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3 years ago

Solve the system by elimination 4x+3y=-5 -x+3y=-10

Mathematics

1 answer:

Sedaia [141]3 years ago

3 0

Subtract the 2nd row from the 1st row

5x = 5

Solve for x in the equation above

x = 1

Substitute x = 1 into any of the two equations above

Let's pick the first equation; 4x + 3y = -5

4 * 1 + 3y = -5

Solve for y in the equation above

y = -3

Therefore,

x = 1

y = -3

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grandymaker [24]

The answer should be 2x-5

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3 years ago

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Evaluate the expression without using a calculator Tan(arccos3/4)

julia-pushkina [17]

9514 1404 393

Answer:

(√7)/3

Step-by-step explanation:

The relationship between tangent and cosine is ...

tan(α) = √(1/cos(α)² -1)

The cosine of the angle is given as 3/4, so the tangent is ...

tan(arccos(3/4)) = √(1/(3/4)² -1) = √(16/9 -1) = √(7/9)

tan(arccos(3/4)) = (√7)/3

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3 years ago

A water wheel has a radius measuring between 13 feet and 24 feet. The wheel is able to turn 7π9 radians from its starting positi

madam [21]

Answer:

31.76 ft and 58.64 ft

Step-by-step explanation:

The radius measures between 13 feet and 24 feet.

The wheel is able to turn 7π/9 radians before getting stuck.

We need to find the range of distances that the wheel could spin before getting stuck. That is, the length of arc.

Length of an arc is given as:

$L = \frac{\theta}{2\pi} * 2\pi r$

where θ = central angle = 7π/9 radians

r = radius of the circle

Therefore, for 13 feet:

$L = \frac{7\pi}{18 \pi} * 2 * \pi * 13\\\\L = 31.76 ft$

For 24 feet:

$L = \frac{7\pi}{18 \pi} * 2 * \pi * 24\\\\L = 58.64 ft$

The wheel could spin between 31.76 ft and 58.64 ft before getting stuck.

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3 years ago

Which graph shows the solution to the system of linear inequalities?

ICE Princess25 [194]

Answer:

x = 6 ; Rewritten: 2x-3y-12=0 ; y=-4

Step-by-step explanation:

2x-3 multiply 0=12

x=6 ( that's the function)

Rewritten steps: 2x-3y=12 then move constant to the left by adding its opposite to both sides which gives you 2x-3y-12=12-12. After the sum of two opposites equals 0 which is 2x-3y-12=0

Y Intercept :

2x-3y=12 and to find y intercept, sub x = 0 ; to 2 multiply 0 -3y=12 and then you solve for the equation which is your answer.

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3 years ago

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What is the constant of proportionality of y to x?

AleksAgata [21]

Answer:

2.5

Step-by-step explanation:

We are given a graph with a positive slope where the value of y increases when the value of x increases.

For the given graph, we are to find the constant of proportionality of y to x which is the slope of the given line.

We know the formula of the slope = $\frac{y_2-y_1} {x_2-x_1}$

Substituting the given values in the formula:

$\frac{15-10}{6-4} = \frac{5}{2} = 2.5$

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3 years ago

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