Which of the following functions is graphed below?

Answer:

Step-by-step explanation:

Given

y = x^2 + 10x + 21

Complete the square

y = x^2 + 10x + 21                           Put brackets around the first 2 terms

y = (x^2 + 10x) + 21                         Take 1/2(10) and square it. Add inside the brackets.

y = (x^2 + 10x + 5^2) + 21                 Subtract 5^2 after 21

y = (x^2 + 10x + 25) + 21 - 25          Make  (x^2 + 10x + 25) into a perfect square.

y = (x + 5)^2 - 4

Answer: (x + 5)^2 - 4

Answer:

    6000 in the 6th year    39000 total

Step-by-step explanation:

depreciates 200 per year

7000   6800   6600   6400   6200   6000  

answer:

[tex]\frac{-23}{6}[/tex] or -3.8333 (repeating)

Answer:

Exactly 1 solution

Step-by-step explanation:

The equations are both in slope intercept form: y=mx+b We can use the y-intercept and slope to identify points on each line.

The line given by the first equation y= 1x+1 has a y-intercept of (0, 1) and a slope of 1, so another point on that line is (0 + 1, 1 + 1)= (1, 2).

Now we have two points to graph this line. In a similar manner, we will find that the line given by y=2x-5 passes through (0, -5) and (0 + 1, -5 + 2)= (1, -3). We can use those lines to graph the points.

Upon graphing our system of equations, we see that the lines intersect exactly once.

Since the lines intersect exactly once, the system has exactly one solution.

The system of equation has exactly one solution.

Simultaneous equations are any equations with the same number of unknowns that may be solved at the same time. The system of equations is a simultaneous equation.

Given, the system of equation;

y = x+1                { equation 1}

y = 2x-5              { equation 2}

Subtracting equation 2 to equation 1;

2x-x = 5+1

x = 6

And y = 7

The solution set is (6,7).

Therefore, the system of equation has unique solution.

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Answer:

A. Square

Step-by-step explanation:

Hmm yes looks very much like a square if you ask me. This is right!!

Answer:addaddition

Step-by-step explanation:

just adddd all

Answer:

A) 13.5 Hours

B) 27 Hours

Step-by-step explanation:

So the total journey was 54 hours.

5/8 of that would be 33 and 3/4 hours or how long the airplane journey was.

1/4 would be 13 and a half hours or how long the train journey was

And the remaing amount was the 6 3/4 hours which was the bus journey

So the answers are Fu Da spent 13 and a half hours on the train journey and he spent 27 more hours on the plane than the bus

Answer:

Jake has 144 cookies.

Step-by-step explanation:
Let's say Clementine is x.

Clementine: x
Jake: 2x

Now, let's substitute x with 72 since the number is given.

This means that Jake has 72 * 2 cookies which are 144.

Answer:

The last one {14,15,16,20,22,25, and 51}

Step-by-step explanation:

This set shows an outlier because 51 is a huge jump from 25 which causes it to be the outlier.

The data set {14,15,16,20,22,25,51} contains an outlier. So, option D is correct.

Option A:

{30, 31, 31, 32, 34, 37}

There is an even number of data points.

Diving into 2 groups- {30,31,31} and {32,34,37}

So, [tex]Q_1[/tex]=31 and [tex]Q_3[/tex]=34

Then [tex]Q_3[/tex] - [tex]Q_1[/tex]=34-31=3

Then 1.5×3=4.5

[tex]Q_1[/tex]-4.5=31-4.5=26.5

[tex]Q_3[/tex]+4.5=34+4.5=38.5

So, for this data set, there are no outliers either below or above.

Option B:

{11,12,12,12,13,13,14,14}

There is an even number of data points.

Diving into 2 groups- {11,12,12,12} and {13,13,14,14}

So, [tex]Q_1[/tex]=[tex]\frac{12+12}{2}=12[/tex] and [tex]Q_3[/tex]=[tex]\frac{13+14}{2}=13.5[/tex]

Then [tex]Q_3[/tex] - [tex]Q_1[/tex]=13.5-12=1.5

Then 1.5×1.5=2.25

[tex]Q_1[/tex]-2.25=12-2.25=9.75

[tex]Q_3[/tex]+2.25=13.5+2.25=15.75

So, for this data set, there are no outliers either below or above.

Option C:

{6.1,6.8,7.3,8,9.1,9.5}

There is an even number of data points.

