The zeros or roots of the quadratic function f(x) = 6x² – 24x +1 were found with the help of the formula.
The given quadratic equation is:
[tex]6x^{2} -24x+1=0[/tex]
What is a quadratic equation?Any equation of the form [tex]ax^{2} +bx+c=0[/tex] where a≠0 is called a quadratic equation.
We know the solution of a quadratic equation [tex]ax^{2} +bx+c=0[/tex] is given by:
[tex]x=\frac{-b +\sqrt{b^{2}-4ac } }{2a}[/tex]
[tex]x=\frac{-b -\sqrt{b^{2}-4ac } }{2a}[/tex]
So, the solution of the quadratic equation [tex]6x^{2} -24x+1=0[/tex] will be:
[tex]x=\frac{-(-24) +\sqrt{(-24)^{2}-4(6)(1) } }{2*6}[/tex]
[tex]x=\frac{12+\sqrt{138} }{6}[/tex]
[tex]x=\frac{12-\sqrt{138} }{6}[/tex]
Thus, the zeros or roots of the quadratic function f(x) = 6x² – 24x +1 were found with the help of the formula.
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Answer:
its the fourth one on edge D
Step-by-step explanation:
x=2+23/6 or x=2-23/6
PLEASE HELP!!!!!!!!!!!
Answer:
The answer is B. [tex]\frac{2x+1}{x^{2}-7} ,x\neq \sqrt{7}[/tex]
Step-by-step explanation:
[tex]f(x)=2x+1\\g(x)=x^{2} -7[/tex]
Focusing on the denominator makes it equal to = 0
[tex]x^{2} -7=0\\x^{2} =7\\x=+\sqrt{7},-\sqrt{7}[/tex]
If the denominator equals zero then the equation ends up undefined. A number over zero, zero can not go divided into a number.
A plane leaves an airport traveling at 400 mph in the direction n 45° e. a wind is blowing at 40 mph in the direction n 45° w. what is the ground speed of the plane?
The ground speed of the plane is 402 mph
We have given,
A plane leaves an airport traveling at 400 mph in the direction n 45° e. a wind is blowing at 40 mph in the direction n 45° w.
Now, Draw a right triangle with 400 and 40 as the two legs.
This is a right angle because 45 degrees NE is perpendicular to 45 degrees NW.
So, the two side lengths are 400 and 40
Using the Pythagorean theorem,
What is the Pythagorean theorem?(a^2 + b^2 = c^2)
[tex]400^2+40^2=c^2\\\\c^2=160000+1600\\c^2=161600\\c=401.99[/tex]
Therefore the answer is 401.995, or 402mph.
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Victor wants to learn to snowboard. He went to Snowy Ridge Mountain and rented a snowboard for $35, then took 5 hours of group snowboarding lessons. Victor paid $175 in all.
Which equation can you use to find how much Snowy Ridge charges, x, for each hour of group snowboarding lessons?
What’s the answer for this ?
Step-by-step explanation:
1)-1, 0, 1... do like this
Solve for X. Please help!!!
Answer:
58
Step-by-step explanation:
First, we subtract 32 from 90(90deg-32deg) since the entire corner of the problem is the main area we will be focusing on. We get 58deg, and that's your answer!
Answer:
x = 58
Step-by-step explanation:
Look at the picture I have below.
It shown a complementary and supplementary angle.
As we can see there is complementary and supplementary angle in the given picture you have.
Also note that:
Complementary = 90 degree
Supplementary = 180 degree
Since we are solving for x and it close to complementary thus the equation can be written as:
x + 32 = 90
Subtract both sides by 32
x + 32 - 32 = 90 - 32
90 - 32 = 58
Hence x = 58
Kavinsky
Help Me write the inequality that represents the number line! Sorry the picture is bad quality!
Answer:
x ≤ -6
Step-by-step explanation:
The line is moving towards the left, which means that the numbers are getting smaller. X is going to be less than something.
