Y=f(x)=1/16^x Find the f(x) when x=1/4 Express as a decimal rounding to the nearest thousandth

[tex]2x = 2y -6|\div 2\\y = x + 3 \\\\x=y-3\\y=x+3\\\\y=x+3\\y=x+3[/tex]

Both equations are identical, so there are infinitely many solutions.

Step-by-step explanation: The base of the power in the original equation becomes the base of the log. So we have [tex]^{log}7[/tex].

Next, the exponent in the original equation goes on the other side of the equation and finally, the result in the

original equation goes inside the log.

So we have [tex]^{log}7[/tex] [tex]343[/tex] [tex]= 3[/tex] which is 7³ = 343 written in logarithmic form.

the logarithmic form of the equation [tex]7^3 = 343[/tex] is [tex]log_7(343) = 3[/tex]

To convert the exponential equation [tex]7^3 = 343[/tex] into logarithmic form we first  identify the base of the exponent.

Here, the base is 7.

The exponent is 3 and the result is 343.

Using the logarithmic form formula, which is [tex]log_b(a) = c[/tex] where b is the base, a is the result, and c is the exponent, we can rewrite the equation. This gives us:

[tex]log_7(343) = 3[/tex]

Therefore, the logarithmic form of the equation [tex]7^3 = 343[/tex] is [tex]log_7(343) = 3[/tex]

Answer:

the answer is

[tex]x = 48[/tex]

Step-by-step explanation:

[tex] \frac{x}{6} = 8[/tex]

[tex]x = 48[/tex]

Answer:

$4,500

Step-by-step explanation:

Given:

Price Bought: $3,900

Transportation: $200

Repair: 900

Total amount spent = 3,900 + 200 + 900 = $5,000

10% of amount spent = 10% x 5,000 = 0.1 x 5000 = $500 (= amount loss)

TV was sold at a 10% loss,

selling price = $5,000 - $500 = $4,500

Answer:

Rs.4500

Step-by-step explanation:

1.total cost of TV=3900+200+900

                           =5000

2. loss=10/100*5000

           =500

selling price of TV=5000-500

                              =Rs.4500

Answer:

60 * 8 = 480 miles per minute *2 = 960 miles

Step-by-step explanation:

Answer:

x^(-5)+4x+1

given f(x)=4x+1 and g(x)=x^(-5)

Step-by-step explanation:

f(x)=4x+1

g(x)=x^(-5)

(f+g)(x) means you are just going to do f(x)+g(x)

or (4x+1)+(x^(-5))

There are absolutely no like terms so it can't be simplified. We can use commutative and associative property to rearrange the expression.

x^(-5)+4x+1

ANSWER

[tex](f + g)(x) = \frac{4{x}^{6} \: + {x}^{5} + 1 }{ {x}^{5} } [/tex]

EXPLANATION

The given functions are:

[tex]f(x) = 4x + 1[/tex]

and

[tex]g(x) = {x}^{ - 5} [/tex]

We now want to find

[tex](f + g)(x)[/tex]

We use this property of Algebraic functions.

[tex](f + g)(x) = f(x) + g(x)[/tex]

We substitute the functions to get:

[tex](f + g)(x) = 4x + 1 + {x}^{ - 5} [/tex]

Writing as a positive index, we get:

[tex](f + g)(x) = 4x + 1 + \frac{1}{ {x}^{5} } [/tex]

The property we used to obtain the positive index is

[tex] {a}^{ - n} = \frac{1}{ {a}^{n}} [/tex]

We now collect LCD to get:

[tex](f + g)(x) = \frac{4x \cdot {x}^{5} \: + {x}^{5} + 1 }{ {x}^{5} } [/tex]

This simplifies to:

[tex](f + g)(x) = \frac{4{x}^{6} \: + {x}^{5} + 1 }{ {x}^{5} } [/tex]

Answer: f(g(x))=x and g(f(x)) = x

              f⁻¹(x) = g(x) YES ARE INVERSES

              f⁻¹(x) ≠ g(x) NOT INVERSES

Step-by-step explanation:

Inverse is when you swap the x's and y's and then solve for y.

If f⁻¹(x) = g(x), then they are inverses of each other.

Similarly, if g⁻¹(x) = f(x), they are inverses of each other.

NOTE: You can also use composition to determine if they are inverses  -->    If (fog)(x) = x, then they are inverses of each other.

