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Related Questions
what is the x-intercept of the graph of the function f(x)=x2-16x+64?
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Answer:
x-intercept: (8,0)
Step-by-step explanation:
Given: [tex]f(x)=x^2-16x+64[/tex]
For x-intercept, Put y=0 and solve for x.
x-intercept: It is a point where y-coordinate zero.
[tex]x^2-16x+64=0[/tex]
[tex]x^2-8x-8x+64=0[/tex]
[tex](x-8)(x-8)=0[/tex]
Equate each factor to 0 and solve for x
x-8 = 0 , x-8 = 0
x=8,8
x-intercept: (8,0)
Hence, The x-intercept is 8.
The x-intercept of the function is 8
The equation of the function is given as:
[tex]f(x) = x^2 - 16x + 64[/tex]
Expand the equation
[tex]f(x) = x^2 - 8x - 8x + 64[/tex]
Factorize the above equation
[tex]f(x) = x(x - 8) - 8(x -8)[/tex]
Factor out x - 8
[tex]f(x) = (x - 8) (x -8)[/tex]
Set f(x) to 0, to calculate the x-intercept
[tex](x - 8) (x -8)=0[/tex]
Rewrite as:
[tex](x - 8)^2=0[/tex]
Take the square roots of both sides
[tex]x - 8=0[/tex]
Solve for x
[tex]x = 8[/tex]
Hence, the x-intercept of the function is 8
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What is the area of the polygon given below?
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(4*7)+(13*9)+(6*6)=181
Answer:
181 square units
Step-by-step explanation:
What is the midpoint of (4,8) and (3,12)
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Double-checking my answer.. Given 3^2x = 9^6, what value of x satisfies this equation? (Use Laws of Exponents).
Thanks:)
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Solve for X:
3^2x = 9^6
Simplify
9x=9^6
9x=531441
Divide both sides by 9.
(9x)/9=(531441)/9
x=59049
Hope this helps!
-Benjamin
(05.01 MC)
The table and the graph each show a different relationship between the same two variables, x and y:
A table with two columns and 5 rows is shown. The column head for the left column is x, and the column head for the right column is y. The row entries in the table are 3,210 and 4,280 and 5,350 and 6,420. On the right of this table is a graph. The x axis values are from 0 to 10 in increments of 2 for each grid line. The y axis values on the graph are from 0 to 550 in increments of 110 for each grid line. A line passing through the ordered pairs 2, 110 and 4, 220 and 6, 330 and 8, 440 is drawn.
How much more would the value of y be in the table than its value on the graph when x = 11?
100
165
395
440
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The value of y in the table is 165 more than the value of y in the graph
The points on the table are represented as:
(3,210) and (4,280)So, the equation of the table is calculated using:
[tex]y = \frac{y_2 -y_1}{x_2 -x_1}(x -x_1) + y_1[/tex]
This gives
[tex]y = \frac{280 - 210}{4 - 3} (x - 3) + 210[/tex]
[tex]y = 70(x - 3) + 210[/tex]
Expand
[tex]y = 70x - 210 + 210[/tex]
[tex]y = 70x [/tex]
When x = 11,
We have:
[tex]y = 70 \times 11[/tex]
[tex]y = 770[/tex]
The points on the graph are represented as:
(2,110) and (4,220)So, the equation of the graph is calculated using:
[tex]y = \frac{y_2 -y_1}{x_2 -x_1}(x -x_1) + y_1[/tex]
This gives
[tex]y = \frac{220 - 110}{4 - 2} (x - 2) + 110[/tex]
[tex]y = 55 (x - 2) + 110[/tex]
Expand
[tex]y = 55x - 110 + 110[/tex]
[tex]y = 55x[/tex]
When x = 11,
We have:
[tex]y = 55 \times 11[/tex]
[tex]y = 605[/tex]
Calculate the difference between the y-values
[tex]y_2 - y_2 =770 - 605[/tex]
[tex]y_2 - y_2 =165[/tex]
Hence, the value of y in the table is 165 more than the value of y in the graph
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Which polynomial is a perfect square trinomial? (1 point) 49x2 − 28x + 16 4a2 − 20a + 25 25b2 − 20b − 16 16x2 − 24x − 9?
