Step-by-step explanation:
[tex]4 {x}^{2} - 3x + 2 = 0[/tex]
We know that,
For the given quadratic equation
[tex]a {x}^{2} + bx + c = 0[/tex]
[tex]x = \frac{ - b ± \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
On comparing with the given equation we get
a=4,b=(-3),c=2
On substituting we get,
[tex]x = \frac{ - ( - 3) ± \sqrt{ {( - 3)}^{2} - 4(4)(2)} }{2(4)} [/tex]
[tex]x = \frac{3 ± \sqrt{9 - 32} }{8} [/tex]
[tex]x = \frac{3 + \sqrt{23}i }{8} or x = \frac{3 - \sqrt{23}i }{8} [/tex]
[tex]\large{\underline{\underline{\pmb{\frak {\color {red}{Question:}}}}}}[/tex]
[tex] \sf \red{solve \: for \: x}[/tex]
[tex] \sf \red{ \bold{4x^{2} - 3x + 2 = 0}}[/tex]
[tex]\large{\underline{\underline{\pmb{\frak {\color {blue}{Solution:}}}}}}[/tex]
Here,
a = 4, b = - 3 and c = 2
By, using Quadratic formula, we get:
[tex]x = \frac{ - b \pm \sqrt{ {b}^{2} - 4.a.c } }{2.a} \\ \\ = \frac{ - ( - 3) \pm \sqrt{ { (- 3)}^{2} - 4 \times 4 \times 2 } }{2 \times 4} \\ \\ = \frac{3 \pm \sqrt{9 - 32} }{8} \\ \\ = \frac{3 \pm \sqrt{23} }{8} \\ \\ = \frac{3 \pm4.79}{8} [/tex]
Either,
[tex] \frac{3 + 4.79}{8} \\ \\ = \frac{7.79}{8} \\ \\ = 0.97[/tex]
Or,
[tex] \frac{3 - 4.79}{8} \\ \\ = \frac{ - 1.79}{8} \\ \\ = - 0.23[/tex]
[tex] \boxed{ \huge \frak \red{brainlysamurai}}[/tex]
Find an angle in the range between 0° and 360° that is coterminal with 950°
Answer:
230°
Step-by-step explanation:
950-360 =590
590-360 =230°
The volume of a rectangular prism, in cubic meters, is given by the expression x to the 3rd power
Answer:
power of 3
Step-by-step explanation:
that formula of rectangular prism V=L×b×h when all of number are in meter will not convert if the number of cubic are not all meter must convet to be in meter by dividing by 10, 100 or 1000
In a dice game if you roll a 2, 4, or 6 you get the value of the die. If you roll as 1, 3, or 5 you lose $5. What is the expected value of the game?
Please Need help
Answer: -$0.5
Step-by-step explanation:
event Probability
+ $2 1/6
+ $4 1/6
+ $6 1/6
- $5 3/6
E(X) = (2*1/6)+(4*1/6)+(6*1/6)+(-5*3/6) = -$0.5
All triangles are similar
AD= x-2
CD=x+3
Find the value of x
Answer:
Could you provide more context of the question?
Johanna, Elizabeth, and Dan are preparing a chemical solution for a research project. When
working alone, either Johanna or Elizabeth can prepare the solution in six minutes. Dan can
prepare the solution in four minutes if he works alone. How many minutes will it take the thre
of them to prepare the solution if they work together?
Using the together rate, it is found that they would prepare the solution in 1.71 minutes working together.
What is the together rate?It is the sum of each separate rate.
In this problem, the rates are given by:
Johanna's: 1/6.Elizabeth's: 1/6.Dan's: 1/4.Hence the together rate is given by:
[tex]\frac{1}{x} = \frac{1}{6} + \frac{1}{6} + \frac{1}{4}[/tex]
[tex]\frac{1}{x} = \frac{1}{3} + \frac{1}{4}[/tex]
[tex]\frac{1}{x} = \frac{4 + 3}{12}[/tex]
7x = 12
x = 12/7
x = 1.71.
They would prepare the solution in 1.71 minutes working together.
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Write the equation for the line in slope-intercept form.
