8.2 end of unit assessment Triangle ABC and DEF are similar

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 probability that the last passenger end up in his/her assigned seats is 0.20.

In the given question, there are 6 people in line to board a plane with 6 seats.

The first person has lost his boarding pass, so he takes a random seat.

Everyone that follows takes their assigned seat if it's available, but otherwise takes a random unoccupied seat.

We have to find the probability the last passenger ends up in his/her assigned seat.

Given 6 people with 6 Seats.

The probability that the last passenger end up in his/her assigned seats = 1/5

The probability that the last passenger end up in his/her assigned seats = 0.20.

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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:

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

The area of the new parallelogram is A = n²bh

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

b = base of the original parallelogram.

h = height of the original parallelogram.

n = Factor of the products

The area of a parallelogram from the base and the height is calculated as

A = bh

In this case, we have

Each dimension of a parallelogram is multiplied by a positive number n.

This means that

Base = bn

Height = hn

So, we have

Area = bn * hn

Evaluate

A = n²bh

Hence, the area expression is A = n²bh

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Answer: it’s B

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

and you will see the value of x and y

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:

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:

x = -3, y = 28

Step-by-step explanation:

-5x + y = 13

y = 13+5x

-3x+3(13+5x)=3 substitute

-3x + 39 + 15x = 3

12x + 39 = 3

12x = -36

x = -3

-5(-3) + y = 13 substitute into -5x+y=13

15 + y = 13

y = 28

Answer: omg never seen somthing dat complex :O

Step-by-step explanation:

The probability of the two fair six sided dice thrown together and getting sum of shown numbers to 7 is equal to ( 1/ 7).

As given in the question,

Number of times both 6-sided fair dice rolled out = 2

Dice is numbered from 1 to 6

As both the dice rolled together order does not matter

Total possible outcomes are:

= { ( 1,1 ), (1,2) , (1,3),(1,4), (1,5), 1,6), (2,2), (2,3),(2,4),(2,5), (2,6), (3,3),(3,4), (3,5) ,(3,6), (4,4), (4,5), (4,6), (5,5), (5,6), (6,6) }

Total number of outcomes = 21

Dice shows sum of numbers to 7 are

= {(1,6), (2,5), (3,4), }

Number of favourable outcomes = 3

Probability of the thrown dice sum shows number 7

= (Number of favourable outcomes)/ (Total number of outcomes)

= 3 /21

= 1 / 7

Therefore, probability of the two six sided dice thrown together and show sum of numbers to 7 is equal to (1/7).

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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 answer to this Question based on angles is described below

What is Angle?

It is a measure of how much an ray has turned clockwise or anticlockwise.

wrt to a stationary fixed arc

Solution:

First we need to find A4

A2 is given as 131 hence G is also 131 by Vertically Opposite angles

And A and G are equal as Corresponding angles

Now we need A13 it will be same as A7 which is 74 by Alternate Angles

Now we need A9

we can see A9 + A13 = A7 + A6

A9 + 74 = A4

A9 + 74 = 131

A9 = 57

For A17

A17 + A9 + A13 = 180

A17 + 131 = 180

A17 = 49

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When the arc's area is 24 square feet and its radius is 12 feet, the arc's length is 36.56 feet.

An arc is a section of a circle's or curve's border in mathematics. It is additionally known as an open curve. The circumference, commonly referred to as the perimeter, is the measurement around a circle that defines its edge. A sector is referred to as a component of a circle made up of the circle's arc and its two radii. It is a section of the circle made up of the arc's circumference and the radii of the circle at its ends. A slice of pizza or a pie can be used as an analogy for the form of a circle's sector.

Here,

area of sector=24π ft²

radius of sector=12 ft

area=θ/360*Π*12²

24π=θ/360*Π*12²

2=θ/360*12

2*360/12=θ

θ=60°

length of arc=2r+θ/360*(2Πr)

=2*12+60/360(2*3.14*12)

=24+2*2*3.14

length of arc=36.56 ft

The measure of arc is 36.56 feet when the area of arc is 24π feet² and it has the radius of 12 feet.

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The value of x from given exponential equation is 6 / 23. An equation with exponents is called an exponential equation if one of the exponents is a variable.

The mathematical expression f(x)=exp or ex denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras.

When the input variable x appears as an exponent in the formula f(x) = axe, an exponential function is indicated. The exponential curve is influenced by both the exponential function and the value of x.

Exponential growth and decay are the two different kinds of exponential functions.

23x = 6

Divide both sides by the same factor

23x /23 =6 /23

Simplify

x = 6/ 23

The value of x = 6 /23

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Answer:

Step-by-step explanation: why do I have a code to go for a walk in a few weeks to see what you are looking at and see what we can see when we can see how much we will be in our room for a few weeks to get the rest of the stuff done and we can make a new change of the time for you guys and we will miss it it is a great time for us and I will keep you posted if I need your assistance and help with the help for me am 11 sorry

Mommy mommy daddy mommy bye bye daddy daddy mommy daddy daddy bye daddy mommy daddy daddy love mommy mommy daddy mommy bye bye daddy daddy mommy daddy daddy bye daddy mommy daddy daddy love mommy mommy daddy mommy bye bye daddy daddy mommy daddy daddy bye daddy mommy

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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When a triangle rotated 180 degree counterclockwise, the new coordinates of the triangle would be (3,-1) (-2,-4) and (-5,3)

We know that if we rotate a point P(x, y) with 180 degrees counterclockwise about the origin then the translated point would be P'(-x,-y).

