Answer:
[tex]\displaystyle x = 1, - 2 + i, -2 -i[/tex]
Step-by-step explanation:
We are given that:
[tex]\displaystyle f(x) = 2x^3 + 6x^2 + 2x - 10 \text{ and } f(1) = 0[/tex]
And we want to find all zeros of f algebraically.
Since f(1) = 0, then (x - 1) is a zero of f.
We can hence factor by synthetic division:
[tex]\begin{table}[]\begin{tabular}{lllll}\multicolumn{1}{l|}{1} & 2 & 6 & 2 & -10 \\\multicolumn{1}{l|}{} & & 6 & 2 & 10 \\ \cline{2-5} & 2 & 8 & 10 & -10 \\ & & & & \end{tabular}\end{table}[/tex][tex]\begin{tabular}{lllll}\multicolumn{1}{l|}{1} & 2 & 6 & 2 & -10 \\\multicolumn{1}{l|}{} & & 2 & 8 & 10 \\ \cline{2-5} & 2 & 8 & 10 & 0 \\ & & & & \end{tabular}[/tex]
Therefore:
[tex]\displaystyle \begin{aligned} f(x) & = 2x^3 + 6x^2 + 2x- 10 \\ \\ & = (x-1)(2x^2 + 8x + 10) \\ \\ &= 2(x-1)(x^2 + 4x + 5)\end{aligned}[/tex]
Therefore, by the Zero Product Property:
[tex]\displaystyle x-1 = 0 \text{ or } x^2 +4x + 5 = 0[/tex]
From the quadratic formula:
[tex]\displaystyle \begin{aligned}x & = \frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\ & = \frac{-(4)\pm\sqrt{(4)^2 - 4(1)(5)}}{2(1)} \\ \\ &= \frac{-4\pm\sqrt{-4}}{2} \\ \\ &= \frac{-4\pm 2i}{2} \\ \\ & = -2\pm i \end{aligned}[/tex]
Therefore, all the zeros of f include:
[tex]\displaystyle x = 1, - 2 + i, -2 -i[/tex]
Shane and Damien are racing. Shane ran 8 miles in 4 hours. Damien ran 8 miles in 2 hours. How much faster did Damien run than Shane?
Damien ran 4 mph faster than Shane
Damien ran 2 mph faster than Shane
Damien ran 6 mph faster than Shane
Given SA 108 units squared SA=192 units squared V-1408 units squared Find Volume of the smaller figure
A screening test for a newly discovered disease is being evaluated. In order to determine the effectiveness of the new test, it was administered to 900 workers. 150 of the individuals diagnosed with the disease tested positive. A negative test finding occurred in 60 people who had the disease. A total of 50 persons not diseased tested positive for it. Assume the prior probability is not known. What is the overall accuracy of the test
The overall accuracy of the screening test for a newly discovered disease is being evaluated for this case is 87.78% approximately.
What is the accuracy of a test?Accuracy of a test is the ratio of the correct results to the total results the test gives.
Thus, we have:
[tex]\rm Accuracy =\dfrac{\text{Total number of correct results}}{\text{Total number of results}} = \dfrac{TP + TN}{TP + FP + TN + FN}[/tex]
where T represents True, F represents False, N represents Negative, and P represents Positive. The negativity and positivity are the results of the test.
For this case, we're specified that:
The test is happening for diagnosis of a newly discovered disease.Total number of tests done = total number of workers administered = 900True positive (TP)= test result positive (ie test saying that the person has disease) when disease is actually present (that actual presense is known by some other method, and here we're evaluating the quality of 'disease testing procedure' in consideration) = 150 in count.False Negative (FP)= test result negative (no disease detected by the test) when person is diseased in reality = 60False positive (FN) = test result positive when person has no disease in reality = 50As total 900 tests were done, so we get: True negative(TN) = 900 - TP - FP - FN = 640(as each test result would be one of the TP, TN, FP, FN and these four no test result can lie in more than one of these categories).
Now, we have:
true results = TP + TN = 640 + 150 = 790
total results = 900
Thus, we get:
[tex]\text{Test accuracy} = \dfrac{TP + TN}{TP + FP + TN + FN} = \dfrac{790}{900} \approx 0.8778 = 87.78%[/tex]
Thus, the overall accuracy of the screening test for a newly discovered disease is being evaluated for this case is 87.78% approximately.