Answer:
y=[tex]\frac{2}{3}x[/tex]+4
Step-by-step explanation:
[tex]\frac{rise}{run}[/tex]
plus the y intercept
which is 4
The required equation in slope-intercept form is y = - [tex]\frac{2}{3}[/tex]x + 4
What is an equation?An equation represents any two expressions or statements are equal that means they are having an equal to (=) sign in brtween them.
What is slope intercept form?The equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept is called slope-intercept form of the equation.
How to find the slope ?Slope of a line is the inclination of the straight line towards x axis.
If a straight line passes through two points (a , b) and (c , d), then slope(m) of the straight line can be calculated by the formula,[tex]m = \frac{d - b}{c-a}[/tex]
According to the problem, the straight line passes through (6 , 0) , (3 , 2) , (0, 4) , (-3 , 6).
Slope (m) = [tex]\frac{2-0}{3-6}[/tex] = - [tex]\frac{2}{3}[/tex]
How to write the equation in slope-intercept form?The equation can be written as
y = - [tex]\frac{2}{3}[/tex]x + b
Now , this line passes thorugh (0,4). So, (0,4) will satisfy the equation∴ putting (0,4) in the equation, we get,
y = 4
∴ The required equation is y = - [tex]\frac{2}{3}[/tex]x + 4.
For check we can satisfy the point ( -3 , 6) in the equation.- [tex]\frac{2}{3}[/tex](-3) + 4 = 6
CLearly, the point satisfies the equation.
So, the equation y = - [tex]\frac{2}{3}[/tex]x + 4 is correct
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3 Westbrook Elementary has 12 classes participating in field day. Each class has 24 student teams of 6 to compete in each activity. What is the minimum number of teams needed fo participate? A) 45 B) 46 47 D) 48
Answer: D 48
Step-by-step explanation:
You are at a mall and you have $40. You have already spent $7 on lunch. Write an inequality that would represent the possible amount of money you can still spend at the mall. Write a one step inequality without solving!
Answer:
y ≤ 33
Step-by-step explanation:
You have $40. You spent $7 already.
40-7=33.
You have $33 now. You can spend less or only up to $33.
we have 23 marbles: 6 red marbles, 5 green marbles, 3 blue marbles, and 9 yellow marbles. We are drawing one marble from the bag. What is the probability of drawing a red or a yellow marble?
Answer:
15/23
Step-by-step explanation:
What is probability?
Probability in simple terms is the likelihood of something happening.
We can say that probability = # of favorable outcomes ( what we want to happen ) / total # of outcomes ( simply what's expected to happen )
Here, we want to find the probability of drawing a red or yellow marble.
So # of favorable outcomes = drawing a red or yellow marble and total # of possible outcomes would be simply the total number of marbles
Given:
There are 23 marbles totalThere are 9 yellow marbles There are 6 red marblesGiven this we can determine what the # of favorable outcomes are as well as how many total marbles are.
So in total there are 23 marbles, so total number of outcomes = 23
And there are 6 red marbles and 9 yellow marbles, so number of favorable outcomes = 6 + 9 = 15
Plugging these values into the probability formula we get 15/23
So the probability of drawing a red or yellow marble would be 15/23
Answer:
P(red or yellow marble)= 15/23
Step-by-step explanation:
If we have 23 marbles in the bag, 6 red and 9 yellow, we add the 6 and 9 to get 15. So there are 15 marbles that are red/yellow out of the 23 in the bag. This means the probability is 15/23. Hope this helps <3
A 5-column table with 6 rows titled Number of cans collected. Column 1 has entries 7, 8, 10, 11, 11, 14. Column 2 has entries 16, 17, 18, 18, 24, 25. Column 3 has entries 28, 29, 30, 30, 35, 37. Column 4 has entries 38, 40, 40, 41, 41, 41. Column 5 has entries 42, 42, 42, 42, 42, 43.
Students from Grover Middle School are recycling aluminum cans. The table shows the total number of cans brought in each school day for a period of six weeks. They collected a total of 862 cans. Use the drop-down menus to define the terms.
Mean:
Median:
Mode:
Range:
✔ 36
Robert is using the following data samples to make a claim about the house values in his neighborhood
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER. Find the values of the variables. Then find the side lengths of the square.
