Answer:
Completing the square is always confusing, but if you keep in mind it's just a way to write (A + B )^2 so that the problem is in some easier form it makes a bit better sense. A perfect square has some helpful properties.. anyway..
Step-by-step explanation:
Given: [tex]x^{2}[/tex] - 12x +23 = 0 ( not a perfect square , tough to work with )
take 1/2 of the second term coefficient 12/2 = 6 and square it
[tex]x^{2}[/tex] - 12x + ([tex]-6)^{2}[/tex] +23 = [tex](-6)^{2}[/tex]
[tex]x^{2}[/tex] -12x + [tex]6^{2}[/tex] +23 = [tex]6^{2}[/tex]
now there is a perfect square :)
(x - 6)^2 =36-23
(x - 6)^2 = 13
take the square root of both side now
x -6 = [tex]\sqrt{13}[/tex]
x = [tex]\sqrt{13}[/tex] +6
sooo what is supposed to happen in these problems is that square root of 13 is supposed to work out to something that is easy to find the root of ... maybe in your answers you left out the square roots? so maybe A is right :/
We want to solve a quadratic equation by completing squares.
What we need to use is the general relation:
[tex](a + b)^2 = a^2 + 2ab + b^2[/tex]
We will see that the solutions are:
[tex]x = 6 \pm \sqrt{13}[/tex]
We start with the equation:
[tex]x^2 - 12x + 23 = 0\\[/tex]
We can rewrite the middle term as:
[tex]x^2 - 2*6*x + 23 = 0\\[/tex]
Now remember that 6*6 = 36
Then we can add 13 and subtract 13 to get:
[tex]x^2 - 2*6*x + 23 + 13 - 13 = 0\\x^2 - 2*6*x + 36 - 13 = 0\\x^2 - 2*6*x + (-6)^2 - 13 = 0\\(x - 6)^2 - 13 = 0[/tex]
Then the solutions are:
[tex](x - 6) = \pm \sqrt{13} \\\\x = 6 \pm \sqrt{13}[/tex]
If you want to learn more, you can read:
https://brainly.com/question/17177510
Jerome's sister told him to multiply both the amount of water and the amount of drink
mix by the same number to keep the ratio of water to drink mix the same and still
increase the total amount of energy drink.
a) Complete the table below. (2 points)
Original
Ratio
X1
x2
*3
X4
Drink mix help me plz fast
(cups)
3
Water (cups)
8
Answer:
See below
Step-by-step explanation:
a) Completing table:
×1 column: 3×1 = 3, 8×1 = 8 ⇒ numbers 3 / 8×2 column: 3×2 = 6, 8×2 = 16 ⇒ numbers 6 / 16×3 column: 3×3 = 9, 8×3 = 24 ⇒ numbers 9 / 24×4 column: 3×4 = 12, 8×4 = 32 ⇒ numbers 12 / 32b) Yes, Jerome's sister is correct because 3/8 ratio is same as 3n/8n where n is the number both numerator and denominator are multiplied to, it keeps the ratio as is but helps to increase the amount of drink
Find the value of x.
&
35°
116°
820
Which expression is equivalent to
23x + 11y + 18x?
A. 52x
B. 34x + 18y
C. 23x + 29y
D. 41x + 11y
What is the solution to the inequality below?
-8m > 40
Answer:
m<-5
Step-by-step explanation:
Answer:
In inequality form: m<-5 ; In interval notation: negative infinity, -5
Step-by-step explanation:
good night dears...❤️❤️❤️
Answer:
gn
Step-by-step explanation:
Answer:
Good Night! :)
What does the x equal
([tex]\sqrt{\frac{2}{3}[/tex]) plsexplain and solve hurry
Answer:
√6/3
Step-by-step explanation:
Answer:
srry i need points
Step-by-step explanation:
a car travels 30 1/5 hour.what is the average speed,in miles per hour,of the car?
Answer:
4
Step-by-step explanation:
because if its one out of 5 divide 5 by 30 then u get 4
Describe how to transform the graph of f into the graph of g. (2 points)
f(x) = x2 and g(x) = -(-x)2
The graph shifts left one unit.
Reflect the graph of f across the y-axis and then reflect across the x-axis.
Reflect the graph of f across the y-axis.
Reflect the graph of f across the x-axis.
Answer:
Reflect the graph across the x-axis from the positive Quadrant of x-axis to the negative quadrant of x-axis while maintaining the coordinates.
