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1 year ago

EAB and DCB are two right triangles. The figure has BED≅ BDE. Point B is the midpoint of segment AC. Prove: EAB≅ DCB

1 answer:

5 0

See the attached picture.

you are given that ABCE is an isosceles trapezoid. 

you are given that AB is parallel to EC. 

this means that AE is congruent to BC. 

you are given that AE and AD are congruent. 

triangle EAD is an isosceles triangle because AE and AD are congruent. 

this means that angle 1 is equal to angle 3. 

since angle 1 is equal to angle 2 and angle 3 is equal to angle 1, then angle 3 is also equal to angle 2. 

this means that AD and BC are parellel because their corresponding angles (angles 3 and 2) are equal. 

since AB is parallel to EC and DC is part of the same line, than AB is parallel to DC. 

you have AB parallel to DC and AD parallel to BC. 

if opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram. 

that might be able to do it,depending on whether all these statements are acceptable without proof. 

they are either postulates or theorems that have been previously proven. 

if not, then you need to go a little deeper and prove some of the statements that you used.. 

here's my diagram.

this is not a formal proof, but should give you some ideas about how to proceed. 

you can also prove that angle 4 is equal to angle 2 because they are alternate interior angles of parallel lines. 

you can also prove that angle 6 is equal to angle 5 because they are alternate interior angles of parallel lines.

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An hourglass composed of two identical cones is 18 cm tall.the radius of each cone is 4cm if you want to fill the bottom half of

Kitty [74]

Check the picture below.

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1 year ago

A cylinder has a base area of 28.2 m2 and a height of 3.1 m. Estimate the volume of the cylinder. A) 31 m3 B) 31 m2 Eliminate C)

Irina18 [472]

The answer can't be C or D because the unit of volume is always cubed. The formula for volume of cylinder is (pi)(r^2)(h) . The pi(r^2) part is the formula for area of a circle which is what the base of the cylinder is. Fortunately the area is already given as 28.2. Plug that into the volume formula and plug in 3.1 for the height and multiply. I get 87.42 and the answer choice B seems to be the closest option

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2 years ago

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A member of a student team playing an interactive marketing game received the fol- lowing computer output when studying the rela

nirvana33 [79]

Answer:

$p_v = 2*P(t_{n-2} > |t_{calc}|)= 0.91$

So on this case for the significance level assumed $\alpha=0.05$ we see that $p_v >\alpha$ so then we can conclude that the result is NOT significant. And we don't have enough evidence to reject the null hypothesis.

So on this case is not appropiate say that :"the more we spend on advertising this product, the fewer units we sell" since the slope for this case is not significant.

Step-by-step explanation:

Let's suppose that we have the following linear model:

$y= \beta_o +\beta_1 X$

Where Y is the dependent variable and X the independent variable. $\beta_0$ represent the intercept and $\beta_1$ the slope.

In order to estimate the coefficients $\beta_0 ,\beta_1$ we can use least squares procedure.

If we are interested in analyze if we have a significant relationship between the dependent and the independent variable we can use the following system of hypothesis:

Null Hypothesis: $\beta_1 = 0$

Alternative hypothesis: $\beta_1 \neq 0$

Or in other words we want to check is our slope is significant (X have an effect in the Y variable )

In order to conduct this test we are assuming the following conditions:

a) We have linear relationship between Y and X

b) We have the same probability distribution for the variable Y with the same deviation for each value of the independent variable

c) We assume that the Y values are independent and the distribution of Y is normal

The significance level assumed on this case is $\alpha=0.05$

The standard error for the slope is given by this formula:

$SE_{\beta_1}=\frac{\sqrt{\frac{\sum (y_i -\hat y_i)^2}{n-2}}}{\sqrt{\sum (X_i -\bar X)^2}}$

Th degrees of freedom for a linear regression is given by $df=n-2$ since we need to estimate the value for the slope and the intercept.

In order to test the hypothesis the statistic is given by:

$t=\frac{\hat \beta_1}{SE_{\beta_1}}$

The p value on this case would be given by:

$p_v = 2*P(t_{n-2} > |t_{calc}|)= 0.91$

So on this case is not appropiate say that :"the more we spend on advertising this product, the fewer units we sell" since the slope for this case is not significant.

3 0

1 year ago

You have a rectangular yard that measures 16 feet long 14 feet wide. It is covered in grass except for the center, where there i

aalyn [17]

First, get the area of the rectangular yard.
Area = L x W
Area = 16 X 14
Area = 224 square feet

Get the area of the circular fountain.
Area = pi x r^2
Area = 3.1415 x (4/2)^2
Area = 12.57 square feet

Getting grass portion.
224 - 12.57 = (C) 211.43 square feet

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1 year ago

Mr. Matthew is testing the online popularity of his custom made belts and wallets that were marketed differently. Some items wer

Tomtit [17]

See the attached figure
===========================
After 3 days, the total number of belts sold will be the same as the total number of wallets sold. The number of belts and the number of wallets Mr. Matthew sold after this many days is 27.

======================================================
Explanation of the answer:
The equation that represents the number of belts sold = 3^x ⇒⇒⇒ blue graph

The equation that represents the number of wallets sold = 4x+15 ⇒⇒⇒ red graph

The point of intersection represents the total number of belts sold will be the same as the total number of wallets sold.

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2 years ago

Read 2 more answers