PLEASE HELP! 47: Complete the two-column proof.

Answer:

a) CE=PR

b) TR=FE

c) <F=<T

d) <P=<C

e) RPT=ECF

Step-by-step explanation:

By solving the two equations, the values of x , y and x-y are found to be 1, 25/3 and -22/3 respectively.

Given two equations are;

5x+3y=30..........(1)

−5x−2y=−25.........(2)

Now , from (2)

−5x−2y=−25

⇒ 5x +2y = 25 (multiply both sides with '-' sign)

⇒ y = [tex]\frac{(25 -5x)}{2}[/tex]

Solving the system;

substitute the above vale of y in eq (1)

5x + 3y = 30

⇒ 5x + 3 ( [tex]\frac{(25 -5x)}{2}[/tex]) = 30

⇒  5x + ([tex]\frac{(75 - 15x)}{2}[/tex]) = 30

⇒  [tex]\frac{10x+75-15x}{2}[/tex] = 30

⇒ -5x + 75 = 60

⇒  -5x = -5

⇒ x = 1

∴ x = 1

Now substitute the value of x in (1)

5x + 3y = 30

⇒ 5 × 1 + 3y = 30

⇒ 3y = 25

⇒ y = 25/3

∴ y = 25/3

Now using the value of x and y , we can find the value of x - y

x - y = 1 -25/3 = (3 - 25)/ 3 = -22/3

∴ x - y = -22/3

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Answer:

first and second, which are the same number line

Step-by-step explanation:

250x + 300 ≥ 1,550 ( subtract 300 from both sides )

250x ≥ 1,250 ( divide both sides by 250 )

x ≥ 5

since x is greater than or equal to the number line will have a solid circle at 5, indicating x can be equal to 5.

the arrow will point to the right, indicating the values x can be greater than 5.

this solution is represented on both graph 1 and graph 2

The given statement is true all else being equal, the further the t statistic falls from 0, either in the positive or negative direction, the more likely it is that the difference between two population averages is statistically significant.  

The T Statistic is used in a T test when you are deciding if you should support or reject the null hypothesis. It’s very similar to a Z-score and you use it in the same way: find a cut off point, find your t score, and compare the two. You use the t statistic when you have a small sample size, or if you don’t know the population standard deviation.

Here we have the statement All else being equal, the further the t statistic falls from 0, either in the positive or negative direction, the more likely it is that the difference between two population averages is statistically significant.

And we need to identify whether the statement is true or not.

As per the definition of t statistics, we have identified that the t statistic falls from 0. which states that is goes on the negative direction.

Hence, the more likely it is that the difference between two population averages is statistically significant.

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Answer:

p=12345

Step-by-step explanation:

Answer:

  see attached

Step-by-step explanation:

You want the graphed triangle rotated 90° CW about the point (2, -1).

After rotation 90° CW, points will be as far to the south and west of the center of rotation as they are east and south in the original image. This is shown by the blue triangle in the attachment.

Answer:

2nd equation

Step-by-step explaination:

1st. -7≠-2(3)

2nd. Sastifies all

3rd. -10≠-3(4)

4th. -4≠-2(2)-3

Answer:

f(x) = ³√(x–1) + 4

f-¹(x) = (x + 1)³ + 4

Step-by-step explanation:

i hope this helped

Answer:

10) 1/2 lao per minute

11) 15 grams per serving

Step-by-step explanation:

10)

laps per minute

The laps are increasing by 1 as the minutes are increasing by 2

11)

The grams are increasing by 15 as the servings are increasing by 1

Therefore the solution of this question is Sam can draw 2 lines of reflection.

If a figure is reflected in a line or a point, the image and preimage are consistent. A reflection converts each point in a figure into an image along a predetermined line. Line of Reflection refers to the fixed line.

To determine the quantity of lines that will reflect a rectangle back onto itself.

Due to the fact that the line of reflection is the perpendicular bisector of the segment connecting a point with its image. The perpendicular bisector of a side must be the line of reflection if one side of the rectangle is to map to itself.

