Solve the equation by using the quadratic formula.
3x² - 1 = 7x
Answers
Answer:
Solutions: [tex]\displaystyle\mathsf{x\:=\:\frac{7+ \sqrt{61}}{6}}[/tex] , [tex]\displaystyle\mathsf{x\:=\:\frac{7 - \sqrt{61}}{6}}[/tex]Step-by-step explanation:
We are given the following quadratic equation, 3x² - 1 = 7x, which requires us to find its possible solutions using the quadratic formula.
Definitions:In a quadratic equation, the leading term has a second-degree (or squared) variable. The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are real numbers, and that a ≠ 0. Quadratic Formula:The quadratic formula is given by:
[tex]\displaystyle\mathsf{x\:=\:\frac{-b\pm\sqrt{b^2-4ac}}{2a}}[/tex]
We will use this formula to solve for the roots or the solution of the given quadratic equation.
Solution:Step 1: transform the given equaton into standard form.
First, we must subtract "7x" from both sides of the equation:
3x² - 7x - 1 = 7x - 7x
3x² - 7x - 1 = 0 ⇒ This is the standard form of the given quadratic equation where a = 3, b = -7, and c = - 1.
Step 2: Plug in the values for a, b, & c into the quadratic formula.
The derived values for a, b, & c from the previous step are: a = 3, b = -7, and c = - 1. Substitute these values into the following quadratic formula:
[tex]\displaystyle\mathsf{x\:=\:\frac{-b\pm\sqrt{b^2-4ac}}{2a}}[/tex]
[tex]\displaystyle\mathsf{x\:=\:\frac{-(-7)\pm\sqrt{(-7)^2-4(3)(-1)}}{2(3)}}[/tex]
Step 3: Following the PEMDAS Order of Operations, start by applying the Power rule of Exponents [tex]\displaystyle\mathsf{(a^m)^n = (a^{m*n})}[/tex] (under the radical) :
[tex]\displaystyle\mathsf{x\:=\:\frac{-(-7)\pm\sqrt{49-4(3)(-1)}}{2(3)}}[/tex]
Step 4: Next, multiply the integers under the radical, PEMDAS Order of Operations.
[tex]\displaystyle\mathsf{x\:=\:\frac{-(-7)\pm\sqrt{61}}{2(3)}}[/tex]
Step 5: Multiply the integers in the denominator, and apply the multiplication integer rule, -(-a) = a.
[tex]\displaystyle\mathsf{x\:=\:\frac{7\pm\sqrt{61}}{6}}[/tex]
Since [tex]\displaystyle\mathsf{\sqrt{61}}[/tex] is not a perfect square, it can remain the same.Step 6: Separate the solutions.
[tex]\displaystyle\mathsf{x\:=\:\frac{7+ \sqrt{61}}{6}}[/tex] , and [tex]\displaystyle\mathsf{x\:=\:\frac{7 - \sqrt{61}}{6}}[/tex]
Final Answer:Therefore, the solution to 3x² - 1 = 7x are: [tex]\displaystyle\mathsf{x\:=\:\frac{7+ \sqrt{61}}{6}}[/tex], [tex]\displaystyle\mathsf{x\:=\:\frac{7 - \sqrt{61}}{6}}[/tex].
_____________________Keywords:Quadratic equation
Quadratic function
Standard form
Parabola
______________________Learn more about quadratic equations here:
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Related Questions
Camile uses specialized equipment designed by Olivia to analyze and predict weather and atmospheric changes. Which describes the career pathways of Camile and Olivia?
Olivia is in the Engineering and Design pathway and Camile is in the Science and Meteorology pathway.
Olivia is in the Engineering and Computer pathway and Camile is in the Physical Science and Math pathway.
Camile is in the Engineering and Technology pathway and Olivia is in the Science and Math pathway.
Camile is in the Science and Math pathway and Olivia is in the Engineering and Technology pathway.
Answers
Answer:
Olivia is in the Engineering and Design pathway and Camile is in the Science and Meteorology pathway.
Step-by-step explanation:
Engineering & Design pathway⇒ A methodological series of steps that are used by engineers in creating functional products and processes.
Science & Methodology pathway⇒ Steps used by scientists to create explanations based on the evidence which they have gathered.
