Quadratic equations are all those equations that can be reformulated in a standard format (αx² + bx + c(=0) where the value of x is unknown and the values of the coefficients (a, b and c) are unknown.
These equations can always be solved using the quadratic formula, although sometimes it is also possible to use factorization or isolation of variables.
[tex]\large\displaystyle\text{$\begin{gathered}\sf (x-7)^{2}=8 \end{gathered}$}[/tex]Expand squared
[tex]\large\displaystyle\text{$\begin{gathered}\sf (x-7)(x-7)=8 \end{gathered}$}[/tex]It is distributed
[tex]\large\displaystyle\text{$\begin{gathered}\sf x(x-7)-7(x-7)=8 \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf x^{2} -7x-7(x-7)=8 \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf x^{2} -7x-7x+49=8 \end{gathered}$}[/tex]Combine like terms.
[tex]\large\displaystyle\text{$\begin{gathered}\sf x^{2} -14x+49=8 \end{gathered}$}[/tex]Move terms to the left
[tex]\large\displaystyle\text{$\begin{gathered}\sf x^{2} +14x+49-8=0 \end{gathered}$}[/tex]Subtract the numbers
[tex]\large\displaystyle\text{$\begin{gathered}\sf x^{2} -14x+41=0 \end{gathered}$}[/tex]Use the quadratic formula.
[tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{-b\pm\sqrt{b^{2}-4ac } }{2a} \end{gathered}$}[/tex]
In standard form we identify "a", "b" and "c" from the original equation and add to the quadratic formula.
a = 1b = -14c = 41[tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{-(-14)\pm\sqrt{(-14)^{2}-4\cdot1\cdot41 } }{2\cdot1} \end{gathered}$}[/tex]
Simplify
Calculate the exponentmultiply the numbersSubtract the numbersCalculate the square rootmultiply the numbersWe multiply the numbers[tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{14\pm4\sqrt{2} }{2} \end{gathered}$}[/tex]
Separate equations
To solve for the unknown variants, we split the equation into two: one with a plus sign and the other with a minus sign.
[tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{14+4\sqrt{2} }{2} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{14-4\sqrt{2} }{2} \end{gathered}$}[/tex]
Solve
Order and isolate the variant to find each solution.
[tex]\large\displaystyle\text{$\begin{gathered}\sf x=7+2\sqrt{2} \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x=7-2\sqrt{2} \end{gathered}$}[/tex]
[tex]\red{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\blue{Answer \ \ \longmapsto \ \ x=7\pm2\sqrt{2} }} \end{gathered}$}}}[/tex]
Learn more at:https://brainly.com/question/22842654Skandar. Write a variable expression that represents the following word phrase:
Four less than half the difference of 3 and x
Answer: [tex]\frac{3-x}{2}[/tex]-4
Step-by-step explanation:
(3-x)/2 -4=[tex]\frac{3-x}{2}[/tex]-4
below is a sequence of numbers:
0.5, 3, 5.5, 8, …
Calculate:
(a) the 8th term,
Answer: ______________
(b) the 100th term,
Answer: ______________
(c) which term has a value of 148.
Answer:
a) 18
b)248
c) 58
Step-by-step explanation:
The formula is:
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n-1)d
[tex]a_{n}[/tex] Is the number at the n term
[tex]a_{1}[/tex] Is the first number in the sequence
n Is the number for the term
d is the common difference. How much is added each time in the sequence. In this case, 2.5
Put in the numbers that you know and solve for the unknown.
A:
[tex]a_{8}[/tex] = 0.5 + (8 -1)(2.5)
[tex]a_{8}[/tex] = 0.5 +(7)(2.5)
[tex]a_{8}[/tex] = 0.5 + 17.5
[tex]a_{8}[/tex] = 18
B:
We follow the same pattern, but we are now looking for [tex]a_{100}[/tex].
