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2 years ago

Rationalize the following

Mathematics

1 answer:

IRINA_888 [86]2 years ago

6 0

Step-by-step explanation:

$\frac{1}{ \sqrt{2} + 1 }$

(On Rationalizing )

$= \frac{1}{ \sqrt{2} + 1} \times \frac{ \sqrt{2} - 1}{ \sqrt{2} - 1 }$

$= \frac{ \sqrt{2} - 1 }{( { \sqrt{2} )}^{2} - {(1)}^{2} }$

$= \frac{ \sqrt{2} - 1}{2 - 1}$

$= \frac{ \sqrt{2} - 1}{1}$

$= \sqrt{2} - 1(ans)$

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What is the solution to the system of equations shown below?

Alexxandr [17]

Answer:

b. (1, 3, -2)

Step-by-step explanation:

A graphing calculator or scientific calculator can solve this system of equations for you, or you can use any of the usual methods: elimination, substitution, matrix methods, Cramer's rule.

It can also work well to try the offered choices in the given equations. Sometimes, it can work best to choose an equation other than the first one for this. The last equation here seems a good one for eliminating bad answers:

a: -1 -5(1) +2(-4) = -14 ≠ -18

b: 1 -5(3) +2(-2) = -18 . . . . potential choice

c: 3 -5(8) +2(1) = -35 ≠ -18

d: 2 -5(-3) +2(0) = 17 ≠ -18

This shows choice B as the only viable option. Further checking can be done to make sure that solution works in the other equations:

2(1) +(3) -3(-2) = 11 . . . . choice B works in equation 1

-(1) +2(3) +4(-2) = -3 . . . choice B works in equation 2

7 0

2 years ago

A basketball is price at 37.00 if there is a 7% sales tax what is the final cost of the basketball

Vladimir79 [104]

Answer:

$39.59

Step-by-step explanation:

37 increase 7% =

37 × (1 + 7%) = 37 × (1 + 0.07) = 39.59

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2 years ago

Assume that a sample is used to estimate a population proportion μ . Find the margin of error M.E. that corresponds to a sample

hichkok12 [17]

Answer:

$MoE = 1.645\cdot \frac{13.1}{\sqrt{772} } \\\\MoE = 1.645\cdot 0.47147\\\\MoE = 0.776\\\\$

Step-by-step explanation:

Since the sample size is quite large, we can use the z-distribution.

The margin of error is given by

$MoE = z_{\alpha/2}(\frac{s}{\sqrt{n} } )$

Where n is the sample size, s is the sample standard deviation and $z_{\alpha/2}$ is the z-score corresponding to a 90% confidence level.

The z-score corresponding to a 90% confidence level is

Significance level = α = 1 - 0.90= 0.10/2 = 0.05

From the z-table at α = 0.05

z-score = 1.645

$MoE = 1.645\cdot \frac{13.1}{\sqrt{772} } \\\\MoE = 1.645\cdot 0.47147\\\\MoE = 0.776\\\\$

Therefore, the margin of error is 0.776.

3 0

2 years ago

Help?... 1/3(-3) + 13

ra1l [238]

Answer: 12

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

Ellis is painting wooden fenceposts before putting them in his yard. They are each 6 feet tall and have a diameter of 1 foot. Th

Dominik [7]

The amount of the paint that Ellis needs to paint all the surfaces of the 12 fenceposts will be 226.08 square feet.

<h3>What is a cylinder?</h3>

A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.

Ellis is painting wooden fenceposts before putting them in his yard. They are each 6 feet tall and have a diameter of 1 foot. There are 12 fenceposts in all.

The amount of the paint that Ellis needs to paint all the surfaces of the 12 fenceposts will be

The area of the one fence post will be

Area = πdh

Area = 3.14 x 1 x 6

Area = 18.84 square feet

Then the paint for 12 fence posts will be

Total area = 12 x 18.84

Total area = 226.08 square feet

More about the cylinder link is given below.

brainly.com/question/3692256

#SPJ1

6 0

1 year ago

Rationalize the following​

Rationalize the following