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3 years ago

Which of the following is equivalent to

Mathematics

2 answers:

Montano1993 [528]3 years ago

8 0

Answer:

Choice B is correct.

Step-by-step explanation:

Given expression is

18-√-25

We have to simplify it.

As we know that

√-a=√-1.√a

Since we know that √-1=i

Hence,√-a=√ai

we can simplify given expression by using above equation.

18-√-25

18-√-1√25

18-i√25

18-√25i

As 25 is square of 5.

Hence ,

18-5i which is the answer.

enot [183]3 years ago

6 0

Answer:

Option (2) is correct.

$18-\sqrt{-25}=18-5i$

Step-by-step explanation:

Given expression $18-\sqrt{-25}$

We have to find an equivalence value to the expression.

Radical rule,

$\sqrt{-a}=\sqrt{-1} \sqrt{a}$

Also, $i=\sqrt{-1}$

Consider the given expression,

$18-\sqrt{-25}$

Applying radical rule to $\sqrt{-25}$

$\sqrt{-25}=\sqrt{-1}\sqrt{25}=5i$

Thus, the expression becomes,

$18-\sqrt{-25}=18-5i$

Thus, option (2) is correct.

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3 years ago

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3 years ago

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Nata [24]

Answer:

8 C sometimes

9 64x^8 y^11

10 c 1.28r^2/ t^9

Step-by-step explanation:

Algebraic Operations

Some basic rules must be fresh in our minds when trying to simplify complex algebraic expressions. For example, the power rule respect to the product or quotient:

$\displaystyle \left(\frac{x^n.y^m}{z^p}\right)^q= \frac{x^{qn}.y^{qm}}{z^{qp}}$

$\displaystyle \frac{x^n.x^q}{x^p}= x^{n+q-p}$

$\displaystyle x^{-n}=\frac{1}{x^n}$

Let's face the questions at hand

8. A number is raised to a negative exponent is negative?

Following the expressions recalled above, let's pick the expression

$\displaystyle 3^{-2}=\frac{1}{3^2}=\frac{1}{9}$

This is a negative power resulting in a positive number

Now we pick

$\displaystyle (-2)^{-3}=\frac{1}{(-2)^3}=-\frac{1}{8}$

This time, the negative power leads to a negative result, so it doesn't matter the sign of exponent to determine the sign of the result

Answer: C sometimes

9 simplify(4xy^2)^3(xy)^5

$(4xy^2)^3(xy)^5=4^3x^3(y^2)^3x^5y^5$

$=64x^3y^6x^5y^5$

$=64x^8y^{11}$

10 simplify(2t^-3)^3(0.4r)^2

$(2t^{-3})^3(0.4r)^2=2^3(t^{-3})^30.4^2r^2$

$=8t^{-9} 0.16 r^2$

$=1.28t^{-9} r^2$

$\displaystyle \frac{1.28 r^2}{t^9}$

7 0

3 years ago

Last year, the mean running time for a certain type of light bulb was 8.5 hours. This year, the manufacturer has introduced a ch

Free_Kalibri [48]

Answer:

H0 : μ = 8.5

H1 : μ > 8.5

1 sample t test ;

Test statistic = 2.53

Pvalue = 0.994

No, we fail to reject the Null ;

There is no significant evidence to support the Claim that the mean running time of light bulb is greater Tha last year.

Step-by-step explanation:

H0 : μ = 8.5

H1 : μ > 8.5

Test statistic :

(xbar - μ) ÷ (s/sqrt(n))

(8.7 - 8.5) ÷ (0.5 / sqrt40)

Test statistic = 2.53

The Pvalue :

P(Z < 2.53) = 0.9943

Pvalue = 0.994

Decison region :

Reject H0 ; if Pvalue < α

0.9943 > 0.05 ; We fail to reject the Null

5 0

3 years ago