Using the quadratic formula to solve 5x = 6x^2 – 3, what are the values of x?
Answers
Answer:
Correct Choice: Second Option
[tex]\displaystyle x=\frac{5\pm \sqrt{97}}{12}[/tex]
Step-by-step explanation:
Standard Form of Quadratic Function
The standard representation of a quadratic function is:
[tex]f(x)=ax^2+bx+c[/tex]
where a,b, and c are constants.
Solving with the quadratic formula:
[tex]\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
We have the following equation to solve:
[tex]5x = 6x^2 -3[/tex]
Rearranging all the terms to the left side:
[tex]6x^2 -5x- 3=0[/tex]
Comparing with the general form of the quadratic equation: a=6, b=-5, c=-3. Apply the formula:
[tex]\displaystyle x=\frac{-(-5)\pm \sqrt{(-5)^2-4(6)(-3)}}{2(6)}[/tex]
[tex]\displaystyle x=\frac{5\pm \sqrt{25+72}}{12}[/tex]
[tex]\boxed{\displaystyle x=\frac{5\pm \sqrt{97}}{12}}[/tex]
Correct Choice: Second Option
Related Questions
Dons plumbing charges $15 per hour plus a service fee of $40 for coming out to your house. Write the equation modeling this situation.
Answers
Answer:
15x+40
Step-by-step explanation:
x would be the number of hours he is at the home
Select all of the expressions that are equivalent to 4v5.
Answers
Answer:
The answer is A and D.................................
When Mrs. Adams drove from Houston to Austin, her car averaged 24 miles per gallon of gas.
This situation can be written in the equation y = 24x. What does the slope represent?
A. the number of miles per gallon
b. the total number of gallons of gas
c .the total number of miles
d. the price of a gallon of gas
Answers
Are these right please help
Answers
Answer: 1 is correct. 2 is incorrect it should be 0. 3 is incorrect it should be undefined. 4 is incorrect it should be -4/3. The rest is all correct
Step-by-step explanation:2=0, 3=undefined, and 4=-4/3
Three students were given the expression shown and were asked to take a
common factor out of two of the terms.
Use the drop-down menus to complete the statements about whether each
student's answer is an equivalent expression. Then choose an expression
that is equivalent
4 - 9x + 21
Answers
Step-by-step explanation:
The question is incomplete. Find the complete question attached.
Let us analyze each of the students expression and determine the correct one if there are any.
Chang expression after factoring: 4-3(3x+7)
In order to know whether chang's factorization is similar to the expression, we will expand and compare with the given expression as shown;
= 4-3(3x+7)
Open the parenthesis
= 4 - 3(3x)-3(7)
= 4 - 9x - 21
This shows that Chand expression is wrong.
Hence Chang expression is not an equivalent expression because when -3 is factored out from the bracket, it supposed to leave a negative sign instead of positive.
Benjamin expression after factoring: 4+3(3x+7)
In order to know whether Benjamin's factorization is similar to the expression, we will expand and compare with the given expression as shown;
= 4+3(3x+7)
Open the parenthesis
= 4 + 3(3x)+3(7)
= 4 +9x + 21
This shows that Benjamin expression is wrong.
Hence Benjamin expression is not an equivalent expression because the positive values within the expression is supposed to be negative sign instead
Habib expression after factoring: 4+12x
The equation is obviously wrong and not an equivalent expression because the constant value 21 does not have a variable x and cannot be added to -9x according to what Habib did.
Given the expression
4 - 9x + 21
The correct simplification of the expression is as shown;
4 - 3(3x - 7)
Note that when -3 is factored out, the sign inside the parenthesis also changes
Please help if you can!! I would appreciate it alot!
People attending a baseball game either supported the home team or the visiting team. If 1144 of the people attending supported the home team and 1456 supported the visiting team, what percentage supported the home team?
