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3 years ago

2. Factorise : (i) 9x² + y² + 64 - 6xy +16y - 48x

Mathematics

1 answer:

kumpel [21]3 years ago

4 0

Answer:

9x² + y² + 64 - 6xy - 16y - 48x

= 9x² - 6xy - 48x + y² - 16y + 64

= 9x² - 6x(y - 8) + y² - 2.8y + 8²

= (3x)² - 6x(y - 8) + (y - 8)²

= [3x - (y - 8)]²

= (3x - y + 8)²

Step-by-step explanation:

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my son had his 18 months visit to the doctor last week.the nurse took several measurement while we were there.his length(height)

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18 months ……33inches, weight 25.5 pounds

When he was born = 9 months…20 inches, weight 8, 4 pounds

Every 9 months his height growth is 33-20 = 13 inches, his weight is 25.5-8.4=17.1 pounds

Pounds. This means, for every 9 months, his growth is 13 inches and his weight is 17.1 pounds. For example we can determine his growth in 3 years.

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3 years ago

graph the parabola y equals negative x squared + 3 to graph a parabola plot the vertex and four additional points two on each si

Nataliya [291]

You don't have the graph icon here, so we'll have to graph this parabola without it.

Your parabola is y = -x^2 + 3., which resembles y = a(x-h)^2 + k. We can tell immediately that this parabola opens down and that the vertex is (0,3).

Plot (0,3). Besides being the vertex, this point is also the max. of the function.

Now calculate four more points. Choose four arbitrary x-values, such as {-2, 1, 4, 5} and find the y value for each one. Plot the resulting four points. Draw a smooth curve thru them, remembering (again) that the vertex is at (0,3) and that the parabola opens down.

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2 years ago

A jar contains only pennies, nickels, dimes, and quarters. There are 23 pennies, 22 dimes, and 20 quarters. The rest of the

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Answer:

1. 65 coins

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Step-by-step explanation:

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2 years ago

Solve the system of equations using multiplication. 3x – 3y = –3 5x – y = –13 What is the solution of the system?

love history [14]

ANSWER

The solution is

x=-3,y=-2

EXPLANATION

First equation

3x – 3y = –3

Second Equation:

5x – y = –13

Multiply the second equation by 3 to get:

Third equation:

15x-3y=-39

Subtract the first equation from the third equation:

$15x - 3x = - 39 - - 3$

$12x = - 36$

Divide both sides by 12,

$x = \frac{ - 36}{12} = - 3$

Put x=-3 into the first equation:

$3( - 3) - 3y = - 3$

$- 9 - 3y = - 3$

Group like terms,

$- 3y = - 3 + 9$

$- 3y = 6$

$y = - 2$

The solution is

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6 0

3 years ago

A cylinder has a 12-inch diameter and is 15 inches tall. It is filled to the top with water. A 6-inch-diameter ball is placed wi

Tems11 [23]

The volume of the cylinder is the space occupied by the cylinder. The volume of the water in the cylinder is 1583.36266 in³.

<h3>What is the volume of a cylinder?</h3>

The volume of the cylinder is the space occupied by the cylinder. It is calculated with the help of the formula,

$\text{Volume of the cyllinder}= \pi r^2h$

As it is given that the diameter of the cylinder is 12 inches while the height of the cylinder is 15 inches, also, it has a ball of the diameter of 6 inches placed inside the cylinder, therefore, the volume of the water that is inside the cylinder is the difference in the volume of the cylinder and the volume of the spherical ball.

$\text{Volume of the cyllinder}= \pi r^2h = \dfrac{\pi}{4}d^2 h$

Substitute the values,

$\begin{aligned}\text{Volume of the cyllinder}&= \dfrac{\pi}{4}d^2 h\\& = \dfrac{\pi}{4} \times (12^2) \times 15\\ &=1696.46\rm\ in^3\end{aligned}$

Now, the volume of the ball is equal to the volume of the sphere therefore, the volume of the ball can be written as,

$\text{Volume of the sphere} = \dfrac{4}{3}\pi r^3$

$= \dfrac{4}{3}\pi r^3\\\\= \dfrac{4}{3}\times \pi \times (3^3)\\\\= 113.097\rm\ in^3$

Further, the volume of the water that is inside the cylinder can be written as,

The volume of water = Volume of the cylinder - Volume of the sphere

= 1696.46 - 113.097

= 1583.36266 in³

Hence, the volume of the water in the cylinder is 1583.36266 in³.

Learn more about Volume of the Cylinder:

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2 years ago

2. Factorise : (i) 9x² + y² + 64 - 6xy +16y - 48x​

2. Factorise : (i) 9x² + y² + 64 - 6xy +16y - 48x