Use the calculator to graph the quadratic and determine solution to the equation x2+x-6=0
Answers
A graph of this quadratic equation x² + x - 6 = 0 is shown below.
The solutions to the equation x² + x - 6 = 0 are (-3, 0) and (2, 0).
What is the graph of a quadratic function?In Mathematics, the graph of a quadratic function always form a parabolic curve or arc because it is u-shaped. Based on the graph of this quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive one (1) and the value of "a" is greater than zero (0).
Since the leading coefficient (value of a) in the given quadratic function x² + x - 6 = 0 is positive one (1), we can logically deduce that the parabola would open upward and the solution would be on the x-intercepts (-3, 0) and (2, 0). Also, the value of the quadratic function f(x) would be minimum at -6.25.
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Related Questions
WORK OUT THE VALUE of 19+7⌹2-5
Answers
Answer:
17.5
Step-by-step explanation:
Remember PEMDAS
step 1 : divide 7 by 2
7 ÷ 2 = 3.5
step 2 : rewrite the equation
19 + 3.5 - 5
step 3 : add 19 + 3.5
19 + 3.5 = 22.5
step 4 : subtract 22.5 - 5
22.5 - 5 = 17.5
Help!
Solve the equation: a/0.4 = –20
Answers
Answer:
i think this might be it? but most likely :) <3
Step-by-step explanation:
Kenya wants to buy a car. Dealer A said she could pay $2000 upfront and $150 per month after. When will she have paid $3500Kenya went to Dealer B who said she could pay just $500 upfront and $200 per month after. When will the total amount paid be the same for both offers
Answers
We know that:
DEALER A.
$2,000 upfront and $150 per month after.
DEALER B.
$500 upfront and $200 per month after.
To know the answer, first, we need to represent each offer as an equation.
In the first case, dealer A has a rate of 150 (money per month), and 2000 is the independent term of the linear equation, so we express this like
\(y=150x+2000\)Where x is months.
In the second offer, dealer B has a rate of 200, and the independent term is 500. So, its equation is
\(y=200x+500\)Now we have both equations, we substitute the second into the first one
\(200x+500=150x+2000\)Then, we solve for x
\(200x-150x=2000-500\rightarrow50x=1500\)We divide the equation by 50
\(\frac{50x}{50}=\frac{1500}{50}\rightarrow x=30\)This means the payment will be equal after 30 months.Question 11 of 25
Company A charges a $120 annual fee plus $7 per hour car share fee.
Company B charges $100 plus $9 per hour. What is the minimum number of
hours that a car share needs to be used per year to make company A a better
deal?
A. 12
B. 11
O C. 10
D. 9
Answers
Answer: is A
Step-by-step explanation:
If x ÷(-3) < 0 which of the following statements are true
x > 0
x < 0
or there isnt enough information to determine the sign of x
Answers
Answer:
x > 0
Step-by-step explanation:
\(x \div ( - 3) < 0 \\ \frac{x}{ - 3} < 0 \\ x > 0 \times - 3 \\ x > 0\)
(3)a train travel 252 km in 42 hours. what amount of time will it take to complete a journey of 350km. (4) calculate the cost of 15 article at $1.95 each cost. (5) if 25 article cost 43.75 how much does each cost. (6) A car travel 240km on 20 liter of petrol. how many liters of petrol is needed to travel 600km
Answers
Answer:
(3)
Distance the train can travel=252km
Distance the train can travel in 1 hour=252÷42=6km
The time needed to cover 350km= 350÷6=58.4 hours.
(4)
The cost of 1 articles=$1.95
The cost of 15 articles= 15(1.95)=$29.25
(5)
Cost of 25 articles= 43.75
Cost of 1 article= 43.75/25=1.75
(6)
Liters of petrol needed when a car travels 240km=20litre
liters of petrol needed when a car travels 600km= 20/240 x600
20/24x60
20/4x10
5x10=50liter
Which point could not be part of a function that includes (3, -1), (4, 2), (5, 4), (-2, 0), and (8, -3)?
(6, -7)
(2,2)
(3, -2)
(7, 4)
Answers
Answer:
(3, -2) is the correct choice.
If the movie theater seats 328 people, what is the maximum amount of money the theater can bring in during a show?
