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3 years ago

Given ABCE is a rectangle, D is the midpoint of CE Prove AD =~ BD

Mathematics

1 answer:

Bas_tet [7]3 years ago

5 0

Since the congruent operator is â‰… and since AD is congruent to BD, I'm going to assume that you want to prove that AD is congruent to BD.
1. DE is equal to CD by definition since D is the midpoint of CE.
2. AE is equal to BC since opposite sides of a rectangle are equal to each other.
3. Angle AEC is equal to Angle BCE since all angles in a rectangle are right angles and all right angles are equal to each other.
4. Triangles ADE and BDC are congruent to each other because we have SAS congruence for both triangles.
5. AD is congruent to BC since they're corresponding sides of congruent triangles.

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3 years ago

A bottled water distributor wants to determine whether the mean amount of water contained in 1-gallon bottles purchased from a n

mash [69]

Answer:

We fail to reject H0; Hence, we conclude that there is no significant evidence that the mean amount of water per gallon is different from 1.0 gallon

Pvalue = - 2

(0.98626 ; 1.00174)

Since, 1.0 exist within the confidence interval, then we can conclude that mean amount of water per gallon is 1.0 gallon.

Step-by-step explanation:

H0 : μ= 1

H1 : μ < 1

The test statistic :

(xbar - μ) / (s / sqrt(n))

(0.994 - 1) / (0.03/sqrt(100))

-0.006 / 0.003

= - 2

The Pvalue :

Pvalue form Test statistic :

P(Z < - 2) = 0.02275

At α = 0.01

Pvalue > 0.01 ; Hence, we fail to reject H0.

The confidence interval :

Xbar ± Margin of error

Margin of Error = Zcritical * s/sqrt(n)

Zcritical at 99% confidence level = 2.58

Margin of Error = 2.58 * 0.03/sqrt(100) = 0.00774

Confidence interval :

0.994 ± 0.00774

Lower boundary = (0.994 - 0.00774) = 0.98626

Upper boundary = (0.994 + 0.00774) = 1.00174

(0.98626 ; 1.00174)

7 0

3 years ago

What does the expression n+3 represent?

Sati [7]

Do you know what n equals so i can solve it?<span />

5 0

3 years ago

Our work: -2x + 4 = 5 - 3x

Vikentia [17]

Answer:

x=1

Step-by-step explanation:

-2x + 4 = 5 - 3x

Add 3x to each side

-2x+3x + 4 = 5 - 3x+3x

x +4 =5

Subtract 4 from each side

x+4-4 =5-4

x =1

6 0

3 years ago

the base of this right prism is an equilateral triangle. the approximate height of the base is 15.6 cm. what is the approximate

Andrew [12]

Hello!

To find the surface area you can divide the prism into the 2D shapes it is made of

First list out all the shapes

2 triangles with bases of 18 and heights of 15.6
3 rectangles with side lengths of 20 and 18

First find the area of the triangles

The equation to find the area of a triangle is

$A = \frac{hb}{2}$

A is area
h is height
b is base

Put in the values you know

$A = \frac{18 * 15.6}{2}$

Solve

A = 140.4

The triangles have an area of 140.4 units

Next we find the area of a the rectangles

To do this we multiply the sides

18 * 20 = 360

The rectangles have areas of 360 units

Now we add all the areas

There are 2 triangles and 3 rectangles

140.4 + 140.4 + 360 + 360 + 360 = 1360.8

The answer is B) 1360.8cm squared

Hope this helps!

6 0

3 years ago