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1. 7h + 2h - 5h
Α 4h
Β. 14h
Answer:
A 4h
Step-by-step explanation:
[tex]7 + 2 - 5 = 9 - 5 = 4[/tex]
Which classification best represents a triangle with side lengths 10 in., 12 in., and 15 in.? acute, because 102 122>152 acute, because 122 152>102 obtuse, because 102 122>152 obtuse, because 122 152>102
The triangle with side lengths of 10 in., 12 in., and 15 in. is acute because 10^2 + 12^2 > 15^2
What is the acute angle?An acute angle is defined as the measure of an angle that is less than 90 degrees.
The side lengths of the triangles are 10, 12 and 15
The smallest side lengths are: 10 and 12
The sum of the squares of these side lengths is
[tex]10^2 + 12^2[/tex]
For the triangle to be acute, then the following must be true
[tex]10^2 + 12^2 > 15^2[/tex]
Evaluate the exponents
[tex]244 < 255[/tex]
The above inequality is true.
Hence, the triangle is acute because 10^2 + 12^2 > 15^2
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HURRYYY PLEASEEE
The diagram shows a cone of a height of 5 cm and a base radius of 12 cm.
What is its volume?
Answer:
volume V = 314.159265 cm³
Step-by-step explanation:
By formula, Volume is = (1/3)πr²h
0.33×3.14×12×12×5
is = 314.159265 m3
Other info
radius r = 5 m
height h = 12 m
slant height s = 13 m
volume V = 314.159265 m3
lateral surface area L = 204.203522 m2
base surface area B = 78.5398163 m2
total surface area A = 282.743339 m2
The diagram shows a right angled triangle. What is the value of h.
Round to 1 decimal place
Answer:
h = 13.4cm
Step-by-step explanation:
BAC + ACB = 90°
BAC + 48° = 90°
BAC = 42°
cos(BAC) = AB/BC
cos(42°) = h/18
h = 13.377 ≈ 13.4cm
Surface Area of Cylinders 4 cellus 6 = SA = 2tr2 + 2nrh 2πη2 + 2πχh (Use 3.14 for 7.) Resources 5 in. Find the surface area. Help square inches 30 in. Do NOT round your answer. B If
Answer:
1099in²
Step-by-step explanation:
SA = [tex] \sf A=2\pi rh+2 \pi r² [/tex]
⇒ SA=2πrh+2πr²
⇒ SA = 2((3.14)(5)(30)+(2)(3.14)(5²)
⇒ SA = 2((3.14)(5)(30)+(2)(3.14)(25)
⇒ SA = 1099
Surface Area = 1,099 in²
Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm? acute, because 62 102 < 122 acute, because 6 10 > 12 obtuse, because 62 102 < 122 obtuse, because 6 10 > 12
If the square sum of the perpendicular and base is less than the square of hypotenuse then the angle will be an obtuse angle. Then the correct option is C.
What is a Pythagoras theorem?The Pythagoras is the sum of the square of two sides is equal to the square of the longest side. And it is given as
P² + B² = H²
A triangle with side lengths of 6 cm, 10 cm, and 12 cm.
We know that if the square sum of the perpendicular and base is greater than the square of hypotenuse then the angle will be an acute angle.
Ans if the square sum of the perpendicular and base is less than the square of hypotenuse then the angle will be an obtuse angle.
Then we have
6² + 10² < 12²
Then the angle will be an obtuse angle.
More about the Pythagoras theorem link is given below.
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Answer: C
Explanation: Obtuse, because 6^2+10^2<12^2
Multiply and combine like terms to determine the product of these polynomials.
(3x – 4)(2x + 5)
Answer: Find attached the workings in the picture.
Step-by-step explanation:
1/9 divided by 1/8 in fraction form
Answer: 8/9
Step-by-step explanation: Math in the image
How do i solve this pls help
Answer:
7.07106781
simplified
7.07
Step-by-step explanation:
I need help please....
Answer:
[tex]y \geqslant - x - 4[/tex]
Step-by-step explanation:
y≥-x-4 is the required equation
Mark plants 9 red rose bushes and 4 yellow rose bushes.What is the ratio of yellow rose bushes planted to the total number of roes bushes planted?