Answers
Answer:
how much money does it cost for one person??
What does the term human capital refer to?
Answers
Answer:
its a captial of humans
Step-by-step explanation:
Answer: knowledge
Step-by-step explanation:
Human capital is a loose term that refers to knowledge, experience and skills of an employee. ... It states that companies have an incentive to seek productive human capital and to add to the human capital of their existing employees.
7.) +9 – +16 = N
8.) +85 – +12 = N
9.) –6 –2 = N
10.) +13 – +12 = N Someone please need it right now
Answers
Arithmetic operations on the directed numbers gives;
7) -7
8) +73
9) - 8
10) + 1
What are directed numbers?Any given number which has either a positive or negative sign is a directed number. Thus all numbers are directed in one way or the other. Some examples are: 8, +2, - 8.35, 10, 520 etc.
Performing an arithmetic operations on the given question, we have;
7) +9 - + 16 = +9 -(+16)
applying the rule of signs
+9 - (+16) = + 9 - 16
= -7
8) +85 - + 12 = +85 - (+12)
applying the rule of signs
+85 - (+12) = +85 - 12
= +73
9) -6 - 2
applying the rule of signs
-6 -2 = -8
10) +13 - + 12 = +13 - (+12)
applying the rule of signs
+13 - (+12) = +13 - 12
= +1
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Jasmine has a circular swimming pool with a radius of 4.2 meters. What is the circumference of the pool? Use 3.14 for π
. Round to the nearest hundredth if necessary.
__ m
Answers
If the radius of Jasmine's swimming pool is 4.2 meter, then it's circumference is 26.4 meters.
The "Circumference" of a circle is known as the distance around the boundary of a circle.
The circumference of a circle is given by the formula : 2 × π × radius,
where π (pi) is a mathematical constant approximately equal to 3.14,
We are given that Jasmine's swimming pool has a radius of 4.2 meters.
So, we can calculate the circumference of the pool as :
⇒ Circumference = 2 × 3.14 × 4.2 meters,
⇒ Circumference ≈ 26.4 meters,
Therefore, the circumference of Jasmine's swimming pool is 26.4 meters.
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State the property illustrated in the equation:
26 x (4x x y) = (26 × 4x) x y
O commutative property of multiplication
O property of multiplicative inverses
O associative property of multiplication
d
O distributive property
Answers
Answer:
O commutative property of multiplication
Step-by-step explanation:
Let's solve for x.
26(4xy)=(26)(4)xy
Step 1: Add -104xy to both sides.
104xy+−104xy=104xy+−104xy
0=0
It doesn't matter what order the numbers are multiplied in (commutative property), the result of multiplying 0 by anything (or anything by 0) is 0. No matter the type of number, whether it be an integer, fraction, decimal, or even imaginary, the product of that number and 0 is 0.
Find the 61st term in the following
arithmetic sequence:
–8, 0, 8, 16, . ..
Hint: Write a formula to help you.
1st term + common difference (desired term - 1)
Enter
Answers
Answer:
472 is the 61st term
Step-by-step explanation:
The 61st term of the given arithmetic sequence is 472.
What is Arithmetic Sequence?Arithmetic sequence is a sequence of numbers where the numbers are arranged ion a definite order such that the difference of two consecutive numbers is a constant. This constant of difference is called common difference which is commonly denoted by the letter 'd'.
Given arithmetic sequence is,
-8, 0, 8, 16, .............
We have to find the 61st term of the given sequence.
nth term of an arithmetic sequence is,
aₙ = a + (n - 1)d
Here a is the first term, d is the common difference.
From the given sequence,
first term, a = -8
Common difference, d = 0 - -8 = 8
a₆₁ = -8 + (61 - 1) 8
= -8 + (60 × 8)
= -8 + 480
= 472
Hence the 61st term of the given arithmetic sequence is 472.
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Paulas cat weighs 8 5/8 pounds. Calebs cat weighs 11 1/8 pounds. What is the total weight of both cats?
Answers
Answer:
19 6/8 or 19 3/4
I’m not sure if you want the smallest possible fraction or not. If you don’t know just put the second one. K.