[tex]f(x) = \dfrac{1}{x+4}-9\\\\\\\text{Swap the x's and y's. NOTE: f(x) is y}\\x=\dfrac{1}{y+4}-9\\\\\\\text{Add 9 to both sides}\\x+9=\dfrac{1}{y+4}\\\\\\\text{Flip the fractions}\\\dfrac{1}{x+9}=y+4\\\\\\\text{Subtract 4 from both sides}\\\dfrac{1}{x+9}-4=y\\\\\\\boxed{f^{-1}(x)=g(x)\text{ so f(x) and g(x) are inverses of each other}}[/tex]

[tex]f(x) = 3x+27\\\\\\\text{Swap the x's and y's NOTE f(x) is y}\\x=3y+27\\\\\\\text{Subtract 27 from both sides}\\x-27=3y\\\\\\\text{Divide everything by 3}\\\dfrac{1}{3}x-\dfrac{27}{3}=y\\\\\\\text{Simplify}\\\dfrac{1}{3}x-9=y\\\\\\\boxed{f^{-1}(x)\neq g(x)\text{ so f(x) and g(x) are NOT inverses of each other}}[/tex]

[tex]\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{-4})~\hspace{10em} slope = m\implies \cfrac{3}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-4)=\cfrac{3}{5}(x-2)\implies y+4=\cfrac{3}{5}(x-2) \\\\\\ y+4=\cfrac{3}{5}x-\cfrac{6}{5}\implies y=\cfrac{3}{5}x-\cfrac{6}{5}-4\implies y=\cfrac{3}{5}x-\cfrac{26}{5}[/tex]

Final answer:

The expression 5÷7a is equivalent to 5a/7 when rewritten in simplest algebraic form. It represents multiplying 5 by the reciprocal of 7a. None of the provided answer options match this expression. Option. A

Explanation:

The expression 5÷7a can be rewritten as 5÷7 × a or 5/7a. This is because division by a number is the same as multiplying by its reciprocal. Thus, we take the reciprocal of 7a to be (1/7)a or a/7, multiply it by 5, giving us 5a/7. This is how we denote division within algebraic expressions and simplifies the equation.

If the question is looking for an equivalent single-term expression, none of the given options (5×7b, 7÷5b, 7×1/5c, 35d, 5×1/7) are correct, as they are all different in terms of algebraic structure and value. However, if you're looking for an equivalent expression in the simplest algebraic form, the equivalent expression for 5÷7a is simply 5a/7.

Answer:

(f+g)(x) = [tex]\sqrt{5x+7}+\sqrt{5x-7}[/tex]

Step-by-step explanation:

f(x) = [tex]\sqrt{5x+7}[/tex]

and g(x) = [tex]\sqrt{5x-7}[/tex]

We need to find (f+g)(x)

(f+g)(x) = f(x) + g(x)

(f+g)(x) = [tex]\sqrt{5x+7}+\sqrt{5x-7}[/tex]

It can't be further solved so,

(f+g)(x) = [tex]\sqrt{5x+7}+\sqrt{5x-7}[/tex]

Answer:

decreasing

Step-by-step explanation:

since its negative it will slope down

The graph is increasing.

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them.

Given: range:  -3 < X <-1

The graph related to this question is attached below

as, seen from the graph the graph slope will rise up from -3 to -1.

Hence, the graph is increasing.

Learn more about graph here:

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Answer:

32

Step-by-step explanation:

Possible outcomes in a fair sided die 1,2,3,4,5,6 = 6 possible outcomes

Odd numbers = 1,3,5 = 3 odd numbers

Probability of rolling an odd number = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]

Total number of rolls = 64

expected number of odd number rolls in 64 roll,

= [tex]\frac{1}{2}[/tex] x 64 = 32

For this case we must find the product of [tex](3x + 5) (x + 4)[/tex]

By definition, the distributive property states that:

[tex](a + b) (c + d) = ac + ad + bc + bd[/tex]

Then, according to the expression we have:

[tex]3x ^ 2 + 12x + 5x + 20 =\\3x ^ 2 + 17x + 20[/tex]

Answer:

[tex]3x ^ 2 + 17x + 20[/tex]

Option C

Answer:

C

Step-by-step explanation:

Each term in the second factor is multiplied by each term in the first factor, that is

3x(x + 4) + 5(x + 4) ← distribute both parenthesis

= 3x² + 12x + 5x + 20 ← collect like terms

= 3x² + 17x + 20

Answer: 13.2

Step-by-step explanation: First, turn the percent into a decimal by dividing it by 100.

22/100 = 0.22

Multiply the decimal by 60.

