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sweet-ann [11.9K]

2 years ago

11

In a complete sentence, describe the positions of these numbers on the number line in relation to each other. Then, write an ine

quality statement comparing the numbers, using the symbol > or <.

1 answer:

Tasya [4]2 years ago

7 0

Answer:

ussugdfxysuwneuduchske

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A bridge constructed over a bayou has a supporting arch in the shape of an inverted parabola. Find the equation of the parabolic

babymother [125]

Answer: f(x) = -0.016x² + 1.6x

Step-by-step explanation:

If the lenght of the road over the arch is 100m, we can consider a coordinate plane and say that the road starts at point (0,0) and finishes at (100,0). The vertice of the parabola is at point (50,40), because the maximum height is 40 and it is always in the middle point of the roots.

So, we have

(0,0) (50,40) (100,0)

A quadratic function is always on the form: f(x) = ax² + bx + c

0 = a0² + b0 + c

40 = a50² + b50 + c

0 = a100² + b100 + c

0 = a0² + b0 + c → c = 0 ∴

40 = a50² + b50

0 = a100² + b100

_________________________

2500a + 50b = 40 (*2)

10000a + 100b = 0

_________________________

5000a + 100b = 80

10000a + 100b = 0 (-)

__________________________

-5000a = 80

-a=80/5000

a=-0.016

∴

2500a + 50b = 40

2500.(-0.016) + 50b = 40

-40 + 50b = 40

50b = 80

b = 80/50

b = 1.6

This way f(x) = -0.016x² + 1.6x

6 0

2 years ago

There are 20 triangles and 8 circles. What is the simplest ratio of circles to total shapes?

Rudik [331]

Answer:

5 to 2

Step-by-step explanation:

You can simplify both 20 and 8 by 4.

20/4 = 5

8/4 = 2

3 0

2 years ago

Help plzzz will give brainliest

Rasek [7]

Answer:

the amswer is 5 hope this helps you

3 0

2 years ago

Which expression is equivalent to 8a + 12b?

Jet001 [13]

Answer:

4 (2 a + 3 b)

Step-by-step explanation:

Simplify the following:

8 a + 12 b

Factor 4 out of 8 a + 12 b:

Answer: 4 (2 a + 3 b)

4 0

2 years ago

On a coordinate plane, triangle A B C is shown. Point A is at (0, 0), point B is at (3, 4), and point C is at (3, 2). What is th

Elena L [17]

Answer:

The area of triangle for the given coordinates is 1.5 $\sqrt{4.6}$

Step-by-step explanation:

Given coordinates of triangles as

A = (0,0)

B = (3,4)

C = (3,2)

So, The measure of length AB = a = $\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}$

Or, a = $\sqrt{(3-0)^{2}+(4-0)^{2}}$

Or, a = $\sqrt{9+16}$

Or, a = $\sqrt{25}$

∴ a = 5 unit

Similarly

The measure of length BC = b = $\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}$

Or, b = $\sqrt{(3-3)^{2}+(2-4)^{2}}$

Or, a = $\sqrt{0+4}$

Or, b = $\sqrt{4}$

∴ b = 2 unit

And

So, The measure of length CA = c = $\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}$

Or, c = $\sqrt{(3-0)^{2}+(2-0)^{2}}$

Or, c = $\sqrt{9+4}$

Or, c = $\sqrt{13}$

∴ c = $\sqrt{13}$ unit

Now, area of Triangle written as , from Heron's formula

A = $\sqrt{s\times (s-a)\times (s-b)\times (s-c)}$

and s = $\frac{a+b+c}{2}$

I.e s = $\frac{5+2+\sqrt{13}}{2}$

Or. s = $\frac{7+\sqrt{13}}{2}$

So, A = $\sqrt{(\frac{(7+\sqrt{13})}{2})\times ((\frac{(7+\sqrt{13})}{2})-5)\times (\frac{7+\sqrt{13}}{2}-2)\times (\frac{7+\sqrt{13}}{2}-\sqrt{13})}$

Or, A = $\sqrt{(\frac{(7+\sqrt{13})}{2})\times (\frac{(\sqrt{13}-3)}{2})\times (\frac{4+\sqrt{13}}{2})\times (\frac{7-\sqrt{13}}{2})}$

Or, A = $\frac{3}{2}$ × $\sqrt{1+\sqrt{13} }$

∴ Area of triangle = 1.5 $\sqrt{4.6}$

Hence The area of triangle for the given coordinates is 1.5 $\sqrt{4.6}$ Answer

7 0

2 years ago

Read 2 more answers