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3 years ago

What is y + 11 = 1/3(x + 3) in standard form?

1 answer:

3 0

Standard form is y=Mx+b so first step is to isolate y:
Y=1/3(x+3)-11

Then use order of operations to simplify the x to a whole number. First multiply by three:
3y=x+3-33

Now combine like terms:
3y=x-30

Finally,
Divide to make y have a coefficient if one:

Y= 1/3x -10

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150 adults complete a survey.

NARA [144]

Ratio of men:women in the simplest form is 7:8

Step-by-step explanation:

Step 1: Given total adults = 150. Number of women = 80. Find the number of men.

Number of men = 150 - 80 = 70

Step 2: Find the ratio between men and women.

Men:Women = 70:80 = 7:8

3 0

3 years ago

If a ship's path is mapped on a coordinate grid, it follows a straight-line path of slope 3 and passes through point (2, 5).

Ugo [173]

Part A: The equation of the ship's path is $y=3x-1$

Part B: The two ships sails perpendicular to each other.

Explanation:

Part A: It is given that $m=3$ and point (2, 5)

Substituting these in the slope intercept form, we have,

$y-y_{1}=m\left(x-x_{1}\right)$

$\begin{aligned}y-5 &=3(x-2) \\y-5 &=3 x-6 \\y &=3 x-1\end{aligned}$

Thus, the equation of the ship's path in slope intercept form is $y=3x-1$

Part B: The equation of the second ship is $x+3 y-6=0$

Let us bring the equation in the form of slope intercept form.

$\begin{aligned}3 y &=-x+6 \\y &=-\frac{1}{3} x+2\end{aligned}$

Thus, from the above equation the slope is $m=-\frac{1}{3}$

To determine the two ships sailing perpendicular to each other, we have

$m_{1} \times m_{2}=-1$

where $m_{1}=3$ and $m_{2}=-\frac{1}{3}$

$\begin{aligned}3 \times-\frac{1}{3} &=-1 \\-1 &=-1\end{aligned}$

Since, both sides of the equation are equal, these two ships sails perpendicular to each other.

3 0

2 years ago

25 percent of 60 students in a class failed in the test. how many students failed the test

Alik [6]

Answer:

15 students

Step-by-step explanation:

25% = 1/4, so you can just do 1/4 of 60 or 1/4 * 60. 60/4 = 15 students.

5 0

3 years ago

Read 2 more answers

Which point is an x-intercept of the quadratic function f(x) = (x – 4)(x + 2)?

lozanna [386]

The quadratic equation is in factored form, which is f(x) = (x - a)(x - b), where a and b are the x-values for the x-intercepts.

The x-values for the x-intercepts are 4 and -2. We know that the y-value at any x-intercept must be 0 (otherwise it isn't an x-intercept).

Thus, either the points (4,0) or (-2,0) must be your answer (the question is only asking for one x-intercept).

7 0

3 years ago

Read 2 more answers

Please help ASAP<br> Trigonometry

stellarik [79]

Answer:

Step-by-step explanation:

Use SOH CAH TOA to recall how the trig functions fit on a triangle

SOH: Sin(Ф)= Opp / Hyp

CAH: Cos(Ф)= Adj / Hyp

TOA: Tan(Ф) = Opp / Adj

now decide which parts we know and what we want to slove for and pick the function that has those in it

we also know that small angle down at the point b/c we can use that the inside of trianle angles add to 180

180 = 75 + 90 + X

15° = X

where x is the angle at that sharp point on the triangle

I want to use that 15° angle in one of the above formulas as it's Opposite of that side we want to know, and also adjcent to that side we know , so i'll pick TOA since it's got all of those in it. Opp = x for this triangle

Tan(15) = Opp / 15

15* Tan(15) = Opp

4.0192 = Opp

so that's x

x = 4.0162 units , what ever they are

the angle is 43° and we know the adjacent side and we want the Hypotenuse , now i'll pic CAH since it's got those pieces in it

Cos(43)= 31 / Hyp

some algebra just to switch Hyp out of the denominator

Hyp = 31 / Cos(43)

some tapping on my calculator

Hyp = 41.714

That's x for the second triangle

x = 41.71 units , what ever they are

8 0

3 years ago