0.22 x 60 = 13.2

Answer:

Monsoon

Step-by-step explanation:

in High tide every 1 hour, you move 3 km that is faster then Monsoon which every 2 hours you move 5 km because if you multiply 1 by 2 you get 2 (hours) but if you multipy 3 by 2 yuo get 6 and 6 is more than 5. if you use this method one more time then to you will find that the answer is Monsoon.

The river rafting adventure that offers the lowest average speed would be the option Monsoon.

We don't write symbols like currency generally and understand it from context.

Also, a sign of multiplication is often hidden if there are non-numeric symbols and numbers being multiplied are written together.

The table below shows the details of three different river rafting adventures.

Adventure Duration (in hours)

Distance (\text{km})(km)left parenthesis, k, m, right parenthesis

High Tide 111 333 Monsoon 222 555 Tsunami 4

In High tide every 1 hour, you move 3 km which is faster than Monsoon

Every 2 hours you move 5 km because 1 x 2 gives 2 (hours)

But 3 x 2 = 6 and 6 is more than 5.

Therefore, The answer is Monsoon.

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The Measure of angle c is 144 because line segment mn is a transversal and angles a and b are corresponding angles. option B) is correct choice.

Corresponding angles are angles that are in the same position relative to the transversal and on opposite sides of it. In this case, angles a and b are both alternate interior angles, so they are corresponding angles.

Alternate interior angles are angles that are on opposite sides of the transversal and inside the parallel lines.

Since corresponding angles are congruent, we know that the measure of angle a is equal to the measure of angle b. We are also given that the measure of angle a is 100 degrees. Therefore, the measure of angle b is also 100 degrees.

The sum of the measures of the angles in a triangle is 180 degrees. Therefore, the measure of angle c is equal to 180 degrees - 100 degrees - 100 degrees = 144 degrees.

The other options are incorrect:

Option A: The measure of angle c cannot be 36 degrees because angle b and angle c are vertical angles, and vertical angles are always congruent.

Option B: The measure of angle c cannot be 144 degrees because of the properties of the exterior angles of a triangle. The exterior angle of a triangle is equal to the sum of the two remote interior angles, and the two remote interior angles in this case are angles a and b, which have a combined measure of 200 degrees. Therefore, the measure of angle c must be less than 144 degrees.

Option C: The measure of angle c cannot be 44 degrees because line segment MO is not a transversal. A transversal is a line that intersects two parallel lines. In this case, line segment NO is the transversal.

Option D: The measure of angle c cannot be 100 degrees because angles m and c are not alternate interior angles. Alternate interior angles are angles that are on opposite sides of the transversal and inside the parallel lines. In this case, angle m is an alternate interior angle, but angle c is an exterior angle.

Therefore, the best answer is The measure of angle c is 144 because line segment mn is a transversal and angles a and b are corresponding angles. option B) is correct choice.

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Answer:

C. 3x^2 -13x + 7

Step-by-step explanation:

Lets start in the ones place:

    +3

 - (-4)

_______

    +7

Now go to the tens place:

   -5x

  -(8x)

________

  -13x

Lastly, go to the hundreds place:

   6x^2

  -(3x^2)

_________

   3x^2

So, the correct answer is "3x^2 -13x + 7", which is C.

I hope this helps! :)

Answer:

C) 3x squared - 13x + 7

Step-by-step explanation:

To subtract this problem you need to combine like terms

6x squared - 3x squared = 3x squared

-5x - 8x = -13

3 - -4 = 7

Since you combined the like terms put it back into an expression

3x squared - 13x + 7

Since the 13 is negative it becomes a subtraction sign in this expression.

The 7 is positive so it becomes an addition sign.

[tex]\bf x= \begin{cases} 6\\ 4 \end{cases}\implies \begin{cases} x=6\implies &x-6=0\\ x=4\implies &x-4=0 \end{cases} \\\\\\ (x-6)(x-4)=\stackrel{y}{0}\implies \stackrel{\mathbb{F~O~I~L}}{x^2-10x+24}=0\implies \stackrel{\textit{adding a common factor of 5}}{5(x^2-10x+24)=0} \\\\\\ 5x^2-50x+120=0\implies 5x^2-50x+120=y[/tex]

now, the common factor of 5 simply makes the parabola steeper, but the roots are the same, whilst the vertex of it changes

Final answer:

To write a quadratic equation given the roots and the leading coefficient, use the formula ax² + bx + c = 0, where the roots are the values of x when the equation equals zero, and the leading coefficient determines the value of a.

