Piece wise functions

#a

V={Vowels of English alphabets}

#b

C={cube numbers between 0 to 50}

#c

M={y:y is a multiple of 3 less than 20}

The rate of the plane in still air is 870km/h and the rate of the wind 210km/h.

Speed has the dimensions of distance divided by time.

Let Speed of airplane be x km/h and Speed of Wind be y km/h

Speed direction of wind (x+y)

Speed in opposition of wind (x-y)

Now, using speed x time= distance

7( x-y)=4620

(x-y)=4620/7

=660------------------(1)

Similarly,

8(x+y)=8640

(x+y) =8640/8=1080-----------------------(2)

Adding (1) and (2)

2x=1740

x=870 km/h

Subtracting (1) from (2)

2y=420

=>y=210 km/h

So rate of airplane =870km/h

rate of wind=210km/h

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Work Shown:

yz = y(x^2+2x-5)

yz = y(x^2) + y(2x) + y(-5)

yz = x^2( y ) + 2x( y ) - 5( y )

yz = x^2( 3x+5 ) + 2x( 3x+5 ) - 5( 3x+5 )

yz = x^2*3x + x^2*5 + 2x*3x + 2x*5 - 5*3x - 5*5

yz = 3x^3 + 5x^2 + 6x^2 + 10x - 15x - 25

yz = 3x^3 + 11x^2 - 5x - 25

The volume of the bottom section of the figure is:

V = 48 cm³

Remember that for a rectangular prism of length L, width W, and height H, the volume is V.

V = L*W*H

For the bottom section the dimensions are:

Length = 6cm

Width = 4cm

Height = 4cm - 2cm = 2cm

Replacing these in the volume equation we get:

V = (6cm)*(4cm)*(2cm) = 48cm³

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Answer:

Step-by-step explanation:That’s t up to you STOP CHEATING!!

Answer:

Step-by-step explanation:

this year you earned $75500. Last year you earned $72400. What the rate of change on your earnings since last y?

Answer:

22045278

Step-by-step explanation:

               5  8  2  9

                3  7  8  2

               11  6  5  8

        4  6  6  3  2  0

    4  0  8  0  3  0  0

 1  7  4  8  7  0  0  0        

2  2  0  4  5  2  7  8

Answer:

22045278

Step-by-step explanation:

It seems tricky, but if you break it down step by step it will make it a lot easier.

Hope it helped and you can do it!!

Answer:

6 23/25

Step-by-step explanation:

[tex]0.92\\\\\frac{0.92\cdot \:100}{100}\\\\=\frac{92}{100}\\\\= \frac{4\cdot \:23}{4\cdot \:25}\\\\=\frac{23}{25}\\\\= 6+\frac{23}{25}\\\\=6\frac{23}{25}[/tex]

Let S be the given sum, so

[tex]S = 8 + 8 \left(\dfrac14\right) + 8 \left(\dfrac14\right)^2 + \cdots + 8 \left(\dfrac14\right)^9[/tex]

[tex]\displaystyle S = 8 \left(1 + \dfrac14 + \frac1{4^2} + \cdots + \frac1{4^9}\right)[/tex]

Multiply both sides by 1/4.

[tex]\displaystyle \frac S4 = 8 \left(\frac14 + \frac1{4^2} + \frac1{4^3} + \cdots + \frac1{4^{10}}\right)[/tex]

Subtract this from S to eliminate all the but the first term in S and the last term in S/4 :

[tex]\displaystyle S - \frac S4 = 8 \left(1 - \frac1{4^{10}}\right)[/tex]

Solve for S :

[tex]\displaystyle \frac{3S}4 = 8 \left(1 - \frac1{4^{10}}\right)[/tex]

[tex]\displaystyle S = \frac{32}3 \left(1 - \frac1{4^{10}}\right) = \boxed{\frac{349,525}{32,768}}[/tex]

Answer:

D.

Step-by-step explanation:

If you look at the pattern, the first shape (square) has four sides. Then, you have 5 sides, and finally, 6 sides.

Thus, a pattern of 4, 5, 6. So, the next shape must have 7 sides, leaving the only possible answer as D.

Answer:

A. 12 + (negative 9)

Step-by-step explanation:

8 + 4 - 9 = 3

12 - 9 = 3

-12 + 9 = -3

-4 - 9 = -13

4 - 9 = -5

this means that 8 + 4 - 9 = 12 - 9

making A the right expression

Answer:

J

Step-by-step explanation:

To find perimeter we add. 10+6 is 16. The third side has to be much bigger than this. So, J is the answer and J is 19 which wouldnt make sense as the length of the third side.

In this situation, attendee number thirty will be the first one o receive both the bobblehead and the ticket.

Bobblehead:

Ticket:

It can be concluded the attendee number 30 will be the first one to receive both the ticket and the bobblehead.

