The vertex form of the quadratic equation, written in standard form, f(x) = 2 · x² - 20 · x + 8 is f(x) + 75 = 2 · (x - 5)².
What is the vertex form of a quadratic equation?In this problem we have a quadratic equation in standard form, whose form is defined by f(x) = a · x² + b · x + c, where a, b, c are real coefficients, and we need to transform it into vertex form, defined as:
f(x) - k = C · (x - h)² (1)
Where:
(h, k) - Vertex coordinatesC - Vertex constantThis latter form can be found by algebraic handling. If we know that f(x) = 2 · x² - 20 · x + 8, then its vertex form is:
f(x) = 2 · x² - 20 · x + 8
f(x) = 2 · (x² - 10 · x + 4)
f(x) + 2 · 25 = 2 · (x² - 10 · x + 25)
f(x) + 75 = 2 · (x - 5)²
The vertex form of the quadratic equation, written in standard form, f(x) = 2 · x² - 20 · x + 8 is f(x) + 75 = 2 · (x - 5)².
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At the beginning of this year, you went out and purchased $300 worth of gold coins. Every 3 months for the next 8 years, you purchase an additional $300 worth of coins. At the end of the first 3 years, the price of gold starts to come back down, and when you decide to cash out, your coins are only worth what you paid for them. What is the value of your account now?
Answer:
9900
Step-by-step explanation:
You start with 300, and add 300 32 times (once for every 3 months in 8 years).
[tex]300+9600=9900[/tex]
Please answer this question
Answer:
1 and 4
Step-by-step explanation:
x-1 = 0
x = 1
x^2 - 5x + 4
(x-4)(x-1) = 0
x can't be 1 or 4
Answer: 1 and 4
Step-by-step explanation:
1. To find excluded values, we need to make the denominator equal to zero.
x² - 5x + 4 = 0
2. Then we need to find the x the product of them was 4, but they add up to -5, which are -4 and -1. We get:
(x - 4)(x - 1) = 0
x - 4 = 0 x - 1 = 0
x = 4 x = 1
These two numbers will make the denominator equal to 0, the denominator cannot be equal to 0, so they are excluded numbers.
why kilogram is more appropriate unit than milligram?
Step-by-step explanation:
that question is fundamentally wrong.
"appropriate" completely depends on the situation and circumstances.
if we are dealing with a weight that a human can feel, lift and distinguish from other weights without any special tool, then we are usually using kg. because then we humans can "connect" with the case, and deal with every day numbers.
if we are dealing with tiny little quantities like dosages of substances in a pill or other medication, then milligram is more than "appropriate".
because then, as humans, we are still dealing with numbers we can understand. like tens or hundreds.
if we kept kg in such situations, we would have to deal with numbers like 0.000008 kg vs. 0.000021 kg, where we could not see the magnitude of difference right away.
K
An employment agency specializing in temporary construction help pays heavy equipment operators $124 per day and general laborers $82 per day If thirty-seven people were hired
and the payroll was $3916, how many heavy equipment operators were employed? How many laborers?
The number of heavy equipment operators hired was?
The number of general laborers hired was?
Step-by-step explanation:
x = number of heavy equipment operators
y = number of general laborers
x + y = 37 (37 people were hired)
out if this we get e.g.
x = 37 - y
124x + 82y = 3916 (daily rate for each role, in total 3916)
now we use the first equation in the second :
124(37 - y) + 82y = 3916
4588 - 124y + 82y = 3916
672 - 42y = 0
672 = 42y
y = 16
x = 37 - y = 37 - 16 = 21
21 heavy equipment operators were hired.
16 general laborers were hired.
solve the system of equations using substitution
The solution to the given simultaneous equation; x + 2y = -4, 2x + 5y = 1 using substitution method is x = -22 and y = 9
Simultaneous equationx + 2y = -4
2x + 5y = 1
Using Substitution method
From equation (1)
x = -4 - 2y
Substitute x = -4 - 2y into equation (2)
2x + 5y = 1
2(-4 - 2y) + 5y = 1
-8 - 4y + 5y = 1
- 4y + 5y = 1 + 8
y = 9
Substitute y = 9 into
x + 2y = -4
x + 2(9) = -4
x + 18 = -4
x = -4 - 18
x = - 22
Therefore, the solution to the given simultaneous equation; x + 2y = -4, 2x + 5y = 1 using substitution method is x = -22 and y = 9
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Four seniors and six juniors are competing for four places on a quiz bowl team.
