The rectangle below has a height of 2y + 5 and a base of y' + 6y
What is the area of the entire rectangle in proper polynomial format?
[A] 3* + 12y* + 5y? +60y
[B] 60 + 5y + 12y +
(C) 60y + 5y? +12y + yo
[D] 2y +12y + 5y + 30y
b
ОООО
Choice [A]
Choice [B]
Choice (C)
Choice [D]
d
Answers
Answer:
Choice D
Step-by-step explanation:
The area can be found simply by multiplying the height by the base:
\((2y + 5)(y + 6)\\= 2y^2 + 12y + 5y + 30\\= 2y^2 + 17y + 30\)
So answer D is the correct one (note that they do not group like terms, leaving 12y + 5y in that form instead of adding them together).
Related Questions
You recently spent $22 to purchase a notebook, a box of pencils, and a package of pens. The box of pencils costs $2 less than the notebook. The package of pens costs 3 times as much as the box of pencils. Write and solve an algebraic equation to find the cost of each item you purchased.
Answers
Answer:
The answer is down below:
Step-by-step explanation:
Notebook: 22-x
Pens: (22 - x - 2) x 3.
Pencils: 22 - x - 2.
We use x for notebooks because it is the only item that doesn't have an "equation" for us to solve so we use "x" instead. hope this helped you out.
Notebook: 22-x
Pens: (22 - x - 2) x 3.
Pencils: 22 - x - 2.
We use x for notebooks because it is the only item that doesn't have an "equation" for us to solve so we use "x" instead. hope this helped you out .Notebook: 22-x
Select all the expressions that are
equivalent to 10.08.
13.117+ 1.3
2.88 x 3.5
21.168÷ 2.1
168 x 0.06
201.6 x 0.05
Answers
The expressions 2, 3, 4, and 5 are equivalent to 10.08.
We need to determine which of the given expressions are equivalent to 10.08.
As per the question, simplify each expression and see if it equals 10.08.
1). 13.117 + 1.3 = 14.417
Thus, this is not equivalent to 10.08
2). 2.88 x 3.5 = 10.08
Thus, this is equivalent to 10.08
3). 21.168 ÷ 2.1 = 10.08
Thus, this is equivalent to 10.08
4). 168 x 0.06 = 10.08
Thus, this is equivalent to 10.08
5). 201.6 x 0.05 = 10.08
Thus, this is equivalent to 10.08
Therefore, expressions 2, 3, 4, and 5 are equivalent to 10.08.
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Sketch the graph of the level curves of the function for the given values of z: f(x, y) = 2e^-x - y, z = -7, 11. What type of functions are the level curves? Rational Functions with x-axis symmetry Decreasing exponential functions Increasing exponential functions Natural logarithm functions Rational Functions with symmetry about the origin For what values of y do the level curves have a y-intercept for these values of z? (Put the smaller y-value first.) What are the y values of the asymptotes of the level curves for these values of Z? (Put the smaller y-value first.)
Answers
a) The function f(x, y)= \(2e^-^x - y, z = -7, 11.\) The curves are decreasing exponential functions.
b) The y - intercept of the level curves for the value of k are found as:
k = -7 => y = 9
c)The y values of the asymptotes of the level curves for these values of k are found as
k = -7 => y = 7.
Level Curves:The level curves of a function of two variables
z = f(x, y)
are the curves where the function assumes a constant value k.
Therefore, the curves are solution of the equation
f(x, y) = k
The level curves of the function for the given values of z.
f(x, y) = \(2e^-^x - y, z = -7, 11.\)
are found solving the equation
\(f(x,y) =k = > 2e^-^x-y=k\\\\= > y= 2e^-^x-k\)
The curves are decreasing exponential functions. See the graph of the function.
b) The y - intercept of the level curves for the value of k are found as:
x = 0 => y = 2 - k
k = 11 => y = -9
k = -7 => y = 9
c) The y values of the asymptotes of the level curves for these values of k are found as
\(\lim_{x \to \infty} 2e^- ^x-k=-k\)
k = 11 => y = -11
k = -7 => y = 7.
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Help please!!!!!!! URGENT
Answers
Answer:
nvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
Step-by-step explanation:
cgfgbgfgggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg
The turtle's distance from his starting point is increasing
between
seconds.
The turtle's distance from his starting point is constant
between
seconds.
The turtle's distance from his starting point is
decreasing between
seconds.
