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2 years ago

Make x the subject of y(x+z)=3z(x+y)

Mathematics

2 answers:

marissa [1.9K]2 years ago

7 0

y(x+z) + 3z(x+y)

yx + yz + 3xz + 3yz

yx =3xz +4yz

yx - 3xz = 4yz

Divide both sides by yz

x - 3x = 4yz / yz

-2x = 4

nirvana33 [79]2 years ago

5 0

First distribute
a(b+c)=ab+ac
y(x+z)=yx+yz

3z(x+y)=3zx+3zy

so now we have
yx+yz=3zx+3zy
make all x's on one side
subtract 3zy frm btohs ides
yx-3zx+yz=3zy
subtract yz frmo both sides
yx-3zx=3zy-yz
undistribute the x on the left side
x(y-3z)=2zy
divide both sides by (y-3z)
x= $\frac{2zy}{y-3z}$

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Explain how you could write a quadratic function in factored form that would have a vertex with an x-coordinate of 3 and two dis

skad [1K]

The definition of quadratic function is given by:

 $(1) \ f(x)=ax^{2}+bx+c \\ \\ where \ a, b, c \ are \ real \ values$ 

So the problem asks for two conditions:

1. Write the quadratic function in factored form. 
2. The vertex has an x-coordinate of 3.

Then the equation (1) must be written as follows:

 $f(x)=(x-m)(x-n) \\ \\ where \ m \ and \ n \ are \ the \ roots$ 

To satisfy the two conditions:

$\frac{m+n}{2}=3$

So we are free to choose the value of one root, say:

$m=1$

Thus:

$n=6-1=5$

Finally, the answer is:

$f(x)=(x-1)(x-5)$

The graph of this function is shown in the figure below.

4 0

2 years ago

Read 2 more answers

15. The floor plan of the basement of a shopping centre is drawn to a scale of 1:400.

maks197457 [2]

Answer:

4 hectares

Step-by-step explanation:

The scale factor is:

k = 1/400

Applied to the area we consider k² as the area is the product of two dimensions.

Find the actual area:

0.25 m² : (1/400)² =
0.25 m² * 160000 =
40000 m² =
40000 * 1/10000 hectares =
4 hectares

6 0

2 years ago

Ben, Bob and Bill are triplets. They were born 5 years before their sister, Stephanie. This year the product of their four ages

maria [59]

Let the triplets' age be x, the sister's age is then x-5.
product of their age as given
xÂł.(x-5)=75749+x+x+x+x-5
x^4 - 5xÂł= 4x +75744
x^4 - 5xÂł -4x -75744=0
resolving the equation,
we get
x = 18
therefore, Age of ben,bob and bill is 18
so , age of stephanie is x-5 = 18-5 = 13
stephanie is 13 years old.

3 0

3 years ago

Consider the following. y = x2 y = 20 − x Maple Generated Plot (a) Find the area of the region by integrating with respect to x.

Hunter-Best [27]

Answer:

area = 121.5

Step-by-step explanation:

See below for a plot and the integral. We assume you are interested in the entire bounded region.

$\displaystyle\text{area}=\int_{-5}^4{(20-x-x^2)}\,dx=\left.20x-\dfrac{x^2}{2}-\dfrac{x^3}{3}\right|_{-5}^4\\\\=20(4-(-5))-\dfrac{4^2-(-5)^2}{2}-\dfrac{4^3-(-5)^3}{3}\\\\=180+\dfrac{9}{2}-63=121.5$

7 0

2 years ago

An osha inspection was conducted at Raul’s workplace. He is curious about the results and wonders what actions his employers mig

Ivan

Answer : YES!

Explanation : An OSHA inspection when was being conducted at Raul's workplace; He has full right to know about the results and can also ask/question his employer about the actions that they will be taking to fix if any issues are identified during the inspection.

As per the guidelines of OSHA which stands for The Occupational Safety and Health Act, employers are responsible for providing a safe and healthful workplace for their workers, also it gives full right to the employees to know what are the safety measures taken by their organization. OSHA is a federal law that was established in 1970 to ensure that America's workforce has a safe environment in which to work. The Occupational Safety and Health Administration (OSHA), the federal agency that enforces the OSH law was established by the law and was formed in 1971.

5 0

3 years ago