What's 3n+5p+2+n in simplest form

Answers

Answer 1
Answer:
                                     3n  +  5p  +  2  +  n

Add up all the 'n's :    4n  +  5p  +  2

That's all you can do with it.

Answer 2
Answer: Rearrange the terms into an easier format: 5p+3n+n+2. Combine like terms: 5p+4n+2. 3n+5p+2+n in simplest form is 5p+4n+2


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3/10 in.=7/8 mi. (i am doing rates and ratios)

Answers

3/10 in 
1 in =(1/12)ft 
1 ft =(1/5280) mi 

3/10 in=3/10*(1/12)*(1/5280) mi 

the area of a library tabletop is 27 1/8 square feet. The table is 3 1/2 feet wide. What is the length of the table ?

Answers

27⅛ ÷ 3½

in my opinion, turning it into a decimal is easier

27 ⅛ = 27.125
3 ½ = 3.5

so.....
27.125 ÷ 3.5 = 7.75 which is also 7 ¾

Final answer:

To find the length of the table, multiply the area by the reciprocal of the width. Convert the mixed number to an improper fraction and then solve the equation. Simplify the resulting fraction, if possible.

Explanation:

To find the length of the table, we can use the formula for the area of a rectangle, which is length multiplied by width. In this case, we are given the area of the table as 27 1/8 square feet and the width as 3 1/2 feet. So, we can set up the equation: 27 1/8 = length × 3 1/2.

First, we need to convert the mixed number 27 1/8 to an improper fraction. Multiply the whole number (27) by the denominator (8) and add the numerator (1), then write the result over the denominator: 27 × 8 + 1 = 217/8.

Now we can solve the equation: 217/8 = length × 3 1/2. To isolate the variable, we can multiply both sides of the equation by the reciprocal of 3 1/2, which is 2/7. This cancels out the fraction on the right side, giving us: length = (217/8) × (2/7).

To multiply fractions, we multiply the numerators together and the denominators together: length = (217 × 2) / (8 × 7) = 434/56. This fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 2: length = 217/28.

So, the length of the table is 217/28 feet.

Learn more about Length of a table here:

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How many unique triangles can be made where one angle 60° and another angle is an obtuse angle?

Answers

That set of requirements narrows it down to only
an infinite number of possible unique triangles.

-- One angle is 60°.  That leaves 120° for the sum of the other two.

-- One angle is obtuse.  It can be anything more than 90°
and less than 120°.

-- And the third angle gets whatever is left.

-- If you don't mind fractional or decimal parts of degrees, then we
already have an infinite number of possible combinations of angles.
_____________________________________

Every possible combination of angles defines a unique set of
RATIOs among the sides.

But for EVERY unique set of RATIOs, there are an infinite number of possible unique triangles that are SIMILAR to each other.

Example:

If the angles determine that the sides must be in the ratio of 1:2:3,
then the triangle can have sides of

1, 2, and 3
2, 4, and 6
3, 6, and 9
4, 8, and 12
5, 10, and 15
6, 12, and 18
7, 14, and 21
8, 16, and 24
9, 18, and 27
10, 20, and 30
.
.
etc.

These all have the SAME set of ANGLES, and the same RATIO
among the sides, but they're all different unique triangles.

True or false: any nonzero integers, the product and the quotient have the same sign. Why?

Answers

False. This is because no matter what the number is, the properties of multiplication and division stay the same. So, if one odd and even number multiply/divide, then the answer will be negative. But, if two numbers of the same sign (both either negative or positive) are divided/multiplied, they will both be positive. Therefore, the result is not always the same sign as the starting integers

Hope this helped! :D

Systems of Equations: Solve each system by setting the equations equal to each other and solving.y=x
y= -x

Answers


Since ' x ' and '-x ' are both equal to ' y ', they must be equal to each other.

                                     x = -x

Add ' x ' to each side:     2x = 0

Divide each side by  2 :    x = 0
                        whence   y = 0 .

That's the only possible solution to the system [ y = x  and  y = -x ] .


since x and -x both equal y they must be equal to each other:
x= -x 
+x  +x (add x to both sides)
2x=0
x=0 
when x=0, y=0

The range of the function f(k) = k2 + 2k + 1 is {25, 64}. What is the function’s domain? A. {5, 8} B. {-5, -8} C. {3, 8} D. {4, 7} E. {4, 8}

Answers

Answer:

Option D

The domain of the function is: {4, 7}

Step-by-step explanation:

We know that for polynomial functions like f(k) = k^2 + 2k + 1 its domain and its rank are all real numbers. However, for this case we are told that the function range is: the set {25, 64}

This means that the function is bounded.

Then the domain of f(k) are all possible values of k such that f(k) belongs to the interval {25, 64}.

To find the limit values of k then we do f(k) = 25

k^2 + 2k + 1 = 25

k^2 + 2k -24 = 0

Now we factor the expression:

(k + 6)(k-4) = 0

Then k = 4 and k = -6.

Now we do f(k) = 64

k ^ 2 + 2k +1 = 64\n\nk ^ 2 + 2k -63 = 0

We factor the expression:

(k + 9)(k-7) = 0

k = -9 and k = 7.

Finally we search between the options given an interval that matches.

The option that matches is option D {4, 7}

Finally, the domain of the function is: {4, 7}