The negative one is the third root of the equation x³ - 4x² + 2x + 10. Then the correct option is B.
What is polynomial?Polynomial is an algebraic expression that consists of variables and coefficients. Variables are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.
The polynomial equation is given below.
[tex]\rm x ^3-4 x ^2+2 x+ 10 = x ^2 -5 x-3[/tex]
The equation can be written as
[tex]\rm x ^3-5 x ^2+7 x+ 13 = 0[/tex]
The equation has a complex root [tex]- 3 \pm 2 \iota[/tex]
Put x = -1, then we have
[tex]\begin{aligned} (-1) ^3-5 (-1) ^2+7 (-1)+ 13 = 0\\\\-1 - 5 - 7 + 13 = 0\\\\0=0 \end{aligned}[/tex]
The equation is satisfied by the negative one. Then the negative one is the third root of the equation.
More about the polynomial link is given below.
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Answer:
B on edge
Step-by-step explanation:
because B is -1
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 =
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]
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 = 1/27Which 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
:)
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.
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°For a standard normal distribution, find the approximate value of p (negative 0.78 less-than-or-equal-to z less-than-or-equal-to 1.16). use the portion of the standard normal table below to help answer the question.
The approximate value of P(-0.78 ≤ Z ≤ 1.16) is obtained being 0.6593
How to get the z scores?If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.
If we have [tex]X \sim N(\mu, \sigma)[/tex]
(X is following normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex])
then it can be converted to standard normal distribution as
[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]
(Know the fact that in continuous distribution, probability of a single point is 0, so we can write
[tex]P(Z \leq z) = P(Z < z) )[/tex]
Also, know that if we look for Z = z in z-tables, the p-value we get is
[tex]P(Z \leq z) = \rm p \: value[/tex]
For this case, we have to find:
[tex]P(-0.78\leq Z \leq 1.16)[/tex]
It can be rewritten as:
[tex]P(-0.78\leq Z \leq 1.16) = P(Z \leq 1.16) - P(Z < -0.78) \\P(-0.78\leq Z \leq 1.16) = P(Z \leq 1.16) - P(Z \leq -0.78)[/tex]
The p-values for Z = 1.16 and Z = -0.78 from the z-table is found as 0.8770 and 0.2177 respectively, and therefore, we get:
[tex]P(-0.78\leq Z \leq 1.16) = P(Z \leq 1.16) - P(Z \leq -0.78)\\P(-0.78\leq Z \leq 1.16) = 0.8770 - 0.2177 = 0.6593[/tex]
Thus, the approximate value of P(-0.78 ≤ Z ≤ 1.16) is obtained being 0.6593
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Answer:
B.) The answer is 66% if you convert it from decimals
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
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:
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
is 6 and 9 like terms or unlike terms
Answer:
i think they are unlike terms
Step-by-step explanation:
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.
Nikki went to a concert that started at 2:30pm.it ended at 4:00pm. How long was the concert?
started= 2:30 PM
ended= 4:00 PM
to find:the duration of the concert.
solution;( just find the difference of finishing time and starting time)
= 1 hour 30 mins
so, the duration of the concert is 1 hour 30 mins.
0400-0230
= 1 hour 30 minutes
hope this helps :)
1/9 divided by 1/8 in fraction form
Answer: 8/9
Step-by-step explanation: Math in the image
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.
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 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
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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Region R is bounded by the curves y = √x, y = 1, and x = 4. A solid has base R, and cross sections perpendicular to the x-axis are squares. The volume of this solid is
A. 4/3
B. 8
C. 7/6
D. 15/2
The cross sections have side length equal to the vertical distance between y = √x and y = 1, or |√x - 1|. The two curves meet at the point (1, 1), and y = √x meets x = 4 at (4, 2), so we'll be integrating with respect to x on the interval [1, 4]. Over this interval, √x ≥ 1, so |√x - 1| = √x - 1.
A cross section of thickness ∆x has volume
(√x - 1)² ∆x = (x - 2√x + 1) ∆x
Then the volume of the solid is
[tex]\displaystyle \int_1^4 (x - 2\sqrt x + 1) \, dx = \boxed{\frac76}[/tex]
Given SA 108 units squared SA=192 units squared V-1408 units squared Find Volume of the smaller figure
I need help please....
Answer:
[tex]y \geqslant - x - 4[/tex]
Step-by-step explanation:
y≥-x-4 is the required equation
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
9 A boy takes a penalty 40 times against a goalkeeper. He scores 16 times.
What is the relative frequency of him scoring a penalty? zu
(b) If the boy took 200 penalties how many times would you expect him to score?
Answer:
I think for A It is 3.
Step-by-step explanation:
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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Naomi bought stock in a company two years ago that was worth
x
x dollars. During the first year that she owned the stock, it increased by 23%. During the second year the value of the stock increased by 26%. Write an expression in terms of
x
x that represents the value of the stock after the two years have passed.
The expression that represents the value of the stock after two years have passed is 1.5498x
What is the expression that reperesnts the value of the stock after two years?
Percentage is the fraction of an amount expressed as a number out of hundred. The sign used to represent percentages is %.
The value of the stock after year 1 = worth of the stock when it was bought x (1 + percentage increase in year one)
1.23x
The value of the stock after year 2 = worth of the stock in year 1 x (1 + percentage increase in year two)
1.26 x 1.23x = 1.5498x
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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]
How do i solve this pls help
Answer:
7.07106781
simplified
7.07
Step-by-step explanation:
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:
A parking garage is located in the downtown area of a city. The
table below shows the cost for parking in the garage for different
amounts of time.
Hours Parked
Cost of Parking
1
$8.80 1 1/2 $10.70
4
$20.20
5
$24
7 1/2
$33.50
10
$43
a) What equation represents the cost of parking in the garage,
y, for x hours?
b) Sketch a graph to represent the cost of parking over time.
Answer:
a) y = 3.80x +5.00
b) see attached
Step-by-step explanation:
A graph shows the given table values lie on a straight line.
__
a)Finding the slope of the line is made easier by an appropriate choice of a pair of table values:
m = (y2 -y1)/(x2 -x1)
m = (24 -20.20)/(5 -4) = 3.80/1 = 3.80 . . . . using (4, 20.20) and (5, 24)
The y-intercept can likewise be found with an appropriate choice of table values. Solving the slope-intercept equation for b, we get ...
y = mx +b
b = y -mx
b = 8.80 -3.80 × 1 = 5.00 . . . . using the first table value
An equation that represents the cost of parking could be ...
y = 3.80x +5.00
__
b)A graph of the table values and the equation is shown in the attachment.