Please help me with this problem. Tell me the steps to solving

Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.

melamori03 [73]

Answer:

$6+2\sqrt{21}\:\mathrm{cm^2}\approx 15.17\:\mathrm{cm^2}$

Step-by-step explanation:

The quadrilateral ABCD consists of two triangles. By adding the area of the two triangles, we get the area of the entire quadrilateral.

Vertices A, B, and C form a right triangle with legs $AB=3$ , $BC=4$ , and $AC=5$ . The two legs, 3 and 4, represent the triangle's height and base, respectively.

The area of a triangle with base $b$ and height $h$ is given by $A=\frac{1}{2}bh$ . Therefore, the area of this right triangle is:

$A=\frac{1}{2}\cdot 3\cdot 4=\frac{1}{2}\cdot 12=6\:\mathrm{cm^2}$

The other triangle is a bit trickier. Triangle $\triangle ADC$ is an isosceles triangles with sides 5, 5, and 4. To find its area, we can use Heron's Formula, given by:

$A=\sqrt{s(s-a)(s-b)(s-c)}$ , where $a$ , $b$ , and $c$ are three sides of the triangle and $s$ is the semi-perimeter ( $s=\frac{a+b+c}{2}$ ).

The semi-perimeter, $s$ , is:

$s=\frac{5+5+4}{2}=\frac{14}{2}=7$

Therefore, the area of the isosceles triangle is:

$A=\sqrt{7(7-5)(7-5)(7-4)},\\A=\sqrt{7\cdot 2\cdot 2\cdot 3},\\A=\sqrt{84}, \\A=2\sqrt{21}\:\mathrm{cm^2}$

Thus, the area of the quadrilateral is:

$6\:\mathrm{cm^2}+2\sqrt{21}\:\mathrm{cm^2}=\boxed{6+2\sqrt{21}\:\mathrm{cm^2}}$

4 0

3 years ago

A United Nations report shows the mean family income for Mexican migrants to the United States is $27,000 per year. A FLOC (Farm

disa [49]

Answer:

We conclude that the mean family income for Mexican migrants to the United States is $27,000 per year and the provided information is consistent with the United Nations report.

Step-by-step explanation:

We are given that a United Nations report shows the mean family income for Mexican migrants to the United States is $27,000 per year.

A FLOC evaluation of 25 Mexican family units reveals a mean to be $30,000 with a sample standard deviation of $10,000.

Let $\mu$ = true mean family income for Mexican migrants.

So, Null Hypothesis, $H_0$ : $\mu$ = $27,000 {means that the mean family income for Mexican migrants to the United States is $27,000 per year}

Alternate Hypothesis, $H_A$ : $\mu$ $\neq$ $27,000 {means that the mean family income for Mexican migrants to the United States is different from $27,000 per year}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean family income = $30,000

s = sample standard deviation = $10,000

n = sample of Mexican family = 25

So, the test statistics = $\frac{30,000-27,000}{\frac{10,000}{\sqrt{25} } }$ ~ $t_2_4$

= 1.50

The value of t test statistics is 1.50.

Since, in the question we are not given the level of significance so we assume it to be 5%. Now, at 5% significance level the t table gives critical values of -2.064 and 2.064 at 24 degree of freedom for two-tailed test.

Since our test statistic lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the mean family income for Mexican migrants to the United States is $27,000 per year and the provided information is consistent with the United Nations report.

4 0

3 years ago

In its first year of operation, Big Lake Camp had 40 campers. This year’s attendance was 180% of the first year’s. How many camp

Murrr4er [49]

Answer:

72 campers participated this year

Step-by-step explanation:

Percentages

To determine x% of y, we must calculate x*y/100.

The number of campers that participated in Big Lake Camp during its first year was 40. We now want to know the number of campers that participated this year, if the attendance was 180% of the first year's.

The new attendance is calculated as follows:

40 * 180 / 100 = 72

72 campers participated this year

4 0

3 years ago

Please need help thank you

mel-nik [20]

Perimeter 430
Length 172
172 next
430 last(after the =)

5 0

3 years ago

4/5 miles in 1/5 hour unit rate

eduard

Answer:

4 miles an hour

Step-by-step explanation:

5 0

3 years ago