The perimeter of the box has been obtained as 6a^3b^2 + 6ab^5.
What is the perimeter of the box?We know that a box has the shape of a rectangle thus we would have to apply the formula for the area of a rectangle in this case and we would have;
P = 2(l + b)
P = perimeter
l =length
b = breadth
Then we have;
2[(-9a^3b^2 + 13ab^5) + (-10ab^5 + 12a^3b^2)]
Collect the like terms
2[(-9a^3b^2) + 12a^3b^2 + 13ab^5 +(-10ab^5)]
2[3a^3b^2 + 3 ab^5]
6a^3b^2 + 6ab^5
In order of descending exponents of a, the perimeter is 6a^3b^2 + 6ab^5.
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You are a school photographer taking individual and class pictures for two classes of 21 students each on average each individual picture takes three minutes in a class picture takes 10 minutes how long should it take for you to take all the pictures
Given 1 || m
11
n, find the value of x.
m
(8x-20)
(3x+2)
→n
Answer:
x=18
Step-by-step explanation:
They are on a straight line which means they add to 180 and a more precise term, they form a supplementary angle
so knowing that we apply the principal
(8x-20) + (3x+2)=180
8x-20+3x+2=180
8x+3x=180+20-2
11x/11=198/11
x=18
Therefore x=18
Please help me!
If you wanted to find the difference of 6/25 - 4/5, what common denominator should you choose? Why?
Answer:
Choose 1/25 as the common denominator
Step-by-step explanation:
1/25 is the lowest number that both existing denominators can be factored into.
6/25 would remain the same.... 6/25
4/5 would become 20/25..... multiply the top and bottom by 5
So 6/25 - 20/25 = - 14/25
Which set of words describes the end behavior of the function f(x)=−5x(x−4)(x+5)(2x+3)?
Answer:
Falls to the left and rises to the right
Step-by-step explanation:
because
degree =5
leading coefficient =4 and positive it will rise to the right
those are tips to use to determine it :
1. Even and Positive: Rises to the left and rises to the right.
2. Even and Negative: Falls to the left and falls to the right.
3. Odd and Positive: Falls to the left and rises to the right.
4. Odd and Negative: Rises to the left and falls to the right
Answer quick please
Answer:
18
Step-by-step explanation:
3 3/8 becomes 27/8.
27/8 x 16/3=18
You have to flip 3/16 since you are dividing.
Answer:18
Step-by-step explanation:
3 3/8 devided by 3/16=18
Help I can give brainliest
Answer: -4
Step-by-step explanation: The points are (2,4) and (4,-4) using the slope formula, (y2-y1)/(x2-x1) youd get -4 as your slope. Hope this helps!!
Which of the following is a solution to the inequality y < –2x + 3?
Answer:
y < -2x +3
A. (1, 1) → x = 1, y = 1
substitute:
1 < -2(1) + 3
1 < 1 FALSE
B. (3, 0) → x = 3, y = 0
substitute
0 < -2(3) +3
0 < -3 FALSE
C. (-3, 10) → x = -3, y = 10
substitute
10 < -2(-3) +3
10 < 9 FALSE
D. (0, 0) → x = 0, y = 0
substitute
0 < -2(0) + 3
0 < 3 CORRECT
Answer: D. (0, 0)
Step-by-step explanation:
True or false every whole number is a multiple of 1?
PLEASE HELP!!!
Nevaeh and Christian are both driving along the same highway in two different cars to a stadium in a distant city. At noon, Nevaeh is 650 miles away from the stadium and Christian is 450 miles away from the stadium. Nevaeh is driving along the highway at a speed of 50 miles per hour and Christian is driving at speed of 25 miles per hour. Let NN represent Nevaeh's distance, in miles, away from the stadium tt hours after noon. Let CC represent Christian's distance, in miles, away from the stadium tt hours after noon. Graph each function and determine the number hours after noon, t,t, when Nevaeh and Christian are the same distance from the stadium.