What is the approximate probability that all four seniors will be chosen at random?
what’s the % ?
Answer:
.00476
Step-by-step explanation:
In the figure below, the segment is parallel to one side of the triangle. Find the value of x.
x+7
18²/3
0 24
025²/
16
22
Step-by-step explanation:
answer=18^2/3
according to the congruent triangles are present there.
so divide corresponding sides
What is the length of S?
Answer:
c
Step-by-step explanation:
By the Pythagorean theorem,
[tex]28^2 + 15^2 = s^2 \\ \\ s^2 = 1009 \\ \\ s = \sqrt{1009}[/tex]
integer for 1,440 feet below sea level
Find the remainder when f(x)=−2x3+x2−4x+1 is divided by x+3.
The remainder when f(x)=−2x3+x2−4x+1 is divided by x+3. is 76
How to determine the remainder?The function is given as:
f(x)=−2x3+x2−4x+1 is divided by x+3.
Set the divisor to 0
x + 3 = 0
Solve for x
x = -3
Calculate f(-3)
f(-3)=−2(-3)^3+(-3)^2 − 4(-3) + 1
Evaluate the expression
f(-3)= 76
Hence, the remainder when f(x)=−2x3+x2−4x+1 is divided by x+3. is 76
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A car is traveling at a speed of 60 miles per hour. What's the dependent variable in this situation? Question 5 options: A) The speed at which the car travels B) The distance the car has traveled C) The age of the car D) The number of hours the car has traveled
The dependent variable in this situation is; the speed at which the car travels.
Distance and speedSpeed of the car = 60 miles per hourSpeed = Distance / Time
The dependent variable in this situation is; the speed at which the car travels.
The independent variable; The distance the car has traveled.
What is dependent variable?This is the variable whose value depends on one or more variables in the equation.
Independent variable
This is the variable whose value is not dependent on any other in the equation.
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If 55 people enrolled in a psychology course but only 25 completed it, what percent of the students completed the course? (Round to the nearest tenth of a percent.)
Answer:
45%
Step-by-step explanation:
Simply, 25/55 which gives you 0.454545.
Convert that to a percentage and you get 45%
PLS HELP
Which functions have a range of {y e R-00 < y < 00}?
O f(x)
2x+3
Of(x) = x - 8
O f(x) = x² + 7x - 9
O f(x) = -4x + 11
O f(x) = -(x + 1)² - 4
=
Answer:
[tex]\displaystyle{1.) \ \ f(x) = \dfrac{2}{3}x-8}\\\\\displaystyle{2.) \ \ f(x) = -4x+11}[/tex]
Step-by-step explanation:
- Range is a set of all y-values in a set of coordinate points.
A linear equation or function always have range equal to set of real number because you can substitute f(x) as any numbers and you'll still be able to solve for x-variable.
An quadratic equation or function may have range equal to set of positive real number or negative real number depending whether if the coefficient of x² is in positive or negative but consider this:
Suppose we have f(x) = x², f(x) cannot be negative number because that'd make the equation not real. Therefore, a quadratic function does not have [tex]\displaystyle{\mathbb{R}}[/tex] range.
For an exponential function, it's same as quadratic equation. It depends whether if a base is in negative or positive. You can consider like this:
Suppose we have [tex]\displaystyle{f(x)=2^x}[/tex], f(x) cannot be negative number because there are no x-values that make the equation true. Therefore, an exponential function does not have [tex]\displaystyle{\mathbb{R}}[/tex] range as well.
Knowing the first day Anna and Tamara stop for sightseeing and lost 2 hours of travel time and the second day, they gain 1 hour because they did not stop for lunch, write an algebraic expression that represents how many hours Anna and Tamara traveled the first two days. Let x be the number of hours driven.
The algebraic expression that represents the number of hours Anna and Tamara traveled the first two days is (2x - 1) hours.
