Answers
The difference of p and z times the sum of p and z is p² - 2pz - z².
How to represent expression?An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations such as addition, subtraction, division and multiplication.
Hence, the difference of p and z times the sum of p and z can be represented as follows:
Therefore,
(p - z) × (p + z) = (p - z) (p + z)
(p - z) (p + z) = p² - pz - pz - z²
p² - pz - pz - z² = p² - 2pz - z²
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Related Questions
graphing transformations
Answers
Each of the graphs should be matched with the appropriate function as follows;
Graph 1: D. f(x) = (x - 2)² + 3
Graph 2: C. f(x) = -(x - 2)² - 3
Graph 3: B. f(x) = -(x - 3)² - 2
Graph 4: C. f(x) = (x - 3)² + 2
What is the general form of a quadratic function?In Mathematics and Geometry, the standard or general form of a quadratic function can be modeled and represented by using the following quadratic equation;
y = ax² + bx + c
Where:
a and b represents the coefficients of the first and second term in the quadratic function.c represents the constant term.Mathematically, the vertex form of a quadratic function is modeled by this equation:
f(x) = a(x - h)² + k
Where:
h and k represents vertex of the graph.a represents leading coefficient.In conclusion, we can logically deduce that each of the given quadratic function were either vertically translated or horizontally translated.
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F(x) = 2^x
Elija todas las siguientes afirmaciones que describen el gráfico.
A. Cuando x tiende a infinito negativo, f(x) tiende a 0.
B. Cuando x tiende a infinito negativo, f(x) tiende a infinito.
OC. Cuando x tiende a infinito, f(x) tiende a 0.
OD. Cuando x tiende a infinito, f(x) tiende a infinito.
Answers
By analyzing the end behavior of the function we can see that the correct options are A and D.
Which statements are true for the given function?Here we have the exponential function:
[tex]F(x) = 2^x[/tex]
This is an exponential growth, this means that as x increases also does the function, then the end behavior of the function is:
as x → ∞, f(x) → ∞
And when x is a really large negative number, the function tends to zero, then we have:
as x →-∞, f(x) → 0
Then the correct options are A and D.
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10+x/2 evaluate the expression for givin values of the variable
Answers
The value of the expression when x = 4 is 12.
The value of the expression when x = -8 is 6.
We have,
To evaluate the expression 10 + x/2 for a given value of the variable x, we simply substitute the value of x into the expression and simplify.
For example:
If x = 4:
10 + x/2 = 10 + 4/2
= 10 + 2
= 12
So when x = 4, the value of the expression is 12.
If x = -8:
10 + x/2 = 10 + (-8)/2
= 10 - 4
= 6
So when x = -8, the value of the expression is 6.
Thus,
The value of the expression when x = 4 is 12.
The value of the expression when x = -8 is 6.
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Piedmont Hotels is an all-equity company. Its stock has a beta of 1.29. The market risk premium is 7.2 percent and the risk-free rate is 3.0 percent. The company is considering a project that it considers riskier than its current operations so it wants to apply an adjustment of 2.2 percent to the project's discount rate. What should the firm set as the required rate of return for the project?
Answers
The firm set 14.49% as the required rate of return for the project.
What is the required rate of return for Piedmont Hotels' riskier project?We will first calculate the Project's discount rate which can we calculated using the formula that:
= Rf rate + Beta*risk premium
= 3.0% + 1.29*7.2%
= 3.0% + 0.09288
= 0.12288
= 12.29%
The required rate of return for the project will be:
= Project's discount rate + Adjustment rate
= 12.29% + 2.2%
= 14.49%
Thus, the firm set 14.49% as the required rate of return for the project.
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A 138 foot antenna is on top of the top of a tall building. From a point on the ground, the angle of elevation to the top of the antenna is 30.5ﾟ while the angle of elevation to the bottom of of the antenna from the same point is 23.5ﾟHow tall is the building
Answers
Answer:
289
Step-by-step explanation:
Let's call the height of the building "h" and the distance from the point on the ground to the base of the building "d".
From the point on the ground, the distance to the top of the antenna is d + 138, and the distance to the bottom of the antenna is d.
