choose the correct expression to represent the piecewise-defined function? ​

ANSWER

[tex] \sum _{n = 1} ^{6} 2n[/tex]

EXPLANATION

The series is:

2 + 4 + 6 + 8 + 10 + 12

The first term is:

f(1)=2

The common difference is

[tex]d= 4 - 2 = 2[/tex]

The formula for the corresponding sequence is

[tex]f(n) = 2 + 2(n - 1)[/tex]

[tex]f(n) = 2 + 2n - 2[/tex]

[tex]f(n) = 2n[/tex]

The summation notation is:

[tex] \sum _{n = 1} ^{6} 2n[/tex]

Since there is no number line below I’m going to do this.

_________ __________ __________

Just split it into three ,’:b

The two tangent lines for each circle are the same length. Set the equations to equal and solve for x.

1. 4x + 3 = 3x +12

Subtract 3x from each side:

x +3 = 12

Subtract 3 from both sides:

x = 9

2. -2 + x = 2x -7

Subtract 2x from both sides:

-2 - x =  -7

Add 2 to each side:

-x = -5

Multiply both sides by -1:

x = 5

The value of x for both the circles is 9  and 5 .

A tangent for a circle is defined as a straight line which touches the circle at just one point.

The tangent is perpendicular to the radius of the circle at the point of where tangent touches the circle.

It is given in the question to find the value of x

When two tangents meet at a point C , the distance between the point of tangency and the point C is equal for both the tangent.

Therefore for the given circle

For first circle to solve for x , we will equate the two distances

4x + 3 = 3x +12

x +3 = 12

x = 9

-2 + x = 2x -7

-2 - x =  -7

-x = -5

x = 5

Therefore the value of x for both the circles is 9  and 5 .

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It’s a great way to write numbers that are very big numbers or very small numbers.

Have a great day!

Answer: Damien lived in his apartment longer.

Step-by-step explanation: Damien lived in his apartment longer because if you convert five years into weeks you get 260 weeks. 260 weeks is greater than 250 weeks.

Answer: Damien has lived in the apartment longer.

Step-by-step explanation: A year is aproxiamtely 52.1429 weeks long. Divide 250 by a years worth of weeks and you get 4.79 years. Damien has lived in the apartment 5 years making him live in the building longer.

Answer:

2.5 m

Step-by-step explanation:

Consider the ramp, the ground and the back of the lorry to form a right triangle where the ramp is the hypotenuse and the distance from the back of the lorry is the adjacent side, x

Using the cosine ratio in the right triangle

cos32° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{3}[/tex]

Multiply both sides by 3

3 × cos32° = x, hence

x ≈2.5 m

Answer: x<5

How?

-3x-12>3

(Add 12 to both sides)

-3x>15

(Divide -3 by 15)

x<5

(Remeber to flip the signs since you are dividing by a negative.)

Answer:

25 + 144 = 169

Step-by-step explanation:

Take a look at the first possible answer:

5² + 12² = 13².  Is this true or not?

25 + 144 = 169, which is equal to 13².   This set of side lengths represents a right triangle.

Answer:

5² + 12² = 13²

Step-by-step explanation:

[tex] {5}^{2} + {12}^{2} = 25 + 144 = 169 \\ \\ \sqrt{169} = ±13[/tex]

I am joyous to assist you anytime.

13/8

fraction

I think cause you nees to add all of the socks together and put how many socks was black

Hello there!

Answer:

8/13

Step-by-step explanation:

In order to find the probability in questions like this, we would need to find the number that we want to get and the total amount of possibilities.

Important information in the text:

With the information, we can find the probability.

In the question, we are trying to find the probability of picking out a black sock, and there is 8 black socks. The 8 will go on our numerator.

Our denominator would be the total amount of things that leads to our probability. Since we only have 8 black socks and 5 yellow socks, we would add 8 + 5 to get the total amount of socks.

8 + 5 = 13

The 13 will go in the denominator.

When you put all of the stuff together, you should get 8/13. You can't simplify it because 13 is an odd number that can't get any smaller.

8/13 is the probability of picking out a black sock

Answer:

x=9   x=-1

Step-by-step explanation:

We can factor

x^2 -8x-9 =0

What 2 numbers multiply to -9 and add to -8

-9*1 = -9

-9 +1 = -8

(x-9) (x+1) =0

Using the zero product property

x-9 =0   x+1 =0

x=9   x=-1

Answer:

[tex]\large\boxed{x<4\to x\in(-\infty,\ 4)}[/tex]

Step-by-step explanation:

[tex]-4x+28>12\qquad\text{subtract 28 from both sides}\\\\-4x>-16\qquad\text{change the signs}\\\\4x<16\qquad\text{divide both sides by 4}}\\\\x<4[/tex]

Answer:

Option D 4 inches is correct.

Step-by-step explanation:

Area of trapezoid = 48 square inches

Base a = 9

Base b = 15

We need to find the height h.