The linear functions that define their distances are given as follows:
Nevaeh: 650 - 50t.Christian: 450 - 25t.The number of hours after noon in which they will be the same distance away from the stadium is of:
8 hours.
What are the linear functions?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which the parameters are given as follows:
m is the slope.b is the y-intercept.In the context of this problem, the meaning of each parameter is:
The slope is by how much they get closer each hour, which is the velocity as a negative.The intercept is the initial distance.They will be the same distance away at the point of intersection of the graph given at the end of the answer, which is of 8 hours.
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Which problem can be solved by performing this multiplication?
3/4×8/9
Responses
Evan practiced piano this week for 3/4 hour. Last week he practice for8/9 hour. How much longer did Evan practice last week than this week?
Jada rode her bike 3/4 mile. Sarah rode her bike 8/9 the distance that Jada rode her bike. How far did Sarah ride her bike?
Amelie drove 3/4 mile. She then drove another 8/9 mile. How many miles did she drive in all?
Three out of 4 containers hold lemonade. Each container holds 8/9 quart of lemonade. How much lemonade do the containers all hold?
The multiplication 3/4×8/9 can be used to address the problem in response (B). which is the correct answer that would be an option (B).
What is the Multiplication operation?In mathematics, Multiplication operations perform Multiplying values on either side of the operator.
For example 4×2 = 8
As per option (B),
Jada rode her bike for 3/4 mile. Sarah rode her bike 8/9 the distance that Jada rode her bike.
Sarah rides her bike = Sarah rode (8/9) of the (3/4) that Jada rode.
Sarah rides her bike = 3/4 × 8/9
Therefore, this problem can be solved by performing the above multiplication.
Hence, the correct answer would be an option (B).
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at 8 the temp in the city was -8. at noon the same day the temp was 2. what was the difference in temp between 8 and noon
-8 to 0 = 8
0 to 2 = 2
total change = 8 + 2 = 10 degrees
PLEASE HELP AS SOON AS POSSIBLE
Answer:
B
Step-by-step explanation:
Yes, because for each input there is exactly one output. You can have two of the same x values but you cannot have 2 of the same y values. if you have two of the same y values, it is not a function as it doesn't pass the vertical line test.
PLEASE HELP FAST
I am in need of your assistance!
Answer:
30 degrees
Step-by-step explanation:
Answer:
30°
Step-by-step explanation:
The protractor in the picture is positioned correctly - YAY!!
Since we want the measure of ∠BCA, we'll look at the angle from side CB (this is the 0° side) up to side CA. Side CA goes through the numbers 30 and 150, but 150 is based on going backward from 180°, not forward from 0°.
Calculate the interest earned on each simple interest account given the original PRINCIPAL annual interest rate in length of time the account was held match each amount to corresponding account description
$880 at 5.25% for 2 years
$675 at 3.5% for 4 years
$770 at 4.1% for 3 years
We can match the amounts to their corresponding account descriptions as follows:
$92.40 to the account of $880 at 5.25% for 2 years
$94.50 to the account of $675 at 3.5% for 4 years
$94.23 to the account of $770 at 4.1% for 3 years
To calculate the interest earned on a simple interest account, we can use the following formula:
Interest = Principal x Rate x Time
where "Principal" is the initial amount of money invested, "Rate" is the annual interest rate as a decimal, and "Time" is the length of time in years that the money is invested.
Using this formula, we can calculate the interest earned on each of the accounts:
$880 at 5.25% for 2 years:
Interest = 880 x 0.0525 x 2 = $92.40
$675 at 3.5% for 4 years:
Interest = 675 x 0.035 x 4 = $94.50
$770 at 4.1% for 3 years:
Interest = 770 x 0.041 x 3 = $94.23
So the interest earned on each account is as follows:
$880 at 5.25% for 2 years: $92.40
$675 at 3.5% for 4 years: $94.50
$770 at 4.1% for 3 years: $94.23
Therefore, we can match the amounts to their corresponding account descriptions as follows:
$92.40 to the account of $880 at 5.25% for 2 years
$94.50 to the account of $675 at 3.5% for 4 years
$94.23 to the account of $770 at 4.1% for 3 years
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Write y(t)=2sin 4 pi t + 5 cos 4 pi t) in the form y(t) A sin (wt + Ø) and identify the amplitude, angular frequency, and the phase shift of the spring motion.