Answer:
4:13
Step-by-step explanation:
First as stated in the problem, mark is looking to find the ratio of Yellow rose bushes planted the Total amount of rose bushes planted; so therefor we must find the total amount of rose bushes planted first.
9+4 = 13.
13 will be our second number, since it is Yellow : total.
Then, we understand that mark plants 4 yellow rose bushes, so 4 is our first number.
Now; we can put our numbers together.
4 to 13 ; [tex]\frac{4}{13}[/tex] , or 4:13.
I really hope this helps! Have an amazing day!
Answer: There are a total of thirteen (13) rose bushes planted but specifically there are six (6) white, five (5) red, and two (2) yellow rose bushes.
Step-by-step explanation: I done it in my head to figure it out so, i hope this helps you have a good day love.
How do you work out the intersection?
Answer:
Get the two equations for the lines into slope-intercept form. ... Set the two equations for y equal to each other.Solve for x. ... Use this x-coordinate and substitute it into either of the original equations for the lines and solve for y.
Step-by-step explanation:
is 6 and 9 like terms or unlike terms
Answer:
i think they are unlike terms
Step-by-step explanation:
need help asap please
Step-by-step explanation:
first of all, your teacher wrote nonsense in the answer options : an area is always given in squared units. never in cubed units (which would be volume).
the area is : 1/2 × perimeter × apothem
the perimeter is simply 12 × 5 = 60 meters.
apothem = (a/2)×cot(pi/12) = 5/2 × cot(pi/12) =
= 9.330127019... meters
so the area is
1/2 × 60 × 9.330127019... = 279.9038106... m²
therefore, the third answer option is correct (although it is m², and not m³).
by the way, you have question 3 wrong. I answered this with the correct apothem calculation in the explanation for question 4.
A ring-toss toy is composed of a rectangular prism on top of a cylinder. The rectangular prism is completely fill with water. The dimensions of the rectangular prism are shown in the diagram.
a) 90cm3
b) 208cm3
c) 29cm3
d) 480cm3
Answer:
answer = C) 3 x 10 x 16 = 480 cm³
what is the area of a prism
Answer:
The area of prism is calculated by:(a+b)h/2
Write the equation of the line that passes through the points (-1, 3) and (-5, -3)
Answer:
[tex]y= \frac{3}{2}x+\frac{9}{2}[/tex]
Step-by-step explanation:
First find the slope: [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} } = \frac{-3 - (3)}{-5-(-1)} = \frac{-6}{-4} = \frac{3}{2}[/tex]
Next use the point-slope fomula and one of the points to find the line:
[tex]y-y_{1} =m(x-x_{1} )[/tex] and the ordered pair (-1,3)
[tex]y-3=\frac{3}{2}(x-(-1))\\ y-3 = \frac{3}{2}(x+1)\\y-3=\frac{3}{2}x + \frac{3}{2}\\y=\frac{3}{2}x +\frac{3}{2}+3\\y = \frac{3}{2}x + \frac{9}{2}[/tex]
A car rental company charges $28 per day for a rented car and $0.50 for every mile driven. A second car rental
company charges $20 per day and $0.75 for every mile driven. What is the number of miles at which both
companies charge the same amount for a one-day rental?
Answer:
56 miles
Step-by-step explanation:
According to the question, lets say the miles at x they charge the same rental
34 + 0.50x = 20 + 0.75x (Solve equation)
0.75x - 0.50x = 34 - 20
0.25x = 14
x = [tex]\frac{14}{0.25}[/tex]
x = 56
So at 56 miles, they charge the same rental.
Which of the following graphs represent a function?
4 graphs. Graph A is a curved line, graph b is horizontal, vertical, and then horizontal, graph C is a line with positive slope, graph D is a circle.
a.
Graph A and Graph C
b.
Graph A
c.
Graph D
d.
Graph B and Graph D
You throw three number cubes that are numbers 1-6 all at the same time. What is the probability that you would get a triple 3 on the first throw?
Answer:
3/18 but if you have to simplify it, it would be 1/6
Answer:
1/27Step-by-step explanation:
For each cube the probabilty of number 3 is 1/6 since it is one option out of 6 possible numbers.