The formula for area of trapezoid is

Area = (a+b)/2 * h

Putting the values, we get

48 = ( 9+15)/2 * h

48 = (24)/2 * h

48 = 12 *h

=> h = 48/12

h = 4 inches

So, Option D 4 inches is correct.

Answer:

4 in.

Step-by-step explanation:

The area of a trapezium is calculated using the formula:

[tex]Area=\frac{1}{2}(Sum\:of\:the\:bases)\times height[/tex]

The given tra-pezoid has area [tex]48[/tex] square inches.

The bases are given as 9 inches and 15 inches.

We plug in the known values into the formula to get;

[tex]48=\frac{1}{2}(9+15)\times height[/tex]

[tex]48=\frac{1}{2}(24)\times height[/tex]

[tex]48=12\times height[/tex]

Divide both sides by 12.

[tex]\frac{48}{12}=height[/tex]

[tex]4 in.=height[/tex]

Therefore the height of the trapezoid is 2 inches.

Answer:

75 in^3

Step-by-step explanation:

i know because i had the test, and the other persons answer is wrong :)

Answer: 2 2/5

Step-by-step explanation:

You can do 6 * 2/5 = 2 2/5

OR

You can do 2 + 2 + 2/5

6/5 = 1 1/5 * 2 = 2 2/5

Answer:Answer is 2 and 3

Step-by-step explanation:trust me

These lines are only parallel lines because these lines don't touch each other and parallel lines don't touch each other.

Answer:

These lines are only parallel.

Answer:

27 meters

Step-by-step explanation:

a=1/2bh

a=1/2(18)(6)

a=27

Answer:

  66 g

Step-by-step explanation:

You want the combined mass of pebbles that are 4.5 grams or more, given the histogram of masses.

Each dot in the diagram represents one pebble, so the 5 dots above the mass of 4.5 g mean there were 5 pebbles with that mass.

The total mass of pebbles with mass 4.5 g or more will be the sum of the masses of each of the pebbles located in that column, and the columns to its right. Of course, we can use multiplication to simplify the repeated addition:

  5×(4.5 g) +4×(5 g) +3×(5.5 g) +1×(7 g) = 66 g

The combined mass of the pebbles 4.5 g or more is 66 g.

Answer: 34

Step-by-step explanation: 34 answer

The answer is 35. This is because 62 - 27 = 35

The probability that the sum of the two resulting numbers is greater than 5 is 2/3

The probability that the product of the two resulting numbers is odd is 1/3

How to determine the required probabilities

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

Die = {1, 2, 2, 4}

Spinner = {3, 4, 7}

The sample space is represented as

Space = {(1, 3), (1, 4), (1, 7), (2, 3), (2, 4), (2, 7), (2, 3), (2, 4), (2, 7), (4, 3), (4, 4), (4, 7)}

For the sum greater than 5, we have the following space

Space = {4, 5, 8, 5, 6, 9, 5, 6, 9, 7, 8, 11}

In the above, we have

Total = 12

Sum greater than 5 = 8

So, this probability is

P = 8/12 = 2/3

For the product resulting in odd numbers, we have the following space

Space = {3, 4, 7, 6, 8, 14, 6, 8, 14, 9, 12, 21}

In the above, we have

Total = 12

Odd results = 4

So, this probability is

P = 4/12 = 1/3

Hence, the probabilities are 2/3 and 1/3

Answer:

Pemdas subtracting would be last

Step-by-step explanation:

The operation should perform last to evaluate the expression is Addition.

The order of operations, or BODMAS, is a method for carrying out operations in an arithmetic statement.

B - Brackets, O - Order of powers or roots, (in some cases, 'of'), D - Division, M - Multiplication A - Addition, and S - Subtraction.

We have the expression,

(7×4)+(10÷2)×(14.7−9)

Now, using BODMAS first division is performed.

(7×4)+ 5 x (14.7−9)

Now, Multiplication is performed

28 + 5 x (14.7-9)

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Answer:

3. 2x - 1 = 4

4. x/6 = 1/2

The value of the solutions are,

3) x = 5/2

4) y = 3

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

''One less than twice a number, x, is equal to four.''

And, ''A number divided by six is one-half.''

Now,

Since, The algebraic expression is,

''One less than twice a number, x, is equal to four.''

Hence, We can formulate;

⇒ 2x - 1 = 4

Solve for x;

⇒ 2x = 4 + 1

⇒ 2x = 5

⇒ x = 5/2

4) The algebraic expression is,

⇒ ''A number divided by six is one-half.''

Hence, We can formulate;

⇒ y/6 = 1/2

Solve for y as;

⇒ y = 6×1/2

⇒ y = 6/2

⇒ y = 3

Thus, The value of the solutions are,

3) x = 5/2

4) y = 3

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Answer:

C. 0.26

Step-by-step explanation:

If the student selected was a sophomore at the jazz concert, we'd use the table to find the student being out of 35 students in the same situation. To get the correct answer you must take 35 divided by the total number of students attended (137). Therefore, 35/137= 0.255 rounded to the nearest tenth would be 0.26

Hope this helps! :)

Answer:

C) 0.26

Step-by-step explanation:

35 sophomores attended the jazz concert out of 137 total students.

