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4 years ago

Complete the proofs using the most appropriate method. may require CPCTC.

Mathematics

1 answer:

n200080 [17]4 years ago

3 0

For the first one, you did good. I will just suggest a couple things.

Statement Reason

JK ≅ LM Given

<JKM ≅ < LMK Given (You did both of these steps so well done.)

MK ≅ MK Reflexive Property (Your angle pair is congruent but isn't one of the interior angle of the triangles you are trying to prove.)

ΔJMK ≅ ΔLKM SAS

Problem 2: (You also have a lot of great stuff here.)

Statement Reason

DE ║ FG Given

DE ≅ FG Given

<DEF≅<FGH Given

<EDF≅<GFH Corresponding Angles (You don't need to know that F is the midpoint but you got corresponding angle pair which is correct.)

ΔEDF≅ΔGFH ASA

<DFE≅<FHG CPCTC

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Caden states that n^2 +3n + 2n is an equivalent expression to 6n. Why is Caden's statement incorrect?

malfutka [58]

$\begin{gathered} \text{The simplification of n}^2+3n+2n\text{ is:} \\ i)n^2+5n \\ By\text{ collecting common term, this can be written in form of:} \\ ii)\text{ n(n+5)} \end{gathered}$

Thus, options A and D hold, from the simplifications above.

Let's consider the validity of the remaining options provided.

$\begin{gathered} \text{For option B)} \\ \text{substitute for n=1 into the expression n}^2+3n+2n,\text{ we have} \\ 1^2+3(1)+2(1)=1+3+2=6 \\ \text{substitute for n=1 into the expression 6n, we have} \\ 6(1)=6 \\ \text{Thus, the expression n}^2+3n+2n\text{ is equivalent to 6n, for n=1} \end{gathered}$ $\begin{gathered} \text{For option C)} \\ \text{The expression n}^2+3n+2n\text{ does not simplify to 7n} \end{gathered}$ $\begin{gathered} \text{For option E)} \\ \text{substitute for n=4 into the expression n}^2+3n+2n,\text{ we have:} \\ 4^2+3(4)+2(4)=16+12+8=36 \\ \text{substitute for n=6 into the expression 6n, we have:} \\ 6(4)=24 \\ \text{Thus, the two(2) expressions are not equivalent to each other, for n=4} \end{gathered}$ $\begin{gathered} \text{For option F)} \\ \text{substitute for n=3 into the expression n}^2+3n+2n,\text{ we have:} \\ 3^2+3(3)+2(3)=9+9+6=24 \\ \text{substitute for n=3 into the expression 6n, we have:} \\ 6(3)=18 \\ \text{Thus, the two(2) expressions are not equivalent to each other, for n=3} \end{gathered}$

Hence, the correct options that apply are options A, D, E and F

7 0

1 year ago

Which equation represents the line that passes through points (0, 6) and (2, 0)? A.)y = negative one-third x + 2 B.)y = negative

Rudiy27

Find the slope of the line through (x1,y1) = (0,6) and (x2,y2) = (2,0)

m = (y2 - y1)/(x2 - x1)

m = (0 - 6)/(2 - 0)

m = -6/2

m = -3

The slope is -3

Since we're given the point (0,6) to be on the line, we know the y intercept is b = 6.

Plug m = -3 and b = 6 into y = mx+b to get y = -3x+6

Answer: Choice D) y = -3x+6

5 0

3 years ago

Read 2 more answers

The graph of which equation will intercept the y-axis at 1?

kipiarov [429]

Answer: 5x+2y=2

Step-by-step explanation:

5x+2y=2 move 5x to the other side

2y=-5x+2 divide the other side by the 2 from 2y

y=-5x+1

4 0

4 years ago

1. A magazine reported 66% of all dog owners usually greet their dog before greeting their

NISA [10]

Answer:

(a) There is 95% confidence that the true proportion of dog owners who greet their dogs first is between 0.475 and 0.775.

(b) The point estimate is 0.625. The margin of error is 0.15.

Step-by-step explanation:

The (1 - α)% confidence interval for population parameter implies that there is a (1 - α) probability that the true value of the parameter is included in the interval. Or, the (1 - α)% confidence interval for the parameter implies that there is (1 - α)% confidence or certainty that the true parameter value is contained in the interval.

In statistic, point estimation comprises of the use of sample data to estimate a distinct data value (known as a point estimate) which is to function as a "best guess" or "best estimate" of an unidentified population parameter. The point estimate of the population mean (µ) is the sample mean ( $\bar x$ ).

The (1 - α)% confidence interval for population proportion is:

$CI=\hat p\pm z_{\alpha/2}\times \sqrt{\frac{\hat p(1-\hat p)}{n}}$

The margin of error for this interval is:

$MOE=\frac{UL-LL}{2}$

For the hypothesis test, if the confidence interval consist of the null value of the parameter then the null hypothesis is accepted or else rejected.

The 95% confidence interval for the population proportion of owners who greet their dog first is,

CI = (0.475, 0.775)

(a)

The 95% confidence interval for the population proportion, (0.475, 0.775), implies that there is a 0.95 probability that the true proportion of dog owners who greet their dogs first is between 0.475 and 0.775.

Or, there is 95% confidence that the true proportion of dog owners who greet their dogs first is between 0.475 and 0.775.

(b)

The point estimate of the population proportion (p) is the sample mean ( $\hat p$ ).

Compute the point estimate from the 95% confidence interval as follows:

Point estimate = (UL + LL)/2

$=\frac{0.775+0.475}{2}\\=0.625$

The point estimate is 0.625.

Compute the margin of error as follows:

$MOE=\frac{UL-LL}{2}=\frac{0.775-0.475}{2}=0.15$

The margin of error is 0.15.

(c)

The hypothesis to test whether the proportion of all owners who greet their dog first is 66% is:

H₀: The proportion of all owners who greet their dog first is 66%, i.e. p = 0.66

Hₐ: The proportion of all owners who greet their dog first is not 66%, i.e. p ≠ 0.66.

The 95% confidence interval for the population proportion of owners who greet their dog first is,

CI = (0.475, 0.775)

The 95% confidence interval consists of the null value, i.e. p = 0.66.

The null hypothesis was failed to rejected.

Thus, it is plausible that the true proportion of all owners who greet their dog first is 66%.

6 0

3 years ago

For problem 8, find the area of the shaded region. The polygon is a regular polygon. please show work.

MissTica

Answer:

34.7791 [unit²].

Step-by-step explanation:

1) area of the circle is:

πr²;

2) area of the regular polygon is:

6*r²√3*0.25=1.5√3r²;

3) the required area:

πr²-1.5√3r²=r²(π-1.5*√3)=64*(3.1415-1.5*1.7321)=34.7791

4 0

3 years ago