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77julia77 [94]
3 years ago
9

Use synthetic division to show that the number given to the right of the equation is a solution of the equation. Then solve the

polynomial equation.
2x^(3)+x^(2)-8x-4=0; 2

Mathematics
1 answer:
AysviL [449]3 years ago
8 0

Answer:

x = 2 \: or \: x =  - 2 \: or \: x =  -  \frac{1}{2}

Step-by-step explanation:

The given polynomial equation is

2 {x}^{3}  +  {x}^{2}  - 8x - 4 = 0

We perform the synthetic division as shown in the attachment by dividing by x-2.

This gives a remainder of 0 and a quotient of

2 {x}^{2}  + 5x + 2

This means the polynomial equation becomes:

(x - 2)(2 {x}^{2}  + 5x + 2) = 0

We factor the quadratic term by splitting the middle term;

(x - 2)(2 {x}^{2}  + 4x +x +  2) = 0

(x - 2)(2 x(x+ 2) +1(x +  2) )= 0

Collect common factors again:

(x - 2)((x+ 2)(2x +  1) = 0

The solution is:

x = 2 \: or \: x =  - 2 \: or \: x =  -  \frac{1}{2}

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Please help me out!!!
serg [7]

Answer:

x = 76.9

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp side / adj side

tan 70 = x/28

28 tan 70 = x

x=76.92936

Rounding to the nearest tenth

x = 76.9

8 0
3 years ago
Read 2 more answers
A smoothie recipe calls for 13 cup yogurt for each smoothie. How many cups of yogurt are needed to make 7 smoothies?
Sauron [17]
You could also say.
13 x
--- = ---
1 7
Multiply across.
1x=13×7
1x =91
Divide both sides by one.
x=91.
91 cups of yoygurt are needed to make 7 Smoothies.
Or you could do it the easy way.
whatever makes you happy. :)
3 0
3 years ago
Read 2 more answers
What is equivalent to the equation to 1/4 (8 + 6z + 12) ?
Fed [463]
1/4 (8 + 6z + 12) 

------------------------------------------------------------
Combine like terms :
------------------------------------------------------------
1/4 (6z + 20)

------------------------------------------------------------
Apply distributive property :
------------------------------------------------------------
1/4(6z) + 1/4(20)
3/2z + 5

------------------------------------------------------------
Answer: 3/2z + 5
------------------------------------------------------------
7 0
3 years ago
Convert the fraction 7 24 into a repeating decimal.
goldenfox [79]
\dfrac7{24}=\dfrac6{24}+\dfrac1{24}=\dfrac14+\dfrac1{24}

\dfrac1{24}=\dfrac1{8\time3}=\dfrac a8+\dfrac b3=\dfrac{3a+8b}{24}
\implies3a+8b=1

We can choose a=-1 and b=\dfrac12, so that

\dfrac1{24}=-\dfrac18+\dfrac16

Recalling that \dfrac13=0.333\ldots, it follows that \dfrac16=0.166\ldots. So,

\dfrac1{24}=0.125+0.166\ldots=0.04166\ldots
\implies\dfrac7{24}=0.25+0.4166\ldots=0.29166\ldots
6 0
3 years ago
Find the value of 17/ tan ( 40) rounded to the nearest tenth.​
nekit [7.7K]

Answer:

20.30

Step-by-step explanation:

= 17 \div  \tan(40)  \\  = 17 \div 0.8391 \\  = 20.26

To the nearest tenth =20.30

<h2><em>OladipoSeun</em></h2>
6 0
2 years ago
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