How to write Algebraic Word Problems?
We are told that;
On the first day, Anna and Tamara stop for sightseeing and lost 2 hours of travel time.
On the second day, they did not stop for lunch and gained 1 hour.
Now, we are told that x is the number of hours driven per day. Thus, for two days, number of hours driven is expressed as 2x.
Now, since they lost 2 hours on the first day, then total hours travelled is;
2x - 2 hours
On the second day, they gained 1 hour. Thus;
Final total number of hours traveled = 2x - 2 + 1
Final total number of hours traveled = (2x - 1) hours
Thus, we can conclude that the algebraic expression that represents how many hours Anna and Tamara traveled the first two days is (2x - 1) hours.
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Given angle YMC = 170 degrees, find the measure of angle AMC.
Answer:
i think 10 because in triangle there is 180 and 180-170 = 10
Answer:
Step-by-step explanation:
hjhj
TIME REMAINING
51:31
What are the factors of x2 – 100?
(x – 50)(x + 50)
(x – 10)(x + 10)
(x – 25)(x + 4)
(x – 5)(x + 20)
Answer:
(b) (x -10)(x +10)
Step-by-step explanation:
The factorization of the difference of squares is a special form:
a² -b² = (a -b)(a +b)
ApplicationYour expression is recognizable as the difference of squares:
x² -100 = x -10²
Using the above form, the factorization is ...
= (x -10)(x +10) . . . . . . . . matches the second choice
Which is a factor of 144 - 49x²?
O 12-7x²
O 72-7x²
O 12-7x
O 72 + 7x
Answer: C: 12-7x
Step-by-step explanation:
This expression is a good example of the difference of two squares, as 144 is the square of 12, while 49x² is the square of 7x.
Any difference of two squares [tex]a^2-b^2[/tex] can be factored into the sum of their square roots times the difference of their square roots [tex](a+b)(a-b)[/tex].
Let's factor our expression.
[tex]144-49x^2=(12+7x)(12-7x)[/tex]
Out of all the options given, only [tex]12-7x[/tex] is a factor. Hence, option C is correct.
write the equations after translating the graph of y=|x+2| one unit to the right
write the equations after translating the graph of y=|x+2| one unit to the left
In the following activity, match each pair of equivalent expressions(will give 50 points)
PLS HELP ME ASAP I NEED THE ANSWER NOW BEFORE 5 mins PLS Help ME I WILL MARK BRAINLIST IF YOUR ANSWER IS CORRECT AND WAS ANSWERED 4 MIN AGO HELP ME PLSSS
The table below shows that 1 day equals 24 hours. Notice that 12 hours is one-half of that. Use the table to help you determine how many days are equal to 42 hours.
1 day
24 hours
12 hours 12 hours
1 and 1 over 4. days (wrong)
1 and 1 over 2. days
1 and 3 over 4. days
2 days
Answer:
42 - 24 = 18
18/24 = 3/4
the answer would be 1 and 3/4 days
Answer:
1 and 3 over 4 days
Step-by-step explanation:
Since 24 hours is 1 day all we have to do is divide 42 into 24 and see what the resulting fraction is
42/24 = 7/4 (reducing to lowest fraction)
7/4 = 1 3/4 days (7 ÷ 4 gives quotient 1 and remainder is 3)
Answer:
1 and 3 over 4 days
If a translation maps point A(-3,1) to point A′(5,5), the translation is:
A. (x+2,y+4)
B. (x+8,y+6)
C. (x+2,y+6)
D. (x+8,y+4)
Answer:
D is the correct answer -3+8=5 ,1+4=5
I need help with the problem
Answer:
you better give me brainliest
Step-by-step explanation:
The answer is the first two
A large university has 24,000 students. A
randomly selected sample of 750 students
were surveyed and asked how far away
they live from the university. Of those
surveyed, 120 students live more than
500 miles away from the university.
Based on the survey results, estimate the
number of students who live within 500
miles of the university?
Answer:
23370 students live with in 500 miles of the university.
Step-by-step explanation:
large university students =24000
selected students = 750
surveyed students =120 lives far away from university.
students live with in 500mile=?
