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Sergeeva-Olga [200]
3 years ago
13

what is the distance between the line going through points (1, -5/4) and (1/3, -3/4) and the point (2, -3)?

Mathematics
1 answer:
Mamont248 [21]3 years ago
6 0

Answer:

1.60078105936

Step-by-step explanation:

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Suppose you need to get the dent in your car fixed. You see the ads in the newspaper above (mikes repair shop $100 service charg
Norma-Jean [14]

Answer:

<em>Total Cost at Amy's shop is $280 which is less than the total cost at Mike's shop which is $295, so I will take the car to Amy's shop</em>

<em>Point of intersection: (x,y) = (4,360)</em>

Explanation:

Part 1 )

Let x = number of hours worked

Let y = total cost to you

Determining where to take the car:

<em>Total Cost at Amy's shop is $280 which is less than the total cost at Mike's shop which is $295</em>

Mike's repair shop:

Service fee: $100

Per hour rate: $65

Let x is the number of hours worked on. Total cost will be equal to the service fee plus hourly charges. Charges per an hour are $65, so for x hours the charges will be 65x.

Therefore, total cost for Amy's repair shop can be written as:

y = 100 + 65x ------(1)

For 3 hours work: y = 100 + 65(3)

<em>Cost at Mike's, y = $100 + $195 = $295</em>


<em>Amy's repair shop: </em>

Service fee: $40

Per hour rate: $80

Charges per an hour are $40, so for x hours the charges will be 80x.

Therefore, total cost for Amy's repair shop can be written as:

y = 40 + 80x ------(2)

For 3 hours work: x = 3

y = 40 + 80(3)

<em>Cost at Amy's, y  = $40 + $240 = $280</em>


<em>Part 2)</em>

<em>Find the point of intersection</em>

<em>Using elimination method:</em>

<em>y = 100 + 65 x    ------1</em>

<em>y = 40 + 80x      ------2</em>

<em>As the y coefficients are equal we will subtract eq1 from eq2</em>

<em>y - y = 40 + 80x - 100 - 65x</em>

<em>0 = -60 + 15x</em>

60 = 15x

x = \frac{60}{4}

x = 4

put x = 4 in eq 1

we get y = 100 + 65 (4) = 100 + 260 = 360

x = 4, y = 360

Point of intersection: (x,y) = (4,360)



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PLS HELP ME!!! The figure is made up of a cone and a hemisphere. To the nearest whole number, what is the approximate volume of
Pachacha [2.7K]

Hello!

The figure is made up of a cone and a hemisphere. To the nearest whole number, what is the approximate volume of this figure? Use 3.14 to approximate π . Enter your answer in the box. cm³

Data: (Cone)

h (height) = 12 cm

r (radius) = 4 cm (The diameter is 8 being twice the radius)

Adopting: \pi \approx 3.14

V (volume) = ?

Solving: (Cone volume)

V = \dfrac{ \pi *r^2*h}{3}

V = \dfrac{ 3.14 *4^2*\diagup\!\!\!\!\!12^4}{\diagup\!\!\!\!3}

V = 3.14*16*4

\boxed{V = 200.96\:cm^3}

Note: Now, let's find the volume of a hemisphere.

Data: (hemisphere volume)

V (volume) = ?

r (radius) = 4 cm

Adopting: \pi \approx 3.14

If: We know that the volume of a sphere is V = 4* \pi * \dfrac{r^3}{3} , but we have a hemisphere, so the formula will be half the volume of the hemisphere V = \dfrac{1}{2}* 4* \pi * \dfrac{r^3}{3} \to \boxed{V = 2* \pi * \dfrac{r^3}{3}}

Formula: (Volume of the hemisphere)

V = 2* \pi * \dfrac{r^3}{3}

Solving:

V = 2* \pi * \dfrac{r^3}{3}

V = 2*3.14 * \dfrac{4^3}{3}

V = 2*3.14 * \dfrac{64}{3}

V = \dfrac{401.92}{3}

\boxed{ V_{hemisphere} \approx 133.97\:cm^3}

What is the approximate volume of this figure?

Now, to find the total volume of the figure, add the values: (cone volume + hemisphere volume)

Volume of the figure = cone volume + hemisphere volume

Volume of the figure = 200.96 cm³ + 133.97 cm³

\boxed{\boxed{\boxed{V = 334.93\:cm^3 \to Volume\:of\:the\:figure \approx 335\:cm^3 }}}\end{array}}\qquad\quad\checkmark

Answer:

The volume of the figure is approximately 335 cm³

_______________________

I Hope this helps, greetings ... Dexteright02! =)

8 0
3 years ago
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