Switch the rule 2(x - 5) + 12 into simplified (or standard) form.
Please show the work aswell
Answer:
6x + 9
Step-by-step explanation:
2(3x + 1) + 7, distribute 2 through the parentheses
↓
6x + 2+7
↓
6x + 9
Hope this helps!:)
Is anyone else a libra
Answer:
No
Step-by-step explanation:
I'm a Scorpio, the sign everyone hates for some reason
Answer:
I'm a libraaaa <3
Step-by-step explanation:
Can somebody help me
Answer:
AB ≈ 3.14 ft
Step-by-step explanation:
The arc AB is calculated as
AB = circumference of circle × fraction of circle
= πd × [tex]\frac{45}{360}[/tex] ( where d is the diameter )
= 8π × [tex]\frac{1}{8}[/tex]
= π
≈ 3.14 ft ( to 2 dec. places )
Logan saved $35 from cutting the neighbor’s yard. He earns $10 a week from washing dishes, which he also saves. Which function can be used to find s, the amount of money Logan will have saved at the end of w, weeks of washing dishes?
the answer is “s = 10w + 35” since he already has 35 but needs to find out how many weeks he washed the dishes :))
How many times does 20 go into 168?
Answer:
8.4
Step-by-step explanation:
How many times 20 goes into 168 = 168/20
= 8.4
Pls mark as brainliest <3
r!×p(5,r)=40....r=??
2x+5+3x+6= combine like terms to simplify each expression
Answer:
5x +11
Step-by-step explanation:
Answer:
5x+11
Step-by-step explanation:
Please give brainliest
You will get brainliest!
Answer:
15,90
Step-by-step explanation:
it goes by 6
(14 x 6=84) and so on and so forth
Please answer this question!!!
9514 1404 393
Answer:
x = 9 cm
Step-by-step explanation:
The formula for the surface area of a cylinder can be written as ...
SA = 2πr(r +h) . . . . . where r is half the diameter, and h is the height
For the given cylinder, we have ...
972π cm² = 2π(x)(x+5x) = 12πx²
Dividing by 12π gives ...
81 cm² = x²
Taking the square root, we have ...
9 cm = x
Diego measured the length of a pen to be 22 cm.
The actual length of the pen is 23 cm.
What is the percent error for Diego’s measurement?
Explain or show your reasoning.
Answer:
let's talk here as to get rid of him
Чу- 8х + 5x - Зу
OOoO
im gonna assume that ur just simplifying this equation so here it is
y-3x
hope this helped!!
A spinner is evenly divided into eight sections: three are red, three are white and two are green. If the spinner is spun twice, then the probability of getting the same color twice is
Answer:
11/32
Step-by-step explanation:
Given that:
Red section (R) = 3 ; white section (W) = 3 ; green section (G) = 2
Total Number of sections = 8
Probability of getting the same color on two spins :
Probability = (required outcome / Total possible outcomes)
Either P(RR) or P(WW) or P(GG)
(3/8 * 3/8) + (3/8 * 3/8) + (2/8 * 2/8)
9/64 + 9/64 + 4/64
(9 + 9 + 4) / 64
22 / 64
= 11/32
the probability of getting the same color twice is
[tex]\frac{11}{32}[/tex]
Given :
A spinner is evenly divided into eight sections: three are red, three are white and two are green.
Total of 8 sections.
red=3
white =3
green =2
Probability of getting two red color =[tex]\frac{3}{8} \cdot \frac{3}{8}= \frac{9}{64}[/tex]
Probability of getting two white colors =[tex]\frac{3}{8} \cdot \frac{3}{8}= \frac{9}{64}[/tex]
Probability of getting two green colors=[tex]\frac{2}{8} \cdot \frac{2}{8}= \frac{4}{64}[/tex]
Probability (getting same color twice)=[tex]\frac{9}{64} + \frac{9}{64}+ \frac{4}{64}=\frac{22}{64} =\frac{11}{32}[/tex]
Learn more : brainly.com/question/20988561
Please help I’m so confused, I’ve been doing testes all day so my brain is fried. Pleaseee
Answer: 40%
Step-by-step explanation: 20 hours jogging/ 50 total hours gives you .4 which is 40%
The number of entertainment websites in 1995 was 54. By 2004 there were 793 entertainment websites. Approximately what was the rate of change for the number of websites for this period of time?
