Answer:
y = x² -2x +5
Step-by-step explanation:
When a polynomial has q as a zero, it has (x-q) as a factor. Your polynomial has factors (x -(1-2i)) and (x -(1+2i)). The polynomial will be the product of these factors.
__
y = (x -(1 -2i))(x -(1 +2i))
y = ((x -1) +2i)((x -1) -2i) = (x -1)² -(2i)² = x² -2x +1 -4(-1)
y = x² -2x +5
_____
Additional comments
i is the imaginary number √(-1), so i² = -1.
The two given roots differ only in the sign of their imaginary parts, so they are "conjugates" of each other. Complex roots of polynomials with real coefficients always come in conjugate pairs. (In some problems, you will be expected to supply the missing root of a conjugate pair.)
The expression for the product of the factors is simplified using the factoring for the difference of squares:
(a -b)(a +b) = a² -b² . . . . . . . here, we have a=(x-1); b=2i
**PLEASE HELP ASAP**
Ben is concerned that he is not reading enough. He decides to record how many pages he reads each day for the month of April, and he makes a box plot of the data. Then he repeats the process for the month of June. His 2 plots are shown below.
The admission fee to an amusement park is $28. It costs an additional p dollars to rent a locker to hold your belongings. The total cost for 5 people to enter the amusement park and each rent a locker is $180.How much does it cost for one person to rent a locker
Answer: 1040
Step-by-step explanation: 180+28=208
208 times 5 = 1040
What is the answer
(x+8)+4x=(7x-16)
[tex](x+8)+4x = 7x -16\\\\\implies 5x +8 = 7x -16\\\\\implies 7x -5x = 8+16 \\\\\implies 2x = 24\\\\\implies x = \dfrac{24}2\\\\\implies x= 12[/tex]
Can someone plz help Me? :(
the greatest common factor of 48 and 60 is D.) 12
Answer:
Answer: D or 12
Step-by-step explanation:
This one is fairly simple.
The Greatest Common Factor is the largest number that can go into both 48 and 60...
What I did is simply took the largest number from the answer choices: which is 12 and then divided 48 and 60 by 12 each. 12 can go into both of these number whole so 12 is your greatest common factor.
57 % of 200 calculate this please
so percentage is always out of 100
so 57%is upon 100 then it is 200 upon 1 cuz it is a whole
57% of 20057 /100×200/1114 so the ans is 114 i hope u understood itHey there!
57% of 200
= 57% * 200
= 57/100 * 200/1
= 0.57 * 200
= 57(200)/100(1)
= 11,400/100
= 114
Therefore, your answer is: 114
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Find the area between f(x) = 3x and f(x) = x2 on the interval (0,3]
Answer:
[tex]A=4.5[/tex]
Step-by-step explanation:
The area between two curves over the interval [tex][a,b][/tex] is [tex]A=\int\limits^b_a {f(x)-g(x)} \, dx[/tex] where [tex]f(x)[/tex] is the upper function and [tex]g(x)[/tex] is the lower function.
Therefore:
[tex]A=\int\limits^3_0 {3x-x^2} \, dx[/tex]
[tex]A=\frac{3}{2}x^2-\frac{x^3}{3}\Big|_0^3[/tex]
[tex]A=[\frac{3}{2}(3)^2-\frac{(3)^3}{3}]-[\frac{3}{2}(0)^2-\frac{(0)^3}{3}][/tex]
[tex]A=\frac{3}{2}(9)-\frac{27}{3}[/tex]
[tex]A=\frac{27}{2}-\frac{27}{3}[/tex]
[tex]A=\frac{9}{2}[/tex]
[tex]A=4.5[/tex]
So, the area between [tex]f(x)=3x[/tex] and [tex]g(x)=x^2[/tex] on the interval [tex](0,3][/tex] is [tex]4.5[/tex] square units.
2.4x-9.1x+12.5= -39.44
Solve for x
Answer:
x= 2597/335
Step-by-step explanation:
collect like terms
2.4x-9.1x= -6.7x
-39.44-12.5 = -51.94
-6.7x=-51.94
divide both sides by -6.7
x= 2597/335
Santa needs 600 toys. 175 toys have already
been made. 5 elves made the rest of the toys.
