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3 years ago

A rectangle has a height of 3 and a width of 3x^2+4x . Express the area of the entire rectangle.

Mathematics

2 answers:

Leni [432]3 years ago

8 0

Answer:

лдшзщщго

Step-by-step explanation:

mars1129 [50]3 years ago

6 0

Answer: 20x^2 -10x-30

Step-by-step explanation:

You might be interested in

What is the value of 6 in the number 5627 562 <br><br>

natulia [17]

Answer:

If they are different numbers -

5,627 = 600

562 = 60

If they are the same number -

5,627,562 = 600,000 and 60

6 0

3 years ago

Which is the best definition of mathematical proof? a/A sequence of statements that demonstrates the truth of an assertion. b/St

Ivanshal [37]

Answer:

A. A sequence of statements that demonstrates the truth of an assertion.

Step-by-step explanation:

Mathematical proofs are a series of statements in order that help prove that something is true.

Proofs do not prove that something is false, they are not always 3 parts, and they are not in any order, because they have to be in an organized sequence.

So, A is correct.

6 0

3 years ago

Two trains leave the station at the same time, one heading west and the other east. The westbound train travels 20 miles per hou

zavuch27 [327]

2 (x-20)+2x=38
4x-40=380
4x=420
x=150

The train is 130mph.

4 0

4 years ago

X^5 + 243 divided by x+3

ch4aika [34]

-3   | 1   0   0   0   0   243 $\longleftarrow$ coefficients of the polynomial you're dividing
.     |                                   $\longleftarrow$ drop down the leading coefficient
- - - - - - - - - - - - - - - - - - -
.     | 1

On the left side of the frame, we write -3 because we're dividing by $x+3=x-(-3)$ . (The algorithm is followed for division of a polynomial by a factor of $x-c$ .) Since we're dividing a degree 5 polynomial by a degree 1 polynomial, we expect to get a degree 4 polynomial.

-3   | 1   0   0   0   0   243
.     |      -3                         $\longleftarrow$ multiply -3 by 1, write in next column, add to 0
- - - - - - - - - - - - - - - - - - -
.     | 1 -3

Repeat step for the remaining columns.

-3   | 1   0   0   0   0   243
.     |      -3   9
- - - - - - - - - - - - - - - - - - -
.     | 1 -3   9

-3   | 1   0   0      0   0   243
.     |      -3   9   -27
- - - - - - - - - - - - - - - - - - -
.     | 1 -3   9   -27

-3   | 1   0   0      0 0   243
.     |      -3   9   -27   81
- - - - - - - - - - - - - - - - - - - - -
.     | 1 -3   9   -27   81

-3   | 1   0   0      0 0 243
.     |      -3   9   -27   81 -243
- - - - - - - - - - - - - - - - - - - - -
.     | 1 -3   9   -27   81       0

which translates to

$\dfrac{x^5+243}{x+3}=x^4-3x^3+9x^2-27x+81$

So the bottom row of the frame gives the coefficients of each term in the quotient by descending order. Since the last coefficient is 0, this means the remainder upon division vanishes, i.e. $x^5+243$ is exactly divisible by $x+3$ .

- - -

Another way to get the same result is to use a well-known result: for $a+b\neq0$ ,

$a^5+b^5=(a+b)(a^4-a^3b+a^2b^2-ab^3+b^4)\implies\dfrac{a^5+b^5}{a+b}=a^4-a^3b+a^2b^2-ab^3+b^4$

and in this case $a=x$ and $b=3$

3 0

4 years ago

3. A positive number is 56 less than its square. Find the number.

raketka [301]

Answer:8

Step-by-step explanation:

X+56=x^2

X^2-x-56=0

X^2-8x+7x-56=0

X(x-8)+7(x-8)=0

(X+7)(x-8)=0

X+7=0 or x-8=0

X=-7 or x=8

4 0

4 years ago