The solution of quadratic equation 8x² = 6 + 22x is x = 3 and x = -1/4
What is a Quadratic equation ?
A second-degree equation of the form ax² + bx + c = 0 is known as a quadratic equation in mathematics. Here, x is the variable, c is the constant term, and a and b are the coefficients. Since x is a second-degree variable, this quadratic equation has two roots, or solutions.
Given expression is,
8x² = 6 + 22x
Rewrite this expression as,
8x² - 6 - 22x = 0
8x² - 22x - 6 = 0
Now, we get the form quadratic equation i.e, ax² + bx + c = 0
Solve the equation and find roots
8x² - 22x - 6 = 0
2(4x² - 11x - 3) = 0
4x² - 11x - 3 = 0
4x² - 12x + x - 3 = 0
Take common terms out,
4x(x - 3) + 1(x - 3) = 0
we get the brackets same that means we're on right way,
(4x + 1) (x - 3) = 0
split the values into two,
4x + 1 = 0 and x - 3 = 0
4x = -1 x = 3
x = -1/4
Therefore, the solution of quadratic equation 8x² = 6 + 22x is x = 3 and x = -1/4
To read more about Quadratic equation
https://brainly.com/question/28038123
#SPJ1
a tire manufacturer has a 60,000 mile warranty for tread life. the manufacturer considers the overall tire quality to be acceptable if less than 5% are worn out at 60,000 miles. the manufacturer tests 250 tires that have been used for 60,000 miles. they find that 3.6% of them are worn out. with this data, we test the following hypotheses.h0: the proportion of tires that are worn out after 60,000 miles is equal to 0.05.ha: the proportion of tires that are worn out after 60,000 miles is less than 0.05.in order to assess the evidence, which question best describes what we need to determine?
the best question is that if they can examine a sample of tires used for 60,000 miles and determine the proportion that is worn out, then how likely is that proportion to be 3.6% or less?
we are given the information that an A tire manufacturer has a 60,000-mile warranty and the manufacturer considers the overall tire quality to be accepted if less than 5% are worn out at 60,000 miles, also the manufacturer tested 250 tires that have been used for 60,000 miles. they find that 3.6% of them are worn out. So here the Hypotheses can be that:
1) The proportion of tires that are worn out after 60,000 miles is equal to 0.05 and
2) The proportion of tires that are worn out after 60,000 miles is less than 0.05.
We need to deny the first hypothesis with an alternative one. You cannot demonstrate that the average is 3.6%, but if you by one means or another decide that the probability the average is greater than 3.6% is lower than 100% minus your confidence level, at that point you'll be able to deny the first hypothesis and acknowledge the second one as new average.
to know more about Hypotheses refer to the link https://brainly.com/question/18064632?referrer=searchResults.
#SPJ4
Raymond sings in a choir called the Seaville Songbirds. For every 5 modern songs they learn, the choir leader teaches them 3 classical songs.
Based on the given ratio of modern and classical songs learned, the number of modern songs learned if 9 classicals have been learned is 15
What is the number of modern songs learned?Number of modern songs they learn = 5Number of classical songs = 3If the choir has learned 9 classical songs;
Number of modern songs learnt = xEquate the ratio of the number of modern songs to the number of classical songs
5 : 3 = x : 9
5/3 = x/9
cross product5 × 9 = 3 × x
45 = 3x
divide both sides by 3
x = 45/3
x = 15
In conclusion, the number of modern songs they have learned if they learn 9 classical songs is 15
Complete question:
Raymond sings in a choir called the Seaville Songbirds. For every 5 modern songs they learn, the choir leader teaches them 3 classical songs.
If the choir has learned 9 classical songs, how many modern songs have they learned?
Read more on ratio:
https://brainly.com/question/12024093
#SPJ1
i need help with this asap please!!!
Answer:
54°
Step-by-step explanation:
m and the 54° angle are VERTICAL ANGLES. That means they are the same measure.
Answer:
Step-by-step explanation:
54 degree
Bret Rockford bought a home with a 11.5% adjustable rate mortgage for 20 years. He paid $10.67 monthly per thousand on his original loan. At the end of 1 year he owes the bank $70,000. Since then interest rates have increased to 13%. The bank will renew the mortgage at this rate, or Bret can pay the bank $70,000. He decides to renew and will now pay $11.72 monthly per thousand on his loan. (You can ignore the small amount of principal paid during the year.)
The old monthly payment is $
.
The new monthly payment is $
.