How many toys did each elf make, assuming
that they each made they amount?
Answer:
Each elf made 85 toys
Step-by-step explanation:
First we must find out how many more toys need to be made. To do this we just have to subtract 175 from 600. 600 - 175 = 425.
Next we have to divide 425 toys by the 5 elves. 425 divided by 5 is 85.
What is an equation of the line that passes through the points (4, -1) and (8, 5)?
Answer:
y=3/2x-7
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(5-(-1))/(8-4)
m=(5+1)/4
m=6/4
simplify
m=3/2
y-y1=m(x-x1)
y-(-1)=3/2(x-4)
y+1=3/2(x-4)
y=3/2x-12/2-1
y=3/2x-6-1
y=3/2x-7
Tria had one each of five different-shaped number solids having 4, 6, 8, 12, and 20 sides. She rolled two at a time and found probabilities for the sum of the numbers that came up. She recorded the probabilities in the first column of the table. When it came time to fill in the second column, she had forgotten which number solids she had used. Figure out which number solids she must have used and explain your thinking. The first one has been done.
She found out that the probability of 4 is lesser than 5, which combinations did she use?
Answer:The probability of a 3 is 2/80 or 1/40
The probability of a 4 is less than the probability of a 5
Step-by-step explanation:
Jameson Middle School gives bottles of water to teachers and students who are going on a field trip. The school orders 500 bottles of water. They plan to give 35 bottles of water to teachers. They ordered at least 2 bottles of water for each student. How many students could be going on the field trip? Show your work.
Answer:
up to 232
Step-by-step explanation:
Let x = number of students
The number of bottles for the students is 2x since they give 2 bottles per student.
2x + 35 = 500
2x = 465
x = 232.5
Answer: 232
please help me with this
Answer: 3Z
Step-by-step explanation:
please help me asapppppp
ty :)
Answer:
2x + 7y = 35
Step-by-step explanation:
Multiply the equation with 7
7 ( y = -2x/7 + 5 )
7y = -2x + 35
2x + 7y = 35
Exterior Angles and Isosceles Triangles
Step-by-step explanation:
this is not an isoceles triangle.
anyway, we need to remember 2 things :
1. the sum of all angles in a triangle is always 180°.
2. the sum of all angles around a single point on a line is 360° (as this point wound be the center of an invisible circle). and as the line cuts this circle in half, the angles on one side of the line around this point is therefore 180°.
so, the internal angle Q is then
180 = 50 + 55 + Q
Q = 180 - 50 - 55 = 180 - 105 = 75°
the exterior angle x at Q is then
180 = Q + x = 75 + x
x = 180 - 75 = 105°
Find the slope of the line that passes through the points given in the first column and match them with the appropriate result. (10,7) and (1,2)\left(10,7\right)\ and\ \left(1,2\right)(10,7) and (1,2)
Answer:
Step-by-step explanation:
1) The slope of line with the coordinate points (10, 7) and (1, 2) is [tex]\frac{5}{9}[/tex].
2) The slope of line with the coordinate points (9, 9) and (1, 16) is [tex]-\frac{7}{8}[/tex].
3) The slope of line with the coordinate points (9, 3) and (2, 1) is [tex]\frac{2}{7}[/tex].
4) The slope of line with the coordinate points (8, 8) and (1, 2) is [tex]\frac{6}{7}[/tex].
The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The formula to find the slope of a line is slope = [tex]\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]
From the given table, we have
1) The coordinate points are (10, 7) and (1, 2)
Here, slope [tex]=\frac{(2-7)}{(1-10)}[/tex]
[tex]=\frac{5}{9}[/tex]
2) The coordinate points are (9, 9) and (1, 16)
Here, slope [tex]=\frac{(16-9)}{(1-9)}[/tex]
[tex]=-\frac{7}{8}[/tex]
3) The coordinate points are (9, 3) and (2, 1)
Here, slope [tex]=\frac{(1-3)}{(2-9)}[/tex]
[tex]=\frac{2}{7}[/tex]
4) The coordinate points are (8, 8) and (1, 2)
Here, slope [tex]=\frac{(2-8)}{(1-8)}[/tex]
[tex]=\frac{6}{7}[/tex]
Therefore,
1) The slope of line with the coordinate points (10, 7) and (1, 2) is [tex]\frac{5}{9}[/tex].