Hence, [A] Olivia is in the Engineering and Design pathway and Camile is in the Science and Meteorology pathway is the correct answer.
[RevyBreeze]
Answer:
A - Olivia is in the Engineering and Design pathway and Camile is in the Science and Meteorology pathway.
Step-by-step explanation:
4a + (-1.2b) + (-3a) + 7.9b
Answers
i know this because if u add the a’s and b’s together, then u get a + 6.7b
Hey there!
4a + (-1.2b) + (-3a) + 7.9b
REWRITE/REWORD:
= 4a - 1.2b - 3a + 7.9b
COMBINE the LIKE TERMS:
= (4a - 3a) - (1.2b + 7.9b)
= 4a - 3a - 1.2b + 7.9b
= 1a - 6.7b
= a - 6.7b
Therefore, your answer is: a + 6.7b
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
here a subtraction problem that has been solved incorrectly what is the right answer for 74-25=59 but do it in the addition sentence that check the subtraction problem but the choices is 84-25=109 59+25=84 84-59=43
Answers
3x ^3- 12x^2- 15x = 0
factor and solve to find all the zeros
show all work
Answers
Answer:
x = -1 or 5
Step-by-step explanation:
3x^3-12x^2-15x=0
Divide all by 3x.
x^2-4x-5=0
Find the factors of -5 that add up to -4.
This will be 1 and -5.
(x+1)(x-5)=0
x+1=0
x= -1
x-5=0
x=5
The high temperature in a mountain city was 23°C. What was the high
temperature in degrees Fahrenheit?
Answers
3x+25 what would x be
Answers
Answer:
8.3
Step-by-step explanation:
25/3= 8.3
so yes
What type of sequence is this?
15, 12, 9, 6, ...
Answers
Answer:
it has the pattern of -3 every number.
hope that helps
Hey there!
These are the 2 kinds of sequences:
Arithmetic sequence. This is where we use addition/subtraction in order to get the next term.Geometric sequence. This is where we use multiplication/division in order to get the next term.Let's check the given sequence:
15, 12, 9, 6...
Do we use addition, subtraction, multiplication or division?
Well, we definitely do not multiply or divide anything here, so we have an arithmetic sequence.
Do we use addition or subtraction?
Well, let's take another look at our sequence.
15, 12, 9, 6...
As you can see, we use subtraction in order to get the next term.
Hence, we have
[tex]\boxed{\boxed{\bold{an~arithmetic~sequence}}}[/tex]
Hope everything is clear.
Let me know if you have any other questions!
#LearningDoesn'tEnd
:-)
Which of the following best describes the nitrogen fixation process?(1 point) Consumers convert nitrogen gas into ammonia, nitrites, and then nitrates. Waste from consumers adds nitrogen to the soil, which can be used by producers. Consumers convert nitrogen gas into ammonia, nitrites, and then nitrates. Waste from consumers adds nitrogen to the soil, which can be used by producers. Producers convert nitrogen gas into nitrates in the soil. Producers can then absorb nitrates through their roots. Producers convert nitrogen gas into nitrates in the soil. Producers can then absorb nitrates through their roots. Soil bacteria convert nitrogen gas into ammonia, nitrites, and then nitrates. Nitrates are then absorbed by producers. Soil bacteria convert nitrogen gas into ammonia, nitrites, and then nitrates. Nitrates are then absorbed by producers. Producers use the energy from sunlight to fix nitrogen gas in the atmosphere. Producers can then absorb nitrogen through their leaves. Producers use the energy from sunlight to fix nitrogen gas in the atmosphere. Producers can then absorb nitrogen through their leaves.
Answers
Answer:
Soil bacteria convert nitrogen gas into ammonia, nitrites, and then nitrates. Nitrates are then absorbed by producers.
Step-by-step explanation:
.
Answer:
D
Step-by-step explanation:
Soil bacteria convert nitrogen gas into ammonia, nitrites, and then nitrates. Nitrates are then absorbed by producers.
Can you guys please help me answer these two questions !!
Answers
Answer:
(e) 14.4 units²(d) 153.5 ft²Step-by-step explanation:
A calculator is a useful tool for evaluating formulas with numbers given. The attached shows results using a TI-84. Put the numbers in place of the corresponding variables and do the arithmetic.
a) 14.4 square units
b) 153.5 square feet
_____
Additional comment
Be sure your calculator is set to the mode corresponding to the angle measure you're using. Here, it is "degrees." (Often, the default is radians.)