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4a² − 20a + 25 =
(2a)² - 2*2a*5 + 5² =
(2a - 5)²
Andrew makes $6 an hour plus $9 an hour for every hour of overtime. Overtime hours are any hours more than 40 hours for the week. Part A: Create an equation that shows the amount of wages earned, W, for working x hours in a week when there is no overtime. (3 points) Part B: Create an equation that shows the amount of wages earned, S, for working y hours of overtime. Hint: Remember to include in the equation the amount earned from working 40 hours. (3 points) Part C: Andrew earned $330 in 1 week. How many hours (regular plus overtime) did he work? Show your work. (4 points)
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For Part A, all you need to do is write out an equation for how many dollars Andrew would make for x hours during regular hours (not overtime). Since he makes 6 dollars per hour, this will be 6x.
W = 6x
For Part B, create a similar equation for overtime hours. Overtime hours only apply after Andrew has worked 40 hours, so plug that into your first equation and add that to the second equation.
W = 6x
W = 6(40)
W = 240
S = 240 + 9y
For Part C, consider what we now know. If Andrew earns any money over 240 dollars (which is how much he earns after 40 hours), we know he worked overtime. So, we can just plug 330 into the second equation for S and solve for the number of additional hours he worked, y.
330 = 240 + 9y
– 240 – 240
90 = 9y
9 9
10 = y
Now, we can add up the initial 40 hours plus the additional 10 hours, which is 50 hours total.
Hope this helped you out! :-)
Line segment
a.a series of points that extend in two directions without end plane
b.two lines that intersect at 90° angles perpendicular lines
c.lines that lie in the same plane and do not intersect line
d.a flat surface that extends infinitely and has no thickness parallel lines
e.part of a line that has two endpoints
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Point A and Point B are two points on Line L
The line between point A and point B that is also a part of Line L is called line segment
The correct definition of a line segment is given by the option e)
Line segment is a part of a line that has two end points
A circle has a center of (5,-5) and goes through (6,-2). What is the radius?
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The distance between points O and P, that is |OP|, is the radius of this circle,
We use the distance between 2 points formula:
|OP|=[tex] \sqrt{ (x_2-x_1)^{2} + (y_2-y_1)^{2} }= \sqrt{ (6-5)^{2} + (-2-(-5))^{2} }[/tex]
[tex]= \sqrt{ 1^{2}+ (-2+5)^{2}} = \sqrt{1+9}= \sqrt{10} [/tex] (units)
Answer: [tex]\sqrt{10} [/tex] units
Please, would somebody help me solve this math problem? I have no idea how to solve it.
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Plug in the values
(2x+2)(2x)/2
(4x^2+4x)/2
2x^2+2x
Final answer: B
Please solve for c :3
3c - 2 = 5(c+2)
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First of all, solve 5(c+2) by applying the distributive property.
I mean, 5*c and 5*2
So rewrite:
3c - 2 = 5c + 10
Now, you have to solve for c and then move all the Cs to the left of equal and change them sign, same to all known terms but move them to the right instead!
3c - 5c = 10 + 2
-2c = 12
The c can't be negative so divide both terms for -1
2c = -12
divide both terms for 2
2c/2 = -12/2
c = -6
The function $f : \mathbb{r} \rightarrow \mathbb{r}$ satisfies $f(x) f(y) - f(xy) = x + y$ for all $x$, $y \in \mathbb{r}$. find $f(x)$.
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Find the inverse
f(x) = [tex] \frac{x}{x + 2} [/tex]
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Marie is taking a test that contains a section of 10 true-false questions. How many of the possible groups of answers to these questions have at least 5 correct answers of true? Hint: Assign the variable x in the binomial expansion to be the number of true answers and y to be the number of false answers.
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To solve this problem, we use the combination equation to find for the possible groups of answer to the questions. Since we are looking for at least 5 correct answers out of 10 questions, therefore we find for 10 ≥ r ≥ 5. We use the formula for combination:
nCr = n! / r! (n – r)!
