What are the possible zeros for f(x) equals X to the third power minus 2X to the second power minus 4X +15
The roots of the polynomial are done by using a calculator will be -2.3671, 2.1835 + 1.2527i, and 2.1835 – 1.2527i.
What are the roots of the polynomial?The polynomial is given below.
[tex]\rm f(x) = a_0x^n + a_1 x^{n - 1}+ ....+ a_{n-2}x^2 + a_{n-1}x + a_nx^0[/tex]
The roots of the polynomial are equal to n or less than n.
And if one imaginary root is a + bi, then the other imaginary root will be a – bi.
The roots of the polynomial are done by using a calculator.
x = -2.3671, 2.1835 + 1.2527i, 2.1835 – 1.2527i
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Use interval notation to indicate all real numbers between and including −3 and 5.
Answer:
[-3,5]
Step-by-step explanation:
Interval notation is a shorthand way of writing and interval of values. To describe an interval, imagine the two endpoints on the number-line. Then, list the two endpoint values, leftmost point from the number-line first, separated by a comma. Lastly, include the appropriate brackets for each endpoint:
Only two brackets total will be used for each interval, a bracket to start it, and one bracket to end it.If a number is included, a square bracket should be used -- either "[" or "]"If the endpoint number is not meant to be included, a 'curved bracket' (which we usually just call a parenthesis) should be used -- either "(" or ")"For our situation, the two endpoints are -3 and 5. -3 is to the left of 5 on the number-line, so -3 should be listed first
[tex]-3,5[/tex]
Lastly, the directions say "including -3 and 5", so both endpoints should be included.
To include the -3 on the left, we'll use "["To include the 5 on the right, we'll use "]"The final result for the interval is [tex][-3,5][/tex]
Determine the x and y intercepts of the equation y = -3x + 4.
Select one:
O a. y-int y = 4 and x-int x = 4/3
O b. y-int y = 4/3 and x-int x = 4
O c. y-int y = 4 and No x-int
O d. No y-int and x-int x =4/3
Answer:
O c. y-int y = 4 and No x-int
Step-by-step explanation:
In the slope-intercept equation y = -3x + 4, only slope and y-intercept are displayed as it is in slope-intercept format which is y = mx + b; m being the slope and b being the y-intercept.
There is no x-intercept present in a slope-intercept equation.
But due to the 4 being in the place of the y-intercept is the y-intercept of the graph and line depicted off this linear equation (slope-intercept equation).
Hence, the answer is C. Y-intercept = 4 and No x-intercept.
Please help quickly!!
Answer:
D
Step-by-step explanation:
Help please I will do anything
Answer:
? = 12
Step-by-step explanation:
[tex]\frac{7}{12} +\frac{10}{12} =\frac{7+10}{12} =\frac{17}{12}[/tex]
[tex]\frac{17}{12} =\frac{12}{12} +\frac{5}{12} =1+\frac{5}{12} =1\frac{5}{12}[/tex]
Hope this helps
Solve, finding all solutions in [0, 2(pi)]
Answer:
x = π/12, 5π/12
Step-by-step explanation:
We can work this problem a couple of ways. We can convert it to single trig function, shifted horizontally. Or we can convert it to a double-angle equation.
__
horizontal shiftWe recall the sum of angles formula is ...
sin(x+y) = sin(x)cos(y) +cos(x)sin(y)
Using this, we can rewrite the left side of the equation using some angle offset y, and some scale factor k.
k·sin(x +y) = k·sin(y)·cos(x) +k·cos(y)·sin(x) = 2cos(x) +2sin(x)
finding the shift
Equating coefficients of cos(x) and sin(x), we can solve for k and y:
k·sin(y) = 2
k·cos(y) = 2
The ratio of these equations is ...
(k·sin(y))/(k·cos(y)) = 2/2
tan(y) = 1 ⇒ y = π/4
k = 2/sin(π/4) = 2√2
shifted equation
So, our original equation becomes ...