It is a good idea to learn to use a suitable scientific or graphing calculator. Some nice TI-84 work-alike calculator apps are available for iOS and Android platforms. Your school may have a list of exam-approved calculator models that would be useful, or your online curriculum materials may provide a calculator.
It costs 30 dollars per month for a cell phone plus 10 dollars for every GB of data.Which expression can be used to represent the cost of a cell phone bill when x is the number of GB of data used?
a.30 + 10
b.30x + 10
c.10x + 30
d.10x + 30x
Answers
Answer: I Think Its C.( 10x ) + 30
Step-by-step explanation: Hoped This Helped! Thx For The Points!
what is the vertex of f(x)=(x+1)^2-6
Answers
What is the area of the triangle?
A. 32 square centimeters
B. 48 square centimeters
C. 96 square centimeters
D. 60 square centimeters
Answers
Answer:
48
Step-by-step explanation:
A = bh/2
A= 8 x 12 / 2
A= 96 / 2
A = 48
Which expression represents the phrase below?
3 fewer than a number, p
A. 3-P B. p=3
3p
C. 3:p
D. p-3
Answers
Answer:
d) p - 3
3 fewer than menas you need to subtract 3
Step-by-step explanation:
The expression represents the phrase “3 fewer than a number, p” is (p-3).
Given
Expression; the phrase: “3 fewer than a number, p”
What is the phrase?
A small group of words standing together as a conceptual unit, typically forming a component of a clause:
The given number is p which is smaller than a number which is 3.
Expression; the phrase: “3 fewer than a number, p”
Then,
The expression represents the phrase is;
Hence, the expression represents the phrase “3 fewer than a number, p” is (p-3).
Select the correct days. Gina tracks the low temperatures for a city over six days. Identify the days colder than -1.75°F. I WILL MARK BRAINLY PLS HELPP
Answers
Answer:
Monday and tuesday!
Step-by-step explanation:
The reason why this is your answer is that they are even colder than 1.75 celsius.
Thanks!
Mark me brainliest!
Each face of a pyramid is an isosceles triangle with base 30m and vertical height 22m.
Calculate the area of one face.
Answers
Answer:
Step-by-step explanation:
a=[tex]\frac{1}{2}*30*22[/tex]
=15*22
=330 m2
A jar contains some bacteria. Every day the number of bacteria
Loubles. After 20 days the jar is full. When was the jar one-eighth
full?
Answers
Answer:
Day 2 the jug was full
Step-by-step explanation:
If 20days=1full jag what about 1/8 full
1/8×20
=2days
Zero divided by any non-zero number is ____.
Answers
Answer:
zero...................
Translate the verbal rule into an equation.
To get p, add 20 to t, then multiply the result by 4.
Answers
Answer:
p = 4(t + 20)
Step-by-step explanation:
'add 20 to t' can be written as t + 20
'multiply the result by 4' means to multiply t + 20 by 4 → 4(t + 20)
Hope this helps!
Please help!!
Find the volume of the sphere
Answers
Answer:
Formula: [tex]\frac{4}{3}\pi r^3[/tex]
Plug in values: radius = 9.3
Volume: 1072.476π cubic units
Step-by-step explanation:
The formula to find the volume of a sphere is [tex]\frac{4}{3}\pi r^3[/tex], where r = radius. In this case, we leave the volume of sphere in terms of pi.
The only value we can plug in is the radius. In this case, the radius is 9.3 units.Now, we can solve for the volume:
[tex]\frac{4}{3} *9.3^3 * \pi[/tex] [tex]\frac{4}{3} * 804.357 * \pi[/tex] [tex]1072.476 * \pi[/tex] [tex]1072.476\pi[/tex]Expand the logarithm as much as possible. Rewrite the expression as a sum, difference, or product of logs.
ln(1/4k)
Enclose arguments of functions in parentheses and include a multiplication sign between terms. For example, c*ln(h).
ln(1/4k)=
Answers
Step-by-step explanation:
[tex] ln( \frac{1}{4}k ) [/tex]
[tex] ln(k {}^{ - 2} ) [/tex]
[tex] - 2 ln(k) [/tex]
The simplified form of logarithm is [tex]ln(\frac{1}{4k}) = - ln(k) - 2ln(2)[/tex]
What is Logarithm?
