Determine the number of shaded sections for each model

Given segments AB and CD intersect at E.

nata0808 [166]

The length of a segment is the distance between its endpoints.

$\mathbf{AB = 3\sqrt{2}}$
AB and CD are not congruent
AB does not bisect CD
CD does not bisect AB

(a) Length of AB

We have:

$\mathbf{A = (1,2)}$

$\mathbf{B = (4,5)}$

The length of AB is calculated using the following distance formula

$\mathbf{AB = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}$

So, we have:

$\mathbf{AB = \sqrt{(1 - 4)^2 + (2 - 5)^2}}$

$\mathbf{AB = \sqrt{18}}$

Simplify

$\mathbf{AB = 3\sqrt{2}}$

(b) Are AB and CD congruent

First, we calculate the length of CD using:

$\mathbf{CD = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}$

Where:

$\mathbf{C = (2, 4)}$

$\mathbf{D = (2, 1)}$

So, we have:

$\mathbf{CD = \sqrt{(2 -2)^2 + (4 - 1)^2}}$

$\mathbf{CD = \sqrt{9}}$

$\mathbf{CD = 3}$

By comparison

$\mathbf{CD \ne AB}$

Hence, AB and CD are not congruent

(c) AB bisects CD or not?

If AB bisects CD, then:

$\mathbf{AB = \frac 12 \times CD}$

The above equation is not true, because:

$\mathbf{3\sqrt 2 \ne \frac 12 \times 3}$

Hence, AB does not bisect CD

(d) CD bisects AB or not?

If CD bisects AB, then:

$\mathbf{CD = \frac 12 \times AB}$

The above equation is not true, because:

$\mathbf{3 \ne \frac 12 \times 3\sqrt 2}$

Hence, CD does not bisect AB

Read more about lengths and bisections at:

brainly.com/question/20837270

7 0

3 years ago

Khloe and Emma work at a furniture store. Khloe is paid $245 per week plus 9.5% of her total sales in dollars, xx, which can be

ale4655 [162]

Answer: Their weekly pay would be the same if xx equals $1,600

Step-by-step explanation: The first and most important step is to identify what the question requires, and that is, what is the value of the unknown in the equation of their weekly incomes that would make their pay to be the same? Their weekly pay as per individual is given as follows;

Khloe = 245 + 0.095x ———(1)

Emma = 285 + 0.07x ———(2)

Simply put, we need to find the value of x when equation (1) equals equation (2)

245 + 0.095x = 285 + 0.07x

Collect like terms and we now have

0.095x - 0.07x = 285 - 245

0.025x = 40

Divide both sides of the equation by 0.025

x = 1600

Therefore their weekly pay would be at the same level, if x equals $1600

6 0

3 years ago

The product of a number and 4 Plus 2 is 14

netineya [11]

It's 3 because 4×3=12 add 2 and it equals 14

4 0

3 years ago

Read 2 more answers

A sanitation department is interested in estimating the mean amount of garbage per bin for all bins in the city. In a random sam

bekas [8.4K]

Answer:

The 95.7% confidence interval for the expected amount of garbage per bin for all bins in the city

(48.937 , 50.863)

Step-by-step explanation:

Explanation:-

Given data random sample of 46 bins, the sample mean amount was 49.9 pounds and the sample standard deviation was 3.641

The sample size 'n' =46

mean of the sample x⁻ = 49.9

Standard deviation of the sample S = 3.641

Confidence intervals:-

The 95.7% confidence interval for the expected amount of garbage per bin for all bins in the city

$(x^{-} - t_{\alpha } \frac{S}{\sqrt{n} } ,x^{-} + t_{\alpha } \frac{S}{\sqrt{n} })$

Degrees of freedom = n-1 = 46-1 =45

The tabulated value t₀.₉₆ = 1.794 ( from t-table)

$(49.9 - 1.794 \frac{3.641}{\sqrt{46} } ,49.9+ 1.794 \frac{3.641}{\sqrt{46} })$

(49.9 -0.9630 , 49.9+0.9630)

(48.937 , 50.863)

Conclusion:-

The 95.7% confidence interval for the expected amount of garbage per bin for all bins in the city

(48.937 , 50.863)

4 0

3 years ago

Sea Level changes occur at a rate of 10 m per 1,000 per years.

Volgvan

The water will rise 10,000m in 10000000

5 0

3 years ago

Read 2 more answers