Find k so that the three equations 3x-y=2, 2x+8=3y, and y=kx have a common solution

Answer:

[tex]x+11[/tex]

Step-by-step explanation:

In order to simplify this:

[tex]x+15-4[/tex]

You just need to substract like terms:

[tex]15-4=11[/tex]

Hence, the simplified is expression is:

[tex]x+11[/tex]

This represents a line which intercepts with the y-axis at 11 and with the x-axis at -11. I attached you the graph.

The simplified form of the expression is x + 11.

To simplify the expression "x + 15 - 4", you just need to do the addition and subtraction operation:

x + 15 - 4 = x + 11

Simplifying an expression means to make it as easy to understand as possible. This can involve combining like terms, removing unnecessary parentheses, and using the distributive property.

In the expression x + 15 - 4, the like terms are x and 15. These terms can be combined to give x + 11. The parentheses around the 15 are unnecessary, so they can be removed. The simplified expression is x + 11.

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As you can see from the diagram, this is an isosceles triangle (triangle where 2 sides are equal and angles opposite are also equal).

Since there are two 65 degree angles, the sides opposite them are also equal. So we can write:

[tex]6x=3x+9[/tex]

Solving for x:

[tex]6x=3x+9\\6x-3x=9\\3x=9\\x=\frac{9}{3}\\x=3[/tex]

Now, we want to know side length of AB, which is 6x. Plugging in x = 3 into that, we get:

[tex]AB=6(3)\\AB=18[/tex]

Answer choice D is right.

ANSWER: D

The distance between point A at (-12, 6) and point B at (4, 6) is 16 units according to the distance formula for a coordinate plane.

The question is asking for the distance between two points on a coordinate plane. To solve this, we use the distance formula for a coordinate plane which is D = sqrt((X2-X1)^2 + (Y2-Y1)^2), where X1, Y1 and X2, Y2 are the coordinates of the two points. In this case, both Y coordinates are the same (6), which makes the calculation simpler.

In this case, point A is at (-12, 6) and point B is at (4, 6). Subtracting the x-coordinates of A and B, (-12 - 4), we get -16, but we square this to get a positive result, which gives us 256. Since the y-coordinates are the same, the part of the equation dealing with them results in 0. So, the distance D is then the square root of 256, which is 16 units.

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A triangle with sides of lengths x^2-1, 2x, and x^2+1 is a right triangle as confirmed by the Pythagorean theorem. By squaring these lengths and simplifying the resulting equation, it's shown that the squares of the lengths of the two shorter sides sum up to the square of the length of the longest side.

To prove that a triangle with sides of lengths x^2-1, 2x, and x^2+1 is a right triangle, we can apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Therefore, if x^2-1 and 2x are two sides of the triangle and x^2+1 is the hypotenuse, then the equation becomes:

(x^2-1)^2 + (2x)^2 = (x^2+1)^2

If this equation is true, then we have a right triangle. Let's simplify the equation:

x^4 - 2x^2 + 1 + 4x^2 = x^4 + 2x^2 + 1

After simplifying, we get that 2x^2 equals 2x^2, which confirms that we indeed have a right triangle.

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The probability of first picks the red and then blue will be,15/121.

The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts,

No of red marbles =3

No of white marbles = 3

No of blue marbles =5

Total no of the marble is;

T= 3+3+5=11

The probability of picking a red ;

[tex]\rm P_{red}=\frac{3}{11}[/tex]

The probability that the next pick will be blue is;

[tex]P_{( blue})=\frac{5}{11}[/tex]

P(red then blue) is;

[tex]P_{(red \rightarrow blue})=\frac{3}{11} \times \frac{5}{11} \\\\ P_{(red \rightarrow blue})=\frac{15}{121}[/tex]

Hence,the probability of first picks the red and then blue will be,15/121.

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The measure of m<OAC is 45degrees

From the given diagram, we can see that the line A is tangential to the circle at point C, hence m<C = 90 degrees

Taking the sum of angle in a triangle

m<OAC + 45 + 90 = 180

m<OAC = 180 - 135

m<OAC = 45 degrees

Hence the measure of m<OAC is 45degrees

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Answer:

Thanks to point

ok nerd

7360/3680 = 2

3680/1840 = 2

920/2= 460

 month 5 sales will be 460

It will take approximately 44.67 seconds for the elevator to travel from the first floor to the sixty-eighth floor, assuming it travels at a constant speed of 7.5 meters per second throughout the journey.

To determine how long it takes for the elevator to travel from the first floor to the sixty-eighth floor, we must first calculate the total distance traveled and then use the speed of the elevator to find the time.

Since each floor is 5 meters high, the total distance for 67 floors (from the first to the sixty-eighth) is 67 floors × 5 meters/floor = 335 meters.

Given that the elevator travels at a rate of 7.5 meters per second, the time taken to travel this distance can be calculated using the formula:

time = distance/speed

Substituting the values, we get:

time = 335 meters / 7.5 meters/second

time ≈ 44.67 seconds

Therefore, it will take approximately 44.67 seconds for the elevator to travel from the first floor to the sixty-eighth floor, assuming it travels at a constant speed throughout the journey.

Answer: 4(y/2 - 3)/9

hope this helps

To solve the given system of equations using elimination, multiply the first equation by 2 to make the coefficients of 'x' the same in both equations. Then solve for 'x' and substitute the value into the first equation to solve for 'y'. The solution is x = -8 and y = -11.

To solve the given system of equations using elimination, first multiply the first equation by 2 to make the coefficients of 'x' the same in both equations.

10x = -50 + 10y

Next, subtract the equation obtained in step 1 from the second equation.

10y = 42 + 2x - (-50 + 10y)

Simplify the equation and solve for 'x'.

x = -8

Substitute the value of 'x' into the first equation to solve for 'y'.

5(-8) = -25 + 5y

y = -11

Therefore, the solution to the system of equations is x = -8 and y = -11.

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