Diving into 2 groups- {6.1,6.8,7.3} and {8,9.1,9.5}

So, [tex]Q_1[/tex]=6.8 and [tex]Q_3[/tex]=9.1

Then [tex]Q_3[/tex] - [tex]Q_1[/tex]=9.1-6.8=2.3

Then 1.5×2.3=3.45

[tex]Q_1[/tex]-3.45=6.8-3.45=3.35

[tex]Q_3[/tex]+3.45=9.1+3.45=12.55

So, for this data set, there are no outliers either below or above.

Option D:

{14,15,16,20,22,25,51}

There is an odd number of data points.

Diving into 2 groups- {14,15,16,20} and {20,22,25,51}

So, [tex]Q_1[/tex]=[tex]\frac{15+16}{2}=15.5[/tex] and [tex]Q_3[/tex]=[tex]\frac{22+25}{2}=23.5[/tex]

Then [tex]Q_3[/tex] - [tex]Q_1[/tex]=23.5-15.5=8

Then 1.5×8=12

[tex]Q_1[/tex]-8=15.5-8=3.5

[tex]Q_3[/tex]+8=23.5+8=35.5

In this data set, some values are above the value of 35.5 (35.5<51).

So, this data set is said to have outliers.

Therefore, Option D is correct.

The required data set is {14,15,16,20,22,25,51}.

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Step 1: Plotting the Point

Make a polar coordinate system.

It looks like this ( look at the first photo)

Step 2: Graph the polar function

r=10.

Here since our first coordinate is 10, our radius of our point will be 10.

This basically means we will have a circle with a radius of 10. ( look at the second photo).

Step 3: Look for the angle pi/3,

So that how u graph polar coordinates.

Next, a polar form can have multiple representations.

a. Here we want a radius of to be positve, so our r will stay 10.

We want our angle to lie between 2 pi and 4 pi.

So we just add 2 pi to pi/3.

[tex] \frac{\pi}{3} + 2\pi = \frac{\pi}{3} + \frac{6\pi}{3} = \frac{7\pi}{3} [/tex]

So another angle is

[tex](10, \frac{7\pi}{3} )[/tex]

B. We want r to be negative so

[tex]10( - 1) = - 10[/tex]

And we want our angle to be in between 0 and 2 pi. so we add pi to our angle.

[tex] \frac{\pi}{3} + \pi = \frac{\pi}{3} + \frac{3\pi}{3} = \frac{4\pi}{3} [/tex]

So our new representation is

[tex]( - 10, \frac{4\pi}{3} )[/tex]

C. Finally, we want our r to be positvr and our angle to be negative and in between -2pi and 0.

So we just subtract 2 pi.

[tex] \frac{\pi}{3} - 2\pi = \frac{\pi}{3} - \frac{6\pi}{3} = - \frac{5\pi}{3} [/tex]

So our new representation is

[tex](10, - \frac{5\pi}{3}) [/tex]

Answer:

The anser is B

Step-by-step explanation:

There are twice as many silver cars as blue cars

12 x 2 = 24       24 / 12 = 2

Answer:

A: Use these points to plot the shapes reflection (-3,4) (-3,6) (-5,6) (-7,4)

B: The transformation would be described as a reflection over the y axis

C:  The transformation does result in a congruent figure because the shape doesn't change in size or shape and in length or width

Step-by-step explanation:

So our plots from the figure are: (3,4)  (3,6)  (5,6)  (7,4)

This rule (x, y) → (-x, y) is used for the type of transformation that is a reflection but over the y axis.

So using the rule (x, y) → (-x, y) are new points would be:

(-3,4)

(-3,6)

(-5,6)

(-7,4)

Answer:

Id say D but im noot 100% positive so im sorry if its wrong

Step-by-step explanation:

Answer:

$14.00

Step-by-step explanation:

First you round 3.75 to 4.00 because 7 is greater than 5 so it would turn the 3 to 4 than add the zeros it's 4.00. Second You multiply by three so 4.00 × 3 you will get 12.00. Than you round 1.89 to 2.00 because 8 is greater than 5 so it would turn to the 1 to the 2 than add the zeros it's 2.00. Finally you add them together and get $14.00

The volume of the rectangular prism is the number of cubes in it

The calculated volumes of the rectangular prisms are 32 and 36 unit cubes, respectively.

The volume of a rectangular prism is:

Volume = Length * Width * Height

From the question, we have the following prisms:

So, the volumes are:

Volume= 4 * 4 * 2

Volume= 32

Volume= 3 * 4 * 3

Volume= 36

Hence, the volumes of the rectangular prisms are 32 and 36 unit cubes, respectively.

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Answer:

c > 9

Step by Step explanation

Answer:

4.4 degrees C.

