If KL = 2x, LM = 5x, and KM = 7, what is LM?

Given ray OJ bisects angle IOK, we can set an equation for angles IOJ and JOK, solve for x and substitute x into the given measure of angle IOJ: 2*(16)-5 equals 27 degrees.

Since ray OJ bisects angle IOK, it means that angle IOJ and angle JOK are equal in measurement. Given in the problem, angle IOJ= 2x-5 and angle JOK= x+11. Because they are equal, we can set up the equation 2x-5 = x+11.

To solve for x, we subtract x from both sides of the equation, resulting in x-5 =11. And then, if we add 5 to both sides of the equation, the end result is x = 16.

Substituting x into the given measurement for angle IOJ, which is 2x-5, we would get the measure of angle IOJ as 2*(16)-5 = 27 degrees.

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We can use the points (-4, -1) and (0, -2) to solve.

Formula: y2-y1/x2-x1

= -2-(-1)/0-(-4)

= -1/4

Best of Luck!

The required simplified form of the expression 12x⁵/6x² is 2x³.

Exponential expressions, as the name indicates, involve exponents. We already know that the exponent of a number (base) specifies how many times the number (base) has been multiplied. To answer the exponential expressions, we may need to apply the relationship between exponents and logarithms.

The exponential expression is given in the question as:

12x⁵/6x²

To simplify the expression 12x⁵/6x², we can start by dividing 12 by 6 to get:

12x⁵/6x² = (12/6)x⁵/x² = 2x⁵/x²

Then, we can use the quotient of powers rule, which states that when we divide two powers with the same base, we can subtract the exponents to get:

2x⁵/x² = 2x⁵⁻² = 2x³

Therefore, the expression is 2x³ equivalent to the given expression 12x⁵/6x².

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To write a two-variable equation, I would first need to know how much Maya’s allowance was. Then, I would need the cost of playing the arcade game and of riding the Ferris wheel. I could let the equation be cost of playing the arcade games plus cost of riding the Ferris wheel equals the total allowance. My variables would represent the number of times Maya played the arcade game and the number of times she rode the Ferris wheel. With this equation I could solve for how many times she rode the Ferris wheel given the number of times she played the arcade game u welcome

Using the binomial distribution, it is found that:

For each student, there are only two possible outcomes, either they are left-handers, or they are not. The probability of a student being a left-hander is independent of any other student, hence the binomial distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

The expected value is:

[tex]E(X) = np[/tex]

The standard deviation is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

In this problem:

Then:

[tex]E(X) = np = 10(0.16) = 1.6[/tex]

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{10(0.16)(0.84)} = 1.16[/tex]

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Answer:x <= -2 and 2x >= 6 is the smae as

x <= -2 and x >= 3

Step-by-step explanation:

The Calvin has a total of 252 utility coming from Oranges and Starfruit.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given that oranges cost $2 per pound and starfruit costs $5 per pound.

The utility coming from Oranges and Starfruit, therefore he needs to spend his $26 on buying the oranges and starfruit

Since all in all he also spend $23 on it, and still has remaining $3 in his pocket,

Thus his total utility is 252.

Hence, The Calvin has a total of 252 utility coming from Oranges and Starfruit.

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The complete question is

The oranges cost $2 per pound and starfruit costs $5 per pound. calvin has $26 to spend. if calvin buys 4 pounds of starfruit and 3 pounds of oranges, how much is his total utility?

Answer:

7 units

Step-by-step explanation:

The length of the midsegment of this trapezoid will be 7 units.

What is mean by Rectangle?

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The coordinates of the vertices of the trapezoid are,

A = (-2, 4)

B = (4, 3)

C = (4 , -5)

D = (- 2, - 2)

Now,

Since, We know that;

The length of the midsegment of a trapezoid is always equal to the half of the sum of the parallel sides.

Here, Line AD and BC are parallel lines.

And, The length of AD = √(- 2 - (-2))² + (- 2 - 4)²

                                   = √-6²

                                  = 6

And, The length of BC = √(4 - 4)² + (- 5 - 3)²

                                   = √-8²

                                   = 8

Thus, The length of the midsegment of this trapezoid = (6 + 8)/2

                                                                                    = 14/2

                                                                                    = 7 units.

Therefore, The length of the midsegment of this trapezoid will be 7 units.

