Answer:
[tex]\frac{3\±\sqrt{3}}{3}[/tex]
Step-by-step explanation:
Whe have the function [tex]3x^2-6x+2=0[/tex]
To solve this equation we must factor.
To factor, we need to find the points where the function is equal to zero. So we use the quadratic formula
[tex]\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]
Where:
a = 3
b = -6
c = 2
Then
[tex]\frac{-(-6) + \sqrt{(-6)^2-4(3)(2)}}{2(3)} = \frac{3+\sqrt{3}}{3}\\\\and\\\\\frac{-(-6) - \sqrt{(-6)^2-4(3)(2)}}{2(3)}= \frac{3-\sqrt{3}}{3}[/tex]
finally the correct answer is [tex]\frac{3\±\sqrt{3}}{3}[/tex]
Final answer:
To solve the quadratic equation 3x² - 6x + 2 = 0, apply the quadratic formula with a=3, b=-6, and c=2, ultimately finding the solutions x = 1 + √(3) / 3 and x = 1 - √(3) / 3.
Explanation:
To solve the quadratic equation 3x² - 6x + 2 = 0, we can use the quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a) where a, b, and c are coefficients from the equation ax² + bx + c = 0. In this equation, it is given a = 3, b = -6, and c = 2. Substituting these values into the formula gives us:
x = (6 ± √((-6)² - 4 · 3 · 2)) / (2 · 3)
x = (6 ± √(36 - 24)) / 6
x = (6 ± √(12)) / 6
x = (6 ± 2 √(3)) / 6
x = 1 ± √(3) / 3
The two possible solutions for x are then x = 1 + √(3) / 3 and x = 1 - √(3) / 3.
Jackson currently has $35 in his bank account , he is saving $15 a week to eventually buy a new cell phone. He can represent the amount in his account with the equation y=15x+35.
I also need help answer the other questions to
Answer:
1. We have our function y = 15x + 35
a) Where the x represents the numbers of weeks since each week he is saving $15, which is the independent variable.
b) Where the y represents the total money he has, which is the dependent variable.
c) the slope is 15, as x increments, the slope goes up by 15.
d) The y-intercept is 35, because when x = 0, y = 35.
2. To create the table you have to find the value of y, knowing the values of x.
Using our function, when x = 0
y = 15(0) + 35
y = 0 + 35
y = 35
Using our function, when x = 1
y = 15(1) + 35
y = 15 + 35
y = 50
Using our function, when x = 2
y = 15(2) + 35
y = 30 + 35
y = 65
Using our function, when x = 3
y = 15(3) + 35
y = 45 + 35
y = 80
Using our function, when x = 4
y = 15(4) + 35
y = 60 + 35
y = 95
Using our function, when x = 5
y = 15(5) + 35
y = 75 + 35
y = 110
Yes, the table is proportional, because for each week, the value of his money is increasing by 15.
3. To create the graph, you can put the values of the table into the graph
And the graph is not proportional because to be proportional the relationship between “x” and “y” should be constant, meaning that, if “x” changes, “y” changes by the same percentage.
In this case our function has an intercept of 35 meaning that at week 0, he has $35 saved,
after a week: $50,
after two weeks: $65,
So, although is linear, is not proportional because when you double the weeks saved, you don't double the money saved.
Which is a possible number of distinct real roots for a cubic function? Select all that apply.
0
1
2
3
4
Answer: The answer is 1 and 3.
Step-by-step explanation: We are to select the correct options about the number of real roots of a cubic function.
We know that there are three roots of a cubic function, out of which one must be real because the least number of real roots of an odd degree function is 1.
Also, if the second root is real, then the third one must also be real because the complex roots of a function occur in pairs.
Therefore, there is one real root or three real roots for a cubic function.
Thus, the answer is 1 and 3.
Find the surface area of the rectangular solid.
l=16 in, w=13 in, h=15in.
Surface area is in inches and to the 2nd power.
In oder to join a yoga club there is a $100 annual fee and a $5 fee for each class ytouattend. Write an equation in slope-intercept form that models this situation.
Which best describes the function on the graph?
Perform the indicated operation.
(w 3 + 64) ÷ (4 + w)
w² - 4w - 16
w² + 4w - 16
w² - 4w + 16
THE ANSWER IS:
w^2 - 4w + 16
The reason I included the correct answer in the question is that this question was not yet asked and I felt that some people might need to know this. Feel free to answer the question and get the points! :)
w^2 - 4w + 16
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PLS PLS PLS help I am rly confused
Imari went on a hike and recorded the number of each type of bird he saw. The circle graph shows the results of his count. Imari saw 42 sparrows. How many birds did he count in all? Enter your answer in the box. A pie chart depicting a count for bird species. Cardinals are at 13 percent, Sparrows are at 35 percent, Chickadees are at 23 percent, Blue Jays are at 8 percent, Woodpeckers are at 4 percent, and Robins are at 17 percent.Imari went on a hike and recorded the number of each type of bird he saw. The circle graph shows the results of his count. Imari saw 42 sparrows. How many birds did he count in all?
