The roots of the quadratic equation x² + x + 2 = 0 is [tex]-1+\sqrt{-7} /2[/tex] and[tex]-1-\sqrt{-7} /2[/tex]
What are roots?Roots: In mathematics, a solution to an equation, usually expressed as a number or an algebraic formula. The square root of a number is a value that can be multiplied by itself to give the original number. The square root of 9 is 3, because when 3 is multiplied by itself, you get 9.
given quadratic equation is, x² + x + 2 = 0
to find the roots we have formula method ,
x=[tex]-b+\sqrt{b^2-4ac}[/tex][tex]/2a[/tex]
x=[tex]-b-\sqrt{b^2-4ac}[/tex][tex]/2a[/tex]
a=1, b=1 and c=2
sub the values in the above equation
x=[tex]-1+[/tex][tex]\sqrt{1-4(1)(2)}[/tex][tex]/2[/tex]
x=[tex]-1-\sqrt{1-4(1)(2)} /2[/tex]
x= [tex]-1+\sqrt{-7}/2[/tex] and x=[tex]-1-\sqrt{-7} /2[/tex] are the roots of the quadratic equation
to learn more about roots visit:
brainly.com/question/16932620
#SPJ1
through (-3,5), slope=4 slope intercept
The most appropriate choice for equation of line in slope intercept form will be given by-
y = 4x + 17 is the required equation of line
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Here,
Slope = 4
The line passes through (-3,5)
Equation of line = y - 5 = 4[x - (-3)]
y - 5 = 4x + 12
y = 4x+ 12 + 5
y = 4x + 17
To learn more about equation of line in slope intercept form, refer to the link-
brainly.com/question/25514153
#SPJ9
Convert 22 kilograms to pounds. (round
your answer to the nearest tenth)
1 lb = 0.4536 kg
1 kg = 2.205 lbs
22 kgs is equivalent to
lbs
Answer:
48.5 lbs
Step-by-step explanation:
lkg = 2.205 lbs
22kgs = 2.205 x 22
= 48.51 lbs
= 48.5 lbs (to the nearest tenth)
22 kilograms is equivalent to 48.5 pounds.
Given that we need to convert 22 kilograms to pounds.
We have,
1 lb = 0.4536 kg
1 kg = 2.205 lbs
To convert kilograms to pounds, you can use the conversion factor that 1 kilogram is equal to 2.205 pounds.
Therefore, to convert 22 kilograms to pounds, you can multiply 22 by 2.205:
22 kg x 2.205 lbs/kg = 48.51 lbs
Rounded to the nearest tenth, 22 kilograms is equivalent to 48.5 pounds.
Hence 22 kilograms is equivalent to 48.5 pounds.
Learn more about conversion factor click;
https://brainly.com/question/30567263
#SPJ6
SOMEONE PLEASE ANSWER!!!!!!!
Solve for x:
4(4/4x) + 5 = 32
Answer:
6.75
Step-by-step explanation:
A used car was bought for $15,000. When the car was new, it sold for
$25000. If the car depreciates exponentially at a rate of 6% per year, approximately
how old is the car?
Answer:
around 6.66 year old
Step-by-step explanation:
Draw a line representing the "rise" and a line representing the "run" of the line. State
the slope of the line in simplest form.
-10 9
Click twice to plot each segment.
Click a segment to delete it.
34
8
Answer:
slope = rise /run
Step-by-step explanation:
hysnsk
2) Kyle has $150 to spend at the video game store. He buys a new controller for $29 and spends the rest on games. If each game costs $11, how many games did Kyle buy?
A. 4.7
B. 11
C. 14
D. 121
Answer: I think it's B. 11
Step-by-step explanation:
150-29=121
121÷11=11
please look at image and answer question.
Answer: m = 129 degrees
Step-by-step explanation:
A Hexagon has 720 degrees in total
Subtract all the known angles
720 - 90 - 90 - 146 - 130 - 135 = m
m = 129 degrees
Answer:
m = 129°
Step-by-step explanation:
Finding the unknown angle in the polygon:Find the sum of angles of the polygon using the formula,
Sum of angles of polygon = (n - 2)*180
n is the number of sides. n = 6
= ( 6- 2) *180
= 4*180
= 720°
Sum of the angles of given polygon = 720
90 + 146 + 90 + 135 + m + 130 = 720
m + 591 = 720
m = 720 - 591
m = 129°
Seth traveled 1 mile in 57.1 seconds.About how fast does seth travel in miles per hour.