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Answer:

its 12,000

Step-by-step explanation:

The probability we see at least one club and at least one ace would be 0.019225

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

The Total number of cards in a deck = 52

Number of aces in a standard deck = 4

Number of clubs in a standard deck = 13

The Probability = required outcome / Total possible outcomes

P(ace) = 4 / 52 = 0.0769

P(club) = 13 / 52 = 1/4 = 0.25

Therefore, the probability we see at least one club and at least one ace

0.0769 x 0.25

= 0.019225

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Answer:

[tex]y=2x+2[/tex]

Step-by-step explanation:

step 1

Find the slope

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

[tex]A(-4,-6)\ B(2,6)[/tex]

Substitute the values

[tex]m=\frac{6+6}{2+4}[/tex]

[tex]m=\frac{12}{6}=2[/tex]

step 2

we know that

The equation of the line into slope intercept form is equal to

[tex]y=mx+b[/tex]

we have

[tex]m=2[/tex]

[tex]B(2,6)[/tex]

substitute and solve for b

[tex]y=mx+b[/tex] ------> [tex]6=(2*2)+b[/tex]

[tex]6=4+b[/tex]

[tex]b=2[/tex]

The equation of the line is equal to

[tex]y=2x+2[/tex]

Answer:

the answer is in addition the order of the variables does not matter in the expression

Step-by-step explanation:

i took the test

Answer:

Pretty sure its the Transitive Property

Step-by-step explanation:

It's a dropdown on Edge so there's no A B C or D

To prove that point C is the midpoint of segment AB, we apply the segment addition property and the definition of congruent segments.

To prove that point C is the midpoint of segment AB, we can use the segment addition property. We are given that AB = 12 and AC = 6. By applying the segment addition property, we get AC + CB = AB. Substituting the given values, we have 6 + CB = 12. Solving for CB using the subtraction property, we find that CB = 6.

Now, by using the symmetric property, we can see that 6 = AC. Since CB = 6 and 6 = AC, we can conclude that AC is congruent to CB by the definition of congruent segments. This implies that C is the midpoint of AB, as it divides AB into two congruent segments.

Final answer:

To solve the problem, we defined two variables for the larger (x) and smaller (y) numbers. Using the provided information, we set up two equations and solved them to find the numbers: x (the larger number) is 40, and y (the smaller number) is 28.

Explanation:

Step-by-Step Solution to Find the Two Numbers

Let's denote the larger number as x and the smaller number as y. We are given two pieces of information:

The sum of the two numbers is 68.

The smaller number is 12 less than the larger number.

These two statements can be turned into two equations:

x + y = 68 (Equation 1)

y = x - 12 (Equation 2)

Now, we can substitute Equation 2 into Equation 1 to find x:

x + (x - 12) = 68

2x - 12 = 68

Add 12 to both sides:

2x = 80

Divide both sides by 2:

x = 40

Now that we know the larger number, x, we can find y using Equation 2:

y = 40 - 12

y = 28

So, the two numbers are 40 and 28

The third side of the isosceles triangle with the given sides of 2 and 12 is 12 units.

To find the length of the third side of an isosceles triangle where two sides are given as 2 and 12, we must consider two cases.

In an isosceles triangle, two sides are equal in length and the two angles opposite these sides are also equal. This means either the two given sides are the equal sides, which is not possible since they are different lengths, or one of the given lengths will be the base and the equal sides are yet to be determined.

Case 1: If the side of length 2 is the base, the length of the equal longer sides will both be 12.

Case 2: If the side of length 12 is the base, then the length of the two equal sides must both be 2.

However, we must recognize that the first case is incorrect because it does not form a triangle (a triangle cannot have two sides of length 12 and one side of length 2, as the two longer sides would be parallel and never meet to form a triangle).

Therefore, the correct answer is given by Case 2: the third side of the triangle, which is the base, is 12 units long, and the two equal sides are 2 units long each.

the answer is -14

Hope this helps : )

Final answer:

The completing-the-square method allows rewriting quadratic functions to determine the vertex. The coefficient of the squared term determines if the vertex is a minimum or maximum.

Explanation:

The completing-the-square method allows us to rewrite quadratic functions in a form that reveals the vertex of the parabola. To determine if the vertex is a minimum or a maximum, we need to consider the coefficient of the squared term. In the function f(x) = –(x + 4)² + 2, the coefficient is negative, indicating that the parabola opens downwards, and the vertex is a maximum. In the function g(x) = (x − 2)² − 2, the coefficient is positive, indicating that the parabola opens upwards, and the vertex is a minimum.