All categories

2 years ago

Charles is going to buy 3 computer tables for 390$. If he pays the same rate, how much would it cost for 8 computer tables?

Mathematics

1 answer:

Dafna1 [17]2 years ago

7 0

390 divided by 3= $130.
So 130 x 8 = $1040

You might be interested in

Ethan says that the value of 40.7 is 10 times the value of 4.07 is be correct?

VLD [36.1K]

Answer:

He is correct

Step-by-step explanation:

multiplication and division are inverse operations so lets divide to see if he is correct

40.7/10=4.07

he is correct

8 0

2 years ago

Let z=3+i, then find a. Z² b. |Z| c.<img src="https://tex.z-dn.net/?f=%5Csqrt%7BZ%7D" id="TexFormula1" title="\sq

zysi [14]

Given z = 3 + i, right away we can find

(a) square

z ² = (3 + i )² = 3² + 6i + i ² = 9 + 6i - 1 = 8 + 6i

(b) modulus

|z| = √(3² + 1²) = √(9 + 1) = √10

(d) polar form

First find the argument:

arg(z) = arctan(1/3)

Then

z = |z| exp(i arg(z))

z = √10 exp(i arctan(1/3))

z = √10 (cos(arctan(1/3)) + i sin(arctan(1/3))

Any complex number has 2 square roots. Using the polar form from part (d), we have

√z = √(√10) exp(i arctan(1/3) / 2)

and

√z = √(√10) exp(i (arctan(1/3) + 2π) / 2)

Then in standard rectangular form, we have

$\sqrt z = \sqrt[4]{10} \left(\cos\left(\dfrac12 \arctan\left(\dfrac13\right)\right) + i \sin\left(\dfrac12 \arctan\left(\dfrac13\right)\right)\right)$

and

$\sqrt z = \sqrt[4]{10} \left(\cos\left(\dfrac12 \arctan\left(\dfrac13\right) + \pi\right) + i \sin\left(\dfrac12 \arctan\left(\dfrac13\right) + \pi\right)\right)$

We can simplify this further. We know that z lies in the first quadrant, so

0 < arg(z) = arctan(1/3) < π/2

which means

0 < 1/2 arctan(1/3) < π/4

Then both cos(1/2 arctan(1/3)) and sin(1/2 arctan(1/3)) are positive. Using the half-angle identity, we then have

$\cos\left(\dfrac12 \arctan\left(\dfrac13\right)\right) = \sqrt{\dfrac{1+\cos\left(\arctan\left(\dfrac13\right)\right)}2}$

$\sin\left(\dfrac12 \arctan\left(\dfrac13\right)\right) = \sqrt{\dfrac{1-\cos\left(\arctan\left(\dfrac13\right)\right)}2}$

and since cos(x + π) = -cos(x) and sin(x + π) = -sin(x),

$\cos\left(\dfrac12 \arctan\left(\dfrac13\right)+\pi\right) = -\sqrt{\dfrac{1+\cos\left(\arctan\left(\dfrac13\right)\right)}2}$

$\sin\left(\dfrac12 \arctan\left(\dfrac13\right)+\pi\right) = -\sqrt{\dfrac{1-\cos\left(\arctan\left(\dfrac13\right)\right)}2}$

Now, arctan(1/3) is an angle y such that tan(y) = 1/3. In a right triangle satisfying this relation, we would see that cos(y) = 3/√10 and sin(y) = 1/√10. Then

$\cos\left(\dfrac12 \arctan\left(\dfrac13\right)\right) = \sqrt{\dfrac{1+\dfrac3{\sqrt{10}}}2} = \sqrt{\dfrac{10+3\sqrt{10}}{20}}$

$\sin\left(\dfrac12 \arctan\left(\dfrac13\right)\right) = \sqrt{\dfrac{1-\dfrac3{\sqrt{10}}}2} = \sqrt{\dfrac{10-3\sqrt{10}}{20}}$

$\cos\left(\dfrac12 \arctan\left(\dfrac13\right)+\pi\right) = -\sqrt{\dfrac{10-3\sqrt{10}}{20}}$

$\sin\left(\dfrac12 \arctan\left(\dfrac13\right)+\pi\right) = -\sqrt{\dfrac{10-3\sqrt{10}}{20}}$

So the two square roots of z are

$\boxed{\sqrt z = \sqrt[4]{10} \left(\sqrt{\dfrac{10+3\sqrt{10}}{20}} + i \sqrt{\dfrac{10-3\sqrt{10}}{20}}\right)}$

and

$\boxed{\sqrt z = -\sqrt[4]{10} \left(\sqrt{\dfrac{10+3\sqrt{10}}{20}} + i \sqrt{\dfrac{10-3\sqrt{10}}{20}}\right)}$

3 0

2 years ago

Read 2 more answers

According to the graph, the first coordinate of which point is a negative number

kolbaska11 [484]

Answer:

Coordinate D. Because D lies on the 2nd quadrant, meaning that x has a negative value whereas y is positive.

3 0

2 years ago

Read 2 more answers

1) Which linear equation BEST represents the line of best fit for the scatterplot? A) y = x B) y = 3x C) y = -3x D) y = 5x + 1 2

Tresset [83]

Answer:

1) A. y = x + 2

Once a line of best fit has been placed upon a scatter graph it is straightforward to find the equation. The general equation of a straight line is: y = mx + c Where m is the slope (gradient) of the line and c is the y-intercept.

4) d. strong positive correlation.

The slope of the line is positive. Most points lie close to the line.

(I am not sure if this is correct or not, I am so sorry)

3 0

3 years ago

The sum of the first three terms of a sequence is 6 and the fourth term is 16

Sati [7]

Answer:

a₁ = -5, d = 7, a₂ = 2, a₃ = 9, a₄ = 16

equation of sequence: $\boxed{\bold{a_n=7n-12}}$

Step-by-step explanation:

a₁ + a₂ + a₃ = 6

a₁ + a₁ + d + a₁ + 2d = 6

3a₁ + 3d = 6

a₁ + d= 2 ⇒ a₁ = 2 - d

a₄ = 16

a₁ + 3d = 16

2 - r + 3d = 16

2d = 14

d = 7

a₁ = 2-7 = -5

a₁ = -5, d = 7 ⇒ a₂ = -5+7 = 2, a₃ = 2+7 = 9, a₄ = 9+7 = 16

equation of arithmetic sequence:

$a_n=a_1+d(n-1)\\\\a_n=-5+7(n-1)\\\\\underline{a_n=7n-12}$

6 0

2 years ago