How much of a stick of butter is 1/2 cup?

charle [14.2K]

Answer:

$\huge\boxed{\text{D)} \ 15x^4 + 2x^3 - 8x^2 - 22x - 15}$

Step-by-step explanation:

We can solve this multiplication of polynomials by understanding how to multiply these large terms.

To multiply two polynomials together, we must multiply each term by each term in the other polynomial. Each term should be multiplied by another one until it's multiplied by all of the terms in the other expression.

We can do this by focusing on one term in the first polynomial and multiplying it by all the terms in the second polynomial. We'd then repeat this for the remaining terms in the second polynomial.

Let's first start by multiplying the first term of the first polynomial, $3x^2$ , by all of the terms in the second polynomial. ( $5x^2+4x+5$ )

$3x^2 \cdot 5x^2 = 15x^4$
$3x^2 \cdot 4x = 12x^3$
$3x^2 \cdot 5 = 15x^2$

Now, we can add up all these expressions to get the first part of our polynomial. Ordering by exponent, our expression is now

$\displaystyle 15x^4 + 12x^3 + 15x^2$

Now let's do the same with the second term ( $-2x$ ) and the third term ( $-3$ ).

$-2x \cdot 5x^2 = -10x^3$
$-2x \cdot 4x = -8x^2$
$-2x \cdot 5 = -10x$

Adding on to our original expression: $\displaystyle 15x^4 + 12x^3 - 10x^3 + 15x^2 - 8x^2 - 10x$

$-3 \cdot 5x^2 = -15x^2$
$-3 \cdot 4x = -12x$
$-3 \cdot 5 = -15$

Adding on to our original expression: $\displaystyle 15x^4 + 12x^3 - 10x^3 + 15x^2 - 8x^2 - 15x^2 - 10x - 12x - 15$

Phew, that's one big polynomial! We can simplify it by combining like terms. We can combine terms that share the same exponent and combine them via their coefficients.

$12x^3 - 10x^3 = 2x^3$
$15x^2 - 8x^2 - 15x^2 = -8x^2$
$-10x - 12x = -22x$

This simplifies our expression down to $15x^4 + 2x^3 - 8x^2 - 22x - 15$ .

Hope this helped!

7 0

3 years ago

Read 2 more answers

A 5 inch x 7 inch photograph is placed inside a picture frame. Both the length and width of the frame are 2x inches

Sedbober [7]

Answer:

Perimeter = 28 + 8x inches

Step-by-step explanation:

Length of the photograph = 7 inches

Width of the photograph = 5 inches

Both the length and width of the frame are 2x inches larger than the width and length of the photograph.

Length of the frame = 7 inches + 2x inches

Width of the frame = 5 inches + 2x inches

Perimeter of the frame = 2(Length + width)

= 2{(7+2x) + (5+2x)}

= 14 + 4x + 10 + 4x

= 28 + 8x inches

Perimeter = 28 + 8x inches

5 0

3 years ago

Your bill at a café is $26.50. You want to leave a 20% tip for your good service. What is the amount of the tip and the total of

Licemer1 [7]

Your tip total will be $5.30 and your bill total will be $31.80 after tip.

7 0

3 years ago

Read 2 more answers

dog sled race extends 1049 miles, if a musher is twice as far from anchorage as from nome, how many miles has the musher complet

romanna [79]

His distance from one end is ' D ', and his distance from the other end is ' 2D '.

The distance from one end to the other end is (D + 2D) = 3D .

3D = 1,049 miles

Divide each side by 3 :

D = 1,049 / 3 = 349 and 2/3 miles .

The question doesn't tell which end he started from, and where he's headed,
so I guess you have to know that this is the Iditerod race, it STARTS in Anchorage,
and it ENDS in Nome.

He is ' 2D ' from Anchorage, so he has completed [ 2 x (349 and 2/3 miles) ] =
699 and 1/3 miles.

Rounded to the nearest mile, that's 699 miles.

3 0

3 years ago

7th grade math help me pleaseeee

drek231 [11]

Answer:

a

Step-by-step explanation:

For negative correlation, Look for data that is going down

7 0

3 years ago