How do I solve this?

How Do I Solve This?

Answers

Answer 1

Answer:

[tex]\large\boxed{x=\log_\frac{5}{3}5}[/tex]

Step-by-step explanation:

[tex]3^x=5^{x-1}\qquad\text{use}\ a^{n-m}=\dfrac{a^n}{a^m}\\\\3^x=\dfrac{5^x}{5^1}\qquad\text{multiply both sides by 5}\\\\5\cdot3^x=5^x\qquad\text{divide both sides by}\ 3^x\\\\5=\dfrac{5^x}{3^x}\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\5=\left(\dfrac{5}{3}\right)^x\qquad\text{logarithm both sides}\ \log_\frac{5}{3}\\\\\log_\frac{5}{3}5=\log_\frac{5}{3}\left(\dfrac{5}{3}\right)^x\qquad\text{use}\ \log_ab^n=n\log_ab\\\\\log_\frac{5}{3}5=x\log_\frac{5}{3}\dfrac{5}{3}\qquad\text{use}\ \log_aa=1\\\\\log_\frac{5}{3}5=x[/tex]


Related Questions

If the hypotenuse of a 45°-45°-90° triangle is 13, what is the length of one of the legs?

Answers

Answer:

9.19

Step-by-step explanation:

Using Law of sines to find other two lengths:

a/sinA=b/sinB

let a be length of side unknown and b be hypotenuse then sinB=sin90 and sinA=sin45

a/sin45=13/sin90

a=13sin45

a=13(0.707)

  =9.19

As the given triangle is isosceles hence the length of other two legs will be same i.e 9.19 !

find the interest rate on the loan if he borrowed $2,500 @ an annual interest rate of 6% for 15 years

Answers

Answer: $2250

Step-by-step explanation: (2500x.06)=150

150x15=2250

Answer:

I think you want the monthly payment.  (Equation is attached).

Monthly Payment equals 21.10

If you are looking for the total interest paid then we need the

Total Loan Cost Formula. (attached)

The monthly loan rate is .06 / 12 = .005 and

number of payments = 12 months * 15 years = 180

Total Cost = .005 * 2,500 * 180 / 1 -(1.005)^-180

= 3,797.36

Total Cost  3,797.36

Minus Principal 2,500

Equals total interest paid = 1,297.36

Step-by-step explanation:

Maria runs 10 miles every day. If she doubles her usual speed, she can run the 10 miles in one hour less than her usual time. What is her usual speed?

Answers

Answer:

Her usual speed is 5 miles an hour.

Step-by-step explanation:

Since it takes one hour for her to run ten miles that means she is running at 10 miles an hour. So if you divide that by 2 it would be five.

Have a nice and great day.

help me with this question please!

Answers

Answer:

I believe it is A. Truly sorry if I am incorrect.

Step-by-step explanation:

I used an online calculator.

The CORRECT answer is B

Y=f(x)=16^x find f(x) when x=1/2

Answers

Answer:

4

Step-by-step explanation:

Using the rule of exponents

• [tex]a^{\frac{m}{n} }[/tex] ⇔ [tex]\sqrt[n]{a^{m} }[/tex]

f(x) = [tex]16^{\frac{1}{2} }[/tex] = [tex]\sqrt{16}[/tex] = 4

Answer:

f(1/2) = 4

Step-by-step explanation:

f(1/2) has the meaning of wherever you see x on the right hand side, you put in 1/2.

f(1/2) = 16^(1/2) = sqrt(16) [A power of 1/2 is a square root]

f(1/2) = 4

Answer: 4

Please help me I don’t understand

Answers

Answer:

the answer is 50 percent

Step-by-step explanation:because each of the lines count as 25% and the blue boxes are another 25% each.  so the answer is 50%

I don’t know what the answer is I wish I could help

What is the slope of the line described by the equation below y = -6x + 3

Answers

Answer:

slope = - 6

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 6x + 3 ← is in slope- intercept form

with slope m = - 6

Answer: -6

Step-by-step explanation:

Ap3x

Find all solutions of the equation in the interval [0,2pi)

Tan theta -1=0

Write your answer in radians in terms of pi

Answers

Answer:

{π/4, 5π/4}

Step-by-step explanation:

Tan theta -1=0 could be rewritten as tan Ф = 1.  The tangent function is 1 at Ф = π/4.  As the period of the tangent function is π,

tan Ф = 1 will be true for Ф = π/4 + π, or (5/4)π.

The solution set is {π/4, 5π/4}.

The solutions of the given equation are -1, 0, -2, 0, -2 for the values of θ in the interval [0, 2π) respectively.

How the tangent ratio (tan) is defined?