Show your work its about unit rates
Answer:
63.04728546 miles an hour
Step-by-step explanation:
to figure out how many miles an hour Seth travels we are gonna start with how far he goes in one min.to do that we are gonna do 60÷57.1 ( we do this to figure the distance he goes in a minute)60÷57.1=1.050788091Now we know he travels 1.050788091 in one minutewe know that there are 60 mins in an hour so we are gonna multiply that but the miles a second60×1.050788091=63.04728546If you need to figure out any other unit of measurement an hour you do it like this:example: we need to convert miles to kmwe know that 1 mile is 1.60934 kmso we do 1mile in 57.1 seconds is 1.60934km in 57.1 seconds then do the steps aboveI recommend that you do the conversion in the beginning so you don't have to handle really big decimals
An ice cube has lengths 25mm.
It has a mass of 2.325g.
Work out the density in g/cm³.
Analiza lo siguiente ¿qué sucede si divides el número acumulado del año 2 entre el
dinero del año 1, posteriormente divide la cantidad acumulada del año 3 entre la
cantidad acumulada del año 2 y así sucesivamente?
Answer:
iiiiiiiiiiiiiiiiiiiiiiiiiiiiiii
write 4 2/4 as an improper fraction
if h (x) = 2x2 - 5x + 7, find the value of h (-3)
^ (to the second power)
By evaluating h(x) in x = ^-3 and then squaring it, we will see that:
h(-3) = 1,600
How to fid the value of h(3)^2?
Here we have the function:
h(x) = 2x^2 - 5x + 7
First let's evaluate it in x = -3, to do so we just need to replace the variable x by the number 3, we will get:
h(-3) =2*(-3)^2 - 5*-3 + 7
h(-3) = 2*9 + 15 + 7 = 18 + 15 + 7
h(-3) = 40
Now we square it:
h(-3)^2 = 40^2
h(-3)^2 = 1,600
Learn more about evaluating functions.
https://brainly.com/question/1719822
#SPJ1
Which of the following would NOT be an effective way to offer assistance to someone suffering from depression?
Ask someone you trust for help
Avoid any judgement or shame
Offer ideas for ways to cheer them up
Reassure them that they deserve to feel better
Answer: Ask someone you trust for help.
Step-by-step explanation: I chose this answer because if someone is struggling from depression you don't want to go off and tell people about it, I'm not completely sure if this is the answer but i know that the other answers are better. Definitely avoid judgment or shame.
Simon bought a new gaming system. He made an initial payment of $60 to the store , and he will pay $40 each month until the system is paid off. Which equation represents the relationship between m, the number of monthly payments Simon has made, and t, the total amount that Simon has paid the store?
Answer: t = 60 - m + 40 I think I don't really know how to solve this equation but I think this is the answer
in a normal distribution, there is a constant proportion of the area under the curve lying between the mean and any given distance from the mean and is measured in group of answer choices variance units. z score units. raw score units. standard deviation units.
The area under the curve lying between the mean and any given distance from the mean is measured in standard deviation units.
Define normal distribution.The theoretical curve that shows the probability that an experiment will produce a particular result in statistics. The symmetrical and bell-shaped curve shows that whereas trials frequently provide results that are near to the average, they can also vary significantly from it on occasion.
The standard normal distribution is a type of normal distribution that has a mean of 0 and a standard deviation of 1. The standard deviation shows how far a given measurement deviates from the mean, and the standard normal distribution is centered at zero. Sixty-eight percent of the observations for the normal distribution are within one standard deviation of the mean, ninety-five percent are within two standard deviations of the mean, and 99 percent of the data are three standard deviations or less from the mean.