2√2·sin(x +π/4) = √6
Dividing by √2 and using the inverse sine function, we have ...
x +π/4 = arcsin((√3)/2) = π/2 ±π/6
x = π/4 ±π/6
x = π/12, 5π/12
__
double-angle equationIf we square both sides of the original equation, we get ...
(2sin(x) +2cos(x))² = (√6)²
4sin²(x) +8sin(x)cos(x) +4cos²(x) = 6
2sin(x)cos(x) = (6 -4)/4 = 1/2 . . . . use sin² +cos² = 1, subtract 4, divide by 4
Using the trig identity 2sin(x)cos(x) = sin(2x), we can find ...
2x = arcsin(1/2) = π/2 ±π/3 +2kπ . . . . k = an integer;
x = π/4 ±π/6 +kπ . . . . for integer k
x = {π/12, 5π/12, 13π/12, 17π/12}
We know that squaring the equation can introduce extraneous solutions, so we need to try these out. For x in the third quadrant, the sine and cosine values are both negative, so the only useful solutions here are ...
x = π/12, 5π/12
_____
Additional comment
Based on the above, we now know that any trig expression of the form ...
a·sin(x) +b·cos(x)
can be rewritten to the form ...
(√(a² +b²))·sin(x +arctan(b/a)) . . . . . a scaled and shifted sine function
The arctangent will have to take the signs of 'a' and 'b' into account in order to get the angle quadrant right.
if 50 grams of sweets cost 250 rupees find the cost of 380 grams of sweets.
Study each of the growing geometrical patterns. Then do the following for each pattern. (I) Give a verbal description of how the pattern is growing. (ii)Set up a table of values.(III) Write down a numerical description for each pattern (you must relate the number of the frame to the number of figures in the frame). (IV) For each pattern, write down a formula that can be used to calculate the number of building blocks in any term. (v) Write down the value of the 10th frame. Use your formula to determine how many building blocks there are in the 100th frame of each growing pattern. M M Δ Δ Δ 2 (6) (6) (8) [40]
A description of how the pattern is growing is that the pattern is growing by the addition of two blocks every time.
How to illustrate the pattern?A numerical description of the pattern is:
1 - 2 blocks.
2 - 4 blocks.
3 - 6 blocks
4 - 8 blocks.
The formula that can be used to calculate the number if building blocks in any term will be 2n. For example, the number of blocks for the 5th term will be:
= 2n = 2 × 5 = 10
The value for the 10th frame will be:
= 2n
= 2 × 10 = 20
The value for the 100th frame will be:
= 2n
= 2 × 100 = 200
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The May bank statement for Rental shows a balance of $6,000, but the balance per books shows a cash balance of $8,000. Other information includes: 1. A check for $190 to pay the electric bill was recorded on the books as $10. 2. Included on the bank statement was a note collected by the bank for $450 plus interest of $30. 3. Checks outstanding totaled $270. 4. Bank service charges were $60. 5. Deposits in transit were $2,510.
The adjusted cash Balance is $8060 .
What is Bank Balance ?The amount of money in a person's account at any given time is the Bank Balance of that person's account.
Unadjusted bank balance 6000
Difference in the electricity bill -180
Add: Deposit in transit 2510
Less: Outstanding Checks -270
Adjusted cash balance 8060
So answer is a) $8060
Therefore the adjusted cash Balance is $8060 .
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The vertices of a trapezoid are points (0,x), (0,0), (y,0), and (z,x). Find the area in terms of x, y, and z.
I put 1/2x (y+z), I just want to make sure! thank you.
Your answer is correct. The two "bases" of the trapezoid are the line segments (0, 0)-to-(y, 0) and (0, x)-to(z, x), with lengths y and z, respectively. Then the average of the bases is [tex]\frac{y+z}2[/tex]. (We know they're the bases because the line segments are parallel.)
We multiply this by the height, which is given by the length of the line segment (0, 0)-to-(0,x), or x.
Hence the area is
[tex]\dfrac{x(y+z)}2[/tex]
(which is identical to what you have).
1. What is the length of XU?
X
U
Y
36 in
V
Z
W
23 in
Answer: 49 in
Step-by-step explanation:
[23 + XU]/2 = 36 [trapezoid midsegment theorem]23 + XU = 72 [multiply both sides by 2]XU = 49 [subtract 23 from both sides]A parallelogram ABCD is shown with DC equal to 8 feet and the perpendicular distance between AB and DC equal to 3 over 4 foot. Part A: What is the area of the parallelogram? Show your work. (5 points) Part B: How can you decompose this parallelogram into two triangles? If this parallelogram was decomposed into two triangles, what would be the area of each triangle? (5 points)
Answer:
6,3
Step-by-step explanation:
hope this helps
the math section in part B shows the equation for the area of a triangle, but this math could be skipped with a similar problem if you just divide the parraellogram by 2. (logic section)
what is the volume of this complex figure
The volume of the given figure is 210 cubic in..
We need to find the volume of the given figure.
What is volume?Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.
Divide the given figure into two convenient cuboids. That is one with dimensions length=4 in., breadth=2 in. and height=3 in. Another with length=4 in., breadth=4 in. and height=12 in.
We know that, the volume of cuboid =l×b×h cubic units.
Now, the volume of the cuboid=4×2×3=18 cubic in. and the volume of another
cuboid=4×4×12=192 cubic in.
The volume of the given figure=18+192=210 cubic in.
Therefore, the volume of the given figure is 210 cubic in.
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Find two positive numbers such that their sum is 60 and their product is a maximum. Select one: O a. 30 and 30 O b. 25 and 35 O c. 1 and 59 O d. 20 and 40
Answer:
B: 25 and 35
Step-by-step explanation:
25 product 35 875
In a certain town, the ratio of the number of children to the number of adults is 3 to 7. What percent of the town’s population are adults?
Answer:
70%
Step-by-step explanation:
If 3 child and 7 adult is in the town, then there are total 10 people. 7 ÷ 10 is equal to 0.7, which is 70%.
Graph the function f(x) = x+4 -1.
This can be simplified to [tex]f(x)=x+3[/tex], and is thus a line with a slope of 1 and a y-intercept of 3.
Given the equation below, which of the following shows the quadratic formula
correctly applied?
2x² -9x+4 =0
Answer:
Step-by-step explanation:
[tex]x=\frac{-(-9)\pm\sqrt{(-9)^2-4(2)(4)} }{2 \times 2} \\x=\frac{9\pm\sqrt{81-32} }{4} \\x=\frac{9\pm\sqrt{49} }{4} \\x=\frac{9 \pm 7}{4} \\either~x=\frac{9+7}{4} =\frac{16}{4} =4\\or\\x=\frac{9-7}{4} =\frac{2}{4} =\frac{1}{2}[/tex]
Which of the following is equivalent to the radical expression below when
x>=2?
(√x-2)(√x+9)
The equivalent expression of [tex](\sqrt x - 2)(\sqrt x + 9)[/tex] is [tex]x + 7\sqrt x - 18[/tex]
How to determine the equivalent equation?The expression is given as:
[tex](\sqrt x - 2)(\sqrt x + 9)[/tex]
Expand the expression
[tex]x - 2\sqrt x + 9\sqrt x - 18[/tex]
Evaluate the like terms
[tex]x + 7\sqrt x - 18[/tex]
Hence, the equivalent expression of [tex](\sqrt x - 2)(\sqrt x + 9)[/tex] is [tex]x + 7\sqrt x - 18[/tex]
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A company gives each worker a cash bonus every Friday, randomly giving a worker an amount with these probabilities: $10 - 0.75, $50 - 0.25. Over many weeks, what is a worker's expected weekly bonus?