I’m trying to teach myself this…I just need a few answers to get me started! Thank you! I need all work shown please!! Was out for covid and teacher won’t help!
Answers
ANSWER
\(\begin{gathered} y=8x-1000 \\ Profit=\$8 \\ Amount-Lost\Rightarrow\$1000 \end{gathered}\)EXPLANATION
We want to write a linear equation that represents the situation:
The general form of a linear equation is:
\(y=mx+b\)where m = slope; b = y-intercept
Let the profit/loss be y.
Let the number of calendars sold be x.
After selling 80 calendars, they had a loss of $360. This implies that when x is 80, y is -$360:
\((x_1,y_1)=(80,-360)\)After selling 200 calendars, they had a profit of $600. This implies that when x is 200, y is $600:
\((x_2,y_2)=(200,600)\)Now, we have two points that describe the relationship between profit/loss and the number of calendars sold.
To find the linear equation, we first have to find the slope using the formula:
\(m=\frac{y_2-y_1}{x_2-x_1}\)Hence, the slope is:
\(\begin{gathered} m=\frac{600-(-360)}{200-80} \\ m=\frac{600+360}{200-80}=\frac{960}{120} \\ m=8 \end{gathered}\)To find the equation that describes the relationship between profit/loss and the number of calendars sold, apply the point-slope method:
\(y-y_1=m(x-x_1)\)Therefore, the equation is:
\(\begin{gathered} y-(-360)=8(x-80) \\ y+360=8x-640 \\ y=8x-640-360 \\ y=8x-1000 \end{gathered}\)Since the slope represents the rate of the equation (i.e. the profit/loss per calendar sold), and the slope is positive, it implies that the profit made from selling each calendar is $8.
To find how much they would have lost if they sold no calendars, we have to find the value of the equation when x is 0. This is equivalent to the y-intercept of the equation.
Comparing the equation gotten to the general form of the linear equation, we see that the y-intercept of the equation is -$1000 (the negative indicates a loss).
This implies that they would have lost $1000 if they sold no calendars.
You deposit $1500 into an account that pays an interest rate of 4% compounded annually. What is the balance after 5 years? Your friend deposits $1500 into an account that pays a simple annual interest rate of 4%. What is the balance after 5 years?
Answers
Answer:
Compound interest: A = $1824.98
Simple interest: A = $1800
Explanation:
To know the balance after t years for an account that pays with a compounded rate, we can use the following equation:
\(A=P(1+r)^t\)Where P is the initial amount and r is the interest rate.
So, replacing P by $1500, r by 4% or 0.04, and t by 5 years, we get:
\(\begin{gathered} A=1500(1+0.04)^5 \\ A=1500(1.04)^5 \\ A=1824.98 \end{gathered}\)Therefore, in this case, the balance after 5 years is $1824.98
On the other hand, the balance after t years for an account that pays with a simple interest rate can be calculated as:
\(A=P(1+rt)\)So, replacing P by $1500, r by 0.04, and t by 5 years, we get:
\(\begin{gathered} A=1500(1+0.04\cdot5) \\ A=1500(1+0.2) \\ A=1500(1.2) \\ A=1800 \end{gathered}\)Then, the balance after 5 years is $1800
So, the answers are:
Compound interest: A = $1824.98
Simple interest: A = $1800
the answer is actually 81
Answers
Answer:
okay i'll keep this in mind
Step-by-step explanation:
Jamal read 1/11 of a book in 2/5 of an hour at this rate how long will it take him to read the entire book?
Answers
Answer:
264 minutes OR 4.4 hours OR 4 hours and 24 minutes (all the same)
Step-by-step explanation:
if he takes 2/5 of an hour to read the 1/11 of the book, he takes 24 minutes to read 1/11 of the book.
24 * 11 is 264.
Therefore he will take 264 minutes to finish the entire book.
someone pls help me uh
Answers
Answer:
x = -7
Step-by-step explanation:
6+2x=-8
2x=-14
x = -7
Answer:
x= -7
Step-by-step explanation:
6+ 3x = x-8
-x. -x
-----------------
6+2x = -8
-6. -6
---------------
2x = -14
--- ---
2. 2
-------------
x= -7
PLEASE HELP I WILL GIVE BRAINLIEST
Is RST = XYZ? If so, name the postulate that applies.
