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2 years ago

Anyone! Please help me! I don't understand at all what to do! Help would be really appreciated :)

Mathematics

1 answer:

Rom4ik [11]2 years ago

6 0

Answer: They are parallel

Step-by-step explanation:

If two lines are parallel , then they must have the same slope and if two lines are perpendicular , the product of their slope must be -1.

To check this , we must calculate the slope of the two lines given.

Slope = $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

from the first point

$y_{1}$ = 2

$y_{2}$ = 1

$x_{1}$ = 5

$x_{2}$ = -1

substituting the values

slope 1 = 1 - 2 / -3 - 5

slope1 = -1 / -8

slope 1 = 1/8

Using the same format to calculate the slope of the second line

$y_{1}$ = -2

$y_{2}$ = 0

$x_{1}$ = -1

$x_{2}$ = 15

slope 2 = 0 - (-2) / 15 - (-1)

slope 2 = 2/16

slope 2 = 1/8

Since slope 1 = slope 2 , this implies that the lines are parallel

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Hello, I gotta turn it turn in this question today, help!!!!!!

Sladkaya [172]

Answer:

2 or -2

Step-by-step explanation:

If x² - 8x = -12

Step 1

We find x by solving

x² - 8x = -12

We equate to zero

x² - 8x + 12 = 0

We factorise

x² - 6x - 2x + 12 = 0

x(x - 6) -2(x - 6) = 0

(x - 6) (x - 2) = 0

x - 6 = 0, x = 6

x - 2 = 0, x = 2

x = 6 or 2

Step 2

What is x - 4?

When x = 6

= 6 - 4 = 2

When x = 2

= 2 - 4 = -2

Therefore, x - 4 = 2 or -2

3 0

3 years ago

A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. An industrial tank of this shape must h

mestny [16]

Answer:

Radius =6.518 feet

Height = 26.074 feet

Step-by-step explanation:

The Volume of the Solid formed = Volume of the two Hemisphere + Volume of the Cylinder

Volume of a Hemisphere $=\frac{2}{3}\pi r^3$

Volume of a Cylinder $=\pi r^2 h$

Therefore:

The Volume of the Solid formed

$=2(\frac{2}{3}\pi r^3)+\pi r^2 h\\\frac{4}{3}\pi r^3+\pi r^2 h=4640\\\pi r^2(\frac{4r}{3}+ h)=4640\\\frac{4r}{3}+ h =\frac{4640}{\pi r^2} \\h=\frac{4640}{\pi r^2}-\frac{4r}{3}$

Area of the Hemisphere = $2\pi r^2$

Curved Surface Area of the Cylinder = $2\pi rh$

Total Surface Area=

$2\pi r^2+2\pi r^2+2\pi rh\\=4\pi r^2+2\pi rh$

Cost of the Hemispherical Ends = 2 X Cost of the surface area of the sides.

Therefore total Cost, C

$=2(4\pi r^2)+2\pi rh\\C=8\pi r^2+2\pi rh$

Recall: $h=\frac{4640}{\pi r^2}-\frac{4r}{3}$

Therefore:

$C=8\pi r^2+2\pi r(\frac{4640}{\pi r^2}-\frac{4r}{3})\\C=8\pi r^2+\frac{9280}{r}-\frac{8\pi r^2}{3}\\C=\frac{9280}{r}+\frac{24\pi r^2-8\pi r^2}{3}\\C=\frac{9280}{r}+\frac{16\pi r^2}{3}\\C=\frac{27840+16\pi r^3}{3r}$

The minimum cost occurs at the point where the derivative equals zero.

$C^{'}=\frac{-27840+32\pi r^3}{3r^2}$

$When \:C^{'}=0$

$-27840+32\pi r^3=0\\27840=32\pi r^3\\r^3=27840 \div 32\pi=276.9296\\r=\sqrt[3]{276.9296} =6.518$

Recall:

$h=\frac{4640}{\pi r^2}-\frac{4r}{3}\\h=\frac{4640}{\pi*6.518^2}-\frac{4*6.518}{3}\\h=26.074 feet$

Therefore, the dimensions that will minimize the cost are:

Radius =6.518 feet

Height = 26.074 feet

5 0

2 years ago

Find the hypotenuse

Anika [276]

A^2+b^2=c^2
11^2+4^2=c^2
121+16=c^2
137=c^2
$\sqrt{137} = \sqrt{c}$
11.70=c

8 0

2 years ago

Read 2 more answers

Divide the following fractions and reduce to lowest terms 2/3 divided by 4/5

pshichka [43]

Well to divide 2 fraction you first have to find a least common number between the 2 bottom numbers in the fractions, we know automaticall that 15 fits in both the 3 and the 5. now u have to find out what to multiply by each number to get 15, for example what number do you multiply by 3 to get 15?? well it will be 5, so go ahead and multiply it by the fraction (note that what you do in the bottom you have to do in the top) this will give you 10/15, because I multiplied the top and bottom number by 5... lets try the other one what number do you multiply by 5 to get 15?? well it will be 3 so go ahead and multiply that to get 12/15.. now add the top numbers (note that the bottoms always stay the same, you never add or subtract them) when you do you will get 22/15, now you have to see if you can simplify it any further in this case you can't so your final answer is 22/15

Hope this helps

5 0

2 years ago

Don't know how to solve this please help. Show work, thank you

anyanavicka [17]

Hello!

We know that the sum of the three angles of a triangle is equal to 180 degrees. This can be represented using the following formula:

A1 + A2 + A3 = 180

With this knowledge, we can successfully find the missing measurements.

We’ll begin with the large right triangle. Because it is a right triangle, we know that one of its angles is equal to 90 degrees. We are also given that its second angle has a measure of 65 degrees. Insert this information into the formula above and combine like terms:

(90) + (65) + A3 = 180
155 + A3 = 180

Now subtract 155 from both sides of the equation:

A3 = 25

We have now proven that the third angle has a measure of 25 degrees. Looking at the provided image, you’ll notice that this 25 degree angle is adjacent to the 80 degree angle. We can add these neighboring angles to find one of the missing angles of the medium triangle:

25 + 80 = 105

We have now proven that this larger angle has a measure of 105 degrees. Looking again at the provided image, you’ll notice that this triangle also contains a 50 degree angle. Using the “three-angles” formula, we can find the remaining angle of the medium triangle. Insert any known values and combine like terms:

(105) + (50) + A3 = 180
155 + A3 = 180

Now subtract 155 from both sides of the equation:

A3 = 25

We have now proven the third angle of the medium triangle to have a measure of 25 degrees. Consequently, we now have now proven two of the three angles of the smallest triangle. Again using the “three-angles” formula, we can find the measure of the missing angle (x). Insert any known values (using the variable “x” to represent the missing angle) and combine like terms:

(25) + (25) + (x) = 180
50 + x = 180

Now subtract 50 from both sides:

x = 130

we have now proven that the missing angle (x) has a measure of 130 degrees.

I hope this helps!
second angle which has a value of 65 degrees.

3 0

2 years ago