Record your answers in the response box.
Expanding the desired form, we have
\(A \sin(\omega t + \phi) = A \bigg(\sin(\omega t) \cos(\phi) + \cos(\omega t) \sin(\phi)\bigg)\)
and matching it up with the given expression, we see that
\(\begin{cases} A \sin(\omega t) \cos(\phi) = 2 \sin(4\pi t) \\ A \cos(\omega t) \sin(\phi) = 5 \cos(4\pi t) \end{cases}\)
A natural choice for one of the symbols is \(\omega = 4\pi\). Then
\(\begin{cases} A \cos(\phi) = 2 \\ A \sin(\phi) = 5 \end{cases}\)
Use the Pythagorean identity to eliminate \(\phi\).
\((A\cos(\phi))^2 + (A\sin(\phi))^2 = A^2 \cos^2(\phi) + A^2 \sin^2(\phi) = A^2 (\cos^2(\phi) + \sin^2(\phi)) = A^2\)
so that
\(A^2 = 2^2 + 5^2 = 29 \implies A = \pm\sqrt{29}\)
Use the definition of tangent to eliminate \(A\).
\(\tan(\phi) = \dfrac{\sin(\phi)}{\cos(\phi)} = \dfrac{A\sin(\phi)}{\cos(\phi)}\)
so that
\(\tan(\phi) = \dfrac52 \implies \phi = \tan^{-1}\left(\dfrac52\right)\)
We end up with
\(y(t) = 2 \sin(4\pi t) + 5 \cos(4\pi t) = \boxed{\pm\sqrt{29} \sin\left(4\pi t + \tan^{-1}\left(\dfrac52\right)\right)}\)
where
• amplitude:
\(|A| = \boxed{\sqrt{29}}\)
• angular frequency:
\(\boxed{4\pi}\)
• phase shift:
\(4\pi t + \tan^{-1}\left(\dfrac 52\right) = 4\pi \left(t + \boxed{\frac1{4\pi} \tan^{-1}\left(\frac52\right)}\,\right)\)
17. Decide if the answer to x6 is less than, greater than, or equal to 6.
less than
equal to
greater than
Answer:
Equal To
Step-by-step explanation:
I just did it
5h-6-8+7h what’s the answer ?
In the box below, describe the graph. 3x+4y
The graph of the equation 3x + 4y = 0 is a straight line with a negative slope passing through the origin.
The given equation, 3x + 4y = 0, represents a linear graph in the Cartesian coordinate system. Let's analyze its characteristics.
First, note that the equation is in the standard form for a linear equation, which is Ax + By = C, where A, B, and C are constants. In this case, A = 3, B = 4, and C = 0.
To graph this equation, we can rewrite it in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. By isolating y, we have y = (-3/4)x + 0. Since the y-intercept (b) is 0, the line intersects the y-axis at the origin (0,0).
Next, we can examine the slope. The coefficient of x, -3/4, represents the ratio of the change in y (vertical) to the change in x (horizontal) as we move along the line. In this case, the slope is negative, indicating that the line descends from left to right. The magnitude of the slope, 3/4, implies that for every 4 units moved horizontally to the right, the line goes 3 units down vertically.
Therefore, we can conclude that the graph of the equation 3x + 4y = 0 is a straight line passing through the origin (0,0) with a negative slope. It extends indefinitely in both directions, with the line getting steeper as we move to the right.