A. Might not be congruent
B. Congruent - SSS
C. Congruent - ASA
D. Congruent - SAS
Answers
Answer:
D
Step-by-step explanation:
two sides are congruent and in between is an angle
A local newspaper claims that 70% of the items advertised in its classifieds section are sold within 1 week of the first appearance of the ad. To check the validity of the claim, the newspaper randomly selected n = 25 advertisements from last year's classifieds and contacted the people who placed the ads. They found that 14 of the 25 items sold within a week. Based on the newspaper's claim, is it likely to observe x 14 who sold their item within a week? If you could show work.
Answers
The newspaper's assertion is correct, it is unlikely that 14 triumphs will be observed in a sample of 25.
The further answer is described below.
In this problem,
The binomial distribution can be used.
Let p represent the likelihood of an item selling within a week, as reported by the newspaper,
And q represent the probability of an item not selling within a week
Then we have,
p = 0.7
q = 1 - p = 0.3
n = 25 (sample size)
x = 14 (number of items sold within a week in the sample)
The probability of observing exactly x successes in n trials,
Given a probability of success p, is given by the binomial probability formula:
P(X = x) = (n choose x) \(p^{x}\)\(q^{(n-x)}\)
Where (n choose x) = n! / (x! x (n-x)!) is the number of possible ways to choose x items out of n.
Put the values,
P(X = 14) = \(^{25} C_{14}\) 0.7 0.3
= 0.107
So, if the newspaper's assertion is correct, the probability of detecting exactly 14 successes (i.e., things sold within a week) in a sample of 25 is around 0.107 or 10.7%.
If the newspaper's assertion is correct, it is unlikely that 14 triumphs will be observed in a sample of 25.
However, it is not impossible, therefore we cannot rule out the chance that the newspaper's assertion is genuine based just on this sample.
To get a more certain conclusion, a bigger sample size would be required.
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I need help in this with explanation
Answers
Step-by-step explanation:
The figure is made up of an 8x8 square and 4 identical triangles with 8-ft bases and 4 ft in height. Each triangle has an area = (1/2)bh = (1/2)(8)(4) = 16 ft^2. The square part has an area of 8x8 = 64 ft^2. Therefore, the total area of the figure is
A = (area of square) + 4×(area of triangle)
= 64 ft^2 + 4(16ft^2)
= 128 sq ft
Matrix M has x-rows and (11-x) columns. Matrix N has y-rows and (y+5) columns. If MN and NM both are defined, find the values of x and y
Answers
Answer:
\(x=8, y=3\)
Step-by-step explanation:
Recall that if a matrix multiplication of two matrices is defined, then the number of columns of the first matrix is equivalent to the number of rows of the second matrix.
Since matrix M has (11-x) columns and matrix N has y rows, and MN is defined, so it follows:
\(y=11-x----(1)\)
Since matrix N has (y+5) columns and matrix M has x rows, and NM is defined, so it follows:
\(y+5=x----(2)\)
Substitute (1) into (2):
\(11-x+5=x\\2x=16\\\therefore x=8--(3)\)
Substitute (3) into (1):
\(y=11-8=3\)
If f(x)=3x-6, what is f(2)?
a. 12
b.-1
c. -3
d. 0
Answers
As part of their employee benefits , all workers at Middletown Electronics receive a pension that is calculated by multiplying the number of years worked times 1.56% of the average of their three highest years’ salary. Maureen has worked for Middletown for 30 years and is retiring. Her highest salaries are $107,000, $107,800, and $108,198. Calculate Maureen’s pension.
Answers
Maureen's pension would be $50,035.20.
What is Percentage?
To compute a percentage, divide the value by the entire amount and multiply the result by 100. A percentage is a quantity or ratio that is stated as a fraction of one hundred. The percent sign, "%," is frequently used to represent it.
First, we need to calculate the average of Maureen's three highest salaries:
Average = (107,000 + 107,800 + 108,198) / 3
Average = 322,998 / 3
Average = 107,666
Next, we need to calculate 1.56% of this average:
Percentage = 1.56% * 107,666
Percentage = 1,667.84
Finally, we multiply this percentage by the number of years worked to find the pension:
Pension = 30 * 1,667.84
Pension = 50,035.20
So, Maureen's pension would be $50,035.20.
