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mamaluj [8]
3 years ago
9

I'm confused. Can someone help?

Mathematics
1 answer:
VARVARA [1.3K]3 years ago
8 0

a.

The polynomial w^2+18w+84 cannot be factored

The perfect square trinomial is w^2+18w + 81

----------

The reason the original can't be factored is that solving w^2+18w+84=0 leads to no real solutions. Use the quadratic formula to see this. The graph of y = x^2+18x+84 shows there are no x intercepts. A solution and an x intercept are basically the same. The x intercept visually represents the solution.

w^2+18w+81 factors to (w+9)^2 which is the same as (w+9)(w+9). We can note that w^2+18w+81 is in the form a^2+2ab+b^2 with a = w and b = 9

================================================

b.

The polynomial y^2-10y+23 cannot be factored

The perfect square trinomial is y^2-10y + 25

---------

Using the quadratic formula, y^2-10y+23 = 0 has no rational solutions. The two irrational solutions mean that we can't factor over the rationals. Put another way, there are no two whole numbers such that they multiply to 23 and add to -10 at the same time.

If we want to complete the square for y^2-10y, we take half of the -10 to get -5, then square this to get 25. Therefore, y^2-10y+25 is a perfect square and it factors to (y-5)^2 or (y-5)(y-5)

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Equation Given: <img src="https://tex.z-dn.net/?f=h%28t%29%3D-4.9t%5E%7B2%7D%2B358" id="TexFormula1" title="h(t)=-4.9t^{2}+358"
Vilka [71]

Answer:

At 3.44 seconds, the penny is at a height of 300 meters above the ground.

Step-by-step explanation:

Basically, we have to solve an equation here:

-4.9t^{2} + 358 = 300

Hence,

-4.9t^{2} = 300 - 358

t^{2} = \frac{-58}{-4.9}

t = 3.44

Hence, at 3.44 seconds, the penny is at a height of 300 meters above the ground.

Hope this helped!

4 0
2 years ago
Consider the graph of quadrilateral WXYZ. What is the most specific name for quadrilateral WXYZ?
xz_007 [3.2K]

Answer:

The quadrilateral shown on the graph is most likely to be a square.

Choice A

Step-by-step explanation:

All the sides appear to be equal which is a characteristic of squares.

Secondly, the sides appear to be intersecting at right angles

Finally, the sides appear to be parallel to each other.

4 0
2 years ago
Read 2 more answers
The ratio of Mike buying fish to Millie buying fish was 8 to 2. If in total they bought 150 pounds of fish. How many pounds did
Lady bird [3.3K]

Answer: Mike bought 120 pounds of fish and Millie bought 30 pounds  of fish.

Step-by-step explanation:

If the ratio is 8 to 2 then  8/10 will be the probability of Mike buying fist and 2/10 will be the probability of Millie buying fish.

Now multiply each fraction by the total number of pounds to find how many pounds each bought.

8/10 * 150 = 1200/10 = 120

2/10 * 150 = 300/10 = 30  

In this case, Mike bought 120 pounds of fish and Millie bought 30 pounds  of fish.

8 0
3 years ago
Here are some values of sequence Q. Write a recursive definition for the sequence.
Rashid [163]

Answer: Q(n) = Q(n - 1) + 2.5

Step-by-step explanation:

We have 3 values of the sequence Q(n)

These values are:

Q(1) = 3

Q(3) = 8

Q(7) = 18

I would think that this is a geometric sequence.

Remember that the equation for the n-th term of a geometric sequence is:

A(n) = A(1)*r^(n-1)

where r is a constant, and A(1) is the first term of the sequence.

If we rewrite the terms that we know of Q(n) in this way we get:

Q(3) = Q(1)*r^(3 - 1) = 3*r^2 = 8

Q(7) = Q(1)*r^(7 - 1) = 3*r^6 = 18

Then we have two equations:

3*r^2 = 8

3*r^6 = 18

We should see if r is the same for both equations:

in the first one we get:

r^2 = 8/3

r = (8/3)^(1/2) = 1.63

and in the other equation we get:

r^6 = 18/3

r = (18/3)^(1/6) = 1.34

Then this is not a geometric sequence.

Now let's see if this is an arithmetic sequence.

The n-th term of an arithmetic sequence is written as:

A(n) = A(1) + (n - 1)*d

where d is a constant.

If we write the terms of Q(n) that we know in this way we get:

Q(3) = Q(1) + (3 - 1)*d = 3 + 2*d = 8

Q(7) = Q(1) + (7 - 1)*d = 3 + 6*d = 18

We need to see if d is the same value for both equations.

in the first one we get:

3 + 2*d = 8

2*d = 8 - 3 = 5

d = 5/2 = 2.5

In the second equation we get:

3 + 6*d = 18

6*d = 18 - 3 = 15

d = 15/6 = 2.5

d is the same for both terms, then this is an arithmetic sequence.

An arithmetic sequence is a sequence where the difference between any two consecutive terms is always the same value (d)

Then the recursive relation is written as:

A(n) = A(n - 1) + d

Then the recursive relation for Q is:

Q(n) = Q(n - 1) + 2.5

4 0
3 years ago
Amanda is building a fence. She needs a pole to measure 4 5\6 feet from the ground. How can she write it as a fraction.
aleksklad [387]
4 5/6 would be your answer then you figure out how to take away  the whole number

6 0
3 years ago
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