Where,
n = total number of questions = 10
r = questions with correct answers
For 10 ≥ r ≥ 5:
10C5 = 10! / 5! (10 – 5)! = 252
10C6 = 10! / 6! (10 – 6)! = 210
10C7 = 10! / 7! (10 – 7)! = 120
10C8 = 10! / 8! (10 – 8)! = 45
10C9 = 10! / 9! (10 – 9)! = 10
10C10 = 10! / 10! (10 – 10)! = 1
Summing up all combinations will give the total possibilities:
Total possibilities = 252 + 210 + 120 + 45 + 10 + 1 = 638
Answer: 638
In the diagram, is the perpendicular bisector of and is also the angle bisector of . If m = x, which quantity is equal to sin ?
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The quantity equal to sin ∠DPB is sin(x/2), corresponding to option B.
In the given diagram, overline PN serves as the perpendicular bisector of overline AB, implying that point N lies on the midpoint of segment AB.
Additionally, overline PN functions as the angle bisector of ∠CPD. Since ∠CPD measures x degrees, by the angle bisector theorem, ∠DPN and ∠DPB each measure x/2 degrees.
Now, to determine sin ∠DPB, we consider the right triangle DPN. By definition, sin θ = opposite/hypotenuse.
In this triangle, the opposite side to ∠DPB is overline DN, and the hypotenuse is overline DP.
Therefore, sin ∠DPB = DN/DP.
Since ∠DPN = x/2, applying trigonometric ratios in right triangle DPN, sin(x/2) = DN/DP.
Hence, the quantity equal to sin ∠DPB is sin(x/2), corresponding to option B.
The probable question may be:
In the diagram, overline PN is the perpendicular bisector of overline AB and is also the angle bisector of ∠ CPD If m∠ CPD=x , which quantity is equal to sin ∠ DPB ?
A. sin π /2
B. sin x/2
C. cos x/2
D. cos π /3
Find two geometric means between 10 and 1250.
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a 1 = 10, a 4 = 1250
a 4 = a 1 * q^3
1250 = 10 * q^3
q^3 = 1250 : 10
q^3 = 125
q = 5
a 2 = 10 * 5 = 50
a 3 = 10 * 5² = 10 * 25 = 250
Answer: The two geometric means are: 50 and 250, since 10, 50, 250 , 1250 forms a geometric sequence.
A choir has 3 spots open for altos, and 8 altos are interested in them. In how many ways can the open spots be filled?
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n!/(k!(n-k)!), n=number of elements to choose from, k=number of choices made
In this case:
8!/(3!(8-3)!)
56
So there are 56 unique threesomes possible with 8 members.
There are total 56 ways to fill the open spot .
What is combination?
A combination is a way for determining the number of possible arrangements in a collection of items where the order of selection does not matter.
Formula for combination[tex]C(n, r) =\frac{n!}{(n - r)!r!}[/tex]
where,
n is the number of items in set.
r is the number of items selected from the set.
According to the question we have,
Number of altos, n = 8
Number of open spots, r = 3
Therefore, the number of ways to fill open spots = C(8, r)
Number of ways = [tex]\frac{8!}{3!(8-3)!}[/tex]
Number of ways = [tex]\frac{8!}{5!3!}[/tex][tex]= \frac{(8)(7)(6)(5!)}{5!3!}[/tex] = [tex]\frac{(8)(7)(6)}{(3)(2)} =8(7) = 56[/tex]
Hence, there are total 56 ways to fill the open spot .
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4 workers get paid 160,000 for working for five days, how much will 5 workers get paid for working for a day
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Hence,
1 worker gets paid = [tex] \frac{160,000}{4} = 40,000[/tex] for 5 days.
From here we can find out how much 1 worker is paid for 1 day by dividing by 5;
1 worker gets paid = [tex] \frac{40,000}{5} = 8,000[/tex] for 1 day.
Therefore,
5 workers get paid = [tex]8,000 * 5 = 40, 000[/tex] for 1 day.
What do the parallel lines shown on segment BD and segment DC represent? _____________________
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the 2 parallel lines mean that the lines are equal
SO since BD = 18, DC is also 18
BD = 18 = DC
Thus, correctly assuming that the point D is the mid point of line segment BC.
There are 20 wild pigs on an island and the number of pigs doubled each year for the past 5 years. The independent variable is
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The independent variable is time.
Answer:
The independent variable is time.
