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MArishka [77]
2 years ago
11

Express the trig ratios as fractions in simplest terms.

Mathematics
1 answer:
Neporo4naja [7]2 years ago
3 0

Answer:

See below

Step-by-step explanation:

\cos M=\frac{adjacent}{hypotenuse}=\frac{56}{70}=\frac{4}{5}\\\\\sin L=\frac{opposite}{hypotenuse}=\frac{56}{70}=\frac{4}{5}

Hence, both ratios are equal to each other

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2 years ago
Y=-3x^2-6x+24
Lera25 [3.4K]
The x-intercept is the point at which the function intersects the x-axis.
For any point on the x-axis, y = 0. Thus we can plug in 0 for y and solve for x.

y=-3x^2-6x+24 \\ 0=-3x^2-6x+24

Let's split the middle on this quadratic.
To do this we need to find two numbers that add to equal -6 and multiply to equal -72. (-3 times 24)
Consider ways to multiply to get 72.
72 = 36 ×2...that's not going to work.
72 = 24 × 3
72 = 18 × 4
72 = 12 × 6...and 12 minus 6 is 6!
Let's add our signs; our numbers are -12 and 6.
Now, split the middle and factor.

0=-3x^2-12x+6x+24\\0=-3x(x+4)+6(x+4)\\0=(-3x+6)(x+4)

Now you should know that anything multiplied by zero is zero.
So any value that makes one of those factors equal zero is an x-intercept.
Solve each of these equations.

-3x+6 = 0
-3x = -6
x = 2

x+4 = 0
x = -4

Oh, and since all parabolas (graphs of quadratics) are symmetrical, our axis of symmetry will be the average between the two, which is x=-1.

Now for our y-intercepts. For any points on the y-axis, x=0, so if we plug in 0 for x and solve for y we'll get our y-intercept.

y = -3×0² - 6×0 + 24
y = 0 - 0 + 24
y = 24

What about our vertex? Well, we know it's going to line up with the axis of symmetry, so let's just plug in -1 for x.

y = -3×-1² - 6×-1 + 24
y = -3×1 -6×-1 + 24
y = -3 + 6 + 24
y = 27

Thus the vertex is (-1, 27)

The y value is not going to exceed 27, as this is a decreasing quadratic, (we already know y=24 is a possibilty) and this equation goes downwards infinitely, so our range is (-∞, 27)

As for x, well, it's sort of the input for our equation, meaning it can be whatever we want it to be. Thus the domain is (-∞, ∞)




3 0
3 years ago
A parabola is represented by the equation y2 = 5x. which equation represents the directrix?
ivann1987 [24]

The value of the directrix is -5/4.

According to the statement

we have given that the equation of parabola is y2 = 5x. And we have to find that the which equation represents the directrix.

We know that the general equation of parabola is

(y - k)2 = 4a(x - h)  -(1)

and given parabola equation is

y2 = 5x.  -(2)

After comparing the both equations we get k=0 and h=0

And the formula to find the directrix is

x = h - a

Substitute the values of h and a in it then

x = 0-5/4

x = -5/4.

Here the directrix is -5/4.

So, The value of the directrix is -5/4.

Learn more about the Parabola here brainly.com/question/4061870

#SPJ4

7 0
1 year ago
Jade takes 5 minutes more than twice as long as Binh to ride to their friend’s house. If Binh takes x minutes to ride to his fri
skad [1K]

Answer:

It will take Jade (2x + 5) minutes

Step-by-step explanation:

Let us find the expression that represents the time Jade will take

∵ Binh takes x minutes to ride to his friend’s house

∴ The time Binh takes = x minutes

∵ 5 more means + 5

∵ Twice means × 2

∵ Jade takes 5 minutes more than twice as long as Binh to ride to their

   friend’s house

→ Multiply the time Binh takes by 2 and add the product by 5

∵ Binh takes x minutes

∴ The time Jade takes = 2 × x + 5

∴ The time Jade takes = 2x + 5 minutes

∴ It will take Jade (2x + 5) minutes

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3 years ago
nicholas has $5000 to invest for retirement. his goal is to have at least $40000 in 30 years. if he finds an account with contin
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40000=5000e^30r
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