Answers
Answer:
[tex]x = \frac{1 + \sqrt{41} }{10} \: \: or \: \: x = \frac{1 - \sqrt{41} }{10} [/tex]
Step-by-step explanation:
Ensure that the equation is in the form of ax² +bx +c= 0.
5x² -x +1= 3
5x² -x +1 -3= 0 (-3 on both sides)
5x² -x -2=0
Here, a= 5, b= -1, c= -2.
Use the quadratic formula below to solve for x.
[tex]\boxed{x = \frac{ - b± \sqrt{b^{2} - 4ac } }{2a} }[/tex]
[tex]x = \frac{ - ( - 1)± \sqrt{( -1 )^{2} - 4(5)( - 2)} }{2(5)} [/tex]
[tex]x = \frac{1± \sqrt{1 + 40} }{10} [/tex]
[tex]x = \frac{1± \sqrt{41} }{10} [/tex]
[tex]∴x = \frac{1 + \sqrt{41} }{10} \: \: or \: \: x = \frac{1 - \sqrt{41} }{10} [/tex]
Step-by-step explanation:
First, lets understand the question. When it says to find all the "real" solutions, that means you should not give any solutions containing an imaginary number. An imaginary number is basically where we accept that there exists an i (imaginary number) that is equal to [tex]\sqrt{-1\\}[/tex] (square root of negative 1). So we are not considering this concept in this question.
Let's start solving then. Can you think of an equation that may help you solve this problem? The biggest clue is that x is squared. If you said the quadratic formula, then you are perfectly correct!
Remember in order to use the quadratic formula, you must get your equation into the form:
[tex]ax^{2} +bx +c=0[/tex]
Let's do it! Right now we have:
[tex]5x^{2} - x +1=3[/tex]
Get rid of the 3 by subtracting it from both sides:
[tex]5x^{2} -x+1 -3 = 3 - 3\\5x^{2} -x-2=0[/tex]
Okay! it looks like our quadratic form now! By comparing it we can figure out what a, b, and c are in this case:
[tex]a = 5,{ }\\ b = -1, { }\\c = -2[/tex]
Let's get out our quadratic formula now:
[tex]\frac{ -b\frac{+}{} \sqrt{b^{2} -4ac} }{2a}[/tex]
All that's left to do is insert values and solve! (Be really careful when dealing with the negatives):
[tex]\frac{ -1\frac{+}{} \sqrt{(-1)^{2} -4(5)(-2)} }{2(5)}[/tex]
[tex]=\frac{ -1\frac{+}{} \sqrt{41} }{10}[/tex]
Removing the plus/minus we get two answers:
[tex]=\frac{ -1+ \sqrt{41} }{10}\\\\or\\\\=\frac{ -1-\sqrt{41} }{10}[/tex]
These are the most simplified forms! It turns out we didn't even have to worry about imaginary solutions because we didn't end up with a negative sign under the square root. Hope this helps, and good luck!
Related Questions
Help me solve this question for geometry !
Answers
Answer:
X²–49
Step-by-step explanation:
(x+7)(x-7)
x²+7x-7x-49
x²-49
What is the value of X in simplest radical form?
Answers
Answer:
Step-by-step explanation:
pythagoras theorem
a^2+b^2=c^2
24^2+10^2=x^2
576+100=x^2
676=x^2
[tex]\sqrt{676[/tex]=x
26=x
The middle school is 2.72 kilometers from Marsha's house and 1.54 kilometers from Ryan's house. How much farther does Marsha live from the middle school than Ryan? Group of answer choices
Answers
Answer:
1.18 kilometers
Step-by-step explanation:
The middle school is 2.72 kilometers from Marshal house
The school is also 1.54 kilometers away from Ryan house
Therefore the distance of Marshal house from the school can be calculated as follows
= 2.72-1.54
= 1.18 kilometers
Help
Will
Give
Brainlist
Answers
:)))))) and
Answers
Answer:
26%
Step-by-step explanation:
Find x and y
(y+23)
(2x-17)
Answers
Answer:-2
Step-by-step explanation:
_________________ polygons have congruent angles and proportional side lengths.
answers are:
Regular
Similar
Congruent
Parallel
Answers
Step-by-step explanation:
I think its similar
If 2^x = 5, what is 2^3x - 4?
