The trinomial and binomial form of the incomplete algebraic expression is [tex]d^{2}[/tex] -3d + 9/4 and [tex](d-\frac{3}{2}) ^{2}[/tex]
What is a perfect square expression?A perfect square is a quadratic expression that factors into two identical binomials.
For example, if you multiply these two identical binomials factors:
(x + 2)(x + 2)
to complete the square in the expression [tex]d^{2}[/tex] -3d, we square the half of the coefficient of d which is -3/2
so the expression becomes,
[tex]d^{2}[/tex] -3d + [tex](\frac{-3}{2}) ^{2}[/tex] = [tex]d^{2}[/tex] -3d +[tex]\frac{9}{4}[/tex]
The Binomial form of the expression [tex]d^{2}[/tex] -3d + [tex](\frac{-3}{2}) ^{2}[/tex]
can be written by take [tex]d^{2}[/tex] term and the constant and putting them in a bracket and squaring
which becomes
[tex](d - \frac{3}{2} )^{2}[/tex]
In conclusion, the trinomial form of the expression is [tex]d^{2}[/tex] -3d +[tex]\frac{9}{4}[/tex] while the Binomial form of the expression is [tex](d - \frac{3}{2} )^{2}[/tex]
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Two systems of equations are given below.
For each system, choose the best description of its solution.
If applicable, give the solution.
System A
−x2y = 6
+−x+2y6 = 0
We solved the system of equations graphically by graphing both equations and identifying the intercept.
The solution is:
(2.41, -1.03)
How to solve the system of equations?Here we have only one system of equations, which is:
-x²*y = 6
-x + 2y⁶ = 0
There are multiple ways of solving this, for example, we could isolate the variable "y" on the first equation:
y = -6/x^2
And replace that in the second equation, so we have an equation that only depends on x, but there is an easier way.
We can just graph both equations on the same coordinate axis and see in which points do the graphs intercept. Each intercept will be a solution of the system.
The graph can be seen below, there we can see that the only intersection point is at (2.41, -1.03), so that is the solution of the system.
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Solve for a : a+4/5= 1/ 1/2
[tex]a=\frac{6}{5}[/tex].
Step-by-step explanation:1. Write the expression.[tex]a+\frac{4}{5} =\frac{1}{\frac{1}{2} }[/tex]
2. Convert the right hand side of the equation (check attached image 1).[tex]a+\frac{4}{5} =1*\frac{2}{1} \\ \\a+\frac{4}{5} =2[/tex]
3. Subtract 4/5 from both sides of the equation.[tex]a+\frac{4}{5}-\frac{4}{5} =2-\frac{4}{5}\\ \\a=\frac{2}{1}-\frac{4}{5}\\\\a=\frac{2*5}{1*5}-\frac{4}{5}\\ \\a=\frac{10}{5}-\frac{4}{5}\\ \\a=\frac{10-4}{5} \\ \\a=\frac{6}{5}[/tex]
4. Verify your answer.[tex](\frac{6}{5} )+\frac{4}{5} =\frac{1}{\frac{1}{2} }\\ \\\frac{10}{5} =2\\ \\2=2[/tex]
5. Conclude.[tex]a=\frac{6}{5}[/tex].
un edificio de 60 pisos tiene 1,92 hectómetros de altura. ¿qué altura en metros tiene cada piso, si todos poseen la misma altura?
Answer:
La altura en metros de cada piso es:
3.2 metros
Step-by-step explanation:
1 hectómetro = 100 metros.
1.92 metros = 1.92 * 100 = 192 m
192/60 = 3.2 metros/piso
Write an equation for line L in point-slope form and slope-intercept form.
L is parallel to y = 5x.
-6
-4
-2
Ay = 5x
6-
4
2
-6
L
(3,2)
6
X
5
Please Help 2
Find (f/g)(x) if f(x)=x2+x+1 and g(x)=-x2-x-1
Answer:
-1
Step-by-step explanation:
Take -1 as common form the denominator then cancel out the whole term i.e x²-x-1 and -1 remains.
The average daily profit of an electronics store is $31,435. The company estimates that 15% is lost each day to returns, with a margin of error of ±4%. What is the maximum the company can expect for returned items?
$3457.85
$4621.13
$5972.65
$6638.22
Answer:
Step-by-step explanation:
The maximum that the company can expect for returned items is C. $5972.65
How to calculate the value?