The percent increase in her monthly payment (to the nearest tenth) is
%
The old monthly payment was = 10.67 x 70 = 746.9
The new monthly payment is = 11.72 x 70 = 820.4
The percent increase in his monthly payment is =9.8406%
Given,
Sandra Williams bought a home with a 11.5% adjustable rate mortgage for 20 years. He paid $10.67 monthly per thousand on his original loan
According to the question:
So, per thousand value of $70,000 is 70000/1000 =70
Now, the old monthly payment was = 10.67 x 70 = 746.9
He decides to renew and will now pay $11.10 monthly per thousand on his loan.
So, the new monthly payment is = 11.72 x 70 = 820.4
The percent increase in his monthly payment is= 11.72 /10.67 - 1 x 100
9.8406 % and to nearest tenth it is 9.8406%
Hence, the old monthly payment was = 10.67 x 70 = 746.9
the new monthly payment is = 11.72 x 70 = 820.4
The percent increase in his monthly payment is =9.8406%
Learn more about Percent at:
https://brainly.com/question/14517915
#SPJ1
In any triangle the sum of the measures of the angles is 180°. And ABC is three times as large as B and also 16° larger than C. Find the measure of each angle
The measures of the each angle of the triangle is 84, 28 and 68 degrees.
How to find the measure of angles in a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
The triangle has the sum of the measures of the angles as 180°.
Angle A is three times as large as angle B and also 16° larger than C.
Therefore,
let
angle A = x
Angle B = x / 3
Angle C = x - 16
Therefore,
x + x - 16 + x /3 = 180
7 / 3 x - 16 = 180
7 / 3 x = 180 + 16
7 / 3 x = 196
cross multiply
7x = 196 × 3
7x = 588
divide both sides by 7
x = 588 / 7
x = 84
Therefore,
A = 84 degrees
B = 84 / 3 = 28 degrees
C = 84 - 16 = 68 degrees
learn more on triangle here: https://brainly.com/question/14773007
#SPJ1
Kaitlyn bakes two rectangular cakes to put on top of each other. Each cake is 6 inches wide, 12 inches long and 3 inches high. She removes the cake from the pan to frost it. How many square inches of frosting does she need for both cakes?
n how many ways can a math team of 14 students be chosen from a math club which consists of 15 seniors and 11 juniors if the team must consist of 8 seniors and 6 juniors?
Using Combination formula, total 2,24,070 ways to make a math team of 14 selected students in which consist of 8 seniors and 6 juniors.
We have following information,
total number of seniors in math club = 15
total number of juniors in math club = 11
total number of students in math club = 26
A math team of 14 students be choosen from maths club such that it consists 8 seniors and 6 juniors .
Number of ways to choose 8 seniors out of 15 seniors = ¹⁵C₈ = 485
Number of ways to choose 6 juniors out of 11 juniors = ¹¹C₆ = 462
Number of ways to select/choose a math team of 14 students consists 8 seniors and 6 juniors
= 485 × 462 = 2,24,070
Hence, the number of ways to select/choose a math team of 14 students consists 8 seniors and 6 juniors is 2,24,070..
To learn more about Combination formula, refer:
https://brainly.com/question/28065038
#SPJ4
help help help helppp
The coordinate of image of P is (-6,-4)
What in math is a coordinate?
a pair of numbers that utilize the horizontal and vertical breakups from the two reference axes to define a point's location on a coordinate plane. generally expressed by the x-value and y-value pair (x,y).
P (-2,2)
Translation (x,y)=(x-4,y-6)
x= -2
y= 2
x-4= -6
y-6= -4
Hence the coordinate of image of p is (-6,-4)
Learn more about Coordinate of the image at
https://brainly.com/question/20935031
#SPJ1
Lin rode a bike 20 miles in 150 minutes. She rode at a constant speed. How long did it take her to ride 6 miles
Answer: 45 minutes
Step-by-step explanation:
She rides 150/20 minutes per mile which is 7.5 minutes per mile. So it would take her 45 minutes to ride 6 miles because 6 × 7.5 = 45.
Which inequality correctly compares One-half, Three-fourths, and Two-thirds?
One-half < Three-fourths < Two-thirds
One-half < Two-thirds < Three-fourths
Two-thirds < One-half < Three-fourths
Three-fourths < One-half < Two-thirds
An inequality correctly compares One-half, Three-fourths, and Two-thirds is: One-half < Two-thirds < Three-fourths.