Answers
Answer:
the value of x is 2^9/4 then 2^3x-4=2^11/4
Question 3(Multiple Choice Worth 4 points)
(05.01)The graph shows the distance a car traveled, y, in x hours:
A coordinate plane graph is shown. The x-axis is labeled time in hours ,and the y-axis is labeled distance in miles. The line passes through the points 2 comma 60, and 4 comma 120.
What is the rise-over-run value for the relationship represented in the graph?
20
30
1 over 20
1 over 30
Answers
Answer:
hello there,
the answer for this question would be 30
Step-by-step explanation:=
Given: The x-axis represents the time in hours and the y-axis represents the distance in miles.
The line passes through the points and
To find: The rise-over-run value for the relationship in the graph.
m=rise over run
=y2-y2/x2-x1
=120-60/4-2
= 60/2
= 30
Hope this helps. if correct please make me brainliest
thank you,
have a good day!!
complete the solution find the value of y when x equals 1 9x+7y=-12
Answers
9+7y=-12
7y=-12-9
7y=-21
7y/7=-21/7
y=-3
Find the value of X a,57
b,3
C,81
D,27
Answers
Answer:
D. 27
Step-by-step explanation:
sum of exterior angles = 360
2x + 56 + 57 + 85 + 4x = 360
6x + 198 = 360
6× = 360 - 198
6× = 162
× = 27
A parabola and its focus are shown on the graph. The vertex of the parabola is at (0,0).
On a coordinate plane, a parabola opens to the right. It has a vertex at (0, 0) and a focus (3, 0).
What is the equation of the directrix of the parabola?
y = 3
y = –3
x = 3
x = –3
Answers
Answer:
y = -3
Step-by-step explanation:
the length from directrix to vertex is equal to the length from focus to the vertex.
Answer: y=-3
Step-by-step explanation: y = -3 Step-by-step explanation: the length to vertex is equal
The formula to estimate organic growth is Pf=P0 . e^rt
MegaVax manufactures vaccinations. The microbe jagus rashii, is being grown for a vaccine against a new strain of influenza. Jagus rashii grows at a rate of 25.0% per hour. How long will it take for a culture of 1,349 jagus rashii to grow to a population of 75,709?
Express your answer to the nearest hundredth of an hour.
Answers
Answer:
16.12 hrStep-by-step explanation:
If I got it right, we have:
Formula Pf = P0*e^(rt)Pf = 75709P0 = 1349r = 25% = 0.25t = ?Substitute the given values and solve for t:
75709 = 1349*e^(0.25t)e^(0.25t) = 75709/1349e^(0.25t) = 56.1223ln e^(0.25t) = ln 56.12230.25t = 4.03t = 4.03/0.25t = 16.12 hrA community group sells 2,000 tickets for its raffle. The grand prize is a car. Neil and 9 of his friends buy 10 tickets each. When the winning ticket number is announced, it is found to belong to Neil's group. Given this information, what is the probability that the ticket belongs to Neil?
Answers
Answer:
1/10 if its is in the group
Step-by-step explanation:
but if its as the whole thing it would be 1/200 because he has 10 and 10 of 2000 is 1/200
The probability that the winning ticket belongs to Neil is 5%.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
There are a total of 2,000 tickets, and Neil and his 9 friends bought 10 tickets each, so they bought a total of 100 tickets (10 tickets/person x 10 people = 100 tickets).
The probability of Neil's group winning the car is equal to the number of tickets they bought divided by the total number of tickets sold:
Probability = Number of tickets bought by Neil's group / Total number of tickets sold
Probability = 100 / 2000
Probability = 0.05 or 5%
Therefore, the probability that the winning ticket belongs to Neil is 5%.
To learn more on probability click:
https://brainly.com/question/11234923
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If f(x) = −4x 2 + 15, then f(−3)
Answers
Answer:
-21
Step-by-step explanation:
f(-3) = -4(-3)² + 15 = -4(9) + 15 = -36 + 15 = -21
Answer:
f(-3) = -21
Step-by-step explanation:
f(x) = −4x²+ 15
f(-3) = -4(-3)² + 15
f(-3) = -4(9) + 15
f(-3) = -36 + 15
f(-3) = -21
3 in
The volume of
the figure is
cubic in.
6 in
3 in
3 in
7 in
16 in.
Answers
Answer:
6in is the cubic volume
Step-by-step explanation:
If I'm wrong just correct me
A card is drawn from a standard deck. Find the probability of drawing a heart or a 7.
