Answer: The Commutative law. It states a * b = b * a.
So, cba is the same as abc.
Step-by-step explanation:
Commutative law, in mathematics, either of two laws relating to number operations of addition and multiplication that are stated symbolically as a + b = b + a and ab = ba. From these laws it follows that any finite sum or product is unaltered by reordering its terms or factors.
Answer and Explanation:
The number property that allows the re-ordering of multiplication:
[tex]c\cdot b \cdot a[/tex] to [tex]a\cdot b\cdot c[/tex]
is the Commutative Property of Multiplication.
This property states that [tex]A\cdot B = B\cdot A[/tex].
We can test this property by plugging in numbers for A and B.
For example, if [tex]A = 2[/tex] and [tex]B=3[/tex]:
[tex]A\cdot B = 2 \cdot 3[/tex]
[tex]\implies \text{ this is an array of 2 rows and 3 columns:}\\\\\text{ } \ \ \ \ \ \ \begin{array}{c c c} \square \ \ \square\ \ \square \\ \square \ \ \square\ \ \square \end{array} \\ \\ \text{ } \ \ \ \ \ \ \implies 6 \text{ items}[/tex]
__________________________________
[tex]B\cdot A = 3 \cdot 2[/tex]
[tex]\implies \text{ this is an array of 3 rows and 2 columns:}\\\\\text{ } \ \ \ \ \ \ \begin{array}{c c c} \square\ \ \square \\ \square\ \ \square \\ \square \ \ \square \end{array} \\ \\ \text{ } \ \ \ \ \ \ \implies 6 \text{ items}[/tex]
__________________________________
From this example, we can figure out that:
[tex]A \cdot B = B \cdot A = 6[/tex]
Rearrange Fractions
Make x the subject of these equations
y = x/x-7
y = x+2/x-5
y = a-2x/bx+8
y = 5x-12/5x-7
w/8 + 9/x = 2
7 Here is a six-sided shape.
X +9
x + 2
x+6
2x-4
All the measurements are in centimetres. All the corners are right angles.
The perimeter of the shape is 94 cm.
Work out the value of x.
You must show your working.
Answer:
To find the value of x, we need to add up all the sides of the shape and set them equal to the perimeter:
x + 9 + x + 2 + x + 6 + 2x - 4 = 94
Combining like terms, we get:
5x + 13 = 94
Subtracting 13 from both sides, we get:
5x = 81
Dividing both sides by 5, we get:
x = 16.2
Therefore, the value of x is 16.2 cm.
Step-by-step explanation:
Help please I have to answer these questions using the graph.
Using the graph the problem is soled as follows
a. The concentration of the drug in 8 hours is 24 mg/L
b. The concentration of the drug is increasing from 0 to 2 hours and the concentration of the drug is decreasing from 2 to 20 hours
When does the drug have maximum concentrationc. The maximum concentration occurred in 2 hours and the maximum concentration at this time is 64 mg/L
d. The time required for the drug concentration to reduce to 16 mg/L is 8 hours.
at maximum it was at 2 hours while at 16 mg/L it was at 10 hours. by subtraction we have
10 - 2 = 8 hours
e. The graph will predict values close to zero but not equal to zero
f. The concentration of the drug is summarized as follows
The concentration rise to its peak which is 64 mg/L at 2 hours and after this time, the concentration is on a steady decline. at 20 hours it is at about 2 mg/L and continued decreasing
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Is the highlighted answers correct?
In the short run, the firms in a competitive industry will earn positive profits because, the market price is higher than the minimum of the average cost curve. The Option A is correct
Why do firms earn positive profits in the short run?When the market price is between P4 and P6, firms in a competitive industry are able to earn positive profits in the short run because the price is above their average variable cost (AVC) but below their average total cost (ATC).
This means that firms are covering their variable costs and also making a contribution towards their fixed costs. As a result, they are earning positive profits. But, in the long run the firms will enter the industry and increase supply causing market price to decrease towards P4 where firms earn zero economic profits in the long run.
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What is the product of - 3/8 and - 4/12?
Answer:the product of - 3/8 and - 4/12 is 0.125.
NEED HELP ASAP.
The average annual pay of 4 construction workers is $46,200. Three of those workers earned the these annual amounts of pay $42,998, $49,972, and $50,510. What was the annual pay of the fourth worker?
Answer:
$41,320
Step-by-step explanation:
We can use algebra to solve for the annual pay of the fourth worker. Let x be the annual pay of the fourth worker. Then we can set up an equation based on the given information:
(42,998 + 49,972 + 50,510 + x) / 4 = 46,200
We can simplify and solve for x by multiplying both sides by 4:
42,998 + 49,972 + 50,510 + x = 184,800
Subtracting the sum of the other three workers' pay from both sides:
x = 184,800 - 42,998 - 49,972 - 50,510
Simplifying and solving:
x = 41,320
Therefore, the annual pay of the fourth worker was $41,320.