Explanation:

To write a quadratic equation given the roots and the leading coefficient, you can use the formula ax² + bx + c = 0. The roots of the quadratic equation are the values of x when the equation equals zero. The leading coefficient determines the value of a in the equation. In this case, the roots are 6 and 4, and the leading coefficient is 5.

Using the formula, we get: 5x² - (6+4)x + (6)(4) = 0.
Simplifying, we have 5x² - 10x + 24 = 0. This is the quadratic equation with the given roots and leading coefficient.

Answer:

[tex]\large\boxed{B.\ f(4)=22}[/tex]

Step-by-step explanation:

[tex]f(x)=3x+10\\\\f(4)-\text{put x = 4 to the equation of the function}\\\\f(4)=3(4)+10=12+10=22[/tex]

Answer:

3/10

Step-by-step explanation:

Using it's concept, it is found that the probability that the next person to enter kidz kare is between 10 and 15 years old is given by:

C) 3/10.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

From the histogram, we have that out of a total of 10 students, 3 are between 10 and 15 years old, hence:

p = 3/10, which means that option C is correct.

More can be learned about probabilities at https://brainly.com/question/14398287

Answer:

6a^3 + 22a^2 - 6a - 10

Step-by-step explanation:

(3a + 5)(2a^2 + 4a - 2)

distribute 3a

6a^3 + 12a^2 - 6a

distribute 5

10a^2 + 20a - 10

combine like terms/simpify

6a^3 + 22a^2 - 6a - 10

Answer:

6a^3 + 22a^2 +14a-10

Step-by-step explanation:

Hi, to solve this you have to apply the distributive porperty:

So:

[tex](3a +5)x ( 2a^{2} +4a -2)\\6a ^{3} +12a^{2} -6a + 10a^{2} +20a^{2} -10\\\\[/tex]

Then, combine like terms and solve using addition or subtraction:

[tex]6a^{3} +12a^{2} +10a^{2} +20a-6a-10\\6a^{3} +22a^{2} +12a-10[/tex]

In conclusion the product is 6a^3 + 22a^2 +14a-10.

Feel free to ask for more if it´s necessary or if you did not understand something.

Answer:

g (h (x) ) = 5/8

Step-by-step explanation:

We are given the following two functions and we are to find the value of [tex] g ( h ( - 3 ) ) [/tex]:

[tex] g ( x ) = \frac { x + 1 } { x + 2 } [/tex]

[tex] h ( x ) = 4 - x [/tex]

Firstly, we need to find the function :

[tex] g ( h ( x ) ) = \frac { ( 4 - x + 1 ) } { ( 4 - x - 2 ) } = \frac { 5 - x } { 2 - x } [/tex]

Now substituting the value [tex]x=-3[/tex] in it:

[tex] g ( h ( x ) ) = \frac { 5 - (-3) } { 2 - (-3) }  [/tex]

g (h (x) ) = 5/8

Answer:

8/5

Step-by-step explanation:

If g(x) = (x+1)/(x-2) and h(x) = 4 - x

(g*h)(-3) = g(h(-3))

h(-3) = 4 - -3 = 4 + 3 = 7

g(7) = (7 + 1)/(7 - 2) = 8/5

Answer:

56 ounces

Step-by-step explanation:

16 ounces = 1 pound

There are 3.5 pounds so 16 x 3 = 48

Then, the other .5 of the pound would be 16/2 or 8.

48 + 8 + 56

Answer:

56

Step-by-step explanation:

16x3=48

Half of 16 is 8.

Since there is 3 1/2 pounds

You would add the 8 and 48.

48 from the 3 pounds and 8 ounces for 1/2 a pound.

Hence, the answer is 56.

48+8=56

Answer:

y < 1/2x - 2

Step-by-step explanation:

Find the slope of the graph, we can find the slope of the graph by using the formula y2 - y1/x2 - x1. But in order to do so, we must find two perfect points.

Point 1: (0,-2)

Point 2: (4,0)

Now, we would put these points into the formula.

0 -(-2) = 2

4 - 0 = 4

2/4 = 1/2

Therefore, the slope of this graph is 1/2

Now we must find the y intercept, which can be found based on where the line intersects with a y coordinate (ex: 0,y). Based on that, we can come to the conclusion that -2 is our y-intercept

In order to proceed we must know what a linear equation is. A linear equation contains the following:

y = mx + b

m of mx represents the slope, you would leave x as it is.

b represents the y intercept

We have already found what each is, so we can go ahead and put in our slope and y-intercept into the linear equation.

y = 1/2x + -2

Because, we are dealing with an inequality problem, the equal sign must be replaced with an inequality sign and that is determined based on the area of the graph that is shaded.