The worker's expected weekly bonus is $30.0
How to determine the worker's expected weekly bonus?The amounts and the probabilities are given as:
x $10 $50
P(x) 0.75 0.25
The worker's expected weekly bonus is calculated as:
[tex]E(x) = \sum x * P(x)[/tex]
So, we have:
E(x) = $10 * 0.75 + $50 * 0.25
Evaluate the product
E(x) = $17.5 + $12.5
Evaluate the sum
E(x) = $30.0
Hence, the worker's expected weekly bonus is $30.0
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Sara purchased a porcelain sculpture that is in the shape of a square pyramid. The slant height is 6.1 inches and the base 6.4 inches. Find the surface area. Round to the nearest tenth.
The surface area of the square pyramid will be 78.08 square inches.
What is surface area?The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.
Given that:-
Sara purchased a porcelain sculpture that is in the shape of a square pyramid. The slant height is 6.1 inches and the base is 6.4 inches. The surface area will be.
The surface area of the square pyramid will be calculated by the formula:-
[tex]SA = P\times\dfrac{l}{2}[/tex]
[tex]SA = 25.6\times \dfrac{6.1}{2}[/tex]
SA = 78.08 square inches
Therefore the surface area of the square pyramid will be 78.08 square inches.
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My supersonic jet burns 4 gallons of jet fuel in 3 seconds. How many gallons of jet fuel do I need to fly for an hour?
The number of gallons of Jet fuel that is needed to fly for an hour is; 14400 gallons
How to solve simple Algebra?We are given;
Number of gallons burned = 4 gallons
Time to burn 4 gallons = 3 seconds
Now, for 1 hour there are 3600 seconds and so;
Number of gallons that is burnt in 3600 seconds = 3600 * 4
Number of gallons that is burnt in 3600 seconds = 14400 gallons
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Given f(x) = 8x+1 2x-9 O As x-00, f(x) → 9; as x → ∞o, f(x) → 9. -> - O As x-00, f(x) O As x-00, f(x) O As x-00, f(x) - - what is the end behavior of the function? ->> -9; as x -4; as x ∞o, f(x) → -9. - ∞o, f(x) → -4. - 4; as x → ∞o, f(x) → 4. -> - Given f ( x ) = 8x + 1 2x - 9 O As x - 00 , f ( x ) → 9 ; as x → ∞o , f ( x ) → 9 . - > - O As x - 00 , f ( x ) O As x - 00 , f ( x ) O As x - 00 , f ( x ) - - what is the end behavior of the function ? - >> -9 ; as x -4 ; as x ∞o , f ( x ) → -9 . - ∞o , f ( x ) → -4 . - 4 ; as x → ∞o , f ( x ) → 4 . - > -
Answer:
D
After graphing, you can analyze it accordingly.
Which of the following statements must be true about this diagram? Check
all that apply.
A. mz2+ mz3 = mz4
B. mz1+ m2 2 = m/3
C. m23 is greater than m<2
D. m24 is greater than mz1
E. mz1+mz2 = mz4
F. mz4 is greater than m<2
Answer:
D, E, F is the answer.
Step-by-step explanation:
From the diagram:-
m∠ 4 is greater than m∠ 1m∠ 4 is greater than m∠ 2m∠ 1 + m∠ 2 = m∠ 4Therefore, D, E, F.
-------------------------------
Select the graph for the solution of the open sentence. Click until the correct graph appears.
3|x| > 6
I would really appreciate the help!:)
The solution of the inequality will be x > 2 and x < -2. And the graph is drawn below.
What is inequality?Inequality is defined as an equation that does not contain an equal sign.
The inequality is given below.
3|x| > 6
By solving the equation, we have
|x| > 2
x > 2
x < -2
Then the graph will be drawn.
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What is the volume of the complex figure
The volume of the given figure is 104 m³.
We need to find the volume of the given figure.
What is volume?Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.
Divide the given figure into two convenient cuboids. That is one with dimensions length=4 m, breadth=4 m and height=3 m. Another with length=4 m, breadth=7 m and height=2 m.
