All categories

2 years ago

Write an equation for the following: y varies directly with x and z. Find K when x=2, y=12 and z=5.

1 answer:

6 0

$\qquad \qquad \textit{direct joint variation} \\\\ \textit{\underline{y} varies directly with \underline{x} and \underline{z}}~\hspace{8.5em} \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}xz~\hfill } \\\\ \textit{\underline{y} varies directly with \underline{x}, }w^2\textit{ and }z^5~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}xw^2z^5~\hfill } \\\\[-0.35em] ~\dotfill$

$y = kxz\qquad \textit{we know that} \begin{cases} x=2\\ y=12\\ z=5 \end{cases}\implies 12=k(2)(5) \\\\\\ \cfrac{12}{(2)(5)}=k\implies \cfrac{6}{5}=k~\hspace{10em}\boxed{y=\cfrac{6}{5}xz}$

You might be interested in

Write N as a discrete exponential function of t of the form N(t)=A(1+r)t. (HINT: You will need to find (1+r), where r is the rat

Whitepunk [10]

Answer:

$N(t)=84(1+0.0405)^t$ .

Step-by-step explanation:

We have been given that $N(11)=130$ and $N(0)=84$ . We are asked to write N as a discrete exponential function of t of the form $N(t)=A(1+r)^t$ .

Using our given information, we can set an equation as:

$N(0)=A(1+r)^0$

$84=A*1$

$84=A$

Using our given information, we will get:

$N(11)=A(1+r)^{11}$

Substitute the given values:

$130=84(1+r)^{11}$

$\frac{130}{84}=\frac{84(1+r)^{11}}{84}$

$1.5476190476190476=(1+r)^{11}$

Switch sides:

$(1+r)^{11}=1.5476190476190476$

Take 11th root of both sides:

$\sqrt[11]{(1+r)^{11}}=\sqrt[11]{1.5476190476190476}$

$1+r=1.04050024747304$

$r=1.04050024747304-1$

$r=0.04050024747304$

$r\approx 0.0405$

Therefore, our required function would be $N(t)=84(1+0.0405)^t$ .

5 0

2 years ago

Graph y < x2 + 4x. Click on the graph until the correct graph appears.

jonny [76]

Answer: The correct answer is:

_________________________

The given "graph" in the bottom right, lowest corner

Step-by-step explanation:

_________________________

Note: When there is only one (1) equation give for a graph;

and/or: only one (1) "inequality given";

we look for the symbol.

If the symbol is "not" an "equals" symbol (i.e. not an: = symbol) ;

we check for the type of "inequality" symbol.

If there is a: "less than" (<) ; or a "greater than" (>) symbol; the graph of the "inequality" will have "dashed lines" (since there will be a "boundary").

If there is an "inequality" that is a: "less than or equal to" (≤) ;

or a: "greater than or equal to" (≥) ;

→ then there will be not be a dashed line when graphed;

but rather—a "solid line" ; since "less than or equal to" ;

or "greater than or equal to" —is similar to:

"up to AND including"; or: "lesser/fewer than AND including".).

_________________________

Note: We are given the "inequality" :

→ " y < x² + 4x " .

_________________________________

Note that we have a "less than" symbol (< ) ; so the graph will have a:

"solid line" [and not a "dotted line".].

_________________________________

Note that all of the graphs among our 4 answer choices have "dotted lines".

Not that all values (all x and y coordinated) within the "shaded portion" of the corresponding graph are considered part of the graph.

As such, given any point within the shaded part, the x and y coordinates must match the inequality (i.e. the given inequality must be true when one puts in the "x-coordinate" and "y-coordinate" into the "given inequality" :

→ " y < x² + 4x " .

_________________________

Likewise, we can take any point within the "white, unshaded" portion of any of the graph, and take the "x-coordinate" and "y-coordinate" of that point, and the inequality: → " y < x² + 4x " ; will not hold true when the "x-coordinate" and "y-coordinate" values of that point— are substituted into the "inequality".

_________________________

{Note: Answer is continued on images attached.}.

Wishing you the best!

6 0

2 years ago

fref picked 1 4/9 bucket of lemons, and mary picked 1 1/12 buckets of lemons. How many buckets total did they pick

rewona [7]

You will have to add your whole then multiply your fraction

6 0

3 years ago

En una camioneta se pueden transportar 28.5 kilogramos. ¿ Cuántas camionetas se necesitan para transportar 484.5 Kg?

r-ruslan [8.4K]

Answer:

The number of trucks required is 17.

Step-by-step explanation:

28.5 kilograms can be transported in a van. How many trucks are needed to transport 484.5 Kg?

For the transportation of 28.5 kg, one truck is required.

Total mass = 484.5 kg

The number of trucks required is

n = total mass/ mass of one

$n=\frac{484.5}{28.5}\\\\n = 17$

3 0

3 years ago

Help someone please!! don’t understand

Citrus2011 [14]

Radical 2 = 1.4 So 1.4 * 6 = 8.4

a^2 + b^2 = c^2

8.4^2 + 8.4^2 = square root of c

70.56 + 70.56 = 141.12 ≈ 141

Then you must find the square root of 141 which is 11.874 ≈ 11.9

Side a = 8.4
Side b = 8.4
Side c = 11.9

5 0

3 years ago