Using trigonometry, we can set up two equations:
tan(30.5°) = (d + 138) / h (1)
tan(23.5°) = d / h (2)
We can solve equation (2) for d:
d = h tan(23.5°)
Substituting this into equation (1), we get:
tan(30.5°) = (h tan(23.5°) + 138) / h
Simplifying:
tan(30.5°) = tan(23.5°) + 138/h
tan(30.5°) - tan(23.5°) = 138/h
h = 138 / (tan(30.5°) - tan(23.5°)) ≈ 289.12 feet
Therefore, the height of the building is approximately 289.12 feet.
i need help with this prblem
Answers
Answer:
y = x + 2
Step-by-step explanation:
y = mx + b
Point (0, 2) shows that the y-intercept is 2, so b = 2.
y = mx + 2
Now we find the slope using the 2 points, (0, 2) and (2, 4).
m = (4 - 2)/(2 - 0) = 1
y = x + 2
15.Marla and Kelly purchased flowers. Marla
purchased 7 roses for x dollars each and 10
daisies for y dollars each. She spent $40.50 on
the flowers. Kelly bought 3 roses and 15
daisies at the same cost as Marla. She spent
$30.75 on her flowers. The system of
equations below represents this situation.
7x+10y = 40.5
3x + 15y = 30.75
Which statement below is correct?
Answers
A statement which is correct include the following: A. Roses cost $2.75 more than daisies.
How to write an equation to model this situation?In order to write a system of linear equations to describe this situation, we would assign variables to the cost of roses and cost of daisies, and then translate the word problem into a linear equation as follows:
Let the variable x represent the cost of roses.Let the variable y represent the cost of daisies.Based on the information provided about the flowers purchased by Marla and Kelly. we have the following system of linear equations;
7x + 10y = 40.5
3x + 15y = 30.75
By solving the system of linear equations simultaneously, we have:
x = 4 and y = 1.25
Difference = 4 - 1.25
Difference = $2.75
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Simplify: 9-4x³ +2x² +8x³ +1+6x²
Answers
Answer:
it can be simplify as follows:
1. Quadrilateral LBMN is the result of a 180 degree rotation of Quadrilateral ABCD around point B, write the corresponding angles and segments in the table below.
Answers
In the quadrilateral ABCD and LBNM the corresponding angles and line segments are as follow,
∠A = ∠L, ∠D =∠M , ∠C = ∠N , and
AB = LB , CD = NM , DA = ML.
Quadrilateral ABCD rotates 180 degrees around point B,
New quadrilateral formed named LBMN
The corresponding angle after rotation of 180 degrees around B is equals to,
B remain at same position.
A rotates and point L take the position of A.
D rotates and point M take the position of D.
C rotates and point N take the position of C.
Corresponding angle to A is angle L.
Corresponding angle to D is angle M.
Corresponding angle to C is angle N.
Similarly corresponding segments are of ABCD and LBNM are
Line segment AB corresponds to line segment LB.
Line segment CD corresponds to line segment NM
Line segment DA corresponds to line segment ML.
Therefore, in the quadrilateral the corresponding angles and line segments are ∠A = ∠L, ∠D =∠M , ∠C = ∠N , AB = LB , CD = NM , and DA = ML.
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This is for math nation unit 1 please help!!
Answers
Answer: it’s C, cubic
Step-by-step explanation:
Answer:
[C] Cubic
Step-by-step explanation:
Let find define all the answer choices:
Linear- Straight Line
Quadratic - shape of a U or an upside down U
Cubic - trivalent graphs, are graphs all of whose nodes have degree 3
Exponential- curve that has a horizontal asymptote and it either has an increasing slope or a decreasing
As a result, the graph given is a Cubic graph.
RevyBreeze
Lisa is putting colored 11 light bulbs into a string of lights. There are 3 red light bulbs, 2 yellow light bulbs, and 6 pink light bulbs. How many distinct orders of light bulbs are there if two light bulbs of the same color are considered identical (not distinct)?
Answers
The distinct orders of light bulbs are there if two light bulbs of the same color are considered identical = 4,620
Here, the total number of bulbs = 11
The number of red light bulbs = 3
The number of yellow light bulbs = 2
and the number of pink light bulbs = 6
We know that the formula for the permutation with repetition is:
n! / (n1! × n2! x ... × nk!)