We know that, the volume of cuboid =l×b×h cubic units.
Now, the volume of cuboid=4×4×3=48 m³ and the volume of another
cuboid=4×7×2=56 m³.
The volume of the given figure=48+56=104 m³.
Therefore, the volume of the given figure is 104 m³.
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An arithmetic sequence is shown in the graph.
What is the equation for the nth term of the arithmetic sequence?
an = –3 + 5(n – 1)
an = –3 + 5(n + 1)
an = –3 – 5n
an = –3 + 5n
Answer:
an= -3+5(n-1)
Step-by-step explanation:
Try writing out the terms and finding a pattern. In this case, inserting any plotted x-value into the sequence -3+5(n-1) produces the correct y-value.
Answer:
A.) an = -3 + 5(n - 1)
Explanation:
Given: (1, -3), (2, 2), (3, 7), (4, 12), (5, 17)
Arithmetic Series: a + (n - 1)d
['a' is first term, 'n' determines term position, 'd' is common difference]
Determine the following:
a = -3d = second term - first term = 2 - (-3) = 5Putting into equation:
-3 + (n - 1)5-3 + 5(n - 1)Please help! I don't know how to do slopes.
The slope of the given line in the image is -4 , Option A is the answer.
What is the equation of a straight line ?The equation of the straight line is given by
y =mx +c ,
Where m is the slope , C is the intercept
The line is passing through the point
(-1,8) ,(2,-4)
The slope is given by
m = (y₂-y₁) /(x₂-x₁)
m = (-4 - 8 )/(2 +1)
m = -12/3
m = -4
Therefore the slope of the given line in the image is -4 , Option A is the answer.
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The frequency table shows the results of a survey asking people how many
hours they spend online per week. On a piece of paper, draw a histogram to
represent the data. Then determine which answer choice matches the
histogram you drew.
Hours online Frequency
5
8
10
9
7
0-3
4-7
8-11
12-15
16-19
Based on the frequency table given, The option that closely matches the histogram I drew is option C but the last one suppose to be 7 and not 6.
What is the histogram about?Hours online Frequency
5 0-3
8 4-7
10 8-11
9 12-15
7 16-19
Note that in the image attached, you can see how the Hours online were said to be matched with the Frequency.
So since option A and B was not shown to see which matches the option, i can say option c is closest but if look at my own image, you can use it to find the right one.
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Normal annual capacity for star company is 36,000 machine hours, with fixed factory overhead budgeted as Rs. 16,920 and an estimated variable factory overhead rate of Rs. 2.10 per hour, During October actual production required 2,700 machine hours, with a total factory overhead of Rs. 7,400. Required: Compute: 1) The applied factory overhead 2) The over-or underapplied factory overhead amount for October,
The applied factory overhead is $6,939 and the over-or underapplied factory overhead amount for October is $461.
Applied and under applied factory overhead1. Applied factory overhead:
Predetermine overhead rate=Fixed overhead/Machine hours
Predetermine overhead rate=16,920/36,000
Predetermine overhead rate=0.47
Applied overhead=Machine hours×Rate
Variable=2700×2.10 per hour= $5,670
Fixed=2700×0.47 per hour=$1,269
Total overhead applied=$6,939
($5,670+$1,269)
2. Under applied overhead
Total overhead applied $6,939
Less Total factory overhead $7,400
Under applied overhead -$461
($6,939-$7,400)
Therefore the applied factory overhead is $6,939 and the over-or underapplied factory overhead amount for October is $461.
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What is the solution to the following equation?
-3+x= -8
A. x = -5
B. x=5
C. x = 11
D. x=-11
Answer:
[tex]\mathsf {A. x = -5}[/tex]
Step-by-step explanation:
[tex]\implies \mathsf {-3 + x = -8}[/tex]
[tex]\implies \mathsf {x = -8 + 3}[/tex]
[tex]\implies \mathsf {x = -5}[/tex]
