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3 years ago

Is the relationship shown by the data linear? How can you tell if it is or is not? If so, model the data with an equation.

Mathematics

1 answer:

Marat540 [252]3 years ago

4 0

Answer:

linear and y = 2x + 19

Step-by-step explanation:

the x- values increment by 2 and the values of y increment by 4

This indicates a linear relationship exists in the form

y = mx + c ( m is the slope and c the y-intercept )

m = $\frac{rise}{run}$ = $\frac{4}{2}$ = 2

y = 2x + c ← is the partial equation

to find c use any ordered pair from the table

using (- 5, 9 ), then

9 = - 10 + c ⇒ c = 9 + 10 = 19

y = 2x + 19 ← linear equation

As a check

x = - 7 : y = - 14 + 19 = 5 ← correct value of y

x = - 5 : y = - 10 + 19 = 9 ← correct value of y

x = - 3 : y = - 6 + 19 = 13 ← correct value of y

x = - 1 : y = - 2 + 19 = 17 ← correct value of y

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Which solid has a greater volume

Triss [41]

Answer:

The volume of cylinder and the volume of a cone, have equal volume measurements. So, the answer is C).

Step-by-step explanation:

Cylinder:

-Use the formula for the volume of a cylinder. Use both the radius and height for the formula in order to solve and get the volume:

$V = \pi r^2 h$

$V = \pi 2^2 6$

-Solve:

$V = \pi 2^2 6$

$V = \pi \times 2^2 \times 6$

$V = \pi \times 4 \times 6$

$V = \pi \times 24$

$V = 24\pi \approx 75.39$

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

Cone:

-Use the formula for the volume of a cone and the radius and height for the formula and solve the formula to get the volume:

$V = \frac{1}{3} \pi r^2h$

$V = \frac{1}{3} \pi 3^28$

-Solve:

$V = \frac{1}{3} \pi 3^28$

$V = \frac{1}{3} \times \pi \times 3^2 \times 8$

$V = \frac{1}{3} \times \pi \times 9 \times 8$

$V = \frac{1}{3} \times \pi \times 72$

$V = \frac{1}{3} \pi \times 72$

$V = 24\pi \approx 75.39$

-So, according to the volume of a cylinder and the volume of a cone, They both have the same volume.

Cylinder: $75.39$ $ft^3$

Cone: $75.39$ $ft^3$

5 0

3 years ago

Sequences:

joja [24]

Answer:

<u>The sequence is</u>

1, 1 + 2, 1 + 2 + 3, 1 + 2 + 3 + 4, ...

Each term is the sum of the consecutive numbers from 1 to that number.

<u>The nth term is the sum of the first n numbers:</u>

aₙ = 1 + 2 + 3 + ... + n
aₙ = 1/2n(1 + n) (formula for sum of the n terms of arithmetic progression with the first term of 1 and common difference of 1)
aₙ = n(n + 1)/2

1) The number of circles in the nth pile is n(n + 1)/2

2) When n tends to infinity the number of circles tends to infinity

4 0

3 years ago

What is the least common denominator for 2/5 + 3/7

muminat

Answer:

Step-by-step explanation:

2/5 + 3/7

the least common denominator is 35 because 14/35 + 15/35.

3 0

3 years ago

Read 2 more answers

Brianna has six bags of soil filling one flower pot requires 1/3 of a bag of soil how many flower pots can be filled with the si

dimaraw [331]

Answer:

Step-by-step explanation:

$\frac{6}{1}$ ÷ $\frac{1}{3}$

Keep Change Flip

$\frac{6}{1}$ × $\frac{3}{1}$ = $\frac{18}{1}$

3 0

3 years ago

How many gallons of a 80% antifreeze solution must be mixed with 100 gallons of 20% antifreeze to get a mixture that is 70% a

Blababa [14]

To Find :

How many gallons of a 80% antifreeze solution must be mixed with 100 gallons of 20% antifreeze to get a mixture that is 70% antifreeze.

Solution :

Let, x gallons of 80% antifreeze solution is required :

So,

$(x \times 80) + ( 100 \times 20 ) = (x + 100 )\times 70\\\\8x + 200 = 7( x + 100)\\\\x = 500$

Therefore, 500 gallons of 80% antifreeze solution is required.

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3 years ago