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3 years ago

the diagonal of a rectangle is 16 inches. if the height of the rectangle is 8 inches. what is the length of the rectangle?

Mathematics

1 answer:

Yakvenalex [24]3 years ago

4 0

Answer:

Length: 13.9 inches

Step-by-step explanation:

a^2 + b^2 = c^2

a = 8 and c= 16

8^2 + b^2 = 16^2

64 + b^2 = 256

b^2 = 256 - 64

b = sqrt 192

b = 13.9

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Grant's credit card has an apr of 11.28% and it just changed its compounding period from monthly to daily . What happen to the i

madreJ [45]

Answer:

C. It will increase by about 0.6%

Step-by-step explanation:

Since, the effective interest rate is,

$r=(1+\frac{i}{n} )^{n} -1$

Where, i is the stated interest rate,

n is the number of compounding periods,

Here, i = 11.28 % = 0.1128,

n = 365 ( 1 year = 365 days ),

Hence, the effective interest rate would be,

$r=(1+\frac{0.1128}{365})^{365} -1$

=0.119388521952

Now, the changes in effective interest rate = Effective interest rate - Stated interest rate

= 0.119388521952 - 0.1128

= 0.006588521952 ≈ 0.006 = 0.6 %

Hence, It will increased by about 0.6 %,

Option A is correct.

Hope this helps :)

7 0

3 years ago

Three out of seven students in the cafeteria line are chosen to answer survey questions. How many different combinations of thre

Hatshy [7]

Answer:

35 possible combinations would be there.

Step-by-step explanation:

We have total of seven students we have to choose three out of those seven

$^{n}C_r=\frac{n!}{r!\cdot (n-r)!}$

n is the total possibilities n =7 in the given case

And r is the chosen ones

Hence, r=3 in the given case.

Substituting the values of n and r in the formula we get

$^{7}C_3$

$\frac{7!}{3!(7-3)!}$

$\frac{7!}{3!\cdot 4!}$

Using n!=n(n-1)----1

$\frac{7\cdot 6\cdot 5\cdot 4!}{3\cdot 2\cdot 1\cdot 4!}$

Cancel the common factor we get

$35$ possible combinations would be there.

8 0

3 years ago

What is the answer to 32 to the power of 3x+5 = 8 to the power of x-1

KIM [24]

Answer:

-2.333333333333........

5 0

3 years ago

Let f (x)=1/x and g (x)=x^2+5x. A. Find (f×g)(x). B. Find the domain and range of (f×g)(x).

Ira Lisetskai [31]

we are given

$f(x)=\frac{1}{x}$

$g(x)=x^2+5x$

(A)

(f×g)(x)=f(x)*g(x)

now, we can plug it

$(fXg)(x)=\frac{1}{x} (x^2+5x)$

we can simplify it

$(fXg)(x)=\frac{1}{x} (x(x+5))$

$(fXg)(x)=x+5$

(B)

Domain:

Firstly, we will find domain of f(x) , g(x) and (fxg)(x)

and then we can find common domain

Domain of f(x):

$f(x)=\frac{1}{x}$

we know that f(x) is undefined at x=0

so, domain will be

$(-\infty,0)$ ∪ $(0,\infty)$

Domain of g(x):

$g(x)=x^2+5x$

Since, it is polynomial

so, it is defined for all real values of x

now, we can find common domain

so, domain will be

$(-\infty,0)$ ∪ $(0,\infty)$ ..............Answer

Range:

Firstly, we will find range of f(x) , g(x) and (fxg)(x)

and then we can find common range

Range of f(x):

$f(x)=\frac{1}{x}$

we know that range is all possible values of y for which x is defined

since, horizontal asymptote will be at y=0

so, range is

$(-\infty,0)$ ∪ $(0,\infty)$

Range of g(x):

$g(x)=x^2+5x$

Since, it is quadratic equation

so, its range will be

$[-6.25,\infty)$

now, we can find common range

so, range will be

$(-6.25,0)$ ∪ $(0,\infty)$ .............Answer

6 0

3 years ago

On Saturday, Simone’s volleyball team will be having a family picnic. Hot dogs are sold at the local store with 10 hot dogs in a

yulyashka [42]

Answer:The correct answer is 4 packages of hot dogs and 5 packages of hot dog buns

Explanation:

To find the least number of packages of each item the team has to buy, it is necessary to find the Least Common Multiple of the two numbers (10 and 8), which is the lowest integer that is multiple of both 10 and 8, and therefore represents the least number of hot dogs and hot dog buns the team has to buy to get the same number of the two items. Now, to find the LCM follow this process:

1. List the two numbers

2. Now, find the multiplies of each number

10 x 1 = 10 / 10 x 2= 20/ 10 x 3= 30 / 10 x 4 = 40...

8 x 1= 8/ 8 x 2 = 16 / 8 x 3 = 24 / 8 x 4 = 32 / 8 x5 = 40...

3. Notice the first common number in both, in this case, 40 because 10 x 4 = 40 and 8 x 5= 40.

This means the Least Common Multiple is 40, and therefore the team should buy 40 of each item. Additionally, this means they need to buy 4 packages of hot dogs (each package contains 10 units) and 5 packages of hot dog buns (each package contains 8 units).

5 0

3 years ago