750-120=630
24000-630=23370
ASAP help me with this question <3 number 12
Answer:
False
Step-by-step explanation:
Consider an isoscles trapezoid with angles 75° and 105°.
50% prefferd fruit cake 1/5 preferred spong and the remainder preferred cheesecake
What percent like cheesecake?
The percentage of people who preferred cheesecake if 50% prefferd fruit cake 1/5 preferred sponge is 40%.
PercentageTotal percentage = 100%Fruit cake = 50%Percentage remaining = 100% - 50%
= 50%
Sponge cake = 1/5
Percentage of sponge cake = 1/5 × 50%
= 1/5 × 0.5
= 10%
Percent that likes cheesecake = Total - (fruits cake + sponge cake)
= 100% - (50% + 10%)
= 100% - (60%)
= 40%
Therefore, the percentage of people who preferred cheesecake if 50% prefferd fruit cake 1/5 preferred sponge is 40%.
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Between which two integers is the value of √11?
9 and 10
5 and 6
7 and 8
O3 and 4
1 and 2
A bookstore carries 48 magazines. 75% of the magazines are women's magazines. How many women's magazines does the bookstore carry?
Answer:
36
Step-by-step explanation:
75/100
75/100=0.75
0.75*48 =36
Anna does sit-ups to get ready for her first triathlon. When she starts, she does a sit-up every 2 seconds. But, as she gets tired, each sit-up takes longer to do. Is the number of sit-ups Anna does proportional to the time she spends doing them?
Answer: No
Step-by-step explanation: proportional means corresponding in size or amount to something. However, the number of her sit-ups isn't consistent, so it isn't proportional to the time she spends doing them.
Which of the following describes the transformations of g (x) = negative (2) Superscript x + 4 Baseline minus 2 from the parent function f (x) = 2 Superscript x?
Using translation concepts, the transformations are described as follows:
Reflection over the x-axis.Shifted up 4 units.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, the parent function is:
[tex]f(x) = 2^x[/tex]
The transformed function is:
[tex]g(x) = -2^x + 4[/tex]
We have that the transformations in this problem can be described as follows:
f(x) was multiplied by -1, hence it was reflected over the x-axis.4 was added to the function, hence it was shifted up 4 units.More can be learned about translation concepts at https://brainly.com/question/28098112
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the confidence interval for the population variance is
(730.72, 4569.53) is the confidence interval for the population variance σ² given that c = 0.98, s = 39 and n = 15. This can be obtained by using formula for confidence interval and using statistical table for values.
Find the confidence interval for population variance:The formula for finding the confidence interval for population variance is:
[tex]\frac{(n-1)s^{2} }{\chi^{2} _{\frac{\alpha }{2} } } < \sigma^{2} < \frac{(n-1)s^{2} }{\chi^{2} _{1-\frac{\alpha }{2} } }[/tex]
where n is the size of the sample, (n - 1) is the degrees of freedom, s is the standard deviation, α is the significance level.
Here it is given that,
confidence level = 1 - α = 0.98 significance level = α = 0.02standard deviation = 39 sample size n = 15degrees of freedom (n - 1) = 15 - 1 = 14α/2 = 0.02/2 = 0.01
1 - α/2 = 1 - 0.01 = 0.99
For (n - 1) degrees of freedom,
[tex]\chi^{2}_{\frac{\alpha}{2} }[/tex] = 29.141 , and [tex]\chi^{2}_{1-\frac{\alpha}{2} }[/tex] = 4.660 (Using statistical table)
Using the formula we get,
[tex]\frac{(n-1)s^{2} }{\chi^{2} _{\frac{\alpha }{2} } } < \sigma^{2} < \frac{(n-1)s^{2} }{\chi^{2} _{1-\frac{\alpha }{2} } }[/tex]
[tex]\frac{(14)39^{2} }{29.141} < \sigma^{2} < \frac{(14)39^{2} }{4.660}[/tex]
[tex]730.72 < \sigma^{2} < 4569.53[/tex]
The confidence interval for the population variance is (730.72, 4569.53)
Hence (730.72, 4569.53) is the confidence interval for the population variance σ² given that c = 0.98, s = 39 and n = 15.
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