Answers
Answer:
44%
Step-by-step explanation:
1144 is 44 percent of 2600
Bryan ran 184 miles in 23 days. what is the unit rate.
Answers
Answer:
8 miles per day
Step-by-step explanation:
Divide 184 by 23, and you get 8 miles per day
Answer:
8 miles per day
Step-by-step explanation:
Bryan runs 8 miles everyday.
184 divided by 23 is 8
Therefore he runs 8 miles each day
What is the value of -42 +(5-2)(-6)?
0-34
0 -2
10
O 34
Answers
Answer:its A (-34)
Step-by-step explanation:
I took the test
I need help with the first question
Answers
Answer:
Subtract 2k from both sides.
4k−3−2k=2k+5−2k
2k−3=5
Add 3 to both sides.
2k−3+3=5+3
2k=8
Divide both sides by 2.
2k /2 =8/2
k=4
Farmer Bob's son built a track to walk his pet pig. The
track goes around the pig pen. The pig pen is 15 feet long and 21 feet wide. If the pig walks all the way around the track, how many feet did he walk?
Answers
Answer:
72 Feet
Step-by-step explanation:
it is a four sided figure so 15*2 + 21*2 you will get 30 + 42 so the answer is 72
If x is 6, then 7x =
Answers
Answer:42
Step-by-step explanation: You have to multiply 7 per 6 and so the result will be 42.
Which list contains only composite numbers? 12, 37, 54, 80, 117,
31, 44, 57, 64, 92,
26, 53, 66, 84, 96,
6, 24, 51, 72, 105,
Answers
Answer:
6, 24, 51, 72, 105
Step-by-step explanation:
6,24,51,72,105
It was right on my work hoops this helps :)
Please help!!!!!! I'll mark you brainiest!!!! Rewrite the statement in if-then form: Adjacent angles share a common side.
Answers
Answer:
Two angles are adjacent if and only if they share a common side.
Step-by-step explanation:
what is 4/8 simplified
Answers
Answer:
exact form: 1/2
decimal form: 0.5
Step-by-step explanation:
Slope of (10,4), (4,15)
Answers
Answer:
negative 11/6
Step-by-step explanation:
because u have to do x1-x2=slope of x
y1-y2=slope of y
Help meh plsssss ASAP ty
Answers
Help....................
Answers
Answer:
8
Step-by-step explanation:
all outside angles of a regular polygon add up to 360
Find each quotient
-7/12 divided by 1/7
Answers
Answer:
-4 1/12
i just put it in a calculator
Explain how you used the distribute property to find an equivalent expression for
2 (3+8)
WORTH 10 POINTS
Answers
13 would be ur answer
I HAVE 2 MORE QUESTIONS, CAN SOMEONE HELP ME??anyonee?
Answers
the second one is C
What is the product of x and x + 2 ?
FIRST ANSWER GETS BRANLIEST
Answers
Answer:
x² + 2x
Step-by-step explanation:
Given the product
x(x + 2) ← distribute parenthesis by x
= x² + 2x
Which relation is a function?
Answers
Answer: B
Step-by-step explanation:
use 3.14 for pi. round your answer to the nearest whole number
Answers
Answer:
whats the equation
Step-by-step explanation:
Answer:
Kylie drew a circle with a diameter of 8 cm. Paige drew a circle with a radius of 3 cm. Approximately how much larger is the area of Kylie’s circle than the area of Paige’s circle? Use 3.14 for Pi and round to the nearest whole number.
22 centimeters squared
88 centimeters squared
173 centimeters squared
351 centimeters squared
Step-by-step explanation:
How do you evaluate a function.
Answers
Answer:
to evaluate a function, substitute the input
Step-by-step explanation:
(the given number or expression) for the function variable (place holder, x) replace the x with the number or expression. 1. given function f (x)=3x -5 finf (f) 4.
Find the value of d so the line that passes through (a,b) and (c,d) has a slope of 12.