Answers
=======================================================
Explanation:
There are A = 13 hearts and B = 4 copies of "7"
The count A+B = 13+4 = 17 may seem like it's the count of hearts or "7" cards, but we're double counting the 7 of hearts. So the true count is actually 17-1 = 16
There are 16 cards we want (either a heart or a "7") out of 52 total. Therefore, the probability is 16/52 = (4*4)/(4*13) = 4/13
help please will be marked as brainliest if correct and first person to respond
Answers
Answer: Unlock code = 76
==========================================================
Explanation:
Use a factor tree to find the prime factorization of each value
22 = 2*11
30 = 2*3*5
Both values have '2' in common and this is the largest such value. Therefore, the GCF of 22 and 30 is 2.
So E = 2
----------------------------
Since 3 and 8 have no factors in common (other than 1), this means the LCM is 3*8 = 24
We can say that F = 24.
If the numbers had some larger number in common, then we'd have to do a bit more work to find the LCM.
----------------------------
As the hint suggests, we'll use the distributive property to show that
3*(7+10) = G + 30
3*7 + 3*10 = G + 30
21 + 30 = G + 30
21 = G .... subtract 30 from both sides; they cancel and go away
G = 21
----------------------------
Use the same idea for the other equation as well
5*(3 + H) = 15 + 45
5*3 + 5*H = 15 + 45
15 + 5H = 45
5H = 45 ............ subtract 15 from both sides; they go away
H = 45/5 ......... divide both sides by 5
H = 9
------------------------------
The unlock code is
E+F+G+H = 2+24+21+29 = 76
PLLEASEEEEEEEEEEEEEEEEE HELPPPPPPPPPP!!!! ill brainlist/ rate u 5 star.
A ramp is used so a trolley can be wheeled on to a platform.
The cross-section of the ramp is drawn as a right-angled triangle with
the unknown height labelled as x.
1 Is the unknown length in this triangle (shown as x) the length of
the hypotenuse? Explain ur answer.
Answers
Answer:
The hypotenuse is sqrt ( 2x^2)
Step-by-step explanation:
Given a right angled triangle, we can find the hypotenuse of a triangle using the Pythagorean theorem which says that c^2 = a^2 + b^2, where a is the length, b is the perpendicular height and c is the hypotenuse. The length of the triangle (l) is x and the height of the triangle is also x. By substituting the values,
c^2 = x^2 + x^2 = 2x^ 2
There are two possible answers to c but the hypotenuse cannot be negative.
Hence,
c = Sqrt (2x^2)
Please help! 8th grade geometry! Thank you<3
Answers
answer : 48 maybe that’s what they’re looking for .
Answer:
Length of the hypotenuse - 10
Step-by-step explanation:
To find the hypotenuse, we need to use the Pythagorean theorem.
a^2 + b^2 = c^2
8^2 + 6^2 = c^2
64 + 36 = c^2
c^2 = 100
c = 10
Identify the vertex
Answers
Answer:
The vertex is (-2,10)
Step-by-step explanation:
The vertex is the maximum point on a downward facing parabola
The maximum is (-2,10)
The vertex is (-2,10)
At what point do these lines intersect? A
-24x - 4y =-164
y=41 - 6x
Answers
Answer:
Infinite points
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
FunctionsTerms/CoefficientsSolving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
-24x - 4y = -164
y = 41 - 6x
Step 2: Solve for x
Substitute in y [1st Equation]: -24x - 4(41 - 6x) = -164[Distributive Property] Distribute -4: -24x - 164 + 24x = -164[Addition] Combine like terms: -164 = -164Here we see that -164 does indeed equal -164.
∴ We have an infinite amount of solutions.
Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 10 feet and a height of 8 feet. Container B has a diameter of 12 feet and a height of 7 feet. Container A is full of water and the water is pumped into Container B until Container A is empty.
To the nearest tenth, what is the percent of Container B that is full after the pumping is complete?
Answers
Answer:
79.4%
Step-by-step explanation:
the volume of a cylinder is as for any other regular 3D object
base area × height
the base area is for a cylinder a circle.
so, it is
pi×r² × height
the radius (r) is always half of the diameter.
so, volume of cylinder A is
Va = pi×(10/2)² × 8 = pi×25 × 8 = 200pi ft³
the volume of cylinder B is
Vb = pi×(12/2)² × 7 = pi×36 × 7 = 252pi ft³
therefore, in a volume of 252pi ft³ we have 200pi ft³ filled with water.