A rectangle has two distinct perpendicular bisectors of its sides, leading to two lines of reflection that map a rectangle to itself.

Therefore Sam can draw 2 lines of reflection.

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The solution for f(11) in the function when the function f(x) = 12|x + 8| is 228

From the question, we have the following equation that can be used in our computation:

f(x) = 12|x + 8|

The above equation is an absolute value equation

An absolute value equation has the following representation

f(x) = a|x - h| + k

So, we have the following representation

f(x) = 12|x + 8|

Also from the question, we have

f(11)

This means that the value of x is 11, and we calculate f(x) when x = 11

Substitute the known values in the above equation, so, we have the following representation

f(11) = 12|x + 8|

So, we have the following equation

f(11) = 12|11 + 8|

There are constants to add or subtract to both sides of the equation

Also, there are factors to multiply or divide from both sides of the equation

So, we have the following representation

f(11) = 12|19|

Solving further, we have

f(11) = 12 * 19

Evaluate the products

f(11) = 228

Hence, the solution is 228

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Answer:

9.1 units

Step-by-step explanation:

See diagram below ....using pythagorean theorem

Answer:

a) 15

b) 270

Step-by-step explanation:

a)

(√5)² = 5

(√3)² = 3

This is due to the square root and to the power of 2 cancelling each other out if that makes sense. It's the same with (√3)²

So all you're actually doing is 5 × 3 which is 15

b)

It's basically the same except (³√9)³ is cube(d) root and to the power of 3

(³√9)³ = 9

(√30)² = 30

So you do 9 × 30 = 270

:)

Answer: omg never seen somthing dat complex :O

Step-by-step explanation:

Answer:

28.27 sq. units or 9π sq.

Step-by-step explanation:

Answer:

Step-by-step explanation:

since $68 is your total, let's use the example z=y+x

z is our total, and we know that he made a total of $68, therefore z is the number 68.

We also know that James made a total of $48 washing cars, which gives us the answer 48 as y. So in order to find x, we would need to subtract 68 and 48, which is called using the communtative property. Thsi answer would give us the remaining amount of money we do not yet know.

So 68-48= 20. therefore James made $20 at the art contest.

Answer:

y = -2x - 4

Step-by-step explanation:

y = mx +b is the slope intercept form of a line.  The m is the slope and the b is the y intercept.

The y intercept is where the line crosses the y axis.  It crosses at the point (0,-4).  The -4 is where the line crosses the y axis.  It is the b.

The slope is the change in y over the change in x.  To go from point (0,-4) to the point (-2,0)  You go up 4 units and the left 2 units.  Up is positive and left is negative. 4/-2 which simplifies to -2.  This is your m.

A) The two solutions for the system are

tennis ball, t = 3.099 OR t = -7.099

rocket launch, t = 6

B) The solution that is not reasonable is the height of Antonio's rocket, The path traced is not a linear function

C) The rocket and the tennis ball reach same height at 2.32 s

The system of equation of the two motions are

b(t) = -t^2 - 4t + 22.

p(t) = -2t + 12

Solving the quadratic equation gives

b(t) = -t^2 - 4t + 22.

t = 3.099 OR t = -7.099

solution for the linear equation gives

t = 6

The solution that is  not reasonable in this situation is the linear equation

The linear equation because projectile motion do not follow linear part.

time to reach same height

-2t + 12 = -t^2 - 4t + 22.

-t^2 - 2t + 10

solving the equation gives

t = 2.3166 OR -4.3166

take the positive value

t = 2.32 s

time to reach same height is 2.32 s

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Answer:

8

Step-by-step explanation:

16 divided by 2 is 8.

Answer: 8 students

Step-by-step explanation: 16/2=8

Answer: it’s B

Step-by-step explanation: Look at the graph clearly

and you will see the value of x and y

The relationship between x, the number of month, and y, the height of the giraffe in feet is y = 6+0.5.

