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mel-nik [20]
1 year ago
7

Given triangle ABC, A=105°, a=10cm, b=7cm, find B,C and c.

Mathematics
1 answer:
Whitepunk [10]1 year ago
4 0

The value of the side c will be 5.56 cm and angle C is 32.49° and angle B is 42.51°.

<h3>What is law of cosine?</h3>

Let there is a triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:

a² + b² – 2ab cos C = c²

Given triangle ABC, A = 105°, a = 10 cm, b = 7 cm.

Then we have

7² + c² – (2 · 7 · c) cos 105° = 10²

c² + 3.62c – 51 = 0

On solving, we have

c = 5.56

Then the angle C will be

10² + 7² – 2 · 7 · 10 · cos C = 5.56²

                149 – 140 cos C = 30.91

                                 cos C = 0.8435

                                        C = 32.49°

We know that

       ∠A + ∠B + ∠C = 180°

105° + ∠B + 32.49° = 180°

                         ∠B = 42.51°

Learn more about law of cosines here:

brainly.com/question/17289163

#SPJ1

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Y=-3x^2-6x+24
Lera25 [3.4K]
The x-intercept is the point at which the function intersects the x-axis.
For any point on the x-axis, y = 0. Thus we can plug in 0 for y and solve for x.

y=-3x^2-6x+24 \\ 0=-3x^2-6x+24

Let's split the middle on this quadratic.
To do this we need to find two numbers that add to equal -6 and multiply to equal -72. (-3 times 24)
Consider ways to multiply to get 72.
72 = 36 ×2...that's not going to work.
72 = 24 × 3
72 = 18 × 4
72 = 12 × 6...and 12 minus 6 is 6!
Let's add our signs; our numbers are -12 and 6.
Now, split the middle and factor.

0=-3x^2-12x+6x+24\\0=-3x(x+4)+6(x+4)\\0=(-3x+6)(x+4)

Now you should know that anything multiplied by zero is zero.
So any value that makes one of those factors equal zero is an x-intercept.
Solve each of these equations.

-3x+6 = 0
-3x = -6
x = 2

x+4 = 0
x = -4

Oh, and since all parabolas (graphs of quadratics) are symmetrical, our axis of symmetry will be the average between the two, which is x=-1.

Now for our y-intercepts. For any points on the y-axis, x=0, so if we plug in 0 for x and solve for y we'll get our y-intercept.

y = -3×0² - 6×0 + 24
y = 0 - 0 + 24
y = 24

What about our vertex? Well, we know it's going to line up with the axis of symmetry, so let's just plug in -1 for x.

y = -3×-1² - 6×-1 + 24
y = -3×1 -6×-1 + 24
y = -3 + 6 + 24
y = 27

Thus the vertex is (-1, 27)

The y value is not going to exceed 27, as this is a decreasing quadratic, (we already know y=24 is a possibilty) and this equation goes downwards infinitely, so our range is (-∞, 27)

As for x, well, it's sort of the input for our equation, meaning it can be whatever we want it to be. Thus the domain is (-∞, ∞)




3 0
3 years ago
Calculate the slope of the line that contains the points (-2, -4) and (2, 4).
liubo4ka [24]

Answer:

Slope is 2

Step-by-step explanation:

(-2, -4) and (2, 4)

Slope:

m=(y2-y1)/(x2-x1)

m=(4+4)/(2+2)

m=8/4

m = 2

6 0
3 years ago
Which is an equation in point slope form of the line that passes through the points 7,5 and -4,-1
Free_Kalibri [48]

Answer:

the second option is the correct one

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

To calculate m use the slope formula

m = ( y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (7, 5) and (x₂, y₂ ) = (- 4, - 1)

m = \frac{-1-5}{-4-7} = \frac{-6}{-11} = \frac{6}{11}

Use either of the 2 points as (a, b)

using (- 4, - 1), then

y- (- 1) = \frac{6}{11}(x - (- 4)), that is

y + 1 = \frac{6}{11}(x + 4)

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Cindy spends $85 a month on her cell phone plan. She has saved $1,105 to pay her phone bill. How many months will Cindy be able
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Answer: SHE GOT 13 MONTHS YES SHE DO, 13 MONTHS LEFT IS ANSWER

Step-by-step explanation:

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3 years ago
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Answer:

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Step-by-step explanation:

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