Write an equation of the perpendicular bisector of the segment with endpoints Y(10,−7) and Z(−4,1)

Given problem:

 Solve using the property of equality;

               -7 + x = 12

The properties of equality are;

     Addition. Definition. If x = y, then x + c = y + c. ...

     Subtraction. Definition. If x = y, then x – c = y – c. ...

      Multiplication. Definition. If x = y, then xc = yc. ...

     Division. Definition. If x = y and c is not equal to 0, then x / c = y / c

Now;

        - 7 + x = 12;

  base on the properties of equality, to eliminate -7, add +7 to both sides;

        -7 + 7 + x  = 12 + 7

                    x = 19

Based on the properties of equality, the solution is 19

Answer:

C

Step-by-step explanation:

\(-15x+60\leq 105 \\ \\ -15x \leq 45 \\ \\ x \geq -3\)

\(14x+11 \leq -31 \\ \\ 14x \leq -42 \\ \\ x \leq -3\)

The intersection is x = 3.

The newspaper doesn't need any additional fine and performing arts articles in the 12th month to achieve a mean of 24 articles per month.

To find out how many fine and performing arts articles the newspaper needs in the 12th month in order to have a mean of 24 articles per month, we need to calculate the current mean of the available data and then determine the shortfall or excess.

Let's assume the given dot plot represents the number of fine and performing arts articles in their paper each month. Since we don't have the exact data points, we'll work with the given information.

We know that the newspaper wants a mean of 24 articles per month, and they currently need 24 articles per month. Therefore, the total number of articles they need for the 12 months is 24 * 12 = 288 articles.

Now, let's consider the dot plot data. Suppose the mean of the available data is X articles per month.

The sum of the available data points would be the product of the mean (X) and the number of months (12):

Sum of available data = X * 12

To have a mean of 24 articles per month, the sum of the available data should be equal to the total number of articles needed (288):

Sum of available data = 288

Setting up the equation, we have:

X * 12 = 288

Now, we can solve for X:

X = 288 / 12

X = 24

Since the current mean of the available data is already 24 articles per month, there is no shortfall or excess. In order to reach a mean of 24 articles per month, the newspaper doesn't require any more pieces on the artistic and performing arts in the 12th month.

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Answer:

Your y intercept is 1.

Step-by-step explanation:

slope is y2-y1 over x2-x1, or 2.

slope intercept formula is y=mx+b, and if you plug values into formula you get 3=2(1)+b

and if you solve that, 2x1=2, 3-2=1.

then you get 1 as your y intercept.

\(\\ \sf\longmapsto \dfrac{x}{y}+\dfrac{y}{x}=2\)

\(\\ \sf\longmapsto \dfrac{x^2+y^2}{xy}=2\)

\(\\ \sf\longmapsto x^2+y^2=2xy\)

\(\\ \sf\longmapsto x^2+y^2-2xy=0\)

\(\boxed{\sf (a-b)^2=a^2-2ab+b^2}\)

\(\\ \sf\longmapsto (x-y)^2=0\)

\(\\ \sf\longmapsto x-y=\sqrt{0}\)

\(\\ \sf\longmapsto x-y=0\)

Now

\(\\ \sf\longmapsto 4x-4y-4\)

\(\\ \sf\longmapsto 4(x-y-4)\)

\(\\ \sf\longmapsto 4(0-4)\)

\(\\ \sf\longmapsto 4(-4)\)

\(\\ \sf\longmapsto -16\)

Thus, the angle of elevation from the base to the top of the mountain is approximately 26.57 degrees.

To find the angle of elevation from the base to the top of the mountain, we need to use the tangent function.

The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

In this case, the opposite side is the vertical height of the mountain, which is 600 feet, and the adjacent side is the horizontal distance from the base to the top of the mountain, which is 1200 feet.

So, we can use the formula tan(Ф) = opposite/adjacent, where theta is the angle of elevation.

