The roots of the quadratic equation x² - x - 56 = 0 is x = -7 or x = 8
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the equation be represented as A
Now , the value of A is
x² - x - 56 = 0 be equation (1)
On simplifying the equation , we get
x² - 8x + 7x - 56 = 0
Taking the common terms in the equation , we get
x ( x - 8 ) + 7 ( x - 8 ) = 0
Now , on factorizing the equation , we get
( x + 7 ) ( x - 8 ) = 0
We have two factors which can solve the equation ,
when ( x + 7 ) = 0
Subtracting 7 on both sides of the equation , we get
x = -7
And , when ( x - 8 ) = 0
Adding 8 on both sides of the equation , we get
x = 8
Therefore , the roots of the equation are x = -7 and x = 8
Hence , the quadratic equation is solved
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Answer:
x = 8
x = -7
Step-by-step explanation:
To find the solutions of the quadratic equation x^2 - x - 56 = 0, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = 1, b = -1, and c = -56. Plug these values into the formula and calculate the discriminant (the value inside the square root):
Discriminant (D) = b^2 - 4ac = (-1)^2 - 4(1)(-56) = 1 + 224 = 225
Now, calculate the two possible solutions:
x1 = (-(-1) + √225) / (2(1)) = (1 + 15) / 2 = 16 / 2 = 8
x2 = (-(-1) - √225) / (2(1)) = (1 - 15) / 2 = -14 / 2 = -7
So, the correct solutions to the equation x^2 - x - 56 = 0 are:
x = 8 (x = 0 is not a solution)
x = -7
Use the t-distribution to find a confidence interval for a mean given the relevant sample results. Give the best point estimate for , the margin of error, and the confidence interval. Assume the results come from a random sample from a population that is approximately normally distributed. A 95% confidence interval for using the sample results , , and Round your answer for the point estimate to one decimal place, and your answers for the margin of error and the confidence interval to two decimal places.
point estimate = ?
margin of error = ?
The 95% confidence interval is ____ to ______.
Answer: hello your question is incomplete attached below is the complete question
answer :
a) 85.0
b) 27.4
c) (82.26, 87.74 )
Step-by-step explanation:
Given data :
95% confidence interval
x ( mean ) = 85
s = 8.8
n ( sample size ) = 42
using t-distribution
a) calculate the point estimate
The point estimate = 85.0 given that a sample mean is the same as a point estimate of the sample population
b) calculate the Margin of error
df = 42 - 1 = 41
∝ = 0.05
critical value ( T ∝/2 , 41 ) = 2.02
hence ; margin of error ( E )
= 2.74 ( using margin of error calculator )
c) The 95% confidence interval
= 85 ± 2.74
(82.26, 87.74 )
Evaluate each expression for x = 3 & y = 4
4. x² + 2(x+y)
5. (xy)^3
4х² - 3ху
4x -
Using the values for x and y and substituting these values in the expression of equations provided, The answer is 23 and 1728.
What do you mean by equations?An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A collection of one or more linear equations containing the same variables is known as a system of linear equations in mathematics. A set of two or more linear equations with two or more variables each constitutes a system of linear equations, all of which are taken into account simultaneously. Finding a numerical value for each variable in the system that will simultaneously satisfy all of the system's equations is necessary to identify the one and only solution to a system of linear equations.
What do you mean by substitution?When a variable (or set of letters) in an algebraic statement is substituted, its numerical value is used instead. The expression's total value can then be calculated.
x=3 and y=4
[tex]x^2 + 2(x+y)\\=3^2 + 2* (3+4)\\=9+2*7\\=9+14\\=23[/tex]
[tex](xy)^3\\=(3*4)^3\\=12^3\\=1728[/tex]
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6 lb 3 oz − 1 lb 4 oz
Answer:
4.9375 lbs
Step-by-step explanation:
pls help with these questionss!!!
Plz help me plz help
Answer:
46
Step-by-step explanation:
26+20
The ladder is 26ft long, there is still 20ft to go, so 20+26
A line passes through the point (-10,1) and has a slope of 3/2. Write an equation in point-slope form for this line. Please Help Best helped will get brainiest Promise PLS HELP !!!!!!!!!!!!!!!!!!!
Answer:
y - 1 = 3/2 (x + 10)
Step-by-step explanation:
Point-slope form of the equation of a line is a fill-in-the-blank shortcut to write an equation. If you know a point and the slope of a line you can fill in that info and voila! you have the equation.
Here is Point-slope equation:
y - Y = m(x - X)
Because the point given (-10,1) is in the form (X,Y), fill in -10 for X and 1 for Y.
