Mathematics Middle School

how to do this?
[tex]{3}^{2 - x} = {5}^{x} [/tex]
the ans is
[tex] \frac{ ln(9) }{ ln(15) } [/tex]

Answers

Answer 1
This equation uses two properties of logarithms:

[tex]\ln(g^x) = x \ln(g)[/tex]

[tex]\ln(a) + \ln(b) = \ln(ab)[/tex]

So you could take the ln from left and right hand side in the equation, and get:

(2-x)ln 3 = x ln 5

then

2 ln 3 - x ln 3 - x ln 5 = 0 =>

x(ln 3 + ln 5) = 2 ln 3

so x = 2 ln 3 / (ln3 + ln5)

Now using the 1st property you can say 2 ln 3 is ln 3² = ln9
and using the 2nd property you can say ln3 + ln5 = ln15

so x= ln9 / ln15


Related Questions

Based on the graph, what is the dependent variable, the equation relating the two variables, and how far will the dragonfly travel in 24 hours if it continues to fly at the same speed? (look at the image below)

The dependent variable is distance, the equation is x = 20y, and the dragonfly will travel 360 miles.
The dependent variable is distance, the equation is y = 20x, and the dragonfly will travel 480 miles.
The dependent variable is time, the equation is x = 20y, and the dragonfly will travel 360 miles.
The dependent variable is time, the equation is y = 20x, and the dragonfly will travel 480 miles.

Answers

40/2 = 20
so 
y = 20x

y = distance (miles) and x = time (hours)
so if x = 24 then y = 20x = 20(24) = 480

answer
The dependent variable is distance, the equation is y = 20x, and the dragonfly will travel 480 miles. 

Answer:

The dependent variable is distance, the equation is y = 20x, and the dragonfly will travel 480 miles.

Step-by-step explanation:

According to the graph, the dependent variable is Distance in miles, because it's on the vertical axis. Additionally, the independent variable is time in hours, because it's on the horizontal axis. However, you always put time as independent, because nothing affects time.

To find the equation, we just need to find the slope, using two points (0,0) and (2,40).

[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }=\frac{40-0}{2-0}=20[/tex]

Therefore, the equation is [tex]y=20x[/tex], which shows a direct proportion between variables.

Now, in 24 hours, it would travel

[tex]y=20(24)=480[/tex]

It would travel 480 miles.

Therefore, the right answer is the second choice.

What is the volume of a 8 by 4.5 by 3.5 prism

Answers

Always for prisms like a rectangle you multiply all sides so 8 times 4.5 times 3.5 = 126, for a triangular prism  your have to divide by 2 .

Hope this was helpful
126squared becuawse you multiply the length,width,&height

Can someone HELP ME DO THIS??

Answers

the 20% of $43.00 is 8.60 which means 

43.00+8.60 = 51.60

Meal= $43.00
Tip= 20%

Total= Meal + (Meal * 20%)

= $43 + ($43 * 20%)
convert % to decimal (20% ÷ 100 or simply move decimal 2 places left)

= 43 + (43 * 0.20)
multiply inside parentheses

= 43 + 8.60

= $51.60 total


ANSWER: The total, including a 20% tip, is $51.60.

Hope this helps! :)

A research company produced a study to find out what percentage of people in the state of Mississippi would purchase a new product being developed. Out of the 24 participants polled, 12 stated that they would buy the new product. The research company concluded that about 50% of the residents of Mississippi would purchase the new product. Identify a problem with the study.

Answers

The sample size is too small. The company is trying to determine the percent of people in Mississippi that would purchase the product. To make a prediction for the entire state of Mississippi, they should survey more than just 24 people. A random survey should be created and given out across the state.

The conclusion is based on a small sample.

Please help me!!!!!

Question: Kara and Steven are biking around a 1,800 kilometer path. They start biking from the same place, at the same time, and in the same direction. Kara bikes at a speed of 15 km/h and Steven bikes at a speed of 30 km/h. How long will it take before Steven and Kara will be at the same place of the path next time?

Answers

Answer: 120 hours

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

Explanation:

The path is 1800 km. Kara's speed is 15 km/h. If this speed is held the same throughout the path, then it will take her d/r = 1800/15 = 120 hours to travel the entire path until she gets back to her starting point.

For Steven, it takes him d/r = 1800/30 = 60 hours to make the same journey.

The LCM of 60 and 120 is 120

Every 120 hours, both Kara and Steven will be back at the starting point together. 

Note: this is a very very large time value, and this is not considering the fact that the bikers slow down or stop to take a break. 

What is the solution of the system? y = -8x - 2 and y = -6x + 4

A. (-3, 22)
B. (-8/3, 1/22)
C. (-14/3, 6/22)
D. (3/14, - 6/14)

Answers

Plug the x and y coordinates into those equations and whichever one makes sense for BOTH of the equations is a solution
Equation 1:  y = - 8x - 2    

Equation 2: y = - 6x + 4

Equation both equations, we get:

- 8x - 2= - 6x + 4

-8x + 6x = 4 + 2

-2x = 6

x = -3

Using the value of x in first equation, we get:

y= -8(-3) - 2 = 24 - 2 = 22

So, the solution to the given equations is (-3, 22)

So, the answer is option A

What is the area of the shaded region to the nearest tenth of a foot?