The probability of same number on all three cubes is:
P(3,3,3) = 1/3*1/3*1/3 = 1/27What is the sum? startfraction 3 y over y squared 7 y 10 endfraction startfraction 2 over y 2 endfraction startfraction 5 over y minus 5 endfraction startfraction 5 (y 2) over (y minus 2) (y 5) endfraction startfraction 5 over y 5 endfraction startfraction 5 (y minus 2) over (y minus 5) (y 2) endfraction
The sum of the fraction expression is equal to 5/(y+5) then the correct option is C.
What is a fraction number?A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of numerator and denominator.
The expression is given as
[tex]\rm \dfrac{3y}{y^2+7y+10} + \dfrac{2}{y+2}[/tex]
Then the sum of the expression is given as
[tex]\rm \rightarrow \dfrac{3y}{y^2+7y+10} + \dfrac{2}{y+2}\\\\\\\rightarrow \dfrac{3y}{(y+2)(y+5)} + \dfrac{2}{y+2}\\\\\\\rightarrow \dfrac{3y + 2(y+5)}{(y+2)(y+5)}\\\\\\\rightarrow \dfrac{5y+10}{(y+2)(y+5)}\\\\\\\rightarrow \dfrac{5(y+2)}{(y+2)(y+5)}\\\\\\\rightarrow \dfrac{5}{(y+5)}[/tex]
More about the fraction number link is given below.
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Answer:
C on edge 2022
Step-by-step explanation:
5/y+5
у
-8
6
2
2
A
х
-8
- 6
- 2
6
6
o
8
22
4
6
8
What is the range of the function graphed above?
Answer:
From the graph range = (-inf, + inf)
Step-by-step explanation:
range is the y values that the graph can have
6.
The cost of 5. 5 pounds of apples is $40. 81
What is the constant of proportionality that relates
the cost in dollars, y
to the number of pounds of apples, X?
A) 5. 5
B) 5. 94
C) 6. 37
D) 7. 42
F)8. 16
G) Not listed
Answer:
D 7.42
Step-by-step explanation:
y = k x
40.81 = k ( 5.5)
k = 40.81/5.5 =
Find all possible values of x. The triangles are NOT drawn to scale.
Answer:
0 < x < 28
Step-by-step explanation:
The triangle inequality theorem states that the sum of any two sides of the triangle should be greater than the third side.
Therefore,
0 < x < 28All the possible values of x are 26 < x < 28.
What is Triangle?A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.
Sum of the interior angles of a triangle is 180 degrees.
So a triangle has three sides.
We have the triangle inequality theorem which states that,
The length of any side of the triangle is always less than the sum of the other two sides.
And the range of the possible measure of the third side is the sum and the difference of the other two sides.
So x < 27 + 1 = 28
and,
x > 27 - 1 = 26
So 26 < x < 28
Hence the measures of third side is 26 < x < 28.
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PLS HELP WILL MARK YOU BRAINLIEST! NO FAKE ANSWERS!
Answer:
angle HCG- 45/c
angle DF- 105/b
Step-by-step explanation:
m<HCG and m<ECD are opposite angles hence they are equal
m<HCG=45°Now
mDF=
M<ECD+m<ECF45+60105°Which expression is equivalent to (2^0 / 2^3) ^2
A 1/8
B 1/16
C 1/32
D 1/64
D
Step-by-step explanation:[tex](\frac{2^0}{2^3})^2[/tex]__________________________________
Calculate the power[tex](\frac{1}{2^3})^2[/tex]
[tex](\frac{1}{8})^2[/tex]
[tex]\frac{1}{64}[/tex]
__________________________________
Determine true/false[tex]Determine\ whether\ (\frac{2^0}{2^3})^2\ and\ \frac{1}{64}\ are\\ equivalent:[/tex]
[tex]True[/tex]
I hope this helps you
:)
HELP ME PLEASE THERES A PICTURE I WILL GIVE BRAINLIEST TO BEST ANSWER
Answer:
we need to know how many students are in the class
if there are more boys, than the probability of picking a boy is higher, and if there is more girls, the probability of picking a girl is higher and if the amount of boys and girls are the same, then the probability of picking a girl or a boy is the same.
Step-by-step explanation:
Please mark my answer as brainliest