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Snezhnost [94]
3 years ago
13

Given lines p and q are parallel, find the value of x that makes each diagram true.

Mathematics
1 answer:
Klio2033 [76]3 years ago
5 0

Answer: for a the answer is 140° and for b x=25°

Step-by-step explanation:

for a, when you have 2 parallel lines cut by a transversal,the corresponding angles are congruent. and the angle140 is congruent to the corresponding angle as they are vertical angles are congruent.

for b, angle x is congruent to the angle that is supplementary to 155 therefore 180-155=25°

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A surveyor leave her base camp and drive 42 km on a bearing of 032, she then drive 28km on a bearing of 154.How far is she then
aleksklad [387]

Answer:

Step-by-step explanation:

The scenario is represented in the attached photo. Triangle ABC is formed. AB represents her distance from her base camp. We would determine BC by applying the law of Cosines which is expressed as

a² = b² + c² - 2abCosA

Where a,b and c are the length of each side of the triangle and B is the angle corresponding to b. It becomes

AB² = AC² + BC² - 2(AC × BC)CosC

AB² = 42² + 28² - 2(42 × 28)Cos58

AB² = 1764 + 784 - 2(1176Cos58)

AB² = 2548 - 1246.37 = 1301.63

AB = √1301.63

AB = 36.08 km

To find the bearing, we would determine angle B by applying sine rule

AB/SinC = AC/SinB

36.08/Sin58 = 42/SinB

Cross multiplying, it becomes

36.08SinB = 42Sin58

SinB = 42Sin58/36.08 = 0.987

B = Sin^-1(0.987)

B = 81°

Therefore, her bearing from the base camp is

360 - 81 = 279°

8 0
3 years ago
How do you write 1.5 × 104 in standard form?
rewona [7]
I'm assuming you meant 1.5 × 10⁴. Remember, when we write in standard form, you need to use ^ to denote it's 'to the power of'. So it would be 1.5 × 10^4. 

I'm also assuming you meant in decimal form, because that's already in standard form.

However, the answer is 15,000. This is because you lose one zero when multiplying a decimal with one number after it. For each number after the decimal, you take off a zero. Therefore, the end number is 15,000.
5 0
3 years ago
How many centimeter squares would be wrapped around this rectangular prism?
denis23 [38]
You haven't told us whether the rectangular prism is the size of a pack of gum or more like the size of a cruise ship.

Whatever size it is, here's the number of centimeter squares you need to cover the whole outside of it:

(2 x length x width) + (2 x length x height) + (2 x width x height)

with all measurements made in centimeters.
4 0
3 years ago
Evaluate - (2-6)(23).<br> O A. 8<br> O B.<br> 1<br> 8<br> Oc.<br> 1<br> 8<br> D. -8
kumpel [21]

Answer:

-92.

Step-by-step explanation:

2 - 6 is -4.

-4 x 23 is -92.

7 0
3 years ago
Use the graph of the function f to find f(-1)
Vikki [24]
We need the graph!!!!!!!
7 0
3 years ago
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