Answer:
log Subscript 2 Baseline 9 x cubed is equivalent to 2 log subscript 2 Baseline 3 + 3 log subscript 2 Baseline x
Step-by-step explanation:
Given:
log Subscript 2 Baseline 9 x cubed?
Required:
Find the equivalent of the above expression.
First, we need to represent it mathematically;
log Subscript 2 Baseline 9 x cubed = [tex]log_{2} 9x^{3}[/tex]
From Laws of logarithm
[tex]log_{x} AB = log_{x} (A* B)\\log_{x} AB = log_{x}A + log_{x}B[/tex]
Note how the expression is split into two
We'll apply the same logic above, here
First, is to simplify the mathematical expression;
[tex]log_{2} 9x^{3} = log_{2} (9 * x^{3})[/tex]
Then we split into two
[tex]log_{2} 9x^{3} = log_{2}(9) + log_{2}(x^{3})[/tex]
[tex]log_{2} 9x^{3} = log_{2}(3^2) + log_{2}(x^{3})[/tex]
Also from laws of logarithm,
[tex]log_{m}A^{n} = nlog_{m}A[/tex]
We'll apply this law on [tex]log_{2}(x^{3})[/tex] and [tex]log_{2}(3^{2})[/tex]
[tex]log_{2}x^{3} = 3log_{2}x[/tex]
[tex]log_{2}(3^2) = 2log_{2}3[/tex]
So, [tex]log_{2} 9x^{3} = log_{2}(9) + log_{2}(x^{3})[/tex] becomes
[tex]log_{2} 9x^{3} = 2log_{2}3 + 3log_{2}x[/tex]
log Subscript 2 Baseline 9 x cubed is equivalent to [tex]2log_{2}3 + 3log_{2}x[/tex]
[tex]2log_{2}3[/tex] can be represented as 2 log subscript 2 Baseline 3
and
[tex]3log_{2}x[/tex] can be represented as 3 log subscript 2 Baseline x
Hence, log Subscript 2 Baseline 9 x cubed is equivalent to 2 log subscript 2 Baseline 3 + 3 log subscript 2 Baseline x
Answer:
a) log2 9x^3
Step-by-step explanation:
got it right on edg
What to multiply 2/3 by
To show that 4 points are vertices of a square which of the following must be shown
The number of inches of rain,y,after x minutes of rainfall during a storm can be modeled by the equation y=0.003x How many inches of rain will have fallen after 2 minutes
Answer:
Therefore 0.006 inches of rain will have fallen after 2 minutes.
Step-by-step explanation:
Given that,
y = 0.003x
where y is the number of inches of rain after x minutes.
To find the number of inches of rain after 2 minutes, we plug x = 2 minutes in above model equation.
∴ y= 0.003×2
=0.006
Therefore 0.006 inches of rain will have fallen after 2 minutes.
After 2 minutes, 0.006 inches of rain will have fallen based on the equation y = 0.003x. This calculation involves substituting x with 2 and multiplying by 0.003.
To determine how many inches of rain will fall after 2 minutes using the given equation y=0.003x, we substitute x with 2.
Start with the equation: y = 0.003xSubstitute x with 2: y = 0.003 × 2Calculate the value: y = 0.006So, the number of inches of rain that will have fallen after 2 minutes is 0.006 inches.
In the diagram, line p is parallel to side BC.
Triangle A B C. Angle A is 2, angle B is 57 degrees, and angle C is 49 degrees. A line p is parallel to side B C at point A to form 3 angles. Angle 2 is angle A, and angle 1 is the exterior angle.
What is the sum of the measures of ∠1 and ∠2?
What is the sum of the measures of Angle1 and Angle2?
mAngle1 + mAngle2 = °
Answer:
the answer is 131
Step-by-step explanation:
131 is the answer
(i took the test btw)
a solution needs to be cooled at a rate of -7°C per minute. How long will it take for the solutions temperature to change from 0° C to -42° C?
Answer:
6 minutes.
Step-by-step explanation:
There is a difference of 42 between 0° and -42° (given), and 42°/7° per minute= 6 minutes.
Circletown's limits form a perfectly circular shape. It has a population of
20,000and a population density of 480 people per square kilometer. What is the radius of circle town
Answer:
3.64 Km.
Step-by-step explanation:
Given,
Total population = 20,000 people
Population density = 480 people per square kilometer
Area of the circle town
[tex]A = \dfrac{20000}{480}[/tex]
[tex]A = 41.667\ km^2[/tex]
Radius of the circle town
[tex]\pi r^2 = 41.667[/tex]
[tex]r = 3.64\ km[/tex]
Hence, the radius of circle town is equal to 3.64 Km.