Step-by-step explanation:
Given,
The original number of pigs on the island = 20,
Also, the number of pigs doubled each year,
After 1 year the pigs = 20(2),
After 2 years = 20(2)²,
After 3 years = 20(2)³,
......................., so on...
Similarly, the number of pigs after t years would be,
[tex]y=20.2^t[/tex]
⇒ The value of y depends upon t,
⇒ The number of pigs depends upon the time ( in years ),
Since, the variable in which the other variable depends is called independent variable,
Hence, the independent variable must be time.
What causes water molecules to stick together in liquid water?
A. Water vapor
B. Carbon dioxide
C. Sun's gravity
D. Hydrogen bonds
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Given a group of 8 women and 11 men, how many different ways are there of choosing one man and one woman for a committee?
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Final answer:
There are 88 different ways of choosing one man and one woman for a committee.
Explanation:
In order to find the number of different ways of choosing one man and one woman for a committee, we can use the concept of combinations. The number of ways of choosing one item from a group of n items is denoted by n C 1, which is equal to n. So, the number of ways of choosing one man from a group of 11 men is 11, and the number of ways of choosing one woman from a group of 8 women is 8. To find the total number of ways, we multiply these two numbers:
Total number of ways = 11 * 8 = 88
Therefore, there are 88 different ways of choosing one man and one woman for a committee.
HELP If f(x)=15x+3, then f^-1(x)=?
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PM me
The inverse of the function f(x) = 15x + 3 is found by swapping x and f(x) in the equation and solving for f^-1(x), which leads to f^-1(x) = (x - 3) / 15.
Explanation:To find the inverse of the function f(x) = 15x + 3, it is necessary to first swap x and f(x) in the function equation. This results in x = 15f^-1(x) + 3. Secondly, solving for f^-1(x) means isolating this on one side of the equation. That results in f^-1(x) = (x - 3) / 15.
So, the inverse function of f(x) = 15x + 3 is f^-1(x) = (x - 3) / 15.
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What 12 multiplied by 3
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An amusement park charges $9.00 for admission $4.00 per ride. Write an equation that gives the cost in dollars as a function of number of rides
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T = total cost
X= number of rides
T=4.00x+9.00
For each equation below find y if x=2
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B - would be 2 to the second - 1 = 3
The product of the roots of 8x² - 2x = 1 is:
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Answer:
[tex]\text{Product of its zeros = }\frac{-1}{8}[/tex]
Step-by-step explanation:
The quadratic equation is given to be : 8x² - 2x = 1
We need to find the product of its zeros
First finding the number of zeros :
⇒ 8x² - 2x - 1 = 0
⇒ 8x² - 4x + 2x - 1 = 0
⇒ (4x + 1)(2x - 1) = 0
[tex]\implies x = \frac{-1}{4}\:\:and\:\: x = \frac{1}{2}[/tex]
[tex]\text{Product of its zeros = }\frac{-1}{4}\times\frac{1}{2}=\frac{-1}{8}[/tex]
Is the value of [tex] \sqrt{42} [/tex] a rational or irrational number? Is it's value between 3 and 5, 5 and 7, or 7 and 9?
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now, all those three factors are all irrationals. thus their product is also irrational.
[tex]\bf \sqrt{42}\approx 6.48 \qquad\qquad \boxed{5}------6--6.48---\boxed{7}[/tex]
The manager of a baseball team has 15 players to choose from for his nine person batting order. How many different ways can he arrange the players in the lineup. A.5005. B.362880. C.3603600. D.1816214400
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= 15! / (15-9)!
= 1816214400
Answer: D. 1816214400
Step-by-step explanation:
When we select r things from n things in order we apply permutations and the number of ways to select r things = [tex]^nP_r=\dfrac{n!}{(n-r)!}[/tex]
Given : Total player = 15
Required number of players for Batting order = 9
Then the number of different ways to select 9 person batting order so that he arrange the players in the lineup would be [tex]^{15}P_9=\dfrac{15!}{(15-9)!}[/tex]
[tex]=\dfrac{15\times14\times13\times12\times11\times10\times9\times8\times7\times6!}{6!}[/tex]
[tex]=1816214400[/tex]
∴ The number of different ways can he arrange the players in the lineup = 1816214400
Hence, the correct answer is D. 1816214400
An __________ is used to indicate the repeating part of a repeating decimal.