252pi = 100% filling
1% = 100%/100 = 252pi/100 = 2.52pi
how many % are 200pi ?
as many as times 1% fit into 200pi :
200pi/2.52pi = 200/2.52 = 79.36507937... ≈ 79.4%
219.44 in word form
Answers
Answer:
two hundred nineteen and 44
OR
two hundred nineteen point 44
Step-by-step explanation:
do not say AND before nineteen. saying AND represents a decimal point. Both can be used (point or and)
What is the value of X in the figure show
Answers
Answer:
x=11
Step-by-step explanation:
The equation for the problem is 4x-2=42. The angle (4x-2) is equal to 42 degrees because it is vertical to the angle with 42 degrees. If angles are vertical, they are equal to each other.
Add 2 to both sides of the equation.
4x+2=4x 42+2=44
Simplify.
4x=44
Divide 4 by both sides.
4x/4=x 44/4=11
Simplify to get the final answer.
x=11
Matt is saving to buy a new motorcycle. If he deposits $70 at the end of each month in an account that pays an annual interest rate of 3.5%, how much will he have in
60 months? Assume that the compounding is being done monthly
Answers
Answer:
bro I don't know. I just need the points so I can keep getting answers. good luck tho I guess.
please help stuck on probelem
Answers
=========================================================
Explanation:
Draw a horizontal line to cut the figure into a rectangle on top and a triangle down below.
The rectangle has length and width of 6 and 4 (horizontal and vertical components respectively). The area of this rectangle is 6*4 = 24 square units.
The triangle has a base of 6 and a height of 4. The base and height of any triangle are always perpendicular.
The area of the triangle is base*height/2 = 6*4/2 = 24/2 = 12 square units. If you were to cut out half of the triangle and rearrange things, you'll find that a rectangle can be formed. This rectangle is half in area that of the first rectangle we found. This is why we divide by 2 when finding the area of the triangle.
Once you know the two sub-areas, we add them up to get the overall area: 24+12 = 36 square units.
Write an equation in slope-intercept form of
the line that passes through (-6,4) and
(-1,2).
Answers
Answer:
Step-by-step explanation:
(-6 , 4) & (-1 , 2)
Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]= \frac{2-4}{-1-[-6]}\\\\= \frac{-2}{-1+6}\\\\= \frac{-2}{5}[/tex]
m = -2/5 & (-6 , 4)
y -y1 = m(x -x1)
[tex]y - 4 = \frac{-2}{5}(x - [-6])\\\\y - 4 = \frac{-2}{5}(x + 6)\\\\y - 4 = \frac{-2}{5}x + 6*\frac{-2}{5}\\\\y = \frac{-2}{5}x -\frac{12}{5}+4\\\\y=\frac{-2}{5}x-\frac{12}{5}+\frac{4*5}{1*5}\\\\y=\frac{-2}{5}x-\frac{12}{5}+\frac{20}{5}\\\\y=\frac{-2}{5}x+\frac{8}{5}[/tex]
HELP ME RN PLEASEEEE
[WILL GIVE BRAINLY TO CORRECT AND BEST EXPLAINED ANSWER]
Answers
Answer:
[tex]\boxed {\boxed {\sf d= \sqrt{34}}}[/tex]
Step-by-step explanation:
We want to find the distance between two points, so the following formula is used.
[tex]d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
Where (x₁, y₁) and (x₂, y₂) are the points we are finding the distance between.
We are given the points (-2, -1) and (3,2). If we match the corresponding value and variable we see that:
x₁= -2 y₁= -1x₂= 3 y₂= 2Substitute the values into the formula.
[tex]d= \sqrt {(-2-3)^2+(2--1)^2[/tex]
Solve the parentheses.
-2 -3 = -5 2--1 = 2+ 1 = 3[tex]d= \sqrt{(-5)^2+(3)^2[/tex]
Solve the exponents.
(-5)²= -5*-5= 25 (3)²= 3*3=9[tex]d= \sqrt{25+9}[/tex]
Add.
[tex]d= \sqrt{34}[/tex]
This radical cannot be simplified, so the distance between the two points is √34 and choice 3 is correct.
Find the value of x.
Answers
Solve for x. Round to the nearest tenth, if necessary.
Answers
Answer:
Step-by-step explanation:
take 60 degree as reference angle
using cos rule
cos 60=adjacent/hypotenuse
1/2=80/x
x=80*2
x=160