Answer:
3.64
Step-by-step explanation:
A solution has which of the following properties?
a) The average diameter of its solute particles usually is less than 1 nm.
b) Gravity separates its parts.
c) A filter can remove the solute.
d) The top layer is different in composition than the bottom layer.
Answer:
A
Step-by-step explanation:
The rest are incorrect
A solution is a homogeneous mixture composed of a solute dissolved in a solvent. It can be separated by passing it through a filter.
Explanation:A solution is a homogeneous mixture composed of a solute dissolved in a solvent. From the given options, property (c) is most characteristic of a solution. A solution can be separated by passing it through a filter, which removes the solute particles, resulting in a purified solvent. Gravity does not separate the parts of a solution, and the average diameter of solute particles can vary depending on the nature of the solute. Additionally, the composition of a solution is uniform throughout, so there is no distinction between the top and bottom layers.
Learn more about solution composition here:https://brainly.com/question/31373221
#SPJ6
help pls. will mark brainliest
Which dot plot shows a sample that is most representative of the number of pets in a household?
A dot plot going from 0 to 6. There are 3 dots above 0, 5 dots above 1, 4 dots above 2, 3 dots above 3, 2 dots above 4, 0 dots above 5, and 1 dot above 6.
A dot plot going from 0 to 6. There are 2 dots above 1, 3 dots above 2, and 1 dot above 5.
A dot plot going from 0 to 6. There is 1 dot above 0, 2 dots above 1, 1 dot above 2, 1 dot above 3, 1 dot above 4, 1 dot above 5, 2 dots above 6.
A dot plot going from 0 to 6. There is 1 dot above 1, 2 dots above 2, 3 dots above 3, 2 dots above 4, 1 dot above 5.
Answer:a
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
PLEASE HELP TRIG 20 points!! I am standing on a 50 foot cliff in Laguna Beach California looking at my two dogs sitting on the beach below. If my line of sight is 6 feet above the ground in the angles of depression or 51 and 37 how far apart are the dogs
Answer:
28.97 feet
Step-by-step explanation:
Please refer to the attached image for explanations
Emily says she can prove the Pythagorean Theorem using the following diagram. She explains that she can divide the squares on the two shorter sides into grids with equal-sized grid squares. She says she can then rearrange the grid squares to cover the area of the square on the hypotenuse, which proves that the sum of the squares on the two shorter sides equals the square on the hypotenuse.
A 3 by 3 square, a 4 by 4 square, and a 5 by 5 square, put together to form a right triangle with legs 3 and 4 and hypotenuse 5.
Is this a valid geometrical proof that a2 + b2 = c2 for all right triangles
Answer:
Step-by-step explanation:
This is correct for all right angle because Pythagoras theorem has proved that for a right-angle triangle, the square of the hypotenuse length is equal to the sum of the square of the opposite side and square of the adjacent sides
c² = a² + b²
This is true because the squares formed a right angle triangle from their arrangements.
So, let proved with the formula
Let assume one square = 1 unit
A 3 by 3 Square
Length = 3
A 4 by 4 Square
L = 4
A 5 by 5 Square. Hypotenuse
L = 5
a² + b² = c²
3² + 4² = 5²
9 + 16 = 25
25 = 25
Proved, so for all right angle triangles, it is valid
Answer:
A.100 B.10
Step-by-step explanation: Just look at the picture lol
Lindsey surveyed a random sample of students in 7th grade at her school to determine how students get to school each day. The results of the survey are shown below. 8 students walk or ride a bike 15 students ride in a car 25 students take the bus Based on the results of the survey, how many of the 720 students in 7th grade do NOT ride in a car to school?
495 students in 7th grade do not ride a car to school
Step-by-step explanation:
Step 1: Find the percentage of number of students in 7th grade who ride in a car to school in the sample.Number of students walking or riding a bike = 8
Number of students who ride a car = 15
Number of students who take the bus = 25
Total students in the sample = 48
⇒ Percentage of students who rides a car in the sample = 15/48 × 100 = 31.25%
Step 2: Find the equivalent number of students who ride a car in the total number of students.Total number of students = 720
Number of students who ride a car = 31.25/100 × 720
= 225
Step 3: Find the number of students who do not ride a car to school.Number of students who do not ride a car to school = 720 - 225 = 495
Answer:
b
Step-by-step explanation:
If log2 5 = k, determine an expression for log32 5 in terms of k.