Answer: 120
Hope This Helps ^_^
banananana help me i need you
Answer:
Banananana. How do you know that person?
Step-by-step explanation:
5.11 find the probability of a couple having a baby girl when their third child is born, given that the first two children were both girls. assume boys and girls are equally likely. is the result the same as the probability of getting all girls among three children?
Please help me! I don't know the answer.
Lines L and M are parallel. GEOMETRY
The angle measure of ∠2 is equal to 38°.
m∠2 = 38°.
What are the corresponding angles?When two parallel lines are crossed by another line, comparable angles are the angles that are created in matching corners or corresponding corners with the transversal (i.e. the transversal).
Given:
Lines L and M are parallel lines.
And the parallel lines are cut by a traversal line.
From the property of corresponding angles:
The angle measure of ∠2 is equal to 38°.
Therefore, m∠2 = 38°.
To learn more about the corresponding angles;
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:)If Dani has 5,054 of a certain item and she needs to collect 6,000 of it, how much more does she need to reach her goal? :) Just for fun lol
A woman walks 100 yards east along a straight shoreline and then swims 30 yards south into the ocean on a line that is perpendicular to the shoreline. Using her starting point as the pole and the east direction as the polar axis, give her current position polar coordinates. Round the coordinates to the nearest hundredth. Express θ in degrees. (11.40, –88.28°) (104.40, –88.28°) (11.40, –16.70°) (104.40, –16.70°)
Compare the domains of the logarithmic function f(x) and the square root function g(x).
Graph of f(x):
https://homelifetn.ignitiaschools.com/media/g_alg02_ccss_2016/9/al2_9_20a_media02.gif
https://homelifetn.ignitiaschools.com/media/g_alg02_ccss_2016/9/img_alg02u09c03q25d_02.gif
In two or more complete sentences, explain whether or not the domains of the two functions are the same.
PLEASE HELP
Missi designed a stained glass window and made a scale drawing using centimeters as the unit of measurement. She originally planned for the length of the window to be 44 in. but decided to change it to 48 in. If the length of the window in her scale drawing is 4 cm, which statement about the change of scale is true?
A)One cm represented 11 in. in the first scale, but now 1 cm represents 12 in. in the second scale.
B)One cm represented 44 in. in the first scale, but now 1 cm represents 48 in. in the second scale.
C)One cm represented 1 in. in the first scale, but now 1 cm represents 1 in. in the second scale.
D)One cm represented 12 in. in the first scale, but now 1 cm represents 11 in. in the second scale.
Answer:
The correct answer is option A,
One cm represented 11 in. in the first scale, but now 1 cm represents 12 in. in the second scale
Step-by-step explanation:
The earlier planned length was [tex]44 in\\[/tex]
So the scale of the map was
[tex]\frac{44}{4} \\= 11\\1 cm = 11 in\\[/tex]
The second planned length was [tex]48 in\\[/tex]
So the second scale of the map was
[tex]\frac{48}{4} \\= 12\\1 cm = 12 in\\[/tex]
Thus, option A is correct.
Factor completely. a2+3a−28 Enter your answer in the box.
What is the equation of the exponential graph shown?
A rectangle has a a perimeter of 72 ft. The length and width are scaled by a factor 3.5.
What is the perimeter of the resulting rectangle?
Enter your answer in the box.
Genghis Motors wants to build cars and motorbikes on a budget. The company plans to spend at most $75000 and use at least 320 workers to build cars and motorbikes.
8000C+5500M≤75000 represents the number of cars C and motorbikes M the company can build by spending at most $75000.
52C+38M≥320 represents the number of cars and motorbikes the company can build by using at least 320 workers.
Can the company meet both of its expectations by building 4 cars and 6 motorbikes?
3. what is a popular sunday activity for families in mexico city ? ( 1point )
A. vista the beach
b. visit the prado museum
c. stroll by the roman aqueduct
d. go to the chapultepec park
The sum of the square of a positive number and the square of 3 more than the number is 45. what is the number?
The positive integer is [tex]3[/tex]
Let the number be [tex]a[/tex]
square of [tex]a = a^{2}[/tex]
Square of [tex]3[/tex] more than [tex]a[/tex] = [tex](3+a)^{2}[/tex]
[tex](3 + a)^{2} = (3+a)(3+a) = 9 + 3a + 3a + a^{2} = a^{2} + 6a + 9[/tex]
[tex]a^{2} + a^{2} + 9a + 9 = 45[/tex]
[tex]2a^{2} + 6a + 9 = 45[/tex]
Subtract 9 from both sides :
[tex]2a^{2} + 6a = 45 - 9[/tex]
[tex]2a^{2} + 6a = 36[/tex]
Divide through by 2
[tex]a^{2} + 3a = 18\\a^{2} + 3a - 18 = 0[/tex]
Factorize :
[tex]a^{2} + 6a - 3a - 18 = 0\\a(a + 6) - 3(a + 6) = 0\\a + 6 = 0\\or\\a - 3 = 0[/tex]
[tex]a = 3 ;\\or\\a = - 6[/tex]
since, a is a positive integer, then [tex]a = 3[/tex]
Learn more : https://brainly.com/question/18796573
Learn more : https://brainly.com/question/18796573
What is the value of x? Enter your answer in the box. x = . Triangle G E H with segment E D such that D is on segment G H, between G and H. Angle G E D is congruent to angle D E H. E G equals 99.2 feet, G D equals 62 feet, D H equals left parenthesis x plus 2 right parenthesis feet, and E H equals 112 feet.