From the information, the average daily profit of an electronics store is $31,435 and the company estimates that 15% is lost each day to returns, with a margin of error of ±4%.
In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings. Simply said, you may determine the degree of unpredictability in data and research results using the margin of error.
The maximum the company can expect for returned items will be:
= (15% + 4%) × Profit
= 19% × $31,435
= 0.19 × $31,435
= $5972.65
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The function f(x) is graphed below. How many points on the graph
represent a relative extreme value?
From the given graph of the function, the number of points on the graph representing relative extreme value are two (b and d).
As given in the question,
For the given graph of a function,
Number of points represented on the graph are 5
Points are a, b, c, d, e
Point a, c, e are on the x-axis.
Relative extreme value representing the maximum and minimum value of the graphed function.
For the given graph,
Maximum value represented by point d.
Minimum value represented by point b.
Number of points representing relative extreme values are 2 ( b and d).
Therefore, from the given graph of the function, the number of points on the graph representing relative extreme value are two (b and d).
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What is the slope of the line that passes through the points (1, 6) and (1, 31)? Write
your answer in simplest form.
The slope of the line that passes through the points (1, 6) and (1, 31) is, ∞
What is slope?Slope is a ratio of change in y-coordinate w.r.t. change in x-coordinate. The net change in y coordinate is written as, Δy and the net change in x coordinate is written as, Δx.
So formula for the slope is,
m = change in y coordinate/change in x coordinate = Δy/Δx = y₂-y₁/x₂-x₁
Given that,
the line passes through the points, (1,6) and (1,31)
So, we can calculate slope for the line by using formula when two are given,
m = y₂-y₁/x₂-x₁
x₁ = 1
y₁ = 6
x₂ = 1
y₂ = 31
m = 31-(6)/1-1
m ≈ ∞
Therefore, The line is parallel to y-axis
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−18 < 9x
how to solve and answer
Answer:
x> 2
Step-by-step explanation:
18< 9x Divide both sides by 9
2<x or x > 2 All the numbers greater than 2 is a solution.
An advertiser goes to a printer and is charged $42 for 50 copies of one flyer and $61 for 150 copies of another flyer. The printer charges a fixed setup cost plus a charge for every copy of single-page flyers. Find a function that describes the cost of a printing job, if is the number of copies made. C(x) =
Answer:
c(x) = .19x + 32.50
Step-by-step explanation:
The cost depends on the number of copies. The x value is the number of copies and the y value is the cost
c(x) = mx + b We need to find the rate of change.
(50,42) (150.61) The rate of change is the change in y over the change in x.
The y values are 61 and 42. The x values are 150 and 50
[tex]\frac{61-42}{150-50}[/tex] = [tex]\frac{19}{100}[/tex] = .19
We also need the y intercept. We will use the slope of .19 and the x and y values of one of the points. We could use either point, I am going to use the point (50,42)
y = 42
x = 50
m =.19
y=mx + b
42 = .19(50) + b
42 = 9.5 + b Subtract 9.5 from both sides
32.50 = b
y = mx + b
y = .19x + 32.50 or
c(x) = .19x + 32.50
Suppose that the function fis defined, for all real numbers, as follows.
f(x)
-2 if x #2
4 if x=2
Find f(-1), f(2), and f(5).
f (-1)
f(2)
f(5)
The value of the functions f(-1), f(2), and f(5) are -2, 4, -2 respectively.
What is the function?
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). The number of dependent variables for a function is 1 and the number of independent variable for a function is 1.
Given function is:
[tex]f(x)=\left\{\begin{matrix}-2 & \text{if } x \ne2 \\ 4 & \text{if } x=2\end{matrix}\right.[/tex]
The meaning of the above function is when x is not equal 2, then the value of f(x) is -2 and when x is equal 2, then the value of f(x) is 4.
The dependent variable is f(x). The independent variable is x.
So the value of f(-1) is -2 since x = - 1 ≠ 2.
So the value of f(2) is 4 since x = 2.
So the value of f(5) is -2 since x = 5 ≠ 2.
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could you describe the expression 2(3+4) as a product of two factors explain
The expression 2(3+4) can be expressed as 2×7
What are factors?A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.
For example the factors of 8 are 1,2,4,8. i.e 1×8=8, 2×4= 8
considering the expression 2(3+4), the value is 2(7)= 14
Therefore the expression can be expressed as product of two factors (2 and 7) as 2×7.