We use this formula to find the required number of light bulbs.
Here, two light bulbs of the same color are considered identical
We divide by 3! in order to adjust for overcounting, because we have 3 red light bulbs.
simmilarly for the 2 yellow light bulbs, we divide with 2!.
and for the 6 pink light bulbs, we divide by 6!
Thus, the total number of distinct orders of bulbs will be:
11! / (3! × 2! × 6!) = 4,620
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Enter the correct answer in the box.
What is the factored form of this expression?
2x^3+5x^2+6x+15
Write all factors in standard form.
Answers
Answer:
(2x + 5)(x² + 3)------------------
Given expression:
2x³ + 5x² + 6x + 15Group the expression as below and factorize:
2x³ + 5x² + 6x + 15 = (2x³ + 5x²) + (6x + 15) =x²(2x + 5) + 3(2x + 5) = (2x + 5)(x² + 3)Hence the factored form of the expression is (2x + 5)(x² + 3).
The factored form of the expression is,
⇒ (2x + 5)(x² + 3).
Given that;'
The expression is,
⇒ 2x³ + 5x² + 6x + 15
Now, Group the expression as below and factorize:
2x³ + 5x² + 6x + 15
(2x³ + 5x²) + (6x + 15)
x²(2x + 5) + 3(2x + 5)
(2x + 5)(x² + 3)
Hence, the factored form of the expression is (2x + 5)(x² + 3).
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One month Eric rented 3 movies and 5 video games for a total of $34. The next month he rented 9 movies and 7 video games for a total of $56. Find the rental
cost for each movie and each video game.
Rental cost for each movie:
Rental cost for each video game:
G
O
G
Answers
movies 1.75 each
games 5.75 each
Can someone please help me with this, it’s super confusing and I can’t find help anywhere
Answers
Answer:
Step-by-step explanation:
ask ur teacher
Find the area and perimeter of the triangle.
8m
3m
9m
4m
Answers
Answer: Broken Math Problem
Step-by-step explanation:
Lily Starbright, a singer-songwriter, released her first album at the beginning of March. By the
end of March, she had sold 1,040 copies. In April, she sold 1,352 copies. Several of the songs
on the album are now trending, so Lily expects her sales to continue to increase.
Write an exponential equation in the form ya(b) that can model the expected monthly
number of albums sold, y, x months after release.
Answers
Answer: 1040
Step-by-step explanation: y=ab
The exponential equation is: y = 1040(1.3^x)
How to solve
Calculate the value of y, which stands for the albums sold, and x represents the months passed from their release. For an exponential equation structured as y = a(b^x), identify the base b to solve it mathematically.
By analyzing the last month after launch, known as March, 1040 copies were made available for public consumption. One month further down the line, in April, the gross profit jumped up to 1352 units sold.
When we divide the copies traded throughout April by those resold in March, the value identifies the base:
b=1352/1040 ≈ 1.3
Thus, applying the coefficient a for the initial sales registered during March - totaling 1,040 copies - leads us to define the following form for our equations:
y = 1040(1.3^x)
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cant be that hard but i didnt pay attention
Answers
∠ AFE is supplementary to ∠ AFB and the measure of ∠ AFE = 102⁰.
option A.
What is a supplementary?Supplementary angles are the two angles that sum up to 180 degrees.
That is, if the sum of two angles is equal to 180 degrees, then the two angles are supplementary.
From the given diagram we can form the following equation;
∠ AFE + ∠ AFB = 180 (supplementary angles or sum of angles on a straight line )
∠ AFE = 180 - ∠ AFB
∠ AFE = 180 - 78
∠ AFE = 102⁰.
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An article is sold for Rs.150 at a gain. Had it been sold for Rs.135 there would have been a loss equal to 50% of the original gain. Find the cost price of the article.
Answers
The cost price of the article, which is sold for Rs. 150 at a gain but if sold for Rs. 135 would have resulted in a loss equal to 50% of the original gain, is Rs. 127.50.
How the cost of the article is determined:The cost price is the difference between the selling price and the profit or gain.
