3x² + 2x + 2 + 4x² + 5
Answer:
7x^2 + 2x + 7
Hope this helps :)
Answer:
7x²+2x+7
Step-by-step explanation:
Hope this helps. Plz give brainliest.
Which of the following rational functions is graphed below?
Answer:
C \(f(x) = \frac{x}{(x+1)(x-2)}\)
Step-by-step explanation:
The two vertical asymptotes happens when you have a pole, ie you are bringing a denominator to zero while the numerator has a finite value. The two lines have equation \(x=-1\) and \(x=2\). The only solution that works for that constraints is C
A school janitor has moped 1/3 of a classroom in five minutes at what rate is he moping
Answer:
it is eather 1/15 or 0.06
PLEASE HELP TODAY!!!! WILL GIVE BRAINLIST
Hello!
We will go tu use the pythagorean theorem!
So:
BA² = BC² + AC²
AC² = BA² - BC²
AC² = 52² - 20²
AC² = 2304
AC = √2304
AC = 48
In ADEF, what is the length of segment DF?
In triangle DEF, the length of segment DF is 15√3. So correct option is C.
Describe trigonometric ratios?Trigonometric ratios are mathematical functions that relate the angles of a right triangle to the ratios of its sides. There are three primary trigonometric ratios: sine, cosine, and tangent, which are commonly abbreviated as sin, cos, and tan, respectively.
Here are the definitions of these trigonometric ratios:
Sine (sin): The sine of an angle in a right triangle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. This can be written as sin(theta) = opposite / hypotenuse.
Cosine (cos): The cosine of an angle in a right triangle is equal to the length of the adjacent side divided by the length of the hypotenuse. This can be written as cos(theta) = adjacent / hypotenuse.
Tangent (tan): The tangent of an angle in a right triangle is equal to the length of the side opposite the angle divided by the length of the adjacent side. This can be written as tan(theta) = opposite / adjacent.
In triangle DEF, we have a right triangle at E, which means that angle DEF is a 90-degree angle. We are also given that angle DFE is 60 degrees, which means that angle EDF is 30 degrees (since the angles in a triangle add up to 180 degrees).
Let DF = x. Then, we can use the trigonometric ratios of the 30-60-90 degree triangle to solve for x
We know that the ratio of the sides in a 30-60-90 degree triangle is x : x√3 : 2x. Therefore, we have:
DE / DF = x√3 / x = √3
Simplifying this, we get:
x = DE / (√3) = 45 / (√3) = 15√3
Therefore, the length of segment DF is 15√3, which is answer choice C.
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SHOW ALL WORK PLEASE! A right cylinder has a radius of 7 cm and a height of 3 cm.
Answer the following questions and make sure to show all your work.
(a) Find the Surface Area of the cylinder.
(b) Find the Volume of the cylinder.
(c) If you wanted more volume in your cylinder, which of these two ideas would give the most Volume?
1. Doubling the radius to 14 cm, while the height remains 3 cm.
-OR
2. Tripling the height to 9 cm, while the radius remains 7 cm.
Answer:
(a) Surface Area = 140 π cm² = 438.823 cm²
(b) Volume = 147 π cm³ = 461.814 cm³
(c) Doubling the radius, keeping height constant results in more volume
Step-by-step explanation:
Volume of a cylinder with base radius r and height h is given by
V = π r² h
Surface Area A = 2 π r(h + r)
Given r = 7 cm, height = 3cm
(a) Surface Are = 2 x π x 7(7 + 3) = 14 π (10) = 140 π cm² =438.823 cm²
(b) Volume = π x 7² x 3 = 147 π = 461.814 cm³
(c) If we double the radius to 14 cm with height at 3 cm (Option 1), the volume would quadruple to 4 because the new radius is twice the old radius and since volume is proportional to square of radius, new volume will be (2r)² = 4r² where r is the old radius
So new volume = 4 x 461.814 = 1,847.256 cm³
If we triple the height to 9 cm, keeping radius at 7, the volume would only triple since it is directly proportional to height
So new volume = 3 x 461.814 = 1,385.442 cm³
So to get more volume, idea 1, doubling the radius works
Which expression is equivalent to Z +( z 6?
None of the solutions are appropriate since the result of the equation z + (z+6) will be equal to 2z + 6.
An expression is defined.A mathematical expression is the result of combining a number of mathematical symbols with an arithmetic operator, a variable, and a constraint.
In a different sense, expression is highly helpful in identifying the root or end value of a constraint.
for instance, 3x + 5y
The expression restriction is denoted by the symbols = or, >.
Given the phrase,
z + (z+6)
opening the bracket
z + z + 6
⇒ 2z + 6
Hence
"2z + 6 will be the value of the equation z + (z+6)."
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solve the PDE using separation of variables method Uxx = 1/2 Ut 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)
The general solution of the partial differential equation is:
U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)
How to solve Partial Differential Equations?The partial differential equation (PDE) is given as:
Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)
Assume that the solution can be written as a product of two functions:
U(x, t) = X(x)T(t)
Substituting this into the PDE, we have:
X''(x)T(t) = (1/2)X(x)T'(t)
Dividing both sides by X(x)T(t), we get:
(X''(x))/X(x) = (1/2)(T'(t))/T(t)
Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:
(X''(x))/X(x) = -λ²
(1/2)(T'(t))/T(t) = -λ²
Simplifying the second equation, we have:
T'(t)/T(t) = -2λ²
Solving the second equation, we find:
T(t) = Ce^(-2λ²t)
Applying the boundary condition U(0, t) = 0, we have:
U(0, t) = X(0)T(t) = 0
Since T(t) ≠ 0, we must have X(0) = 0.
Applying the boundary condition U(3, t) = 0, we have:
U(3, t) = X(3)T(t) = 0
Again, since T(t) ≠ 0, we must have X(3) = 0.
Therefore, we can conclude that X(x) must satisfy the following boundary value problem:
X''(x)/X(x) = -λ²
X(0) = 0
X(3) = 0
The general solution to this ordinary differential equation is given by:
X(x) = Asin(λx) + Bcos(λx)
Applying the initial condition U(x, 0) = 5*sin(4πx), we have:
U(x, 0) = X(x)T(0) = X(x)C
Comparing this with the given initial condition, we can conclude that T(0) = C = 5.
Therefore, the complete solution for U(x, t) is given by:
U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)
where:
Σ represents the summation over all values of n
λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).
To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):
X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0
X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0
From the first equation, we have Bₙ = 0.
From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.
This implies that 3λₙ = nπ, where n is an integer.
Therefore, λₙ = (nπ)/3.
Substituting the eigenvalues into the general solution, we have:
U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)
where Aₙ are the coefficients that can be determined from the initial condition.
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Find the circumference of the circle with radius 84 cm. use 22/7 for
Answer:
≈ 528cm
Step-by-step explanation:
The formula is pi multiplied by the diameter. So you multiply the radius (84) by two times. Next, you multiply 22/7 by the diameter and you will received 528cm. I hope this answers your question.
Answer:
Today: Wednesday, 04 November 2020
Hour: 21.14 WIB (Indonesia)
_______________________________
r = 84 cm
π = 22/7
C = 2πr
C = 2 . 22/7 . 84
C = 44 . 12
C = 528 cm
(CLASSKICK) HELP ASAP!!!
Answer:
94.3
Step-by-step explanation:
You want to know how to fill in the proportion associated with the question, "What is 115% of 82?"
ProportionThe diagram is intended to help you match parts of the question to parts of the proportion. The attachment shows the intended relation.
The solution is found by multiplying both sides by 82:
(x/82)·82 = (115/100)·82
x = 94.3
EquationThe question can also be written as a statement:
"what" is 115% of 82
When written as an equation, "is" means "equals", and "of" means "times":
what = 115% × 82
Of course, you can use any variable name of your choosing in place of "what". In your diagram, that is "x". And, you know how to write a percentage as a fraction or decimal, so this becomes ...
x = 115/100 × 82 = 1.15 × 82
All that remains is to evaluate this expression.
x = 1.15 × 82 = 94.3
So, the answer to the question is ...
94.3 is 115% of 82.
using the line of best fit
The monthly cell phone bill when shared data equals zero is given as follows:
$26.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.The intercept of the line in this problem is given as follows:
b = 26.
Hence $26 is the monthly cell phone bill when shared data equals zero.
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A certain state uses the following progressive tax rate for calculating individual income tax:
Income
Progressive
Range ($)
Tax Rate
0 - 10,000
3%
10,001 - 50,000
5%
50,001 - 100,000
5.5%
Calculate the state income tax owed on a $40,000
per year salary.
tax = $[?]
Round your answer to the nearest whole dollar amount.
The state income tax owed on a $40,000 per year salary is $1,500.
We have,
To calculate the state income tax owed on a $40,000 per year salary, we need to use the progressive tax rate table given in the problem.
Since $40,000 falls within the income range of $10,001 to $50,000, the tax rate that applies is 5%.
The amount of income that falls within this range.
= $40,000 - $10,000
= $30,000.
So we can calculate the tax owed on this income as:
tax = 5% x $30,000
= 5/100 x 30,000
= $1,500
Therefore,
The state income tax owed on a $40,000 per year salary is $1,500.
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Answer: 1,800
Step-by-step explanation:
Given the two rectangles below. Find the area of the shaded region.
Answer:
The area of the shaded region is 36.
Step-by-step explanation:
First, let's find the area of the rectangle as a whole, which will be 5*10 = 50. How did we get 50? The right side is 5 (from 2+3), and the top is 10 (3+7). Multiplying those numbers together will give you the area.
Now, the problem asks to find the shaded region. Let's solve for the area of the non-shaded region: (7*2) = 14.
Now, we can subtract the whole rectangle area minus the non-shaded region to find the shaded region:
50 - 14 = 36
The zeros of the equation x^2 – 7 x – 8 = 0 are ?
What is the value of n ?
Answer:
n=10
Step-by-step explanation:
5n-20=3n
-20=-2n
10=n
12. What is the value of the following expression when
a = -2 and b = -4?
5(4a3b)+ ab
A-108
B -92
C -12
D12
E 28
Answer:
1st one is b. 2nd one is A
Step-by-step explanation:
i did the quiz
nathan is making blueberry and pineapple kebabs
Answer:yes umm tasty
Step-by-step explanation: water
What will be the result of substituting 2 for x in both expressions below?
+4
x+6-x-2
O Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.
O Both expressions equal 6 when substituting 2 for x because the expressions are equivalent.
O One expression equals 5 when substituting 2 for x, and the other equals 2 because the expressions are not
equivalent.
One expression equals 6 when substituting 2 for x, and the other equals 2 because the expressions are not
equivalent.
Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.
Equivalent Algebraic expressions:Algebra is the branch of mathematics that deals with numbers and values which are represented with letters and symbols.
Sometimes, we do not want to mention a particular number, we can represent the number by a letter or a suitable symbol. This approach is algebraic.
For example, d + d = 2d
This is an example of an algebraic expressionns.
Given the algebraic expressions,
\(\frac{1}{2}x + 4 \\ x + 6 - \frac{1}{2}x - 2\)
Substituting 2 for x in the first expression gives:
(1/2 × 2) + 4
1 + 4
5
Substituting 2 for x in the second expression gives:
2 + 6 - (1/2 ×2) - 2
8 - 1 - 2
8 - 3
5
Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.
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what should be subtracted from 7/12+7/8 to obtain the multiplicated inverse of (4/3-4/9)
To find the subtracted value, we need to calculate the multiplicative inverse of (4/3 - 4/9) and then subtract it from the sum of 7/12 and 7/8.
First, let's find the multiplicative inverse of (4/3 - 4/9):
Multiplicative inverse = 1 / (4/3 - 4/9)
To simplify the expression, we need a common denominator:
Multiplicative inverse = 1 / ((12/9) - (4/9))
= 1 / (8/9)
= 9/8
Now, we need to subtract the multiplicative inverse from the sum of 7/12 and 7/8:
Subtracted value = (7/12 + 7/8) - (9/8)
To perform this calculation, we need a common denominator:
Subtracted value = (7/12 * 2/2 + 7/8 * 3/3) - (9/8)
= (14/24 + 21/24) - (9/8)
= 35/24 - 9/8
To simplify further, we need a common denominator:
Subtracted value = (35/24 * 1/1) - (9/8 * 3/3)
= 35/24 - 27/24
= 8/24
= 1/3
Therefore, subtracting 1/3 from the sum of 7/12 and 7/8 will give you the multiplicative inverse of (4/3 - 4/9).
find two functions f and g
a. f(x) =
b. f(x) =
The functions f and g are:
a. f(x) = 1/x
b. g(x) = x + 2
a) To find two functions f and g such that (fog)(x) = 1/(x + 2), we need to determine how the composition of the two functions f and g produces the given expression.
Let's start by assuming g(x) = x + a, where a is a constant. This means that g(x) adds the constant a to the input x.
Next, let's determine the function f(x) such that (fog)(x) results in the desired expression. We have:
(fog)(x) = f(g(x)) = f(x + a)
b) To simplify the expression 1/(x + 2) and make it match f(g(x)), we can consider f(x) = 1/x.
Substituting the expressions for f(x) and g(x) into (fog)(x), we have:
(fog)(x) = f(g(x)) = f(x + a) = 1/(x + a)
Comparing this with the desired expression 1/(x + 2), we see that a = 2. Therefore, the functions f and g are:
a. f(x) = 1/x
b. g(x) = x + 2
Using these functions, we can verify the composition (fog)(x):
(fog)(x) = f(g(x)) = f(x + 2) = 1/(x + 2)
Thus, (fog)(x) = 1/(x + 2), which matches the desired expression.
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HELP ME PLEASE
I NEED HELP ASAP
IF IM ABLE TO GIVE OUT BRAINLIST THEN I WILL GIVE IT
The manager can find the volume of the container using the formula lwh. The employee correctly determines that the container can be filled with 3 layers of 21. He can find the volume of the container by multiplying the number of bento boxes that fill the container by the volume of one bento box. The volume found by using the formula is equal to the volume of the total numberof bento boxes in the container.
How to calculate the volume of a rectangular prism?In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:
Volume of a rectangular prism = LWH
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.Part a.
Therefore, the manager can use the following formula;
Volume of container = LWH
Volume of container = 7/2 × 3/2 × 3/2
Volume of container = 63/8 cm³.
Part b.
For the number of bento boxes that can fill the container, we have:
Number of bento boxes = Volume of container/Volume of bento boxes
Number of bento boxes = 63/8/(1/2)³
Number of bento boxes = 63/8/1/8
Number of bento boxes = 63/8 × 8
Number of bento boxes = 63 bento boxes = 3 layers × 21.
Part d.
Volume of container = Volume of bento boxes
63/8 cm³ = 63 × 1/8 cm³
63/8 cm³ = 63/8 cm³ (equal).
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In a recent survey of 36 people, 18 said that their favorite color of car was blue.
What percent of the people surveyed liked blue cars? Explain your answer with every step you took to get to it.
Answer: The percentage of people surveyed who liked blue cars is 50%.
Step-by-step explanation:
Total number of people partaking in survey= 36
number of people who like blue cars= 18
therefore, fraction of people who liked blue cars= \(\frac{18}{36}\)
hence, percentage of people who liked blue cars= (18/36)*100 %
= 50%
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Answer:
Percentage of people who like blue-coloured cars is 50%
Number of people who were surveyed=36
Number of people who like blue-colored cars=18
Therefore, Percentage of people who like blue cars= (Number of people who like blue cars/ Number of people who were surveyed)*100
=(18/36)*100
=50%
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The length of a rectangle is twice its width. Find its lenght and width, if its perimeter is 7 1/3 cm.
The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.
Let's assume the width of the rectangle is "b" cm.
According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.
The formula for the perimeter of a rectangle is given by:
Perimeter = 2 * (length + width)
Substituting the given perimeter value, we have:
7 1/3 cm = 2 * (2b + b)
To simplify the calculation, let's convert 7 1/3 to an improper fraction:
7 1/3 = (3*7 + 1)/3 = 22/3
Rewriting the equation:
22/3 = 2 * (3b)
Simplifying further:
22/3 = 6b
To solve for "b," we can divide both sides by 6:
b = (22/3) / 6 = 22/18 = 11/9 cm
Therefore, the width of the rectangle is 11/9 cm.
To find the length, we can substitute the width back into the equation:
Length = 2b = 2 * (11/9) = 22/9 cm
So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.
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Which of these is the correct ratio of strawberries to blueberries for the fruit salad?
A. 8 strawberries: 30 blueberries
B. 8 strawberries: 8 blueberries
C. 4 strawberries: 30 blueberries
D. 32 strawberries: 30 blueberries
The ratio of the strawberries to the blueberries is 32 strawberries: 30 blueberries (option d).
What is the ratio?
Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s). The sign that is used to represent ratio is :.
The ratio of strawberries to blueberries - total number of strawberries : total number of blueberries.
(8 x 4) : 30
32 : 30
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Answer: A. 8 strawberries: 30 blueberries
Step-by-step explanation:
Lines intersected by a transversal can never be parallel lines
true or false
Answer:
True.
Step-by-step explanation:
When two lines are crossed by a transversal, the interior angles between them will always add up to 180 degrees, which means they can never be parallel.
A map of an amusement park is shown on the coordinate plane with the approximate location of several rides.
coordinate plane with points at negative 14 comma 1 labeled Woozy Wheel, negative 6 comma 2 labeled Bumper Boats, negative 2 comma negative 4 labeled Roller Rail, negative 2 comma negative 6 labeled Trolley Train, 2 comma negative 3 labeled Silly Slide, and 6 comma 11 labeled Parachute Plunge
Determine the distance between the Bumper Boats and the Parachute Plunge.
15 units
225 units
8 units
63 units
Answer:the answer is 15 units
Step-by-step explanation:
just took the test
Prove that for any natural n: a the number 7^(n+4) −7^n is divisible by 30.
For, n = 0, 1 we proved that 7⁽ⁿ⁺⁴⁾ - 7ⁿ hence by induction it is divisible by 30 for all n ∈ N.
What is mathematical induction?An inductive proof requires two cases. The first, or base case, establishes the proposition that n = 0 without requiring any prior knowledge of other situations. The second example, the induction step, demonstrates that if the assertion is true for any particular case where n = k, then it must also be true for the subsequent case when n = k + 1. These two actions prove that the statement is true for all n = 1 natural numbers. The base case establishes the truth of the statement for all natural numbers n N, but it does not always start with n = 0. Instead, it frequently starts with n = 1, and it may also start with any fixed natural number n = N.
Given, We have to prove 7⁽ⁿ⁺⁴⁾ - 7ⁿ is divisible by 30 for all n ∈ N.
Let, n = 0.
Therefore,
7⁴ - 7⁰.
= 2401 - 1.
= 2400.
= 30×80, Divisible by 30.
Similarly for n = 1 we have,
7⁵ - 7¹.
= 16807 - 7.
= 16800.
= 30×560.
Hence by induction, the cycle will continue.
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A contractor can by two types of wood. she got 45 expensive wood and 60 cheap wood for the same total price. if the 45 expensive wood cost $3.00 more than the 60 cheap wood, then which equation below shows the correct relationship between the 2 types of wood that she purchased. Also (x =price of the 60 cheap wood)
A.45(x+3)=60x
B.45(x-3)=60x
C.60(x-3)=45x
D.60(x+3)=45x
The correct answer is,
C. 60(x - 3) = 45x.
This equation is based on the information that the 45 expensive wood costs $3.00 more than the 60 cheap wood. In other words, if the price of the 60 cheap wood is x, the price of the 45 expensive wood is x + 3.
Since, Algebra involves working with numbers, equations, and variables to solve real-world problems and understand abstract relationships.
Now, To solve this equation, we must use algebra and solve for x.
First, we multiply both sides of the equation by 4/5. This gives us:
48x + 36 = 45x
-36 = 3x
Finally, we divide left side of the equation by 3, giving us the final solution:
x = -12
Therefore, the price of the 60 cheap wood is $12, and the price of the 45 expensive wood is $15.
that is, 60 (x - 3) = 45x
This equation shows the correct relationship between the two types of wood that the contractor purchased.
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Indicate in standard form the equation of the line passing through the given point and having the given slope.
A(5,5), m=3
Answer:
-4,0 -4,0
Step-by-step explanation:
-4,0 -4,0
HELP QUICKLY!!!
Part A: Using computer software, a correlation coefficient of r 0.51 was calculated. Based on the scatter plot, is that an accurate value for this data? Why or why not? (5 points)
Part B: Instead of comparing the number of pumpkins picked and the day in October, write a scenario that would be a causal relationship for pumpkins picked on the farm.
Answer:
Step-by-step explanation:
For each of the following data sets, a. Create a scatterplot. b. Use LinReg (ax + b) to determine the best fit line and r. Does the line seem to accurately describe the pattern in the data? c. For each of the different choices listed in the above chart, find the equation of the best fit curve and its associated r2 value. Of all of the curves, which seems to provide the best fit? Note: The r2 -value reported in each case is NOT the linear correlation coefficient reported when running LinReg(ax+B) Rather, the value will typically change depending on the curve. The reason why is that each time, the -value is measuring how accurate the fit is between the data and that type of curve. A value r2 of close to 1 still corresponds to a good fit with whichever curve you are fitting to the data.