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blsea [12.9K]
3 years ago
5

Jerry has a bag of counters.

Mathematics
1 answer:
Bad White [126]3 years ago
6 0
Blue is the answer....
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Find the slope of the line represented in the graph
aev [14]

There is no photo attached.

7 0
3 years ago
Which of the following function types exhibit the end behavior f(x)-->0 as x --> -infinity?
ipn [44]
Let's consider the functions one by one.

i) y=x^n,

x --> -infinity means that x is a very very small negative number. To model it in our mind let's think of -10^{15}. This number to an even power becomes 10^{30}, 10^{60}... etc.

Indeed, we can see that the smaller the x, the greater the value x^n. In fact, as x --> -infinity,  f(x)-->+infinity.

ii)
y=x, 

this clearly means that the behaviors of x and y are identical.

As x --> -infinity, y --> -infinity as well.


iii) y=|x|,

We can think of x --> -infinity, again, as a very very small number, like -10^{15}. For this value of x, y is |-10^{15}|, that is 10^{15}.

Indeed, the smaller the x, the greater the y. As in the function in part (i), as x --> -infinity,  f(x)-->+infinity.

iv) 

y=1/x

consider the values of y for the following values of x:

for x=-10, -100, -1000, y is respectively -0.1, -0.01, -0.001.

We can see that the smaller the x, the closer y gets to 0.

Thus, <span>f(x)-->0 as x --> -infinity
</span>
v) n'th root of x in not defined for negative x, when n is even.

vi) y=b^x, b>0

Here note that b cannot be equal to 1, otherwise the function is not exponential.

Let b=5, consider the values of y for the following values of x:

for x=-10, -100, -1000, y is respectively \displaystyle{ \frac{1}{5^{10}},  \frac{1}{5^{100}}, \frac{1}{5^{1000}}.

That is, the smaller the value of x, the closer y gets to 0.

Thus, <span>f(x)-->0 as x --> -infinity</span>
5 0
3 years ago
If there is a 4 digit code and using the digits 1-4, how many possibilities are there?
timurjin [86]

Answer:

64

Step-by-step explanation:

1

2

3

4

1, 2

1, 3

1, 4

2, 1

2, 3

2, 4

3, 1

3, 2

3, 4

4, 1

4, 2

4, 3

1, 2, 3

1, 2, 4

1, 3, 2

1, 3, 4

1, 4, 2

1, 4, 3

2, 1, 3

2, 1, 4

2, 3, 1

2, 3, 4

2, 4, 1

2, 4, 3

3, 1, 2

3, 1, 4

3, 2, 1

3, 2, 4

3, 4, 1

3, 4, 2

4, 1, 2

4, 1, 3

4, 2, 1

4, 2, 3

4, 3, 1

4, 3, 2

1, 2, 3, 4

1, 2, 4, 3

1, 3, 2, 4

1, 3, 4, 2

1, 4, 2, 3

1, 4, 3, 2

2, 1, 3, 4

2, 1, 4, 3

2, 3, 1, 4

2, 3, 4, 1

2, 4, 1, 3

2, 4, 3, 1

3, 1, 2, 4

3, 1, 4, 2

3, 2, 1, 4

3, 2, 4, 1

3, 4, 1, 2

3, 4, 2, 1

4, 1, 2, 3

4, 1, 3, 2

4, 2, 1, 3

4, 2, 3, 1

4, 3, 1, 2

4, 3, 2, 1

3 0
3 years ago
Read 2 more answers
Find the equation of the sphere in standard form centered at (−6,10,5) with radius 5.
Dovator [93]

Answer:

The equation of the sphere in standard form is

x^{2} +y^{2}+z^{2} +12 x-20 y-10 z+136=0

Step-by-step explanation:

<u>Step 1</u>:-

The equation of the sphere having center and radius is

(x-h)^{2} +(y-k)^{2} +(z-l)^{2} = r^{2}

Given centered of the sphere is (-6,10,5) and radius r=5

(x-(-6))^{2} +(y-10)^{2} +(z-5)^{2} = 5^{2}

on simplification,we get

using (a+b)^{2} =a^{2} +2 a b+b^{2}

using (a-b)^{2} =a^{2} -2 a b+b^{2}

simplify , we get

x^{2} +y^{2}+z^{2} +12 x-20 y-10 z+136=0

8 0
3 years ago
How would I do this? Please explain instead of just giving me the answer.
djverab [1.8K]
According to the Pythagorean theorem, the square of the hypotenuse (the longest side) of a right-angled triangle equals to the sum of the squares of the other two sides. In this case, the ladder is the hypotenuse, which equals to the distance between the bottom of the ladder and the tree + the distance we want to find (x):
5² + x² = 13²
25 + x² = 169
x² = 144
x = √144 = 12.
The distance between the ground and the top of the ladder is 12 ft.

4 0
3 years ago
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