What is an inequality?An inequality simply refers to a mathematical relation that can be used to compare two (2) or more numerical values (numbers) and variables in an algebraic equation, especially based on any of the following inequality symbols:
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).Translating the numbers in word to numerical values, we have:
One-half = 1/2 or 0.5
Three-fourths = 3/4 or 0.75
Two-thirds = 2/3 or 0.67
Next, we would compare the above numerical values by using the less than (<) inequality symbol as follows:
0.5 < 0.67 < 0.75
One-half < Two-thirds < Three-fourths.
Read more on inequality here: brainly.com/question/12996324
#SPJ1
a survey showed that a family of four spends an average of $215.60 per day while on vacation. suppose a sample of 64 families of four vacationing at niagara falls resulted in a sample mean of $252.45 per day and a sample standard deviation of $74.50. a. develop a 95% confidence interval estimate of the mean amount spent per day by a family of four visiting niagara falls. 9 pts. b. based on the confidence interval from part (a), does it appear that the population mean amount spent per day by families visiting niagara falls differs from the mean reported by the survey? explain. 1 pt.
The confidence interval is (233.8436; 271.0564).
What is a confidence interval?
The likelihood that a population parameter will fall between a set of values for a specific percentage of the time is referred to as the confidence interval. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.
What is the margin of error?
In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings.
We have,
Sample mean = 252.45
Sample standard deviation = 74.50
n = 64
α = 0.05
By applying the margin of error formula, we get
Margin of Error = tα/2 * s/√n
df = n - 1 = 64 - 1 = 63
t(α/2, df = 63) = 1.998
Margin of Error = 1.998 * 74.50/√64
Margin of Error = 18.6064
The confidence interval = 252.45 ± 18.6064
= (233.8436; 271.0564)
Hence, the confidence interval is (233.8436; 271.0564).
To learn more about the confidence interval from the given link
https://brainly.com/question/26658887
#SPJ4
Find the LCM of
2 x 3 x 3 x 5 and 3 x 3 x 5 x 5
Answer:
LCM of 90 and 225 = 450
I'm not too sure I understand
2 x 3 x 3 x 5 = 90, and 3 x 3 x 5 x 5 = 225
90: 90, 180, 270, 360, 450
225: 225, 450
LCM = 450
What is the value of the expression a(b/c)+ a=3
B=4 C=2
The medical department at a local government agency has compiled test results for sick individuals who have been tested for the flu. They have found that not all people who test positive for the flu actually have the flu, and some people who test negative for the flu actually have the flu. The following tree diagram shows the conditional relative frequencies.
A tree diagram shows sick individuals branching off into two categories, have the flu and do not have the flu, which is labeled 25%. Have the flu branches off into two sub-categories, test positive, which is labeled 95%, and test negative. Do not have the flu branches off into two subcategories, test positive and test negative, which is labeled 92%.
What percent of sick individuals test negative for the flu?
23%
27%
75%
25%
Answer: it is not 27%
Step-by-step explanation:
for a binomial probability distribution with 8 trials and probability of success equal 0.95. what is probability of exactly six successes? (use the binomial tables)
0.0515 is probability of exactly six successes .
What is probability in math?
Probability refers to potential. The subject of this area of mathematics is the occurrence of random events. The range of the value is 0 to 1. To forecast how likely events are to occur, probability has been introduced in mathematics.Binomial probability with
Number of trials (n) = 8
probability of success ( ρ ) = 0.95
ρ = 0.95
p + q = 1
q = 1 - p
= 1 - 0.95
q = 0.05
x ~ bin( n , ρ )
ρ( X = x ) = ⁿCₓ Pˣ . qⁿ⁻ˣ
the probability of exactly six success .
ρ ( X = 6 ) = ⁸C₆ ( 0.95)⁶ ( 0.05 )⁸ ⁻⁶
= 28 ( 0.7351 ) ( 0.05)²
= 28 ( 0.7351 ) ( 0.0025 )
= 0.051457
ρ( X = 6 ) = 0.0515
Learn more about probability
brainly.com/question/11234923
#SPJ4
I need help on this problem can anyone help me?
The polygon's WXYZ and ABCD are similar.
What is similar figures?
The same shape between two figures is referred to as similarity. If two figures have congruent corresponding angles and equivalent length ratios on their corresponding sides, they are said to be similar mathematically. The scale factor is the name of this often used ratio.
Consider, the polygons WXYZ and ABCD
The angles, "∠W and ∠A" and "∠Y and ∠C" are congruent to each other.
Also, the angles "∠Z and ∠D" and "∠X and ∠B" are congruent to each other.
Now consider, the sides
The sides "WZ and AD", "XY and BC" and "WX and AB" , "ZY and DC" are having the equivalent ratio.
Therefore, the polygons WXYZ and ABCD are similar.
To know more about the similar figures, click on the link
https://brainly.com/question/14285697
#SPJ1
the graph shows the relationship between the amount of peaches in pounds xand the cost of peaches in dollars y
PLEASE HELP
The proportional relationship between the amount of peaches in pounds x and the cost of peaches in dollars y is given as follows:
y = 2.5x.
Direct proportional relationshipA direct proportional relationship is a special case of a linear function, with an intercept of zero, hence the output variable symbolized by y is given by the multiplication of the input variable symbolized by x and the constant of proportionality symbolized by k, as follows:
y = kx.
In this problem, we have to find the constant k taking a point of the graph.
The point taken is:
(2,5).
Meaning that when x = 2, y = 5.
Hence the constant is calculated as follows:
5 = 2k
k = 5/2
k = 2.5.
Then the equation is:
y = 2.5x.
More can be learned about proportional relationships at https://brainly.com/question/10424180
#SPJ1
what is 9/10 x (-1 1/4)
Answer:
-2.475
Step-by-step explanation:
Find X and Y, this was too hard for even my parents
Answer:
6x+97
Step-by-step explanation:
Hint: 3 sides of a triangle adds up to 180*.
((i know ur gonna clown on me for not giving the answer(i know the answer :d)but trust me the if u get da hint, ull solve it fine)
I really need help on this one.The amount of milk needed for each of 5 recipes is shown on the line plot.What is the total amount of milk needed for the recipes?
The total amount of milk needed for the recipes, considering the line plot, is of:
5.25 cups.
How to obtain the total amount of milk needed for the recipes?The total amount of milk needed for the recipes is obtained adding all the measures of the line plots.
The measures of the line plot given by the image at the end of the answer are given as follows:
Two measures of 1/4 cups = 0.25 cups, which is half the distance between 0 and 1/2.One measure of 1.25 cups, which is the value at the midpoint between 1 and 1.5.One measure of 1.5 cups.One measure of 2 cups.The total amount is given by the sum of all these measures, hence:
2 x 0.25 + 1.25 + 1.5 + 2 = 5.25 cups.
Missing InformationThe line plot is given by the image at the end of the answer.
More can be learned about line plots at https://brainly.com/question/24644930
#SPJ1
Convert 90°F into °C
Answer:
32.2222
Step-by-step explanation:
Answer: 32.22 degrees Celsius.
Which of these strategies would eliminate a variable in the system of equations?
The strategy which would eliminate a variable in the system of equations is to multiply the top equation by -5 , then add the equation and is denoted as option B.
What is Equation?This is a mathematical term which is made up of two expressions and is connected by an equal sign.
In the example given below:
x - 2y = 11
5x + 3y = -11
We can multiply the top by -5 which will result in:
-5x + 10y = -55 after which it is added to the other to give:
-5x + 5x + 10y + 3y = -55 + (-11)
13y = -66
y = -66/13.
From this we can notice that the variable x was eliminated which is why option B is the correct choice.
Read more about Equation here https://brainly.com/question/18831322
#SPJ1
the real estate group ny reports that the mean monthly rent for a one-bedroom apartment without a doorman in manhattan is $2886. assume the standard deviation is $586. a real estate firm samples 94 apartments. what is the probability that the sample mean rent is less than $2,918.03?
Probability that the sample mean rent is less than $2,918.03 is 0.050154
We are given that the Real Estate Group NY reports that the mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is $2886. Assume the standard deviation is $586.
Also, a real estate firm samples 94 apartments.
Let X = sample mean rent
The sample mean's z-score probability distribution is provided by;
Z = X-u/σ/[tex]\sqrt{n}[/tex] ~ N(0,1)
where, u= population mean monthly rent = $2,886
σ = standard deviation = $586
n = sample of apartments = 94
Now, the probability that the sample mean rent is less than $2,918.03 is given by = P( < $2,918.03)
P( < $2,918.03) = P(Z < 0.52)= 0.050154
The above probability is calculated using z table by looking at value of x = 0.52 in the z table which have an area of 0.050154
Therefore, probability that the sample mean rent is less than $2,918.03is 0.050154
Learn more about Z-score :
brainly.com/question/15016913
#SPJ4
On a coordinate plane, a parabola opens up. It goes through (negative 7, 5), has a vertex at (negative 4, negative 4), and goes through (negative 1, 5).
