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3 years ago

Learning Task 1. Tell whether each picture models a quadratic function or not.

Mathematics

1 answer:

Lostsunrise [7]3 years ago

7 0

The picture for this question is given below.

Answer: All of them models quadratic function.

Step-by-step explanation: A quadratic function is of the form

f(x) = ax² + bx + c, with coefficient a≠0.

This function has a U-shape graphic called parabola. It has a vertex, i.e., a point where the curve changes, which is "classified" as minimum, if the parabola opens up; and as maximum, if the parabola opens down.

The y-intercepts are the points where the curve touches the y-axis and x-intercepts, if they exist, are the roots of the function.

The three pictures below shows three U-shaped curves opening down. This means the three parabolas are representation of 3 different quadratic functions, with a 3 vertex points that are maximum.

You might be interested in

Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.

ludmilkaskok [199]

Answer:

$\dfrac{dy}{dx}=- \dfrac{1}{\left(x - 1\right) \left(x + 1\right)}$

Step-by-step explanation:

Given:

$y = \ln{\left(\dfrac{x + 1}{x - 1}\right)^{\frac{1}{2}}$

using the properties of log we can take the power 1/2 and multiply it.

$y = \dfrac{1}{2}\ln{\left(\dfrac{x + 1}{x - 1}\right)$

now we can differentiate:

$\dfrac{dy}{dx} = \dfrac{1}{2}\dfrac{1}{\left(\dfrac{x + 1}{x - 1}\right)}\left(\dfrac{d}{dx}\left(\dfrac{x+1}{x-1}\right)\right)$

$\dfrac{dy}{dx} = \dfrac{1}{2}\left(\dfrac{x - 1}{x + 1}\right)\left(- \dfrac{2}{\left(x - 1\right)^{2}}\right)$

$\dfrac{dy}{dx}=- \dfrac{1}{\left(x - 1\right) \left(x + 1\right)}$

this is our answer!

8 0

3 years ago

If m XAB=32, what is m BAC?

dalvyx [7]

The picture in the attached figure

we know that
The construction shown is an angle bisector
m<XAB=m<CAX
so
m<BAC=2*[m<XAB]-----> 2*32°----->m<BAC= 64°

the answer is
m<BAC=64°

3 0

4 years ago

In triangle abc, the perimeter is 36, and ab=ac. line ad is perpendicular to bc at the point d, and triangle abd's perimeter is

Musya8 [376]

Let x=ab=ac, and y=bc, and z=ad.

Since the perimeter of the triangle abc is 36, you have:

Perimeter of abc = 36
ab + ac + bc = 36
x + x + y = 36
(eq. 1) 2x + y = 36

The triangle is isosceles (it has two sides with equal length: ab and ac). The line perpendicular to the third side (bc) from the opposite vertex (a), divides that third side into two equal halves: the point d is the middle point of bc. This is a property of isosceles triangles, which is easily shown by similarity.

Hence, we have that bd = dc = bc/2 = y/2 (remember we called bc = y).

The perimeter of the triangle abd is 30:

Permiter of abd = 30
ab + bd + ad = 30
x + y/2 + z =30
(eq. 2) 2x + y + 2z = 60

So, we have two equations on x, y and z:

(eq.1) 2x + y = 36
(eq.2) 2x + y + 2z = 60

Substitute 2x + y by 36 from (eq.1) in (eq.2):

(eq.2') 36 + 2z = 60

And solve for z:

36 + 2z = 60 => 2z = 60 - 36 => 2z = 24 => z = 12

The measure of ad is 12.

If you prefer a less algebraic reasoning:

- The perimeter of abd is half the perimeter of abc plus the length of ad (since you have "cut" the triangle abc in two halves to obtain the triangle abd).

- Then, ad is the difference between the perimeter of abd and half the perimeter of abc:

ad = 30 - (36/2) = 30 - 18 = 12

4 0

4 years ago

Read 2 more answers

Each flower has a specific price. One tulip, one daisy, and 2 mums cost $4.20. On tulip, two daisies and one mum cost $3.80. Two

sineoko [7]

Answer:

The answer to your question is $5.60

Step-by-step explanation:

1 tulip + 1 daisy + 2 mums = $4.20 (1)

1 tulip + 2 daisies + 1 mum = $ 3.80 (2)

2 tulips + 2 mums = $4.80 (3)

1 tulip + 3 daisies + 2 mums = ?

tulip = t daisy = d mum = m

Process

1.- Find the price of each flower using system of equations

Solve equation 3 for tulip

2t = 4.80 - 2 m divide by 2 (4)

t = 2.40 - 1m

2.- Substitute equation 4 in equation 1 and 2

(2.4 - 1m) + 1 d + 2 m = 4.2

(2.4 - 1m) + 2d + 1 m = 3.8

3.- Simplify and solve for each flower

2.4 - 1m + 1d + 2m = 4.2

1d + 1m = 4.2 - 2.4

1d + 1m = 1.8 Equation (5)

2.4 - 1m + 2d + 1m = 3.8

2d = 3.8 - 2.4

2d = 1.4

d = 1.4/2

1d = 0.7

4.- Substitue d in equation 5

1(0.7) + 1m = 1.8

0.7 + 1m = 1.8

1m = 1.8 - 0.7

1m = 1.1

5.- Subtitute m in equation 4

1t = 2.40 - 1(1.1)

1t = 2.40 - 1.1

1t = 1.3

6.- Result

1 tulip + 3 daisies + 2 mums cost = 1.3 + 3(0.7) + 2(1.1)

= 1.3 + 2.1 + 2.2

= $5.6

8 0

3 years ago

Economic Leading Indicators are based on historical results. A.True B False

deff fn [24]

I think it’s A I’m not 100 percent sure tho sorry if I’m wrong

4 0

3 years ago