A given triangle having vertice at (-3,1) (2,4) and (5,-3) is rotated 180 degree counterclockwise.

We need to find the coordinates of the rotated triangle.

(-3,1) -> (3, -1)

(2,4) -> (-2, -4)

and (5,-3) -> (-5, 3)

Therefore, after rotation the triangle would have coordinates (3,-1) (-2,-4) and (-5,3)

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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:

x=2,y=−5

Step-by-step explanation:

Answer:

16.) The solution to this inequality is x < -4 or x > -3.

17.) To solve for b, we need to isolate b on one side of the equation. To do this, we can subtract ab from both sides of the equation, which gives us xy = cd - ab. Then, we can divide both sides of the equation by xy, which gives us b = (cd - ab)/xy.

18.) To solve for a, we need to isolate a on one side of the equation. To do this, we can divide both sides of the equation by 3, which gives us a - b = 3mn. Then, we can add b to both sides of the equation, which gives us a = b + 3mn.

19.) To factor this expression, we first distribute the 3x2 to get 3x2y - 6x2. Then, we notice that the 3x2 and the -6x2 have a common factor of -3x2, so we can factor them out to get -3x2(y - 2) - 5(y - 2). Finally, we notice that the -3x2(y - 2) and the -5(y - 2) have a common factor of -(y - 2), so we can factor them out to get -(y - 2)(3x2 - 5).

20.) To factor this expression, we notice that the kmfd and the -3jkm have a common factor of -jkm, so we can factor them out to get -jkm(f - 3).

21.) To factor this expression, we notice that 49 is a perfect square, so we can write 49 as 72. Then, we can factor out the x from the x2 to get 7x(x - 9).

22.) To factor this expression, we notice that 64 is a perfect square, so we can write 64 as 82. Then, we can factor out the x from the x2 to get 8x(x + y).

23.) To factor this expression, we notice that the x2 and the -35 have a common factor of x - 5, so we can factor them out to get (x - 5)(x + 7).

24.) To factor this expression, we notice that the 2x2 and the 14 have a common factor of 2, so we can factor them out to get 2(x2 + 11x + 7). Then, we notice that the x2 and the 7 have a common factor of x + 1, so we can factor them out to get 2(x + 1)(x + 7).

25.) To factor this expression, we notice that the x2 and the -63 have a common factor of x + 9, so we can factor them out to get (x + 9)(x - 7).

26.) To factor this expression, we notice that the 3x2 and the 7 have a common factor of 3x + 7, so we can factor them out to get 3(x + 1)(x - 2).

We reject the null hypothesis of the given sample data below.

A type of statistical hypothesis known as a "null hypothesis" makes the case that a given set of observations does not have any statistical significance. Using sample data, hypothesis testing is used to determine a hypothesis's credibility. It is represented as H0, and it is sometimes referred to as the "null."

it is given that,

P value=0.0045

Thus, alpha = 0.02

At the point when P esteem is not exactly or equivalent to the importance level, then reject the null hypothesis.

Here p esteem is not as much as the importance level then reject the null hypothesis H0.

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Answer:

2nd equation

Step-by-step explaination:

1st. -7≠-2(3)

2nd. Sastifies all

3rd. -10≠-3(4)

4th. -4≠-2(2)-3

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:

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: A

Step-by-step explanation:

The number of kilograms of carbon dioxide a person exhale each minute is [tex]0.625\times10^{-3}[/tex] .

Given that, a person exhales about [tex]1.25\times10^{-5}[/tex] kilogram of carbon dioxide in [tex]2\times10^{-2}[/tex] minute.

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as  [tex]1.57\times10^7[/tex].

Here,

Number of kilograms of carbon dioxide a person exhale each minute = Weight of carbon dioxide/Number of minutes

= [tex]\frac{1.25\times10^{-5}}{2\times10^{-2}}[/tex]

= [tex]0.625\times10^{-3}[/tex]

Therefore, the number of kilograms of carbon dioxide a person exhale each minute is [tex]0.625\times10^{-3}[/tex] .

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The equation for the first website is y = 5x + 15.

Two or more expressions with an equal sign are defined as an equation.

Given that, the website (1) charges a yearly fee of $15 and $5 for each download.

Therefore, the total cost, y, for x downloads is given by:
y = 15 + 5x

Or, y = 5x + 15

Hence, the equation for the first website is y = 5x + 15.

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Answer:3/5

Step-by-step explanation:

(y2-y1)/(x2-x1)

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

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.