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2 3/5 divided by 9 3/5
Answer:
as decimal
0.27083333333
Answer:
2 3/5 divided by 9 3/5 is 32
2x + 2y = 18
x=3-y Solve for x and y
Answer: x=-y+9
y=-x+9
Step-by-step explanation:
Jesse and Amir were assigned the same book to read. Jesse started reading on Saturday, and he is reading 30 pages a day. Amir didn't start until Sunday, but he is reading 35 pages a day.
How many days will it take Amir to catch up to Jesse, and how many pages will they each have read?
Answer the questions to solve this problem using a system of equations.
1. Write an equation to represent the number of pages Amir has read. Use x to represent the number of days Amir has been reading and y to represent the number of pages he has read. (1 point)
2. Write an equation to represent the number of pages Jesse has read.
Using x, the number of days Amir has been reading, write an expression to represent the number of days Jesse has been reading. Remember that Jesse started reading one day before Amir. Use this expression to write an equation for the number of pages Jesse has read. Let y represent the number of pages read. (1 point)
3. Write the system of equations using your answers from questions 1 and 2.
(2 points)
5. Solve the system of equations. Show your work. (2 points)
6. Interpret your solution. How many days does it take Amir to catch Jesse? At that time, how many pages have they read? (2 points)
1. An equation representing the number of days Amir has been reading and the number of pages he has read is y = 35x.
2. An equation representing the number of days Jesse has been reading and the number of pages she has read is y = 30 + 30x.
3. The system of equations from 1 and 2 is y = 35x and y = 30 + 30x.
4. At the end of Friday, after solving the equations, both Jesse and Amir read 210 pages each, with Jesse spending 7 days and Amir 6 days.
5. For Jesse and Amir, the equation solutions are y is 210 pages and x is 6 days.
6. After solving the equations, it will take Amir 6 days to catch up with Jesse and each person must have read 210 pages or a total of 420 pages.
What is a system of equations?A system of equations involves using more than one equation solved simultaneously.
Jesse's reading rate per day = 30 pages
Amir's reading rate per day = 35 pages
The number of pages read by Jesse, y = 30 + 30x
The number of pages read by Amir, y = 35x
Where x = the number of days they have been reading
Solving the equations:y = 30 + 30x and y = 35x
35x = 30 + 30x
35x - 30x = 30
5x = 30
x = 6 (30/5)
Jesse:y = 30 + 30x
y = 30 + 30(6)
y = 210
Amir:y = 35x
y = 35(6)
y = 210
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HELP ME PLEASE
not sure what to do
Since we are give the area, the length, and the width, we could put it in a formula.
2592=(16)(12)h
Multiply 16 x 12= 192
So now the formula is 2592= 192h
lastly, we divide 192 from 2592
h= 13.5 mm
Complete the number sentence. Must show your work. Please help! I’m confused
Answer:
2 + (-10) = 12
Step-by-step explanation:
The great answers. Thank you. I hope for help to you.
Write a linear function f with f(0)=7 and f(3)=1
y=mx+b
The linear function f with f(0) = 7 and f(3) = 1 is y = -2x + 7
How to represent linear equation?Linear equation can be represented in slope intercept form as follows:
y = mx + c
where
m = slopec = y-interceptTherefore,
f(0) = 7 and f(3) = 1
Using linear equation
7 = m(0) + b
b = 7
1 = m(3) + 7
1 - 7 = 3m
-6 = 3m
m = - 6 / 3
m = -2
Therefore, the linear function is y = -2x + 7
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The mean of 6 numbers is 8.
The numbers are in the ratio 1 : 1 : 2 : 2 : 3 : 3.
Find the range.
The range of six numbers is 8
According to the question,
Total number of Number = 6
Mean of number = 8
Ratio of numbers = 1 : 1 : 2 : 2 : 3 : 3
Let the common factor in numbers be "x"
Then , sum of number will be x + x + 2x + 2x + 3x +3x
=> 12x
Mean = sum of quantity / Number of quantity
8 = 12x / 6
Calculating the value of x,
12x = 48
=> x = 4
Substituting the value of x,
Number will be : 4 , 4 , 8 , 8, 12 , 12
Range = highest number - smallest number
Here , highest is 12 and smallest is 4
Therefore , Range = 12 - 4
=> 8
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A bag has 2 red, 3 green, and 6 orange balls. If a ball is randomly selected from the bag, what is the theoretical probability
that it is the color specified in parts (a) through (d).
a) green
b) not green
c) orange
d) not orange
***
Using theoretical probability, the probability of selecting green ball is 3/11, not selecting green ball is 8/11, selecting orange ball is 6/11 and not selecting orange ball is 5/11.