Part a) Explain what formulas you will use to find the area of the shaded area.

Par b) Explain how you find the area of the shaded region. What was your thought process?

Answers

a) The shaded region is that portion of the rectangle that is not in the circle. You need the formulas for the area of a rectangle and a circle.
 Area of rectangle = length*width
 Area of circle = (π/4)*diameter²

b) The figure shows the width of the rectangle is 14 ft, the same as the diameter of the circle. The length of the rectangle is shows as 21 ft. The shaded area is the difference ...
 Shaded Area = Area of rectangle - Area of circle
 Shaded Area = (21 ft)*(14 ft) - (π/4)*(14 ft)²
Evaluating this expression, we have
 Shaded Area ≈ 294 ft² - 153.9 ft² = 140.1 ft²

how to draw a model to show 5.5 divided by 5

Answers

Answer:

1.1


Step-by-step explanation:


Please help on these!

Answers

Area of the triangle = 1/2 x base x height
Area  = 1/2 x 14 x 5 = 35 unit²

Answer: 35 unit²

Area of the rectangle = length x width
Area of the triangle = 1/2 x base x height
Area = (13 x 8) + (1/2 x 6 x 8) = 104 + 24 = 128 in²

Answer:  128 in²

1.
[tex]A=\dfrac{14\cdot5}{2}=\dfrac{70}{2}=35[/tex]

2. Look at the picture.

[tex]A_I=8\cdot13=104\ in^2\\\\h=19-13=6\ in\\\\A_{II}=\dfrac{8\cdot6}{2}=\dfrac{48}{2}=24\ in^2\\\\A=104+24=128\ in^2[/tex]

Write an equation for a line g(x) perpendicular to f(x) = 4x − 5 and passing through the point (4, 20). plz.....

Answers

The slopes of perpendicular lines are negative reciprocals.The slope of the given line is 4.The slope of the perpendicular is -1/4.
Now we need to find the equation of a line that has slope -1/4 and passes through the point (4, 20).
We use the point-slope form of the equation of a line, where m = slope, and the point is (x1, y1).
y - y1 = m(x - x1)
y - 20 = -1/4(x - 4)
-4y + 80 = x - 4
x + 4y = 84

Final answer:

The equation for the perpendicular line g(x) is g(x) = (-1/4)x + 21, found by using the negative reciprocal of the original slope and the point-slope form of a line.

Explanation:

To find the equation for a line g(x) that is perpendicular to f(x) = 4x - 5 and passes through the point (4, 20), we need to determine the slope of the perpendicular line and then use the point to find the specific equation.

Since the slope of the line represented by f(x) is 4, the slope of any line perpendicular to it will be the negative reciprocal, which is -1/4.

Now, we can use the point-slope form of a line equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through.

Substituting the given point and the slope into the point-slope form, we get:

y - 20 = (-1/4)(x - 4)

Expanding this we have:

y - 20 = (-1/4)x + 1

Adding 20 to both sides to solve for y gives us the final equation of line g(x):

g(x) = (-1/4)x + 21

What are the answers to problem one and to WILL GIVE BRAINLEST AND SHOW YOUR WORK

Answers

The answer is: $19.56

4 * $4.89= $19.56

8, 15, 14, 9, 1, 6, 3
What number would come next in the sequence above, 4, 7, 10, or 12? Explain your answer.

Answers

The next number in the sequence will be 12.

Explanation

The given sequence is:   8, 15, 14, 9, 1, 6, 3

If we express these numbers in words, then we can see that the words are in alphabetical order, like....

Eight,  Fifteen,  Fourteen,  Nine,  One,  Six,  Three

There are two numbers 10 and 12 in the options which starts with letter 'T' , but  alphabetically 'Twelve' will be the next number after 'Three'

So, the next number in the sequence will be 12.

Please help I’m stuck

Answers

Okay so in the little chart at the bottom of the page, the first 2 are true, and the last one is false.

I hope this helps. If it does, please rate as Brainliest

Gracie uses 10 beads on each necklace she makes. She has 60 beads to use. How many necklaces can Gracie make?

Answers

she can make 6 necklaces.
Gracie can make 6 necklaces.
60 divided 10 = 6
Hope this helps lol

What is the measure of X

Answers

Answer:

we can know the answer by using phorem therom so

Step-by-step explanation:

all are 90 degree so x angle will also be 90 degree

now h^2 =p^2+b^2 so

stuck on question x/-4 -5=4

Answers

x/-4 -5=4
  *-4 *-4 *-4
x+20=-16
x=-36

What is eight and nineteen thousandths in decimal form

Answers

8.019!
Hope this helps!

