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2 years ago

Determine the answer to 3 + -5 and explain the steps using a number line

2 answers:

6 0

Adding a positive to a negative, you would look at the number with the greater absolute value, and that number would determine the sign of the sum.

5 - 3 = 2

Since 5 is bigger, you use that sign

-5

-2

Answer: -2

Westkost [7]2 years ago

6 0

-5 -4 -3 -2 -1 0 1 2 3 4 5

That is the number line. Add 3 to -5 and you get -2. ( a negative + a positive = A negative) ( A negative + a Negative = A positive)

Hope that helps :)

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Keenan currently does a total of 888 pushups each day. He plans to increase the number of pushups he does each day by 222 pushup

marishachu [46]

Answer:

8 + 2x = 30

Step-by-step explanation:

Given,

The initial number of push-ups he does in each day = 8,

And, the number of push-ups, he increases per day = 2,

Let x be the number of days after he will reach his target of 30 push-ups,

Since, the number of push-ups she will increase in x days = 2x,

Thus, the number of push-ups she will do after x days = 8 + 2x,

⇒ 8 + 2x = 30, which is the required equation.

4 0

2 years ago

A summer camp has 400 ft of float line with which to rope off three adjacent rectangular areas of a lake for swimming? lessons,

Rashid [163]

Answer:

a) A = x*(400 - 4*x)

b) domain of function A(x) is ( 0 , 100 )

c) dimension of swimming section x = 30 ft maximizes area.

Step-by-step explanation:

Given:

- Total length of float-line used L = 400 ft

- Inner sections length x

Find:

a) Express the total area A as a function of x

b) Find the domain of the function

c) Using the graph, find the dimensions that leads to largest area

Solution:

- The amount of side length of the rectangle can be calculated from the total length given y:

y = L - x - x - x - x

y = L - 4*x

y = 400 - 4*x

- The area of a rectangle is as follows:

A = x*y

- Replace y with the expression derived first:

A = x*(400 - 4*x)

- To find the domain of the function we know that A >= 0:

400*x - 4x^2 > 0

x(400 - 4x) > 0

x > 0 , 400 - 4*x < 0

x < 100

- Hence, the domain of function A(x) is ( 0 , 100 )

- From the graph given, we can see that Area is maximum when x = 30 ft. Denoted by the turning point of the graph.

- Hence, the dimension of swimming section x = 30 ft maximizes area.

5 0

2 years ago

Can someone please help me solve this (7th grade math)

Reil [10]

Answer: 8x = 72

Step-by-step explanation:

and in case you need to go any further at any point, x = 9

3 0

2 years ago

Read 2 more answers

What is the cost of 12.7 gallons of gasoline at $2.15 per gallon?

levacccp [35]

Answer:

$27.31 (rounded to the nearest cent)

8 0

2 years ago

Evaluate the infinite sum:

satela [25.4K]

Consider the k-th partial sum,

$S_k = 1 + \dfrac2\pi + \dfrac3{\pi^2} + \cdots + \dfrac k{\pi^{k-1}}$

More compactly,

$\displaystyle S_k = \sum_{i=1}^k \frac i{\pi^{i-1}} = \frac{(1-\pi)k+\pi^{k+1}-\pi}{(1-\pi)^2\pi^{k-1}}$

(this is just another case of a similar sum you asked about a while ago [24494877])

The infinite sum is the limit of the partial sum as k goes to infinity. We have

$\displaystyle \lim_{k\to\infty} \frac{(1-\pi)k+\pi^{k+1}-\pi}{(1-\pi)^2\pi^{k-1}} = \frac\pi{(1-\pi)^2} \lim_{k\to\infty} \left(\frac{(1-\pi)k}{\pi^k} + \pi - \frac1{\pi^{k-1}} \right) = \boxed{\frac{\pi^2}{(1-\pi)^2}}$

since the non-constant terms in the limit converge to 0.

Alternatively, recall that for |x| < 1, we have

$\dfrac1{1-x} = \displaystyle \sum_{n=0}^\infty x^n$

Differentiating both sides gives

$\dfrac1{(1-x)^2} = \displaystyle \sum_{n=0}^\infty nx^{n-1} = \sum_{n=1}^\infty nx^{n-1}$

also valid for |x| < 1. Take x = 1/π and you get the sum you want to compute.

5 0

2 years ago