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2 years ago

FOR A TEST!! HELP! Complete the similarity ratio for the similar triangles.

Mathematics

1 answer:

tatyana61 [14]2 years ago

7 0

Answer:

add them up

Step-by-step explanation:

add 8 10 10 and 80 25 20

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P(x)= 3x^3-5x^2-14x-4

nexus9112 [7]

$\displaystyle\\
P(x)=3x^3-5x^2-14x-4\\\\
D_{-4}=\{-4;~-2;~\underline{\bf -1};~1;~2;~4\}\\\\
\text{We observe that } \frac{-1}{3} \text{ is a solution of the equation:}\\
3x^3-5x^2-14x-4=0\\\\
$

$\displaystyle\\
\text{Verification}\\\\
3x^3-5x^2-14x-4=\\\\
=3\times\Big(-\frac{1}{3}\Big)^3-5\times\Big(-\frac{1}{3}\Big)^2-14\times\Big(-\frac{1}{3}\Big)-4=\\\\
=-\frac{1}{9}-\frac{5}{9}+\frac{14}{3}-4=\\\\
=-\frac{6}{9}+\frac{14}{3}-4=\\\\
=-\frac{6}{9}+\frac{42}{9}- \frac{4\times 9}{9}=\\\\
 =-\frac{6}{9}+\frac{42}{9}- \frac{36}{9}= \frac{42-6-36}{9}=\frac{42-42}{9}=\frac{0}{9}=0\\\\
\Longrightarrow~~~P(x)~\vdots~\Big(x+ \frac{1}{3}\Big)\\\\
\Longrightarrow~~~P(x)~\vdots~(3x+1)$

$\displaystyle\\
3x^3-5x^2-14x-4=0\\
~~~~~-5x^2 = x^2 - 6x^2\\
~~~~~-14x =-2x-12x \\
3x^3+x^2 - 6x^2-2x-12x-4=0\\
x^2(3x+1)-2x(3x+1) -4(3x+1)=0\\
(3x+1)(x^2-2x -4)=0\\\\
\text{Solve: } x^2-2x -4=0\\\\
x_{12}= \frac{-b\pm \sqrt{b^2-4ac}}{2a}=\\\\=\frac{2\pm \sqrt{4+16}}{2}=\frac{2\pm \sqrt{20}}{2}=\frac{2\pm 2\sqrt{5}}{2}=1\pm\sqrt{5}\\\\
x_1 =1+\sqrt{5}\\
x_2 =1-\sqrt{5}\\
\Longrightarrow P(x)= 3x^3-5x^2-14x-4 =\boxed{(3x+1)(x-1-\sqrt{5})(x-1+\sqrt{5})}$

7 0

2 years ago

Which equation represents the line that passes through the points (4, 6) and (−2, −1)?

KatRina [158]

Find the slope first by using rise/run

$m=\frac{6-(-1)}{4-(-2)}\\m=\frac{6+1}{4+2}\\m=\frac{7}{6}$

$y=mx+b\\y=\frac{7}{6}x+b$

We need to find the y-intercept. Substituting one of given ordered pairs. I will use (-2,-1).

Substitute x = -2 and y = -1 in the equation.

$-1=\frac{7}{6}(-2)+b\\-1=\frac{7}{-3}+b\\-1=-\frac{7}{3}+b\\-1+\frac{7}{3}=b\\b=\frac{4}{3}$

Thus the y-intercept is 4/3.

From y = mx+b, the equation is.

$y=\frac{7}{6}x+\frac{4}{3}$

8 0

2 years ago

Without calculating would 0.4+(2+0.6)be less than, greater than,or equal to 3? Explain

masya89 [10]

The answer would be “Greater than.”

3 0

3 years ago

Question 10 Please Help

svet-max [94.6K]

Answer:

1)· 5x + 2y = 9. First we solve for y. 2y= 9 -5x. y=(9-5x)/2. Now that we have the value of y. We substitute on the original equation and resolve. 5x + 2y = 95x + 2y = 9 5x + 2(9-5x)/2 = 9 5x + 9 - 5x = 9 9 = 9

That would be x = 1

Now substitute and resolve to find y.

5(1) + 2y = 9

5 + 2y = 9

2y = 4

y = 2

So our answer x=1 and y = 2. (1,2)

Proof :

5(1) + 2(2) = 9

5+ 4 = 9

9 = 9

Step-by-step explanation:

hoped it helped for the first one i didnt now the second one

4 0

2 years ago

Find the volume of a sphere with a radius of about 6 cm, what is its surface area?

bulgar [2K]

Pretty sure it’s 452.39cm2

6 0

2 years ago

Read 2 more answers