In the given question,
A bag has 2 red, 3 green, and 6 orange balls.
So total number of balls = 2+3+6 = 11
We have to find the theoretical probability.
(a) We have to find the theoretical probability of selecting green ball.
P(G) = Total number of green balls/Total number of balls
P(G) = 3/11
Hence, the probability of selecting green ball is 3/11.
(b) Now we have to find the theoretical probability of not selecting green ball.
Except green ball there is having red and orange i.e.
Total remaining balls except green = 2+6 = 8
P(G) = Total number of balls except green balls/Total number of balls
P(G) = 8/11
Hence, the probability of not selecting green ball is 8/11.
(c) Now we have to find the theoretical probability of selecting orange ball.
P(G) = Total number of orange balls/Total number of balls
P(G) = 6/11
Hence, the probability of selecting green ball is 6/11.
(d) Now we have to find the theoretical probability of not selecting orange ball.
Except orange ball there is having red and green balls i.e.
Total remaining balls except orange = 2+3 = 5
P(G) = Total number of balls except orange balls/Total number of balls
P(G) = 5/11
Hence, the probability of not selecting orange ball is 5/11.
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A store is having a sale on walnuts and chocolate chips. For 6 pounds of walnuts and 5 pounds of chocolate chips, the total cost is $28. For 2 pounds of walnuts and 3 pounds of chocolate chips, the total cost is $14. Find the cost for each pound of walnuts and each pound of chocolate chips.
Answer:
chocolate- 2 dollars walnuts- 4
Step-by-step explanation:
2 x3=6. 14-6=8
8÷2=4
Suppose you earned a $710,000 bonus this year and invested it at 8.25% per year. how much could you withdraw at the end of each of the next 20 years? select the correct answer.
Withdraw at the end of each of the next 20 years is [tex]710000(1.0825)^{20}[/tex]
What do you mean by simple interest and compound interest?
Simple interest can be defined as the amount that is paid back using borrowed money over a period of time.
simple interest:
Simple interest can be defined as the principal of a loan or deposit that an individual puts into a bank account.
Compound interest:
Compound interest is interest that accrues on the principal and accrues interest.
Given:
Principal, P = $710000
Rate of interest, r = 8.25%
Time period, t = 20 years
withdrawal at the end of 20 years , A = [tex]P(1+r)^{t}[/tex]
A = [tex]710000(1+8.25/100)^{20}[/tex] = [tex]710000(1+0.0825)^{20}=710000(1.0825)^{20}[/tex]
Therefore, withdraw at the end of each of the next 20 years is [tex]710000(1.0825)^{20}[/tex]
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PLEASE HELP ASAP! WILL GIVE BRAINLIEST AND FIVE STAR RATING FOR ACTUAL HELP! Describe the function‘s end behavior. f(x)=−10+6x^5+4x^3
as x→ ∞, f(x)→
as x→ −∞, f(x)→
Possible answers for both are:
-∞
∞
0
an asymptote
Answer: As x approaches infinity, f(x) approaches infinity.
As x approaches -infinity, f(x) also approaches - infinity.
Step-by-step explanation:
You can either graph this function on an online graphing (such as desmos. com) calculator to see the end behavior, or you can try inputting some numbers in. You could put in the number 1,2,3 and see that the graph will keep on increasing to positive infinity, and input the numbers -1,-2,-3 to see that the numbers will decrease to negative infinity.
c) ¿Cuántas combinaciones se pueden hacer en seleccionar los tres lugares ganadores de una carrera de 15
caballos?
Hay un total de 2730 combinaciones posibles.