The difference is determined by subtraction.
Selling price of the article = Rs. 150
Loss if sold at Rs. 135 = 50% of the original gain
Original gain = Rs. 15 (Rs. 150 - Rs. 135)
50% of the original gain = Rs. 7.50 (Rs. 15 x 50%)
Cost price of the article = Rs. 127.50 (Rs. 135 - Rs. 7.50)
Thus, the cost price is Rs. 127.50.
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Mark bought 55 lbs of clay for his art projects. He used 12.4 lbs to make a sculpture, and 0.75 lbs for each mug. How many mugs did Mark make if he had 32.85 lbs of clay left over?
Answers
If Mark used 12.4 lbs to make a sculpture, and 0.75 lbs for each mug then the number of mugs he can make is 57.
Mark bought 55 lbs of clay for his art projects
He used 12.4 lbs to make a sculpture
The left over clay is 55-12.4 = 42.6
We know that 0.75 lbs for each mug
We have to find the number of mugs he can make from left over clay
To find this we have to divide 42.6 by 0.75
Number of mugs = 42.6/0.75
=56.8
=57
Hence, if Mark used 12.4 lbs to make a sculpture, and 0.75 lbs for each mug then the number of mugs he can make is 57.
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PLEASE HELP
Part A:
List the three different types of visuals we use to organize all the possible outcomes in a sample space
1
2
3.
Part B:
Leena is arranging 3 different books in a row on a shelf. A detective story (D), a mystery story (M), and a comic book (C)
1. Pick one of the three types of visuals you listed in Part A to create a sample space for the arrangement of all possible outcomes for arranging the 3 books on a shelf. (1 point)
Fill in the Blank I will choose to create a
for this scenario
2. Create your visual either by hand or using technology
Answers
The three different types of visuals we use to organize all the possible outcomes in a sample space are:
Tree DiagramsTablesVenn DiagramsHow to explain the informationFor the second part of the question, select one of the three styles of graphical representation you listed in Part A to make a sample space for all probable results for putting the 3 books on a rack.
The table will show every feasible end result for setting up the 3 books on a rack.
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3
2
A ABC with vertices at A (-1, -1). B (4,-4), and C (2, -6) is dilated by a scale factor of
create A A'B'C'.
The center of dilation is the point (5,
(5,
-6).
What are the coordinates of vertex.
B'₂
Enter your answers, as decimals, in the boxes.
9
Answers
The coordinates of vertex B' are (76, -86).
What is a dilation?In Mathematics and Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.
Next, we would have to dilate the coordinates of the preimage by using a scale factor of 9 centered at the point D (-5, 5) by using this mathematical expression:
(x, y) → (k(x - a) + a, k(y - b) + b)
For coordinate B, we have;
Coordinate B = (4, -4) → (9(4 - (-5)) + (-5), 9(-4 - 5) + (-5))
Coordinate B = (4, -4) → (9(9) - 5, 9(-9) - 5)
Coordinate B = (4, -4) → (81 - 5, -81 - 5)
Coordinate B' = (76, -86).
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Complete Question:
ΔABC with vertices at A (-1, -1). B (4,-4), and C (2, -6) is dilated by a scale factor of 9 to create ΔA'B'C'. The center of dilation is the point (5, -6).
What are the coordinates of vertex B'?
A plane takes off at a 10 degree angle. How far away is the plane (ground distance) once it reaches an altitude (height) of 30,000 feet?
We are missing a side or and angle? Regular or Inverse Trig?
Answers
The ground distance of the plane is 170,138.5 ft.
What is the ground distance of the plane?
The ground distance of the plane is calculated by applying trigonometry ratio as shown below;
SOH CAH TOA
SOH = sin θ = opposite /hypothenuse side
TOA = tan θ = opposite side / adjacent side
CAH = cos θ = adjacent side / hypothenuse side
The height attained by the plane is the opposite side, while the ground distance is the adjacent side
tan (10) = 30,000 ft/d
d = 30,000 ft/tan(10)
d = 170,138.5 ft
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Dean ran 2.3 fewer kilometers than Sam. If Dean ran 6.8 km, how far did Sam run?
A 2-column table with 4 rows. Column 1 is labeled Situation with entries increasing, difference, finding part of a total, sharing or grouping. Column 2 is labeled Operation with entries +, minus, times, divided by.
Select all that apply.
You know the difference in the distances the boys ran, so this is a subtraction problem.
You are finding the total distance the boys ran, so this is an addition problem.
Dean ran part of the distance Sam ran, so this is a multiplication problem.
The correct equation is s + 2.3 = 6.8.
The correct equation is s – 2.3 = 6.8.
The correct equation is 2.3s = 6.8.
Answers
Answer:
A,E
Step-by-step explanation:
Operation: Minus
To find how far Sam ran, we need to subtract 2.3 from Dean's distance of 6.8 km.
6.8 km - 2.3 km = 4.5 km
Therefore, Sam ran 4.5 km, since Dean ran 2.3 km fewer than Sam.
Answer:
a and e
Step-by-step explanation:
got it right on homework
The velocity v of a meteorite approaching earth is givin by v=k/
Answers
The velocity of the meteorite is 4 km per sec.
Given that, a meteorite is approaching the earth and is 10000 km away from earth,
we need to find the velocity,
v = k / √d
v = 400 / √10000
v = 400 / 100
v = 4 km per sec.
Hence, the velocity of the meteorite is 4 km per sec.
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The velocity at a distance of 6,889 kilometers is 6.795 Km/ sec.
We have,
The velocity v of a meteorite approaching earth is V = k/√d.
The distance from center of Earth = 8836
and, Velocity = 6 Km/ s
So, using the formula for velocity
6 = k/√8836
6 = k/94
k= 564 Km
Now, velocity at 6689 Km
V = 564/ √6889
V =6.795 km/sec
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According to a National Center for Health Statistics, the lifetime odds in favor of dying from heart disease are 1 to 5, so the probability of dying from heart disease is
.
Answers
The probability of dying from heart disease is 0.1667 or 16.67%.
The odds in favor of an event are defined as the ratio of the probability of the event occurring to the probability of the event not occurring. In this case, the odds in favor of dying from heart disease are 1 to 5.
So, we can set up the following equation:
Odds in favor of dying from heart disease = probability of dying / probability of not dying
1/5 = probability of dying / probability of not dying
We can solve for the probability of dying by cross-multiplying:
probability of dying = odds in favor of dying from heart disease / (odds in favor of dying from heart disease + 1)
probability of dying = 1 / (1 + 5)
probability of dying = 1/6
Therefore, the probability of dying from heart disease is 0.1667 or 16.67%.
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I NEED HELP RIGHT AWAY WITH 3 4 5 and 6
Answers
1. AB is a tangent, the triangle is a right triangle
2. AB is not a tangent, the triangle is not a right triangle and hence not a Pythagorean triple
3. arc RS = 100 degrees
4. arc ST = 80 degrees
5. arc RTS = 260 degrees
6. arc RST = 180degrees
7. x = 3
8. x = 7
How to determine whether AB is a tangentA tangent will obey Pythagorean triple hence we have that
AB^2 = AC^2 + BC^2
1. AB^2 = 24^2 + 10^2 = 676
AB = sqrt (676) = 26. hence AB is a tangent
2. AB^2 = 8^2 + 11^2 = 185
AB = sqrt (185) = 13.6. hence AB is not a tangent
Length of arc
3. arc RS = 100 degrees (central angle equals intercepted arc)
4. arc ST = 180 - arc RS = 180 - 100 = 80 degrees
5. arc RTS = 180 + arc ST = 180 + 80 = 260 degrees
6. arc RST = 180degrees (semicircle)
Value of x
7. x + 8 = 5x - 4
8 + 4 = 5x - x
12 = 4x
x = 3
8. 4x + 5 = 6x - 9
4x - 6x = -9 - 5
-2x = -14
x = 7
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Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function.
y''-5y'=δ(t-1), y(0)=7, y'(0)=0.
a.) Find the Laplace transform of the solution.
b.) obtain the solution y(t)
c.)express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t=1.
Answers
The laplace transform is Y(s) = (7 + e^{-s}/s) / (s² - 5s)
The solution y(t) is y(t) = (-e^{5-t} + 2e^{-5} - 6(t-1) + 7u(t-1))/25.
