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3 years ago

The value of y directly varies with x, and y=5.4 when x =9. Find y when x= negative 10

1 answer:

7 0

$\bf \qquad \qquad \textit{direct proportional variation}\\\\
\textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------$

$\bf \textit{we also know that }
\begin{cases}
y=5.4\\
x=9
\end{cases}\implies 5.4=k9\implies \cfrac{5.4}{9}=k
\\\\\\
\cfrac{\quad \frac{54}{10}\quad }{9}=k\implies \cfrac{54}{10}\cdot \cfrac{1}{9}=k\implies \cfrac{3}{5}=k\qquad thus\qquad \boxed{y=\cfrac{3}{5}x}
\\\\\\
\textit{when x = -10, what is \underline{y}?}\qquad y=\cfrac{3}{5}(-10)$

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One year, the population of a city was 352,000. Several years later it was 337,920.

kvasek [131]

here is the method :

you take Value 1 and Value 2

And you do : ( Value 2 - Value 1) / (Value 1 ) * 100

Here we have : Value 1 = 352 000

Value 2 = 337 920

So now we apply :

( 337 920 - 352 000 ) / ( 352 000) * 100 = -4

Population decreased by by 4 %

You can also make :

352 000 * X = 337 920

X = 337 920 / 352 000

X = 0.96

if the multiplier is 0.96 , it's mean that we lost 1 -0.96 = 0.04

which mean - 4%

8 0

2 years ago

What is true of the data in the dot plot? Check all that apply.

otez555 [7]

True answers for data in the plot are

The center is 13

The center is not 14

The Peak is 14.

It has three clusters

It is not symmetric to left or right it is bi-modal.

It is has a range from 10 to 15 most number of data points are 13 to 15.

Total number times Shelly waited is 16 times.

Step-by-step explanation:

While taking cumulative frequency 56.75 percentage comes in 13%.
It is the center point of the data.
The 14 is not the center as it shows 93rd percent.
It has three clusters 0-2 has one cluster,2-4 has 2nd cluster,5-8 third.
It is not skewed on the left is has bi modal frequency has two heights.
The person indeed waited for 16 times adding total dots.
There was a zero 12 which created bi-modal distribution

8 0

3 years ago

Read 2 more answers

The area of a rectangle is represented by the polynomial x^2+3x-6x-18. What are the length, width, and area of the rectangle if

Nitella [24]

Answer:

Length = 15

Width = 6

Area = 90

Step-by-step explanation:

Area of the rectangle = ${x}^{2} + 3x - 6x - 18$

Lets factorise the polynomial

$= > x(x + 3) - 6(x + 3)$

$= > (x + 3)(x - 6)$

We know that Area = Length × Width

Let the length be (x + 3) & width be (x - 6)

Its given in the question that x = 12. So putting the value of x gives ,

Length = $x + 3 = 12 + 3 = 15$

Width = $x - 6 = 12 - 6 = 6$

Area = Length × Width = 15 × 6 = 90

5 0

3 years ago

Given that Cosecant (t) = negative StartFraction 13 Over 5 EndFraction for Pi less-than t less-than StartFraction 3 pi Over 2 En

Sergio [31]

Answer:

$\bold{cot(t) =\dfrac{12}{5}}$

Step-by-step explanation:

Given that:

$Cosec (t) = -\frac{13}5$

for $\pi < t < \frac{3 \pi}2$

That means, angle $t$ is in the 3rd quadrant.

To find:

Value of cot(t)

Solution:

First of all, let us recall what trigonometric ratios are positive and what trigonometric ratios are negative in 3rd quadrant.

In 3rd quadrant, tangent and cotangent are positive.

All other trigonometric ratios are negative.

Let us have a look at the following identity:

$cosec^2\theta -cot^2\theta =1$

here, $\theta =t$

So, $cosec^2t-cot^2t=1$

$\Rightarrow (-\dfrac{13}{5})^2-cot^2t=1\\\Rightarrow (\dfrac{169}{25})-cot^2t=1\\\Rightarrow \dfrac{169}{25}-1=cot^2t\\\Rightarrow \dfrac{169-25}{25}=cot^2t\\\Rightarrow \dfrac{144}{25}=cot^2t\\\Rightarrow cot(t)=\pm\sqrt{\dfrac{144}{25}}\\\Rightarrow cot(t)=\pm\dfrac{12}{5}$

But, angle $t$ is in 3rd quadrant, so value of

$\bold{cot(t) =\dfrac{12}{5}}$

4 0

3 years ago

A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $65. A season pass costs $400. The skier

Vlad [161]

Let x be the number of days.

Daily pass:
65x + 30x
95x

Season pass:
400 + 30x

95x > 400 + 30x
65x > 400
x > 6.15

The number of days can't be 6.15, so you must round. You can't go down because then the price will be more expensive, so you have to round up.

It would take 7 days until the season pass is less expensive than the daily pass.
----------------------
You can check this by plugging in the x.

95x > 400 + 30x
95(7) > 400 + 30(7)
665 > 400 + 210
665 > 600
The daily pass is more expensive than the season pass.

3 0

3 years ago