The dot on -6 is colored in. This means that -6 is included in our inequality. [X could equal -6]
So, we could write the equation x ≤ -6
which function’s domain consists of all real numbers expect 3?
Answer:
f(x)=3x−3
Step-by-step explanation:
hope this helps.
A function is given.
f(x) = (3*0.04*x) + x
What is f (850)?
f(850) =
The function f(x) = (3 * 0.04 * x) + x is a linear function, and the value of f(850) is 952
How to evaluate the function?The function is given as:
f(x) = (3 * 0.04 * x) + x
Substitute 850 for x
f(850) = (3 * 0.04 * 850) + 850
Evaluate the product
f(850) = 952
Hence, the value of f(850) is 952
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Suppose a charity received a donation of $27.9 million. If this represents 22% of the charity's donated funds, what is the total amount of its donated funds?
Round your answer to the nearest million dollars.
well, the total amount is "x", which oddly enough is 100%, and we also know that 22% of that is 27.9 millions, so
[tex]\begin{array}{ccll} \stackrel{millions}{amount}&\%\\ \cline{1-2} x & 100\\ 27.9& 22 \end{array} \implies \cfrac{x}{27.9}=\cfrac{100}{22} \\\\\\ 22x=2790\implies x=\cfrac{2790}{22}\implies x\approx 127[/tex]
What is true about triangle LMN? Check all that apply.
y
LO
L
LMI MN.
N00
The triangle is scalene.
The triangle is equilateral.
The triangle is isosceles.
The triangle is a right triangle.
х
5
23
IN
M
-2
-3
on
Answer: A., D., and E.
Step-by-step explanation: On Edge!!
The given information none of the statements about triangle LMN confirmed as true.
Based on the given options, "Check all that apply," I'll evaluate each statement about triangle LMN:
The triangle is scalene: A scalene triangle is a triangle with three unequal side lengths. Since no information is provided about the side lengths of triangle LMN, determine if it is scalene. Thus, it cannot be confirmed as true.
The triangle is equilateral: An equilateral triangle is a triangle with three equal side lengths. Without any information about the side lengths of triangle LMN, determine if it is equilateral. Thus, it cannot be confirmed as true.
The triangle is isosceles: An isosceles triangle is a triangle with at least two equal side lengths. Without any information about the side lengths of triangle LMN, determine if it is isosceles. Thus, it cannot be confirmed as true.
The triangle is a right triangle: A right triangle is a triangle with one right angle (90 degrees). No information is given about the angles of triangle LMN, so determine if it has a right angle. Thus, it cannot be confirmed as true.
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The bar graph shows how much time a typical student spends on different activities each day. However, the way the graph has been drawn can make it somewhat misleading. Choose the statement that might WRONGLY be made on the basis of the graph.
A) More time is spent on chores than on eating.
B) The largest amount of time is spent sleeping.
C) More students spend more time on homework than on chores.
D) Twice as much time is spent on TV as is spent on homework.
Answer: the Answer is D) Twice as much time is spent on TV as is spent on homework
Step-by-step explanation:
URGENT HELP ASAP GRADE 11 MATH
Step-by-step explanation:
Shouldn't it be x^1 y. It's Because these are cancelled out.
Look at this parallelogram. Find the value of s. perimeter = 20 feet
7ft and s
Answer: 3
Step-by-step explanation: perimeter = 2( length and width )
20 = 2(7 +s)
20 = 14 + 2s
6= 2s
S =3
si 3×+0.15=1,29 cuál es el valor de x
Answer:
x=0.38
Step-by-step explanation:
3x+0.15=1.29 1. -0.15 on both sides
3x=1.14 2. /3 on both sides
x=0.38
Santiago receives an allowance of $7 every week. how much total does he receive.
