MATHEMATICS COLLEGE

Write the equation for the line that passes through (-5, -4) and (3, 12)

Answers

Answer 1

Answer:

Answer:

$y=2\,x+6$

Step-by-step explanation:

Start by finding the slope of the segment that joins the two given points, using the slope formula:

$slope=(y_2-y_1)/(x_2-x_1) =(12-(-4))/(3-(-5)) =(16)/(8) =2$

Now, you can write the general equation of the line in slope-intercept form as:

$y=m\,x+b\ny=2\,x+b$

and find the line's y-intercept (b) by using either one of the given points - for example (3, 12):

$y=2\,x+b\n12=2\,(3)+b\n12=6+b\nb=6$

Therefore, the equation of the line is:

$y=2\,x+6$

Answer 2

Answer:

Answer:

I believe it is y=2x+6.

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HELP MEEEEEEEEEEEEEEEEEEE I DONT GET IT

Answers

The graph goes up by 10 each time. And if we start at the bottom of the graph, and count up to where the line hits another point of the graph. It goes up by 30, and moves right 10. So that means the slope is 3. Hope this helps!

Jay simplify the expression 3x( 3+12÷3)-4 over his first step he added 3+12 to get 15 what was jays error? Find the correct answer

Answers

Hello there!

To simplify this expression, you must follow PEMDAS.

3x(3+12÷3) parentheses first
3x(3+4) do the division
3x(7) addition inside of parentheses
21x multiplication

This means that Jay is incorrect in doing addition first.

I really hope this helps!
Best wishes :)

distribute 3x through all the numbers in () then solve for x and you get 21x-4

What is the pattern in the values as the exponents increase?

Answers

as the exponents increase, the value is multiplied by 2

A rectangular block of aluminum30 mm×60 mm×90 mm is placed in apressurechamber and subjected to a pressure of 100 MPa. If the modulus of elasticity is 75GPa andPoisson's ratio is 0.35, what will be the decrease in the longest side of the block, assuming thatthe material remains within the linear elastic region? What will be the decrease in the volume oftheblock? g

Answers

Answer:

$\Delta V = - 216.415 mm^3$

Step-by-step explanation:

we know that change is length is calculated by following strain relation

$\Delta L = L * \epsilon_x$

where strain is given as

$\epsilon_x = (\sigma_x - \nu(\sigma_y + \sigma_z))/(E)$

$\epsilon_x = (-10^8 - 0.35 ( -10^8 -10^8 (N/m^2)))/(7.5 * 10^10)$

$\epsilon_x = -4.453 * 10^(-4)$

plugging strain value in change in length formula

$\Delta L = 90 * -4.453 * 10^(-4) = - 0.04008 mm$

calculate the length on the longer side

$L_(long) = L = \delta L$

= 90 - 0.04008 = 89.95 mm

intial volume $= 90*60*30 = 1.62 * 10^5 mm^3$

change in volume

$\Delta V =V ( \epsilon_x +\epsilon_y + \epsilon_z )$

$\Delta V = 1.62 * 10^5 (-4.453 - 4.453 - 4.453) * 10^(-4)$

$\Delta V = - 216.415 mm^3$

Final answer:

Calculations involve determining strain from given pressure and Modulus of Elasticity and then determining the decrease in length of the longest side and total volume of the aluminum block when subjected to pressure.

Explanation:

The question is about applying principles of material science under conditions of pressure. The decrease in length and volume of a rectangular block of aluminum when subjected to pressure can be calculated by using the concepts of Modulus of Elasticity and Poisson's Ratio.

First, the strain experienced can be calculated using the formula:

Strain = Pressure / Modulus of Elasticity

Substituting the given values, the strain is found. The change in the longest side (90mm) is calculated by multiplying the original length by the strain. The volume change is calculated using the formula:

Change in volume = Original volume * (-3) * strain

Where original volume is = 30mm * 60mm * 90mm. Here the negative indicates a decrease. This will provide the decrease in the longest side and the total volume of the block when subjected to the given pressure.

Learn more about Material Deformation under Pressure here:

brainly.com/question/31787736

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A rock falls off a balcony. It's height (in feet) is given by the formula f(x)=-16t^2+13.4t+120, where t is measured in seconds. How long will it take the rock to hit the ground? Round your answers to the nearest three decimal places.

Answers

Answer:

3.189 seconds

Step-by-step explanation:

You want f(t) = 0, so ...

0 = -16t^2 +13.4t +120

0 = t^2 -0.8375t -7.5 . . . . divide by -16

0 = (t^2 -0.8375t +0.41875^2) -7.5 -0.41875^2 . . . . complete the square*

0 = (t -0.41875)^2 -7.6753515625 . . . . write as a square

√7.6753515625 = t -0.41875 . . . . . . . . add 7.67... and take positive root

t = 0.41875 +√7.6753515625 ≈ 3.189192 . . . . add 0.41875

It will take the rock about 3.189 seconds to hit the ground.

_____

* We complete the square by adding the square of half the coefficient of the linear term (= (-0.8375/2)^2) inside parentheses and subtracting the same amount outside parentheses. This gives a form inside parentheses that is ...

(t^2 -2at +a^2) = (t -a)^2

Completing the square is complicated a little bit by a leading coefficient that is not 1. That is why we divided by -16 first.

_____

Comment on the question

We note that the rock "falls" from the 120 foot high balcony by first traveling upward at a rate of 13.4 feet per second. We also note that the height function is written f(x), but uses t as the variable. That is, it should be f(t) = ...

An electronics firm sells four models of stereo receivers, three CD decks, and six speaker brands. When the three types of components are sold together, they form a "system." How many different systems can the electronics firm offer?A. 169
B. 72
C. 13
D. 36

Answers

Answer:

B. 72

Step-by-step explanation:

The total number of different systems that can be bundled together is the product of the possible number of ways to select 1 out of 4 stereo receivers, by 1 out of 3 CD decks and by 1 out of 6 speakers. Assuming that the order at which products are picked does not matter, the number of different systems is:

$n=(4!)/((4-1)!1!)*(3!)/((3-1)!1!)*(6!)/((6-1)!1!)\nn=4*3*6\nn=72\ systems$

The electronics firm can offer 72 different systems.

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The distance a vehicle travels can be found by using the formula d = rt, where d is the total distance traveled, r is the rate of speed, and t is the amount of time spent traveling. Grace drives her truck a distance of 80 miles at a steady speed of 50 miles per hour. To the nearest hour, how many hours does she spend driving?

A line passes through A(3,7) and B(-4,9). Find the value of a if C(a, 1) is on the line.

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In the diagram, how many pairs of vertical angles are shown?