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3 years ago

What is the slope of a line that is parallel to the line represented by the equation 3x+4y=12?

Mathematics

1 answer:

mash [69]3 years ago

8 0

Slope-intercept form is:

y = mx + b

"m" is the slope, "b" is the y-intercept (the y value when x = 0)

(there is probably another way to do this, but I will be doing it this way)

Isolate the "y" in the equation

3x + 4y = 12 Subtract 3x on both sides

4y = 12 - 3x Divide 4 on both sides

$y=3-\frac{3}{4}x$ or $y=-\frac{3}{4} x+3$ The slope is -3/4

For lines to be parallel, they have to have the SAME slope. The given line's slope is -3/4, so the slope of the parallel line is also $-\frac{3}{4}$

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Equation editor does not include the grouping symbols “<“ and “>” that are necessary for writing a vector in component for

Scilla [17]

Answer:

{12,2}

Step-by-step explanation:

From the given graph it is clear that the initial point of the vector is (-5,0) and the terminal point (7,2).

If initial point of a vector is $(x_1,y_1)$ and terminal point is $(x_2,y_2)$ , then

$\overrightarrow{v}=(x_2-x_1)i+(y_2-y_1)j$

Using this formula, we get

$\overrightarrow{v}=(7-(-5))i+(2-0)j$

$\overrightarrow{v}=12i+2j$

$\overrightarrow{v}=$

Using braces, we get

$\overrightarrow{v}=\{12,2\}$

Therefore, the required vector is {12,2}.

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3 years ago

If the height of a cone is 7.5 cm and the radius is 2 cm, find the approximate volume of the cone.

larisa86 [58]

Volume: h • pi r^2

Volume: (7.5) • pi (2)^2

Volume: 94.247796

Just round to your teacher’s liking

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2 years ago

13. The radius of Earth is approximately 6.4 x 100 m. Use the formula V = 4/3pr^3

romanna [79]

<u>We are given</u>

Radius of Earth; 6.4 x 100 meters = 640 meters

Clearly, the shape of the earth is a sphere. Thus, to determine the volume of the earth, we will use a formula that determines the volume of a sphere.

$\implies \text{Volume of sphere =} \ \dfrac{4\pi r^{3}}{3}$

When we substitute the radius in the formula, we get;

$\implies\text{Volume of sphere} = \dfrac{4\pi (640)^{3}}{3}$

$\implies\text{Volume of sphere} = \dfrac{4\pi (640)(640)(640)}{3}$

Take π as 3.14

$\implies\text{Volume of sphere} = \dfrac{4\pi (640)(640)(640)}{3}$

$\implies \text{Volume of sphere} = \dfrac{4(3.14)(640)(640)(640)}{3}$

Simplify the numerator;

$\implies \text{Volume of sphere} = \dfrac{4(3.14)(640)(640)(640)}{3}$

$\implies \text{Volume of sphere} = \dfrac{3292528640}{3}$

Divide the numerator by 3;

$\implies \text{Volume of sphere} = \dfrac{3292528640}{3}$

$\implies \text{Volume of sphere} = \boxed{1097509546.67 \ \text{m}^{3} } \ \ \ (\text{Estimated})$

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1 year ago

Jay needs at least 5,000 points to be nominated for MVP she currently has 3800. Write an inequality to find P the total amount o

ddd [48]

Answer:

1200

Step-by-step explanation

3800+p=5000

5000-3800=1200

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3 years ago

You are wakeboarding on a river. You travel 2 miles downstream to a marina for supplies, and then you travel 3 miles upstream to

Zielflug [23.3K]

Let x represent the speed of of boat.

We have been given that the river current is 3 miles per hour.

The speed of boat upstream will be $x-3$ .

The speed of boat downstream would be $x+3$ .

$\text{Time}=\frac{\text{Distance}}{\text{Speed}}$

We have been given that you travel 2 miles downstream to a marina for supplies, and then you travel 3 miles upstream to a dock.

We can represent this information in an equation as:

$\text{Time}=\frac{2}{x+3}+\frac{3}{x-3}$

Since the speed of the boat is 18 miles per hour, so we will substitute $x=18$ in above equation and solve for time.

$\text{Time}=\frac{2}{18+3}+\frac{3}{18-3}$

$\text{Time}=\frac{2}{21}+\frac{3}{15}$

$\text{Time}=\frac{2}{21}+\frac{1}{5}$

$\text{Time}=\frac{2\cdot 5}{21\cdot 5}+\frac{1\cdot 21}{5\cdot 21}$

$\text{Time}=\frac{10}{105}+\frac{21}{105}$

$\text{Time}=\frac{31}{105}$

$\text{Time}=0.295238095$

Since time is in hours, so let us convert our given time in minutes.

1 hour = 60 minutes.

$\text{Time}=0.295238095\times 60\text{ minutes}$

$\text{Time}=17.7142857\text{ minutes}$

Rounding to nearest tenth of minute.

$\text{Time}\approx 17.7\text{ minutes}$

Therefore, it will take approximately 17.7 minutes for the boat to take the trip.

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2 years ago