6. (09.04 LC)
For the equation y = 6x2 – 9x + 22, choose the correct application of the quadratic formula. (5 points)
X
-6+1(6)- 4(-9)(22)
2(-9)
X
6 + (6)- 4-9)(22)
21-9)
--9 +1(-99) - 4(6)(22)
X
2(6)
X
9+(-9) - 4(6)(22)
2(6)
Given:
The quadratic equation is
[tex]y=6x^2-9x+22[/tex]
To find:
The correct application of the quadratic formula.
Solution:
If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then the quadratic formula is
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
We have,
[tex]y=6x^2-9x+22[/tex]
Putting [tex]y=0[/tex], we get
[tex]6x^2-9x+22=0[/tex]
Here, [tex]a=6,b=-9,c=22[/tex]. Using the quadratic formula, we get
[tex]x=\dfrac{-(-9)\pm \sqrt{(-9)^2-4(6)(22)}}{2(6)}[/tex]
The correct application of the quadratic formula is [tex]x=\dfrac{-(-9)\pm \sqrt{(-9)^2-4(6)(22)}}{2(6)}[/tex].
Note: The options are not in proper format.
I NEED HELP ASAP
FIND THE MEASURE OF MISSING ANGLE
Answer:
50
Step-by-step explanation:
a right triangle is = to 180 so you need all angles to add to 180 so you take 180 minus it by 90 and 40 you are left with 50 degrees
말 8.) A baker is ordering eggs for the week. How many cartons of 6 eggs would a baker need to have 225 eggs all together? Explain the reasoning for your answer. (4 pts.)
Answer:
38
Step-by-step explanation:
We know that each carton contains 6 eggs and we need a total of 225. To find this answer, divide 225 by 6, which is 37.5. We would have to round up one because you cannot buy half of a carton. So the answer is 38 cartons.
What is equivalent to the equation y=3x+z/4?
what is the answer of 17x12
Answer:
204
Step-by-step explanation:
17x12=204
NEED HELP MY GRADE DEPENDS ON THIS QUESTION!!!
Write a congruence statement that describes the figures below.
Answer:
✓ triangle GSP = triangle RKF
Step-by-step explanation:
have a great day!
PLEASE HELP
ASAPPPPPP
Which of the following segments is a diameter of O?A. OD
B. DB
C. АС
D. AB
Answer:
AB is the diameter,,,,,,,,,
What is the end behavior for the graph of the function
f(x)=9/10 log [-(x + 9)] + 10?
Answer:If you draw a graph or look it up on Desmos, it curves down around y = 10. It only hits the second and third quadrant. B is the only situation that describes this.
Step-by-step explanation:g
Yoko is mailing packages. Each small package costs her $2.20 to send. Each large package costs her $3.40. How much will
it cost her to send 3 small packages and 1 large package?
Answer:
$10
Step-by-step explanation:
3($2.20)+3.40
6.60+3.40=10
The sum of all even numbers from 0 to 420 is
Answer:
the sum of all even number from 0 to 420 is 175980
7ft
5ft
8ft
7ft
Find the area of each figure
Another friend's distance d from you (in feet) after t seconds is given by
d = |80 - 5t|. What does the 80 in the equation represent? What does the 5 in the equation represent? At what times is she 60 ft from you?
Tyshawn drew a two-dimensional shape. The shape had multiple sides. The
shape had only right angles. There are two pairs of parallel lines. One pair is 4 inches
Answer:
This is a rectangle
Step-by-step explanation:
2D shape with 4 right angles would be a rectangle because 2 sides are equal and the other 2 would be equal to give you 4 right angles
Researchers published a study in which they considered the incidence among the elderly of various mental health conditions such as dementia, bi-polar disorder, obsessive compulsive disorder, delirium, and Alzheimer's disease. In the U.S., 45% of adults over 65 suffer from one or more of the conditions considered in the study. Calculate the probability that fewer than 320 out of the n
Answer:
The step-by-step procedure to solve this question is given, using the normal approximation to the binomial distribution.
Step-by-step explanation:
We use the normal approximation to the binomial distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In the U.S., 45% of adults over 65 suffer from one or more of the conditions considered in the study.