Answer:
The value of x is 68 ft.
Step-by-step explanation:
Given information: [tex]\angle GED\cong \angle DEH[/tex]
Bisector of an angle of a triangle theorem states that an angle bisector of a triangle divides the opposite side into segments that are proportional to the adjacent sides.
In triangle FEH, ED is an angle bisector
[tex]\frac{EH}{EG}=\frac{DH}{GD}[/tex]
[tex]\frac{112}{99.2}\times 62=x+2[/tex]
[tex]70=x+2[/tex]
[tex]70-2=x[/tex]
[tex]68=x[/tex]
Therefore the value of x is 68 ft.
how do you solve FOIL problems for algebra 1
Help please got to finish khan academy I’m really confused
WILL GIVE BRAINLIEST!!! 12 POINTS!!!!!!
The table below represents the height of a shot basketball, f(x), based on its horizontal position in relation to the basket, x.
x f(x)
-24 7
-20 12
-16 15
-12 16
-8 15
-4 12
0 7
If all quantities are in feet, what is the height of the basketball as it passes the hoop?
Answer: _____ feet
The lowest common denominator for the fractions 8/64 and 8/32 is ?
Final answer:
The lowest common denominator for the fractions 8/64 and 8/32 is 32. This is found by identifying 32 as the least common multiple of the denominators 64 and 32, allowing both fractions to be expressed with the same denominator.
Explanation:
Finding the Lowest Common Denominator
To find the lowest common denominator (LCD) for the fractions 8/64 and 8/32, you must identify the smallest number that both denominators can divide into without leaving a remainder. Both 64 and 32 can be divided by 32, so the LCD for these fractions is 32. It's important to understand that finding an LCD involves looking for the least common multiple (LCM) of the denominators. In this case, since 32 is a multiple of 64 (32x2=64), it serves as the LCM of 32 and 64, and consequently, the LCD of the fractions.
To further clarify, each fraction can be expressed with a denominator of 32. For 8/64, when we divide both the numerator and denominator by 8, we get 1/8. This fraction can then be converted to have a denominator of 32 through multiplication by 4 (1/8 * 4/4 = 4/32). Similarly, the fraction 8/32 is already expressed with the desired denominator.
By finding the LCD, it is easier to perform addition, subtraction, or comparison of fractions, as they will share the same denominator.
The lowest common denominator for the fractions [tex]\( \frac{8}{64} \) and \( \frac{8}{32} \) is \( \boxed{64} \).[/tex]
To find the lowest common denominator (LCD) for the fractions [tex]\( \frac{8}{64} \) and \( \frac{8}{32} \)[/tex], we need to determine the least common multiple (LCM) of the denominators 64 and 32.
Step 1: Find the prime factorization of each denominator:
[tex]- \( 64 = 2^6 \)[/tex]
[tex]- \( 32 = 2^5 \)[/tex]
Step 2: Determine the LCM by taking the highest power of each prime that appears in any factorization:
[tex]\[ \text{LCM} = 2^{\max(6, 5)} = 2^6 = 64 \][/tex]
Therefore, the LCD of the fractions [tex]\( \frac{8}{64} \) and \( \frac{8}{32} \) is \( 64 \).[/tex]
Step 3: Verify that ( 64 ) is indeed the LCD:
[tex]- \( \frac{8}{64} = \frac{1}{8} \)[/tex]
[tex]- \( \frac{8}{32} = \frac{1}{4} \)[/tex]
Both fractions can be rewritten with a denominator of ( 64 ):
[tex]- \( \frac{1}{8} = \frac{8}{64} \)[/tex]
[tex]- \( \frac{1}{4} = \frac{16}{64} \)[/tex]
Therefore, ( 64 ) is the lowest common denominator for[tex]\( \frac{8}{64} \) and \( \frac{8}{32} \).[/tex]
Thus, the lowest common denominator for the fractions [tex]\( \frac{8}{64} \) and \( \frac{8}{32} \) is \( \boxed{64} \).[/tex]
Which measure describes how all of the values of a data set vary with a single number?
A) mean
B) median
C) mode
D) range
Answer:
The answer is d. range.
Need help with this too, all connected
Dora is writing statements as shown to prove that if segment ST is parallel to segment RQ, then x = 12.
What Is 7 minutes after 1? And what is 23 minutes after 4?
Answer: 7 minutes after 1 is 1:07 and 23 minutes after 4 is 4:23
Step-by-step explanation: Please mark me brainliest ✨
Good luck on whatever you’re working on!