 given that -1/2 is a zero of f(x) = 4x^3 + 4x^2-x-1.

Sholpan [36]

<u>Answer:</u>

The solution of equation 4x^3 + 4x^2-x-1 = 0 given that -1/2 is a zero of f(x) = 4x^3 + 4x^2-x-1 is $\frac{-1}{2} \text { and } \frac{1}{2} \text { and }-1$

<u>Solution:</u>

Given, cubic equation $4 x^{3}+4 x^{2}-x-1=0$

And $\frac{-1}{2}$ is a zero of $f(x)=4 x^{3}+4 x^{2}-x-1$

We have to find the other two roots of the given quadratic equation.

Let the other two roots be a, b.

Now, we know that, sum of roots of cubic equation $=\frac{-x^{2} \text { coefficient }}{x^{3} \text { coefficient }}$

$\text { Then, } \frac{-1}{2}+a+b=\frac{-4}{4} \rightarrow a+b=-1+\frac{1}{2} \rightarrow a+b=\frac{-1}{2} \rightarrow(1)$

Now, product of roots of cubic equation $=\frac{-\text { constant value }}{x^{3} \text { coefficient }}$

$\begin{array}{l}{\text { Then, } \frac{-1}{2} \times a \times b=\frac{-(-1)}{4} \rightarrow \frac{-1}{2} \times a b=\frac{1}{4}} \\\\ {\rightarrow a b=-2 \times \frac{1}{4} \rightarrow a b=\frac{-1}{2}}\end{array}$

$\text { Now we know that, }(a-b)^{2}=(a+b)^{2}-4 a b$

substitute above value in this formula

$(a-b)^{2}=\left(\frac{-1}{2}\right)^{2}-4 \times\left(\frac{-1}{2}\right)$

$(a-b)^{2}=1 / 4+2 \rightarrow(a-b)^{2}=\frac{2 \times 4+1}{4} \rightarrow(a-b)^{2}=\frac{9}{4} \rightarrow a-b=\frac{3}{2} \rightarrow(2)$

Now, solve (1) and (2)

$\begin{array}{l}{2 a=\frac{3-1}{2}} \\ {2 a=1} \\ {a=\frac{1}{2}}\end{array}$

substitute "a" value in (1)

$\frac{1}{2}+b= \frac{-1}{2} \rightarrow b= \frac{-1}{2} + \frac{-1}{2} \rightarrow b=-1$

Hence, the roots of the given cubic equation are $\frac{-1}{2} \text { and } \frac{1}{2} \text { and }-1$

7 0

2 years ago

Choose all that are correct given the equation (equation: y=1/4x+9)

NISA [10]

Options a, b, and d are all correct.
I just substituted the x values into a calculator and checked if the y value was equal as well

4 0

3 years ago

Solve the equation. 3x + 6 = 24

JulsSmile [24]

Hello!

Question 1
3x + 6 = 24

Subtract 6 from both sides

3x = 18

Divide both sides by 3

x = 6

The answer is 6
------------------------------------------------------------------------------------------------------
Question 2
x/4 + 1 = -5

Subtract 1 from both sides

x / 4 = -6

Multiply both sides by 4

x = -24

The answer is -24
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Hope this helps!

6 0

2 years ago

Lola spends 1/3 of her allowance on movies she spends $8 per week at the movies wright and solve an equation to determine Lola's

Sveta_85 [38]

$24 is her allowance. 1/3 of her allowance is $8. So you would multiply 8 times 3 because 8 is just 1/3 of her allowance and you want to find her total weekly allowance. 8 x 3 = 24

4 0

3 years ago

Read 2 more answers

How can you use a number line to model and compare positive and negative rational numbers

kifflom [539]

Hello There!

Well, as you know a number line is a line where you can place numbers with different spaces between them. It can be used to compare them in distance (the further apart they are on the line, the greater the difference between the two numbers)

Hope This Helps You!
Good Luck :)

- Hannah ❤

6 0

3 years ago