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3 years ago

Is 40 a multiple or a factor

1 answer:

5 0

Hey there!
It can be both. It's a multiple of 8 because 8 times 5 is 40, but it's also a factor of 120 because 80 times 3 is 120.
Hope this helps!

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Write a rule for the nth term of the arithmetic sequence: a11= 50, d = 7

ivolga24 [154]

Answer:

Required rule for $n^{th}$ is $a_{n}=7n-27$ .

Step-by-step explanation:

Given that,

$a_{11} = 50,\ \ d=7$

From the question: we have to write the $n^{th}$ term of Arithmetic sequence.

Arithmetic Sequence or Arithmetic progression (A.P) : It is a sequence which possess that difference between of two successive sequence is always constant.

$a_{1} ,a_{2},a_{3},a_{4}.....................a_{n-1},a_{n}$

where, $a_{1}$ is the first term of A.P

$d$ is the common difference.

$a_{n}$ is the last term or general term.

The above sequence to be in A.P then their common difference should be equal.

$d=a_{2}-a_{1} =a_{3}-a_{2}=a_{4} -a_{3} ..........................a_{n}-a_{n-1}$

Now, Formula of General Term is $a_{n}=a+(n-1)d$

So, $a_{11}= a+(11-1)d\\ a_{11} = a+10d$

Substituting the value of $a_{11} = 50,\ \ d=7$ we get,

$50=a+10\times7\\50=a+70\\a=-20$

Then General term ( $a_{n}$ ) of given data is

$a_{n}=-20+(n-1)7\\a_{n}=-20+7n-7\\a_{n}=7n-27$

Therefore, Required rule for $n^{th}$ is $a_{n}=7n-27$ .

5 0

3 years ago

The height of a tennis ball tossed into the air is modeled by h(x) = 40x â€" 16x 2, where x is elapsed time in seconds. During w

egoroff_w [7]

The time interval x >0.5 and x > 2.04 will the tennis ball be at least 15 feet above the ground.

Given that,

The height of a tennis ball tossed into the air is modeled by,

$\rm h(x) = 40x - 16x^2$

Where x is elapsed time in seconds.

We have to determine,

During what time interval will the tennis ball be at least 15 feet above the ground?

According to the question,

The height of a tennis ball tossed into the air is modeled by,

$\rm h(x) = 40x - 16x^2$

Where x is elapsed time in seconds.

Then,

When the tennis ball be at least 15 feet above the ground,

$h(x) = 15$

Substitute the value of h(x) in the equation,

$\rm h(x) = 40x - 16x^2\\\\ 15 = 40x - 16x^2\\\\ 16x^2-40x+15=0$

Factorize the equation for finding the time interval will the tennis ball be at least 15 feet above the ground is,

$\rm 16x^2-40x+15= 0\\\\x = \dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\x = \dfrac{-(-40)\pm \sqrt{(-40)^2-4 \times 16 \times 15}}{2 \times 16}\\\\x = \dfrac{-(-40)\pm \sqrt{1600- 960}}{32}\\\\x = \dfrac{40\pm \sqrt{640}}{32}\\\\x = \dfrac{40 + 25.29}{32} \\\\x = \dfrac{40 + 25.29}{32} \ and \ x = \dfrac{40 - 25.29}{32}\\\\x = \dfrac{65.29}{32} \ and \ x = \dfrac{14.71}{32}\\\\x = 2.04 \ and \ x = 0.45$

Hence, The time interval x >0.5 and x > 2.04 will the tennis ball be at least 15 feet above the ground.

For more details about Inequality refer to the link given below.

brainly.com/question/17177510

7 0

2 years ago

Please help me with this math problem

Lapatulllka [165]

Step-by-step explanation:

according to the question

55x⁶+22x⁴

11x⁴(5x²+2)

width:11x⁴

length:5x²+2

3 0

3 years ago

30x2+ 11x + 1 = 0 42y2 + 13y + 1 = 0

GrogVix [38]

Answer: 1

Step-by-step explanation:

5 0

2 years ago

5 points

Flauer [41]

Answer:

The payment for driving 80 miles is $78

Step-by-step explanation:

Mathematical model

Mathematical models are used in disciplines like natural sciences and engineering, among many others.

The data provided in the question allows building a model for the charges of the car rental, knowing there are two fees:

A fixed charge of $50

A variable charge or $0.35 per mile driven.

Part A

Using m as the number of miles driven for the day, the model for the payment for the car rental is:

P(m)=50+0.35m

Part B

Find the payment if the car is driven m=80 miles:

P(80)=50+0.35*80

P(80)=50+28=78

The payment for driving 80 miles is $78

4 0

3 years ago