Plugging in the values we have, we get tan(Ф) = 600/1200.

Simplifying this, we get tan(Ф) = 1/2.

To find the angle, we need to take the inverse tangent of both sides. This is denoted by tan^-1 or arctan.

So, we get  Ф = arctan(1/2).

Using a calculator, we get Ф = 26.57 degrees (rounded to two decimal places).

Therefore, the angle of elevation from the base to the top of the mountain is approximately 26.57 degrees. This means that the slope of the mountain is quite steep, and skiers would need to take caution when skiing down.

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x = 4 would be the solution of the given problem.

I can't speak to the first part of this question, as I don't totally have context for what they're asking, but we can solve for x using one of the laws of logarithms, namely:

log.m + log.n = log.mn

Using this law, we can combine and rewrite our initial equation as

log(x^2- x) = 3

Remember that logarithms are simply another way of writing exponents. The logarithm  is just another way of writing the fact . Keeping that in mind, we can express our logarithm in terms of exponents as

log(x^2- x) = 3 --> x^2- 2x = 8

2³ = 8, so we can replace the left side of our equation with 8 to get

x^2 - 2x - 8 =0

(x-4)(x+2) = 0

Hence x = 4 0r -2. As x cannot be negative so it would be 4.

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Answer:

x = 4

Step-by-step explanation:
1.Distribute

2. Subtract 2 from both sides
3. Simplify
4. Divide both sides by same factor

5. Simplify
x = 4

Answer: 4

Step-by-step explanation:

We have to try getting x by itself to solve for it. Since we have two sides that are equal to each other, we can add, subtract, multiply, and divide anything on both sides to try to isolate x.

\(2(x+1)=10\)

We can first divide the left side and the right side by 2. This would remove the 2 being multiplied on the outside.

\(\frac{2(x+1)}{2}=\frac{10}{2}\\x+1=10\div 2\\x+1=5\)

Now, we have a + 1 on the left side that we need to remove to get x by itself. If we are adding something, we can remove that by subtracting the same thing. Hence, we can subtract 1 from both sides to remove the + 1.

\(x+1=5\\x+1-1=5-1\\x+0=4\\x=4\)

After all that simplifying, we get that x equals 4.

IiThe answer is b when a data plot suggests there is a non-linear functional form.

Data is the collection of data term that is organized and formatted in a specific way it's typically contains fact observation or statistics that are collected through a process of measurement or research data set can be used to answer question and help make informed decision they can be used in a variety of ways such as to identify trends on cover patterns and make prediction.

Transforming the explanatory variable in a simple linear regression model is considered when the data plot suggests that the relationship between the two variables is nonlinear. This is done to improve the fit of the model to the data and to better capture the underlying relationship between the two variables. Transforming the explanatory variable can also reduce the variation in the explanatory variable and the Sum of Squared Errors. However, transforming the explanatory variable should not be done solely to get a coefficient estimate with the sign predicted by economic theory.

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By performing the desired calculation using each arrangement and squaring the difference between the result and the target value, you can determine the arrangement that yields the largest squared difference.

To find the arrangement of the 6 numbers that generates the biggest difference squared, you need to consider all possible permutations of the numbers. For each arrangement, perform the desired calculation using the given, such as addition, subtraction, multiplication, or any other specified operation.

Once you have the calculated result for each arrangement, calculate the squared difference between the result and the target value. This is done by subtracting the target value from the calculated result and then squaring the difference.

By comparing the squared differences obtained for each arrangement, you can identify the arrangement that yields the largest squared difference. This arrangement will have the maximum difference squared between the calculated result and the target value.

It's important to note that the specific calculation or operation to be performed is not mentioned in the question. Therefore, you need to specify the operation or provide more information to determine the exact steps for performing the calculation.