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Answer:

My sister is doing this, I if remember correctly graph B?

[tex]\dfrac{n(n-3)}{2}=44\\\\n(n-3)=88\\n^2-3n-88=0\\n^2+8n-11n-88=0\\n(n+8)-11(n+8)=0\\(n-11)(n+8)=0\\n=11 \vee n=-8[/tex]

Therefore, the number of sides is 11.

Using the information in the diagram, the measure of [tex]\overset{\LARGE\frown}{CD}[/tex] is 89.0°

From the question, we are to determine the measure of [tex]\overset{\LARGE\frown}{CD}[/tex]

Consider the right triangle

The measure of [tex]\overset{\LARGE\frown}{CD}[/tex] is twice the measure of the unknown angle

Let the unknown angle in the right triangle be x

∴ The measure of [tex]\overset{\LARGE\frown}{CD}[/tex] = 2x

Then,

x + 90° + 45.5° = 180° (Sum of angles in a triangle)

x = 180° - 90° - 45.5°

x = 44.5°

Thus,

The measure of [tex]\overset{\LARGE\frown}{CD}[/tex] = 2×44.5°

The measure of [tex]\overset{\LARGE\frown}{CD}[/tex] = 89°

Hence, the measure of [tex]\overset{\LARGE\frown}{CD}[/tex] is 89.0°

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I predict that the solid with the  greater surface area to volume ratio would be the cube.

The volume of the cube is 27in³

The surface area of the cube is

The ratio of surface area to volume for the cube is 2.

The volume of the sphere is 113.14 in³

The surface area of the sphere is 113.14 in²

The ratio of surface area to volume is 1.

The volume of a cube = side length³

3³ = 27 in³

The surface area of a cube = 6a²

a = side length

6 x (3²) = 54 inches²

Ratio of surface area to volume = 54 / 27 = 2

The volume of the sphere= 4/3πr³

4/3 x 22/7 x 3³ = 113.14 in³

The surface area of the sphere = 4πr²

4 x 22/7 x 3² = 113.14 in²

Ratio of surface area to volume = 113.14 / 113.14 = 1

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Answer and explanation:

vertex: (3,25) The vertex is the minimum/maximum of a parabola where the direction it's moving in changes. For this question, that point is (3,25).

zeroes: x=6 and x=0 The zeroes of an equation are the points that y=0. Since it doesn't look like they want the full coordinate points, I would list x=6 for the point (6,0) and x=0 for the point (0,0).

y-intercept: x=0 The y-intercept is the point at which the graph crosses the y-axis, which here happens at (0,0), or x=0.

Highest point: 25 The highest point is the maximum of the graph, meaning it's the highest y-value that the graph has. Here, this is 25 (it's also the y-value for the vertex).

Time: 3 seconds The time it takes for Simon to reach the highest point is just the x-value of the vertex, so 3.

Total air time: 6 seconds This value is the total time that the y-value of the graph is above 0. To find this, you must subtract the x-values of the zeroes from each other. Since 6-0=0, Simon is in the air for 6 total seconds.

Hope this helps! :)

A fraction is a way to describe a part of a whole. The fraction that can replace the question mark is 1/2.

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

The fraction that can replace the question mark is,

9 × ? = (3/2) + (3/2) + (3/2)

9 × ? = 3(3/2)

9 × ? = 9/2

9 × ? = 9/2

? = 9/(2×9)

? = 1/2

Hence, the fraction that can replace the question mark is 1/2.

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Answer:

-5 degrees is colder than -3 degrees farienheight.

Step-by-step explanation:

Let's take this and eliminate every answer-

"The lowest temperature is -3 degrees."

-5 is lower than -3.

"The highest temperature is -5 degrees."

-5 degrees is the lowest temperature, not the highest!

"-5 is warmer than 3 degrees."

-5 is the LOWEST TEMPERATURE.

This leaves us with "-5 is colder than -3 degrees," which is correct because -5 is the smallest temperature and therefore, it is the coldest.

#1

#2

Answer:

1. x < 2.5

2. x > 2.5

Step-by-step explanation:

Question 1

Given inequality:

-4x + 5 > -5

Subtract 5 from both sides:

⇒ -4x + 5 - 5 > -5 - 5

⇒ -4x > -10

Divide both sides by -4 (remembering to flip the sign as we are dividing by a negative):

⇒ -4x ÷ -4 > -10 ÷ -4

⇒ x < 2.5

Question 2

Given inequality:

-25 > -5(x + 2.5)

Expand the brackets:

⇒ -25 > -5x - 12.5

Add 12.5 to both sides:

⇒ -25 + 12.5 > -5x - 12.5 + 12.5

⇒ -12.5 > -5x

Divide both sides by -5 (remembering to flip the sign as we are dividing by a negative):

⇒ -12.5 ÷ -5 > -5x ÷ -5

⇒ 2.5 < x

⇒ x > 2.5

The value of x in both case is 17 and 10.