The slope given is 3/2, fill that in for m.
y - Y = m(x - X)
y - 1 = 3/2 (x - -10)
y - 1 = 3/2 (x + 10)
The equation is
y - 1 = 3/2 (x + 10)
Q6.4☆ Points: 2 Suppose that Angela wants to use her sample to create a 68% confidence interval for the true population median of boba weight per drink and she knows that the population SD is 2 grams. What is the minimum sample size she needs to create a confidence interval that has a width of 0.4 grams?
Answer:
She needs a sample size of 25.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.68}{2} = 0.16[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.16 = 0.84[/tex], so Z = 0.995.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
The population SD is 2 grams.
This means that [tex]\sigma = 2[/tex]
What is the minimum sample size she needs to create a confidence interval that has a width of 0.4 grams?
She needs a sample size of n.
n is found when M = 0.4. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.4 = 0.995\frac{2}{\sqrt{n}}[/tex]
[tex]\sqrt{n} = \frac{0.995*2}{0.4}[/tex]
[tex](\sqrt{n})^2 = (\frac{0.995*2}{0.4})^2[/tex]
[tex]n = 24.8[/tex]
Rounding up:
She needs a sample size of 25.
How do i rewrite the sum in the form a(b+c) such that the integers b and c have no common factor. 35+42
Rewriting the sum in the form a(b+c) such that the integers b and c have a common factor. 35+42 is 7(5 + 6).
How to factorize the number?The process of factorization simply has to do with the division of arithmetic algebraic expressions into the sum of their factors. in this case, multiplying the variables will yield the original expression. It means the writing of a number into smaller or simpler numbers that give the original number.
The common factor to both 35 and 42 is 7. This will be:
35 + 42 = 7(5 + 6)
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Complete question
How do i rewrite the sum in the form a(b+c) such that the integers b and c have a common factor. 35+42
I really need help. Pweez?
Answer:
37
Step-by-step explanation:
top triangels 3 x4 = 12
Side triangels 1 x 5 = 5
the squer 4x 5 = 20
20 +5 +12= 37
Answer:
Step-by-step explanation:
20 inches i think
This is my question!
Answer:
J
Step-by-step explanation:
mode = 56
mean = 37.4
median = 35
The next model of a sports car will cost 12.8% more than the current model. The current model costs $42,000. How much will the price increase
in dollars? What will be the price of the next model?
Answer:
$5,376
$47,376
Step-by-step explanation:
Given :
Price of current model = $42,000
Percentage increase in price = 12.8%
Price increase in dollars :
12.8% of $42000
0.128 * $42000
= $5,376
Price of the next model :
Price of current model + increase in price
$42000 + $5376
= $47,376
Some of company x’s new practices and systems are unethical. Business ethics is a set of codes about how a business should conducts itself. In what ways is company x not applying practices
By altering schedules without giving adequate notice, terminating employees without giving adequate notice, and making false claims about its products, company x is not adhering to best practises.
Which kinds of codes are examples?These include bar codes, ISBNs, ASCII codes, postal codes, and bank account numbers; many of these contemporary codes use a checking mechanism, also known as a check digit. The ISBN system, now used uniformly on all new books, is one illustration of this.
How should business ethics be defined?Adopting sensible company procedures and policies with reference to apparently contentious issues is referred to as practicing business ethics. Corporate governance, market manipulation, bribery, racism, social duty, and fiduciary responsibilities are a few of the topics that come up in an ethical discussion.
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Answer:
The first one is right...
Step-by-step explanation:
Il give brainliest to correct answer
Answer:
x=18
Step-by-step explanation:
brainliest?
6. Find the greatest odd integer value of x that satiste the inequality 3x < -105.
Answer:
x<-35
Step-by-step explanation:
Triangle ABC has side lengths 39, 80, and 89. Do the side lengths form a right triangle? Explain.
please water it down for me i cant understand it
Answer:
Yes
Step-by-step explanation:
If a right triangle, then the Pythagorean theorem will show an equality of the sum of the squares of the two shorter legs equal to the square of the longest leg.
does 39² + 80² = 89² ?
1521 + 6400 = 7921, yes
it is a right triangle
HELP ME PLSSSS I'M LOST
Answer:
1. 1/2, 0.5, 50%
2.1/4, 0.25, 25%
Step-by-step explanation:
1) 1/2 (Fraction), 0.50 (Decimal), and 50%
Explanation: 50 squares are shaded out of the 100 squares. 50 is the numerator and 100 is the denominator, then you just simplify it to get your answer. For the decimal, you just have to divide 50 by 100, and for the percentage, every time the denominator is 100, the numerator will always be the percentage of that fraction.