[tex]a_{100}[/tex] = 0.5 + (100-1)(2.5)
[tex]a_{100}[/tex] = 0.5 + 247.5
[tex]a_{100}[/tex] = 248
C:
This time we know the value of the number in the sequence, we do not know which term it is.
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1)d Put in what we know
148 = 0.5 + (n -1)2.5 Distribute the 2.5
148 = 0.5 + 2.5n - 2.5 Combine like terms
148 = 3 + 2.5n Subtract 3 from both sides of the equation
145 = 2.5n Divide both sides by 2.5
58 = n
I need Help please :(
Step-by-step explanation: See attached step by step
a) down payment, b) amount of the loan, c) monthly payment, and d) finance charge.
Shelly Lemony obtains a small business equipment loan for $120,000. Her down payment is 20% and the APR is 8% for 12 months.
a) Shelly Lemony's down payment is $24,000.
b) The loan amount is $96,000.
c) The monthly payment is $8,350.89.
d) The finance charge is $4,210.68.
What is the down payment?The down payment represents the initial up-front partial payment for the purchase of the equipment on loan.
The down payment reduces the cost of the equipment to the loan amount. Finance companies demand a down payment to ascertain the buyer's willingness and ability to proceed with the loan arrangement.
It is a sign of commitment to meet the loan contract obligations.
Data and Calculations:Monthly Pay: $8,350.89
Total Loan Amount = $96,000.00
Upfront Payment $24,000.00
Equipment loan = $120,000
Number of periods = 12 months
APR = 8%
Total of 12 Loan Payments = $100,210.68
Total Loan Interest = $4,210.68
Total Cost (price, interest, tax, fees) = $124,210.68
Thus, Shelly will make a down payment of $24,000 or 20% of the equipment loan.
Learn more about down payments at https://brainly.com/question/26173748
#SPJ1
A 19-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third piece is three inches more than five times the length of the first piecefind the lengths of the pieces. 3 + 5x
Using algebraic expressions and equations to solve this problem, a 19- inch piece of steel is cut into three pieces measuring 2 inches, 4 inches, and 13 inches.
An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".
If the second piece is twice as long as the first piece, we can write this as an algebraic expression "2x" where x is the length of the first piece.
If the third piece is three inches more than five times the length of the first piece, we can write this as an algebraic expression "3 + 5x" where x is the length of the first piece.
If the three pieces were cut from a single piece of steel 19-inches long, we can write the equation for the sum using the algebraic expressions.
let x = length of first piece
2x = length of second piece
3 + 5x = length of third piece
x + 2x + 3 + 5x = 19 inches
Solving for x,
8x = 19 -3
8x = 16
x = 2 inches
length of first piece = 2 inches
Substitute the value of x in the expressions for the second and third piece.
length of second piece = 2x
length of second piece = 2(2)
length of second piece = 4 inches
length of third piece = 3 + 5x
length of third piece = 3 + 5(2)
length of third piece = 3 + 10
length of third piece = 13 inches
Learn more about algebraic expressions and equations here: brainly.com/question/13818690
#SPJ4
Brian rolls a fair dice 12 times.
How many times would Brian expect to roll a number greater than 4?
Answer:
I times the 12 by 5 and divided by 2 and subtract by 12
I get 18 and I thought it is 18
Answer:
Step-by-step explanation:
If a fair dice is rolled 6 times, 2/6 times the number would be greater than 4
If rolled 12 times, then 4/12 times the number would be greater than 4
4/12 = 1/3
Irwin has flowering plants in 15% of his garden. Which of the following is equivalent to 15%?
Answer: Im not sure
Step-by-step explanation:
You didnt list the options therefore i cant answer this for you. :I
Put the following equation in slope intercept form, simplifying all fractions. 12x+8y=-24
The slope intercept form of the equation 12x ₊ 8y = ₋24 is
y = ₋3/2 x ₋ 3
Given the equation is 12x ₊ 8y = ₋24
we are asked to convert the given equation into slope intercept form.
Finding a line's equation requires using the slope-intercept form of a straight line. We must know both the line's slope and the point at which the line crosses the y-axis in order to use the slope-intercept formula.
12x ₊ 8y = ₋24
⇒ 12x ₊ 8y ₊ 24 = 0
we re-arrange the equation of the line to write it in the standard form
y = mx + b.
12x ₊ 8y = ₋24
8y = ₋12x ₋ 24
now divide the terms on the right side by 8.
y = ₋12x/8 ₋ 24/8
y = ₋3/2x ₋ 3
hence we get the slope intercept form as y = ₋3/2x ₋ 3, where m=s₋3/2 and b = ₋3
Learn more about Coordinate geometry here:
brainly.com/question/11337174
#SPJ9
Answer:
I don't know to be honest
Step-by-step explanation:
that's great
PLEASE SOLVE ITS FOR A TEST I NEED IT
Answer:
The answer is Option C
Answer:
I think the answer would be C
Step-by-step explanation:
Angle DEF is an inscribed angle on a circle, and m
O 48°
O 96°
O 132°
O 24°
∠24°
What is an inscribed angle in a circle?
Inscribed angles are angles whose vertices are on a circle and that intersect an arc on the circle. The measure of an inscribed angle is half of the measure of the intercepted arc and half the measure of the central angle intersecting the same arc.
given that intercepted arc = ∠48°
The intercepted arc is the arc that is inside the inscribed angle and whose endpoints are on the angle.
If the intercepted arc is twice the size of the inscribed angle, then the inscribed angle is half the size of the intercepted arc. So if the intercepted arc is 48 degrees, the inscribed angle is 48 / 2 = 24 degrees.
To learn more about inscribed angle
visit https://brainly.ph/question/10538167
#SPJ9
1. A block of aluminum occupies a volume of 22.0 mL and weighs
66.8 g. What is its density?
Answer:
3.04 g/mL
Step-by-step explanation:
density = mass/volume
density = 66.8 g / 22.0 mL
density = 3.04 g/mL
2/5d+4/9e=-2d+7/18e-1
solve for e
Answer:
[tex]e=\frac{-5e-90}{216}[/tex]
Step-by-step explanation:
[tex]\frac{2}{5}d+\frac{4}{9}e=-2d+\frac{7}{18}e-1[/tex]
[tex]\frac{2}{5}d+\frac{4e}{9}=-2d+\frac{7}{18}e-1 < - Muiltiply[/tex]
[tex]\frac{2}{5}d+\frac{4e}{9}=-2d+\frac{7e}{18}- < - Muiltiply Again\\[/tex]
[tex]\frac{2}{5}d+\frac{4e}{9}-\frac{4e}{9}=-2d+\frac{7e}{18}-1-\frac{4e}{9} < - Subtract BothSides[/tex]
[tex]\frac{2}{5}d=-2d-\frac{e}{18}-1 < - Simplify[/tex]
[tex]\frac{2}{5}d+2d=-2d-\frac{e}{18}-1+2d < - AddToBothSides[/tex]
[tex]\frac{12}{5}d=-\frac{e}{18}-1 < - Simplify[/tex][tex]\frac{12d}{12}=-\frac{\frac{5e}{18}}{12}-\frac{5}{12} < - DivideBothSides[/tex]
[tex]e=\frac{-5e-90}{216}[/tex]
What is the difference between quantitative data and qualitative data? in what situations could the number 42 be considered qualitative data? what are the characteristics of a relational database?
The number 42 could be qualitative if it is a designation instead of a measurement, count, or calculation.
Qualitative data describes qualities or characteristics. It is collected using questionnaires, interviews, or observation, and frequently appears in narrative form. For example, it could be notes taken during a focus group on the quality of the food at Cafe Mac, or responses from an open-ended questionnaire. Qualitative data may be difficult to precisely measure and analyze. The data may be in the form of descriptive words that can be examined for patterns or meaning, sometimes through the use of coding. Coding allows the researcher to categorize qualitative data to identify themes that correspond with the research questions and to perform quantitative analysis.
Quantitative data is numbers-based, countable, or measurable. Quantitative data is numeric, the result of a measurement, count, or some other mathematical calculation. Qualitative data is descriptive. The number 42 could be qualitative if it is a designation instead of a measurement, count, or calculation.
The seven characteristics that define relational database are:
Accuracy and Precision
Legitimacy and Validity
Reliability and Consistency
Timeliness and Relevance
Completeness and Comprehensiveness
Availability and Accessibility
Granularity and Uniqueness
To know more about "quantitative data and qualitative data"
Refer this link:
https://brainly.com/question/11961159
#SPJ4
4. (03.01)
Is the following relation a function? (1 point)
Yes
No
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
No, The given relation isn't a function.
[ For a relation to be a function, every value that lies in the domain ( set A ) should have only one corresponding value in its Range ( set B ) but here, -1 has two corresponding values that are : (-1) and (2) ]
Therefore, conclusion can be made that the given relation isn't a function.
Answer:
Not a function.
Step-by-step explanation:
Functions
A function is a special type of relation where each input (x-value) has a single output (y-value).
One-to-one: Each value in the range (y-values) corresponds to exactly one value in the domain (x-values).Many-to-one: Some values in the range (y-values) correspond to more than one (many) value in the domain (x-values).The given function is not a function as the input value of x = -1 has multiple output values of y = 2 and y = -1.
Filip is inviting 6 friends to a party. Each friend wants 5 cookies and each box has 8 cookies. How many boxes should Filip get?
Brittney is 4 years older than Dakota. The variable b stands for Brittney's age. Which expression stands for Dakota's age?
A. 4b
B. 4 - b
C. b + 4
D. b - 4
Hayfa does 336 jumping jacks in 8 minutes. How many does Hayfa do in 1 minute?
Answer:42
Step-by-step explanation:
Hayfa dose 336 jumping jacks in 8 mins so you divide 336 by 8 and that equals 42
Answer:
42 jumping jacks
Step-by-step explanation:
To find how many Hayfa does in a minute divide 336 by 8
➟ 336/8
➟ 42
∴ Hayfa can do 42 jumping jacks in a minute
Continuation of Qn on part ii)
Answer:
Step-by-step explanation:
Let x1, x2, x3 be three independent random variables with binomial distributions b(4,1/2), b(6,1/3), and b(12,1/6), respectively. find (a) p(x1 = 2,x2 = 2,x3 = 5).
0.00345 is the value of p(x).
What means binomial distribution?
When each trial has the same probability of achieving a given value, the number of trials or observations is summarized using the binomial distribution. The likelihood of observing a specific number of successful outcomes in a specific number of trials is determined by the binomial distribution.P(x₁= 2 , x₂ = 2 , x₃ = 5 )
p( x₁= 2) . p( x₂ = 2) . p( x₃ = 5) .........( as these are independent variable)
[c⁴₂ ( 0.5 )² ( 0.5 )² ] [ c⁶₂ ( 1/3)²(2/3)⁴ ] [ c¹²₅ (1/6)⁵ (5/6)⁷
= 0.375 × 0. 329 × 0.028
= 0.00345
Learn more about binomial distribution
brainly.com/question/14565246
#SPJ4
3y+4x=9
I have to find the literal solution
Answer:
Step-by-step explanation:
3−4x/3 this is for x
y = -4/3x + 3 this is for why I’m not sure which one your trying to solve for
Use the picture to solve for Y.
Answer:
y=2x+5
y=-1.5x+9
3y=-2x+10
Step-by-step explanation:
2x+y=5
y=2x+5
9-y=1.5x
-y=1.5-9
y=-1.5x-9
2x=-3y+10
3y=-2x+10
please help! i can’t figure this out I’ve somebody help QUICKKKK !!!!