Answers
Answer:
d = 12c-12a+b
Step-by-step explanation:
The formula for calculating the slope of a line passing through two points (x1, y1) and (x2, y2)is expressed as:
m = y2-y1/x2-x1
Given the coordinates (a,b) and (c,d) and slope m = 12
Substitute into the formula as shown:
m = d-b/c-a
12 = d-b/c-a
Make d the subject of the formula:
12 = d-b/c-a
cross multiply
12(c-a) = d-b
12c-12a = d-b
add b to both sides
12c-12a + b = d-b+b
12c-12a + b = d
Hence d = 12c-12a+b
What is the equation of the line using the information
below?
m= 10 and b=-3
Equation=
Answers
Answer:
y= 10x-3
Step-by-step explanation:
If you are using the y=mx+b model, the above answer is correct. M represents the slope and B represents the y-intercept.
A recipe that makes 16 cookies calls for 14 cup of sugar and 23 cup of flour. Janelle wants to proportionally increase these amounts to get a new recipe using one cup of sugar.
1. Using the new recipe, how much flour should she use? Explain or show your work.
16 cookies ¼ cup of sugar ⅔ cups of flour
??? 1 cup of sugar 2 ⅔ cups of flour
Answers
Answer:
64 cookies : 1 cup of sugar : 8/3 or 2 2/3 cup of flour
Step-by-step explanation:
16 cookies : 1/4 cup of sugar : 2/3 cup of flour
Multiply each part by 4 to find how much flour and how many cookies would be used in the same recipe with 1 cup of sugar.
64 cookies : 1 cup of sugar : 8/3 or 2 2/3 cup of flour
Write the change in elevation and the change in temperature as rational numbers.
Answers
Answer:
The airplane is rising, so the change in elevation is +1,000 feet. The temperature is dropping, so the change in temperature is -20 degrees Fahrenheit.
Answer:
The airplane is rising, so the change in elevation is +1,000 feet. The temperature is dropping, so the change in temperature is -20 degrees Fahrenheit.
Step-by-step explanation:
What is the equation in point slope form for a linear function with a slope of m=−4 that passes through the point (2,−7)?
Answers
Answer: y+7=-4(x-2)
Step-by-step explanation:
point slope formula is y-y1=m(x-x1)
it gives you m = -4
(x1,y1) = (-1,-7)
y-(-7) = -4(x-2)
negative of a negative number is positive
y+7=-4(x-2)
you leave that as your answer because thats what point slope for is
its in that form ^
The equation in point slope form for a linear function is [tex]y=4x+15[/tex]
Given the following points:
Points on the x-axis = 2 Points on the y-axis = -7 Slope, m = -4
To write an equation in point slope form for a linear function:
The standard form of an equation of line is given by the formula;
[tex]y-y_1=m(x-x_1)[/tex]
Where:
x and y are the points. m is the slope.Substituting the given parameters into the formula, we have;
[tex]y-(-7)=-4(x-2)\\\\y+7=4x-8\\\\y=4x-8+7\\\\y=4x+15[/tex]
Read more: https://brainly.com/question/18123312
PLEASE HELP
-1 2/3 + (-2 1/6) A. Use the real number properties to write an equivalent expression for this sum.
B. Find the sum. Express your answer as a mixed number in lowest terms.
Answers
Answer:
-3 5/6
Here is what i did to solve it.:
-1 2/3 = -5/3, and -2 1/6 = -13/6. The LCD is 6.
We convert -5/3 to -10/6 and combine this result with -13/6:
-10/6 - 13/6 = -23/6
This last result can be rewritten as -3 5/6.
Hope this help, stay safe and have a nice day! :))))))
Answer:
-3 5/6
Here is what i did to solve it.:
-1 2/3 = -5/3, and -2 1/6 = -13/6. The LCD is 6.
We convert -5/3 to -10/6 and combine this result with -13/6:
-10/6 - 13/6 = -23