If the sum of two angles is 180 degrees then they are said to be b angles, which form a linear angle together. Whereas if the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right angle together.

1. As the given angle is 90 degree i.e., complementary angle.

So,

 22+4x=90

  4x= 90-22

  4x= 68

    x= 17

2. As the figure for the linear pair i.e., supplementary angle

So,

110+7x=180

7x=70

x=10

Hence the value of x in both case is 17 and 10.

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In trapezoid ABCD ,length of AB is equals to 8.4units(nearest tenth).

" Trapezoid is defined as the quadrilateral whose one pair of opposite side is parallel."

According to the question,

Given

Length of AE=5.2

Length of  AC=11.7

Length of  CD=10.5

As shown in figure

In trapezoid ABCD,

AB is parallel to CD, AC is the transversal.

AC and BD intersect at point E.

In ΔABE and ΔCDE,

∠BAE ≅∠ECD

∠ABE ≅∠EDC

By AA theorem,

ΔABE ~ ΔCDE

Therefore,

[tex]\frac{AE}{EC}=\frac{AB}{CD}[/tex]

  AE + EC = AC

⇒ 5.2 + EC = 11.7

⇒ EC = 11.7 - 5.2

⇒ EC = 6.5units

Substitute the value in the given proportion we get,

   [tex]\frac{5.2}{6.5}=\frac{AB}{10.5}[/tex]

⇒ [tex]AB = \frac{(10.5)(5.2)}{6.5}[/tex]

⇒[tex]AB = 8.4[/tex] units

Hence, in trapezoid ABCD ,length of AB is equals to 8.4units(nearest tenth).

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B postulates and C axioms are accepted without proof in a logical system.

A theorem is a statement that can be proven true using standard mathematical operations and reasoning. A theorem, in general, is an embodiment of a general principle that is part of a larger theory. A proof is the process of demonstrating that a theorem is correct.

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Answer:

11

Step-by-step explanation:

2x-13=9

2x=9+13

2x=22

x=11

Answer:

432

Step-by-step explanation:

To find the volume of a rectangular prism  you multiply, L × W × H

    L = 6     W = 8    H =9  you plug that in  6 × 8 × 9= 432

     so the volume is 432in²

The best type of chart for quickly deriving the mode of a sample data is called the Stem-and-Leaf Plot.

In statistics, the Stem-and-Leaf Plot is an easy-to-make easy-to-read kind of graph that is derived from the table holding the sample data.

The Box-and-Whisker Plot on the other hand is best for visually depicting the five-number summary of any set of data, which are:

It is to be noted that referenced plots are not indicated hence, the general answer.

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The best type of chart for quickly deriving the mode of a sample data is called the Stem-and-Leaf Plot.

What is a Stem-and-Leap Plot?

In statistics, the Stem-and-Leaf Plot is an easy-to-make easy-to-read kind of graph that is derived from the table holding the sample data.

The Box-and-Whisker Plot on the other hand is best for visually depicting the five-number summary of any set of data, which are:

Minimum

First Quartile

Median (Second Quartile)

Third Quartile; and

Maximum.

It is to be noted that referenced plots are not indicated hence, the general answer.

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The balloon’s vertical distance above the ground is 721.7 f

In order to determine the balloon's vertical distance, we will use the SOH CAH TOA identity

Given the following parameters

Angle of depression = 30 degrees

Horizontal distance =1250 feet

Required

vertical distance H

Using the SOH CAH TOA identity

tan 30 = H/1250

H = 1250tan30
H = 721.7 feet

Hence the balloon’s vertical distance above the ground is 721.7 feet

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Answer:

721.7                                          

Step-by-step explanation:

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

4|3x-1| + 3 > 11

4|3x-1| > 11-3

4|3x-1| > 8

|3x-1| > 2

3x-1>2 or 3x-1<-2

3x>2+1 3x<-2+1

3x>3 3x<-1

x>1 x<-1÷3

Solution: ]-♾️ , -1÷3 [ U ] 1,+♾️ [

The limit of [tex]\lim_{x \to -3}\sqrt{ x^2-8}[/tex] as x approaches negative 3 is 1

The limit of the function given in question can also be written as:

[tex]\lim_{x \to -3}\sqrt{ x^2-8}[/tex]

To determine the required limit, we will simply substitute the value of x into the function as shown:

[tex]\lim_{x \to -3}\sqrt{ x^2-8}=\sqrt{ (-3)^2-8}\\\lim_{x \to -3}\sqrt{ x^2-8}=\sqrt{9-8}=1\\[/tex]

Hence the limit of [tex]\lim_{x \to -3}\sqrt{ x^2-8}[/tex] as x approaches negative 3 is 1

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Answer: the answer is b. 1

Step-by-step explanation: just got it right on edge