A tangent of an angle is defined as the ratio of the sine of the angle to the cosine of the angle.

tan θ = (sin θ)/(cos θ)

Solving the given equation:

The given equation is

tan θ - 1 =0

solving for the values in between [0, 2π)

In this interval, the possible values for θ(in the case of tan) are 0, π/4, 3π/4, 5π/4, and 7π/4.

So, the solutions are:

for θ = 0,

⇒ tan (0) - 1 = -1

for θ = π/4,

⇒ tan(π/4) - 1 = 0

for θ = 3π/4,

⇒ tan(3π/4) - 1 = -2

for θ = 5π/4,

⇒ tan(5π/4) - 1 = 0

for θ = 7π/4,

⇒ tan(7π/4) - 1 = -2

Thus, the solution set for the given equation in the interval [0, 2π) is {-1, 0, -2, 0, -2}

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Please help!!!!!!!!!!

Answers

Answer:

1.

[tex]\dfrac{1}{2}at^2=vt-d[/tex]

2.

[tex]at^2=2(vt-d)[/tex]

3.

[tex]a=\dfrac{2(vt-d)}{t^2}.[/tex]

Step-by-step explanation:

First, express from the formula [tex]d=vt-\dfrac{1}{2}at^2[/tex] the term [tex]\dfrac{1}{2}at^2:[/tex]

[tex]\dfrac{1}{2}at^2=vt-d[/tex]

Now multiply this equation by 2:

[tex]at^2=2(vt-d)[/tex]

and divide it by [tex]t^2:[/tex]

[tex]a=\dfrac{2(vt-d)}{t^2}.[/tex]

jelanie wrote the system of linear equations below to represent the number of student and adult tickets he and his friend sold to their school play 12s+10a=128 16s+21a=232 jelani also wrote the augmented sound matrix to represent this system which matrix could melanin have written

Answers

Answer:

[tex]\left[\begin{array}{ccc}12&10&|128\\16&21&|232\end{array}\right][/tex]

Step-by-step explanation:

The two equations Jelani wrote are:

12s+10a=128

16s+21a=232

The coefficient matrix is:

[tex]\left[\begin{array}{cc}12&10\\16&21\end{array}\right][/tex]

The constant matrix is:

[tex]\binom{128}{232}[/tex]

The augmented matrix is the combination of the coefficient matrix and the constant matrix.

[tex]\left[\begin{array}{ccc}12&10&|128\\16&21&|232\end{array}\right][/tex]

Answer:

[tex]\large\boxed{\left[\begin{array}{ccc}12&10&128\\16&21&232\end{array}\right] }[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}ax+by=n\\cx+dy=m\end{array}\right\Rightarrow\left[\begin{array}{ccc}a&b&n\\c&d&m\end{array}\right][/tex]

[tex]\text{We have the system of equations:}\\\\\left\{\begin{array}{ccc}12s+10a=128\\16s+21a=232\end{array}\right\Rightarrow\left[\begin{array}{ccc}12&10&128\\16&21&232\end{array}\right][/tex]

help me thx if u help me

Answers

The last option is the answer. x> -4

because as we can see from the number line x is larger than -4 and the dot on the -4 is not filled in so that mean that -4 is not included.

hence the answer is x> -4

In circle P, what is the measure of DAB

*HELPP​

Answers

Answer:

218°

Step-by-step explanation:

We are given that arc AD is 128° and arc AB is 90°, because the measure of an arc is equal to its corresponding central angle, and ∠APB = 90°, since right angles are 90°.

Also, arc DAB combines arc AD and AB. That means that we add the measures. 90 + 128 = 218°

Find A U B. A){3,7}B){3,5,6,7}C){2,3,5,7,8,9,12}D){3,5,6,7,8,11,12}

Answers

Answer:

{3,5,6,7}

Step-by-step explanation:

We need only to pick numbers from 2 sums, A and B, together

The union of the two sets is:

A U B = {3, 5, 6, 7, 8, 11, 12}.

Option D is the correct answer.

What is a set?

A set is a collection of items where there are operations such as:

Union of sets, the intersection of sets, and the complement of sets.

We have,

The union of two sets A and B, denoted as A U B, is the set that contains all elements that are in either set A or set B or in both.

To find A U B, we combine the elements of both sets and remove any duplicates.

A = {3, 5, 6, 7}

B = {6, 7, 8, 11, 12}

To find A U B, we combine the elements of both sets:

A U B = {3, 5, 6, 7, 8, 11, 12}

Therefore,

A U B = {3, 5, 6, 7, 8, 11, 12}.

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The complete question.

