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Andy’s total bill for lunch was$20. The cost of the drink was 15 percent of the total of the bill and the rest is the cost of th

Julli [10]

Divide 20 by 15 and you will get the answer

7 0

3 years ago

Choose whether it's always, sometimes, never

Keith_Richards [23]

Answer: An integer added to an integer is an integer, this statement is always true. A polynomial subtracted from a polynomial is a polynomial, this statement is always true. A polynomial divided by a polynomial is a polynomial, this statement is sometimes true. A polynomial multiplied by a polynomial is a polynomial, this statement is always true.

Explanation:

1)

The closure property of integer states that the addition, subtraction and multiplication is integers is always an integer.

If $a\in Z\text{ and }b\in Z$ , then a+b\in Z.

Therefore, an integer added to an integer is an integer, this statement is always true.

2)

A polynomial is in the form of,

$p(x)=a_nx^n+a_{n-1}x^{x-1}+...+a_1x+a_0$

Where $a_n,a_{n-1},...,a_1,a_0$ are constant coefficient.

When we subtract the two polynomial then the resultant is also a polynomial form.

Therefore, a polynomial subtracted from a polynomial is a polynomial, this statement is always true.

3)

If a polynomial divided by a polynomial then it may or may not be a polynomial.

If the degree of numerator polynomial is higher than the degree of denominator polynomial then it may be a polynomial.

For example:

$f(x)=x^2-2x+5x-10 \text{ and } g(x)=x-2$

Then $\frac{f(x)}{g(x)}=x^2+5$ , which a polynomial.

If the degree of numerator polynomial is less than the degree of denominator polynomial then it is a rational function.

For example:

$f(x)=x^2-2x+5x-10 \text{ and } g(x)=x-2$

Then $\frac{g(x)}{f(x)}=\frac{1}{x^2+5}$ , which a not a polynomial.

Therefore, a polynomial divided by a polynomial is a polynomial, this statement is sometimes true.

4)

As we know a polynomial is in the form of,

$p(x)=a_nx^n+a_{n-1}x^{x-1}+...+a_1x+a_0$

Where $a_n,a_{n-1},...,a_1,a_0$ are constant coefficient.

When we multiply the two polynomial, the degree of the resultand function is addition of degree of both polyminals and the resultant is also a polynomial form.

Therefore, a polynomial subtracted from a polynomial is a polynomial, this statement is always true.

3 0

3 years ago

Read 2 more answers

You bike 1 mile the first day of your training, 1.3 miles the second day, 1.9 miles the third day, and 3.1 miles the fourth d

JulsSmile [24]

Answer:

19.9 miles

Step-by-step explanation:

In this problem we have:

$d_1=1 mi$ is the distance travelled during the 1st day

$d_2=1.3 mi$ is the distance travelled during the 2nd day

$d_3=1.9 mi$ is the distance travelled during the 3rd day

$d_4=3.1 mi$ is the distance travelled during the 4th day

We notice that the difference between the distance travelled on the (n+1)-th day and the distance travelled on the n-th day doubles every day. In fact:

$d_2-d_1=0.3\\d_3-d_2=2\cdot 0.3 = 0.6\\d_4-d_3=2\cdot 0.6 = 1.2$

Which can be rewritten using the general formula:

$d_{n+1}-d_n=2(d_n-d_{n-1})$

This means that

$d_{n+1}=d_n+2(d_n-d_{n-1})$

By applying this formula recursively, we can find the 7th term, which is the distance travelled on the 7th day:

$d_1=1\\d_2=1.3\\d_3=1.9\\d_4=3.1\\d_5=3.1+2\cdot 1.2=5.5\\d_6=5.5+2\cdot 2.4=10.3\\d_7=10.3+2\cdot 4.8=19.9 mi$

So, the distance travelled on the 7th day is 19.9 miles.

7 0

4 years ago

How does the volume of the cylinder compare to the volume of the cone

aniked [119]

A cylinder with the same radius and height as a cone will have 3 times the volume of the cone.

Vcone = (1/3)*π*r^2*h
Vcylinder = π*r^2*h

5 0

3 years ago

Mr.sanchez drives 120 miles in 3 hours. At the same rate, how far will he drive in 5 hours

Rina8888 [55]

To elaborate:

To do this problem, we assume that Mr. Sanchez is driving at a constant rate.

According to this information, he has driven 120 mi in 3 hr. To find how much he drives in 5 hr, we first have to find how many mi he drives in 1 hour. To do this, we divide 120 miles by 3 hours, since we assume that he managed to drive an equal amount in each hour.

120/3=40

Therefore Mr. Sanchez drove at a rate of 40 mph.

However, this isn't the final answer. 40 miles is the distance for one hour of driving. To find the distance for 5 hours, we have to multiply the distance by 5 as well.

40 times 5=200

In conclusion, Mr. Sanchez will drive 200 miles in 5 hours.

4 0

3 years ago

Read 2 more answers