Answer:
[tex]log_3_2(5)=\frac{1}{5} k[/tex]
Step-by-step explanation:
Let's start by using change of base property:
[tex]log_b(x)=\frac{log_a(x)}{log_a(b)}[/tex]
So, for [tex]log_2(5)[/tex]
[tex]log_2(5)=k=\frac{log(5)}{log(2)}\hspace{10}(1)[/tex]
Now, using change of base for [tex]log_3_2(5)[/tex]
[tex]log_3_2(5)=\frac{log(5)}{log(32)}[/tex]
You can express [tex]32[/tex] as:
[tex]2^5[/tex]
Using reduction of power property:
[tex]log_z(x^y)=ylog_z(x)[/tex]
[tex]log(32)=log(2^5)=5log(2)[/tex]
Therefore:
[tex]log_3_2(5)=\frac{log(5)}{5*log(2)}=\frac{1}{5} \frac{log(5)}{log(2)}\hspace{10}(2)[/tex]
As you can see the only difference between (1) and (2) is the coefficient [tex]\frac{1}{5}[/tex] :
So:
[tex]\frac{log(5)}{log(2)} =k\\[/tex]
[tex]log_3_2(5)=\frac{1}{5} \frac{log(5)}{log(2)} =\frac{1}{5} k[/tex]
If f(x) and it's inverse function, f-1(x), are both plotted on the same coordinate plane, what is there correct point of intersection? (0,-2) (1,-1) (2,0) (3,3)
Answer:
The plot coordinates are (3,3).
Step-by-step explanation:
Given:
A fucntion f(x) and its inverse is f-1(x)
To find :
The plot of the coordinates for the intersection.
Solution:
Now we know that inverse fucntion is changing the y=f(x) and then
changing to x to y and y to x
So given function is f(x)
Inverse function is y,
But value of inverse function is f-1(x)
So y=f(x)=f-1(x)
Therefore it becomes
y=x
Hence the value is y=x coordinates
i.e. (3,3)
Sean is making accessories for the soccer team she uses 671.16 in at work on headbands for 39 players and three coaches she also uses 336.57 in the fabric on wristbands just for the players how much fabric is used on the headband and wristband for each player
Answer:
Headband: 15.98 in.
Wristband: 8.63 in.
Step-by-step explanation:
In this problem, we call:
h = the amount of fabric used for each headband
w = the amount of fabric used for each wristband
We are told that:
Sean uses 671.16 in at on headbands for 39 players and three coaches, so the total number of headbands made is 42
Therefore, we can write
[tex]671.16 = 42 h[/tex]
And solving for h, we find
[tex]h=\frac{671.16}{42}=15.98 in.[/tex]
Then we also know that Sean uses 336.57 in the fabric on wristbands just for the players, so he produced 39 wristbands; so we can write:
[tex]336.57 = 39w[/tex]
And solving for w,
[tex]w=\frac{336.57}{39}=8.63 in.[/tex]
What is 20% of 45?
A.
7
B.
12
C.
9
D.
13
Answer:
C. 9
Step-by-step explanation:
Mulitply .20 by 45
Answer:
C. 9
Step-by-step explanation:
20%- 0.2
multiply 0.2 and 45
Your answer is 9
What shape is the base of a
Cylinder?
Answer:
a circle
Step-by-step explanation:
hope this helps
Answer:
A Circle!
Step-by-step explanation:
Lucy is a dress maker. She sees 4/7 of a dress in 3/4 hour. How many dresses will Lucy sew in 1 hour
Answer:
for this we'll have to get 4/3
Multiply 3 from 4 which will give us 4/7 x 4/3. That should give us 1 hour: 16/ 21 dresses
hope this helps lmk :)
PLEASE HELP URGENT!!!!!!!!!
Use the net to compute the surface area of the three-dimensional figure.
A) 56 units2
B) 62 units2
C) 68 units2
D) 74 units2
62 units is the answers
Step-by-step explanation:
The correct answer is C) 68 units². The net to compute the surface area of the three-dimensional figure is C) 68 units².
To compute the surface area of a three-dimensional figure, one must consider all the faces that make up the shape. The net of a three-dimensional figure provides a two-dimensional representation of all these faces. By calculating the area of each face and summing them up, we can find the total surface area.
Let's assume the net provided shows a figure composed of rectangles and triangles. We will calculate the area of each face as follows:
1. For rectangles, the area is given by the formula A = length × width.
2. For triangles, the area is given by the formula A = 1/2 × base × height.
Let's denote the lengths of the sides of the rectangles as l and w, and the base and height of the triangles as b and h, respectively.