2) The slope of line with the coordinate points (9, 9) and (1, 16) is [tex]-\frac{7}{8}[/tex].
3) The slope of line with the coordinate points (9, 3) and (2, 1) is [tex]\frac{2}{7}[/tex].
4) The slope of line with the coordinate points (8, 8) and (1, 2) is [tex]\frac{6}{7}[/tex].
To learn more about the slope of a line visit:
https://brainly.com/question/14511992.
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The area of a triangle is 30 square inches.
The base of the triangle is x - 6 inches,
and the height is x + 5 inches.
Find the value of x, and the dimensions of the triangle.
A = 1/2bh
x=
base=
height=
Answer:
x=10
base=4inches
height=15inches
Step-by-step explanation:
A=1/2bh
30=1/2(x-6)(x+5)
60= x²+5x-6x-30
x²-x-90=0
x²-10x+9x-90=0
x(x-10) +9(x-10)=0
(x+9)(x-10)=0
x= -9 or 10
x cannot be negative
Therefore x= 10
base= 10-6
=4inches
height=10+5
=15inches
2 1/5 liters of water and 1 1/3 liters of juice are used for a team breakfast,
How many liters of drink were used for the breakfast?
Enter your answer as a mixed number in simplest form by filling in the boxos,
Answer:
3 8/15
Step-by-step explanation:
2 1/5 + 1 1/3 = 3 8/15
Omar bought N packages of pencils each package had 15 pencils write an equation P to represent the total number of pencils Peque Omar bought.
I need Helppppp!!!!
plizzzz
Answer:
N x 15 = P
Step-by-step explanation:
I need helppp pleaseee
Answer:
One solution
Step-by-step explanation:
Start by simplifying the equation.
Distribute 3 to 4 and 2 to get 12x + 6Combine 8x and -2x to get 6xThen you have 12x + 6 = 6x + 24,
Continue to solve
Subtract 6 from the left and right to get 12x = 6x + 18Subtract 6x from both sides to get 6x = 18Divide both sides by 6 to get x = 18Because x is equal to one digit and not x = x or 3 = 5, you have one solution
(Infinite) or (none)
Hope this helps!
Find the midpoint of the segment with the following endpoints. (10,6) and (4,9)
Answer:
(7,7.5)
Step-by-step explanation:
midpoint formula:
(10+4)/2=7
(6+9)/2=7.5
(7,7.5)
a farm has chickens and cows all the cows have 4 legs and all chickens have 2 legs. altogether there are 82 cow and chicken legs on the farm.complete the table to show some possible combinations of chickens and cows to get 82 total legs.
mark me brinilylist pls
How i can answer this question
Answer:
B
D
C
Glad I coild help you out.
Answer:
B,C and D
Step-by-step explanation:
They all expand back to 16x + 20.
Solve x/2 - 8 = y for x
Answer:
B) x=2y + 16
Step-by-step explanation:
First, you'd multiply the x/2 by 2 to get x by itself.
You do the same throughout the whole equation.
Then isolate the x by getting rid of the -16 to the other side by adding 16
Your final answer should be:
B) x=2y + 16
The value of x for the given equation x/2 - 8 = y will be x = 2y + 16 thus option (B) is correct.
What is the equation?A formula known as an equation uses the same sign to denote the equality of two expressions.
In another word, the equation must be constrained with some constraints.
As per the given equation,
x/2 - 8 = y
Add 8 both sides,
x/2 - 8 + 8 = y + 8
x/2 = y + 8
Multiply by 2 both sides,
x/2 × 2 = (8 + y) × 2
x = 2y + 16
Hence "x = 2y + 16 will be the value of x in the equation x/2 - 8 = y".