Answers
Answer:
10 seconds, decreasing, standing still
Step-by-step explanation:
A square plywood platform has a perimeter which is 11 times the length of a side decrease by 35 find the length of a side (p= 4L)
Answers
The rule of the perimeter of the square is
\(P=4L\)L is the length of its side
Since the perimeter is 11 times the length decrease by 35
Then multiply L by 11, then subtract 25 from the product
\(\begin{gathered} P=11\times L-35 \\ P=11L-35 \end{gathered}\)Substitute the value of P in the rule above
\(11L-35=4L\)Add 35 to both sides
\(\begin{gathered} 11L-35+35=4L+35 \\ 11L=4L+35 \end{gathered}\)Now, subtract 4L from both sides
\(\begin{gathered} 11L-4L=4L-4L+35 \\ 7L=35 \end{gathered}\)Divide both sides by 7
\(\begin{gathered} \frac{7L}{7}=\frac{35}{7} \\ L=5 \end{gathered}\)The length of the side of the square is 5 units
a unity feedback control system is characterized by an open-loop transfer function
G(s)H(s)=k/s(s+10)
determine the system gain k so that the system will have a damping ratio of 0.5. for this value of k, find the rise time, settling time, and peak overshoot. assume that the system is subjected to a step input of 1v
Answers
A unity feedback control system is characterized by an open-loop transfer function G(s)H(s)=k/s(s+10). The system gain k so that the system will have a damping ratio of 0.5 is 4. The corresponding rise time is 2.3s, settling time is 4.4s, and peak overshoot is 0.26.
To determine the system gain k so that the system will have a damping ratio of 0.5, we can use the equation ζ=1/2ωn. Rearranging the equation yields k=2ωn2. Using the damping ratio of 0.5, this yields k=4.
For this value of k, the rise time, settling time, and peak overshoot can be determined using the following equations:
Rise Time: Tr=4.6/ωn
Settling Time: Ts=4.4/ζωn
Peak Overshoot: Mp=e^(-ζπ/√1-ζ^2)
Given that the damping ratio is 0.5 and the system is subjected to a step input of 1V, we can determine the rise time, settling time, and peak overshoot.
Rise Time: Tr=4.6/ωn=4.6/2=2.3s
Settling Time: Ts=4.4/0.5ωn=4.4/1=4.4s
Peak Overshoot: Mp=e^(-0.5π/√1-0.5^2)=0.26
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Suppose that the function g is defined, for all real numbers, as follows. x < - 1; g(x)= 2&ifx<-1\\ 3&ifx=-1\\ -1&ifx>-1; x = - 1; x > - 1 Graph the function g.
Answers
The given piecewise-defined function is:
\(g(x)=\begin{cases}{2\qquad\text{ if }x<-1} \\ {3\qquad\text{ if }x=-1} \\ {-1\qquad\text{ if }x>-1}\end{cases}\)It is required to graph the function.
To do this, graph each piece with respect to the corresponding domain.
Graph g(x)=2 over x<-1:
Notice that an open circle is at x=-1 since it is not included in the interval x<-1.
Graph g(x)=3 for x=-1. This is just a point:
Finally, graph g(x)=-1 for x>-1:
There is an open circle at x=-1 since it is not included in the interval x>-1.
Thus, the required graph of the piecewise-defined function is shown below:
Anyone got answers please
Answers
Sorry, but I only know the following answers:
4. b = -2
5. b = 0
6. b = 0
really sorry :'(
hope this helps, though!
the original purchase price of a car is 12,000. Each year, its value depreciates (loses value) by 5%. Three years after its purchase, what is the value of the car?
Answers
Answer:
10,200
Step-by-step explanation:
P(1-r)^n
r = decimal form of the interest rate percent
n = amount of years
principal times (1 - decimal form of the interest rate percent) to the (amount of years) power
12000 (1-.05)^3
use PEMDAS
12000 times (.95)^3
12000 times .857375 =
ANSWER:
10288.5
Suppose that x and y vary inversely, and x=12 when y=5. Write the function that models the inverse variation.
Answers
y = 60 / x
Step-by-step Explanation:
If x and y vary inversely, then their product is a constant. We can use this fact to write the function that models the inverse variation.
Let k be the constant of proportionality. Then, we have:
x * y = k
Given that x = 12 when y = 5, we can solve for k:
12 * 5 = k
k = 60
Therefore, the function that models the inverse variation is:
x * y = 60
Or, equivalently:
y = 60 / x
This function expresses y as a function of x, where y varies inversely with x, and 60 is the constant of proportionality.
The statement is expressed as:
\(y \alpha 1/x\)
To convert to an equation introduce k, the constant of variation.
\(y=k * 1/x\\\)
To find k use the condition that \(x = 12\) when \(y = 5\)
\(y=k/x\)
\(5=k/12\)
\(k=5*12\)
\(k=60\\\)
Therefore, \(y =60/x\) is the function.
