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ratelena [41]
3 years ago
10

What are the solution(s) to the quadratic equation x^2 - 25 = 0?

Mathematics
1 answer:
katovenus [111]3 years ago
5 0
5935 their 5939 3934
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Explain why the x-coordinates of the points where the graphs of the equations y = 2−x and y = 8x+4 intersect are the solutions o
Luda [366]
Part 1)
We have two lines:  y = 2-x   and   y = 8x+4
Given two simultaneous equations that are both required to be true.
the solution is the points where the lines cross
Which is where the two equations are equal
Thus the solution that works for both equations is when
2-x = 8x+4
because
where that is true is where the two lines will cross and that is the common point that satisfies both equations.

Part 2) Make tables to find the solution to 2−x = 8x+4. take the integer values of x between −3 and 3

see the attached table
The table shows that none of the integers from [-3,3] work because in no case does
<span>2-x = 8x+4
</span>
To find the solution we need to rearrange the equation to the form x=n
2-x =8x+4
8x+x=2-4
9x=-2
x=-2/9

 The only point that satisfies both equations is
where
 x = -2/9
Find y:
   y = 2-x  = 2 - (-2/9) = 2 + 2/9 = 20/9
Verify we get the same in the other equation
y = 8x+4   =  8(-2/9) + 4 = 20/9 
Thus the only actual solution, being the point where the lines cross,
 is the point (-2/9, 20/9)------> (-0.22,2.22)

Part 3) how can you solve the equation 2−x = 8x+4 graphically?
<span>The point on the graph where the lines cross is the solution to the system of equations
</span>
using a graph tool
see the attached figure

the solution is the point (-0.22,2.22)

4 0
3 years ago
THANK YOU , PLEASE INCLUDE EXPLANATION
frosja888 [35]

Remark

This will be a little late, but I'll answer it anyway. The more you see of the sine law, the clearer it will be.


Step One

Set up the sine Law.

\dfrac{Sin(x)}{12}=\dfrac{sin(75)}{22}


Step Two

Substitute values

Sin(x) = ??

sin(75) = 0.9659


\dfrac{Sin(x)}{12}=\dfrac{0.9659}{22}


Step Three

Cross multiply and Solve

22* Sin(x) = 12 * 0.9659

22* Sin(x) = 11.591 divide by 22

sin(x) = 11.591 / 22

sin(x) = 0.5269


Step Four

You have to know how to use the inverse of an angle to get the answer. I do it as my calculator would do it. If it doesn't work with yours, let me know.


x = sin^-1(0.5269)

2nd F

Sin^-1

(

0.5269

)

=

You should get 31.79 degrees.

5 0
3 years ago
Daisy's teacher asked her class to draw a triangle whose sides measured 2 inches, 3 inches, and 4 inches. She correctly drew the
harina [27]

Answer:

I dont think so since a triangle adds to 180 degrees

Step-by-step explanation:

but im stuck between c and d

sorry I couldnt complete;ly answer it for u!

have a nice day!

4 0
2 years ago
A woman had $200. She went to a meatshop,
alukav5142 [94]
Ok then after that what’s the question ?
6 0
3 years ago
A sample of 11001100 computer chips revealed that 62b% of the chips fail in the first 10001000 hours of their use. The company's
STALIN [3.7K]

Answer:

Rule

If;

P-value > significance level --- accept Null hypothesis

P-value < significance level --- reject Null hypothesis

Z score > Z(at 90% confidence interval) ---- reject Null hypothesis

Z score < Z(at 90% confidence interval) ------ accept Null hypothesis

Null hypothesis: H0 = 0.60

Alternative hypothesis: Ha <> 0.62

z score = 1.35

P value = P(Z<-1.35) + P(Z>1.35) = 0.0885 + 0.0885= 0.177

Since z at 0.10 significance level is between -1.645 and +1.645 and the z score for the test (z = 1.35) falls with the region bounded by Z at 0.1 significance level. And also the two-tailed hypothesis P-value is 0.177 which is greater than 0.1. Then we can conclude that we don't have enough evidence to FAIL or reject the null hypothesis, and we can say that at 0.10 significance level the null hypothesis is valid.

Question; A sample of 1100 computer chips revealed that 62% of the chips fail in the first 1000 hours of their use. The company's promotional literature states that 60% of the chips fail in the first 1000 hours of their use. The quality control manager wants to test the claim that the actual percentage that fail is different from the stated percentage. Determine the decision rule for rejecting the null hypothesis, H0, at the 0.10 level.

Step-by-step explanation:

Given;

n=1100 represent the random sample taken

Null hypothesis: H0 = 0.60

Alternative hypothesis: Ha <> 0.62

Test statistic z score can be calculated with the formula below;

z = (p^−po)/√{po(1−po)/n}

Where,

z= Test statistics

n = Sample size = 1100

po = Null hypothesized value = 0.60

p^ = Observed proportion = 0.62

Substituting the values we have

z = (0.62-0.60)/√{0.60(1-0.60)/1100}

z = 1.354

z = 1.35

To determine the p value (test statistic) at 0.01 significance level, using a two tailed hypothesis.

P value = P(Z<-1.35) + P(Z>1.35) = 0.0885 + 0.0885= 0.177

Since z at 0.10 significance level is between -1.645 and +1.645 and the z score for the test (z = 1.35) falls with the region bounded by Z at 0.1 significance level. And also the two-tailed hypothesis P-value is 0.177 which is greater than 0.1. Then we can conclude that we don't have enough evidence to FAIL or reject the null hypothesis, and we can say that at 0.10 significance level the null hypothesis is valid.

3 0
3 years ago
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