According to the question,

We have the following information:

A baby giraffe measures 6 feet tall when it is born and grow an average of 1/2 foot each month.

Now, x represents the number of months and y represents the height of the baby giraffe in feet.

Now, converting 1/2 from fraction into decimal form:

1/2 = 0.5 feet

Now, the equation to find the height of the giraffe will be given using the following equation;

y = 6+0.5x

Hence, the relationship between x, the number of month, and y, the height of the giraffe is y = 6+0.5.

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Answer:

16/5

Step-by-step explanation:

[tex]1\frac{1}{5}=\frac{6}{5} \\ \\ 2=\frac{10}{5} \\ \\ \frac{6}{5}+\frac{10}{5}=\frac{16}{5}[/tex]

Answer:

1 and 2 are functions, 3 is not a function.

Step-by-step explanation:

One x-value can lead to one y-value. If the x-value leads to more than one y-value like #3, then the relation is not a function.

If each input value leads to only one output value, classify the relationship as a function. If any input value leads to two or more outputs, do not classify the relationship as a function.

Answer: A

Step-by-step explanation:

The abscissa or x-coordinate of any point on Y-axis is zero.

Which line is the x-coordinate?

Two parallel lines, known as axes (pronounced AX-eez), that are perpendicular to each other make up a coordinate grid. Typically, the term "x-axis" refers to the horizontal axis. The y-axis is the common name for the vertical axis.

The ordinate and abscissa are other names for the x-axis and y-axis, respectively. These two axes can be used to find or represent any point on the coordinate plane as an ordered pair of the form (x,y).

The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept.

In order to represent the equation in y-intercept (y=mx+b) form, the slope and y-intercept must be included. The slope is the ratio of the y-to-x change. Draw a sloping triangle connecting the two spots you find on the line.

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The probability that at least one of the cubes will have the face labeled 5 showing and that the sum of the showing faces will be greater than 8 is 5/36.

A probability is a numerical representation of the possibility or chance that a specific event will take place. Probabilities can be written as percentage between 0 and 1.

Number of sample spaces that are labeled 5 and display a sum more than 8 / total sample space gives the likelihood that at least one of the cubes will have the face labeled 5 showing and that the sum of the faces showing will be greater than 8.

When two cubes are rolled, the total sample space is 36.

The sample space that is labelled 5 and has a sum greater than 5 are: (4,5) , (5, 4) , (5, 5), (5, 6) , (6,5) = 5

The probability = 5/36

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Answer:3/5

Step-by-step explanation:

(y2-y1)/(x2-x1)

(2-(-1))/(6-1)=3/5

The table is attached below.

What are table entries?

Entities are gathered at tables. A group of properties makes up an entity. Each object may contain up to 252 name-value pairs for its properties.

From the information given, we can make a table to display all the options available for Michael to choose clothing options.

The table is attached as follows:

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There are 12 clothing options for Michael to choose from in his closet. By the fundamental principle of counting, the possible number of options is calculated.

The fundamental principle of counting states that an operation/event can be performed in 'm' ways and a second operation/event can be performed in 'n' ways. Then there are (m × n) ways for the two operations to be performed together.

It is given that,

Michael is having three shirts - yellow, green, and orange; two pairs of shorts: navy, gray and two footwear: tennis shoes and sandals.

So, we can write

the number of shirts = 3

the number of shorts = 2

the number of footwear = 2

Then, according to the fundamental principle of counting, all these are multiplied to get the total number of ways that he can wear them together.

I.e., 3 × 2 × 2 = 12

Therefore, there are 12 combinations for him to choose one among these.

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The round-off of the number 4⁸/₉ will be 5. The correct option is C.

When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number. For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done.

A number can be rounded off to its lower value if the number after the decimal is between 0 and 4. The number will be rounded off to its higher value if the number after it is between 5 and 9.

The given number is 4⁸/₉. The round-off of the number will be done as,

4⁸/₉ = 4.88888888

The nearest number will be 5.

Therefore, the round-off of the number 4⁸/₉ will be 5. The correct option is C.

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