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Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable? (If an answer does not exist, enter DNE.) f(x) = 10 − 6e7 − x, x > 7 10 − 6 7 x, x ≤ 7 x = ; ---Select---
Answers
The function f(x) is not continuous at x = 7. To determine the x-values at which the function f(x) is not continuous, we need to analyze the function for any potential points of discontinuity.
The given function is defined as:
f(x) = 10 − 6e^(7 − x), x > 7
f(x) = 10 − 6x, x ≤ 7
To check for continuity, we need to examine the behavior of the function as x approaches 7 from both the left and the right sides.
From the right side (x > 7), the function is given by:
f(x) = 10 − 6e^(7 − x)
As x approaches 7 from the right side (x → 7+), the exponent e^(7 - x) approaches 1, resulting in the function becoming:
f(x) = 10 - 6(1) = 4
So, from the right side, the function is continuous at x = 7.
From the left side (x ≤ 7), the function is given by:
f(x) = 10 − 6x
As x approaches 7 from the left side (x → 7-), the function becomes:
f(x) = 10 - 6(7) = -32
Therefore, from the left side, the function is discontinuous at x = 7.
In summary, the function f(x) is not continuous at x = 7.
Regarding the removable discontinuities, there are none in this case since the function is simply defined differently for x ≤ 7 and x > 7. Removable discontinuities occur when a function has a hole or a point of discontinuity that can be "filled in" or "removed" by redefining the function at that specific point. However, in this case, the function is already defined distinctly for the two regions separated at x = 7, and there are no singular points where the function is not defined.
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Students in a fitness class each completed a one-mile
Which statements are true about a histogram with one-
walk or run. The list shows the time it took each person
minute increments representing the data? Select three
to complete the mile. Each time is rounded to the
options.
nearest half-minute.
5.5, 6, 7, 10, 7.5, 8, 9.5, 9, 8.5, 8, 7, 7.5, 6, 6.5, 5.5
O A histogram will show that the mean time iS
approximately equal to the median time of 7.5
minutes.
O The histogram will have a shape that is left-skewed.
O The histogram will show that the mean time is greater iS
than the median time of 7.4 minutes.
O The shape of the histogram can be approximated with
a normal curve.
0 The histogram will show that most of the data is
centered between 6 minutes and 9 minutes.
Answers
In linear equation, The histogram will show that most of the data is centered between 6 minutes and 9 minutes.
What in mathematics is a linear equation?
An x-y linear relationship, or two variables in which the value of one of them (often y) relies on the value of the other one, is what is known as a linear equation in two variables (usually x).The dependent variable in this scenario is y since it depends on the independent variable, x.5.5+6+7+10+7.5+8+9.5+9+8.5+8+7+7.5+6+6.5+5.5=111.5
Since there are 15 values,
their mean is 111.5/15=7.43 which is very close to the mean.
A)A histogram will show that the mean time is approximately equal to the median time of 7.5 minutes
D)The shape of the histogram can be approximated with a normal curve.
E)The histogram will show that most of the data is centered between 6 minutes and 9 minutes.
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it's not 25 seconds apparently. please help!
Answers
Answer:
-4.278
Step-by-step explanation:
Find the area and the circumference of a circle with radius 3km.Write your answers in terms of π, and be sure to include the correct units in your answers.
Answers
To find:
a) Area of the circle.
b) Circumference of the circle.
Solution:
a) It is known that the area of a circle is whose radius is r is given by:
\(Area=\pi r^2\)So, the area of the given circle is :
\(\begin{gathered} A=\pi(3)^2 \\ =9\pi km^2 \end{gathered}\)b)
It is known that the circumference of a circle whose radius is r is given by:
\(C=2\pi r\)So, the area of the given circle is :
\(\begin{gathered} C=2\pi(3) \\ =6\pi km \end{gathered}\)What is (−3x+5)−(−7x+2) ?
Answers
=(-3x+5)+7x-2
=(-3x)+7x+5-2
=4x+3
Write an
expression using scale factor, k, for each dimension?
1D
2D
3D
Answers
Due in 10 minutes please help !! ASAP Erin buys 2 packs of potatoes costing £2 each, 3 packs of carrots for £3 per pack, and 3 turnips costing 90p each.
If she pays with a £20 note, how much change would she get in pounds, £?
Answers
2(2) + 3(3) =
4 + 9 = 13
I don't know what 90p means but basically, u have to multiply that by 3 and add it to our current total which is 13.
Then, u substract the total cost from the 20 and you should get the change.
