All categories

1 year ago

In the diagram shown, AE 1/3AC and ED ll CB. Explain why df must be one-fourth length of CD

Mathematics

1 answer:

Blizzard [7]1 year ago

8 0

The value of the length DF is 1/4 of that of CD because of the Angle Bisector Theorem for triangles.

<h3>What is the Angle Bisector Theorem?</h3>

The Angel Bisector Theorem states that if a ray bisects an angle of a triangle, it dissects the side of the triangle that is opposite to the dissected angle into parts that are proportionate to the adjacent sides.

Note that the angle that has been dissected here is ∠CBD. Thus,

$\frac{DF}{CF}$ = $\frac{BD}{BC}$

See the link below for more about Angle Bisector Theorem of the Triangle:

brainly.com/question/21475560

You might be interested in

If 50% is 10 what is 25%

kaheart [24]

Step-by-step explanation:. The first says “I know that 10 is one-tenth of 100. I will therefore divide 50 by 10. The answer is 5”.

This is fine when the numbers are relatively simple. But suppose the numbers are more complicated.

What is 22% of 46?

Now it’s much less straightforward. You can’t just work out what 22% is, expressed as a fraction, and anyway, it’s not a simple fraction.

Instead, you have to divide 46 into 100 equal parts, and work out what 22 of them would be when added together.

So: 46 ÷ 100 = 0.46 [remember, when you divide by 100, you move the decimal point two places to the left].

0.46 × 22 = 10.12

Answer: 22% of 46 is 10.12.

Hope this helped :)

8 0

2 years ago

What is the volume of this right rectangular prism? Enter your answer as a decimal in the box. cm³ A rectangular prism with a le

Irina-Kira [14]

The volume of a rectangular prism is equivalent to the equation Bh. But to find the base you must first do lw or in this equation 6.1 times 5.4. That equals to 32.94. You then use the height, or in this case 8 and multiply it times 32.94. Your final answer should be 263.52 cm. cubed.

6 0

2 years ago

Read 2 more answers

Fizzy Waters has been involved in multiple lawsuits regarding the alkaline substance concentration in their product and getting

ser-zykov [4K]

Answer:

Step-by-step explanation:

For the sample, n = 12

Mean, x = (158.2 + 162.8 + 161.5 + 161.2 + 166.5 + 160.1 + 158.4 + 175.6 + 159.9 + 168.8 + 161.9 + 163.7)/12 = 163.22

Variance, s² = (summation(x - mean)²/n

Summation(x - mean)² = (158.2 - 163.22)^2 + (162.8 - 163.22)^2 + (161.5 - 163.22)^2 + (161.2 - 163.22)^2+ (166.5 - 163.22)^2 + (160.1 - 163.22)^2 + (158.4 - 163.22)^2 + (175.6 - 163.22)^2 + (159.9 - 163.22)^2 + (168.8 - 163.22)^2 + (161.9 - 163.22)^2 + (163.7 - 163.22)^2 = 273.5368

Variance, s² = 273.5368/12 = 22.79

This is a test for a single variance. We would set up the test hypothesis.

For the null hypothesis,

H0: σ² ≥ 25

For the alternative hypothesis,

H1: σ² < 25

The formula for determining the test statistic,x² is

x² = (n - 1)s²/σ²

Where n - 1 is the degree of freedom, df.

df = 12 - 1 = 11

x² = (11 × 22.79)/25 = 10.0276

For a test of 90% reliability, Confidence level = 0.9

Cl = 1 - alpha(level of significance)

alpha = 1 - 0.9 = 0.1

The critical value from the chi-square distribution table is 17.28. Since 17.28 > 10.0276, we would reject the null hypothesis. Therefore, the filling machine does not need repair because the variance of the process is not more than 25 oz.

8 0

2 years ago

Help me from 6-9 (geometry)

elena55 [62]

Answer:

6) Two angles are called supplementary when their measures add up to 180 degrees. For example, two right angles are supplementary angles.

7) When the sum of two angles is equal to 90 degrees, they are called complementary angles. For example, 30 degrees and 60 degrees are complementary angles.

8) you have to plot the points on the graph and draw a line and label it with L at one point and M at another point.

9) x = 20

m < A = 65

m < B = 25

Step-by-step explanation:

3x + 5 + 2x - 15 = 90

3x + 2x + 5 - 15 = 90

5x - 10 = 90

5x - 10 + 10 = 90 + 10

5x = 100

5 / 5x = 100 / 5

x = 20

A = 3x + 5

A = 3(20) + 5

A = 60 + 5

A = 65

B = 2x - 15

B = 2(20) - 15

B = 40 - 15

B = 25

8 0

2 years ago

Write an equation in point-slope form for the line through the given point with

Oliga [24]

Answer:

Here you go.

Step-by-step explanation:

Hope this helps you!

5 0

3 years ago