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4 years ago

What is the solution of the system?

Mathematics

2 answers:

steposvetlana [31]4 years ago

6 0

Answer:

(-3,3)

Step-by-step explanation:

Just took the test! Its correct.

IgorC [24]4 years ago

4 0

What you must do for this case is to solve the system of two equations with two unknowns.
To find the values of x and y.
We have then:
-3x + 9y = 36
4x + 12y = 24
Resolving:
Step 1:
(1/3) * (- 3x + 9y) = (36) * (1/3)
(1/4) * (4x + 12y) = 24 * (1/4)
-x + 3y = 12
x + 3y = 6
Step 2:
6y = 18
y = 18/6
y = 3
Step 3:
-x + 3y = 12
-12 + 3y = x
-12 + 3 (3) = x
x = -3
answer:
x = -3
y = 3

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Please solve the equation (15m + 3)/2 = -6

stiv31 [10]

Answer:

m = - 1

Step-by-step explanation:

Given

$\frac{15m+3}{2}$ = - 6

Multiply both sides by 2 to clear the fraction

15m + 3 = - 12 ( subtract 3 from both sides )

15m = - 15 ( divide both sides by 15 )

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3 years ago

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Evaluate each trigonometric equation for θ.

liberstina [14]

Answer:

sinФ = 8/17

cosФ = 15/17

tan Ф = 8/15

csc Ф = 17/8

sec Ф = 17/15

cot Ф = 15/8

Step-by-step explanation:

Let us revise the trigonometry functions

Sin(x) = opposite/hypotenuse

Cos(x) = adjacent/hypoteouse

Tan(x) = opposite/adjacent

Csc(x) = hypotenuse/opposit

Sec(x) = hypotenues/adjacent

Cot(x) = adjacent/opposite

In the given figure

The opposite side to angle Ф = 8

The adjacent side to angle Ф = 15

Find the hypotenuse using Pythagoras' theorem

$Hypotenuse = \sqrt{8^{2}+15^{2} }$

$Hypotenuse = \sqrt{64+225}$

$Hypotenuse = \sqrt{289}$

$Hypotenuse = 17$

Let us use the rules above to find the trigonometry functions

sinФ = 8/17

cosФ = 15/17

tan Ф = 8/15

csc Ф = 17/8

sec Ф = 17/15

cot Ф = 15/8

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3 years ago

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uranmaximum [27]

Answer:

Step-by-step explanation:

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4 years ago

The middle person in a row is the 18th, how many persons are in the row?

Alex17521 [72]

Answer:

Step-by-step explanation:

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3 years ago

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PLEASE HELP ME <br>...This is my homework and I don't understand how to do it.

musickatia [10]

The probability that a point chosen at random lies in the shaded region is 0.28

<h3>Calculating the area of a shaded region and probability</h3>

From the question, we are to find the probability that a point chosen at random lies in the shaded region.

The shaded region is a triangle.

The probability that a point chosen at random lies in the shaded region = Area of the triangle / Area of the circle

First, we will calculate the unknown side of the triangle

Let the unknown side be x.

Then, from the <em>Pythagorean theorem</em>, we can write that

12² = 6² + x²

144 = 36 + x²

x² = 144 - 36

x² = 108

x = √108

x = 6√3

From formula,

Area of a triangle = 1/2 × base × height

Area of the triangle = 1/2 × 6 × 6√3

Area of the triangle = 18√3 square units

Now, we will determine the area of the circle

Area of a circle = πr²

Where r is the radius

From the given information,

Diameter of the circle = 12

But,

Radius = Diameter / 2

Therefore,

r = 12/2

r = 6

Thus,

Area of the circle = 3.14 × 6²

Area of the circle = 113.04 square units

Now,

The probability that a point chosen at random lies in the shaded region = 18√3 / 113.04

The probability that a point chosen at random lies in the shaded region = 0.2758

The probability that a point chosen at random lies in the shaded region ≈ 0.28

Hence, the probability is 0.28

Learn more on Calculating area of a shaded region here: brainly.com/question/23629261

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