2 in a math contest, the contestants were given the following piecewise graph. For

I am very confused and don't know where to start!

stealth61 [152]

Well, lets start with #3!
<1 is equivalent to <3 because they are vertical angles.
This means that <2 and <4 are congruent because they are vertical angles. We know that a straight line is 180 degrees. So, <1 and <2 added together will equal 180, therefore, <2 is ___________

Since the two lines are parallel, any angle on the other side is congruent, as long as that angle is in the same place as the other. So, we can see that <1 and <7 are in the same place, just moved down. So, <7 is __________.

5 0

3 years ago

The City Sights tour company had the same ratio of tourists to guide on both days this weekend.On Saturday,there were 120 touris

vivado [14]

Answer: There were 6 guides on Sunday.

Step-by-step explanation:

I suppose that this is a question about equivalent ratios:

It is said that the company had the same ratio of tourists to guides on Saturday and Sunday.

RATIO OF TOURISTS TO GUIDES:

SATURDAY: 120 : 18

SUNDAY: 40 : ?

Divide 120 by 40:

120/40 = 3

Divide 18 by 3:

18/3 = 6

Therefore:

SAT: 120 : 18

SUN: 40 : 6

Check it by multiplying both numbers in the ratio 40 : 6 by 3:

40 • 3 : 6 • 3

= 120 : 18

(You get the ratio from Saturday)

Hope this helps!

8 0

3 years ago

What are the divisors of 64

DanielleElmas [232]

Divisors of 64;
1, 2, 4, 8, 16, 32, 64

3 0

4 years ago

Calculate y as a function of x when dy/dx = 4x3 + 3x2 - 6x + 5

PtichkaEL [24]

Answer:
y = x⁴ + x³ - 3x² + 5x + C

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Separable differential equations such as these ones can be solved by treating dy/dx as a ratio of differentials. Then move the dx with all the x terms and move the dy with all the y terms. After that, integrate both sides of the equation.

$\begin{aligned}
\dfrac{dy}{dx} &= 4x^3 + 3x^2 - 6x + 5 \\
dy &= (4x^3 + 3x^2 - 6x + 5) dx \\
\int dy &= \int (4x^3 + 3x^2 - 6x + 5) dx 
\end{aligned}$

In general (understood that +C portions are still there),

$\int x^{m} = \dfrac{x^{m+1}}{m+1}$

Note that ∫dy = y since it is ∫1·dy = ∫y⁰ dy = y¹/(0+1) = y
For the right-hand side, we use the sum/difference rule for integrals, which says that

$\int \big[f(x) \pm g(x)\big]\, dx = \int f(x)\,dx \pm \int g(x) \, dx$

Applying these concepts:

$\begin{aligned} 
 \int dy &= \int (4x^3 + 3x^2 - 6x + 5) \, dx \\
y &= \int 4x^3\,dx + \int 3x^2 \, dx - \int 6x\, dx + \int 5\, dx \\
&= \frac{4x^4}{4} + \frac{3x^3}{3} - \frac{6x^2}{2} + 5x + C \qquad \text{(only one $C$ is needed)} \\
&= x^4 + x^3 - 3x^2 + 5x + C
\end{aligned}$

The answer is y = x⁴ + x³ - 3x² + 5x + C

6 0

3 years ago

Two students in your class, Tucker and Karly, are disputing a function. Tucker says that for the function, between x = –3 and x

Effectus [21]

The difference between Tucker and Karly's take is that Tucker's solution is analytical while Karly's is graphical. But both are correct either way.

For Tucker's solution, let's say at x=-3 the value for y is 4, and at x=3, the value of y is still 4, then the average rate of change or slope is 0. Note that the slope of the curve is Δy/Δx. Since there is no change for Δy, the slope is zero.

For Karly's solution, even if the curve travels high or low but would have the same elevation of x=-3 and x=3, the average rate of change is still zero. It is actually just same with Tucker's but Karly just verbalizes her solution that was observed visually.

7 0

3 years ago