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3 years ago

He measures of the angles of a triangle are in the extended ratio 4 : 5 : 6. what is the measure of the smallest angle?

1 answer:

5 0

In a triangle, the three interior angles always add to 180°

4x + 5x + 6x = 180
15x = 180
x = 180/15
x = 12

the measure of the smallest angle = 4x = 4*12 = 48°

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Find all the zeros of the polynomial function p(x) = x3 – 5x2 + 33x – 29

hram777 [196]

Answer:

$\large \boxed{\sf \ \ x=1, \ \ x=2+5i, \ \ x=2-5i \ \ }$

Step-by-step explanation:

Hello,

I assume that we are working in $\mathbb{C}$ , otherwise there is only one zero which is 1. Please consider the following.

First of all, we can notice that 1 is a trivial solution as

$p(1) = 1^3-5\cdot 1^2 + 33\cdot 1-29=1-5+33-29=0$

It means that (x-1) is a factor of p(x) so we can find two real numbers, a and b, so that we can write the following.

$p(x)=(x-1)(x^2+ax+b)=x^3+ax^2+bx-x^2-ax-b=x^3+(a-1)x^2+(b-a)x-b$

Let's identify like terms as below.

a-1 = -5 <=> a = -5 + 1 = -4

b-a = 33

-b = -29 <=> b = 29

$\boxed{ \ p(x)=(x-1)(x^2-4x+29) \ }$

Now, we need to find the zeroes of the second factor, meaning finding x so that:

$x^2-4x+29=0 \ \text{ complete the square, 29 = 25 + 4} \\ \\ x^2-2\cdot 2 \cdot x+2^2+25=0 \\ \\ (x-2)^2=-25=(5i)^2 \ \text{ take the root } \\ \\x-2=\pm 5i \ \text{ add 2 } \\ \\ x = 2+5i \ \text{ or } \ x = 2-5i$

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

5 0

3 years ago

Find x in the given figure if m∠AOC = 124°.

Nastasia [14]

Answer:

A) 8

Step-by-step explanation:

Add angles AOB and BOC to get angle AOC.

Since we know the value of AOC is 124 and AOB+BOC=AO

Then (8x+25)+(6x-13)=124.

Combine like terms to get 14x+12= 124.

Solve for x by subtracting 12 from 124, then divide the answer by 14.

3 0

3 years ago

−2(x+23)+1=5 does someone know the answer

irinina [24]

-2x-46+1=5
the answer ends up being
x=-25

6 0

3 years ago

My parents recently moved to the Poconos, they got 30 or more inches of snow from this last snow storm. It took my Dad 2 hours t

never [62]

To determine how much will it take to clean a 120ft driveway considering that it took him 2hs to clear 10ft and that the cleaning rate is constant, you can use cross multiplication:

10ft______2hs

120ft_____xhs

If the cleaning rate is the same, then the ratios between both are the same: