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2 years ago

14

Which choice is equivalent to the expression √20 + √80

2 answers:

salantis [7]2 years ago

7 0

Answer:

13.41

Step-by-step explanation:

Hope it helps!

Korvikt [17]2 years ago

5 0

Answer:

6 $\sqrt{5}$

Step-by-step explanation:

Using the rule of radicals

$\sqrt{a}$ × $\sqrt{b}$ ⇔ $\sqrt{ab}$

Simplifying the radicals

$\sqrt{20}$

= $\sqrt{4(5)}$

= $\sqrt{4}$ × $\sqrt{5}$ = 2 $\sqrt{5}$

$\sqrt{80}$

= $\sqrt{16(5)}$

= $\sqrt{16}$ × $\sqrt{5}$ = 4 $\sqrt{5}$

Then

$\sqrt{20}$ + $\sqrt{80}$

= 2 $\sqrt{5}$ + 4 $\sqrt{5}$

= 6 $\sqrt{5}$

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I need help please and thanks

lakkis [162]

Answer:

the answer is associative

Step-by-step explanation:

3 0

2 years ago

19. Heather invests $4,900 in an account with a 3.5% interest rate, making no other deposits or withdrawals. What will Heather’s

denis-greek [22]

Answer:

$\$5,828.28$

Step-by-step explanation:

we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$t=5\ years\\ P=\$4,900\\ r=0.035\\n=2$

substitute in the formula above

$A=\$4,900(1+\frac{0.035}{2})^{2*5}$

$A=\$4,900(1.0175)^{10}=\$5,828.28$

5 0

2 years ago

Trig proofs with Pythagorean Identities.

lorasvet [3.4K]

To prove:

$$\frac{1}{1-\cos x}-\frac{\cos x}{1+\cos x}=2 \cot ^{2} x+1$

Solution:

$$LHS = \frac{1}{1-\cos x}-\frac{\cos x}{1+\cos x}$

Multiply first term by $\frac{1+cos x}{1+cos x}$ and second term by $\frac{1-cos x}{1-cos x}$ .

$$= \frac{1(1+\cos x)}{(1-\cos x)(1+\cos x)}-\frac{\cos x(1-\cos x)}{(1+\cos x)(1-\cos x)}$

Using the identity: $(a-b)(a+b)=(a^2-b^2)$

$$= \frac{1+\cos x}{(1^2-\cos^2 x)}-\frac{\cos x-\cos^2 x}{(1^2-\cos^2 x)}$

Denominators are same, you can subtract the fractions.

$$= \frac{1+\cos x-\cos x+\cos^2 x}{(1^2-\cos^2 x)}$

Using the identity: $1-\cos ^{2}(x)=\sin ^{2}(x)$

$$= \frac{1+\cos^2 x}{\sin^2x}$

Using the identity: $1=\cos ^{2}(x)+\sin ^{2}(x)$

$$=\frac{\cos ^{2}x+\cos ^{2}x+\sin ^{2}x}{\sin ^{2}x}$

$$=\frac{\sin ^{2}x+2 \cos ^{2}x}{\sin ^{2}x}$ ------------ (1)

$RHS=2 \cot ^{2} x+1$

Using the identity: $\cot (x)=\frac{\cos (x)}{\sin (x)}$

$$=1+2\left(\frac{\cos x}{\sin x}\right)^{2}$

$$=1+2\frac{\cos^{2} x}{\sin^{2} x}$

$$=\frac{\sin^2 x + 2\cos^{2} x}{\sin^2 x}$ ------------ (2)

Equation (1) = Equation (2)

LHS = RHS

$$\frac{1}{1-\cos x}-\frac{\cos x}{1+\cos x}=2 \cot ^{2} x+1$

Hence proved.

5 0

3 years ago

A manufacturer determines that the cost of making a computer Compass is 2.161616 write the class as a fraction and as a mixed nu

Ivanshal [37]

First of all you times 2.16.... by 100 to get 21.61616.....

you then minus the original number to get 21.4.

You can then times that by 10 to why 214 and you can divide 214 by 99:
214/99 = 2.161616

Hope this helps! :)

7 0

3 years ago

What's the value of a when 3-a+5-2a=17

Flura [38]

Here's are the steps to solving it.

3-a+5-2a=17
-3a=9
a=-3

6 0

3 years ago

Read 2 more answers