To know more about standard deviation units, visit:
https://brainly.com/question/4499618
#SPJ4
Can someone pls help me right quick what’s the answer
Answer:
3rd one
Step-by-step explanation:
Add. Write your answer as a fraction or as a whole or mixed number
10
1/4 + 5 1/2 =
Submit
Addition of 10 + 1/4 + 5 1/2
= 10 + 1/4 + 11/2 ....................(5 1/2 can be written as 11/2)
On taking the LCM of the denominators, we can write:
[(10 x 4) + 1 + (11 x 2)]/4
= (40 + 1 +22) /4 = 63/4
So, in fraction the solution is 63/4
In mixed number the solution can be written as: 15 3/4
What are Fractions?In general, any number of equal pieces is represented by a fraction, which is a portion of the entire. A fraction, such as one-half, eight-fifths, or three-quarters, indicates the number of parts of a particular size when it is used in daily speech. In uncommon fractions, such as compound fractions, complex fractions, and mixed numerals, numerators and denominators are also employed. Common fractions with a positive sign have natural integers for both the numerator and denominator. The denominator tells us how many of those equal parts make up a unit or a whole, whereas the numerator reflects the total number of equal parts.Since there is no such thing as a zero-part whole, the denominator cannot be zero.To learn more about Fractions, refer to:
https://brainly.com/question/10354322
#SPJ9
To solve -3 = -19 + d/5, what steps would you use?
The value of d is 4 by law of exponents.
What are exponents?
The mathematical procedure known as exponentiation uses the base b and the exponent, or power, n. Its translation is "b to the n" and its symbol is Bn. The how many times a number has been amplified by itself is known as an exponent. When written as 23, the phrase "2 to the third" actually means "2 x 2 x 2 = 8," not 23, and "2 x 3 = 6," respectively.
Keep in mind that a number multiplied by one equals the original number.
Exponents are a way to express very big numbers as powers of smaller numbers. The exponent, so to speak, is the amount of times an integer has been multiplied by itself.
Applying the laws of exponents,
Given that, -3 = -19 +d/5
-3 = -19 +d5
-3 + 19=d5
d = 4
The value of d is 4 by law of exponents.
Learn more about exponents here:
https://brainly.com/question/11975096
#SPJ1
A bus carrying students stops every 30 minutes between 6am and 11am.students arrive at the bus top at random times. the time that a student waits is uniformly distributed from 0-30 mins. 1. calculate the area under the curve 2.calculate the mean 3.calculate the standard deviation 4.what is the probability that a student will wait more than 25 mins for a bus?
Using the uniform distribution, it is found that:
1. The area under the curve is of 1.
2. The mean is of 15 minutes.
3. The standard deviation is of 8.7 minutes.
4. The probability that a student will wait more than 25 mins for a bus is of 1/6.
What is the uniform probability distribution?The uniform distribution has two bounds, given by a and b, in which each possible outcome is equally as likely.
The area under the curve gives the sum of the probabilities of all outcomes, hence it is of 1, as the sum of the probabilities is of 1 = 100%.
The time that a student waits is uniformly distributed from 0-30 mins, hence the bounds of the interval are given by:
a = 0, b = 30.
The mean is given by:
M = (a + b)/2 = 30/2 = 15 minutes.
The standard deviation is given by:
[tex]S = \sqrt{\frac{(b - a)^2}{12}} = \sqrt{\frac{900}{12}} = 8.7[/tex]
The probability of finding a value higher than a measure x is given by:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
Considering the bounds in this problem, the probability that a student will wait more than 25 mins for a bus is:
P(X > 25) = (30 - 25)/(30 - 0) = 5/30 = 1/6.
More can be learned about the uniform distribution at https://brainly.com/question/28852504
#SPJ1
Write an equation in slope-intercept form for the line with slope 1/3 and y-intercept -7 then graph the line
The equation of the line is y = 1/3x - 7
The definition of linear equationsLinear equations are equations that have constant average rates of change.
How to determine the equation of the line?The given parameters are
Slope, m = 1/3
y-intercept, c = -7
A linear equation is represented as
y = slope * x + y-intercept
i.e.
y = mx + c
Where m = 1/3 and c = -7
So, we have
y = 1/3x - 7
Hence. the linear equation is y = 1/3x - 7
See attachment for the graph
Read more about linear equation at
brainly.com/question/14323743
#SPJ1
You are going to the carnival and your guardians said you can spend no more than $24 on rides. if rides cost $0.75 each, how many rides can you go on?
In the following diagram, Figure D'C'B'A is obtained by a dilation of Figure DCBA about the point A
The area of the figure formed by the dilation is 36 square units.
Area is particularly essential in modern mathematics. In addition to its importance in geometry and calculus, area is linked to the determination of determinants in linear algebra and is an essential feature of surfaces in differential geometry.
A dilation occurs when an figure is reduced to a smaller size using a fixed center.
From the given diagram we can find the sides of the square that is the transformed image as 9 - 3 = 6 units
Area of the A'B'C'D' square = 36 square units.