2) 1/4 (Fraction), 0.25 (Decimal), and 25%
Explanation: 25 squares are shaded out of the 100 squares. 25 is the numerator and 100 is the denominator, then you just simplify it to get your answer. For the decimal, you just have to divide 25 by 100, and for the percentage, every time the denominator is 100, the numerator will always be the percentage of that fraction.
a family buys a new home for $212,500 and pays a 20% down payment ($42,500). if the mortgage is for 15 years at 5.75% interest which is their monthly house payment
Answer:
Their monthly house payment is of $2,184.65.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
A family buys a new home for $212,500 and pays a 20% down payment ($42,500).
This means that the loan is of 212,500 - 42,500 = $170,000, that is, [tex]P = 170,000[/tex]
Value of the loan in 15 years:
15 years means that [tex]t = 15[/tex]
5.75% interest means that [tex]r = 0.0575[/tex]
Compounded yearly, so [tex]n = 1[/tex]
Then
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(15) = 170000(1 + \frac{0.0575}{1})^{15}[/tex]
[tex]A(15) = 393237[/tex]
Monthly payment:
Total of $393,237 in 15*12 months. So
[tex]M = \frac{393237}{15*12} = 2184.65[/tex]
Their monthly house payment is of $2,184.65.
A phone company offers two monthly plans. Plan A costs $13 plus an additional $0.14 for each minute of calls. Plan B costs $24 plus an additional $0.10 for each minute of calls.
For what amount of calling do the two plans cost the same? Minutes
What is the cost when the two plans cost the same? $
Answer:
m = number of minutes calls
Plan A : 30 + 0.15 m
Plan B: 16 + 0.20 m
For what amount of calling do the two plans cost the same?
30 + 0.15m = 16 + 0.20m
0.05m = 14
m = 280
280 minutes of calling, the two plans cost the same
What is the cost when the two plans cost the same?
Plan A: 30 + 0.15 m = 30 + 0.15 (280) = 72
Plan B: 16 + 0.20 m = 16 + 0.20 (280) = 72
It's cost $72 when the two plans cost the same
How many lines of symmetry does this picture have?
Answer:
1
Step-by-step explanation:
if you put the line of symmetry anywhere else but down vertically it would not work .
Which is a rational function?
A. Y= 2/x
B. Y=x^2 - x + 4
C. Y= x-3^x/x^2
D. Y= x-5/2
A rational function is the algebraic expression y = 2 / x. (Correct choice: A)
What function is a rational function?
Rational functions are algebraic expressions, whose form is described below:
R(x) = P(x) / Q(x)
Where:
P(x) - Numerator polynomic function.Q(x) - Denominator polynomic function.Please notice that Q(x) must be a polynomial whose grade is greater than zero.
Polynomials are algebraic expressions of the form:
P(x) = ∑ cₙ · xⁿ, for n = {0, 1, 2, 3, ..., n, ..., m}, where m is the grade of the polynomial.
Therefore, by direct inspection, we conclude that algebraic expression y = 2 / x is a rational expression.
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(4 x 5) + ( 4 x 2) = 4 x (5 + n)
Answer:
Step-by-step explanation:
1. (4x5) is 20
2. (4x 2) is 8
3. 20 plus 8 is 28
4. 28= 4x (5+n)
5. isolate n by dividing 4 on both sides= 28/4= 4+n
6. subtract 4 on both sides to get 7-4=n
7. n=3
Can anyone of u pls help me???
4
- + 2 = x = 10
5
this is how i see it..... 4 5ths plus 2 equals 10
3. The ratio of brown-haired students to blonde-haired students is 5 to 2. There are
1340 brown-haired students in the school. How many students have blonde
hair?
Solve the inequality: −2x > −6
Answer:
x < 3
Step-by-step explanation:
What is the simplified expression for cot^2x/1+cot^2x
Answer:
2cot²(x)
Step-by-step explanation:
The simplified expression for cot²x/1+cot²x, cos²x.
What are periodic functions?A periodic function has a range that is determined for a fixed interval and a domain that includes all real number values.
Any function that has a positive real integer p such that f (x + p) = f (x), with all x being real values, is said to be periodic.
Given, A trigonometric function [tex]\frac{cot^2x}{1 + cot^2x}[/tex],
Now, Using different trig identities we have,
[tex]= \frac{cot^2x}{cosec^2x}[/tex]
[tex]= \frac{\frac{cos^2x}{sin^2x}}{\frac{1}{sin^2x}}[/tex]
[tex]= {\frac{cos^2x}{sin^2x}}\times\frac{sin^2x}{1}[/tex].