Decimal form of eight and nineteen thousandths is 8.019.

Eight and nineteen thousandths in decimal form is written as 8.019.

To represent this in decimal form, we can think of the place value chart: 8 (whole number part), 0 (tenth place), 1 (hundredth place), and 9 (thousandth place).

Therefore, 8.019 is the decimal form of eight and nineteen thousandths.

Find M angle P
The diagram is not a scale

Answers

Angle P is equal to 74. Do you need to know the working?

The answer would be angel M would be 74

What is the angle of this triangle

Answers

[tex]A_\Delta=\dfrac{1}{2}\sin65^o\cdot8\cdot12=48\sin65^o\\\\\sin65^o=0.9063\\\\P_\Delta=48\cdot0.9063=43.5024\approx43.5\ cm^2[/tex]
[tex]\text{Given that the formula for Area is } \dfrac{1}{2} \text{ab} \sin(\text{c})[/tex]

[tex]\text{Area = } \dfrac{1}{2} \text{(12)(8)} \sin(\text{65}\textdegree)[/tex]

[tex]\text{Area = }43.5 \text{ cm}^2[/tex]

what is 88.6 times 5.01

Answers

88.6*5.01= about 443.886

Sandra has four color cards: one blue, one red, one green, and one yellow. If she puts them in a box, in how many different orders could she draw them out?
A. 16
B. 24
C. 32
D. 64

Answers

A. 16 i don't know tho..

a traffic light on a busy north-south street is programmed according to this pattern: green for 4 minutes followed by red for 2 minutes. mr gomez goes through this intersection on his way to an from work everyday. last week, he kept a record of the number of times it was green as he approached the intersection and the number of times he had to stop because the light was res. his record is as follows green green red green green green green green green green, what is the therorerical probability that the light will be green each time mr gonez approaches the intersection

Answers

It would be 2/3.

The theoretical probability is the expected amount of times that the light would be green. The light is green for 4 minutes and red for 2 minutes for each series. That means 4 out of the total 6 minutes are green.

4/6 = 2/3

How is the expression (5 + y) ⋅8 described by its factors and terms?

It has two factors and the factor (5 + y) has one term.
It has three factors and the factor (5 + y) has one term.
It has three factors and the factor (5 + y) has two terms.
It has two factors and the factor (5 + y) has two terms.

Answers

It has two factors and the factor (5+y) has two terms.

The factors are the two things that are multiplied together to make the expression.  In this expression, (5+y) and 8 are multiplied, so these are the two factors.

The factor (5+y) has two terms, 5 and y.

Food express is running a special promotion in which customers can win a free gallon of milk with their food purchase if there is a star on the receipt so far 147 of the first 156 customers have not received a star in the receipts what is experimental probability of winning a free gallon of milk

Answers

Formula
P(nw) = no wins / total
no wins = 147
Total = 156 

Calculation for no wins 
P(nw) = 147 / 156 = 0.9423

Calculation for winners.
P(w) = 1 - 0.9423
P(w) = 0.05769

Another way.
You could calculate the winners from the total
156 - 147 = 9

P(w) = 9/156 = 0.05769 Same answer as before. Pick the method you like best.

a rectangular box has a volume of 105 cubic centimeter the width of the rectangular box is X centimeters the length is 2x - 3 cm and the height is 3 cm

Answers

Volume = Length x Width x Height

105 = 3x(2x - 3) 

105 = 6x² - 9x

6x² - 9x - 105 = 0

2x² - 3x - 35 = 0

(x - 5)(2x + 7) = 0

x = 5 0r x = -7/2 (rejected, because it is negative)

Answer: x = 5
Answer is five okgffddbj

Which number has the greatest value?

Answers

There is no true answer to that, thus the answer is infinity.
probably infinity bc numbers are eternal

Which line in the graph contains the point (4,3) and has a slope of 2/5?

A.) Line s
B.) Line t
C.) Line r
D.) Line p

Answers

the correct answer is C) line R because it is the only one that contains the point (4,3) and the slope of 2/5.

Need help on this question

Answers

Your answer to this question is B.
The letter T has at least one right angle

It has two right angles, the other letters do not have at least one right angle

It takes a ship 3 hours to cover 72 km with the current and 4 hours against the current. Find the speed of the ship in still water and the speed of the current.

Answers

x- speed of the ship in still water
a- speed of current
(x+a)- speed with current
(x-a) - speed against current

(x+a)*3=72
(x-a)*4=72

      x+a=24
+    x-a=18
    2x    =42
      x = 21

x+a=24,    21+a=24,    a=3

The speed of the ship in still water = 21 km/h, 
the  speed of the current =3 km/h.

Answer:

ship  = 21 km/h,

current =3 km/h.

Step-by-step explanation:

What is the answer to this question?

Answers

I Think it is 48000. Maybe??
I used a surface area calculator and my answer is 33680 cm^2
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