On Friday afternoon, students were surveyed to show who they would be rooting for in the big football game between the two rivaling schools. The data from the survey is shown in the two-way table. Use this information to answer the questions below.
Based on the information given, which of the following statements are true? Select all that apply.
*
1 point
Approximately 59% of the freshmen will be cheering for UCLA.
79% of the sophomores will be cheering for USC.
The proportion of seniors that like UCLA is greater than the proportion of freshmen that like UCLA..
Approximately 55% of the student body will be cheering for UCLA.
83/158 are seniors that will be cheering for UCLA.
The truth of the remaining statements, you would need to examine the proportions of seniors and freshmen who like UCLA, the overall proportion of the student body cheering for UCLA, and the number of seniors cheering for UCLA out of the total number of surveyed students.
To determine which statements are true, you need to refer to the data in the two-way table. The table should provide information on the number or proportion of students from each class (freshmen, sophomores, seniors) who will be cheering for each team (UCLA, USC). Based on this information, you can evaluate the statements.
For example, if the table shows that out of 100 freshmen surveyed, 59% will be cheering for UCLA, then the first statement would be true. Similarly, if the table shows that out of 100 sophomores surveyed, 79% will be cheering for USC, then the second statement would be true.
To determine the truth of the remaining statements, you would need to examine the proportions of seniors and freshmen who like UCLA, the overall proportion of the student body cheering for UCLA, and the number of seniors cheering for UCLA out of the total number of surveyed students.
Once you have the actual data from the two-way table, you can compare it to the statements and identify which ones are true.
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What is the Total Surface area in Units Squared of this shape?
What is the Volume in Unit Cubes?
pls help multiple choice
Answer:
256r^6/t^9
Step-by-step explanation:
start by dividing or simplifying the numbers on the fraction.
4096/16 = 256
Now you multiply the powers on top with the power outside the parenthesis. So (r^-2t^3)^-3
so you now have r^6 t^-9
your equation looks like 256 r^6 t^-9/r^0
But you can't have negative numbers for your powers so we are going to add/subtract with the bottom of the fraction. There are no t's to add/subtract so the t's move to the bottom and become positive. the r has a 0 power so it goes away.
Your equation is now. 256r^6/t^9
Hope that made sense. Good luck!
Andrea conducts a science experiment and observes that the height of a plant depends on the amount of sunlight it receives. The plant’s height is 37 centimeters, and it grows at a rate of 0.004 centimeter per hour of sunlight. If the number of hours of sunlight is represented by the variable s, which function can represent the height of the plant?
The corrected function that represent the height of the plant is h(s) = 0.004s + 37.
How is the Function derived?Using the provided growth rate, the plant's height, h, can be described as a function of the number of hours of sunshine, s:
h(s) = 0.004s + 37
This function indicates that the plant's height increases by 0.004 millimeters every hour of sunlight, starting at a height of 37 cm.
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describe the translation from the blue parabola to the red parabola
Answer:
translation (5, 0)
Step-by-step explanation:
the blue has been translated 5 units to the right (x-axis). no change on y-axis. this translation is (5,0)
* 5 will be above the 0. hard to do with the formatting options on here
1
Find the distance between the parallel lines with the given equations:
x+y=1
x + y = 5
a. 2
b. 2√2
C. 5
d. 5./2
Please select the best answer from the choices provided
AB
3
4
5
6
The distance between the parallel lines with the given equations include the following: B. 4 units.
How to determine the distance between the coordinates for each points?In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represent the data points (coordinates) on a cartesian coordinate.
Note: Each interval on the coordinate plane represent 1 unit.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(5 - 1)² + (0 - 0)²]
Distance = √[(4)² + (0)²]
Distance = √[16 + 0]
Distance = √16
Distance = 4 units.
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Natalie is admiring a statue in Campbell Park from 8 meters away. If the distance between the top of the statue to Natalie's head is 10 meters, how much taller is the statue than Natalie?
Natalie is 2 meters taller than the statue.
To solve this problem
Calculating the distance in height between Natalie's head and the statue's peak is necessary.
According to the information provided, Natalie is located 8 meters from the statue, and Natalie's head is 10 meters from the top of the monument.
With the aid of the comparable triangles idea, we can establish the ratio shown below:
(height of statue) / (distance to statue) = (height difference) / (distance to Natalie's head)
Let's denote the height of the statue as "H" and the height difference as "D." The proportion can be written as:
H / 8 = D / 10
To find the height difference (D), we can rearrange the equation:
D = (H / 8) * 10
Given that the distance between the top of the statue and Natalie's head is 10 meters, we can substitute this value into the equation:
10 = (H / 8) * 10
Dividing both sides by 10:
1 = H / 8
Multiplying both sides by 8:
H = 8
Therefore, the height of the statue is 8 meters.
We deduct Natalie's height (10 meters) from the statue's (8 meters) height to find the height gap between the two:
Height difference = Statue's height - Natalie's height
= 8 - 10
= -2
The negative value indicates that Natalie's height is 2 meters taller than the statue.
Therefore, Natalie is 2 meters taller than the statue.
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Nate is a supply-sider economist. As such, Nate predicts that the deregulation of industries would result in __________.
Nate is a supply-sider economist. As such, Nate predicts that the deregulation of industries would result in increased economic growth, efficiency, and productivity.
What is supply-side economics?Supply-side economics is an economic theory that focuses on policies aimed at stimulating economic growth and productivity by focusing on the supply side of the economy.
It emphasizes the importance of factors such as tax cuts, deregulation, and incentives for businesses and individuals to promote investment, production, and innovation.
Supply-side economists believe that by reducing barriers and costs for businesses, such as lowering taxes and reducing regulations, there will be increased incentives for economic activity, leading to higher output, job creation, and overall economic prosperity.
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Please help!! I will give brainlist
Determine the measure of the unknown angle or arc. Show your work.
The measure of the unknown angle or arc are 142 degrees, 65 degrees and 36 degrees
How to determine the measure of the unknown angle or arcFigure 1
The measure of the angle is calculated as
Angle 1 = 1/2 * 284 degrees
Evaluate the expression
Angle 1 = 142 degrees
Figure 2
The measure of the angle is calculated as
Angle 1 = 1/2 *(72 + 58) degrees
Evaluate the expression
Angle 1 = 65 degrees
Figure 3
The measure of the angle is calculated as
Angle 1 = 1/2 *(138 - 66) degrees
Evaluate the expression
Angle 1 = 36 degrees
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Which one is a rectangular pyramid
Answer:
The third one is rectangular pyramid.
Step-by-step explanation:
The third one is rectangular pyramid because it has a rectangle on the bottom.
Peter had a sum of money. He gave his wife $1400 and spent $400 on a TV set. Then he gave 2/5 of the remaining money to his 3 children. Each child received 1/12 of the money, how much did each child receive?
Peter had no money left to give to his children and each child received $0.
Let's start by finding the amount of money Peter had initially:
Initial money = Money is given to wife + Money spent on TV + Remaining money
Initial money = $1400 + $400 + Remaining money
Initial money = $1800 + Remaining money
Next, we need to find the amount of money Peter had left after giving $1400 to his wife and spending $400 on a TV set:
Remaining money = Initial money - Money is given to wife - Money spent on TV
Remaining money = ($1800 + Remaining money) - $1400 - $400
Remaining money = $1800 + Remaining money - $1800
Remaining money = $0
This means that Peter spent all his money on his wife and the TV set, so he had no money left to give to his children.
Therefore, each child received $0.
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The given figure is a right triangular prism.
In the prism:
• DF = 22 in.
• EG = 11 in.
• Volume of the prism = 1936 cubic in.
What is the length of AD?'
Use the given information to complete the worksheet.
Thank you!
The length of side AD is,
⇒ AD = 16
We have to given that;
The given figure is a right triangular prism.
In the prism:
• DF = 22 in.
• EG = 11 in.
• Volume of the prism = 1936 cubic in.
Since, Volume of right triangular prism is,
V = 1/2 (bh) x L
Substitute all the values we get;
V = 1/2 (22 × 11) × AD
1936 = 121 × AD
AD = 16
Thus, The length of side AD is, 16
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(ANSWERED- EASY POINTS!!) The polynomial is a difference of perfect squares. Use the formula a2 – b2 = (a + b)(a – b) to factor completely.
81x2 – 49
The value of a is ____.
The value of b is ____.
The product of the prime factors is ____.
The polynomial is a difference of perfect squares. Use the formula a2 – b2 = (a + b)(a – b) to factor completely.
81x2 – 49
The value of a is ✔ 9x.
The value of b is ✔ 7.
The product of the prime factors is
✔ (9x – 7)(9x + 7).
Answer:
This equation is a perfect square binomial so you would just square root the front and then square root the back to get (9x+7)(9x-7)
Step-by-step explanation:
The front is 81x^2 and the back is 49 which are both perfect squares.
