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kkurt [141]
3 years ago
8

10th grade geometry Help!!!

Mathematics
1 answer:
Airida [17]3 years ago
7 0

Answer:

m∠W = (4x)° = 4 × 18 = 72°

m∠Y = (3x)° = 3 × 18 = 54°

m∠Z = (3x)° = 3 × 18 = 54°

Step-by-step explanation:

m∠W = (4x)°

m∠Y = (3x)°

m∠Z = (3x)°

i.e.,

We Know That,

The sum of a Triangle is 180°

So,

m∠W + m∠Y + m∠Z

i.e.,

(4x)° + (3x)° + (3x)° = 180°

10x° = 180°

x = 180/10

x = 18°

Now,

m∠W = (4x)° = 4 × 18 = 72°

m∠Y = (3x)° = 3 × 18 = 54°

m∠Z = (3x)° = 3 × 18 = 54°

Thus, x = 18°

<h3><u>FOR</u><u> </u><u>VERIFICATION ONLY</u><u>:</u></h3>

(4x)° + (3x)° + (3x)° = 180°

4 × 18 + 3 × 18 + 3 × 18 = 180

72° + 54° + 54° = 180°

180° = 180°

Hence, L.H.S = R.H.S

<u>-TheUnknown</u><u>S</u><u>cientist</u>

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❶ Find the values of x, y and z in each of the case given below ⟼
Ket [755]

Answer:

1)

y = 45° (converse of alternate interior angle theorem)

z = 45° (alternate interior angle theorem)

k = 135° (exterior angle theorem)

2)

Cos θ + Sin θ = √2 Cos θ

(Cos θ + Sin θ)² = (√2 Cos θ)²

(Exponential property of equality)

Cos² θ + Sin² θ + 2 (Cos θ • Sin θ) = (√2 Cos θ)²

(Distributive property)

1 + 2(Cos θ • Sin θ) = (√2 Cos θ)²

(Definition of the pythagorean identity).

This identity is true because, if a² + b² = c². The triangle must be a right triangle, and a right triangle always has a 90° angle tangent to the triangle, and the tangent of 90° is 1, cos applied to the adjacent over hypotenuse, and sin applies to the opposite over hypotenuse, so this identity must work).

1 + 2(Cos θ • Sin θ) = 2 Cos² θ

(definition of an exponent)

1 + 2(Cos θ • Sin θ) – 1 = 2 Cos² θ – 1

(subtraction property of equality)

2(Cos θ • Sin θ) = 2 Cos² θ – 1

2(Sin θ • Cos θ) = 2 Cos² θ – 1

(Associative property of multiplication ; the input for both functions are θ so this rule works, this is an exception)

Sin (2x) = 2 Cos² θ – 1

(double angled identity of 2 sine and cos)

5 0
3 years ago
BRAINLIESTTT ASAP!!! PLEASE ANSWER :)<br> Explain your answer.
baherus [9]

Answer:

x=14

Step-by-step explanation:

2(3x-4)=5x+6

first get rid of the parentheses by multiplying the  2

6x-8 = 5x+6

put like terms on one side of the equation. Start with the 5x, move it to the left side

(6x-8)-5x = (5x+6)-5x

x-8 = 6


Again, put like terms on one side of the equation. Move the 8 to the right side

(x-8)+8 = 6+8

=> x = 14


B)

4x - 3 = 2(x-1)

Start again by getting rid of the parentheses to make it a clean equation... aka distribute the 2:

4x-3 = 2x - 2

Move the like terms to one side of the equation. Start with x.. move 2x to the left:

(4x-3)-2x = (2x-2)-2x

=> 2x-3 = -2

Move the like terms to one side of the equation.Now move the -3 to the other side:

(2x-3)+3 = -2+3

=> 2x=1

Lastly, divide by 2 on both sides to find out what x is:

(2x)/2=1/2

=> x = 1/2


..so no, Charlie was incorrect.


6 0
3 years ago
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What is the equation of the line in slope-intercept form?
stepladder [879]
Slope intercept form is y=mx+b where m is the slope and b is the y part of an intercept where x is 0. So the equation for slope (y1-y2)/(x1-x2) with y1 and y2 the y values of 2 points and x1 and x2 those points' x values, so if you would use the points (-2,0) and (0,5) (I used intercepts because they are easier, but you can use any points on the line) you would get (0-5)/(-2-0) and then 5/2 for the slope. plugging in then you get y=5/2*x+5
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8 0
3 years ago
An environmentalist wants to find out the fraction of oil tankers that have spills each month. Suppose a sample of 836 tankers i
Alexxandr [17]

Answer:

<em>The 99% confidence interval for the population proportion of oil tankers that have spills each month.</em>

<em>(0.6489 , 0.7311)</em>

Step-by-step explanation:

<u><em>Step(i)</em></u>:-

Given sample size 'n' = 836

Suppose a sample of 836 tankers is drawn. Of these ships, 577 did not have spills.

sample proportion

                    p^{-}  = \frac{x}{n} = \frac{577}{836} = 0.690

<em>The 99% confidence interval for the population proportion is determined by</em>

<em></em>(p^{-} - Z_{0.01} \sqrt{\frac{p(1-p)}{n} } , p^{-} + Z_{0.01} \sqrt{\frac{p(1-p)}{n} })<em></em>

<u><em>Step(ii)</em></u><em>:-</em>

<em>The Z- value = 2.576</em>

<em></em>(0.690 - 2.576 \sqrt{\frac{0.690(1-0.690)}{836} } , 0.690 + 2.576 \sqrt{\frac{0.690(1-0.690)}{836} })<em></em>

<em>On calculation , we get</em>

<em>(0.690 -  0.0411 , 0.690 + 0.0411)</em>

<em>(0.6489 , 0.7311)</em>

<u><em>Final answer</em></u><em>:-</em>

<em>The 99% confidence interval for the population proportion of oil tankers that have spills each month.</em>

<em>(0.6489 , 0.7311)</em>

<em></em>

<em></em>

8 0
4 years ago
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