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George measured the weight of a random sample of 49 cartons of apples. The mean weight was 45.5 pounds, with a standard deviation of 3. z equals fraction numerator x with bar on top minus mu over denominator begin display style bevelled fraction numerator sigma over denominator square root of n end fraction end style end fraction To see if the cartons have a significantly different mean weight from 46 pounds, what would the value of the z-test statistic be
Answer:
1.16667
Step-by-step explanation:
When told in the question that random number of sample is tested
z test statistic formula = x - x bar(x with bar above it) /Standard error
From the question
x = raw score = 46 pounds
x bar (x with bar above it)= sample mean = 45.5 pounds
Standard Error = σ/√n
Standard deviation = σ = 3
n = random number of samples = 49
z = 46 - 45.5/3/√49
z = 0.5/ 3/7
z =0.5/ 0.4285714286
z = 1.16667
Therefore , the value of the z test statistic = 1.16667
Answer:
1.17
Step-by-step explanation:
How many different ways do you think there are to shade 3/8 of the square?
Therefore , the solution of the given problem of unitary method comes out to be any other restrictions or criteria would determine how many possible methods there are to shade 3/8 of the square.
Definition of a unitary method.Use the tried-and-true fundamental method, the actual variables, and any relevant information gleaned from general and specific questions to complete expression the assignment. Customers may be given another chance to taste the products in response. If these adjustments don't happen, we'll lose out on significant advancements in our understanding of programmes.
Here,
The phrase "shade 3/8 of the square" might be interpreted in a variety of ways, which might result in various solutions. Here are a few potential explanations and their accompanying responses:
1) The most straightforward interpretation is to shade 3/8 of the square as a single, continuous area.
There are countless ways to shade precisely 3/8 of the square in this interpretation.
2) Discrete Interpretation: Using a grid or discrete cells to shade 3/8 of the square.
The number of alternative ways relies on the size of the grid or the number of discrete cells if the square is divided into a grid or cells and the requirement is to shade exactly 3/8 of the cells. F
3) Interpretation based on constraints: Shading 3/8 of the square with specific restrictions.
In conclusion, the exact interpretation and any other restrictions or criteria would determine how many possible methods there are to shade 3/8 of the square. It is challenging to estimate the precise number of potential solutions in the absence of more details.
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I need help with this question.
1. The function f that determines the height of the beanstalk is \(h(t) = 7 * (1.15)^t\)
2. f(1)/f(0) = 1.15.
3. f(2)/f(1) = 1.149.
What function f determines the height of the beanstalk?Let h be the height of the beanstalk in inches after t days. Then we can write: \(h(t) = 7 * (1.15)^t\) where 1.15 is the factor by which the height increases each day.
Computation of the value of the following ration:i. To compute f(1)/f(0), we need to substitute t = 1 and t = 0 into the function f and divide:
f(1)/f(0) = [7 * (1.15)^1] / [7 * (1.15)^0]
f(1)/f(0) = 1.15/1
f(1)/f(0) = 1.15
ii. To compute f(2)/f(1), we need to substitute t = 2 and t = 1 into the function f and divide:
f(2)/f(1) = [7 * (1.15)^2] / [7 * (1.15)^1]
f(2)/f(1)= (1.3225) / (1.15)
f(2)/f(1) = 1.149
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The equation z = 30x represents a(n) _____ variation.
a. direct
b. joint
c. inverse
d. combined
The equation z = 30x represents a direct variation the two variables, z and x, are directly proportional to each other. a.
Direct variation can be defined as a relationship between two variables where their values increase or decrease at the same rate.
In the case of the given equation, as x increases, z also increases proportionally.
Similarly, if x decreases, z will also decrease proportionally.
Direct variation can be represented as y = kx, where y and x are the variables, and k is the constant of variation.
In the given equation, we can see that z is the dependent variable, and x is the independent variable.
We can rewrite the equation as z = kx, where k = 30.
To understand how direct variation works, let's consider an example. Suppose we have an equation y = 5x, where y represents the cost of buying x apples at $5 per apple.
Here, the cost of buying apples is directly proportional to the number of apples purchased.
For instance, if we buy 10 apples, the total cost will be 10 × $5 = $50.
Similarly, if we buy 20 apples, the total cost will be 20 × $5 = $100.
Thus, we can see that the cost increases as the number of apples purchased increases, and vice versa.
The given equation z = 30x represents a direct variation is a type of relationship between two variables where their values increase or decrease proportionally.