A = {3, 5, 6, 7}
B = {6, 7, 8, 11, 12}

a dealer purchased a car for 24500 and marked it up 17%. what is the sticker price of the car?
a) $27,599
b) $26,500
c) $28,665
d) $28,425

Answers

The answer is B.$28,665!!

Answer:

C

Step-by-step explanation: 17 percent of 24500 is 4165 so 24500 plus 4165 is 28665, therefore the answer is C

mark me brainliest if this is right :)

Can someone give me an explanation of how to do this.

Answers

[tex]\bf \sqrt{6x^2}\cdot \sqrt{18x^2}\implies \sqrt{(6x^2)(18x^2)}\implies \sqrt{108x^2x^2}\implies \sqrt{108(x^2)^2} \\\\\\ \begin{cases} 108=&2\cdot 2\cdot 3\cdot 3\cdot 3\\ &2^2\cdot 3^2\cdot 3\\ &(2\cdot 3)^2\cdot 3\\ &6^2\cdot 3 \end{cases}\implies \sqrt{6^2(x^2)^2\cdot 3}\implies 6x^2\sqrt{3}[/tex]

Answer:

the correct answer is option D. 6x²√3

Step-by-step explanation:

It is given that

√6x² * √18x²

To find the value of √6x² * √18x²

√6x² * √18x² = √(6x² ) * (18x²)

 = √(6 * 18 x² *x²)

 = √(6 * 6 * 3 x² *x²)

 = 6x√3

The equivalent of √6x² * √18x² =   6x²√3

Therefore the correct answer is option D.   6x²√3

The least common denominator of 1/2, 1/8, and 1/10 is
A. 10.
B. 40.
C. 16.
D. 80.

Answers

the answer would be B

Answer: Option B.

Step-by-step explanation:

Descompose the denominator of each fraction into its corresponding prime factors. Then:

[tex]2=2*1\\8=2*2*2=2^3\\10=2*5[/tex]

Now you need to choose the commons a non-commons with the highest exponent. These are: 2³, 1 and 5.

Finally you need to multiply them to get that the Least common denominator of [tex]\frac{1}{2},\ \frac{1}{8}\ and\ \frac{1}{10}[/tex] is. Therefore, this is:

[tex]LCD=2^3*1*5\\LCD=40[/tex]

This matches with the option B.

1. (16 points) John wants his friends to figure out what number he is thinking of. He gives
them three clues: an
It is a whole number.
The number divided by 2 is greater than 9 and less than 13.
The sum of its prime factors is 9.
A. What are the possible numbers that John could be describing?

Answers

i’m sorry this isn’t an answer but hat kind of people play a game like that?

Answer: John is thinking of the number 20

please rate my answer

For a certain experiment, if we expect to get a red marble twelve times in 60 trials, what is the theoretical probability of getting a red marble? 1/12 1/10 1/5 1/4

Answers

Answer:

1/5

Step-by-step explanation:

You expect to get 12 red marbles out of 60 trials.

So, you expect to get a red marbles 12/60 of the times.

We can simplify that 12/60 to 1/5, which is a choice of answers. :-)

We assume here you correctly assume your probability level when you did your forecast of 12/60.  And either you're picking from a small pool and re-insert the marble, or you have a very large amount of marbles (at least 60).

How much is one ninth of three eights

Answers

Answer:    3/72, but read the explanantion!

Step-by-step explanation: Since we are trying to find 1/9 of 3/8, which is division, we use the method K, C , F

KCF stands for keep, change, flip.

1/9     (keep)             =                1/9

divided by (change) =        multiplied by

3/8 (flip)                    =                8/3

You then proceed with simple multiplication.

1/9*3/8= 3/72

3/72= 4.1666......

Hope this helps!!

Answer:

1/24

Step-by-step explanation:

Multiply:

1     3       1

--- * --- = -----

9    8      24

How do you factor this?
2z^2-12z+10=0

Answers

Answer:

This can't be factored right now! But if it is 2z^2+12z+10=0 than it will be factored like this:

2*(z+5)(z+1)

Step-by-step explanation:

2*(z^2+6z+5)=0

2*(z+5)(z+1)

[tex]2x^2-12z+10=0[/tex]

Common multiple is 2.

[tex]2(z^2-6z+5)=0[/tex]

Simplify inside parentheses.

[tex]2(z-5)(z-1)=0[/tex] is your answer

find the third quartile using the box plot shown. A=42. B= 45 C=38. D=48

Answers

Answer:

The correct answer is B.

Which function is represented by the graph below? (5 points) f(x) = 3x f(x) = 3x − 3 f(x) = 3x + 3 f(x) = 3(x + 3)

Answers

Answer:

The correct function should be  f(x) = 3^(x + 3).