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Let us first do the stretch factor of 2

and then, we have to translate 3 units to the left

So we get that

Answer:

I believe the answer is y=4x+4

Step-by-step explanation:

because the 4 that is on the  Y axis is the Y axis

and the 4 on the x axis will be the one with the variable

Hopefully this helps.

an equation of the plane is:

(2z+6)x + (3x-2z-21)y + (-2x-3y+8)z - 13 = 0

To find an equation of the plane, we need a point and a normal vector.

The line x = 4 - t, y = 2t - 1, z = -3t is contained in the plane, so we can choose a point on the line as our point in the plane. Let's take t = 0, so x = 4, y = -1, z = 0. Therefore, the point (4, -1, 0) is in the plane.

To find a normal vector, we can take the cross product of two vectors that are in the plane. One vector is the direction vector of the line, which is <1, 2, -3>. Another vector can be found by subtracting the given point from a general point in the plane. Let's choose the point (x, y, z). Then a vector from (3, 5, -1) to (x, y, z) is <x-3, y-5, z+1>. So another vector in the plane is <x-3, y-5, z+1> - <4, -1, 0> = <x-7, y-4, z+1>.

Taking the cross product of these two vectors, we get:

<1, 2, -3> x <x-7, y-4, z+1> = <2z+6, 3x-2z-21, -2x-3y+8>

This is a normal vector to the plane. Therefore, an equation of the plane is:

(2z+6)x + (3x-2z-21)y + (-2x-3y+8)z + d = 0

where d is a constant. To find d, we can plug in the coordinates of the given point:

(2(-1)+6)(3) + (3(4)-2(-1)-21)(5) + (-2(4)-3(-1)+8)(-1) + d = 0

Solving for d, we get d = -13.

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The correct statement about the factors of the number is: Sixteen is not a factor of the number because the exponent of 2 is not even.

Given the prime factorization of the number as 2³ * 3² * 5, we can determine the factors by considering the combinations of the prime factors raised to different powers.

In this case, the number does not have 16 as a factor because the exponent of 2 is 3, which is not even. A number is divisible by 16 only if it has at least four factors of 2 (2²² or higher power of 2) in its prime factorization.

The other statements are not true:

Fifteen is not a factor of the number because it includes the prime factors 3 and 5, but not the prime factor 2.

Fifteen being odd and the number being even is not a determining factor for divisibility.

Sixteen is not a factor of the number because the exponent of 2 is 3, not 4 or greater.

Therefore, the only true statement is that Sixteen is not a factor of the number because the exponent of 2 is not even.

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The mean and standard deviation (SD) of the population consisting of the numbers {1, 2, 3, 4} are (a) Mean = 2.5 and SD = 1.118.

To calculate the mean of a population, we sum up all the numbers in the population and divide it by the total number of elements. For the given population {1, 2, 3, 4}, the sum of the numbers is 1 + 2 + 3 + 4 = 10, and there are four elements in the population. Thus, the mean is 10/4 = 2.5.

To calculate the standard deviation of a population, we first find the difference between each element and the mean, square each difference, calculate the average of the squared differences, and then take the square root. However, in this case, since the population consists of only four numbers, we can directly calculate the standard deviation by finding the square root of the variance, which is the average of the squared differences from the mean.

The squared differences from the mean for this population are (1-2.5)², (2-2.5)², (3-2.5)², and (4-2.5)², which are 2.25, 0.25, 0.25, and 2.25, respectively. The average of these squared differences is (2.25 + 0.25 + 0.25 + 2.25)/4 = 1, and the square root of the variance is √1 = 1. Thus, the standard deviation is 1. Therefore, the correct answer is (a) Mean = 2.5 and SD = 1.118.

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In general, an appropriate null hypothesis is one that states there is no significant difference or relationship between two variables.

Therefore, out of the options given, the appropriate null hypothesis would be "selection was not a significant factor."
An appropriate null hypothesis is "Selection has no effect on the observed outcome. "it means that any differences observed in the data are due to chance, and not due to a specific selection process or factor. The null hypothesis serves as a starting point in statistical analysis, and researchers aim to either accept or reject it based on the evidence collected.

