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san4es73 [151]
3 years ago
9

Peter has decided to save $30 each week to buy a new stereo system.Write a direct variation equation for the amount of money, m,

that Peter has saved in, w, weeks.
Mathematics
1 answer:
Lena [83]3 years ago
3 0
M=w-30 is the answer if you want to find how much you want to find each week.
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Which of the following of x and y would make up the following expression represent a real number? (4+5i)(x+yi)
salantis [7]

Answer:

x = 4 and y = - 5

Step-by-step explanation:

note that the product of a complex number and it's conjugate is real

That is

(a + bi)(a - bi) where a, b are real

= a² - abi + abi - b²i²

= a² + b² ← a real number

For (4 + 5i)(x + yi) to be real

we require (x + yi) to be the conjugate of 4 + 5i , that is 4 - 5i

(4 + 5i)(4 - 5i) ⇒ x = 4 and y = - 5



8 0
3 years ago
Retro Rides is a club for owners of vintage cars and motorcycles. Every year the club gets together for a ride. This year, 53 ve
kari74 [83]
21 cars, 32 motorcycles.
create a system of equations using x for cars and y for motorcycles.
\left \{ {{x+y=53} \atop {4x+2y=148}} \right.
multiply the top equation by 2 to prepare for elimination method
\left \{ {{2x+2y=106} \atop {4x+2y=148}} \right.
subtract terms
\left \{ {{2x+2y=106} \atop {-4x-2y=-148}} \right.  = (-2x = -42)
divide both sides by negative 2 to solve for x
x =21
plug in x  into original equation to solve for y.
21 + y = 53
subtract both sides by 21
y=32



8 0
3 years ago
Each 1/2 inch on a scale model represents an actual length of 1/6 of a yard. What length on the model represents 1 yard?
ivanzaharov [21]

Answer:

The file contains the solution to the question

8 0
2 years ago
Determine the mass of a solid steel ball that has a diameter of 10 cm. The density of pure steel is 8.09 g/cm3
Basile [38]

Answer:

<em>The mass of the steel ball is 4,235.9 gr</em>

Step-by-step explanation:

<u>Density</u>

The density ρ of a substance is a measure of its mass per unit volume:

\displaystyle \rho=\frac{m}{V}

If the density and the volume are given, the mass can be calculated by solving the above formula for m:

m=\rho.V

We know the density of pure steel ρ=8.09 gr/cm3 and the diameter of a solid steel ball d=10 cm.

We need to calculate the volume of the sphere:

The volume of a sphere of radius r is given by:

\displaystyle V=\frac{4}{3}\cdot \pi\cdot r^3

The radius is half the diameter: r= 10/2 = 5 cm. Thus:

\displaystyle V=\frac{4}{3}\cdot \pi\cdot 5^3

Calculating:

V=523.6\ cm^3

The mass is:

m=8.09 gr/cm^3 \cdot 523.6\ cm^3

m=4,235.9 gr

The mass of the steel ball is 4,235.9 gr

4 0
3 years ago
How many centimeters are in 8 meters?
Law Incorporation [45]

Answer:

800 centimeters.......

3 0
3 years ago
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