Side of the original square = 18 units.
Area of the ABCD square = 18² = 324 square units
Scale factor of dilation = 324/36 = 9 times.
Hence from the figure we can calculate the area of the transformed figure to be 36 square units which is dilated by a factor of 9 times.
To learn more about dilation visit:
https://brainly.com/question/16789982
#SPJ1
If a rectangle is 13 units wide and x units long what is the area
The area of Rectangle is 13x (13*x)
How to find area of rectangle ?
The formula of Area of Rectangle is A = W*L
A = area
W = width
L = length
so , to find area of rectangle
we have wide of 13 units , length x units
apply this in formula,
a = 13*x
so the area =13x
Some formulas of rectangle :
Area a = length * widthPerimeter p = 2( l +w)Diagonal d = [tex]\sqrt{W^{2} + L^{2} }[/tex]To learn more about find about rectangle refer :
https://brainly.com/question/17554232
#SPJ9
help me with this please!
Answer:
The bottom one is correct.
This is the graph of f(x). What is the value of f(2)?10 УA. 6ОВ. 2С. 5ООD. 9
To solve this problem we must take into account that the y-axis has intervals of 2 units length, and the x-axis has intervals of 1 unit length. We want to know the value of the function when x = 2, so we look for that value of x in the x-axis, we trace a vertical line from x = 2 to the curve that represents the function, and then a horizontal line to the y-axis, and we read the value of y:
Answer: D. 9
Can someone help me with this question?
ty <3
From the given milliliters of water and oil, the quantity of water is more than the oil , difference is of 450milliliters .
As given in the question,
As shown in the given diagram we have:
Mark of measure on water container is in between 600 and 800.
Mark represents it is 700milliliters
Mark of measure on oil container is in between 200 and 400.
Mark represents it is 250milliliters
700 milliliters is more than 250milliliters
700 > 250
Difference = 700 -250
= 450 milliliters
Therefore, from the given milliliters of water and oil, the quantity of water is more than the oil , difference is of 450milliliters .
Learn more about milliliters here
brainly.com/question/8513068
#SPJ1
What property is illustrated in the
example below?
94 (x + 2) = 94x + 188
A. Associative
B. Distribuive
C. Commutative
Answer:
B. Distributive
Step-by-step explanation:
Hello, there!
The number outside of the parentheses are being multiplied within the parentheses separated by a symbol, so distributive. (:
Hope this helped, and best of luck with the rest of your assignment.
Tell whether the events are independent or dependent. Explain.You throw the bowling ball at the pins.You have two throws to knock down ten pins.First throw:You knock down 6 pins.Second throw:You knock down 1 pin.
Given
You throw the bowling ball at the pins.You have two throws to knock down ten pins.
Procedure
The events are not independent. Before the first throw, there will be 10 pins to knockdown. Let the number of pins knocked down in the first throw is x.
In the second throw, there will not be 10 pins to knockdown. The number of pins to knockdown in the second throw depends on the number of pins being knocked down in the first throw. Hence, the number of pins to knockdown in the second throw is (10 - x). Thus, the events are dependent
Kiersti drove 58 mph for 1 hour and 52 minutes. Estimate the distance she traveled
Answer:
110 miles
Step-by-step explanation:
58 (1 + 52/60)
= 58 (1 + 13/15)
= 58 + 50.267
= 108.267 miles
= approximately 110 miles
if you dilate something by 1 half, what would you have to dilate it to to get it back to the same number.
If I dilate a number by 1 half, then I will have to dilate it again by 2, to get the same to the same number.
As per the question statement, I dilate a number by 1 half.
We are required to calculate that by what should I dilate the result, to reverb back to the same number that I started with.
To solve this question, first we need to understand the concept of Dilation.
Dilation means to create an Image.If dilation of a number or object enlarges it, then it is known as enlargement.On the other hand, if dilation creates a smaller image, then it is known as Reduction.Here, since our first dilation of the original number, say "x" reduces it by 1 half, that is, x becomes (x/2),
To get back to x, we will need to multiply (x/2) by 2 again.
[(x/2) * 2] = x.
Therefore, I will need to enlarge our result with a multiplication with 2 to get back to our original number.
Dilation: Dilation means to change the size of an object without changing its shape, where the size of the object may be increased or decreased based on the scale factor.To learn more about Dilation, click on the link below.
https://brainly.com/question/13176891
#SPJ1
