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3 years ago

Grade 8 Math

1 answer:

8 0

Add 31 to both sides.

Since you brought the 9n over to the left side you have to get rid of other numbers that aren't n on that side

So you add the 31 to both side to remove it from the left

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Three security cameras were mounted at the corners of a triangles parking lot. Camera 1 was 110 ft from camera 2, which was 137

Nata [24]

Answer:

<em>Camera 2nd has to cover the maximum angle, i.e. </em> $78.70^\circ$ .

Step-by-step explanation:

Please have a look at the triangular park represented as a triangle $\triangle ABC$ with sides

a = 110 ft

b = 158 ft

c = 137 ft

1st camera is located at point C, 2nd camera at point B and 3rd camera at point A respectively.

We can use law of cosines here, to find out the angles $\angle A, \angle B, \angle C$

As per Law of cosine:

$cos C = \dfrac{a^{2}+b^2-c^2 }{2ab}\\cos B = \dfrac{a^{2}+c^2-b^2 }{2ac}\\cos A = \dfrac{b^{2}+c^2-a^2 }{2bc}$

Putting the values of a,b and c to find out angles $\angle A, \angle B, \angle C$ .

$cos C = \dfrac{110^{2}+158^2-137^2 }{2\times 110 \times 158}\\\Rightarrow cos C = \dfrac{12100+24964-18769 }{24760}\\\Rightarrow cos C =0.526\\\Rightarrow C = 58.24^\circ$

$cos B = \dfrac{110^{2}+137^2-158^2 }{2\times 110 \times 137}\\\Rightarrow cos B = \dfrac{12100+18769 -24964}{30140}\\\Rightarrow cos B = \dfrac{5905}{30140}\\\Rightarrow cos B =0.196\\\Rightarrow B = 78.70^\circ$

$cos A = \dfrac{158^{2}+137^2-110^2 }{2\times 158 \times 137}\\\Rightarrow cos A = \dfrac{24964+18769-12100}{43292}\\\Rightarrow cos A = \dfrac{31633}{43292}\\\Rightarrow cos A = 0.731\\\Rightarrow A = 43.05^\circ$

<em>Camera 2nd has to cover the maximum angle</em>, i.e. $78.70^\circ$ .

6 0

4 years ago

Using the side lengths determine whether the triangle is acute obtuse or right 24 30 18

SIZIF [17.4K]

Answer:

It is a Right Triangle.

Step-by-step explanation:

30^2 = 900

24^2 = 576

18^2 = 324

576 + 324 = 900

This satisfies the Pythagoras theorem so it is a Right Triangle.

8 0

3 years ago

Read 2 more answers

Please Help!! Asap!!

Brilliant_brown [7]

Answer:

A because it's most likely to be like that at tryouts

4 0

3 years ago

Factor: 4x^2-12x+9=0

Andreas93 [3]

Use formula $a^2-2ab+b^2=(a-b)^2$

$4x^2-12x+9
\\(2x)^2-2(2x)(3)+3^2
\\(2x-3)^2$

6 0

3 years ago

Read 2 more answers

Six of the nine students are from middle gerogia state college. What is the probability that all three interviewed students are

ozzi

Answer:

0.2381 = 23.81%

Step-by-step explanation:

To calculate this probability, we can calculate the probability of each student of the 3 students interviewed being from middle georgia state college.

If inicially there are six students from middle georgia state college among the nine students, the probability of the first student chosen being from middle georgia state college is 6/9.

Then, as one student was already picked, we have now 5 students from middle georgia state college in a total of 8 students, so the probability of the second student will be 5/8.

In the same way, the third student will be picked in a group of 7 students, where 4 are from middle georgia state college, so the probability is 4/7.

Multiplying all the probabilities, we have the probability of all three students interviewed being from middle georgia state college:

P = (6/9) * (5/8) * (4/7) = 120/504 = 0.2381 = 23.81%

6 0

4 years ago