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2 years ago

Evaluate f (x) = 3 (2)x for x=-1

Mathematics

1 answer:

kap26 [50]2 years ago

8 0

The value of the function at x = -1 is 5

<h3>What is function?</h3>

Function can be defined as an expression, rule, or law that defines a relationship between one variable known as the independent variable and another called the dependent variable.

From the information given, we have that;

f (x) = 3 (2)x with x=-1

Now, let's substitute the value of x as - 1 in the function given;

f (x) = 3 (2)x

f (x) = 3 (2) -1

Expand the bracket;

f (x) = 6 - 1

f(x) = 5

Thus, the value of the function at x = -1 is 5

Learn more about functions here:

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You have a 12 inch ruler being used as a miniature seesaw. A pencil is placed under the 4 inch mark. A weight is placed at the 2

nlexa [21]

Answer:

The number of pencils that needs to be placed at the other 1 inch end to get a balance again is approximately 3 pencils

Step-by-step explanation:

The given parameters are;

The length of the ruler used as a seesaw = 12 inch

The location where the pencil is placed = Under the 4 inch mark

The location where the weight is placed to balance the seesaw = The 2 inch mark

Therefore, the pencil at the 4 inch mark is fulcrum

The location where a pencil is placed on the ruler = The 12 inch end

The number of pencils, x, that needs to be placed at the other 1 inch end to get a balance again is given as follows;

The distance of the pencil at the 12 inch end from the fulcrum = 12 inches - 4 inches = 8 inches

The distance of the pencils placed at the 1 inch end from the fulcrum = 4 inches - 1 inch = 3 inches

Therefore at balance point, (equilibrium) the anticlockwise moment = The clockwise moment, which gives;

The mass of 1 pencil × 8 inches = x × The mass of 1 pencil × 3 inches

x = (The mass of 1 pencil × 8 inches)/(3 inches × The mass of x × 1 pencil)

x = 8/3 = 2. $\overline 6$ ≈ 3 pencils

The number of pencils that needs to be placed at the other 1 inch end to get a balance again = x ≈ 3 pencils.

4 0

3 years ago

Find the zeros of each function by using a graph and a table f(x)=x^2+3x-18.

Debora [2.8K]

1) Finding the zeros of this function f(x) =x² +3x -18

f(x) = x²+3x-18 Factoring this equation, and rewriting it

Which two numbers whose sum is equal to 3 and their product is equal to 18?

6 -3 = 3 and 6 *-3 = -18

So we can rewrite as (x +6) (x-3)

(x+6)(x-3)=0 Applying the Zero product rule, to find the roots

x+6=0,

x=-6

x-3=0,

x=3

S={3,-6}

2) Setting a table, plugging in the values of x into the factored form: (x-6)(x-3)

x | y |

1 | -14 (1 +6)(1-3) =-14

2 | -8 (2 +6)(2-3) =-8

3 | 0

4 | 10

-5 | -8

-6 | 0

3) Plotting the function:

5 0

1 year ago

hello! So the people in Indian server were bad(as they would not answer and instead spam) so I switched servers and I hope you a

Art [367]

Answer:

$\displaystyle E=26log2-24log3+8log 5$

Step-by-step explanation:

Logarithms

There are certain properties of the logarithms we'll need to recall in order to simplify the expression given in the question. We'll list them below

$log(x.y)=logx+logy\\log(x/y)=logx-logy\\logx^y=y.logx$

We'll also need to factor the following numbers into their prime factors:

$20=2^2\cdot 5$

$16=2^4$

$15=3\cdot 5$

$25=5^2$

$24=2^3\cdot 3$

$81=3^4$

$80=2^4\cdot 5$

The original expression is

$\displaystyle E=log20+16log\frac{16}{15}+12log\frac{25}{24}+log\frac{81}{80}$

Plugging in the factored values

$\displaystyle E=log(2^2\cdot 5)+16log\frac{2^4}{3\cdot 5}+12log\frac{5^2}{2^3\cdot 3}+log\frac{3^4}{2^4\cdot 5}$

Applying the properties we have

$\displaystyle E=log2^2+log 5+16(log2^4-log3-log 5)+12(log5^2-log2^3-log 3)+log3^4-log2^4-log 5$

$\displaystyle E=2log2+log 5+16log2^4-16log3-16log 5+12log5^2-12log2^3-12log 3+log3^4-log2^4-log 5$

$\displaystyle E=2log2+log 5+64log2-16log3-16log 5+24log5-36log2-12log 3+4log3-4log2-log 5$

Simplifying

$\boxed{\displaystyle E=26log2-24log3+8log 5}$

7 0

4 years ago

The most confused that i have been

Trava [24]

Answer:

(-5, -3)

Step-by-step explanation:

To graph the two equations, you can look at two things, the slope and the y-intercept.

The two equations are in slope-intercept form, y= mx + b. m is the slope and b is the y-intercept. The slope is rise/run and the y-intercept is where the line crosses the y-axis.

In the first equation, the slope is -1 and the y-intercept is -8. So, to graph you would start at (0, 8) and move up one unit and then left one unit to get the next point.

For the second equation, the slope is 2/5 and the y-intercept is -1. So, to graph you would do the same thing. Start at (0, -1) and then go up 2 units and right 5 units to get the next point.

I've attached a graph below if you need it.

6 0

3 years ago

A survey found that 31% of all teens buy soda (pop) at least once each week. Seven teens are randomly selected. The random varia

kumpel [21]

Answer:

The value of n is 7.

Step-by-step explanation:

For each teen, there are only two possible outcomes. Either they buy soda at least once each week, or they do not. Since they were selected randomly, the teens are independent of each other, which means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In the binomial distribution, we have that n is the size of the sample. In this question, seven teens are randomly selected, which means that the value of n is 7.

7 0

3 years ago