Answer:
x = 36°
m<1 = 36°
m<2 = 144°
m<3 = 36°
m<4 = 144°
m<5 = 144°
m<6 = 36°
Step-by-step explanation:
✔️x° + 4x° = 180° (linear angle pair theorem)
5x = 180
x = 180/5
x = 36°
For easy identification, the six angles to be found have been labelled <1 to <6 as shown in the attachment below.
✔️m<1 = x° (vertical angles pair)
m<1 = 36° (substitution)
✔️m<2 = 4x° (vertical angles pair)
Plug in the value of x
m<2 = 4(36)
m<2 = 144°
✔️m<3 = x° (alternate interior angles theorem)
m<3 = 36° (substitution)
✔️m<4 = 4x° (corresponding angles theorem)
m<4 = 4(36) (substitution)
m<4 = 144°
✔️m<5 = 4x° (alternate exterior angles theorem)
m<5 = 4(36)
m<5 = 144°
✔️m<6 = x° (corresponding angles theorem)
m<6 = 36°
Answer:
m∠Q = 35°
m∠M = 60°
Step-by-step explanation:
In the isosceles triangle, the measures of the base angles are equal
In Δ RQS
∵ RQ = RS
→ That means Δ RQS is an isosceles triangle
∴ Δ RQS is an isosceles triangle
∵ ∠Q and ∠S are the base angles
∴ m∠Q = m∠S
→ The sum of the measures of the interior angles in any Δ is 180°
∴ m∠Q + m∠S + m∠R = 180°
∵ m∠R = 110°
∴ m∠Q + m∠S + 110 = 180
→ Subtract 110 from both sides
∴ m∠Q + m∠S = 70°
∵ m∠Q = m∠S
→ Divide their sum by 2 to find the measure of each one
∴ m∠Q = m∠S = 70 ÷ 2 = 35°
∴ m∠Q = 35°
In Δ MNP
∵ MN = NP = PM
→ That means ΔMNP is an equilateral triangle
∴ Δ MNP is an equilateral triangle
→ In the equilateral triangle, all angles are equal in measures
∴ m∠M = m∠N = m∠P
∵ m∠M + m∠N + m∠P = 180
→ Divide their sum by 180 to find the measure of each angle
∴ m∠M = m∠N = m∠P = 180 ÷ 3 = 60°
∴ m∠M = 60°
Answer:
Option a) A 95% confidence interval for the mean diameter of the 120 bearings in the sample is .
Step-by-step explanation:
We are given the following information in the question:
Sample size, n = 120
Sample mean = 10 mm
Standard Deviation = 0.24 mm
Formula:
Hence, the correct interpretation for the confidence interval is given by option a).
A 95% confidence interval for the mean diameter of the 120 bearings in the sample is .
We have to consider the factor of sampling of 120 ball bearings from a population of 10,000 ball bearings.
Answer:
Divide the length (in) by 36 the length of 1 yard
Step-by-step explanation:
Answer:
A) 6x + 6y = 24, Yes, they have the same solution set
Step-by-step explanation:
Let's first start by multiplying the equation by 3:
(2*3)x + (2*3)y = 24
6x + 6y = 24
Now lets find the solution set for both:
6y = -6x + 24
y = -x +4
2y = -2x + 8
y = -x +4
Yes, they have the same solution set