Now, let's calculate the area of each face:
- Rectangle 1: A1 = l × w
- Rectangle 2: A2 = l × w (assuming it has the same dimensions as Rectangle 1)
- Triangle 1: A3 = 1/2 × b × h
- Triangle 2: A4 = 1/2 × b × h (assuming it has the same dimensions as Triangle 1)
The total surface area (SA) is the sum of the areas of all faces:
SA = A1 + A2 + A3 + A4
SA = (l × w) + (l × w) + (1/2 × b × h) + (1/2× b × h)
SA = 2lw + bh
SA= 2*5*3+19*2
SA=68
After performing these calculations with the given measurements from the net, we would find that the total surface area is 68 units².
Therefore, the correct answer is C) 68 units²."
A school picnic your teacher asks you to Market food trip every 10 yards Sullivan students can play football with the teacher accidentally gave you a meter stick instead of yardstick how far apart a meter should you mark the line if you want the one that has to be in the right places
1 yard = 0.9144 meters
1 yard * 10 = 0.9144 meters * 10
10 yards = 9.144 meters
9.144 meters
Deshaun took 2 5/8 hours to clean the bathroom. Then took 1/4 hours to clean the den . How much total time did deshaun take to clean the two rooms ?
Answer:
2.875 hours 2 5/8 plus 1/4 equals 2.875
1. Elena bought 320 tropical fish for a museum display. She bought 7 times as many triggerfish as parrotfish. How many of each type of fish did she buy?
Which is a system of equations to model the problem if x represents the number of parrotfish Elena bought and y represents the number of triggerfish she bought?
A. x + 7y = 320
y = 7x
B. x + y = 7
y = 320x
C. x + y = 320
y = 7x
D. x−y=320
y = 7x
2. Nancy bought 360 tropical fish for a museum display. She bought 8 times as many goldfish as angelfish.
How many of each type of fish did she buy?
A. 40 angelfish, 320 goldfish
B. 160 angelfish, 200 goldfish
C. 20 angelfish, 160 goldfish
D. 320 angelfish, 40 goldfish
3. Michael and Kathryn bowl together and their combined total score for one game was 425 points. Michael’s score was 70 less than twice Kathryn’s. What were their scores?
Which is a system of equations to model the problem if x represents Kathryn’s score and y represents Michael’s score?
A. x + y = 70
y = 2x – 425
B. x + y = 425
y = 2x – 70
C. x – y = 425
y = 2x – 70
D. x + y = 425
y = 2x + 70
4. Michael and Kathryn bowl together and their combined total score for one game was 425 points. Michael’s score was 70 less than twice Kathryn’s.
What were their scores?
A. Kathryn: 260, Michael: 165
B. Kathryn: 150, Michael: 275
C. Kathryn: 275, Michael: 150
D. Kathryn: 165, Michael: 260
5. A collection of nickels and dimes is worth $6.10. There are 67 coins in all.
How many nickels are there?
A. 12
B. 18
C. 49
D. 55
Answer:
D
Step-by-step explanation:
If im wrong, please correct me in the comments.
Answer:
5. D, Let d represent the number of dimes and n represent the number of nickel. We have been given that a collection of coins has 67 coins in all. This means that total number of nickels and dimes is 67. We can represent this information in an equation as:
Since we know that a dime is worth $0.10, so d dimes will be worth 0.10d.
A nickel is worth $0.05, so n nickels will be worth 0.05n. We are also told that the collection is worth $6.10. We can represent this information in an equation as:
We will use substitution method to solve system of linear equations. From equation (1) we will get, upon substituting in equation (2) we will get, Let us divide both sides of our equation by .
What is the value of r?
4r + 19
What is the length of segment EF?
units
9r-6
18r+ 3
Answer:
Since opposite sides of parallelogram are equal therefore
9r-6=8r+3
r=9
EF=4r+19{opposite sides of parallelogram are equal}
=4×9+19
36+19
=55
Here is you answer.
Step-by-step explanation:
The value of r is 9 units and length of segment EF is 55 units.
What is Parallelogram?a parallelogram is a simple quadrilateral with two pairs of parallel sides.
The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
We know that opposite sides are equal
CF=DE
9r-6=8r+3
r=9
Now let us find the length of segment EF
EF=4r+19
=4(9)+19
=36+19
=55 units
Hence, the value of r is 9 units and length of segment EF is 55 units.
