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3 years ago

Find the volume of a prism with a length of 6ft, width of 9ft, and height of 7ft.

Mathematics

1 answer:

Ipatiy [6.2K]3 years ago

3 0

Answer:

Step-by-step explanation:

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Find the quotient of these Complex Numbers. (5-i) / (3+2i)

JulsSmile [24]

Let the given complex number

z = x + ix = $\dfrac{5-i}{3+2i}$

We have to find the standard form of complex number.

Solution:

∴ x + iy = $\dfrac{5-i}{3+2i}$

Rationalising numerator part of complex number, we get

x + iy = $\dfrac{5-i}{3+2i}\times \dfrac{3-2i}{3-2i}$

⇒ x + iy = $\dfrac{(5-i)(3-2i)}{3^2-(2i)^2}$

Using the algebraic identity:

(a + b)(a - b) = $a^{2}$ - $b^{2}$

⇒ x + iy = $\dfrac{15-10i-3i+2i^2}{9-4i^2}$

⇒ x + iy = $\dfrac{15-13i+2(-1)}{9-4(-1)}$ [ ∵ $i^{2} =-1$ ]

⇒ x + iy = $\dfrac{15-2-13i}{9+4}$

⇒ x + iy = $\dfrac{13-13i}{13}$

⇒ x + iy = $\dfrac{13(1-i)}{13}$

⇒ x + iy = 1 - i

Thus, the given complex number in standard form as "1 - i".

5 0

3 years ago

Three friends collected aluminum cans from the neighborhood to recycle in total they receive 300 cans many collected 90 Jim coll

spin [16.1K]

Given

Total cans = 300

Manny= 90

Jim =100

Bob=110

Now their percentage

Manny percentage

$\begin{gathered} manny=\frac{90}{300}\times100\text{ \%} \\ \\ Manny\text{ percentage=}\frac{90}{3}\text{ \%} \\ \\ Manny\text{ percentage =30 \%} \end{gathered}$

Jim Percentage

$\begin{gathered} Jim=\frac{100}{300}\times100\text{ \%} \\ Jim\text{ percentage=}\frac{1}{3}\times100\text{ \%} \\ Jim\text{ percentage=33.333\%} \end{gathered}$

Bob percentage

$undefined$

6 0

1 year ago

Which is the value of x in the equation? 4(x-3) = 40

mario62 [17]

Answer:14

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

The width and length of a rectangle (in feet)are consecutive odd integers. If the length is increased by 5 feet, the area of the

Tresset [83]

Original:
The width and length of a rectangle are consecutive odd integers
so W = x and L = x + 2

If the length is increased by 5 feet, then new L = x + 2 + 5 = x + 7

A = L x W
60 = (x + 7) x
60 = x^2 + 7x
x^2 + 7x - 60 = 0
(x - 5)(x + 12) = 0
x = 5 and x = -12

From here you have x = W = 5 ft and L = x + 2 = 5 + 2 = 7 feet

Area of original = 5 x 7 = 35

answer
the area of the original rectangle: 35 ft^2

4 0

3 years ago

Of a number is what percentage of that number?

earnstyle [38]

Answer:

13/10 = 130%

13/10 x 100

= 130%

7 0

4 years ago