Answer: A
Step-by-step explanation:
Complete the table.
Answer:
-1, 2
Step-by-step explanation:
Plug the "x" on the top row into the "x" on the equation.
y = 3(0) - 1 = -1
y = 3(1) - 1 = 2
A traditional unit of length in japan is the ken (1 ken = 1.97 m). what are the ratios of (a) square kens to square meters?
The ratios of (a) square kens to square meters (1 ken² / 1 m²) is 3.88
For given question,
We have been given the unit conversion.
A traditional unit of length in Japan is the ken
and 1 ken = 1.97 m
We need to find the the ratios of (a) square kens to square meters.
First we find the square of 1 ken.
⇒ 1 square kens = (1.97 m)²
⇒ 1 square kens = 1.97 × 1.97 m²
⇒ 1 square kens = 3.88 m² ..................(1)
And 1 square meters = 1 m² ................. (2)
Now we take the ratio of square kens to square meters.
From (1) and (2),
⇒ 1 ken² / 1 m² = 3.88 / 1
⇒ 1 ken² / 1 m² = 3.88
Therefore, the ratios of (a) square kens to square meters (1 ken² / 1 m²) is 3.88
Learn more about the ken here:
https://brainly.com/question/2627020
#SPJ4
The ratio of girls to boys in a a gardening club was 6:2 there were 16 boy how many are girls
Answer:
I don't know
Step-by-step explanation:
tdhdujdjbd
If you are examining a function over an interval ( a , b ) , for a and b finite, is it possible not to have an absolute maximum or absolute minimum?
Yes, it is not possible to have an absolute maximum or absolute minimum.
Here,
We are examining a function over an interval ( a , b ) , for a and b finite,
We have to find, is it possible not to have an absolute maximum or absolute minimum.
What theorem indicates the existence of absolute maxima or absolute minima of a function?
If f is continuous on a closed interval [a, b] (that is: on a closed and bounded interval), then, the Extreme Value Theorem indicates the existence of an absolute maximum or minimum value of f on the interval [a, b].
Now,
The function is define over an interval (a, b).
Hence, the function is define on open interval.
So, it is not possible to have an absolute maximum or absolute minimum.
Learn more about the existence of maxima and minima visit:
https://brainly.com/question/6787214
#SPJ4
Suppose the graph of y=x^2 is shifted left 6 units. Complete the modified equation: y=
Please help me
The modified equation is expressed as g(x) = x^2 - 6
Translation of coordinateTranslation is the process of changing the position on an x-plane.
Given the function of a graph expressed as y=x^2
If the function is shifted 6 units to the left, hence the resulting function is given as;
g(x) = x^2 - 6
Hence the modified equation is expressed as g(x) = x^2 - 6
Learn more on translation here; https://brainly.com/question/12861087
#SPJ1
A standard train ticket in a certain city costs 3 per ride. people who use the train also have the option of purchasing a frequent-rider pass for 18.75 each month. with the pass, a ticket costs only 2.25 per ride. how many train rides in a month make the frequent-rider pass a better deal than standard train tickets?
a. 26 or more rides
b. 24 or more rides
c. 25 or more rides
d. 27 or more rides
Number of train rides to make the frequent-rider pass a better deal than standard train tickets is 26 or more rides.
As given,
Cost of standard train ticket = 3 per ride
Price of frequent rider pass= 18.75 each month
Cost of ticket using rider pass = 2.25 per ride
let x be the number of rides
Equation:
18.75 + 2.25x < 3x
⇒ 0.75x > 18.75
⇒ x > 25
Therefore, number of train rides to frequent-rider pass a better deal than standard train tickets is 26 or more rides.
Learn more about numbers here
brainly.com/question/17429689
#SPJ4
Need help asap
will give u brainliest
If a+b+c =9 and a²+ b²+c²=35,find the value of a³+b³+c³-3abc
Here is your Answer
step by step explanation
Hit thanks, if it's help full