All categories

2 years ago

Given: AB ∥ DC

Mathematics

1 answer:

RSB [31]2 years ago

5 0

Answer:

$A=1,720.16\ units^2$

Step-by-step explanation:

we know that

The area of the trapezoid is equal to

$A=\frac{1}{2}(DC+AB)DE$

step 1

Find the measure of angle DAE

m∠ADC+m∠DAE=180° -----> by consecutive interior angles

we have

m∠ADC = 134°

substitute

134°+m∠DAE=180°

m∠DAE=180°-134°=46°

step 2

In the right triangle ADE

Find the length side AE

cos(∠DAE)=AE/AD

$AE=cos(46\°)(40)\\AE=27.79\ units$

step 3

In the right triangle ADE

Find the length side DE

sin(∠DAE)=DE/AD

$DE=sin(46\°)(40)\\DE=28.77\ units$

step 4

Find the area of ABCD

$A=\frac{1}{2}(DC+AB)DE$

we have

$DC=32\ units\\AB=DC+2(AE)=32+2(27.79)=87.58\ units\\DE=28.77\ units$

substitute

$A=\frac{1}{2}(32+87.58)28.77$

$A=1,720.16\ units^2$

You might be interested in

WILL GIVE FIRST RIGHT ANSWER BRAINIEST

saw5 [17]

Answer:

2 integers: $7 and $8

5-by-step explanation:

compute 3 times square root of 5 and get 6.708. . .

Plot that.

Compute 5 times the square root of 3 and get 8.6602...

Plot that.

See which whole numbers are between those two points. Only two: 7 and 8

Since the question includes $ signs (WHY??) include the $ in your answer.

8 0

2 years ago

• A researcher claims that less than 40% of U.S. cell phone owners use their phone for most of their online browsing. In a rando

antiseptic1488 [7]

Answer:

We failed to reject H₀

Z > -1.645

-1.84 > -1.645

We failed to reject H₀

p > α

0.03 > 0.01

We do not have significant evidence at a 1% significance level to claim that less than 40% of U.S. cell phone owners use their phones for most of their online browsing.

Step-by-step explanation:

Set up hypotheses:

Null hypotheses = H₀: p = 0.40

Alternate hypotheses = H₁: p < 0.40

Determine the level of significance and Z-score:

Given level of significance = 1% = 0.01

Since it is a lower tailed test,

Z-score = -2.33 (lower tailed)

Determine type of test:

Since the alternate hypothesis states that less than 40% of U.S. cell phone owners use their phone for most of their online browsing, therefore we will use a lower tailed test.

Select the test statistic:

Since the sample size is quite large (n > 30) therefore, we will use Z-distribution.

Set up decision rule:

Since it is a lower tailed test, using a Z statistic at a significance level of 1%

We Reject H₀ if Z < -1.645

We Reject H₀ if p ≤ α

Compute the test statistic:

$Z = \frac{\hat{p} - p}{ \sqrt{\frac{p(1-p)}{n} }}$

$Z = \frac{0.31 - 0.40}{ \sqrt{\frac{0.40(1-0.40)}{100} }}$

$Z = \frac{- 0.09}{ 0.048989 }$

$Z = - 1.84$

From the z-table, the p-value corresponding to the test statistic -1.84 is

p = 0.03288

Conclusion:

We failed to reject H₀

Z > -1.645

-1.84 > -1.645

We failed to reject H₀

p > α

0.03 > 0.01

We do not have significant evidence at a 1% significance level to claim that less than 40% of U.S. cell phone owners use their phones for most of their online browsing.

8 0

2 years ago

A mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror. The pipe is lo

vodomira [7]

Answer: $x^2=32y$

Step-by-step explanation:

Given: A mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror.

The pipe is located 8 inches from the vertex of the mirror.

Assume the vertex is at the origin.

If the parabola opens upwards

then the coordinates of focus= (0,8)

We know that equation of parabola with focus (0,a) and open upards is of the form (vertex=(0,0)) is

$x^2=4ay$

Substitute the value of a=8 in equation, we get

$x^2=4\times8y$

$\Rightarrow\ x^2=32y$

Therefore, equation of the parabola that models the cross section of the mirror is $x^2=32y$

3 0

2 years ago

Jason bought a table for $98.00. The finance charge was $12 and she paid for it over 10 months. Use the formula, and calculate h

lutik1710 [3]

Answer:2.00

Step-by-step explanation:

approximate apr=(finance charge divided by#months)12 / amount financed

8 0

2 years ago

Use the double intercept approach to find the graph of –1 = –y + x. A. B. C. D.

navik [9.2K]

Answer:

Intercepts at (-1, 0) and (0, 1).

Step-by-step explanation:

The double intercept form for the equation of a line is

ax + by = 1

-1 = -y + x

y = 0

x = -1 Multiply each side by -1

-x = 1

The x-intercept is at (-1, 0).

=====

x = 0

-1 = -y Multiply each side by -1

y = 1

The y-intercept is at (0, 1).

=====

The graph (see below) is a straight line passing through the points (-1, 0) and (0, 1).

5 0

2 years ago