Divide 35 by 137, which is roughly 0.25547445...

Round two decimal places and you will get 0.26.

Answer:

B

Step-by-step explanation:

B is the correct answer.  Since Mrs. Hooper and Mr. Anderson had to call a total of 8 parents, you know the first equation must be either A or B (H + A = 8).

Since you know that Mrs. Hooper had to call 2 more parents than Mr. Anderson, the equation will have to have H + 2 on one side; that's how you know the correct answer is B.

The set of equations which correctly describes the phone calls made is A. H + A = 8 ; H = A + 2.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given that,

H denote the number of calls Mrs. Hooper made and A denote the number of calls Mr. Anderson made.

Mrs. Hooper and Mr. Anderson had to call a total of eight parents.

So, the equation representing this is, H + A = 8

Mrs. Hooper needed to call two more students than Mr. Anderson.

H = A + 2

So the set of equations are,

H + A = 8 ; H = A + 2

Hence the correct option is A. H + A = 8 ; H = A + 2

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Answer:

Graph of given function doesn't exist.

Step-by-step explanation:

Given equation is [tex]|x|=-2[/tex].

Now we need to determine about how do you graph [tex]|x|=-2[/tex].

We know that [tex]|x|[/tex] represents absolute value function.

By definition of absolute value function, we know  that output of [tex]|x|[/tex] must always be positive.

But in given equation [tex]|x|=-2[/tex], we have output -2 which is negative.

That is not possible.

Hence there is no solution to the given problem [tex]|x|=-2[/tex].

So the graph of given function doesn't exist.

Answer:

Part 1) [tex]20\ students[/tex]

Part 2) [tex]95\%[/tex]

Part 3) [tex]9\ games[/tex]

Step-by-step explanation:

Part 1) Using proportion

[tex]\frac{15}{75\%}=\frac{x}{100\%}\\ \\x=15*100/75\\ \\x=20\ students[/tex]

Part 2) Using proportion

[tex]\frac{40}{100\%}=\frac38}{x\%}\\ \\x=100*38/40\\ \\x=95\%[/tex]

Part 3) Using proportion

[tex]\frac{18}{100\%}=\frac{x}{50\%}\\ \\x=18*50/100\\ \\x=9\ games[/tex]

Answer:

what he said

Step-by-step explanation:

Check the picture below.

For this case we have that by definition, the volume of a cylinder is given by:

[tex]V = \pi * r ^ 2 * h[/tex]

Where:

V: It's the volume

A: It is the radius of the cylinder

h: It is the height of the cylinder

We have to:

[tex]V = \pi * (7.2) ^ 2 * 12\\V = \pi * 51.84 * 12\\V = 1954.32195794513 \ m ^ 3[/tex]

On the other hand, the volume of the cone is given by:

[tex]V = \frac {\pi * r ^ 2 * h} {3}[/tex]

V: It's the volume

A: It is the cone radius

h: It is the height of the cone

We have:

[tex]V = \frac {\pi * (7.2) ^ 2 * 11} {3}\\V = \frac {\pi * 51.84 * 11} {3}\\V = 597.153931594347 \ m ^ 3[/tex]

Thus, the total volume is given by:

[tex]V = 2551.47588954 \ m ^ 3[/tex]

If we round up we have:

[tex]V = 2551.48 \ m ^ 3[/tex]

Answer:

[tex]V = 2551.48 \ m ^ 3[/tex]

Answer:

2x+7

Step-by-step explanation:

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

y-x> 0 -----> inequality A

y> x

The solution of the inequality A is the shaded area above the dashed line y=x

x+1<0 ----> inequality B

x < -1

The solution of the inequality B is the shaded area at the left of the dashed line x=-1 (open circle)

therefore

The solution of the system of inequalities in the attached figure

I did this earlier for a senior but believed I got it wrong based on that I fixed it to this : 62.5 was the percentage so 6250% so 18x 62.5 1125 HEY that’s reasonable please keep in mind I’m in middle school and you should double check this

From conservation of angular velocity the larger pulley will rotate at a speed of 500 rpm.

The conservation of angular velocity states that the angular velocity for a conjugate system will be always equal to the angular velocity of a part of the same system.

Mathematically -

r1ω1 = r2ω2 = r3ω3 = ................. = rnωn

where r is the radius of the circular belts, ω is the angular velocity and n is the total number of segments in the conjugate system.

Given that a pair of belted pulleys have diameters of 18 in. and 12 in. Also given that the smaller pulley turns at 750 rpm.

The radius of the pulleys are 9 in. and 6 in. respectively.

Let x rpm be the speed of the larger pulley turn.

From conservation of angular velocity, we have

⇒ 6 * 750 = 9 * x

⇒ x = (6 * 750)/9

∴  x = 500 rpm

Therefore, from conservation of angular velocity the larger pulley will rotate at a speed of 500 rpm.

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