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100 POINTS PLEASE HELP ME ALGEBRA
The range of the graph of the exponential function is (b) {y | y > 0}
Calculating the range of the graphFrom the question, we have the following parameters that can be used in our computation:
The graph of the exponential function
The rule of an exponential function is that
The domain is the set of all real numbers
This means that the input value can take all real values
However, the range is always greater than the constant term
From the graph, the constant term is 0
So, the range is y > 0
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Aldrin bought 5 pencils and 7 notebooks. A notebook cost 10. 80 more than a pencil write an algebraic equation showing that the total amount of the school supplies bought is210. 00
Answer:
5x + 7(x + 10.80) = 210.00
Step-by-step explanation:
Let x be the cost of a pencil in dollars. Then, the cost of a notebook is 10.80 dollars more, which is x + 10.80 dollars.
Aldrin bought 5 pencils and 7 notebooks, so the total cost is:
5x + 7(x + 10.80) = 210.00
Simplifying and solving for x, we have:
5x + 7x + 75.60 = 210.00
12x = 134.40
x = 11.20
Therefore, a pencil costs 11.20 dollars and a notebook costs 10.80 dollars more, which is 22.00 dollars.
We can check that the total cost of 5 pencils and 7 notebooks at these prices is indeed 210.00 dollars:
5 pencils * 11.20 dollars/pencil + 7 notebooks * 22.00 dollars/notebook = 56.00 dollars + 154.00 dollars = 210.00 dollars
packaging idaho produce company ships potatoes to its distributors in bags whose weights are normally distributed witb. nean weight of 50 pounds and a standard deviation of .5 pounds. if a bag of potatoes is selected at random from a shipment, what is the probability that it weighs more than 51 pounds
The probability that it weighs more than 51 pounds exactly 53 pounds.
Given that, mean weight of 50 pounds and a standard deviation of 0.5 pounds.
We need to find the probability that it weighs more than 51 pounds,
P(X = 53) = 0
z = (51 - 50) / 0.5 = 2.00
P(X > 51) = P(z > 2.00) = 0.0228
z1 = (49 - 50) / 0.5 = -2.00
z2 = (51 - 50) / 0.5 = 2.00
P(49 < X < 51) = P(-2.00 < z < 2.00) = P(z < 2.00) - P(z < -2.00) = 0.9772 - 0.0228 = 0.9544
Hence, the probability that it weighs more than 51 pounds exactly 53 pounds.
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I am struggling to find domain and range please help thank you
Answer:
Domain: 0, 1, 2, 3, 4,
Range: 1, 2, 3, 4, 5,
Step-by-step explanation:
Based on the graph the domain of the function is 0, 1, 2, 3, 4, and the range is 1, 2, 3, 4, 5, therefore, the answer is:
What is the slope of the line that passes through the points (2, 3) and (6, 8)?
(x1, y1) and (x2, y2)
(2, 3) and (6,8)
slope = y2 - y1 / x2 - x1
= 8 -3 / 6 - 2
= 5/4
Answer:
I had the same question, its not 5/4 I got it wrong it 4/3
Step-by-step explanation:
get it right
please look at the picture
6x-7y=-10
12x-5=16
2xay=10
-10+16+x=10
10=-10+16+x=6x
6x+10=16x
ay=16x
PLZ DO APPLICATIONS OF SYSTEMS OF EQUATIONS PLZZZZZZZZZZZZ
Two ski rental companies have different pricing systems. Company A charges a flat fee of $10
plus $5 per hour. Company B does not charge a flat fee but charges $7 per hour rented. After
how many hours do both companies charge the same amount?
Find the number of ways of
arranging the letters of the
words DANGER, so that no vowel
occupies odd place.
Answer: 6 * 24 = 144 ways.
Step-by-step explanation:
Solution:
Given word => DANGER.
The condition is that vowels can't occupy odd places so, we will let them occupy even places.
A total number of arrangements will be = 6 * 24 = 144 ways.
Answer: 6x24 = 144 ways.