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Answer: Original value: 0.076952

Value (with 3 decimal places): 0.077

Step-by-step explanation: hope this helps

Answer: \(x = \pm2\sqrt{7}\\\\\)

Work Shown:

\(x^2 = 28\\\\x = \pm\sqrt{28}\\\\x = \pm\sqrt{4*7}\\\\x = \pm\sqrt{4}*\sqrt{7}\\\\x = \pm2\sqrt{7}\\\\\)

This can be rewritten into \(x = 2\sqrt{7} \ \text{ or } \ x = -2\sqrt{7}\)

Answer:

No

Step-by-step explanation:

The sum of the smaller sides is not bigger than the largest side, 122. ( 31 + 89 = 120 < 122)

The correct expression for "five times the sum of b and two" is determined by understanding the order of operations.

To represent "five times the sum of b and two" in an algebraic expression, we need to consider the order of operations. The phrase "the sum of b and two" indicates that we need to add b and two together first.

The correct expression is given by option c. (b + 2) * 5. This expression represents the sum of b and two inside the parentheses, which is then multiplied by five.

Option a, 5(b + 2), implies that only the variable b is multiplied by five, without including the constant term two.

Option b, 5b - 2, represents five times the variable b minus two, which is different from the given expression.

Option d is not provided, so it is not applicable in this case.

Therefore, the correct expression is c. (b + 2) * 5, which means five times the sum of b and two.

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Answer:

GH

Step-by-step explanation:

Answer:

Bc=Gh since they correspond meaning same side equal

The amount of the sum Rs 1200 for one and a half year at 40 percent of interest compounded quarterly is Rs 1893.09.

The amount of the sum Rs 1200 for one and a half year at 40 percent of interest compounded quarterly can be calculated as follows:

Given, Principal = Rs 1200Time = 1.5 yearsInterest rate = 40% per annum, compounded quarterly

Let r be the quarterly rate of interest. Then we can convert the annual interest rate to quarterly interest rate using the following formula: \text{Annual interest rate} = (1 + \text{Quarterly rate})^4 - 1$$

Substituting the values, we get:0.40 = (1 + r)^4 - 1 Solving for r, we get:r = 0.095 or 9.5% per quarter

Now, we can use the formula for the amount of money after time t, compounded quarterly: $A = P \left( 1 + \frac{r}{4} \right)^{4t}

Substituting the values, we get:A = Rs 1200 x $\left(1 + \frac{0.095}{4} \right)^{4 \times 1.5}= Rs 1893.09

Therefore, the amount of the sum Rs 1200 for one and a half year at 40 percent of interest compounded quarterly is Rs 1893.09.

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Answer:

An expression like "x" is called a VARIABLE!

Answer:

D= 7(2g-H)/U

Step-by-step explanation:

Answer:

80cubic cm

Step-by-step explanation:

Answer:

Yes.

because 2:3 =0.666...

Step-by-step explanation:

Answer:

yes i agree

Step-by-step explanation:

i agree because 0.66 is 2/3 of 1 if you take 1 and divide it by 3 you get 0.33 which would be 1/3 so 2/3 would be 0.66

Answer:

y=3/4x-4

Step-by-step explanation:

the y intercept is -4 and then you plug in the slope

The equation has just two solutions, which are 11 and 7.

While the inequality will have a range of solutions, which is:

7 ≤ w ≤11

That is the difference.

Here we have an inequality:

|w - 9| ≤ 2

And an equation:

|w - 9| = 2

To solve these we can start by solving the equation, it gives two equations:

w - 9 = 2

w - 9 = -2

With these we can get two solutions for w,:

w = 2 + 9 = 11

2 = -2 + 9 = 7

Then the equation has just two solutions, which are 11 and 7.

While the inequality will have a range of solutions, which is:

7 ≤ w ≤11

That is the difference between the two.

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