The given polynomial, 81x^2 - 49, is a difference of perfect squares. To factor it completely, we can use the formula a^2 - b^2 = (a + b)(a - b).
In this case, a^2 = 81x^2 and b^2 = 49. Taking the square root of both sides, we have a = 9x and b = 7.
Therefore, the value of a is 9x and the value of b is 7.
To factor the polynomial completely, we use the formula (a + b)(a - b). Substituting the values of a and b, we have:
(9x + 7)(9x - 7)
The product of the prime factors is (9x - 7)(9x + 7).
I hope this helps!
The SOLVE Process_ The Lamp Post Shadow. The Task: At a certain time of day, the length of the shadow of a 5-foot-tall lamp post was 8 feet. Part A. What is the angle of elevation from the top of the shadow of the lamppost to the top of the lamppost? Provide evidence, including a drawing, to support your answer. Part B What will be the length, to the nearest foot, from the top of the lamppost to the top of its shadow at a time of day when the angle of elevation is half of the current angle of elevation? Provide evidence, including a drawing, to support your answer.
The correct answer is : Part A: The angle of elevation from the top of the shadow to the top of the lamppost is 0 degrees.
Part B: The length from the top of the lamppost to the top of its shadow cannot be determined without knowing the value of [tex]\frac{\theta}{2}[/tex], the current angle of elevation.
Part A: To determine the angle of elevation from the top of the shadow to the top of the lamppost, we can use trigonometry. Let's denote the angle of elevation as θ.
In a right triangle, the tangent of an angle is equal to the ratio of the length of the opposite side to the length of the adjacent side. In this case, the opposite side is the height of the lamppost (5 feet), and the adjacent side is the length of the shadow (8 feet).
Using the tangent function:
[tex]\(\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{5}{8}\)[/tex]
To find θ, we can take the inverse tangent (arctan) of both sides:
[tex]\(\theta = \arctan\left(\frac{5}{8}\right)\)[/tex]
The value of θ can be calculated using a scientific calculator or by referencing trigonometric tables.
|
|\
| \
| \
| \
| \
| \
-----------+------\
Lamp Post \
| \
| Shadow \
|____________\
Part B: To find the length from the top of the lamppost to the top of its shadow when the angle of elevation is half of the current angle (θ/2), we can use trigonometry again.
Let's denote the new length of the shadow as x. We want to find x when the angle of elevation is θ/2.
Using the tangent function again:
[tex]\(\tan\left(\frac{\theta}{2}\right) = \frac{\text{opposite}}{\text{adjacent}} = \frac{5}{x}\)[/tex]
Rearranging the equation to solve for x:
[tex]\(x = \frac{5}{\tan\left(\frac{\theta}{2}\right)}\)[/tex]
Substituting the value of θ from Part A:
[tex]\(x = \frac{5}{\tan\left(\frac{\arctan\left(\frac{5}{8}\right)}{2}\right)}\)[/tex]
Evaluating the expression on the right-hand side will give us the approximate length from the top of the lamppost to the top of its shadow at half the angle of elevation.
Lamp Post
|
|\
| \
| \
| \
| \
| \
|______\
| x \
|________\
| Shadow
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You and another person are sunbathing on the beach near a lifeguard station. The other person chooses a spot that is the same distance from the shoreline but 30 feet closer to the station than you. The angles of elevation from you and the other person to the top of the lifeguard station are 26° and 51°, respectively. Estimate the height of the lifeguard station to the nearest tenth of a foot.
If you pour a cup of coffee that is 200F, and set it on a desk in a room that is 68F, and 10 minutes later it is 145F, what will the temperature be 15 minutes after you originally poured it?
The solution is: 126.8 F will the temperature be 15 minutes after you originally poured it.
Here, we have,
since the coffee cooled (200 - 145) = 55 degrees
in 10 minutes, it would cool another (55/2) = 27.5 degrees in the next
5 minutes, and arrive at 117.5F . Not only would you be wrong, but
your coffee would not do that. It would be warmer than 117.5F .
This is a classic example of a process whose speed depends on
how far it still has to go. Just like a little kid walking to school,
the closer it gets to its final destination, the slower it goes.
As the temperature of the coffee gets closer and closer to 68F,
it cools slower and slower.
The equation that describes the temperature of your coffee is
Temp = 68 + ( 132 e^-minutes/18.55) .
After 10 minutes, Temp = 68 + (132 e^-0.539)
=68 + (132 x 0.583)
= 68 + (76.99)
= 145F .
After 15 minutes, Temp = 68 + (132 e^-0.809)
= 68 + (132 x 0.445)
= 68 + ( 58.8 )
= 126.8 F .
