All categories

2 years ago

Figure GHTA below is a parallelogram. = 6 cm, = 8 cm, and the measure of = 60°. Find the area.

Mathematics

2 answers:

Kruka [31]2 years ago

4 0

Answer:

multiply

Step-by-step explanation:

vampirchik [111]2 years ago

4 0

Answer:

The area of parallelogram GHTA is $41.568 cm^2$ .

Step-by-step explanation:

Given parallelogram GHTA

GH = 8 cm =-AT

GA = 6 cm

∠ GAT =∠ GHT = 60°

To find = Area of parallelogram

Solution:

Draw perpendicular GO on the base AT.

In ΔGOA

$\sin 60^o=\frac{GO}{GA}=\frac{GO}{6 cm}$

(sin 60°=0.8660)

GO = 5.196 cm

Area of the parallelogram: GO × AT

$=5.196 cm\times 8 cm =41.568 cm^2$

The area of parallelogram GHTA is $41.568 cm^2$ .

You might be interested in

1.) You are one of five people who have been hired to mow the lawn at the local college. Each week, the dimensions of the plot y

iren [92.7K]

Answer:

1a) Length = 7x + 3 & Width = 4x - 2

1b) Area = $28x^2 -2x -6$

1c) Area = 2774 sq. m

2. $(x-4)(y+7)$

Step-by-step explanation:

1a)

The length given as words is "3 more than 7 times x"

The width given as words is "4 times x minus 2"

The expression for length would be 7x + 3

The expression for width would be 4x - 2

1b)

The area is length * width

Since we already know the algebraic expressions for length and width from part (a) above, we use the formula:

Area = (7x+3)(4x-2) = 28x^2 -14x + 12x - 6 = 28x^2 -2x -6

Area = $28x^2 -2x -6$

1c)

Given x = 10, we put this into the area expression we found in (b) above.Let's see:

$28x^2 -2x -6\\=28(10)^2 -2(10) -6\\=2774$

Area = 2774 sq. m

We can group the first two terms and next two terms and write up:

$xy-4y+7x-28\\(xy-4y)+(7x-28)\\y(x-4)+7(x-4)\\(x-4)(y+7)$

That's the factored form.

8 0

2 years ago

Read 2 more answers

A copper smelting process is supposed to reduce the arsenic content of the copper to less than 1000 ppm. let μ denote the mean a

Hitman42 [59]

The rejection region is give by

$|z_{test}|\ \textgreater \ z_{\alpha/2}$

where the test statistics is given by

$\frac{\bar{x}-\mu}{\sigma/\sqrt{n}} = \frac{980-1000}{100/\sqrt{75}} \\ \\ = \frac{-20}{100/8.6603} = \frac{-20}{11.5470} =-1.73$

i.e. $|z_{test}|=|-1.73|=1.73$

Thus, $z_{\alpha/2}=1.73$

Using the statistical table, the level of the test is 0.04.

6 0

2 years ago

The population p of a small community on the outskirts of a city grows rapidly over a 20-year period: t05101520p1002004509502000

myrzilka [38]

Answer:

The population of the small community, 5 years into the future, after the initial 20-year period = 4268.

Step-by-step explanation:

t | 0 | 5 | 10 | 15 | 20

p | 100 | 200 | 450 | 950 | 2000

The exponential function will look like

p = aeᵏᵗ

where a and k are constants.

Take the natural logarithms of both sides

In p = In aeᵏᵗ

In p = In a + In eᵏᵗ

In p = In a + kt

In p = kt + In a.

We then use linear regression to fit the data of In p against t to obtain k and In a.

t | 0 | 5 | 10 | 15 | 20

p | 100 | 200 | 450 | 950 | 2000

In p | 4.605 | 5.298 | 6.109 | 6.856 | 7.601

In p = kt + In a.

y = mx + b

m = k and b = In a

Performing a linear regression analysis on the now-linear relationship between In p and t and also plotting a graph of the variables.

The regression equation obtained is

y = 0.151x + 4.584

The first attached image shows the equations necessary for the estimation of the linear regression parameters.

The second attached image shows the use of regression calculator and the plot of the function In p versus t.

Comparing

y = 0.151x + 4.584

With

In p = kt + In a.

y = In p

k = 0.151

x = t

In a = 4.584

a = 97.905

The exponential function relating p and t,

p = aeᵏᵗ now becomes

p = 97.905 e⁰•¹⁵¹ᵗ

So, to predict the population 5 years into the future, that is 5 years after the 20 year period.

we need p at t=25 years.

0.151 × 25 = 3.775

p(t=25) = 97.905 e³•⁷⁷⁵ = 4268.41 = 4268.

Hope this Helps!!!

7 0

2 years ago

A marketing firm wants to estimate how much root beer the average teenager drinks per year. A previous study found a standard de

Verdich [7]

Answer:

At least 832 teenargers must be interviewed.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.99}{2} = 0.005$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.005 = 0.995$ , so $z = 2.575$

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

How many teenagers must the firm interview in order to have a margin of error of at most 0.1 liter when constructing a 99% confidence interval

At least n teenargers must be interviewed.

n is found when M = 0.1.

We have that $\sigma = 1.12$

$M = z*\frac{\sigma}{\sqrt{n}}$

$0.1 = 2.575*\frac{1.12}{\sqrt{n}}$

$0.1\sqrt{n} = 2.575*1.12$

$\sqrt{n} = \frac{2.575*1.12}{0.1}$

$(\sqrt{n})^{2} = (\frac{2.575*1.12}{0.1})^{2}$

$n = 831.7$

Rounding up

At least 832 teenargers must be interviewed.

4 0

2 years ago

A group of 85 people were asked whether or not they prefer a bagel or a muffin for breakfast and whether or not they prefer milk

gladu [14]

Answer:

The answer(s) would be WY/WZ, or WYZ (If this is multiple choice)

Step-by-step explanation:

The reasoning is that in the "IRL Equation" the polls showed that orange juice was prefered over milk, and didn't matter whether they wanted a bagel or muffin. All that matters in this equation is that it is one sided (For the 1st poll that is) and now you are able to narrow down the possibilities of the answer(s).

5 0

2 years ago