Step-by-step explanation:

C = 5/9 (F - 32)

When F = 40:

C = 5/9( 40 - 32)

= 5/9 * 8

= 40/9

= 4.4 degrees C,

Answer:

B

Step-by-step explanation:

As stated in the problem x is the number of hours that he works.

x = 6y

All of the other answers establish y as 6, but B is the only answer that has 6 Infront of y (Pretty much multiplying it)

If you were to plug 6 into Y you would get 6(6)

6 times 6 equals thirty six.

x ≠ 36

The type of toy the kids enjoyed the most is the doll.

The total number of kids evaluated = 80

The percentage of kids that like train = 30%

The percentage of kids that like doll = 70%

30% of 80 = 30/100×80

= 2400/100

= 24

70% of 80 = 70/100×80

= 5600/100

= 56

Therefore, the type of toy the kids enjoyed the most is the doll.

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Answer:

Each of them would sell four items.

Step-by-step explanation:

Tom - 15+3+3+3+3= $27

His sister - 7+5+5+5+5= $27

Answer:

[tex]165[/tex].

Step-by-step explanation:

Since repetition isn't allowed, there would be [tex]11[/tex] choices for the first donut, [tex](11 - 1) = 10[/tex] choices for the second donut, and [tex](11 - 2) = 9[/tex] choices for the third donut. If the order in which donuts are placed in the bag matters, there would be [tex]11 \times 10 \times 9[/tex] unique ways to choose a bag of these donuts.

In practice, donuts in the bag are mixed, and the ordering of donuts doesn't matter. The same way of counting would then count every possible mix of three donuts type [tex]3 \times 2 \times 1 = 6[/tex] times.

For example, if a bag includes donut of type [tex]x[/tex], [tex]y[/tex], and [tex]z[/tex], the count [tex]11 \times 10 \times 9[/tex] would include the following [tex]3 \times 2 \times 1[/tex] arrangements:

Thus, when the order of donuts in the bag doesn't matter, it would be necessary to divide the count [tex]11 \times 10 \times 9[/tex] by [tex]3 \times 2 \times 1 = 6[/tex] to find the actual number of donut combinations:

[tex]\begin{aligned} \frac{11 \times 10 \times 9}{3 \times 2 \times 1} = 165\end{aligned}[/tex].

Using combinatorics notations, the answer to this question is the same as the number of ways to choose an unordered set of [tex]3[/tex] objects from a set of [tex]11[/tex] distinct objects:

[tex]\begin{aligned}\begin{pmatrix}11 \\ 3\end{pmatrix} &= \frac{11 !}{(11 - 3)! \times 3 !} \\ &= \frac{11 !}{8 ! \times 3 !} \\ &= \frac{11 \times 10 \times 9}{3 \times 2 \times 1} = 165\end{aligned}[/tex].

There are 6 letters, hence 6! = 720 total permutations of BUBBLE. But there are 3 indistinguishable copies of B, so we divide by the number of ways we can rearrange them, 3! = 6. Then there are

6!/3! = 720/6 = 120

distinguishable permutations of BUBBLE.

A) Isosceles

E) Obtuse

Ways to Define a Triangle

Triangles can be defined in two ways: by angles and by sides. Equilateral, isosceles, and scalene are based on side length. Acute, right, and obtuse are based on angle measurements. Triangle may only fall under one category for side length and one for angle measure (2 categories total).

Side Length

First, let's define equilateral, isosceles, and scalene.

The triangle above has 2 congruent sides as shown by the tick marks on the left and right sides. This means the triangle is isosceles.

Angle Measurements

Now, let's define acute, right, and obtuse.

The largest angle in the triangle is 98 degrees, which is obtuse. This means that the triangle is obtuse.

Answer:

  f(3) = -20

Step-by-step explanation:

To find the value of a function, substitute the number for the variable and do the arithmetic.

  f(x) = -2x^2 +x -5 . . . . . . given

  f(3) = -2(3^2) +(3) -5 . . . . function value for x = 3

  f(3) = -2(9) +3 -5 = -18 +3 -5

  f(3) = -20

Answer:

4.4%

Step-by-step explanation:

The overall probability is the product of the individual probabilities.

Total number of marbles: 15

Original number of blue marbles: 6

First drawing (6 blue and 15 total):

p(blue) = 6/15 = 2/5

Second drawing (5 blue and 14 total):

p(blue) = 5/14

Third drawing (4 blue and 13 total):

p(blue) = 4/13

p(blue followed by blue followed by blue) = 2/5 × 5/14 × 4/13 = 40/910 = 4/91

p(blue followed by blue followed by blue) = 4/91 = 0.043956... = 4.4%

Answer:

All three sides and angles are different in measurement.

Step-by-step explanation:

Answer:14

Step-by-step explanation: i did the math probly wrong but i made an educated guess