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11111nata11111 [884]
3 years ago
14

It costs a family of two $25 to go to the state fair, and a family of six $65. Find the equation, rate of change, and initial va

lue of the function that represents this situation?
Mathematics
1 answer:
motikmotik3 years ago
6 0

Answer:

Step-by-step explanation:

Given:

Family of 2

Cost, C1 = $25

Family of 6

Cost, C2 = $65

Given that 2 points are given above as the following in coordinate form:

A(2,25) and B(6,65)

Rate of change is given as = (y2 - y1)/(x2 - x1)

= (65 - 25)/(6-2)

= 40/4

Therefore,

(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)

(y - 25)/(65 - 25) = (x - 2)/(6 - 2)

(y - 25)/40 = (x - 2)/4

(y - 25) = 40/4 × (x - 2)

(y - 25) = 10 × (x - 2)

Expanding,

y - 25 = 10x - 20

y = 10x - 20 + 25

y = 10x + 5

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1 Point
I am Lyosha [343]

Option C

The ratio for the volumes of two similar cylinders is 8 : 27

<h3><u>Solution:</u></h3>

Let there are two cylinder of heights "h" and "H"

Also radius to be "r" and "R"

\text { Volume of a cylinder }=\pi r^{2} h

Where π = 3.14 , r is the radius and h is the height

Now the ratio of their heights and radii is 2:3 .i.e  

\frac{\mathrm{r}}{R}=\frac{\mathrm{h}}{H}=\frac{2}{3}

<em><u>Ratio for the volumes of two cylinders</u></em>

\frac{\text {Volume of cylinder } 1}{\text {Volume of cylinder } 2}=\frac{\pi r^{2} h}{\pi R^{2} H}

Cancelling the common terms, we get

\frac{\text {Volume of cylinder } 1}{\text {Volume of cylinder } 2}=\left(\frac{\mathrm{r}}{R}\right)^{2} \times\left(\frac{\mathrm{h}}{\mathrm{H}}\right)

Substituting we get,

\frac{\text {Volume of cylinder } 1}{\text {Volume of cylinder } 2}=\left(\frac{2}{3}\right)^{2} \times\left(\frac{2}{3}\right)

\frac{\text {Volume of cylinder } 1}{\text {Volume of cylinder } 2}=\frac{2 \times 2 \times 2}{3 \times 3 \times 3}

\frac{\text {Volume of cylinder } 1}{\text {Volume of cylinder } 2}=\frac{8}{27}

Hence, the ratio of volume of two cylinders is 8 : 27

7 0
3 years ago
Which of the following is a radical equation?<br> x√3=13<br> x+3√3=13<br> √x+3=13<br> x+3=√13
Shtirlitz [24]
The answer would be: <span>√x+3=13

</span>A radical equation is an equation with at least one variable put on a radical form. In this question, there is only one kind of variable which is x. Then, you need to find the equation where x is in the radical form. The radical form can be expressed with square root symbol.
The option with √x would be only <span>√x+3=13
</span>
7 0
3 years ago
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irina1246 [14]

Answer:

Answers in the pics

Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask me in the comments below ;)

8 0
3 years ago
find the value of the variable. if your answer is not an interger, leave it in simplest radical form.
kotykmax [81]

Answer:

A

Step-by-step explanation:

using the sine ratio in the right triangle, then

sin 45° = \frac{opposite}{hypotenuse} = \frac{x}{5}

multiply both sides by 5

note the exact value of sin 45° = \frac{\sqrt{2} }{2}

x = 5 × sin 45° = 5 × \frac{\sqrt{2} }{2} = \frac{5\sqrt{2} }{2}




4 0
3 years ago
A given line has a slope of - ⅚.  (ie, m = -⅚)
Nastasia [14]

Answer:

Step-by-step explanation:

The slope of the line parallel to that line is -5/6 because parallel lines have the same slope.

8 0
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