This means that [tex]p = 0.45[/tex]
Mean and standard deviation for the approximation, for a sample of n:
[tex]\mu = E(X) = np = 0.45n[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{0.45*0.55n}[/tex]
Calculate the probability that fewer than 320 out of the n
Using continuity correction, this is [tex]P(X < 320 - 0.5) = P(X < 319.5)[/tex], which is the pvalue of Z when X = 319.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{319.5 - 0.45n}{\sqrt{0.45*0.55n}}[/tex]
Just have to replace the value of n, find Z, and then find its pvalue.
A bread recipe calls for 1/3 cup of white flour and 5 1/3 cups of whole wheat flour. How much flour do I need in total of my recipe?
Answer:
5 2/3
Step-by-step explanation:
If Siny = x Sin (a+y). Prove that
dy/dx=[Sin²(a+y)]/Sina
Answer:
Use Trigonometric formulae to simplify expressions
Step-by-step explanation:
Re-order to group the x and y,
Sin(y) / Sin(a+y) = x
to differentiate apply d/dx to both sides
[tex]\frac{d}{dx}[/tex]Sin(y) / Sin(a+y) = [tex]\frac{d}{dx}[/tex]x
use division rule on left side which will give
[tex]\frac{dy}{dx}[/tex]Cos(y)Sin(a+y) - [tex]\frac{dy}{dx}[/tex]Cos(a+y)Sin(y) / Sin²(a+y) = 1
Group them so dy/dx is on the left hand side:
[tex]\frac{dy}{dx}[/tex] = Sin²(a+y) / Cos(y)Sin(a+y) - Cos(a+y)Sin(y)
Apply trigonometric sum formula to expand Sin(a+y) and Cos(a+y),
[tex]\frac{dy}{dx}[/tex] = Sin²(a+y) / Cos(y)[Sin(a)Cos(y) + Cos(a)Sin(y)] - Sin(y)[Cos(a)Cos(y) - Sin(a)Sin(y)]
Simplify it
[tex]\frac{dy}{dx}[/tex] = Sin²(a+y) / (Cos²(y) + Sin²(y))(Sin(a))
[tex]\frac{dy}{dx}[/tex] = Sin²(a+y) / (1)(Sin(a))
Prove that the figure is a parallelogram. If so, classify the parallelogram. Be specific and justify your answer.
What is the perimeter and area?
Answer:
Step-by-step explanation:
If it is a parallelogram the opposite sides will a have the same slope.
Using the diagram we see from the coordinates of A and B:
Slope of AB = (5 - -1)/(-1 - -5)
= 6/4
= 3/2.
In the same way
slope of CD = (2 - -4) / (1 - -3)
= 3/2.
So AB and CD can be shown to be parallel.
Similarly the lines BC and AD are parallel.
So the figure is a parallelogram
Finding the perimeter (counting the units between the points):
Perimeter = 2AB + 2BC
By Pythagoras:
AB = sqrt (6^2 + 4^2) = sqrt 52
BC = sqrt (3^2 + 2^2) = sqrt 13
So Perimeter = 2sqrt52 + 2sqrt13
= 4sqrt13 + 2 sqrt13
= 6sqrt13
or 21.63 unit^2 to 2 decimal places.
Area = sqrt52 * perpendicular distance between the lines AB and CD.
5(3m+2)
please help me
Answer:
(5x3m) + (5x2) = 15m + 10
Step-by-step explanation:
multiply 5 to 3m plus 5 to 2 which is equivalent to 15m + 10
A theatre has 46 rows.
There are 42 seats in each row.
During a show at the theatre, there are 50 empty seats.
Work out how many people are watching the show.
Answer:
1882
Step-by-step explanation:
46x42=1932 1932-50=1882
If x = 13, how could the angles be classified? Are the angles complementary or supplementary?
Answer:
To be complement sum of angle must be 90°
But to be supplement sum of angle must be 180°
Step-by-step explanation:
Salma has ridden 18 miles of a bike course. The course is 20 miles long. What percentage of the course has Salma ridden so far?