Ms. Lee takes out a loan to start a business. She borrows $5,000 of a simple annual interest rate of 6. 5% for 5 years. What is the total amount of interest Ms Lee must pay
Answers
Answer:
A = $6,625.00
Step-by-step explanation:
A = P(1 + rt)
A = 5000(1 + (0.065 × 5)) = 6625
What expreion repreent the um of 2 divided by x and 15
215÷x215÷x
(215)÷x(215)÷x
152÷x152÷x
(152)÷x
Answers
The required expression will be 2/x+15 as the problem says "the sum of 2 divided by x and 15".
What is expression?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases. A phrase in language may contain an action on its own, but it does not constitute a complete sentence.
Here,
2 divided by x,
=2/x
sum of 2/x and 15,
2/x+15
The conclusion is "the sum of 2 divided by x and 15," hence the necessary equation will be "2/x+15."
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Determine how many feet each member of Lola's family walked.
Lola's pet turtle walked 10 feet, and then half that length again.
Lola's baby brother walked 3 feet, and then half that length again.
Lola's hamster walked 6.5 feet, and then half that length again.
Lola's mom walked x feet, and then half that length again.
Answers
Step-by-step explanation:
Lola's pet turtle walked 10 feet, and then half that length again. This means that Lola's pet turtle walked:
= 10 + (1/2 × 10) = 10 + 5 = 15 feet
Lola's baby brother walked 3 feet, and then half that length again. Total length walked will be:
= 3 + (1/2 × 3) = 3 + 1.5 = 4.5 feet
Lola's hamster walked 6.5 feet, and then half that length again. Total length walked will be:
= 6.5 + (1/2 × 6.5) = 6.5 + 3.25 = 9.75
Lola's mom walked x feet, and then half that length again. Total length walked will be:
= x + (1/2 × x) = x + 0.5x = 1.5x
Total feet walked by the whole member of the family will be:
= 15 + 4.5 + 9.75 + 1.5x
= 29.25 + 1.5x
Answer:
turtle: 10 + 5 = 15
brother: 3 + 1 1/2 = 4 1/2
hamster: 6 1/2 + 3 1/4 = 9 3/4
Mom: x + 1/2x = 1 \(\frac{1}{2}\)x
Step-by-step explanation:
Which expression is equivalent to 91 + 39?
(A) 13(7 + 39)
(B) 3(30 + 13)
(C) 13(7 + 3)
(D) 7(13 + 6)
Answers
Explation:
7+3= 10
13x10=130
91+39=130
Hope this helped!
Jason has already made 5 birdhouses. If he decides to make 4 birdhouses each week, which expression can be used to find the total number of birdhouses he has made after w weeks?
Help my little sister please
Answers
The main answer to the question is that the expression that can be used to find the total number of birdhouses Jason has made after w weeks is:
5 + 4w
The explanation for this is that Jason has already made 5 birdhouses, so this is his starting point.
Then, he decides to make 4 birdhouses each week.
We can represent this by multiplying the number of weeks by 4, which gives us 4w.
Adding the initial 5 birdhouses to this gives us the total number of birdhouses made after w weeks.
In summary, the expression to find the total number of birdhouses Jason has made after w weeks is 5 + 4w, which takes into account his starting point of 5 birdhouses and his weekly production of 4 birdhouses.
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The expression denotes the z-score with an area of _______ to its right.
Answers
The given expression represents the z-score with an area to its right, indicating the probability of observing a value greater than the z-score.
The z-score, also known as the standard score, measures the distance between a given data point and the mean of a distribution in terms of standard deviations. It is calculated by subtracting the mean from the data point and dividing the result by the standard deviation. The resulting z-score represents the number of standard deviations a data point is away from the mean.
When we refer to the expression denoting the z-score with an area to its right, we are essentially talking about the cumulative probability associated with the z-score. This probability represents the area under the normal distribution curve to the right of the given z-score. In other words, it indicates the likelihood of observing a value greater than the z-score.
By utilizing statistical tables or software, we can determine the exact value of the area or probability associated with a given z-score. This information is useful in various applications, such as hypothesis testing, confidence intervals, and determining percentiles in a distribution. It allows us to make inferences and draw conclusions based on the relative position of a data point within a distribution.
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2/9 21% 0.21 11/50 least to greatest
Answers
Answer:
21%, 0.21, 11/50, 2/9
Step-by-step explanation:
To arrange from least to greatest, we need to first express all as percemtage;
2/9 = 2/9 * 100 = 200/9 = 22.2%
21% = 0.21
0.21 = 0.21 * 100 = 21%
11/50 = 11/50 * 100 = 11*12 = 22%
Hence the values from least to greatest is 21%, 0.21, 11/50, 2/9
if x is rational and y is irrational then x+y is irrational
Answers
Yes, the statement "if x is rational and y is irrational, then x + y is irrational" is true.
To understand why, let's break it down step by step:
1. First, let's define what it means for a number to be rational or irrational:
- A rational number is a number that can be expressed as the ratio of two integers, where the denominator is not zero.
- An irrational number is a number that cannot be expressed as the ratio of two integers.
2. Given that x is rational and y is irrational, we can express x and y as follows:
- x = a/b, where a and b are integers and b is not zero.
- y = c, where c is an irrational number.
3. Now, let's consider the sum x + y:
- x + y = (a/b) + c
4. To prove that x + y is irrational, we'll assume the contrary, that is, x + y is rational. This means we can express x + y as the ratio of two integers:
- x + y = p/q, where p and q are integers and q is not zero.
5. We can rewrite this equation as follows:
- (a/b) + c = p/q
6. Rearranging the equation, we get:
- (a/b) = (p/q) - c
7. Since (p/q) is a rational number and c is an irrational number, the right side of the equation (p/q) - c would be the difference between a rational and an irrational number.
8. However, the difference between a rational number and an irrational number is always irrational. Therefore, the right side of the equation is irrational.
9. This contradicts our assumption that (a/b) is rational, leading us to conclude that x + y must be irrational.
In conclusion, if x is rational and y is irrational, then x + y is always irrational.
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Central Market sells 5 jars of jam for $3.00. Valley Market sells jars of jam at 59 cents per jar. Yasmin bought 10 jars from Central Market, and Nadia bought 10 jars from Valley Market.
Answers
Answer:
Yasmin will spend $6
Nadia will spend $5.9
Step-by-step explanation:
Step one:
the cost of 5 jars at Central market is $3
the cost of 1 jar = 3/5= $0.6
60 cents per jar
we are told that Valley Market sells jars of jam at 59 cents per jar.
$0.59
Step two:
If Yasmin buys 10 jars from Central Market,
Yasmin will spend = 10*0.6= $6
If Nadia buys 10 jars from Valley Market.
Nadia will spend = 10*0.59= $5.9
The market difference is 6-5.9= $0.1
Calculate the amount of property tax Alice Brown owes on her home, which has an assessed value of $90,000. The tax rate in her community is $31. 00 per $1,000 of assessed value.
Answers
Answer:
$2,790
Step-by-step explanation:
This is the concept of commercial arithmetic, the amount of tax calculated from $90,000 will be:
Rate*value
=31/1000*90000
=$2,790
the answer is $2,790
Assume that a country is endowed with 5 units of oil reserve. There is no oil substitute available. How long the oil reserve will last if (a) the marginal willingness to pay for oil in each period is given by P = 7 - 0.40q, (b) the marginal cost of extraction of oil is constant at $4 per unit, and (c) discount rate is 1%?
Answers
Given the marginal willingness to pay for oil, the constant marginal cost of extraction, and a discount rate of 1%, the oil reserve will last for approximately 10.8 periods.
To determine how long the oil reserve will last, we need to find the point at which the marginal cost of extraction equals the marginal willingness to pay for oil. In this case, the marginal cost is constant at $4 per unit. The marginal willingness to pay is given by the equation P = 7 - 0.40q, where q represents the quantity of oil extracted.
Setting the marginal cost equal to the marginal willingness to pay, we have:4 = 7 - 0.40q
Simplifying the equation, we get:0.40q = 3
q = 3 / 0.40
q ≈ 7.5So, at q ≈ 7.5, the marginal cost and marginal willingness to pay are equal. We can interpret this as the point at which the country would extract the oil until the quantity reaches 7.5 units. To determine how long this would last, we need to divide the total oil reserve (5 units) by the extraction rate (7.5 units per period):5 / 7.5 ≈ 0.67
Since the extraction rate is less than 1 unit per period, it means that the oil reserve will last for approximately 0.67 periods. However, the discount rate of 1% needs to be taken into account. To calculate the present value of the oil reserve, we discount each period's value. Using the formula for present value, we find that the oil reserve will last for approximately 10.8 periods.
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what's the absolute value of 4.5 ?
Answers
Answer:
the absolute value or 4.5 is 4.5
Step-by-step explanation:
Answer:
4.5
Step-by-step explanation:
absolute value: the distance away from zero, it will always be positive because distance can't be negative.
thus, the absolute value of 4.5 = the distance of 4.5 to zero, which is 4.5
|4.5| = 4.5