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3 years ago

Is the expression below completely factored? If not, complete the factorization.

Mathematics

1 answer:

Ket [755]3 years ago

6 0

Answer:

A) No, because the greatest common factor is 8y?, and the completely factored form is 8y2(4y2 - 6y + 3).

Step-by-step explanation:

Considering the expression

4y(8y3 – 12y2 + 6y)

From the elements in the parenthesis, 2 and y can still be factored out such that what will be left of each element

8y3/2y = 4y2

12y2/2y = 6y

6y/2y = 3

Hence

4y(8y3 – 12y2 + 6y) = 4y*2y(4y2 - 6y +3)

= 8y2(4y2 - 6y + 3)

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Valentina has $2.90 of change in her pocket. She has only 20 cent and 59 cent coins, 7 coins in total. If t is the number of 20c

LenaWriter [7]

Answer:

The value of t is 2 cents.

Step-by-step explanation:

First, I must assume that you mean 50-cent coins, since the 59-cent coin does not exist and besides doing so, it does not give an exact number of coins.

To calculate the value of t, you must first consider some equations where it is included.

First, the total value of Valentina's money. It should also include the number of 50 cent coins, I will call it "s". The equation would be the following (considering that 1 $ is 100c):

20 * t + 50 * s = 290 (1)

We can add another equation that mentions the statement that says there are 7 currencies, therefore:

t + s = 7 (2)

If I clear this equation, as follows:

s = 7-t (3)

I can replace it in my first equation, and it would be as follows:

20 * t + 50 * (7-t) = 290 (4)

The development of the equation is as follows:

20 * t + 50 * 7 -5 * t = 290

20 * t + 350 - 50 * t = 290, rearranging the equation

20 * t - 50 * t = 290 - 350

-30 * t = -60

t = -60 / -30

t = 2

So the value of t is 2 cents.

Now the number of 50 cents coins would be

s = 7 - t, replacing the value of t

s = 7 - 2 = 5

Then it would be 2 coins of 20 cents and 5 coins of 50 cents. 

Checking the answer:

2 * 20 + 50 * 5 = 40 +250 = 290

3 0

4 years ago

Let h(x)=e−x+kx, where k is any constant. For what value(s) of k does h have (a) No critical points? (b) One critical point? (c)

mrs_skeptik [129]

Answer:

a) for k≤0 , h has no critical point

b) for k>0 , h has a critical point

c) for k=0 , has a horizontal asymptote

Step-by-step explanation:

for the function

h(x)=e^(−x)+k

h has a critical point when the first derivative is =0 or is undefined. Since e^(−x) and k*x are continuos functions for all x then the second case is discarded. Then

dh/dx = -e^(−x)+k = 0

k = e^(−x)

x = ln (1/k)

since ln (1/k) should be possitive then k should be >0 . Thus h(x) has a critical point when k>0 and do not have any when k≤0

h has a horizontal asymptote when

lim h(x)=a when x→∞ (or -∞)

then

when x→∞, lim h(x)= lim e^(−x)+k*x = lim e^(−x) + k* lim x = 0 + k*∞ = ∞

on the other hand , when k=0 , lim h(x)= lim e^(−x)= 0 , then h has a horizontal asymptote for k=0

for x→(-∞) , e^(-x) rises exponentially , thus there is no k such that h has an horizontal asymptote when x→(-∞)

6 0

4 years ago

PLEASE HELP! A company makes triangular plates for individual slices of pizza. For each plate, the base is 7 inches and the heig

GREYUIT [131]

24
.........................

5 0

3 years ago

4 1/5 + 2 5/6 = ? 6 1/6 6 1/30 7 1/4 7 1/30

grigory [225]

Answer:

7 1/30

Step-by-step explanation:

4 1/5 + 2 5/6

Get a common denominator of 30

4 1/4 = 4 1/5*6/6 = 4 6/30

2 5/6 *5/5 = 2 25/30

4 6/30 + 2 25/30

6 31/30

Rewriting

6 30/30 + 1/30

6 + 1 + 1/30

7 1/30

6 0

3 years ago

Read 2 more answers

When a trinomial is factored as (x+m)(x+n), what is the product of m and n?

Olin [163]

When m and n are multiplied, you get the c value of the quadratic.
This is also known as the y intercept, which is a constant.
Final answer: A

5 0

3 years ago