The solution can be expressed as a piecewise-defined function:
y(t) = -e^{5-t}/25 + 2e^{-5}/25 - 6(t-1)/25 + 7/25, t < 1
y(t) = -e^{5-t}/25 + 2e^{-5}/25 - 6(t-1)/25 + 7/25 + (t-1)/25, t ≥ 1
We have,
a.)
To find the Laplace transform of the solution, we first take the Laplace transform of both sides of the differential equation using the initial value theorem, which states that the Laplace transform of the derivative of a function y(t) is sY(s) - y(0):
s²Y(s) - s y(0) - y'(0) - 5(sY(s) - y(0)) = e^{-s}
Simplifying and solving for Y(s), we get:
Y(s) = (7 + e^{-s}/s) / (s² - 5s)
b.)
To obtain the solution y(t), we use partial fraction decomposition to separate Y(s) into two terms:
Y(s) = A/(s-5) + B/s + C/(s-5)^2
Multiplying both sides by the denominator, we get:
7 + e^{-s}/s = A(s-5)² + Bs (s - 5) + C(s)
Setting s = 0, we get:
7 = 25A - 5B + 0C
Setting s = 5, we get:
7 + e^{-5}/5 = 0A + 5B + 5C
Taking the derivative with respect to s and setting s=0, we get:
0 = 10A - B
Solving these equations, we get:
A = -1/25
B = -2/5
C = 6/25
Therefore, the solution y(t) is:
y(t) = (-e^{5-t} + 2e^{-5} - 6(t-1) + 7u(t-1))/25
Where u(t) is the unit step function.
c.)
The solution can be expressed as a piecewise-defined function as follows:
y(t) = -e^{5-t}/25 + 2e^{-5}/25 - 6(t-1)/25 + 7/25, t < 1
y(t) = -e^{5-t}/25 + 2e^{-5}/25 - 6(t-1)/25 + 7/25 + (t-1)/25, t ≥ 1
At t = 1, there is a discontinuity in the first derivative of the solution due to the presence of the delta function in the original differential equation.
This causes a sudden jump in the slope of the graph of the solution.
Thus,
The laplace transform is Y(s) = (7 + e^{-s}/s) / (s² - 5s)
The solution y(t) is y(t) = (-e^{5-t} + 2e^{-5} - 6(t-1) + 7u(t-1))/25.
The solution can be expressed as a piecewise-defined function as:
y(t) = -e^{5-t}/25 + 2e^{-5}/25 - 6(t-1)/25 + 7/25, t < 1
y(t) = -e^{5-t}/25 + 2e^{-5}/25 - 6(t-1)/25 + 7/25 + (t-1)/25, t ≥ 1
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What is the value of x in the equation 4x+2x-3=15?
Answers
Answer:
x = 3
Step-by-step explanation:
4x + 2x - 3 = 15 ← collect like terms on left side
6x - 3 = 15 ( add 3 to both sides )
6x = 18 ( divide both sides by 6 )
x = 3
Answer:
x=3
Step-by-step explanation:
You can start of by adding 4x and 2x because they both share the same variable "x". Now you have 6x-3=15. Using the addition property of equality, you can add 3 on both sides of the equation to cancel it out. You are left with 6x=18. Divide both sides by 6 and that leaves you with x=3
Round to the nearest tenth, then find the difference. 13.56 − 10.02 = ___ pleas help in test and am about to leave soon.
Answers
The difference between 13.56 and 10.02 is 3.54.
What is subtraction?Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.
The difference between 13.56 and 10.02 can be calculated by doing the subtraction. As,
(13 + 0.56) - (10 + 0.02)
= (13 - 10) + (0.56 - 0.02)
= 3 + 0.54
= 3.54
Learn more about Subtraction here:
https://brainly.com/question/1927340
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It's a beautiful fall day! Mari and her friends decide to have a picnic in the park. Each friend is bringing something to eat or drink. Mari is bringing watermelon. Before she leaves her house, Mari cuts a watermelon into 16 equal pieces. At the picnic, she eats 3 pieces of watermelon.What fraction of the watermelon does Mari eat?