Hence, The solution is: 126.8 F will the temperature be 15 minutes after you originally poured it.
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Need Help You Can Get 35 point!!!
The width of a rectangular field is represented by x meters. The length of the field is 10 more than twice its width . The area of the field is 5500m^2
Part A
Write an equation that can be used to determine the dimensions, in meters, of the field.
Part B
What is the width, in meters, of the field?
The width is ( ) meters.
Part A: The equation that can be used to determine the dimensions, in meters, of the field is 5500 = 2x² + 10x
Part B: width is 50 meters.
How to determine the valueThe formula for calculating the area of a rectangle is expressed with the equation;
A = lw
Such that the variables are expressed as;
A is the areal is the lengthw is the widthWe then have that;
l = 2x + 10
Substitute the values
5500 = (2x + 10)(x)
expand the bracket
5500 = 2x² + 10x
2x² + 10x - 5500
x² + 5x - 2750
x² + 55x - 50x - 2750
x(x + 55) - 50(x + 55)
x = 50 meters
Length = 2(50) + 10
Length = 100 + 10 = 110 meters
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What is the value of x in this figure?
Enter your answer in the box.
X =
Answer:
48
Step-by-step explanation:
When looking at this you know that all the angle are a full 360. Knowing this you see that both side are the same. So that means they both are 48.
Which congruence statements can be used to show that by the SAS congruence theorem?
Answer:
Choice B
Step-by-step explanation:
You spin the spinner once. 5,3,4 What is P(even)? Write your answer as a fraction or whole number.
Question 12(Multiple Choice Worth 1 points)
(06.02 MC)
The three sides of a triangular fence have lengths 3x + 4, y-5, and 7x - 1. What is the total perimeter?
10x + y - 2
10x + y + 8
10x + y
3x+y-2
Answer:
A. 10x + y - 2 Ans
B. Solution
(3x + 4) + (y - 5) + ( 7x - 1) =0
grouping
(3x + 7x) + (y) + (4 - 5 - 1) =0
10x + y -2 =0
therefore
perimeter is 10x + y - 2
Demand for a tie-dyed shirt is given by the formula
p = 5 + 100 / √q
where p is the price in dollars you can charge to sell q shirts per month. If you currently sell shirts for $10 each and you raise the price by $1 each month, how fast will the demand drop?
The demand will drop by 741 T-shirts per dollar increase in price.
How fast will the demand drop?We will use derivative of p formula with respect to q to find how fast the demand will drop [tex]dp/dq = -50/\sqrt{q^3}[/tex]
At the initial price of $10, the corresponding demand is:
p = 5 + 100/√q = 10
Solving for q, we get:
q = 10000/9
Now, we will find rate of change of demand as the price increases by differentiating the demand formula with respect to p:
[tex]\frac{dq}{dp} = -1/\frac{dp}{dq}[/tex]
At p = 10, we have:
dq/dp = -1/(-50/√(10000/9)^3)
dq/dp = -1/(-0.00135)
dq/dp = 740.740740741
dq/dp = 741.
Full question:
Demand for your tie-dyed T-shirts is given by the formula p = 5+ 100/ √ q where p is the price in dollars you can charge to sell q T-shirts per month. If you currently sell T-shirts for $10 each and you raise price by $1 each month, how fast will the demand drop?
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How many flowers spaced every three inches are needed to surround a circular garden with a 200ft radius. Use 3.14 for pi
Answer:
5024 flowers spaced every three inches are needed to surround the circular garden with a 200 ft radius.
Step-by-step explanation:
The formula for the circumference (C) of a circle is:
C = 2 * π * r
Given a radius of 200 ft
C = 2 * 3.14 * 200
C = 6.28 * 200
C = 1256 ft
with each flower spaced every 3 inches apart. Convert the spacing to feet (1 ft = 12 inches)
Divide the circumference by the spacing between the flowers:
Number of flowers = C / spacing
Number of flowers = 1256 / (1/4)
Number of flowers = 1256 * 4
Number of flowers = 5024
Find the real zeros of the polynomial function
f
(
x
)
=
x
8
+
6
x
7
+
7
x
6
.
Answer:
Step-by-step explanation:
f(x) = x^8 + 6x^7 + 7x^6
= x^6 ( x^2 + 6x + 7)
= x^6 (x = [tex]\frac{-6 +- \sqrt{36 - 28} }{2}[/tex] )
= x^6 (x = -3 +- [tex]\sqrt{2}[/tex] ) = 0
= x = 0 or x = -3 +- [tex]\sqrt{2}[/tex]