The graph of the function f(x) = x2 + 8x + 12 is shown. Which statements describe the graph? Check all that apply.
The vertex is the maximum value.
The axis of symmetry is x = –4.
The domain is all real numbers.
The range is all real numbers.
The function is increasing over (–∞, –4).
The x-intercepts are at (–6, 0) and (–2, 0).
Answer:
B: The axis of symmetry is x + -4.
C: The domain is all real numbers.
F: The x-intercepts are at (-6, 0) and (-2, 0).
Step-by-step explanation:
worked on edge 2022
The answer is the First, Third, and Last
solve for b: 84,250=b(1.008)120
Answer: 696.511
Step-by-step explanation:
84,250 = b(1.008)120
84250 = 120.96b
b = 696.511
In the given figure, l ∥ m and n are a transversal. If ∠1=80° and ∠5=100°,
find the measure of <2 , ∠3, ∠4.
Please give brief explanation
The value of angle ∠5 will be equal to 120°.
What are lines and angles?Straight lines with little depth or width are present. You will learn about a variety of lines, including transversal, intersecting, and perpendicular lines.
A figure called an angle is one in which two rays originate from the same point. In this area, you might also encounter contrasting and related viewpoints.
Given that In the given figure, l ∥ m and n are transversal and the angles are ∠1=80° and ∠5=100°.
First, calculate angle 2,
∠1 = ∠2 = 80 ( By alternate interior angles)
Calculate the angle ∠4,
∠4 = 180 - 80 - 40
∠4 = 180 - 120
∠4 = 60°
Calculate the angle ∠5,
∠5 = 180 - 60
∠5 = 120
Therefore, the value of angle ∠5 will be equal to 120°.
To know more about lines and angles follow
https://brainly.com/question/25770607
#SPJ1
help
How many terms are in the following
expression:
5x + 3 - x +2x + 2/3x
A coffee company surveyed 40 potential customers to see where they would
like the company's new organic coffee sold. Respondents were given the
following four locations and asked to choose as many as they liked: grocery
stores, drugstores, health food stores, and big box stores. The results are
summarized in the bar graph below, with the number of times each location
was chosen noted above the corresponding bar.
According to the statistics presented in the bar graph of responders of four locations per 40 potential customers, the average number of places chosen per potential client is 2.5.
We are given;
Total number of potential customers =40
From the bar graph number of respondents are following;
At grocery stores = 40
At drugstores respondents = 32
At health food stores = 8
At big box stores = 20
So,
The average number = Total number of respondents / Total number of potential customers
The average number = (40 + 32 + 8 + 20) / 40
The average number = (100) / 40
The average number = 2.5
Thus, according to the statistics presented in the bar graph of responders of four locations per 40 potential customers, the average number of places chosen per potential client is 2.5.
To learn more about the bar graph visit:
https://brainly.com/question/8644324
#SPJ1
ints
mily
Question 5
Which of the following is true?
O1-51-4
O1-41 <1-51
O1-51-5
O 1-41 > 151
Question 6
After simplification, the second option |−4| < |−5| is true.
In the given question,
There are four options. We have to check which option is true.
The given options are
1) |−5| < 4
2) |−4| < |−5|
3) |−5| = −5
4) |−4| > |5|
To find the true option we solve the given option one by one.
The first option is
|−5| < 4
Now solving
As we know that every value from the mod always give positive value.
So if we solve |−5| then the value is 5 and 5 is greater than 4. But in the given statement states that 4 is greater that 5. So the first statement is wrong.
Now solving the second statement.
|−4| < |−5|
After solving |−4|, the value is 4 and |−5| is 5.
So the simplified statement is 4 < 5 which is true.
Hence, the second statement is true.
Now we get the true statement so we haven't solve any further option.
If you want the solve next option the the way of solving the option is same.
Hence, the second option |−4| < |−5| is true.
To learn more about simplification link is here
brainly.com/question/8874934
#SPJ1
given f(x) =2x^2+5, evaluate f(4)
Answer:
f(4) = - 27
Step-by-step explanation:
substitute x = 4 into f(x) , that is
f(4) = - 2(4)² + 5 = - 2(16) + 5 = - 32 + 5 = - 27
Answer:
69
Step-by-step explanation:
Replace x with 4
-2(4)^2 +5
-8^2+5
64+5
69