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1 year ago

Theorem: A line parallel to one side of a triangle divides the other two

Mathematics

1 answer:

Nonamiya [84]1 year ago

7 0

Answer: Segment BD = 15

Step-by-step explanation: Ok. So, we know that segment DE is parallel to segment BC and segment EF is parallel to segment AB. The triangle proportionality theorem states that if a line is parallel to one side of a triangle and also intersects the other two sides, the line divides the sides proportionally. To put it more simply; because segment EF is parallel to segment AB, triangles ADE and EFC are proportional and similar. From there we must find the scale factor by which these two triangles are proportional.

We can do this by dividing the corresponding segments by; each other.

24 ÷ 20 = 1.2

Scale Factor = 1.2

Then we divide segment AD (18) by the scale factor (1.2).

18 ÷ 1.2 = 15

Since segment EF is parallel to segment AB, segment EF corresponds and is congruent to segment DB.

So,

Segment BD = 15

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NEED HELP ASAP. WILL GIVE BRAINLY

balu736 [363]

Answer:

A. x = 2 and y =2

B. x = 3 and y = -1

Step-by-step explanation:

A. { x = 3y − 4

2x − y = 2

1) Substitute the value of x

2(3y − 4) − y = 2

2) Solve the equation for y

y = 2

3) Substitute the value of y

x= 3(2) -4

4) Solve the equation for x

x = 2

Final Solution: x = 2 and y =2

B. { 3x + 2y = 7

−x + y = −4

1) Multiply both sides of the equation by 3

-3x + 3y = -12

2) Eliminate one variable by adding the equations

3x + 2y = 7

5y = -5

3) Divide both sides of the equation by 5

y = -1

4) Substitute the given value of y into the equation -x + y = -4

-x + (-1) = -4

5) Solve the equation for x

x = 3

Final Solution: x = 3 and y = -1

5 0

1 year ago

Do teachers find their work rewarding and satisfying? An article reports the results of a survey of 397 elementary school teache

Tju [1.3M]

Answer:

The 95% confidence interval would be given (0.0109;0.1651).

We are confident at 95% that the difference between the two proportions is between $0.0109 \leq p_{elementary} -p_{High school} \leq 0.1651$

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$p_A$ represent the real population proportion for elementary school

$\hat p_A =\frac{226}{397}=0.569$ represent the estimated proportion for elementary school

$n_A=397$ is the sample size required for Brand A

$p_B$ represent the real population proportion for high school teachers

$\hat p_B =\frac{129}{268}=0.481$ represent the estimated proportion for high school teachers

$n_B=268$ is the sample size required for Brand B

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

The confidence interval for the difference of two proportions would be given by this formula

$(\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.