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Step2247 [10]
3 years ago
9

If the vertices of triangle QRS have coordinates Q(1, −2), R(3, −2), and S(2, −4), which coordinates are the coordinates of the

vertices of triangle QꞌRꞌSꞌ when triangle QRS is reflected across the x-axis?
A. Qꞌ(−1, −2), Rꞌ(−3, −2), Sꞌ(−2, −4)
B. Qꞌ(1, 2), Rꞌ(3, 2), Sꞌ(2, 4)
C. Qꞌ(2, 1), Rꞌ(2, 3), Sꞌ(4, 2)
D. Qꞌ(2, −4), Rꞌ(6, −4), Sꞌ(4, −8)
Mathematics
1 answer:
Artist 52 [7]3 years ago
8 0
B
The value of x does not change in reflection across the x axis while the sign of the value of y is reversed because it travels a distance equal to its distance from the x-axis in the negative y-axis.
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Which of these statements are correct about a line segment with a length of 12 units in a coordinate plane? Select all that appl
Vitek1552 [10]

Correct statements are:

If it is reflected across the y-axis, its length still will be 12 units.

If it is rotated 270° about the origin, its length still will be 12 units.

If it is translated 15 units up, its length still will be 12 units.

<u>Step-by-step explanation:</u>

Whatever it may be rotation, reflection or translation, the size of the line will never change. So length of the line is same as 12 units in the image.

So the wrong statements are

If its reflected across y = -x then the length will no longer be 12 units.

If it is rotated 90° about the origin, then the length will no longer be 12 units.

If it is translated 18 units to the right,  then the length will no longer be 12 units.

7 0
3 years ago
Solve for xx. Round to the nearest tenth, if necessary.
jasenka [17]

Step-by-step explanation:

S+T+U=180°{sum of angle of triangle}

  • 68°+90°+U=180°
  • U=180-158°
  • U=22°

sin theta= p/h

sin22°=x/83

o.37=x/83

x=0.37×83

x=30.71

x=31

stay safe healthy and happy.

6 0
2 years ago
A study of 420,076 cell phone users found that 131 of them developed cancer of the brain or nervous system. Prior to this study
Keith_Richards [23]

Answer:

a) 95% Confidence interval = (0.026%, 0.037%) to 3 d.p

b) The result of the 95% confidence interval does not agree with the previous rate of such cancer because the value 0.0224% does not lie within this confidence interval obtained.

Step-by-step explanation:

Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample proportion) ± (Margin of error)

Sample proportion = (131/420076) = 0.0003118483 = 0.0312%

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error)

Critical value at 95% confidence interval for sample size of 420,076 is obtained from the z-tables because the sample size is large enough for the properties of the sample to approximate the population properties.

Critical value = 1.960 (from the z-tables)

Standard error = σₓ = √[p(1-p)/n]

n = sample size = 420,076

σₓ = √(0.0003118×0.999688/420076) = 0.0000272421 = 0.0000272

95% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]

CI = 0.000312 ± (1.96 × 0.0000272)

CI = 0.000312 ± 0.0000534

95% CI = (0.0002586055, 0.0003653945)

95% Confidence interval = (0.000259, 0.000365)

95% Confidence interval = (0.0259%, 0.0365%) = (0.026%, 0.037%) to 3 d.p

b) The result of the 95% confidence interval does not agree with the previous rate of such cancer because the value 0.0224% does not lie within this confidence interval obtained.

Hope this Helps!!!

7 0
3 years ago
6x + 2y &gt; 48<br><br> solve for y
kozerog [31]

Answer:

y > 24 − 3x

Step-by-step explanation:

Step 1: First, you need to factor out the common term 2.

2 (3x + y) > 48

Step 2: Then, you divide both sides by 2.

3x+y>\frac{42}{2}

Step 3: Next, you have to simplify \frac{42}{2}  into 24.

3x + y > 24

Step 4: Lastly, subtract 3x from both sides and you're done!

y > 24 − 3x

7 0
3 years ago
Solve for z<br><br> −4z + 31 ≥ 17z + 23
Natali [406]

z  \leqslant  \frac{8}{21}

3 0
3 years ago
Read 2 more answers
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