A function assigns the values. The function that represents the graph below is f(x) = 3⁽ˣ⁺³⁾.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

The function that can represent the graph below can be found by plotting the function on the calculator.

f(x) = 3ˣ – 3  ⇒ Black

f(x) = 3⁽ˣ⁺³⁾  ⇒ Red

f(x) = 3ˣ  ⇒ Blue

f(x) = 3ˣ + 3  ⇒ Green

Hence, the function that represents the graph below is f(x) = 3⁽ˣ⁺³⁾.

Learn more about Function:

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find the value of r in (4, r), (r, 2) so that the slope of the line containing them is -5/3

Answers

[tex]\bf (\stackrel{x_1}{4}~,~\stackrel{y_1}{r})\qquad (\stackrel{x_2}{r}~,~\stackrel{y_2}{2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{2-r}{r-4}=\stackrel{\stackrel{given}{\downarrow }}{-\cfrac{5}{3}}\implies 3(2-r)=-5(r-4) \\\\\\ 6-3r=-5r+20\implies 6+2r=20\implies 2r=14\implies r=\cfrac{14}{2}\implies r=7[/tex]

Answer:

r = 7

Step-by-step explanation:

looking at the slope -5/3, -5 is the change in y and 3 is the change in x. so, we  have to start from the point ( 4 , r ) and get to the next point ( r , 2 ) by using the given slope. we would first add 3 to our x value in the first point since that's our change in x and we would get r = 7. then we can substitute that in the other point and it works perfectly.

i hope this helps :)

Anyone know if this is right?

Answers

(n-1)^2 = n^2 +1 -2n so the third option form top down

Answer:

n² - 2n + 1

Step-by-step explanation:

You are to square;

(n - 1)²

This is the same as,

(n - 1)(n - 1)

Multiplying the above we get;

n² - n - n + 1

Finally,

n² - 2n + 1

what is the expression for the difference between five times a number and twice that number?​

Answers

Answer:

5x-2x

///////////////

Step-by-step explanation:

Answer:

[tex]5x-2x[/tex]

Step-by-step explanation:

Let's call that number [tex]x[/tex].

when we are asked for a difference we must substract quantities.

In this case we need the difference between five times a number  (the number is represented by [tex]x[/tex]) and twice that number:

five times the number x is equal to

[tex]x+x+x+x+x=5x[/tex]

twice that number x is equal to:

[tex]x+x=2x[/tex]

thus, the difference is: [tex]5x-2x[/tex]

A total of 771 tickets were sold for the school play. They were either adult tickets or student tickets. There were 71 more student tickets sold than adult tickets. How many adult tickets were sold?

Answers

Answer:

350

Step-by-step explanation:

771=x+x+71   (x+71 is kids,x is adults)

2x=700

x=350

To find out how many adult tickets were sold, we set up equations based on the given information: total tickets and the difference between student and adult tickets. By solving these equations, we determined that 350 adult tickets were sold.

The question involves determining how many adult tickets were sold for a school play, given that a total of 771 tickets were sold and there were 71 more student tickets than adult tickets. To solve this, we can set up an equation to represent the situation.


Let A represent the number of adult tickets and S represent the number of student tickets. We know that:

A + S = 771 (The total number of tickets).S = A + 71 (There were 71 more student tickets than adult tickets).


Substituting the second equation into the first gives us A + (A + 71) = 771.

Simplifying, we get 2A + 71 = 771.

Subtracting 71 from both sides gives us 2A = 700.

Dividing both sides by 2 gives us A = 350.


Therefore, 350 adult tickets were sold for the school play

what is 8 times 5/6​

Answers

Answer:

it is 6.66

Step-by-step explanation:

When planning her crops, Farmer Sue knows that her 15 acres can support apples and pecans. She wants to make $8,500 from her crops. She can make $1,050 per acre of apples (the variable a) and $2,500 per acre of pecans (the variable p). Which equation below would be a constraint in her system of equations? (1 point)

Answers

Answer:

A+P=15 or B

Step-by-step explanation:

Trust me u son of a gun. Alexa, play the one song with those guys in paris

What is the domain of y=cos(2x)?

Answers

Answer is C: (-∞, ∞)

Answer:

Step-by-step explanation:

There is no restriction on the input values of x , since it is periodic it can have any real value. Hence the domain of cos (2x) is (-∞,∞).

Because cos is periodic the output value keeps on repeating for any smaller or bigger input x .

245.5 cm - 20 cm in standard form​

Answers

Answer:

Standard form of 245.5 cm - 20 cm

=225.5 cm

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