Answer:
7 for each week
Step-by-step explanation:
7:1 = 7 dollars in 1 week
14:2
21:3
28:4
35:5
42:6
49:7
56:8
63:9
70:10
77:11
84:12
Answer:
How many weeks 23 34 85? if its 23 161 if its 34 238 and if its 85 595
Step-by-step explanation:
Estimate the product by rounding 4.46 x 5.75
Answer:
24
Step-by-step explanation:
Round;
4.46 ≈ 4
5.75 ≈ 6
So;
4 x 6 = 24
Hope this helps!
Answer:
I think that the answer is 25
Step-by-step explanation:
I didn't really undertsand the question so I just multiplied 4.46 times 5.75 and than rounded to the nearest ones place. The answer was 25.645
Hope this helped sorry if it is not the answer that you were looking for have a nice day.
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A bicycle wheel travels 28π in. for each revolution. What is the radius of the wheel? Enter your answer in the box.
Answer:
The wheel radius is 18
Step-by-step explanation: Just got it right
Create a linear function f(x) that represents this relationship in terms of x
Answer:
the linear function is f(x)=6x-24
Step-by-step explanation:
I hope it helped you
A large multiplex movie house has many theaters. The largest theater has 41 rows. There are 19 seats in the first row. Each row has two seats more than the previous row. How many total seats are there in this theater?
Answer:
101
Step-by-step explanation:
I time 41x2 than add 19
At the sewing store, Rita bought a bag of mixed buttons. She got 16 buttons in all. 12 of the buttons were large. What percentage of the buttons were large?
Answer:
75%
Step-by-step explanation:
Given:
Total = 16 buttons
Large = 12 buttons
To Find:
What percentage of the buttons were large?
Solution:
Since, we know that it asking for percentage(%) of buttons were large. As well as total is 16 buttons and 12 button were large.
Thus,
Formula : a/b × 100
Let's
a = 12
b = 16
Therefore,
12/16 × 100
.75 × 100
= 75%
Hence, the percentage of the buttons that Rita bought were large is 75%
Kavinsky
Consider the diagram below.
Which of the following is a correct congruence statement for the triangles?
ABCDEF
AABC SAEDF
ABC SAEFD
Answer:
ΔABC ≅ ΔEFD
Step-by-step explanation:
The congruence statement will list corresponding parts of the figures in the same order.
The left side of the statement is ΔABC, so we need to find the parts that correspond to A, B, and C, and list them in the same order. We notice that A is the marked angle, as is E. B is the other end of the line segment with 1 hash mark, as is F. Then corresponding vertices are ...
A and EB and FC and DConsequently, the congruence statement must be ...
ΔABC ≅ ΔEFD
I need help with a math equation
Answer:
-29
Step-by-step explanation:
Remove the brackets: -20 - 9
= -29
What does the expression (8x)^2 represent?
Answer:
D
Step-by-step explanation:
(8x)² is the area of a square with a side length 8x,
because we want to find out how much space is inside a square that has two dimensions 8x length and 8x width.
Two numbers have a product equal to 24x²-74x + 42. One number is represented by the expression -8x+6. Find the binomial expression that represents the other number
Answer:
-3x + 7
Step-by-step explanation:
Divide -8x + 6 into the product to find the other is -3x+7
How do you recognize an Arithmetic Sequence? Can you find terms within an arithmetic sequence using a formula
Answer:
An arithmetic sequence is an ordered set of numbers where the difference between each consecutive term is the same (this is called the "common difference").
The formula for each term in an arithmetic sequence is:
[tex]\sf a_n=a+(n-1)d[/tex]
where:
a is the first term in the sequenced is the common difference between consecutive termsn is the position of the term in the sequenceExample
Sequence: 3, 10, 17, 24, 31, ...
