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3 years ago

Use the slope formula to find the slope of the line that passes through the points (4, -1) and (3, -1) *

Mathematics

1 answer:

GenaCL600 [577]3 years ago

7 0

Answer:

slope = 0

Step-by-step explanation:

Calculate m using the slope formula

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

with (x₁, y₁ ) = (4, - 1 ) and (x₂, y₂ ) = (3, - 1 )

m = $\frac{-1-(-1)}{3-4}$ = $\frac{-1+1}{-1}$ = $\frac{0}{-1}$ = 0

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Oil is pumped into a tank at a rate of Q(t)=45-t gallons per minute where time is t is measured in minutes how many gallons are

FinnZ [79.3K]

Answer:

15 gallons

Step-by-step explanation:

Given that:

Pumping rate is modeled by the equation :

Q(t)=45-t gallons per minute ; where t is in minutes

Number of gallons in tank after 30 minutes ;

Q(t)=45-t

Q(30) = 45 - 30

Q(30) = 15

Hence, Number of gallons in tank after 30 minutes is 15 gallons

5 0

3 years ago

3.1 Find the equation of the line passing through (4, 5) and parallel to the line 3x – 2y = 4.

valentinak56 [21]

$\rule{50}{1}\large\blue\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}$

<em>Find the equation of the line passing through (4, 5) and parallel to </em>

<em />

<em> </em> $\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}$

First of all, We need to convert this equation from standard form (ax+by=c) into slope-intercept form (y=mx+b).

$\rightarrow$ First, add 2y on both sides:-

$\Large\textsf{3x+2y=4}$

$\rightarrow$ Now, subtract 3x on both sides:-

$\Large\textsf{2y=-3x+4}$

$\rightarrow$ Divide by 2 on both sides

$\Large\text{$y=-\displaystyle\frac{3}{2}x +2$}$

$\rule{300}{3}$

Now, let's find the equation of the line that's parallel to the given line.

Remember, if lines are parallel to each other, then their slope's the same.

So the slope of the line that's parallel to the line whose equation we just found, is

$\Large\text{$-\displaystyle\frac{3}{2}$}$

Now let's write the equation in point-slope form:-

$\hookrightarrow\sf{y-y_1=m(x-x_1)}$

Replace numbers with letters, as follows:-

$\sf{y-5=-\displaystyle\frac{3}{2} (x-4)}$

The equation above is the equation in point-slope form.

Incase you need it converted to slope intercept form, refer to the steps below ~

Multiply -3/2 times x and -4:-

$\hookrightarrow\sf{y-5=-\displaystyle\frac{3}{2} x-6}$

Now, Add 5 on both sides:-

$\hookrightarrow\sf{y=\displaystyle\frac{3}{2} x+1}$

$\Uparrow\sf{Our\:equation\:in\:slope\;intercept\;form}$

<h3>Good luck with your studies.</h3>

#TogetherWeGoFar

$\rule{300}{1}$

4 0

2 years ago

Divid 15 into two parts such that the sum of their reciprocal is 3/10

emmasim [6.3K]

Let x and y be the 2 parts of 15 ==> x + y=15 (given)

Reciprocal of x and y ==> 1/x +1/y ==> 1/x + 1/y = 3/10 (given)

Let's solve 1/x + 1/y = 3/10 . Common denominator = 10.x.y (reduce to same denominator)

==> (10y+10x)/10xy = 3xy/10xy ==> 10x+10y =3xy

But x+y = 15 , then 10x+10y =150 ==> 150=3xy and xy = 50

Now we have the sum S of the 2 parts that is S = 15 and
their Product = xy =50
Let's use the quadratic equation for S and P==> X² -SX +P =0
Or X² - 15X + 50=0, Solve for X & you will find:
The 1st part of 15 is 10 & the 2nd part is 5

4 0

3 years ago

Evaluate each trigonometric equation for θ.

liberstina [14]

Answer:

sinФ = 8/17

cosФ = 15/17

tan Ф = 8/15

csc Ф = 17/8

sec Ф = 17/15

cot Ф = 15/8

Step-by-step explanation:

Let us revise the trigonometry functions

Sin(x) = opposite/hypotenuse

Cos(x) = adjacent/hypoteouse

Tan(x) = opposite/adjacent

Csc(x) = hypotenuse/opposit

Sec(x) = hypotenues/adjacent

Cot(x) = adjacent/opposite

In the given figure

The opposite side to angle Ф = 8

The adjacent side to angle Ф = 15

Find the hypotenuse using Pythagoras' theorem

$Hypotenuse = \sqrt{8^{2}+15^{2} }$

$Hypotenuse = \sqrt{64+225}$

$Hypotenuse = \sqrt{289}$

$Hypotenuse = 17$

Let us use the rules above to find the trigonometry functions

sinФ = 8/17

cosФ = 15/17

tan Ф = 8/15

csc Ф = 17/8

sec Ф = 17/15

cot Ф = 15/8

4 0

3 years ago

What is another name for ray ca?

zzz [600]

I would say ray ac, because it shouldn't matter which order you put the letters.

7 0

3 years ago