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Which shows the following expression after the negative exponents have been eliminated? A^3 b^-2/ab^-4 A=/0, b=/0
Answers
Simplify the following expression.
(38x+61y)-(3x-11y)
the answer is 35x+72y for plato im only putting this question up to help people with the same problem i had, ill give brainliest out to the first person who works this out and gives a intelligent response.
Answers
Answer:
35x+72y
Step-by-step explanation:
well you are subtracting the terms 3x and -11y from the terms 38x and 61y. so to start you multiply 3x and -11 by negative one to get rid of the parentheses. you then you combine like terms.
Mr. Curtis is taking his family to Disney World. He stopped for gas and paid $48.51 for 12.6 gallons of gas. What is the price of gas per gallon?
Answers
Answer:
$3.85 per gallon.
Step-by-step explanation:
48.51 / 12.6 = 3.85
Answer: The answer would be 1 gallon=$3.85
Step-by-step explanation:
A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the gpa of male students are µ = 3. 5 and σ = 0. 5. Suppose a random sample of 100 male students is selected and the gpa for each student is calculated. What is the probability that the random sample of 100 male students has a mean gpa greater than 3. 42?
Answers
The probability that the random sample of 100 male students has a mean gpa greater than 3. 42 is 0.9452.
What is Standard deviation?A statistic known as the standard deviation is used to describe how volatile or dispersed a group of numerical values is. While a big standard deviation denotes that the values are scattered across a wider range, a low standard deviation indicates that the values tend to be close to the set mean.
From the given information, a scores random sample of 100 male students is selected and the GPA for each student is calculated which follows approximately normal with a mean of 3.5 and standard deviation of 0.5. That is,
µ = 3. 5 and σ = 0. 5
and the random sample of 100 male students has a mean GPA 3.42 is considered.
The z-score value is,
Z=( 3.42-3.5)/ (0.5/√100)
Z= -0.08/0.05
Z=-1.6
The value of z-score is obtained by taking the difference of x and µ. Then the resulting value is divided with the standard deviation by sample size.
The probability that the random sample of 100 male students has a mean GPA greater than 3.42 is obtained below:
The required probability is,
P(X>3.42)=P(z>-1.6)
= 1- P(Z≤-1.6)
From the “standard normal table”, the area to the left of Z=-1.6 is 0.0548.
P(X>3.42)= 1- P(Z≤-1.6)
=1-0.0548
=0.9452
The probability that the random sample of 100 male students has a mean GPA greater than 3.42 is 0.9452.
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Sameer has 6 markers in the bottom of his backpack. 1 is red, 2 are blue, and 3 are green.
He calculates the theoretical probability of choosing a blue marker at random. Then he
tests this probability by choosing a marker without looking, noting the color, and putting the
marker back into the backpack. Sameer gets a blue marker in 8 out of 18 trials. How does
Sameer's experimental probability compare to the theoretical probability, and what is the
reason for any difference between them?
A. The theoretical probability is less than the experimental probability. If Sameer did more
trials of the experiment, the two values likely would be closer.
B.
The theoretical probability is greater than the experimental probability. If Sameer did
fewer trials of the experiment, the two values likely would be closer.
C.
The theoretical probability is the same as the experimental probability. Sameer's
calculation of the experimental probability was correct.
D. The theoretical probability is less than the experimental probability. Sameer did too
many trials of the experiment.
Answers
The theoretical probability is greater than the experimental probability. So correct option is B.
Describe probability ?Probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in many fields, including mathematics, statistics, science, finance, and engineering, to make predictions and inform decision-making. It is a fundamental concept in probability theory and plays a crucial role in many real-world applications.
Probability theory is an important branch of mathematics that is used to model and analyze random phenomena, such as games of chance, weather patterns, and stock prices. It has applications in many fields, including science, engineering, economics, and finance.
B. The theoretical probability is greater than the experimental probability. If Sameer did fewer trials of the experiment, the two values likely would be closer. The reason for the difference is likely due to chance variation or random sampling error. With more trials, the experimental probability would likely approach the theoretical probability.
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