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2 years ago

8

Show that (1 + 2V3)2 = 13 +4V3

1 answer:

umka2103 [35]2 years ago

7 0

Answer is 072 i think

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Rosa works due north of home. Her husband Juan works due east. They leave for work at the same time. By the time Rosa is 7 miles

polet [3.4K]

<span>This is a right triangle problem. c^2 = a^2 + b^2
Let b = 7 mi (Rosa's distance from home)
Let a = the east leg (Juan's distance from home
(a+1) = c (hypotenuse, distance between them)

(a+1)^2 = a^2 + 7^2

FOIL (a+1)(a+1)
a^2 + 2a + 1 = a^2 + 49

Combine like terms
a^2 - a^2 + 2a = 49 - 1
2a = 48
a =

<span>a = 24 mi, Juan's distance from home

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8 0

2 years ago

three sets of the sum of a number and four are added to the sum of seven times the same number and thirteen

almond37 [142]

The algebraic expression for given statement is: 10x + 25 or 3(x + 4) + (7x + 13)

<em><u>Solution:</u></em>

Given the statement:

Three sets of a sum of a number and four are added to the sum of seven times the same number and thirteen

Let us first understand the given statement,

Let the number be "x"

" sum of a number and four" means x + 4

"Three sets of a sum of a number and four" translated to 3(x + 4)

"sum of seven times the same number and thirteen" means 7x + 13

<em><u>Thus the algebraic expression for given statement is:</u></em>

$3(x+4)+(7x + 13)$

<em><u>Using distributive property in above expression</u></em>

$a(b+c) = ab + bc$

Therefore,

$3(x+4)+(7x + 13) = 3x + 12 + 7x + 13$

<em><u>Combine the like terms</u></em>

$3(x+4)+(7x + 13) = 10x+25$

Thus the required expression for given statement is: 10x + 25 or 3(x + 4) + (7x + 13)

7 0

2 years ago

A newspaper article states that 90% of drivers in Iowa wear their seatbelt. Suppose we are interested in estimating the proporti

konstantin123 [22]

Answer:

The sample size is $n = 3457$

Step-by-step explanation:

From the we are told that

The population proportion is p = 0.90

The margin of error is E = 0.01

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally the sample size is mathematically represented as

$n =[ \frac{ Z_{\frac{\alpha }{2} } }{E} ]^2 * p(1-p)$

=> $n =[ \frac{ 1.96 }{0.01} ]^2 * 0.90(1-0.90)$

=> $n = 3457$

8 0

3 years ago

Use the following data set to complete the problems.

Yuri [45]

Answer:

The interval 44-47 has a frequency of 3 .

The interval 48-51 has a frequency of 4.

The interval 56-59 has a frequency of 1.

The given data set is:

42, 43, 46, 47, 47, 48, 49, 50, 51, 53, 55, 55, 59

The number lying in the interval 44-47 are :46, 47, 47

So the interval 44-47 has a frequency of 3.

The number lying in the interval 48-51 are :48, 49, 50, 51

So, the interval 48-51 has a frequency of 4.

The number lying in the interval 56-59 is: 59

So, the interval 56-59 has a frequency of 1.

Step-by-step explanation:

7 0

1 year ago

Write a real life scenario that is represented by the integer -120.

Lorico [155]

Let's say that you owed your friend $120, you'd be -$120 in debt. Once you pay her off you'd be in the positives.

6 0

2 years ago