A. 82 websites per year
B. 739 websites per year
C. 12.18 websites per year
D. 424 websites per year
Answer:
Step-by-step explanation:
2004 - 1995 = 9 years
793 - 54 = 739 new sites
739 / 9 = 82.1111111111
approx 82 websites per year change.. ( delta is change )
(x⁴ + 8x³ - 45x + 30) ÷ (x + 7)
Topic is Polynomials. Find the answer using long division. Please, provide detailed steps.
Answer:
Step-by-step explanation:
I added 3 images labelled Synthetic division 1 , 2 , 3 . I hope you understand this. It's really hard to type the method in the format so I used an online calculator symbolab.
Answer:
The quotient is: [tex]x^3+x^2-7x+4[/tex]
The remainder is: 2
Step-by-step explanation:
We need to solve the polynomials [tex](x^4 + 8x^3 - 45x + 30) \div (x + 7)[/tex]
by using long division.
The long division is done in figure attached.
The quotient is: [tex]x^3+x^2-7x+4[/tex]
The remainder is: 2
can someone please help me with this question?
Answer:
BA ≈ 1.88
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesTrigonometry
[Right Triangle Trig] sin∅ = opposite over hypotenuseStep-by-step explanation:
Step 1: Define
We are given a right triangle. We can use trig to find the missing length
Step 2: Identify Variables
POV from angle C
Angle = 28°
Adjacent = BA
Hypotenuse = 4
Step 3: Solve for BA
Substitute [sine]: sin28° = BA/4Isolate BA: 4sin28° = BAEvaluate: 1.87789 = BARewrite: BA = 1.87789Round: BA ≈ 1.88Solve for x 6x^2=2x-1
Answer:
[tex]\displaystyle x=\frac{1\pm i\sqrt{5}}{6}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Algebra I
Standard Form: ax² + bx + c = 0Quadratic Formula: [tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]Algebra II
Imaginary Roots: √-1 = iStep-by-step explanation:
Step 1: Define
6x² = 2x - 1
Step 2: Rewrite
Subtract 2x on both sides: 6x² - 2x = -1Add 1 to both sides: 6x² - 2x + 1 = 0Step 3: Identify Variables
a = 6
b = -2
c = 1
Step 4: Solve for x
Substitute [QF]: [tex]\displaystyle x=\frac{2\pm\sqrt{(-2)^2-4(6)(1)} }{2(6)}[/tex]Exponents: [tex]\displaystyle x=\frac{2\pm\sqrt{4-4(6)(1)} }{2(6)}[/tex]Multiplication: [tex]\displaystyle x=\frac{2\pm\sqrt{4-24} }{12}[/tex](Square Root) Subtract: [tex]\displaystyle x=\frac{2\pm\sqrt{-20} }{12}[/tex]Factor: [tex]\displaystyle x=\frac{2\pm \sqrt{-1} \sqrt{20} }{12}[/tex]Simplify: [tex]\displaystyle x=\frac{2\pm 2i\sqrt{5} }{12}[/tex]Factor GCF: [tex]\displaystyle x=\frac{2(1\pm i\sqrt{5} )}{12}[/tex]Simplify: [tex]\displaystyle x=\frac{1\pm i\sqrt{5}}{6}[/tex]Farmer John can till his field 1.5 times faster than Farmer Bob. If they work together, they can till the field in 6 hours. How long would it take Farmer John on his own
Answer:
It would take Farmer John 10 hours on his own to till his field.
Step-by-step explanation:
Let;
J = Time spent by John alone
B = Time spent by Bob alone = 1.5 * J = 1.5J
Time spent by both = 6
Using reciprocal, time spent by John alone can be calculated as follows:
(1 / J) + (1 /1.5J) = 1 / 6
Multiply through by 6J and solve for J, we have:
(6J / J) + (6J / 1.5J) = 6J / 6
6 + (6 / 1.5) = J
J = 6 + 4 = 10
Therefore, it would take Farmer John 10 hours on his own to till his field.
What is the average of 139 and 78?
Answer:
108.5
Step-by-step explanation:
(139 + 78)/2 = 217/2 = 108.5
Answer:
108.5
Step-by-step explanation:
add 139 and 78 then divide by 2
What is the solution to the system below?
x + y = 5
x - y = 3
( x, y ) = ( 4, 1 )
hope it helps!
Answer:
x= 4
y= 1
Step-by-step explanation:
by adding 2 equations
2x = 8
x= 4
by sub. in Equation 1
4+y=5
y = 5-4
y= 1
Y=x2+2x+5
Write each function in vertex form.