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2 years ago

Solve the system by using the elimination method.

Mathematics

1 answer:

Inessa05 [86]2 years ago

6 0

Answer:

(8, 4 )

Step-by-step explanation:

Given the 2 equations

5x - 5y = 20 → (1)

- 3x + 5y = - 4 → (2)

Add the 2 equations term by term to eliminate the y- term

2x + 0 = 16

2x = 16 ( divide both sides by 2 )

x = 8

Substitute x = 8 into either of the 2 equations and solve for y

Substituting into (2)

- 3(8) + 5y = - 4

- 24 + 5y = - 4 ( add 24 to both sides )

5y = 20 ( divide both sides by 5 )

y = 4

solution is (8, 4 )

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Question:

Genrish500 [490]

Answer:

x=56 and the exterior angle is 116

Step-by-step explanation:

We will call the unknown angle in the triangle y. Angle y and the angle (2x +4) form a straight line so they make 180 degrees.

y + 2x+4 =180

Solve for y by subtracting 2x+4 from each side.

y + 2x+4 - (2x+4) =180 - (2x+4)

y = 180-2x-4

y = 176-2x

The three angles of a triangle add to 180 degrees

x+ y+ 60 = 180

x+ (176-2x)+60 = 180

Combine like terms

-x +236=180

Subtract 236 from each side

-x+236-236 = 180-236

-x = -56

Multiply each side by -1

-1*-x = -56*-1

x=56

The exterior angle is 2x+4. Substitute x=56 into the equation.

2(56)+4

112+4

116

8 0

3 years ago

Suppose that replacement times for washing machines are normally distributed with a mean of 9.3 years and a standard deviation o

Harlamova29_29 [7]

Answer:

The probability is 0.0643

Step-by-step explanation:

* Lets revise some definition to solve the problem

- The standard deviation of the distribution of sample means is called σM

- σM = σ/√n , where σ is the standard deviation and n is the sample size

- z-score = (M - μ)/σM, where M is the mean of the sample , μ is the mean

of the population

* Lets solve the problem

- The mean of the washing machine is 9.3 years

∴ μ = 9.3

- The standard deviation is 1.1 years

∴ σ = 1.1

- There are 70 washing machines randomly selected

∴ n = 70

- The mean replacement time less than 9.1 years

∴ M = 9.1

- Lets calculate z-score

∵ σM = σ/√n

∴ σM = 1.1/√70 = 0.1315

∵ z-score = (M - μ)/σM

∴ z-score = (9.1 - 9.3)/0.1315 = - 1.5209

- Use the normal distribution table of z to find P(z < -1.5209)

∴ P(z < -1.5209) = 0.06426

∵ P(M < 9.1) = P(z < -1.5209)

∴ P(M < 9.1) = 0.0643

* The probability is 0.0643

5 0

3 years ago

Jackie runs and dances for a total of 55 minutes every day. She dances for 25 minutes longer than she runs.

butalik [34]

Answer:

Jackie runs for $15$ minutes and dances for $40$ minutes.

Step-by-step explanation:

Let the time she dances be $x$ and the time she runs for be $y$ minutes respectively.

$x+y =55\\x =y+25$

Use the substitution method here ,

$y+25+y=55\\2y+25=55\\2y=55-25\\y=\frac{30}{2} \\y=15\\x=y+25\\x=15+25\\x=40$

Therefore Jackie runs for $15$ minutes and dances for $40$ minutes.

8 0

2 years ago

The ray ‾ ⇀gj is the angle bisector of ∠fgh and m∠fgh = 75° how do you find ∠fgj

Anton [14]

For a better understanding of the solution/explanation given here please go through the diagram in the file attached.

By definition, an angle bisector is a ray that divides an angle into two congruent angles.

In our question we have been given that GJ is the ray that is the angle bisector and that has been shown in the diagram.

Now, since, $m\angle FGH=75^{\circ}$ , therefore, the ray $\underset{GJ}{\rightarrow}$ will divide the original angle $m\angle FGH=75^{\circ}$ into two congruent angles, $\angle GJH$ and $\angle FGH$ . Since, the division is equal, the values of both these angles will be half of the original angle. Thus, we will have: