The point P(4,4) is reflected over the line x=5. What are the coordinates of the resulting point, P'?

107+73 = 180

107-73 = 34

========================================================

Explanation

Rule: Supplementary angles always add to 180 degrees.

This is our system of equations.

[tex]\begin{cases}x+y = 180\\x-y = 34\\\end{cases}[/tex]

Add the equations straight down.

After the y terms go away, we have this new equation: 2x = 214 which solves to x = 107 after dividing both sides by 2.

Then use this x value to find y

x+y = 180

107+y = 180

y = 180-107

y = 73

Or you could say

x-y = 34

107-y = 34

-y = 34-107

-y = -73

y = 73

Either way, we get the same y value each time. This helps confirm the answer.

Another way to confirm the answer is shown in the next section below.

---------------------

Check:

x+y = 180

107+73 = 180

180 = 180 .... confirms the 1st equation

x-y = 34

107-73 = 34

34 = 34 ... the other equation is confirmed.

In short,

Answer: -5

h(0) = -5(0) - 5

h(0) = -5

Answer:

Jessica rode her bike 16 miles per week and Pablo rode his bike 17 miles per week.

Step-by-step explanation:

Answer:

Jessica's and Pablo's statement both are correctly comparing the number of miles they rode per week.

Step-by-step explanation:

You are told that Jessica rode her bicycle for 128 miles in 8 weeks and equally the same distance each week.

Therefore you can easy tell how much she rode her bicycle for 8 weeks by dividing 128 by 8 which is 16miles per week

While in Pablo's statement tell us the same as Jessica's statement since you can divide it like Jessica's statement 95 divided by 5 equals 19miles per week

Therefore , the solution of the given problem of equation comes out to be y = (-1/5)x + 4 is the required equation.

The equivalent sign (=) is used in arithmetic equations to signify the equality of two propositions. It is shown that it is possible to compare various numerical factors by using mathematical techniques, which have served as manifestations of reality. For instance, the equal sign divides the number 12 even the solution y + 6 = 12 in two distinct portions. How many characters also are present from either end of such a character can be calculated. Conflicting symbol readings are prevalent.

Here,

The given equation of line j is y+5=5(x+5) which can be rewritten in slope-intercept form as y = 5x + 20.

Since line k is perpendicular to line j, the slope of line k will be the negative reciprocal of the slope of line j. The slope of line j is 5, so the slope of line k will be -1/5.

We are also given that line k includes the point (5,3). We can use this point and the slope of line k to find the equation of line k using point-slope form:

y - 3 = (-1/5)(x - 5)

Simplifying and rearranging, we get:

y = (-1/5)x + 4

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The solution to the system of equation is x = -2 and y = -3.

System of equation can be solved using different method such as elimination method, graphical method and substitution method,

here we have,

Therefore, let's solve the system of equation by using substitution method.

-2x+ 7y = 15

6y=x

substitute the value of x in equation(i)

-2* 6y+ 7y = 15

or, -12y + 7y = 15

or, -5y = 15

or, y = -3

so, we get,

x = 6/ -3

or, x = -2

Hence, The solution to the system of equation is x = -2 and y = -3.

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The scale factor of the dilation that takes P to Q is,

⇒ 4/5

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

⇒ Quadrilateral P and Q are similar.

Hence, The scale factor of the dilation that takes P to Q is,

⇒ 2 / 2.5

⇒ 20 / 25

⇒ 4/5

Thus, The scale factor of the dilation that takes P to Q is, 4/5.

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Answer:

x = 108

Step-by-step explanation:

To solve the equation x/6 - 6 = x/18 + 6, we first need to get rid of the fractions by multiplying both sides by the least common multiple of the denominators, which in this case is 18.

So, we have:

18(x/6 - 6) = 18(x/18 + 6)

Simplifying this, we get:

3x - 108 = x + 108

Next, we want to isolate the variable x on one side of the equation, so we'll subtract x from both sides:

2x - 108 = 108

Finally, we'll add 108 to both sides to get:

2x = 216

Dividing both sides by 2, we get:

x = 108

Therefore, the value of x that makes the equation true is 108.

The following statements are true:

Line AB and line CG are parallel.

Line CG and line RS are perpendicular.

Line segment CG lies in plane X.

What is a line segment?

A line segment is a section of a straight line that is enclosed by two clearly defined endpoints and contains every point on the line located within. The Euclidean distance between two ends of a line segment determines its length.

Here, we have

Given: Planes X and Y intersect at a right angle. Line A B and Line C G lie in plane X and do not intersect. Line R S lies in plane Y.

A) Line AB and Line CG are parallel: As both lines, AB and CG lie in plane X. Thus both are parallel and option A is the correct option.

B) Line AB and Line RS are parallel: As a line, AB lies in plane X and line RS lies in plane Y. Thus both are perpendicular and not parallel. Option B is the incorrect option.

C)Line CG and Line RS are perpendiculars: As line CG lies in plane x and line RS lies in plane Y. Thus both are perpendicular. Option C is the correct option.

D) Line AB and Line RS must intersect: line RS passes from the middle of plane Y and line AB passes from the left of plane X center. Thus they do not intersect each other. Option D is the incorrect option.

E) Line segment CG lies in plane X: As shown in the diagram, line CG lies in plane X. Thus option E is the correct option.

F) Line segment RS lies in plane X: As shown in the diagram, and the line lies RS in plane Y. Thus option F is the incorrect option.

Hence, The following statements are true:

Line AB and line CG are parallel.

Line CG and line RS are perpendicular.

Line segment CG lies in plane X.

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The solution to the system is (x,y) = (48,19).

To find the solutions to the system of equations, we need to find the values of x and y that satisfy both equations simultaneously. One way to do this is to set the two expressions for y equal to each other and solve for x:

2/3x−5 = 1/2x+3

Multiplying both sides by 6 (the least common multiple of 3 and 2) to clear the fractions, we get:

4x - 30 = 3x + 18

Simplifying, we get:

x = 48

Now that we know x, we can substitute it into either of the original equations to find the corresponding value of y. Let's use the first equation:

y = 2/3(48) - 5 = 19

So the solution to the system is (x,y) = (48,19).

Since there is exactly one solution, the answer is (D) 1 solution.

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In statistics, the chi-square critical value is the threshold value that is used to determine whether the calculated chi-square test statistic is significant or not.

The chi-square critical value is determined based on the significance level (also known as alpha), which is the probability of rejecting the null hypothesis when it is true. The significance level is typically set at 0.05 or 0.01.

The chi-square critical value can be found using a chi-square distribution table or a statistical software program. The critical value is determined based on the degrees of freedom (df), which is the number of categories minus one.

Once the chi-square critical value is determined, it can be compared to the calculated chi-square test statistic to determine whether the test is statistically significant or not. If the calculated chi-square test statistic is larger than the critical value, we can reject the null hypothesis and conclude that there is a significant association between the variables.

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1)

The area of the electronic board on the scale drawing is 1800 cm².

2)

Using the scale factor 5:1.

Length:

1 = 50

5 = 250 cm

Width:

1 = 36 cm

5 = 180 cm

3)

The area of the actual electronic board is 45000 cm²

A scale factor is defined as the ratio between the scale of a given original object and a new object,

We have,

Scale factor = 5 : 1

Now,

Electronic board dimensions:

Length = 50 cm

Width = 36 cm

Now,

Area of the electronic board on the scale drawing.

= length x width

= 50 x 36

= 1800 cm²

Now,

Actual dimensions:

Length = 250 cm _____(1)

Width = 180 cm _____(2)

Using the scale factor 5:1.

1 = 50

5 = 250 cm

And,

1 = 36 cm

5 = 180 cm

Area of the actual electronic board.

From (1) and (2)

= 250 x 180

= 45000 cm²

Thus,

The area of the electronic board on the scale drawing is 1800 cm².

The area of the actual electronic board is 45000 cm²

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Here  is a scatter plot that compares hits to at bats for players on a baseball team, as the number of bats increase, the number of hits increases.

A scatter plot is also known as a scatter chart, scattergram, or XY graph. The scatter diagram plots numerical data pairings, one variable on each axis, to demonstrate their connection. Today everyone is wondering when to utilise a scatter plot.

Scatter plots are used in the following scenarios.

When we have numerical data that is paired

When there are several dependent variable values for a single independent variable value

In some instances, such as finding probable root causes of issues, evaluating if two items that appear to be connected both arise with the same precise reason, and so on.

The points will fall along a line or curve if the variables are correlated. The closer the points are to the line, the better the connection. One of the seven key quality tools is this cause examination tool.

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A tablespoon is a volume measurement unit based on a piece of flatware (symbol: Tbsp). The value of 4 tablespoons is equivalent to 0.25 cups.

A metric tablespoon is exactly 15 mL, but a tablespoon in the United States is around 14.8 mL.

In both the imperial and American customary systems of measurement, a cup is a unit of volume.

250 millilitres is the definition of a metric cup.

There are 4.25 tablespoons in 0.25 cups (4 tbsp).

You may use the formula below to convert tablespoons to cups:

16 tablespoons make create a cup.

So, you may divide 4 by 16 to convert 4 tablespoons to cups:

4 tbsp / 16 tbsp/cup equals 0.25 cups.

Hence, 4 tablespoons are equal to 0.25 cups.

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Jade was 416 meters above the ground when she deployed her canopy.

What is kinematics?

kinematics, specifically the equation of motion for constant velocity, to solve the problem of finding the height above the ground when a person deploys their canopy while descending.

We can use the formula:

height = rate x time

To determine how high Jade was above the ground when she deployed her canopy. Let's denote the height she was at when she deployed her canopy as "h".

From the given information, we know that Jade descended at a constant rate of 40 meters every 5 seconds, so her rate of descent is 40/5 = 8 meters per second.

We also know that it took her exactly 57 seconds to reach the ground. Therefore, the time she spent descending with her canopy deployed is 57 - 5 = 52 seconds.

Using the formula, we can write:

h = 8 x 52

Simplifying this equation gives us:

h = 416

Hence, Jade was 416 meters above the ground when she deployed her canopy.

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Answer:

Function.

Step-by-step explanation:

This graph is a function because all points on the line are different and do not intersect. (vertical line test)

Hope it helped!

The number of seconds that the ball isat its maximum height is 5 seconds.

It should be noted that to find the time at which the softball is at its maximum height, we need to find the vertex of the parabolic equation h = -4t^2 + 40t + 5.5.

The vertex of a parabola of the form h = at^2 + bt + c is given by the formula t = -b / (2a).

In this case, a = -4 and b = 40, so the time at which the ball reaches its maximum height is:

t = -b / (2a) = -40 / (2*(-4)) = 5 seconds.

Therefore, the ball is at its maximum height after 5 seconds.

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Two softball players are practicing catching fly balls. One player throws a ball to the other and the path of the softball is modeled by the equation h = -4t2 +40t +5.5, where h is the height (in feet) of the softball and is the time in seconds that have elapsed. b

After how many seconds is the ball at its maximum height?

Answer: $275,000

Step-by-step explanation:

The binary conversion of 2 is 10.

In binary, there are only two possible digits, 0 and 1. Each digit in a binary number represents a power of 2, with the rightmost digit representing 2^0 (which is 1), the second digit representing 2^1 (which is 2), the third digit representing 2^2 (which is 4), and so on.

So in the binary number 10, the rightmost digit represents 2^0, which is 1, and the second digit represents 2^1, which is 2. Adding these two powers of 2 together gives a total value of 2 in binary.

To convert a decimal number to binary, you can divide the number by 2 and record the remainder at each step until the quotient is 0. Then, the binary number is simply the remainders read in reverse order. In this case, 2 divided by 2 is 1 with a remainder of 0, so the first digit of the binary number is 0. 1 divided by 2 is 0 with a remainder of 1, so the second digit of the binary number is 1. Therefore, the binary conversion of 2 is 10.

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A ) The balance would be approximately $5562.35 when the interest is compounded quarterly.

B) The balance would be approximately $5565.09 when the interest is compounded monthly.

Annual interest rate refers to the interest rate over a period of one year with the assumption that the interest is compounded every year.

a) If the interest is compounded quarterly, we can use the formula:

A = P(1 + r/n)^(n*t)

where

In this case, P = $5500, r = 0.01356 (1.356% as a decimal), n = 4 (since interest is compounded quarterly), and t = 1 (since we are calculating the balance after one year).

Substituting these values into the formula, we get:

A = $5500(1 + 0.01356/4)^(4*1) ≈ $5562.35

So the balance would be approximately $5562.35 when the interest is compounded quarterly.

b) If the interest is compounded monthly, we can use the same formula, but with n = 12 (since interest is compounded monthly):

A = $5500(1 + 0.01356/12)^(12*1) ≈ $5565.09

So the balance would be approximately $5565.09 when the interest is compounded monthly.

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On factorizing each equation we get

a) x² + 6x + 9 =  (x + 3) (x + 3)  

b) x² - 6x + 8 = (x - 4) (x - 2)  

c) x² - 4x - 32 = (x - 8) (x + 4)  

d) x² + x - 42 = (x + 7) (x - 6)  

Factorization is the process of finding the factors of an expression or number. In algebra, factorization involves expressing an algebraic expression as a product of its factors.  

To factorize the following split the middle term and group out the common factors as given below.

Here we have four equations that can be factorized as follows

a) x² + 6x + 9  

=> x² +3x + 3x + 9         [ Split middles term ]

=> x(x + 3) +3(x + 3)      [ Grouping the terms ]

=> (x + 3) (x + 3)  

∴  a) x² + 6x + 9 =  (x + 3) (x + 3)  

b) x² - 6x + 8

=> x² - 4x - 2x + 8               [ Split middles term ]

=> x(x - 4) -2(x - 4)              [ Grouping the terms ]  

=> (x - 4) (x - 2)

∴ x² - 6x + 8 = (x - 4) (x - 2)  

c) x² - 4x - 32  

=> x² - 8x + 4x - 32         [ Split middles term ]  

=> x(x - 8) + 4(x - 8)         [ Grouping the terms ]    

=> (x - 8) (x + 4)

∴ x² - 4x - 32 = (x - 8) (x + 4)  

d) x² + x - 42  

=> x² + 7x - 6x - 42             [ Split middles term ]  

=> x(x + 7) - 6(x + 7)            [ Grouping the terms ]    

=> (x + 7) (x - 6)

∴ x² + x - 42 = (x + 7) (x - 6)  

Therefore,

On factorizing each equation we get

a) x² + 6x + 9 =  (x + 3) (x + 3)  

b) x² - 6x + 8 = (x - 4) (x - 2)  

c) x² - 4x - 32 = (x - 8) (x + 4)  

d) x² + x - 42 = (x + 7) (x - 6)  

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Answer:

4√3 or 6.9282Km

Step-by-step explanation:

Let the triangle be ABC, right angled at B

Angle A = 60 degrees

Angle C = 30 degrees

BC = 6 km

To find AB,

Tan30°=AB/BC

Now we know that tan30° is 1/√3 so,

1/√3 = AB / 6

6/√3 = AB

6√3/3 =AB

2√3 = AB

Now we have the value of two sides so we can use the Pythagoras Theorem to find the hypotenuse, which is g

AB² + BC² = AC²

(2√3)² + 6² = g²

12 + 36 = g²

48 = g²

Therefore g = √48km or 4√3km or 6.9282Km

In 2004, as per the run, the distance to the nearest tenth of a mile is 3.11 miles.

The distance that Kenenisa Bekele of Ethiopia ran in 2004 is equal to 5,000 meters, which is equivalent to 3.11 miles to the nearest tenth of a mile. To calculate this distance, you can use a simple conversion formula.

To convert meters to miles, you need to divide the number of meters by 1609.34.

In this case, we would divide 5,000 meters by 1609.34, which gives us 3.11 miles.

=> 5000/ 1609.34 = 3.11 miles.

This is the total distance that Kenenisa Bekele ran in 2004 to the nearest tenth of a mile.

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Answer:-7

Step-by-step explanation:

The weight of gallon of water is 8.345 pounds according to density of water.

The gallon is a unit of volume and we need to find the weight of one gallon of water. So, the weight and volume are related to each other by the formula -

Density = mass/volume

Now, we know the volume and need the density of water in pounds per gallon.

The density of water is 8.345 pounds per gallon.

So, keeping the values in formula

Mass = density × volume

Mass = 8.345 × 1

Performing multiplication on Right Hand Side of the equation

Mass = 8.345 pounds

The weight of water is 8.345 pounds.

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