= cos²x.
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The solid below is made of twelve identical rectangular prisms. The overall dimensions of the composite solid are 36 inches (in.) by 36 inches by 24 inches. What is the volume, in cubic inches, of a single prism?
Whoever answers correctly will get Brainliest.
Answer:
A
Step-by-step explanation:
Volume of the solid = base x width x height = 36 x 36 x 24 = 31 104 in^3
Volume of one prism = total volume / 12 = 31 104 / 12 = 2592 in^3
A six-sided die is tossed three times. The probability of observing three ones in a row is
1 / 156
1 / 216
3 / 46
1 / 120
Reason:
There are 6 sides to the number cube. It gives 6*6*6 = 216 ways to roll three such dice. Only one of those ways has the sequence "1,1,1" that we're after. Therefore, the probability is 1/216.
It roughly approximates to 0.0046296; which is about a 0.46% chance of happening.
This all assumes that each side is equally likely. The answer will be different if the die is loaded in some fashion.
i’m need help !!!! thanksss
Answer:
x=77
Step-by-step explanation:A triangle is always 180 degreesin total so u would take 26 away from 180 witch is 154 then devide it as the angles that are left are corresponding angles. Then you dwvide 154 by 2 witch is 77. X=77
You are a researcher studying the health habits of people living in a large rural area. In particular, you are interested in the amount of weight gained early in life.
You want to estimate the population mean of all weight gains for the area's baby girls in their first year. To estimate the population mean of all such weight
gains, you select a random sample of 15 baby girls from this area and you record the weight (in kg) each gained in their first year. Assume the population is
approximately normally distributed.
Based on your sample, follow the steps below to construct a 90% confidence interval of the weight gains in the first year for all the area's baby girls. (If
necessary, consult a list of formulas.)
(a) Click on "Take Sample" to see the results for your random sample.
Take Sample
Sample size:
0
Point estimate:
0
Number of baby girls
4
Sample standard deviation:
0
15
Sample mean
Enter the values of the sample size, the point estimate of the mean, the sample standard deviation, and the critical value you need for your 90%
confidence interval. (Choose the correct critical value from the table of critical values provided.) When you are done, select "Compute".
Standard error:
5.538
Margin of error:
Sample standard
deviation
1.921
X
Confidence
level
S
Critical value
Therefore , the solution of the given problem of median comes out to be
confidence interval = [ 51.708 , 64.558 ].
Define median.When a dataset is ordered, the median value is the one that appears exactly in the middle of the dataset. The difference between the lowest and highest 50% of data is a measure of central tendency or average. Depending on whether you have an odd or even number of data points, the procedures for determining the median , mode change.
Here,
(48, 51, 65, 71, 61, 45, 48, 72, 74, 66, 43, 47, 70, 66, 45) sample data; sample mean, x = 58.133; sample size, n = 15; standard deviation, s = 11.6;
Standard deviation equals sd/√(n)
where, n = sample size and sd = standard deviation
Margin of error is equal to t alpha/2 and the standard error is (11.6/√( (15)) = 2.995. (standard error)
where ta/2 is the t-table level of significance, alpha is 0.05 from the standard normal table, the two-tailed value of |t alpha/2| with n-1 = 14 d.f is 2.145, and the margin of error is 2.145 * 2.995, which equals 6.425. The confidence interval for this margin of error is [58.133 6.425] = [51.708, 64.558].
being that,
sample data: (48 , 51 , 65 , 71 , 61 , 45 , 48 , 72 , 74 , 66 , 43 , 47 , 70 , 66 , 45 )
sample mean, x =58.133
standard deviation, s =11.6
sample size, n =15
level of significance, alpha = 0.05
from standard normal table, two tailed value of |t alpha/2| with n-1 = 14 d.f is 2.145
we use CI = x ± t a/2 * (sd/ √((n))
where,
x = mean
sd = standard deviation
a = 1 - (confidence level/100)
ta/2 = t-table value
CI = confidence interval
confidence interval = [ 58.133 ± t a/2 ( 11.6/ sqrt ( 15) ]
= [ 58.133-(2.145 * 2.995) , 58.133+(2.145 * 2.995) ]
= [ 51.708 , 64.558 ]
Therefore , the solution of the given problem of median comes out to be
confidence interval = [ 51.708 , 64.558 ].
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Find the sales price of the following item. Choose the correct answer.
A set of tableware listed at $53.98, marked down 50%
Answer: $26.99
Step-by-step explanation:
53.98/2=26.99