To learn more on Parallelogram click:
https://brainly.com/question/29147156
#SPJ5
After falling 23°F the temperature is now 51°F what was the starting temperature
Answer:74 degrees
Step-by-step explanation:
You would have to add the starting point to the current temperature.(51+23=74)
Find the volume of a right circular cone that has a height of 19.9 cm and a base with a radius of 9.6 cm. Round your answer to the nearest tenth of a cubic centimeter.
Answer:
1920.5
Step-by-step explanation:
Final answer:
To find the volume of a cone with specific dimensions, use the formula V = 1/3 π r² h. Substitute the given values for radius and height, then calculate the volume rounded to the nearest tenth.
Explanation:
The volume of a right circular cone can be found using the formula V = 1/3 × π × r² × h, where r is the radius and h is the height of the cone.
Plugging in the values (r = 9.6 cm, h = 19.9 cm) gives V = 1/3 × 3.142 × 9.62 × 19.9 = 200.5 cm³
A newspaper conducted a statewide survey concerning the 1998 race for state senator. The newspaper took a SRS of =1000 registered voters and found that 520 would vote for the Republican candidate. Let represent the proportion of registered voters in the state who would vote for the Republican candidate.
Answer:
52% will vote for republican candidate
Step-by-step explanation:
If there are 1000 registered voters and 520 of them will vote for Republican candidate
Then the proportion of this voters that will vote for republican candidate can be give as
(520/1000)*100% = 52%
Consider a circle whose equation is x2 + y2 + 4x - 6y - 36 = 0. Which statements are true? Check all that apply.
To begin converting the equation to standard form, subtract 36 from both sides.
To complete the square for the x terms, add 4 to both sides.
The center of the circle is at (-2, 3).
The center of the circle is at (4.-6).
The radius of the circle is 6 units.
The radius of the circle is 49 units.
The answer is B and C
Answer: b & c
I got the answer right on my quiz
The following statements are true:
- To begin converting the equation to standard form, subtract 36 from both sides.
- To complete the square for the x terms, add 4 to both sides.
- The center of the circle is at (-2, 3).
- The radius of the circle is 7 units.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2pir.
The area of a circle is πr².
We have,
To convert the equation to standard form, we need to complete the square for both the x and y terms.
x² + y² + 4x - 6y - 36 = 0
x² + 4x + y² - 6y = 36
(x² + 4x + 4) + (y² - 6y + 9) = 49
(x + 2)² + (y - 3)² = 7²
So the center of the circle is at (-2, 3) and the radius of the circle is 7 units.
Therefore, the following statements are true:
- To begin converting the equation to standard form, subtract 36 from both sides.
- To complete the square for the x terms, add 4 to both sides.
- The center of the circle is at (-2, 3).
- The radius of the circle is 7 units.
And,
The statement "The center of the circle is at (4.-6)" is false, and the statement "The radius of the circle is 49 units" is also false.
Thus,
The following statements are true:
- To begin converting the equation to standard form, subtract 36 from both sides.
- To complete the square for the x terms, add 4 to both sides.
- The center of the circle is at (-2, 3).
- The radius of the circle is 7 units.
Learn more about Circle here:
https://brainly.com/question/11833983
#SPJ5
Wich is equivalent to √10 3/4x
Answer:
8 (square root) 10^3x
Step-by-step explanation:
mark me as brainliest pls
§ALEX§
How do you solve problems like this. Rhonda earned $324.65 delivering newspapers. She promised her sister 0.2 of her earnings for helping her. How much does Rhonda owe her sister?
Answer:
64.93
Step-by-step explanation:
324.65(0.2) = 64.93
You simply want to find 20% of 324.65. To do this, you just need to multiply.
what is 9*10^2 times as much as 3*10^-2
Answer:
I believe it is three
Step-by-step explanation:
An angle measures 32° more than the measure of its complementary angle. What is the measure of each angle?
The two angles are 29 degrees and 61 degrees. The steps involve setting up and solving a simple equation based on the definition of complementary angles.
Explanation:To solve this question we first need to know that complementary angles add up to 90 degrees. Let's assume the measure of one angle is X. Since the other angle is 32 degrees more than the first, we represent it as X + 32.
Following the principle of complementary angles, we can set up an equation: X + (X + 32) = 90, simplifying gives 2X + 32 = 90.
Subtracting 32 from both sides we get: 2X = 58. Finally, if we divide each side by 2 we get X = 29 degrees. Therefore, one angle measures 29 degrees and the other, which is 32 degrees more, measures 61 degrees.
Learn more about Complementary Angles here:https://brainly.com/question/15592900
#SPJ12