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2 years ago

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Imagine you are hanging two identical picture frames. Each frame is 28 inches wide and the wall you are hanging them on is 10 fe

et wide. There needs to be 8 inches of space in between the two frames. How far do the frames need to be from the left and right side of the walls in order to be centered?

1 answer:

Alex Ar [27]2 years ago

7 0

Answer:

28 inches

Step-by-step explanation:

<u>Sum of the width of the two frames and a gap between them:</u>

28*2 + 8 = 64 in

<u>The gaps from the left and right are equal to x:</u>

x = (10 feet - 64 in)/2 = (120 in - 64 in)/2 = 28 in

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Which expression represents the number 2i4−5i3+3i2+−81‾‾‾‾√ rewritten in a+bi form?

vichka [17]

Answer:

The expression $-1+14i$ represents the number $2i^4-5i^3+3i^2+\sqrt{-81}$ rewritten in a+bi form.

Step-by-step explanation:

The value of $i$ is $i=\sqrt{-1}[tex] or [tex]i^{2}=-1[\tex].Now [tex]i^{4}$ in term of $i^{2}[\tex] can be written as, [tex]i^{4}=i^{2}\times i^{2}$

Substituting the value,

$i^{4}=\left(-1\right)\times \left(-1\right)$

Product of two negative numbers is always positive.

$\therefore i^{4}=1$

Now $i^{3}$ in term of $i^{2}[\tex] can be written as, [tex]i^{3}=i^{2}\times i$

Substituting the value,

$i^{3}=\left(-1\right)\times i$

Product of one negative and one positive numbers is always negative.

$\therefore i^{3}=-i$

Now $\sqrt{-81}$ can be written as follows,

$\sqrt{-81}=\sqrt{\left(81\right)\times\left(-1\right)}$

Applying radical multiplication rule,

$\sqrt{ab}={\sqrt{a}}\sqrt{b}$

$\sqrt{\left(81\right)\times\left(-1\right)}={\sqrt{81}}\sqrt{-1}$

Now, $\sqrt{\left(81\right)=9$ and $\sqrt{-1}}=i$

$\therefore \sqrt{\left(81\right)\times\left(-1\right)}=9i$

Now substituting the above values in given expression,

$2i^4-5i^3+3i^2+\sqrt{-81}=2\left(1\right)-5\left(-i\right)+3\left(-1\right)+9i$

Simplifying,

$2+5i-3+9i$

Collecting similar terms,

$2-3+5i+9i$

Combining similar terms,

$-1+14i$

The above expression is in the form of a+bi which is the required expression.

Hence, option number 4 is correct.

5 0

3 years ago

9.1k = 63.7 what does this equal

zheka24 [161]

Step-by-step explanation:

9.1k=64.7

Find k

64.7/9.1=7

Plug in 7

9.1(7)=64.7

Multiply 9.1 and 7=63.7

63.7=64.7

Divide

1.02 or 1 1/50

Hope that helps somewhat

5 0

2 years ago

Read 2 more answers

Reduce to simplest form. <br> -7/12 +3/8

gayaneshka [121]

Answer:

ok so you should get -5/24 in simplest form.

Decimal form- -0.2083 repeating

Step-by-step explanation:

Hope this helped :)

4 0

2 years ago

Help plz if anybody know the answer

Tanzania [10]

Answer: x^2+29x+39

You would first have to set up an equation, which would be ((2x+9)⋅(x+6))-((x-5)⋅(x-3)) to find the area of both rectangles.

Then you can simplify it, which gives us 2x^2+21x+54-(x^2-8x+15)

Then simplify it even more which gives us 2x^2+21x+54-x^2+8x-15

Then we can get our answer: x^2+29x+39

Hope that helps :)

4 0

2 years ago

Find all pairs of prime numbers (a,b) such that a^b✖️b^a+1 is prime

Alenkasestr [34]

The pairs of prime numbers (a,b) between 1 and 10 inclusive such that a^b * b^a+1 is prime are

<h3>How to determine the pairs of numbers?</h3>

The expression that is a prime number is given as:

a^b * b^a + 1

The boundary or range of numbers of a and b is not given.

So, we make use of numbers between 1 and 10

i.e. 1 ≤ a ≤ 10 and 1 ≤ b ≤ 10

Using the above range, we have the following program to determine the pairs of prime numbers (a, b).

for a in range(1,11):

for b in range(1,11):

num = (a* *b) * (b* *a) + 1

flg = False

if num > 1:

for i in ra nge(2, num):

if (num % i) == 0:

flg = True

break

if not flg:

print(str(a)+","+str(b))

The output of the above program is:

(1,1), (1,2), (1,4), (1,6), (1,10), (2,1), (2,2), (2,3), (2,4), (3,2), (4,1), (4,2), (4,4) and (4,6)

The above represent all pairs of prime numbers (a,b) such that a^b * b^a+1 is prime

Read more about prime numbers at:

brainly.com/question/25710806

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1 year ago