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ELEN [110]
3 years ago
14

Johnny went to an apple farm to pick some apples. The admission to get in was $5.00 and the apples cost $0.75 per pound.

Mathematics
1 answer:
sasho [114]3 years ago
6 0

Answer:

y=0.75x+5

Step-by-step explanation:

It would be this equation because you start at 5, which is the y-intercept, then you add 0.75 for every pound of apples. So on a graph you would start at 5 on the y-line then go up by 0.75

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13. Write an equation for the given function given the amplitude, period, phase shift, and vertical shift.
Paul [167]

Answer:

y=4sin(\frac{2\pi(t+\frac{4}{3}\pi ) }{4\pi } )-2

Step-by-step explanation:

Let's start with the original function.

y=a sin\frac{2\pi t}{T}

We can immediately fill in the amplitude 'a' and period 'T' , as the question defines these for us, and provides values for 'a' and 'T', 4 and 4\pi respectively.

y=4sin(\frac{2\pi t}{4\pi } )

Now we only have phase shift and vertical shift to do. Vertical shift is very easy, you can just add it to the end of the right side of the expression. A positive value will shift the graph up, while a negative value will move shift the graph down. We have '-2' as our value for vertical shift, so we can add that on as so:

y=4sin(\frac{2\pit }{4\pi } )-2

Now phase shift the most complicated of the transformations. Basically, it is just movement left or right. A negative phase shift moves the graph right, a positive phase shift moves the graph left (I know, confusing!). Phase shift applies directly to the x variable, or in this case the t variable. To achieve a -4/3 pi phase shift, we need to input +4/3 pi into the function, because of the aforementioned negative positive rule. Here is what the function looks like with the correct phase shift:

y=4sin(\frac{2\pi(t+\frac{4}{3}\pi ) }{4\pi } )-2

This function has vertical shift -2, phase shift -4/3 \pi, amplitude 4, and period 4\pi.

Desmos.com/calculator is a great tool for learning about how various parts of an equation affect the graph of the function, If you want you can input each step of this problem into desmos and watch the graph change to match the criteria.

8 0
3 years ago
ANSWER QUICK PLS 53 PTS HURRY
GalinKa [24]

B & C

hope this helps

5 0
3 years ago
12
Tamiku [17]

Answer:

30%. Based on the given conditions, formulate: 12/40 Cross out the common factor: 3/10 Multiply a number.

Step-by-step explanation:

5 0
2 years ago
HELP PLEASE!!!!!!!!!!!!
Bogdan [553]

Answer:

See the explanation.

Step-by-step explanation:

We are given the function f(x) = x² + 2x - 5

Zeros :

If f(x) = 0 i.e. x² + 2x - 5 = 0

The left hand side can not be factorized. Hence, use Sridhar Acharya formula and  

x= \frac{-2+\sqrt{2^{2}-4\times(-5)\times1 } }{2} and  

x= \frac{-2-\sqrt{2^{2}-4\times(-5)\times1 } }{2}

⇒ x = -3.45 and 1.45

Y- intercept :

Putting x = 0, we get, f(x) = - 5, Hence, y-intercept is -5.

Maximum point :

Not defined

Minimum point:  

The equation can be expressed as (x + 1)² = (y + 5)

This is an equation of parabola having the vertex at (-1,-5) and axis parallel to + y-axis

Therefore, the minimum point is (-1,-5)

Domain :  

x can be any real number

Range:  

f(x) ≥ - 6

Interval of increase:

Since this is a parabola having the vertex at (-1,-5) and axis parallel to + y-axis.

Therefore, interval of increase is +∞ > x > -1

Interval of decrease:

-∞ < x < -1

End behavior :  

f(x) = x^{2} +2x-5 =x^{2}  (1+\frac{2}{x} -\frac{5}{x^{2} } )

So, as x tends to +∞ , then f(x) tends to +∞

And as x tends to -∞, then f(x) tends to +∞. (Answer)

7 0
3 years ago
Consider the enlargement of the pentagon. A small pentagon has a bottom side length of x centimeters and left side length of 7 c
il63 [147K]

Answer:

3.3 cm

Step-by-step explanation:

From the above question, we can draw out a proportion

= Small pentagon = Large pentagon

= x/7 = 7/15

Cross Multiply

x × 15 = 7 × 7

15x = 49

x = 49/15

x = 3.2666666667 cm

Approximately= 3.3 cm

7 0
3 years ago
Read 2 more answers
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