X=_____
Y=_____
Step-by-step explanation:
I am not sure this is a square.
this could be a rectangle.
to be safe, I am following that path.
in a rectangle opposite sides are of equal length.
that means
y - 1 = 2y - 7
y = 2y - 6
0 = y - 6
y = 6
3x - 4 = 3y - 13
3x - 4 = 3×6 - 13
3x - 4 = 18 - 13 = 5
3x = 9
x = 3
as it turns out, it is a square, so we could have used every side expression to be equal with every other side expression, but better safe than sorry ...
What is the value of x in the isosceles trapezoid below?
с
14x"
O A. 30
O B. 40
(3x+10)
А
B
O
C. 20
O D. 10
The sum of the opposite angle of the Isosceles trapezoid is supplementary. The value of x from the given diagram is 10
Isosceles trapezoidThe sum of the opposite angle of the Isosceles trapezoid is supplementary. According to the theorem;
14x + 3x + 10 = 180
17x = 180 - 10
17x = 170
Divide both sides by 17
17x/17 = 170/17
x = 10
Hence the value of x from the given diagram is 10
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Find the number which has the greatest difference when its square is subtracted from this number.
The number is 1.
What is a square number?when a number multiplies itself the result is said to be the square of that number.
Analysis:
The square of 1 remains 1.
if you subtract the square of 1 from 1, you will have 0.
and zero is the greatest difference in this regard because every other number gives a negative result.
Example, 3 is a number, the square of 3 is 9. and 3 - 9 = -6 smaller than 0.
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0.5 is the number.
Explanation:Let the number be x,
When this number is subtracted from its square
x - x²
In order to find the greatest number, use vertex formula: x = -b/2a
Identify the following: a = -1, b = 1, c = 0
Hence solve, x = -1/2(-1) = -1/-2 = 1/2
So, the number is 0.5
Difference: (0.5) - (0.5)² = 0.5 - 0.25 = 0.25
A student researches the average cost of electricity, in cents per kilowatt-hour, in the United States since 2000 and creates the scatter plot
below
Electricity Costs
14
12
10
Cost per kilowatt-Hour
(cents)
8
2 4 6 8 10
Years Since 2000
Which of the following best models a linear function fitted to the data in the scatter plot?
A graph which best models a linear function fitted to the average cost of electricity (data) in the scatter plot is shown in the image attached below.
What is a linear function?A linear function can be defined as a type of function with an algebraic equation of the first order that has two (2) variables, with each of its term having an exponent of one.
In Mathematics, the resulting points of a scatter plot shows any association (correlation) between the data plotted on the graph.
Based on the average cost of electricity, a graph which best models a linear function fitted to the data in the scatter plot is shown in the image attached below.
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The following figure shows a cube.
Which expression represents the surface area of the cube?
7 Choose 1 answer:
6X49
7X7X7
6X14
7+7+7+7+7+7
[tex]7[/tex] · [tex]7[/tex] · [tex]7[/tex]
Sure Hope this helps you :D
Answer:
6 x 49
Step-by-step explanation:
Khan Academy
Write an equation of the line that passes through the point (6,-9) with the given slope m= 3
Answer:
y = 3x - 27
Step-by-step explanation:
Since the slope is three, that is the only one that can be the answer.
answer: y = 3x - 27
explanation:
equation of a straight line: y = mx + c
( m is the slope and c the y- intercept )
here m = 3 , then y = 3x + c ← is the partial equation
to find c substitute (6, - 9) into the partial equation
-9 = 18 + c ⇒ c = -9 - 18 = - 27
y = 3x - 27 ← equation of line
What is the sum of all the angles that are labeled?
Image of a full circle divided into five smaller angles. Four of these angles are known. The measurements are eighty degrees, ninety two degrees, forty degrees, and twenty three degrees.
Group of answer choices
225°
235°
Based on the information provided, the sum of all the labeled angles is 235° (option b).
How to calculate the sum of all labeled angles?To calculate the sum of all the labeled angles we must add the different values of each labeled angle as shown below:
80° + 92° + 40° + 23° = 235°
According to the above, it can be inferred that the correct option is B because the result of the sum of the values coincides with this sum.
