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NeTakaya
3 years ago
7

A figure has a vertex at (-1,-3). If the figure has line symmetry about the y-axis, what are the coordinates of another vertex o

n the figure
Mathematics
1 answer:
zlopas [31]3 years ago
4 0

The coordinates of another vertex on the figure is:

\boxed{(1,-3)}

<h2>Explanation:</h2>

If a figure has a vertex at (-1,-3) and the figure has a symmetry about the y-axis, then the coordinates of another vertex on the figure is:

Point \ (1,3)

This is so because the rule for reflecting any point (x,y) across  the y-axis is the point (-x,y). So you just need to multiply the x-coordinate of the original point by -1 in order to get the coordinate of another vertex.

<h2>Learn more:</h2>

Transformations: brainly.com/question/12537916

#LearnWithBrainly

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Given △ABC. m∠A&gt;m∠B&gt;m∠C. Perimeter=30. Which side of △ABC may have length 7?
lisabon 2012 [21]

<u>Solution-</u>

As given in △ABC,

m\angle A>m\angle B>m\angle C

As from the properties of trigonometry we know that, the greater the angle is, the greater is the value of its sine. i.e

\sin A>\sin B>\sin C

According to the sine law,

\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}

In order to make the ratio same, even though m∠A>m∠B>m∠C, a must be greater than b and b must be greater than c.

\Rightarrow a>b>c

Also given that its perimeter is 30. Now we have to find out whose side length is 7. So we have 3 cases.

Case-1. Length of a is 7

As a must be the greatest, so b and c must be less than 7. Which leads to a condition where its perimeter won't be 30. As no 3 numbers less than 7 can add up to 30.

Case-2. Length of b is 7

As b is greater than c, so c must 6 or less than 6. But in this case the formation of triangle is impossible. Because the triangle inequality theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side. If b is 7 and c is 6, then a must be 17. So no 2 numbers below 7 can add up to 17.

Case-3. Length of c is 7

As this is the last case, this must be true.

Therefore, by taking the aid of process of elimination, we can deduce that side c may have length 7.


5 0
3 years ago
What is 7vr - (-7rv)=
nata0808 [166]

Answer:

14vr

Step-by-step explanation:

7vr - (-7rv)=

Subtracting a negative is like adding

7vr + (7rv)=

Changing the order of rv to vr

7vr + (7vr)=

Combing like terms

14vr

8 0
3 years ago
With double-digit annual percentage increases in the cost of health insurance, more and more workers are likely to lack health i
Dahasolnce [82]

Answer:

1.  χ² = <u>  15.3902 </u>

2. The p value is :_____.a. less than .005

3.  Conclusion

a. health insurance coverage is not independent of the size of the company

4. The percentages of employees

Small %=   33/50= 0.66

Medium %= 68/75 = 0.91

Large %= 88/100= 0.88

Step-by-step explanation:

1) We set up our null and alternative hypothesis as

H0: the employee health insurance coverage is independent of the size of the company

against the claim

Ha: the employee health insurance coverage is not independent of the size of the company

2) the significance level alpha is set at 0.05

3) the test statistic under H0 is

χ²= ∑ (O - E)²/ E where O is the observed and E is the expected frequency

which has an approximate chi square distribution with ( 3-1) (2-1)=  2 d.f

4) Computations:

Under H0 , the observed frequencies are :

Observed       Expected E        (O-E)         (O-E)²             (O-E)²/E

33                   42                      -9               81                    1.928  

68                  63                         5              25                  0.3968

88                  84                         4               16                  0.1904

17                    8                           9              81                  10.125

7                     12                          -5             21                    1.75

<u>12                    16                         -4              16                     1              </u>

<u>                                                                                           15.3902    </u>

Expected Values are calculated using the formula :

Row Total * Column Total / sample size

E1= (33+17) (33+ 68+88)/ 50+75+100= 42

E4= (33+17) (17+ 7+ 12)/ 50+75+100=8

E2= (68+7) (33+ 68+88)/ 50+75+100= 63

E5= (68+7)  (17+ 7+ 12)/ 50+75+100= 12

E3= (88+12) (33+ 68+88)/ 50+75+100= 84

E6= (88+12)  (17+ 7+ 12)/ 50+75+100= 16

5) The critical region is χ² ≥ χ² (0.05)2 = 5.99

6) Conclusion:

The calculated χ² = <u>  15.3902    </u>falls in the critical region χ² ≥  5.99  so we reject the null hypothesis that the employee health insurance coverage is NOT independent of the size of the company.

2. The p value is :_____.

a. less than .005

The p-value is .000385.

3.  Conclusion

a. health insurance coverage is not independent of the size of the company

4. The percentages of employees

Small %=   33/50= 0.66

Medium %= 68/75 = 0.91

Large %= 88/100= 0.88

3 0
2 years ago
3x + 4 = 8x – 11 does anyone know how to do this ​
Nataly [62]

Answer:

x = 3

Step-by-step explanation:

Subtract 8x from both sides.

3x+4−8x=8x−11−8x

−5x+4=−11

Subtract 4 from both sides.

−5x+4−4=−11−4

−5x=−15

Divide both sides by -5.

−5x

−5

=

−15

−5

x=3

8 0
2 years ago
Read 2 more answers
In the expression 3(2^0), what is the order of operations? Explain how would you evaluated the expression.
Over [174]

We'll use PEMDAS which stands for

P = parenthesis

E = exponents

M = multiplication

D = division

A = addition

S = subtraction

It tells us the order in how to evaluate math expressions. We start with parenthesis, then move to exponents, etc until we get to subtraction as the last step.

We have parenthesis so we focus on whats inside it. We evaluate 2^0 to get 1. Any nonzero number to the exponent 0 is always 1. In other words, x^0 = 1 where x is nonzero.

So 3(2^0) turns into 3(1) or 3*1

Then we multiply that to get 3*1 = 3

So overall, 3(2^0) = 3

4 0
3 years ago
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