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butalik [34]
3 years ago
12

For each fraction if you multiply both the numerator and the denominator by the same number is the resulting fraction equivalent

to the original fraction ?
Mathematics
1 answer:
lukranit [14]3 years ago
5 0
Yes, it is. 

example : 
1/2 * 2/2 = 2/4...so 1/2 and 2/4 are equivalent because 2/4 reduces to 1/2

1/3 * 3/3 = 3/9...so 3/9 is equivalent to 1/3 because 3/9 can reduce to 1/3
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PLEASE HELP!!! :))
Nina [5.8K]

For a better understanding of the solution given here please find the attached file which has the relevant diagram.

To answer this question we will have to make use of <u>the Isosceles Triangle Theorem</u> which states that the perpendicular bisector of the base of an isosceles triangle is also the angle bisector of the vertex angle. Thus, as a corollary we know that is EF is the angle bisector of the vertex angle ∠E, then, EF is the perpendicular bisector of the of the base DK.

Please follow the diagram of a complete understanding of the logic and the solution.

As EF is the angle bisector as given in the question, thus we will have:

m\angle DEK=2\times m\angle DE F=2\times 43^{\circ}=86^{\circ}.

Also, from the Theorem we know that KF will be half of DK and thus, KF will be:KF=\frac{1}{2}DK= \frac{1}{2}\times 16=8 centimeters.

Likewise, from the same theorem we have: m\angle EFD=90^{\circ}

4 0
3 years ago
Evaluate p(-2)=x^3-4x-5
Pani-rosa [81]

Step-by-step explanation:

p(x) =  {x}^{3}  - 4x - 5 \\ p( - 2) =  {( - 2)}^{3}  - 4( - 2) - 5 \\  =  - 8 + 8 - 5 \\  =  - 5

3 0
3 years ago
Read 2 more answers
The circumference of a circle is 50.24 centimeters. Find the radius of the circle. (Use 3.14 for π.)
Deffense [45]
2piR=circumference

2(3.14)R=50.24

R=8 cm
4 0
3 years ago
Read 2 more answers
A researcher has two percentages and wants to know if the percentages are statistically different. The researcher calculates the
love history [14]

Answer:

p_v =2*P(Z>4.21) =2.55x10^{-5}

And we can use the following excel code to find it:"=2*(1-NORM.DIST(4.21,0,1,TRUE)) "

With the p value obtained and using the significance level assumed for example\alpha=0.05 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the percentage 1 is significantly different from the percentage 2.

D) Are statistically different.

Step-by-step explanation:

The system of hypothesis on this case are:  

Null hypothesis: \mu_1 = \mu_2  

Alternative hypothesis: \mu_1 \neq \mu_2  

Or equivalently:  

Null hypothesis: \mu_1 - \mu_2 = 0  

Alternative hypothesis: \mu_1 -\mu_2\neq 0  

Where \mu_1 and \mu_2 represent the percentages that we want to test on this case.

The statistic calculated is on this case was Z=4.21. Since we are conducting a two tailed test the p value can be founded on this way.

p_v =2*P(Z>4.21) =2.55x10^{-5}

And we can use the following excel code to find it:"=2*(1-NORM.DIST(4.21,0,1,TRUE)) "

With the p value obtained and using the significance level assumed for example\alpha=0.05 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the percentage 1 is significantly different from the percentage 2.

And the best option on this case would be:

 D) Are statistically different.

4 0
3 years ago
(5)^2 - (-9)^2 / (5) - (-9)
timama [110]
89/5
Alternative form

1) 17.8
2)17 4/5
4 0
2 years ago
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