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EastWind [94]
3 years ago
6

Write an equation of the line passing through (-3,4) and (6,5) and give the answer in standard form

Mathematics
1 answer:
Andru [333]3 years ago
3 0
Let's start by putting it into slope-intercept form, which is
y=mx+b where m=slope and b=y-intercept (the value of y when x=0)

Find the slope between (-3, 4) and (6, 5).
Formula for slope: m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}
Plug in our x and y values...
m=\frac{5-4}{6-(-3)}=\frac{1}9
Our slope is 1/9.

We can interpret this slope rise/run = 1/9 as
<em>"When y changes by 1, x changes by 9. (and vice versa)"
</em>We want to find the y-intercept. (the value of y when x=0)
Let's take the point (-3, 4).
We want to add 3 to that x to make it 0.
According to our slope, this means adding 1/3 to y. (1 to 9 = 1/3 to 3)
Our y-intercept is at (0, 4 1/3), with the value we use in our eqn. b = 4 1/3.
Let's use an improper fraction, b = 13/3.

Now our equation is y=\frac{1}9x+\frac{13}3
Let's convert to standard form, ax+by+c=0.
Just multiply by the LCD of our fractions (in this case, 9)
9y=x+39
Now move everything to the left side.
\boxed{-x+9y-39=0}
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John has a cylindrical propane tank that measures 8" in diameter and 8" tall If John
kirza4 [7]

Answer:

2 times as large

Step-by-step explanation:

For the original cylinder, we can say that the volume of a cylinder is equal to V= πr²h. For this cylinder, we can say that  V = π * radius² * height. The radius is equal to 1/2 of the diameter, so the original radius is 8/2 = 4. Therefore, the volume of the original cylinder is V = π * radius² * height = π * 4² * 8 = π * 16 * 8 = π * 128

For the new cylinder, "twice as wide" means that the diameter is twice as big as the original one. Half the height means that the height is halved. The new diameter is therefore 8 * 2 = 16 (meaning that the new radius is 16/2=8) while the new height is 8/2 = 4. The new volume is thus

V = π * radius² * height = π * 8² * 4 = π * 64 * 4 = π * 256

To see how much larger the new tank volume is, we can divide (new tank volume) by (old tank volume), resulting in

π * 256 / (π *128) = 2

8 0
3 years ago
The area of the triangle is 28.7 square centimeters. What is the base length of the triangle in centimeters?
Montano1993 [528]

In order to derive the base of a triangle from its area, you need its height as well.

In fact, if we solve the area formula for the base, we have

A=\dfrac{bh}{2} \iff 2A = bh \iff b=\dfrac{2a}{h}

So, the base length would be

b=\dfrac{2\cdot 28.7}{h} = \dfrac{57.4}{h}

where h is the height relative to the base you're interested in.

3 0
2 years ago
Problem Page A table of values of a linear function is shown below. x −1 0 1 2 3 y −6 −8 −10 −12 −14 Find the slope and y -inter
Ivenika [448]
When x=0, y=-8, so that is the y-intercept.

When x increases by 1, y decreases by 2, so the slope is -2.

The equation of the function is
.. y = -2x -8
3 0
3 years ago
Find the value of x. Round to the nearest degree as needed.
Bas_tet [7]

9514 1404 393

Answer:

  x° = 29°

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relevant trig relationships. Here, you have the hypotenuse and the side opposite the unknown angle. So, the appropriate relation is ...

  Sin = Opposite/Hypotenuse

  sin(x°) = 12/25

  x° = arcsin(12/25) ≈ 28.69°

The value of x is about 29.

4 0
2 years ago
Show that the following statement is an identity by transforming the left side into the right side. sin θ (sec θ + csc θ) = tan
ExtremeBDS [4]

Answer:

Step-by-step explanation:

Required to prove that:

Sin θ(Sec θ + Cosec θ)= tan θ+1

Steps:

Recall sec θ= 1/cos θ and cosec θ=1/sin θ

Substitution into the Left Hand Side gives:

Sin θ(Sec θ + Cosec θ)

= Sin θ(1/cos θ  + 1/sinθ )

Expanding the Brackets

=sinθ/cos θ + sinθ/sinθ

=tanθ+1 which is the Right Hand Side as required.

Note that from trigonometry sinθ/cosθ = tan θ

8 0
3 years ago
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