The power to which a number must be increased in order to obtain another number is known as the Logarithm. A power is the opposite of a logarithm. In other words, if we subtract an exponentiation from a number by taking its logarithm
The properties of Logarithm are :
log A + log B = log ABlog A − log B = log A/Blog Aⁿ = n log AGiven data ,
The equation is
[tex]A = ln(\frac{1}{4k})[/tex]
Now , from the logarithm rule log A − log B = log A/B , we can simplify
[tex]ln(\frac{1}{4k}) = ln(1) - ln (4k)[/tex]
And , [tex]ln(1) = 0[/tex]
So ,
[tex]ln(\frac{1}{4k}) = - ln (4k)[/tex]
Now , from the logarithm rule log A + log B = log AB , we get
[tex]ln(\frac{1}{4k}) = - ( ln(k) + ln(4) )[/tex]
[tex]ln(\frac{1}{4k}) = - ln(k) - ln(4)[/tex]
And , [tex]ln(4) = 2 ln(2)[/tex]
So ,
[tex]ln(\frac{1}{4k}) = - ln(k) - 2ln(2)[/tex]
Hence , the simplified form of logarithm is [tex]ln(\frac{1}{4k}) = - ln(k) - 2ln(2)[/tex]
To learn more about logarithm click :
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A rectangular prism has a length of 10 in., a width of 2 in., and a height of 3 1/2 in.
The prism is filled with cubes that have edge lengths of 1/2 in.
How many cubes are needed to fill the rectangular prism?
Enter your answer in the box.
To fill the rectangular prism,
cubes are needed.
Answers
Answer:
2.5
hope this helps
help i dont know this i have this test i have 30 min
Answers
Answer:
Step-by-step explanation:
The Value of Y is 3 MORE than X.
For example, Because the equation is x+3=y
x is any number on the top row,
y is any number on the bottom row,
Meaning 1 + 3 = 4 Because 1 is on the x row, and 4 is on the y row.
You find the number you want to try and do x+3=y
Anyway answer is at the top.
|After four games a hockey team had scored an
average of 6 goals per game.
How many goals would the team need to score in
its fifth game to have an average of 8 goals for the
five games played?
Answers
Hey guys can u help me on this one, I quite don’t get it
Answers
Answer:
try 130
Step-by-step explanation:
dont murder me if my math is wrong....
Find the value of xx, yy, and zz, in the rhombus below.
Answers
Answer:
Step-by-step explanation:
A jar contains some bacteria. Every day the number of bacteria
doubles. After 20 days the jar is full. When was the jar one-eighth
full?
Answers
Answer:
Day 2
Step-by-step explanation:
Every 20 days, one jar is full.
To find when it was 1/8 full, we multiply the 20 days by 1/8.
20 x 1/8 = 2
Day 2
Suppose that I wrote 150 words of my English paper yesterday and today I begin typing at a rate of 35 words per minute. Is the total number of words typed a linear function of the number of minutes since I began typing today?
Answers
Explanation:
x = number of minutes
35x = number of extra words after x minutes
This is because you add on 35 words per minute (wpm). So for instance, after 10 minutes, you add on 35x = 35*10 = 350 more words.
This is on top of the initial 150 words you already wrote yesterday. So we add the 35x onto the 150 to get the expression 35x+150. This represents the number of words total from yesterday and today combined.
Saying y = 35x+150 shows we have a linear function of the form y = mx+b
m = 35 = slope
b = 150 = y intercept
find the polynomial f(x) of degree 5 that has the following zeros -3(mulitiplicity 2),5,8,-7
Answers
Answer:
Step-by-step explanation:
(x + 3)²(x - 5)(x - 8)(x + 7)
3x+4y=36 solution for y?
Answers
3x+4y=36
-3x -3x
4y=36-3x
/4 /4
y = 9 - 3/4x
these numbers form an addition and subtraction fact family for 8,3,11 what is the answer
Answers
Answer:
A fact family is a set of related addition and subtraction number sentences that include the same numbers. The numbers 2, 4, and 6 can be written in two different addition sentences. The numbers 2, 4, and 6 can be written in two different subtraction sentences. These four number sentences make up a fact family.