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2 years ago

A line passes through the point (0, –4) and has a slope of 2/3. What is the equation of the line?

Mathematics

1 answer:

pshichka [43]2 years ago

3 0

Step-by-step explanation:

the answer is in the above image

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What is the selling price of a $2,499 motorcycle if a $249 discount is given?

erma4kov [3.2K]

The answer is $2,250. (D). To get the answer you do 2,499-249= 2,250. Hope this helps!!

5 0

3 years ago

I need the written form for 293,805

yan [13]

Two hundred ninety three thousand eight hundred and five

5 0

3 years ago

The prices of commodities X,Y,Z are respectively x, y, z, rupees per unit. Mr. A purchases 4 units of Z and sells 3 units of X a

liubo4ka [24]

Answer:

$(x,y,z)=(1477, 1464, 1437)$

Step-by-step explanation:

Consider the selling of the units positive earning and the purchasing of the units negative earning.

Mr. A purchases 4 units of Z and sells 3 units of X and 5 units of Y
Mr.A earns Rs6000

So, the equation would be

$3x + 5y - 4z = 6000$

Mr. B purchases 3 units of Y and sells 2 units of X and 1 units of Z
Mr B neither lose nor gain meaning he has made 0₹

hence,

$2x - 3y + z = 0$

Mr. C purchases 1 units of X and sells 4 units of Y and 6 units of Z
Mr.C earns 13000₹

therefore,

$- x + 4y + 6z = 13000$

Thus our system of equations is

$\begin{cases}3x + 5y - 4z = 6000\\2x - 3y + z = 0\\ - x + 4y + 6z = 13000\end{cases}$

<u>Solving </u><u>the </u><u>system </u><u>of </u><u>equations</u><u>:</u>

we will consider elimination method to solve the system of equations. To do so ,separate the equation in two parts which yields:

$\begin{cases}3x + 5y - 4z = 6000\\2x - 3y + z = 0\end{cases}\\\begin{cases}2x - 3y + z = 0\\ - x + 4y + 6z = 13000\end{cases}$

Now solve the equation accordingly:

$\implies\begin{cases}11x-7y=6000\\-13x+22y=13000\end{cases}$

Solving the equation for x and y yields:

$\implies\begin{cases}x= \dfrac{223000}{151}\\\\y= \dfrac{221000}{151}\end{cases}$

plug in the value of x and y into 2x - 3y + z = 0 and simplify to get z. hence,

$\implies z= \dfrac{217000}{151}$

Therefore,the prices of commodities X,Y,Z are respectively approximately 1477, 1464, 1437

6 0

2 years ago

What is the equation of the circle with center (16, - 12) and a radius of 5

eimsori [14]

Answer:

x^2+y^2-32x+24y+375=0

Step-by-step explanation:

Equation of circle with given centre (h,k) and radius=r is

(x-h)^2+(y-k)^2=r^2

Given centre are=(16, - 12) and radius= 5

So equation of circle=

(x-16)^2+(y- -12)^2=5^2

x^2-32x+256+y^2+24y+144=25

x^2+y^2-32x+24y+375=0

Answer

5 0

2 years ago

How did we transform from f(x) =x2 to g(x) = -3x2

Oksi-84 [34.3K]

Answer:

f(x) is reflected over the x-axis and vertically scaled by a factor of 3

Step-by-step explanation:

If you compare the two functions, you see that ...

g(x) = -3f(x)

Multiplication by -1 effects a reflection over the x-axis. (All y-values are transformed to their opposite.)

Multiplication by 3 is a vertical scaling by a factor of 3.

Taken together, f(x) is reflected over the x-axis and vertically scaled by a factor of 3.

7 0

2 years ago