¿Qué es permutación y combinación?Las permutaciones y combinaciones forman principios de conteo, que se aplican en muchas situaciones diferentes. Una permutación es el número de arreglos diferentes que se pueden hacer a partir de un conjunto dado. Cuando se trata de permutaciones, los detalles importan porque el orden o el orden importan. Este orden en el que escribe los nombres de los países es importante, ya que escribir los nombres de los tres países {EE. UU., Brasil, Australia} o {Australia, EE. UU., Brasil) o {Brasil, Australia, EE. UU.} es diferente. En combinación, los nombres de los tres países son solo un grupo, y el orden o secuencia no importa. Obtenga más información sobre permutaciones y combinaciones en el siguiente contenido. Las permutaciones y las combinaciones son métodos que se utilizan para contar el número de resultados posibles en diversas situaciones. Las permutaciones se entienden como arreglos y las combinaciones se entienden como alternativas. Siguiendo los principios básicos del conteo, hay reglas de suma y reglas de multiplicación para una fácil aplicación del conteo. Supongamos que hay 14 niños y 9 niñas. Al elegir un niño o una niña como maestro de salón, el maestro de salón puede elegir 1 de cada 14 niños y 1 de cada 9 niñas. Puede hacerlo en sus 14 + 9 = 23 maneras (usando la regla de la suma de conteo).Cálculoen carrera de 15 caballos si se consideran 3 posiciones
entonces número de combinaciones posibles = 15 * 14 * 13 = 2730 combinaciones posibles
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A local farmer had a mouse problem in his barn. He estimated there were about 800 mice to start with. He adopted some cats and noticed that the number of mice was decreasing by 8%/wk. The graph models the number of mice x weeks after the farmer adopted the cats.
Identify and interpret the key features of the exponential function modeled in terms of this situation.
Select each correct answer.
The asymptote indicates that as the number of weeks the farmer has had the cats increases, the population of mice approaches 0.
The y-intercept represents the number of mice the farmer had in the barn at the time he adopted the cats.
The line x = 0 is an asymptote of the graph.
The point (0,30) contains the x-intercept.
The line y = 0 is an asymptote of the graph.
The y-intercept is 800.
The asymptote indicates that there were never more than 800 mice in existence.
Answer:
The asymptote indicates that as the number of weeks the farmer has had the cats increases, the population of mice approaches 0.
The y-intercept represents the number of mice the farmer had in the barn at the time he adopted the cats.
The line y = 0 is an asymptote of the graph.
The y-intercept is 800.
Step-by-step explanation:
Took the test
Find a point-slope form for the line that satisfies the stated conditions. Slope 4, passing through (-8,1)
Answer: (y - 1) = 4(x + 8)
Step-by-step explanation:
The point-slope form is (y - y₁) = m(x - x₁), where:
m = slope = 4(x₁, y₁) = (-8, 1)So, the point-slope of this line would be (y - 1) = 4(x + 8).
Divide: 5,108 ÷ 5
How many groups?
The groups would 1 x 1000+ 2 x 10 + 1 x 1 + 6 x 1/10
what is Division?One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components. How many groups will be created, for instance, if 30 students need to be separated into groups of five for a sporting event? The division operation can be used to quickly and easily fix such issues. In this case, we must divide 30 by 5. 30 x 5 = 6 will be the outcome.
Given:
Divide: 5,108 ÷ 5
Now, dividing
5 | 5108 | 1021.6
5
_______
0 10
10
_____
0 8
5
_____
3 0
3 0
______
0
Hence, the groups would 1 x 1000+ 2 x 10 + 1 x 1 + 6 x 1/10
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Melinda needed to mail a package. She used .02 stamps and .10 stamps to mail the package. If she used 15 stamps worth .78 how many of each type of stamp did she use
The number of each type of stamp used is as follows:
9 of 0.02 stamps6 of 0.1 stampsHow to find how many of each type of stamp used?Melinda needed to mail a package. She used .02 stamps and .10 stamps to mail the package. She used 15 stamps worth 0.78. The number of each type of stamp she used can be calculated as follows:
let
x = number of 0.02 stamp
y = number of 0.10 stamp
Using system of equation,
x + y = 15
0.02x + 0.10y = 0.78
multiply equation(ii) by 50
x + y = 15
x + 5y = 39
4y = 24
y = 24 / 4
y = 6
Hence,
x = 15 - 6
x = 9
Therefore, the number of 0.02 stamps is 9 and the number of 0.10 stamp is 6.
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Find the y-intercept of the following function. f(x)=21x2−31x−68
The y-intercept for the given function is (0, -68).
The given function is f(x)=21x²-31x-68.
What is a y-intercept?An intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept.
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: (31/42,−6673/84)
Focus: (31/42,−556/7)
Axis of Symmetry: x=31/42
Directrix: y=−3337/42
Plot (0, -68) and (31/42, -6673/84)
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
y-intercept is (0, -68).
Hence, the y-intercept for the given function is (0, -68).
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Graph the equation y= - 7/2 x + 2 on the coordinate plane
Refer to the attachment for your graph.