Since, the graph is shaded downwards we will be using the "less than sign", in addition if you haven't noticed, the line is dotted so we will NOT be using any "equal to symbols"

So, after applying all of this together, we can conclude that the inequality that describes this graph is y < 1/2x - 2

Should you have any further questions, please let me know in the comment section below.

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}x^2+y^2=36\\x+y=6&\text{subtract y from both sides}\end{array}\right\\\left\{\begin{array}{ccc}x^2+y^2=36&(1)\\x=6-y&(2)\end{array}\right\qquad\text{substitute (2) to (1):}\\\\(6-y)^2+y^2=36\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\6^2-(2)(6)(y)+y^2+y^2=36\\36-12y+2y^2=36\qquad\text{subtract 36 from both sides}\\2y^2-12y=0\qquad\text{distributive}\\2y(y-6)=0\iff2y=0\ \vee\ y-6=0\\\\2y=0\qquad\text{divide both sides by 2}\\y=0\\\\y-6=0\qquad\text{add 6 to both sides}\\y=6[/tex]

[tex]\text{put the values of y to (2):}\\\\for\ y=0:\\x=6-0=6\\\\for\ y=6\\x=6-6=0[/tex]

Answer:

SD(σ)=2.91548

Step-by-step explanation:

Definition:

Standard deviation (SD) measures the volatility or variability across a set of data. It is the measure of the spread of numbers in a data set from its mean value and can be represented using the sigma symbol (σ)

To find out SD you must know the value of Mean and Variance.

Mean=sum of values / N (number of values in set)

Mean=7+5+10+11+12/5

Mean=45/5

Mean=9

Variance=((n1- Mean)2 + ... nn- Mean)2) / N-1 (number of values in set - 1)

Variance=((7-9)^2 +(5-9)^2+(10-9)^2+(11-9)^2+(12-9)^2))/5-1

Variance=((-2)^2+(-4)^2+(1)^2+(2)^2+(3)^2)/4

Variance=(4+16+1+4+9)/4

Variance=34/4

Variance=8.5

Standard Deviation(σ)=√Variance

σ = √8.5

By taking the square root of √8.5 we get;

σ = 2.91548

Thus the value of Standard Deviation(σ)=2.91548....

You must remember that a polynomial is written like so...

ax^2 + bx + c

In this case...

a = 1

b = 3

c = -10

To factor you must find two numbers who both add up to b (3) AND multiply to c (-10)

-2 + 5 = 3

-2 * 5 = -10

so...

(x - 2)(x + 5)

To find the zero you must set each factor equal to zero and solve for for x like so...

x - 2 = 0

x = 2

x + 5 = 0

x = -5

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

x= -5 and x= 2

Step-by-step explanation:

choice A ("decreases by about 0.9°") is more likely the correct description of the slope.

Step 1: Look for the trend between temperature and latitude

Generally, as we move north in latitude (higher latitude values), temperatures tend to decrease. Analyze the high temperatures in the table. Warmer temperatures are at lower latitudes and cooler temperatures are at higher latitudes.

Step 2: Interpret the slope

The slope of the best fit line tells you how much the temperature changes (on the y-axis) on average with every one-degree increase in latitude (on the x-axis). Since temperature decreases as latitude increases, the slope will be negative.

The temperature decreases by a certain value for each 1-degree increase north in latitude. The answer choices with a positive slope (increase in temperature) can be eliminated (choices C and D). Looking at the remaining choices (A and B), a lower negative value indicates a smaller decrease in temperature with increasing latitude.

We know that generally, temperatures get cooler as we move north (higher latitudes). This means as the latitude values increase (on the x-axis), the temperature values (on the y-axis) should decrease.

Slope and Interpretation: The slope of the best fit line through the temperature data tells us how much temperature changes (goes up or down) on average with every one-degree increase in latitude. Since temperature goes down (decreases) with increasing latitude, the slope will be negative.

Answer:

Lol I just took this text couple weeks ago. The answer is (1,1) Solve the system of equations by substitution.

3/8x + 1/3y = 17/24

x + 7y = 8

x = -7y + 8 and substituting it to the first equation

3/8x + 1/3y = 17/24

3/8(-7y + 8 )+ 1/3y = 17/24

Solving for the value of y = 1

And substituting y =1 to the second equation

X= 1

(1, 1)

Answer:

1,1

Step-by-step explanation: