Answer:
[tex]\textsf{A)} \quad 5u^3-2u^2+5u+8[/tex]
Step-by-step explanation:
Given expression:
[tex](-2u^3+5u-1)+(7u^3-2u^2+9)[/tex]
Remove parentheses:
[tex]\implies -2u^3+5u-1+7u^3-2u^2+9[/tex]
Collect like terms:
[tex]\implies -2u^3+7u^3-2u^2+5u-1+9[/tex]
Combine like terms:
[tex]\implies 5u^3-2u^2+5u+8[/tex]
Option A
Is the graph increasing, decreasing, or constant?
Answer:
Decreasing
Step-by-step explanation:
Because the equation of that graph is Y=-X, and the - in the X represents that the graph is decreasing.
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Create a comparative box plot for the morning and afternoon dogs, and label each with its five-number summary.
Sara's dogs:
Morning:
39, 21, 12, 27, 23, 19, 19, 31, 36, 25
Afternoon:
15, 51, 8, 16, 43, 34, 27, 11, 8, 39
Answer:
see attached
Step-by-step explanation:
Morning:
12, 19, 19, 21, 23, 25, 27, 31, 36, 39
Min value: 12
Lower quartile (Q1): 19
Median (Q2): 24
Upper Quartile (Q3): 31
Max value: 39
Afternoon:
8, 8, 11, 15, 16, 27, 34, 39, 43, 51
Min value: 8
Lower quartile (Q1): 11
Median (Q2): 21.5
Upper Quartile (Q3): 39
Max value: 51
Answer:
7. AM IQR: 12 PM: IQR: 28 8. see below in explanation
Step-by-step explanation:
7. 31-19=12
39-11= 28
You subtract Q1 from Q3 to get the IQR.
8. I believe the morning group of dogs would be easier to walk as one group because the group has a closer range of weights (12-39) compared to the afternoon group of (8-51). Walking a large group of dogs with similar weights would be easier than walking a group of very small and very large dogs at the same time because their pace of walking would be so different.
Grandma baked 969696 cookies and gave them to her grandchildren. One of the grandchildren, Cindy, received ccc fewer cookies than she would have received had all of the cookies been evenly divided among the 888 grandchildren.
How many cookies did Cindy receive?
Cindy gets (12-c) amount while others get 12 cookies.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
From the question, we are informed that Grandma baked 96 cookies
And there are 8 grandchildren available
To calculate the number of cookies each of them gets we have,
= 96 /8
= 12 cookies
This means each gets 12 cookies
But Cindy received fewer cookies with less C amount.
Therefore Cindy gets (12-c) amount while others get 12 cookies.
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use the number line to find each product
- (3)(-3) =
Answer:
it's 9
Step-by-step explanation:
type it in a calculater
Calculate the perimeter of this shape.
5. (3.5pts) Given the equation y = y²x+2 cos(x) find . Show each step of your work.
dx
Answer:
[tex]\dfrac{dy}{dx}=\dfrac{y^2-2 \sin(x)}{1-2xy}[/tex]
Step-by-step explanation:
Given equation:
[tex]y=y^2x+2 \cos(x)[/tex]
To find the derivative of the given equation, use implicit differentiation.
Add d/dx in front of each term:
[tex]\dfrac{d}{dx}\:y =\dfrac{d}{dx}\:y^2x+\dfrac{d}{dx}\:2 \cos(x)[/tex]
Differentiate terms in x only (and constant terms) with respect to x:
[tex]\dfrac{d}{dx}\:y =\dfrac{d}{dx}\:y^2x-2 \sin(x)[/tex]
Use the chain rule to differentiate terms in y only:
(in practice this means to differentiate with respect to y then place dy/dx on the end)
[tex]\dfrac{dy}{dx}\: =\dfrac{d}{dx}\:y^2x-2 \sin(x)[/tex]
Use the product rule on the term in x and y:
[tex]\textsf{let }u=y^2 \implies \dfrac{du}{dx}=2y \dfrac{dy}{dx}[/tex]
[tex]\textsf{let }v=x \implies \dfrac{dv}{dx}=1[/tex]
[tex]\implies u\dfrac{dv}{dx}+v\dfrac{du}{dx}=y^2+2xy \dfrac{dy}{dx}[/tex]
Therefore:
[tex]\dfrac{dy}{dx} =y^2+2xy \dfrac{dy}{dx}-2 \sin(x)[/tex]
Rearrange to make dy/dx the subject:
[tex]\dfrac{dy}{dx}-2xy \dfrac{dy}{dx} =y^2-2 \sin(x)[/tex]
[tex]\dfrac{dy}{dx}(1-2xy)=y^2-2 \sin(x)[/tex]
[tex]\dfrac{dy}{dx}=\dfrac{y^2-2 \sin(x)}{1-2xy}[/tex]
PLEASE HELP!! I cant choose!
Tariq refuses to shoplift from the neighborhood store because he believes stealing is wrong. What concept is this an example of?
A) Self-efficacy
B) Empathy
C) Perspective
D) Ethics
Given:
AD = CB
DC = BA
Prove:
∠3 = ∠2
Which of the following triangle congruence theorems would be used in this proof?
ASA
AAS
SSS
The congruence theorem that can be used to prove that both triangles are congruent is: C. SSS.
What is the SSS Congruence Theorem?The SSS congruence theorem is a triangle theorem which states that two triangle are congruent if they have three pairs of corresponding sides that are congruent.
The triangles in the image given have the following three corresponding sides that are congruent:
AD ≅ CBDC ≅ BAAC ≅ CA (reflexive property)Therefore, the congruence theorem to prove they are congruent is: C. SSS.
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Use the following scenario to answer the question below:
You are deciding between two cars with different engines and want the bigger of the two. One engine displaces 350 cubic inches. The other displaces 5,500 cubic centimeters. How many significant figures do the values in this problem involve?
A. 4
B. 1
C. 3
D. 2
The bigger engine is about 235.5 cubic centimeters larger than the smaller engine.
We need the answer in cubic centimeters. So let's convert 350 cubic inches to cubic centimeters. We will do it unit conversion way (the long way).
We will write cubic inches as three inches side-by-side
350 in^3
What is the ratio of the centimeter?This way, we can multiply this by the ratio of centimeters to inches [2.54 cm = 1 inch], so that the units cancel and we have cubic centimeters (what we desire).
350 in^3*3.54cm/1in*3.54cm/1in*3.54cm/1in
So, we can cancel the three inches top and bottom thus we have the answer in centimeters cubed. And the value is
350 in^3*3.54cm/1in*3.54cm/1in*3.54cm/1in.
350 in^3*3.54cm/1in*3.54cm/1in*3.54cm/1in=5735.47.
So 350 cubic inches is approximately 5735.5 cubic centimeters (rounded to 1 decimal place).
This is larger than a 5500 cubic centimeters engine.
5735.5-5500=235.5cubic centimeters.
The bigger engine is about 235.5 cubic centimeters larger than the smaller engine.
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A triangular brace has an angle measure of 30 degrees, with a side opposite
this angle measuring 8 inches. The base of the triangular brace, which is
adjacent to the given angle measure, is 11 inches in length. Which of the
following statements is correct?
A. There is not a solution for the angle opposite the side measuring
11 inches.
B. The angle opposite the side measuring 11 inches has one solution
of approximately 43 degrees.
C. The angle opposite the side measuring 11 inches has one solution
of approximately 62 degrees.
D. The angle opposite the side measuring 11 inches, has two
solutions of approximately 43 degrees and 137 degrees.
The angle opposite the side measuring 11 inches has one solution of approximately 43°. Thus, the correct option is B.
What is Sine rule?The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. It is given by the formula,
[tex]\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ A}{\beta} =\dfrac{Sin\ A}{\gamma}[/tex]
where Sin A is the angle and α is the length of the side of the triangle opposite to angle A,
Sin B is the angle and β is the length of the side of the triangle opposite to angle B,
Sin C is the angle and γ is the length of the side of the triangle opposite to angle C.
Using the sine rule, the measurement of the angle of opposite the side measuring 11 inches can be done. Therefore, the measure can be written as,
8/ Sin(30°) = 11/ Sin(θ)
Sin(θ) = [11 × Sin(30°)]/8
Sin(θ) = 0.6875
θ = Sin⁻¹ (0.6875)
θ = 43.4325° ≈ 43°
Hence, The angle opposite the side measuring 11 inches has one solution of approximately 43°. Thus, the correct option is B.
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How many real solutions exist for this system of equations? y = x^2 + 4 y = 4x
Answer:
This system of equations has one real solution, (2, 8).
Step-by-step explanation:
Given:
y = x² + 4
y = 4x
1. Substitute the given value of y into y = x² + 4:
⇒ 4x = x² + 4
2. Solve for x (by factoring):
⇒ 4x = x² + 4
⇒ 0 = x² - 4x + 4
⇒ 0 = (x - 2)² [perfect square rule: a² -2ab + b² = (a - b)²]
⇒ 0 = (x - 2)² [take the square root of both sides]
⇒ [tex]\sqrt{0} = \sqrt{(x - 2)^2}[/tex]
⇒ 0 = x - 2 [add 2 to both sides]
⇒ 0 + 2 = x - 2 + 2
⇒ 2 = x
3. Find the value of y by substituting the given value of x into y = 4x:
⇒ y = 4(2)
⇒ y = 8
4. Check your work:
⇒ y = x² + 4 and ⇒ y = 4x
⇒ 8 = 2² + 4 and ⇒ 8 = 4(2)
⇒ 8 = 4 + 4 and ⇒ 8 = 8 ✔
⇒ 8 = 8 ✔
Solution: (x, y) ⇒ (2, 8)
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You are building a brick patio. the length of the patio is (x+11) feet.
the total area of the patio can be represented by x^2+14x+33. write an expression for the width of the patio
The expression that represents the width of the patio is (x+3) feet
Calculating areaFrom the question, we are to determine the width of the patio
The area of the patio = Length of the patio × Width of the patio
From the given information,
Length of the patio = (x+11) feet
Area of the patio = x^2+14x+33 = x²+14x+33
Putting the parameters into the formula,
x²+14x+33 = (x+11) × Width of the patio
∴ Width of the patio = (x²+14x+33) / (x+11)
First, we will factor x²+14x+33
x²+14x+33
x²+11x+3x+33
x(x+11) +3(x+11)
(x+3)(x+11)
Thus,
Width of the patio = [(x+3)(x+11)] / (x+11)
∴ Width of the patio = (x+3) feet
Hence, the expression that represents the width of the patio is (x+3) feet
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Which recursive formula can be used to generate the sequence below, where f(1) = 3 and n ≥ 1? 3, –6, 12, –24, 48, … f (n 1) = –3 f(n ) f (n 1) = 3 f(n ) f (n 1) = –2 f(n ) f (n 1) = 2 f(n)
The recursive formula will be equal to f(n + 1) = –2 f(n).
The complete question is given below:-
Which recursive formula can be used to generate the sequence below, where f(1) = 3 and n ≥ 1?
3, –6, 12, –24, 48, …
f (n + 1) = –3 f(n )
f (n + 1) = 3 f(n )
f (n + 1) = –2 f(n )
f (n + 1) = 2 f(n)
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
The recursive formula for this sequence is calculated as we will put the different values of n to find the values of the function in the series.
n = 1
f(n) = 3
n = 2
f(2) = -2 (3) = -6
n = 3
f(3) = -2 (-6) = 12 and so on
Therefore the recursive formula will be equal to f(n + 1) = –2 f(n).
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Elijah made 14 quarts of punch for a party. How many gallons of punch did he make?
Answer:
3.5 gallons of punch
Step-by-step explanation:
There are 4 quarts in 1 gallon.
Set up equation to convert 14 quarts to gallons: 14÷4 = 3.5.
Elijah made 3.5 gallons of punch.
he price of a used motorbike is 4975. Danny, a buys the motorbike for 3781. What is the discount percent given?
well, we know the discount is 4975 - 3781 = 1194.
if we take 4975 to be the 100%, what is 1194 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 4975 & 100\\ 1194& x \end{array} \implies \cfrac{4975}{1194}~~=~~\cfrac{100}{x}\implies \cfrac{26}{6}=\cfrac{100}{x} \\\\\\ 26x = 600\implies x=\cfrac{600}{26}\implies x\approx 23.08[/tex]
Answer:
0.76
Step-by-step explanation:
4975 × 0.76 = 3781
the discount percent given is .76%
What is the perimeter of WXYZ?
There are two triangles, triange WXZ and triangle YXZ having a common side XZ. The vertex W and vertex Y are on opposite sides of the side XZ. The length of the side WX is 15 and the length of the side XZ is 11. Angle ZWX is congruent to angle WXZ and all the angles of the triangle YXZ are congruent.
Its 48
33+15
Step-by-step explanation:11+11+11+15= Perimeter
33+15 = Perimeter
48 = Perimeter
A "golden rectangle” is a rectangle where the ratio of the longer side to the shorter side is the "golden ratio.” These rectangles are said to be visually pleasing. An example of a "golden rectangle” has a length equal to x units and a width equal to x – 1 units. Its area is 1 square unit. What is the length of this golden rectangle?
The length of the given golden rectangle is; 1.618 units
How to find the length of a golden triangle?We are told that, for the golden rectangle;
Length = x units,
Width = (x - 1) units,
Area = 1 unit².
The area of this rectangle will have the formula;
A = x(x - 1)
Thus;
x(x - 1) = 1
Expanding gives;
x² - x - 1 = 0
Using online quadratic equation calculator, we have;
x = 1.618 or -0.618.
Length has to be positive and so we choose x = 1.618
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Write the equation of a line that goes through point (0, −8) and has a slope of 0.
Answer: y = -8
Step-by-step explanation:
Lines that have a slope of Zero means that the line is horizontal and y is always the same. So your equation is y = -8
Answer:
y = - 8
Step-by-step explanation:
A line with a slope of 0 is a horizontal line parallel to the x- axis with equation
y = c ( c is the value of the y- coordinates the line passes through )
the line passes through (0, - 8 ) with y- coordinate - 8 , then
y = - 8 ← equation of line
The volume of a box is 143.4 in3. find the volume of a larger, similarly shaped box that has a scale factor of 3. round your answer to the nearest tenth.
3,871.8 in3
430 in3
1,290.6 in3
47.8 in3
Answer:
1,290.6 in3
nut.
???? please help lol
Answer:
150π ft²10π ft.Step-by-step explanation:
Area of the sector :
[tex]Area (sector) = \pi r^{2} \times \frac{\theta}{360^{o}}[/tex]
Finding the area given r = 30 ft. and θ = 60° :
⇒ Area = π × (30)² × 60/360
⇒ Area = π × 900/6
⇒ Area = 150π ft²
===========================================================
Length of the arc :
[tex]Length (arc) =2 \pi r} \times \frac{\theta}{360^{o}}[/tex]
Finding the arc length given r = 30 ft. and θ = 60° :
⇒ Arc Length = 2 × π × 30 × 60/360
⇒ Arc Length = 60/6 × π
⇒ Arc Length = 10π ft.
Answer:
1. 150π ft²
2. 10π ft²
Step-by-step explanation:
Hello there!
Here is how we solve the given problem:
Area of the sector of a circle refers to the fractional circle area. Which is given by; (∆°/360°) × πr². Where ∆° is the angle subtended by the arc.the arc length also refers to the length swept by the arc with angle theta (∆°) - subtended. Given byL = ∆°/360° ×2πr
From our problem,
∆ = 60°, r = 30ft
Lets substitute the values
1. A = (∆°/360°) × πr²
= 60°/360° × π × 30²
= 150π ft²
2. L = ∆°/360° × 2πr
= (60/360) × 2 × 30 × π
= 10π ft²
NOTE:
Use the formulas given below to be on a save side;
A = (∆°/360°) × πr² L = ∆°/360° × 2πr.I hope this helps.
Have a nice studies. :)
Lawrence poured 27.328 L of water into a right rectangular prism- shaped tank. The base of the tank is 40 cm by 28 cm. When he finished pouring the water, the tank was ⅔ full. ( 1L=1,000 cm 3).
By using the given dimensions and volume of water, we will see that the height of the tank is 36.6cm
How to find the height of the tank?We know that 27,238 cm³ is the volume of water on the tank, and this is equal to 2/3 of the volume of the tank.
So we can write:
27,238 cm³ = (2/3)*V
Then the volume of the tank is:
V = (3/2)*27,238 cm³ = 40,992 cm³
The base of the tank measures 40cm by 28cm, then:
B = 40cm*28cm = 1,120 cm²
Then the height H is such that:
H*1,120 cm² = 40,992 cm³
Solving for H:
H = (40,992 cm³)/(1,120 cm²) = 36.6cm
The height of the tank is 36.6 centimeters.
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What is the rate of change ( slope) for the given line
It’s extremely hard to tell, but it looks like it’s 3 over 2, which is 3/2.
3/2 is 1.5, or just 3/2. Since the line is going down, the slope would be negative, so -3/2.
Hope this helps!
Answer:
Step-by-step explanation:
-3/2 i think
THis might be wrong tho
Now Ann is x years old and her sister is eight years younger than her. After five years , Anne's age is twice the age of her sister.
Write down the ages of Anne and her sister after five years in terms of x.
Please help me friends
Answer:
You can refer to the given attachment
in a school of 330 students , 85 of them are in drama ,200 of them are in a sports teAM AND 60 OF THEM DO DRAMA AND SPORTS.
fIND THE PROBABILITY THAT A STUDENT CHOSEN AT RANDOM ISNT IN DRAMA OR SPORTS
THE PROBABILITY THAT A STUDENT CHOSEN AT RANDOM ISNT IN DRAMA OR SPORTS is 7/22.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
Let's denote students
D = in the drama club ,
S = in a sports team
So, P(D) = 85/330
P(S) = 200/330
P(D and S) = 60/300
P(D or S) = P(D) + P(S) - P(D and S)
P(D or S) = 85/330 + 200/330 - 60/330
P(D or S) = 15/22
P(neither D nor S) = 1- 15/22
P(neither D nor S) = 7/22
Thus, THE PROBABILITY THAT A STUDENT CHOSEN AT RANDOM ISNT IN DRAMA OR SPORTS is 7/22.
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Here is a diagram of a black circle inside a white square and a diagram of a small grey square inside a white square.
The two white squares are the same size.
AB = 8x.
The sides of the square are tangents to the circle at the points E, F, G and H.
W, X, Y and Z are the midpoints of AB, BC, CD and DA respectively.
Work out the ratio of the area of the black circle to the area of the white square to the area of the grey square. Give your answer in its simplest form.
Hi, I don't understand this. Can someone please explain? It's 50 points.
The ratio of the area of the black circle to the area of the white square to the area of the gray square is π : 4 : 2
How to determine the ratio of the areas?The side length AB is given as:
AB = 8x
The area of the white square is calculated as
White = (AB)²
This gives
White = (8x)²
Evaluate
White = 64x²
The side length AB represents the diameter of the black circle.
So, the radius is:
r =AB/2
This gives
r = 8x/2 = 4x
The area is then calculated as:
Circle = πr²
This gives
Circle = π(4x)²
Evaluate
Circle = 16πx²
Next, calculate AW and AZ using:
AZ = AW = AB/2
Evaluate
AZ = AW = 8x/2 = 4x
Calculate WZ using the following Pythagoras theorem
WZ² = AW² + AZ²
This gives
WZ² = (4x)² + (4x)²
Evaluate
WZ² = 2(4x)²
Take the square root of both sides
WZ = 4x√2
The area of the gray square is:
Gray = WZ²
This gives
Gray = 2(4x)²
Evaluate
Gray = 32x²
At this point, the areas are:
White = 64x²Circle = 16πx²Gray = 32x²The ratio is then represented as:
Ratio = Circle : White : Gray
This gives
Ratio = 16πx² : 64x² : 32x²
Divide through by 16x²
Ratio = π : 4 : 2
Hence, the ratio of the area of the black circle to the area of the white square to the area of the gray square is π : 4 : 2
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A(n) _________ is a statistical relationship between two variables, such that knowing one of the variables makes it possible to predict the other.
A correlation is a statistical relationship between two variables, such that knowing one of the variables makes it possible to predict the other.
What is correlation?A correlation can be defined as the relationship that exists between two variables when one of them is related to the other in some way.
It is also a measure that expresses the extent to which two variables are closely or linearly related which entails that they change together at a constant time.
Hence, correlation is a statistical relationship between two variables, such that knowing one of the variables makes it possible to predict the other.
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what is the domain of the function shown in the table. X {3, 5, 7, 9} Y {-4, -3, 3, 4}
Answer:3,5,7,9
Step-by-step explanation:I’m pretty sure all the inputs are the domains
There are 5 dessert courses in a restaurant. They will be presented two at a time in an order. How many different arrangements are there?
Answer:
3 I think.
Step-by-step explanation:
5 would be broken up to 2 groups of 2 and 1 group of 1.
In 20 different ways 5 dessert courses can be arranged taken 2 at a time.
What are permutation and combination?A permutation is an arrangement of things where order matters, AB and BA are two different permutations.
The combination is a selection of things where order does not matter, AB and BA are the same combinations.
Given, There are 5 dessert courses in a restaurant and they will be presented two at a time in an order.
Here we have to use permutation as order matters.
Now, the permutation of 5 different things taken 2 at a time is,
= [tex]^5P_2[/tex].
= 5!/(5 - 2)!.
= 5!/3!.
= 5 × 4.
= 20 different ways.
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How many solutions exist for each system of equations?
x + 2y = –1
2x + 3y = 0
Answer:
2 solutions x = 3 y = -2.
Step-by-step explanation:
x + 2y = –1
2x + 3y = 0
Multiply first equation by -2:
-2x - 4y = 2 Adding this to second equation:
- y = 2
y = -2.
Plug this into first equation:
x - 4 = -1
x = 3.
Translate the english phrase into an algebraic expression: the quotient of m and the sum of n and p.
enter all quotients as fractions.
The English phrase can be written as the fraction:
[tex]\frac{m}{n + p}[/tex]
How to write the algebraic expression?Remember that the quotient between two numbers gives a fraction.
Now, we have the sentence:
"the quotient of m and the sum of n and p."
Then we know that the numerator is m, and the denominator is (n + p) (the sum of n and p).
So the expression will just be the fraction:
[tex]\frac{m}{n + p}[/tex]
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