For more about the equation,
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A restaurant chain would like to measure the proportion of customers who are generally satisfied with the service provided by its staff. At the end of the meal, as the check is delivered to the table, the server asks those at the table to rate their satisfaction with the service provided as "Very Satisfied,” "Satisfied,” or "Not Satisfied.” During a one-week period, 147 customers were surveyed and 135 (93%) reported they were either Satisfied or Very Satisfied. How might the results be biased in obtaining an estimate of all customers who are satisfied with service?
Because of response bias, the survey results may overestimate the true proportion of satisfied customers.
Because of response bias, the survey results may underestimate the true proportion of satisfied customers.
Because of voluntary response bias, the survey results may overestimate the true proportion of satisfied customers.
Because customers were surveyed over a one-week period, the results should provide an accurate estimate of satisfied customers.
PLEASE HELP
Based on the information given regarding the bias, the correct option is A. Because of response bias, the survey results may overestimate the true proportion of satisfied customers.
From the information given, it can be depicted that the type of bias that's present is the response bias because the customers may not respond truthfully to the server.
Therefore, because of response bias, the survey results may overestimate the true proportion of satisfied customers. In this case, the survey will show a higher number of satisfied customers which isn't a true reflection.
Learn more about bias on:
https://brainly.com/question/24491228
Answer:
a
Step-by-step explanation:
A line passes through the point -10,9 and has a slope of 1/2. Write an equation in slope-intercept form for this line
Answer:
Step-by-step explanation:
The slope intercept form of an equation of a line is y = mx + b, where m is the slope and b is the y-intercept (the value of y when x=0).
Since the slope is (1/2), we can write:
y = (1/2)x + b
We want a value of b such that it forces the line to go through point (-10,9). Enter that point in the equation and solve for b:
y = (1/2)x + b
9 = (1/2)*(-10) + b
9 = -5 + b
b = 14
The eqyuation of a line with a slope of (1/2) and goes through point (-10,9) is:
y = (1/2)x + 14
See attachment.
if sarah works 40 hours a week and earns 660 dollars per payroll. how much does she make an hour
Answer:16.50
Step-by-step explanation: hope it helps
Answer:
16.50
Step-by-step explanation:
Find the slope of a line parallel to each given line.
y = x - 1
Answer:
1
Step-by-step explanation:
First, you should put the equation in slope intercept form (y = mx + b), where m is the slope. A parallel line will have the same slope so if 1x is your slope for the first equation, 1 should also be the slope for the 2nd equation
15(x + 3)2
Box the exponent (s)
please help
Answer:
"2" is the exponent
Step-by-step explanation:
There is no exponent in your expression.
__
When the expression is typeset, the superscript text is considered to be an exponent:
[tex]15(x+3){\boxed{^2}}[/tex]
When the expression is written in plain text, the exponent is indicated by a caret (^):
[tex]\textsf{15(x+3)\^\ \!\!\boxed{\textsf{2}}}[/tex]
Answer:
[tex] {15x}^{2} + 90x + 135 \\ [/tex]
Step-by-step explanation:
[tex]15 {(x + 3)}^{2} \\ 15(x + 3)(x + 3) \\ 15 |(x(x + 3) + 3(x + 3)| \\ 15( {x}^{2} + 3x + 3x + 9) \\ 15( {x}^{2} + 6x + 9) \\ {15x}^{2} + 90x + 135 \\ [/tex]
a scale model of a building 8 inches tall. if the actual height of the building is 496 feet. what is the scale
Answer:
8 inches= 62 ft
Step-by-step explanation:
496 divided by 8
A food production company is choosing between two suppliers of grain. Supplier A sells grain for $5.25 per bushel plus a
delivery fee of $3 per bushel Supplier B sells the grain for $6.50 per bushel plus a flat delivery fee of $1,500 each week.
Which supplier would cost more if the production company bought 500 bushels of grain each week?
O Supplier B would cost $625 more than supplier A.
O Supplier B would cost $600 more than supplier A
O Supplier A would cost $875 more than supplier B.
O Supplier A would cost $800 more than supplier B.
Answer:
Supplier B would cost $625 more than supplier A.
Step-by-step explanation: