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exis [7]
2 years ago
7

What is the square root of 8 and why?

Mathematics
1 answer:
kicyunya [14]2 years ago
8 0

Rewrite <span>88</span> as <span><span><span>22</span>⋅2</span><span><span>22</span>⋅2</span></span>.Factor <span>44</span> out of <span>88</span>.<span><span>√<span>4<span>(2)</span></span></span><span>4⁢2</span></span>Rewrite <span>44</span> as <span><span>22</span><span>22</span></span>.<span><span>√<span><span>22</span>⋅2</span></span><span><span>22</span>⋅2</span></span>Pull terms out from under the radical.<span><span>2<span>√2</span></span><span>2⁢2</span></span>The result can be shown in both exact and decimal forms.Exact Form:<span><span>2<span>√2</span></span><span>2⁢2</span></span>Decimal Form:<span>2.82842712<span>…</span></span>
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2. Factor f(x) = x4 + 10x3 + 35x2 + 50x + 24 completely showing all work and steps with synthetic division. Then sketch the grap
telo118 [61]

We need to use rational root theorem to find out roots here.

The rational root theorem states that if p(x) is a polynomial with integer coefficients and if \frac{p}{q} is a zero of p(x) then p is a factor of constant term and q is a factor of leasing term coefficient.

Here factors of constant term are 1,2,3,4,6,8,12,24,-1,-2,-3,-4,-6,-8,-12, and -24.

And factors of leading coefficient is -1,1.

Hence possible roots may be -1,1,-2,2,-3,3,-4,4,-6,6,-8,8,-12,12,-24 and 24.

Let us plugin these in f(x) to find zeroes.

f(-1)=(-1)^{4}+10(-1)^{3}+35(-1)^{2}+50(-1)+24 =1-10+35-50+24=0

Hence x=-1 is a zero which means x-(-1)=x+1 is a factor.

Let us use synthetic division to find quotient.

-1 | 1  10  35  50  24

  <u>| 0  -1  -9  -26   -24</u>

   <u> 1    9  26  24    0</u>

Hence quotient is x^{3} +9x^{2} +26x+24

Since all coefficients are positive, root must be negative. Let's plugin all remaining negative numbers in the quotient.

(-2)^{3}+9(-2)^{2}+26(-2)+24 = 0

Hence x+2 is another factor.

Let us find quotient again using synthetic division.

-2 | 1   9  26   24

   <u>| 0  -2  -14   -24</u>

   <u>  1    7    12     0</u>

Hence quotient is x^{2} +7x+12

Again we got quotient with all positive coefficients, let us plugin remaining negative numbers from rational root theorem.

(-3)^{2}+7(-3)+12=-9-21+12=0

Hence x+3 is also a factor.

Let us find quotient using synthetic division.

-3 | 1  7  12

   <u>| 0 -3  -12</u>

    <u> 1    4    0</u>

Hence quotient is x+4.

So, f(x)=x^{4}+10x^{3}+35x^{2}+50x+24 =(x+1)(x+2)(x+3)(x+4)

Please have a look at the graph attached.

4 0
3 years ago
Tom has 12.42 centimeters of yarn. If he wants to make the yarn into pieces that are 0.54 centimeters long, how many pieces can
natta225 [31]

Answer:

23 pieces of yarn

Step-by-step explanation:

12.42cm divided by 0.54cm = 23

pls mark brainliest....:)

5 0
3 years ago
Can I please get some help on this question ?
Vikki [24]

Answer: 15 Units

Step-by-step explanation:

Im smart

8 0
2 years ago
Read 2 more answers
Justin and his children went into a bakery and where they sell cookies for $0.75 each and brownies for $1.25 each. Justin has $1
enot [183]

Answer:

Justin could buy up to 8 cookies.

Step-by-step explanation:

7 * 1.25 = 8.75

15 - 8.75 = 6.25

6.25/.75 = 8.3333333

5 0
3 years ago
1/2(x+10)= 1/4 (x-8) x= <br> (must be a fraction)
Alex_Xolod [135]

Answer:

x=-9\frac{1}{3}

Step-by-step explanation:

\frac{1}{2}(x+10)=\frac{1}{4}(x-8)

\frac{1}{2}x+5=\frac{1}{4}x-2

\frac{1}{2}x-\frac{1}{4}x=-5-2

\frac{3}{4}x=-7

x=-\frac{28}{3}=-9\frac{1}{3}

5 0
3 years ago
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