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f(x)=4x 2 +2x+6 What is the value of the discriminant of f
Answer: -92
Step-by-step explanation:
discriminant formula: [tex]b^2-4ac[/tex]
[tex]f(x) = 4x^2+2x+6[/tex]
a = 4
b = 2
c = 6
[tex]b^2-4ac\\2^2-(4(4)(6))\\4-(96)\\4-96\\-92[/tex]
Since the discriminant equals -92, and -92 is less than 0, we know the equation will not have real solutions
Number 11 please. Need help
Answer:
11a. 3,117
11b. 33
Step-by-step explanation:
11a. -165 + 3217 + 65
The easiest way to do this would be,
-165 + 65 = -100 than -100 + 3217
-100 + 3217 is the same as 3217 - 100
-100 + 3217 = 3,117
11b. 173 + (-43) + (-97)
this is the same as 173 - 43 - 97
173 - 43 = 130 and 130 - 97 = 33
Find sin(A), cos(A), and tan(A) for the triangle pictured
Answer:
See below ~
Step-by-step explanation:
sin (A) = opposing side / hypotenuse
sin(A) = 5√29cos(A) = adjacent side / hypotenuse
cos(A) = 2/√29tan(A) = opposing side / adjacent side
tan(A) = 5/2 = 2.5Mike is buying eight tickets for a concert. A package of five tickets costs $74.45. Individual tickets cost $17.25 each. What is the least amount that Mike can pay for eight tickets? Be sure to include a decimal point in your answer.
Answer:
$126.20
Step-by-step explanation:
Given:
Mike is buying eight tickets for a concert.
A package of five tickets costs $74.45.
Individual tickets cost $17.25 each.
To Find:
What is the least amount that Mike can pay for eight tickets? Be sure to include a decimal point in your answer.
Solve:
Since we know that:
A package of five tickets costs $74.45.
Individual tickets cost $17.25 each.
Hence we know that 5 + 3 = 8
Thus,
$74.45 = 5 tickets
Now for the 3 tickets we can do individual tickets which cost $17.25
$17.25 × 3 = 51.75
Then we add both together:
51.75 + 74.45 = $126.20
Kavinsky
How many different orders of top-three finishers are possible?
Drag the tiles to the correct locations on the equation. Not all tiles will be used.
Using the permutation formula, it is found that the number of different orders of top-three finishers that are possible is given as follows:
[tex]nPr = \frac{14!}{11!} = 2184[/tex].
The order in which the cars finish is important, hence the permutation formula is used instead of the combination formula.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]nPr = \frac{n!}{(n-r)!}[/tex]
In this problem, 3 cars are taken from a set of 14, hence the number of different orders is given as follows:
[tex]nPr = \frac{14!}{11!} = 2184[/tex].
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What does the term unit fraction mean? Provide an example.
Answer:
A unit fraction is a fraction whose numerator is 1. Example is: (1/1, 1/2, 1/3)
Step-by-step explanation:
Answer:
In math, a unit fraction can be defined as a fraction whose numerator is 1. It represents 1 shaded part of all the equal parts of the whole.
Step-by-step explanation:
For example: 1/4, 1/6, 1/25
Answer it please!!!! I need help with it!
Answer:
2=B
Step-by-step explanation:
Insert 2 in the down phrase
Answer:
answer is C.1
Step-by-step explanation:
the value is g(2)= 1
Which expression is equivalent to 9(4 + r)?
Answer:
36+9r
by multiplying 9 &4 you get with 36. countinue multiplying and you also get 9r
Step-by-step explanation:
hope this helps
a bag contains 3 black,3 yellow ,2 green marble what is the probability
Answer:
1/8 for everything
Step-by-step explanation:
add all together and thats the probability
Find missing angle
100°
100°
X=
Answer:
200 + X
Step-by-step explanation:
Need help!! Giving out 100 points to who answers this right!! NEED HELP STAT
Answer: The area of the shape is 156.
Answer:156
Step-by-step explanation:
Question 7: 10 pts
For Thursday's English class, 4 students are assigned to give presentations. How many different ways can the
teacher order the student presentations?
4 ways
16 ways
24 ways
7 ways
The teacher ordered the students in 24 ways.
We have given that the total number of students is 4.
4 students are assigned to give presentations.
We have to find the arrangement of the 4 students.
What is the arrangement?
An arrangement (or ordering) of a set of objects is called a permutation. (We can also arrange just part of the set of objects.)
In a permutation, the order that we arrange the objects n is important.
4 students can be arranged by 4! ways.
[tex]4!=4*3*2*1\\ =12*2\\=24[/tex]
Therefore option 3 is correct.
The teacher ordered the students in 24 ways.
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