The first term in the sequence is 3, therefore a = 3
The common difference can be found by subtracting one term from the next: d = 10 - 3 = 7
Substituting these values into the equation for the nth term:
[tex]\implies \sf a_n=3+(n-1)7[/tex]
[tex]\implies \sf a_n=3+7n -7[/tex]
[tex]\implies \sf a_n=7n -4[/tex]
Therefore, if we want to find the 5th term of the sequence, simply input
n = 5 into the found equation:
[tex]\implies \sf a_5=7(5)-4=31[/tex]
Yes we can find terms
The formula is
a_n=a+(n-1)dWhere
a=first terma_n=nth termd=common differenceNada drives her car at an average speed of 60 miles per hour. She is planning a drive between 150 and 180 miles. Write and solve an inequality to model how many hours Nada will be driving
The inequality model that can be used to solve the number of hours it would take Nada to drive is 2.5 ≤ x ≤3.
What is the number of hours it would take Nada to drive?
Average speed is the total distance travelled per time.
Average speed = total distance / total time
Time = total distance / average speed.
Time if she drives 150 miles = 150 / 60 = 2.5 hours
Time if she drives 180 miles = 180 / 60 = hours
2.5 ≤ x ≤3.
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.
The largest packet has 35
cards, 14 of which are blue
And rest are green
we know that,
probability = no. of favourable outcomes/total outcomes
so,
probability of getting a blue card
=> 14/35 = 2/5probability of getting a green card
=> 21/35 = 3/5And IQ.
(2)
QUESTION THREE
(30 MARKS)
3. 1 Apart from being in the education sector, Richfield also has a fleet of cars available for rent.
Statistics shows that the Mercedes AMG G63 is the most rented car among their fleet and one in
four customers request this make.
If 5 of today's rentals are selected, what is the probability that 2 clients would have rented an
AMG G63?
(15)
3. 2 Bicycles for hire at the Durban Beach front are deemed beyond repair when one or both its
wheels are damaged. According to current statistics, there is an 8% chance that the front wheel
gets damaged and a 12% chance the back wheel gets damaged.
What is the probability that a hired bike will be deemed beyond repair, provided that the wheels
get damaged independently of each other?
(15)
The probability that 2 clients would have rented an AMG G63 from the 5 people will be 0.0625.
How to calculate probability?From the information given, the probability that 2 clients would have rented an AMG G63 from the 5 people will be:
= 0.25 × 0.25
= 0.0625
The probability that a hired bike will be deemed beyond repair, provided that the wheels get damaged independently of each other will be:
= 8% × 12%
= 0.08 × 0.12
= 0096
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The circumference of a circle is 3π cm. What is the area of the circle?
Question 3 options:
9πcm2
1.5πcm2
6πcm2
2.25πcm2
circumference of circle: 2πr
2πr = 3πr = 1.5 cmarea of circle: πr^2
πr^2π(1.5)^22.25πPlease help! I know me have 10 minutes! Find all solutions to 20cos(2pi/5 x) = 10✔️2
Answer: A
Step-by-step explanation:
You have:
[tex]20cos(\frac{2\pi }{5} x)=10\sqrt{2}[/tex]
Begin by dividing both sides by 20 to get:
[tex]cos(\frac{2\pi }{5} x)=\frac{\sqrt{2} }{2}[/tex]
Take the arccosine of both sides to get:
[tex]arccos(cos(\frac{2\pi }{5} x))=arccos(\frac{\sqrt{2} }{2})[/tex]
[tex]\frac{2\pi }{5} x=arccos(\frac{\sqrt{2} }{2} )[/tex]
First of all, lets find the right side. Cosine of what gives sqrt 2 over 2? That would be pi/4, plus 2npi. Another solution would be 7pi/4, plus 2npi. We have:
[tex]\frac{2\pi }{5} x=\pi /4+2n\pi[/tex]
[tex]\frac{2\pi }{5} x=7\pi /4+2n\pi[/tex]
Isolate 'x' to get:
[tex]x=\frac{5}{2\pi } (\pi /4+2n\pi)=\frac{5}{8} +5n[/tex]
[tex]x=\frac{5}{2\pi } (7\pi /4+2n\pi)=\frac{35}{8} +5n[/tex]