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2 years ago

If x varies directly with y and x=3.5 when y=14 find x when y=18

1 answer:

4 0

$\bf \qquad \qquad \textit{direct proportional variation}
\\\\
\textit{\underline{x} varies directly with \underline{y}}\qquad \qquad x=ky\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------\\\\
\textit{we also know that }
\begin{cases}
x=3.5\\
y=14
\end{cases}\implies 3.5=k14\implies \cfrac{3.5}{14}=k
\\\\\\
\cfrac{1}{4}=k\qquad therefore\qquad \boxed{x=\cfrac{1}{4}y}
\\\\\\
\textit{when y = 18, what is \underline{x}?}\qquad x=\cfrac{1}{4}(18)$

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How do you graph -1/5x-1 and 4/5x-6

kakasveta [241]

Answer:

The points for the given to linear equations is (5 , - 2) and (5 , - 1)

The points is plotted on the graph shown .

Step-by-step explanation:

Given as :

The two linear equation are

y = $\dfrac{-1}{5}$ x - 1 ...........1

y = $\dfrac{4}{5}$ x - 6 ...........2

Now, Solving both the linear equations

Put the value of y from eq 2 into eq 1

I.e $\dfrac{4}{5}$ x - 6 = $\dfrac{-1}{5}$ x - 1

Or, $\dfrac{4}{5}$ x + $\dfrac{1}{5}$ x = 6 - 1

Or, $\dfrac{4 + 1}{5}$ x = 5

or, $\dfrac{5}{5}$ x = 5

∴ x = 5

Now, Put the value of x in eq 1

So, y = $\dfrac{-1}{5}$ x - 1

Or, y = $\dfrac{-1}{5}$ × 5 - 1

or, y = $\dfrac{-5}{5}$ - 1

Or, y = - 1 - 1

I.e y = -2

So, For x = 5 , y = - 2

Point is ( $x_1$ , $y_1$ ) = (5 , - 2)

Again , put the value of x in eq 2

So, y = $\dfrac{4}{5}$ x - 6

Or, y = $\dfrac{4}{5}$ × 5 - 6

Or, y = $\frac{4\times 5}{5}$ - 6

Or, y = 4 - 6

I.e y = - 2

So, For x = 5 , y = - 2

Point is ( $x_2$ , $y_2$ ) = (5 , - 2)

Hence, The points for the given to linear equations is (5 , - 2) and (5 , - 2)

The points is plotted on the graph shown . Answer

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3 years ago

Of all rectangles with a fixed perimeter of p, which one has the maximum area? (give the dimensions in terms of p.)

TiliK225 [7]

<span>For all rectangles with a fixed perimeter of p the rectangle with the maximum area is one where the length is p/4 and the width is p/4, in other words a square. The area of such a rectangle would be (p*p) /16.</span>

8 0

3 years ago

Find the area pf a trapezoid with a base of 26.7 ft , a height of 15.4 and top of 9.9 ft

evablogger [386]

Hello!

To find the area of the trapezoid, you use the formula A=1/2h(a+b), where a and b represent the two base lengths.

Since we already know the two bases and the height, we can just plug them into the equation to find the area.

A=1/2·15.4(26.7+9.9)
A=1/2·15.4(36.6)
A=1/2·563.64
A=281.82

The area is 281.82 ft².

I hope this helps!

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3 years ago

Someone help me plz?

Marina CMI [18]

Answer:

Distance

Step-by-step explanation:

Distance is unknown in the given situation.

4 0

2 years ago

Read 2 more answers

The feet of the average adult woman are 24.6 cm long, and foot lengths are normally distributed. If 16% of adult women have feet

nevsk [136]

Answer:

Approximately 16% of adult women have feet longer than 27.2 cm.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The feet of the average adult woman are 24.6 cm long

This means that $\mu = 24.6$