Can you plz help right answer plz
Answer:
4.8 inches
Step-by-step explanation:
For each ordered pair, determine whether it is a solution to 7x - 4y= -5.
find the volume of a plastic cube vuilding block with a side length of 12 centimeters
Step-by-step explanation:
Length of the plastic cube (L) = 12 cm
Volume of the cube
= L³
= ( 12)³
= 1728 cm³
Hope it will help :)❤
pleeeaassseee brainliest to first person
Answer:
B. 128
Step-by-step explanation:
Answer:
by using Pythagoras law
hypotenuse ²=perpendicular ²+base²
h²=100²+80²
h²=10000+6400
h=√16400=128.06m
128m is the required answer.
On average, there are 12 potholes per mile on a particular stretch of the state highway. Suppose the potholes follow a Poisson distribution on the highway. a. Find the probability of finding fewer than two potholes in a quarter-mile stretch of the highway. (Do not round intermediate calculations. Round your final answer to 4 decimal places.) b. Find the probability of finding more than one pothole in a quarter-mile stretch of the highway. (Do not round intermediate calculations. Round your final answer to 4 decimal places.)
Answer:
a) 0.1992 = 19.92% probability of finding fewer than two potholes in a quarter-mile stretch of the highway.
b) 0.8008 = 80.08% probability of finding more than one pothole in a quarter-mile stretch of the highway.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
a. Find the probability of finding fewer than two potholes in a quarter-mile stretch of the highway.
Mean of 12 potholes per mile, which means that in a quarter-mile stretch, the mean is [tex]\mu = \frac{12}{4} = 3[/tex]
This probability is:
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3}*(3)^{0}}{(0)!} = 0.0498[/tex]
[tex]P(X = 1) = \frac{e^{-3}*(3)^{1}}{(1)!} = 0.1494[/tex]
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.0498 + 0.1494 = 0.1992[/tex]
0.1992 = 19.92% probability of finding fewer than two potholes in a quarter-mile stretch of the highway.
b. Find the probability of finding more than one pothole in a quarter-mile stretch of the highway.
This is
[tex]P(X > 1) = 1 - P(X < 2)[/tex]
We have that [tex]P(X < 2) = 0.1992[/tex]
So
[tex]P(X > 1) = 1 - P(X < 2) = 1 - 0.1992 = 0.8008[/tex]
0.8008 = 80.08% probability of finding more than one pothole in a quarter-mile stretch of the highway.
Note: When solving for k, round to four decimal places. A culture started with 5,000 bacteria. After 3 hours, it grew to 6,500 bacteria. Predict how many bacteria will be present after 13 hours. Round your answer to the nearest whole number. P = Aekt Enter the correct answer. DONE + ?
Answer:
5000 * (e^((1 /4) * ln(55 / 50) * (13))) = 6,815.47 from My text book
Step-by-step explanation:
WILL GIVE BRAINLIEST
Find the area of the shaded region. Round to the tenths place. SHOW YOUR WORK
https://d3rqz33hmpm7kb.cloudfront.net/2021-01-15/5f6e19a9f9b9f1c16c230aae/6001f53de589b94a3a0f092f_rich-text-file-2021-01-15T20-04-46-084Z.imagepng
A ladder is standing on horizontal ground and rests against a vertical
wall. The ladder is 4.5 m long and its foot is 1.6 m from the wall.
Calculate how far up the wall the ladder will reach. Round your
answer to three decimal places. (Show your working)
Answer:
I don't know how to tell you the answer on this one because you need to know how tall the wall is for this one
Step-by-step explanation:
A student received a coupon for 12% off the total purchase price at a clothing store. Let b be the
original price of the purchase. Use the expression below for the new price of the purchase. Write an
1. equivalent expression by combining like terms.
b-0.12b
Answer:
the equivalent expression is 0.88(x)
Step-by-step explanation:
Given that
There is 12% off on the total purchase price
Based on the above information
The expression that used the given terms i.e.
b - 0.12b
i.e.
1 - 0.12
= 0.88(x)
Hence, the equivalent expression is 0.88(x)