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lions [1.4K]
3 years ago
9

Compare linear functions using______ and graphs.

Mathematics
1 answer:
Darya [45]3 years ago
8 0
Fractions. Is your answers
You might be interested in
what is the first term of a geometric sequence in which the second term is 6 and the fourth term is 54
IRISSAK [1]
For a geometric sequence:
U_{n} = a * r^{n - 1}
U_{n} = the nth term, i.e. U₂ is the second term, U₃ is the third term, etc.
a = first term (U₁)
r = multiplier
n = number corresponding to the postion of the nth term in the sequence, e.g. for U₂, n = 2, for U₃, n = 3

According to the information:
U₂ = 6
U₄ = 54
So:
U_{2} = a * r^{(2) - 1} = 6 \\\\ a * r^{1} = 6 \\\\ ar = 6 \\
U_{4} = a * r^{(4) - 1} = 54 \\\\ a * r^{3} = 54 \\\\ ar^{3} = 54
Now, we have two equations in terms of a and r;
We can work out a by first working out r;
If we let the U₂ eq'n be [1] and the U₄ eq'n be [2];
Then, we do [2] ÷ [1] to cancel out the a and get an equation with only r that we are able to solve and then just solve it, like so:
\frac{ar^{3}}{ar} =  \frac{54}{6} \\\\ r^{2} = 9 \\\\ r = 3
Note: r has to be 3, and not -3, as the two given terms of the sequence tell us that the terms of the sequence will get bigger from each term to the next so r has to be above 1.

Now that we know r, we can sub it back into either [1] or [2] and solve for a, Its quicker and easier to sub it into [1] as we have no powers greater than 1 and we have smaller numbers to deal with (but you would get the same value of a either way), so:
U₂ = ar = 6
a(3) = 6
a = 6/3
a = 2
5 0
3 years ago
Help with number two
BabaBlast [244]

Answer:

y = -2x+1

Step-by-step explanation:

We have a point and a slope, so we can use the point slope form of a line

y-y1 = m(x-x1)  where m is the slope and (x1,y1) is the point

y-3 = -2(x--1)

y-3=-2(x+1)

Distribute the 2

y-3 = -2x-2

Add 3 to each side

y-3+3 = -2x-2+3

y = -2x+1

This is in slope intercept form

7 0
3 years ago
Assume that the pond contains 90 fish: 64 purple, 25 green, and 1 red. A contestant pays $0.55 to randomly catch one fish and re
Licemer1 [7]

Answer:

The carnival is losing (on average) $0.15 on each play

Step-by-step explanation:

To find out how much the carnival wins or looses in each play one subtract the expected value (EV) from each play from the amount charged by the carnival for each play ($0.55). If the expected value is higher than what the carnival charges, the carnival is losing money.

Expected is the sum of the payouts of each bet multiplied by its likelihood:

EV= \frac{64*0.40+25*1.15+1*9.00}{90}\\EV= 0.70

Since the expected value is higher than $0.55, the carnival is losing money, on average, on each play:

0.55-0.7 = -0.15

The carnival is losing (on average) $0.15 on each play

6 0
3 years ago
I need help with 13 on both pictures. The first picture is the answer and the second picture is the question not getting the ans
natita [175]

Problem 13

If we want to multiply (x^3-3x^2+2x) with (x^3-2x^2+x), then we can set up a diagram shown below. The terms are along the outside. The stuff inside is the result of multiplying each pair of outer terms.

  • Example: x^3 times x^3 = x^6 in the top left corner
  • Another example: 2x times x = 2x^2 in the bottom right corner.

This is known as the box method to keep track of all the terms multiplied.

Once the table is filled out, we add up each term inside the boxes. Combine like terms if possible. Notice that I color-coded the like terms (eg: the x^3 terms are in green boxes).

The final answer is x^6 - 5x^5 + 9x^4 - 7x^3 + 2x^2

6 0
2 years ago
Triangle XYZ has vertices at X(–2, –1), Y(–3, –6), and Z(–7, –5). If triangle XYZ is rotated 90° clockwise, what will be the coo
Delvig [45]

Answer:1. Is right 3 down 5, because to get from x(0,0) to x'(3,-5), you need I shift to the right 3 and downwards 5.

2. Counterclockwise 180 degrees. This is because 180 degrees is half of a full rotation (360 degrees), meaning the point would be the same no matter which way you rotated 180 degrees.

3. Clockwise 90 degrees. Going counter clock wise 270 degrees is like going around 3/4 of a circle (because 270/360 is 3/4). Just as well, going clock wise 90 degrees is like going 1/4 of the circle, but in the opposite direction. This means they will both land at the same point.

Hope this Helps!

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
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