Answer:
Vertex ( 5 ,8) .
Step-by-step explanation:
Given : f(x) = 2(x − 5)² + 8.
To find : Determine the vertex of the function .
Solution : We have given
f(x) = 2(x − 5)² + 8.
Vertex form of parabola : f (x) = a(x - h)² + k, where (h, k) is the vertex.
On comparing f(x) = 2(x − 5)² + 8. with vertex form of parabola.
a = 2 , h = 5 , k = 8 .
Vertex ( 5 ,8) .
Therefore, Vertex ( 5 ,8) .
Answer: (5,8)
Step-by-step explanation:
The given function :[tex]f(x) = 2(x - 5)^2 + 8.[/tex]
We know that the vertex form of a quadratic equation is given by :
[tex]f (x) = m(x - a)^2+ b[/tex] (1)
, where (a,b)= Vertex of the function f(x).
When we compare the given function [tex]f(x) = 2(x - 5)^2 + 8.[/tex] to equation (1) , we conclude that the given function is already in its vertex form.
with a= 5 and b= 8
Therefore , the vertex of the function [tex]f(x) = 2(x - 5)^2 + 8.[/tex] = (5,8)
HELP!!!! FAST!!! Which graph represents a reflection of f(x) = 2(0.4)x across the y-axis?
Answer: The correct option is A.
Explanation:
The given function is,
To find the graph of this function after the reflecting across y-axis, first we have to find the graph of the equation.
The value of the function is 2 when x=0, so, the graph of given equation intersect the y-axis at 2.
In the equation . Since , so the given function is decreasing function
The value of f(x) is always positive, so the graph of f(x) is always above the x-axis. Thus, the graph must be above the x-axis after reflection across y-axis.
So, the option (2) and (4) and incorrect.
When we reflect the graph across the y-axis then,
It means when x approaches to large negative number the f(x) approaches to 0 and when x approaches to large positive number the f(x) approaches to infinite.
Therefore, the correct option is show in first graph.
Tons of points
what is the common difference in the following arithmetic sequence 2/3 1/6 -1/3 -5/6 \
Answer:
The common difference is -1/2
Step-by-step explanation:
we know that
In an Arithmetic Sequence the difference between one term and the next is a constant and is called the common difference
we have
a1=2/3
a2=1/6
a3=-1/3
a4=-5/6
so
a2-a1=1/6-2/3=-1/2
a3-a2=-1/3-1/6=-1/2
a4-a3=-5/6-(-1/3)=-5/6+1/3=-1/2
therefore
The common difference is -1/2
What is the slope of a line that is perpendicular to the line y = 1/6 x + 4?
-6
To find the slope of the perpendicular line, start with the original slope, 1/6.
The slope of a perpendicular line is the opposite and inverse of the slope of the original line. So, start by finding the inverse. This is done by simply flipping the numerator and the denominator to get 6/1, which is simplified to 6.
Finally, find the opposite of 6. You can find the opposite of a number by multiplying or dividing it by -1. If it is a positive number, just add a negative sign, and if it is already a negative number, take away the negative sign. So, the opposite of 6 is -6, which is out final answer.
the price television was reduced from $250 to $200 by what percentage was the price of the televison reduced
Answer: is 20%
Step-by-step explanation: I took the percentage of 200 out of 250 and it was 80% so the answer is 20%
For me the answer is 80% I hope it helps. please add brainlist
Jesse paid for dinner. He had a steak for
$26.00 and Melissa had chicken cutlets for
$23.50. There was 8% tax and Jesse left the
waiter a 20% tip on the final bill. Jesse looks in
his pocket and he has $51.00 left in his pocket.
How much money did Jesse start the night with?
The answer I got was $114.36
Please help with perimiter
Answer:
The perimeter of question #1 is 36. The second one is 24 then the third is 19 then 28 then 54
Step-by-step explanation:
Answer:
The perimeter of one is 36. The second one is 24. The third is 19. The fourth is 28. The last is 54.
Step-by-step explanation: Adding all the sides is how you find perimeter. Use πr + 2r, where r is the radius minus the side of the semicircle that touches the other shape since that is inside the shape.
Which is the correct classification of √18?
irrational number, non-repeating decimal
irrational number, terminating decimal
rational number, terminating decimal
rational number, non-repeating decimal
Answer:
irrational number, non-repeating decimal
Step-by-step explanation:
√18 = √9·√2 = 3·√2.
√2 is an irrational, non-repeating decimal (my calculator shows it to be approx. 1.414213562..... )
and so √18 is the same.
Answer:
Irrational number, Non-repeating decimal
Step-by-step explanation:
Dictonary definition of
IRRATIONAL NUMBER:
"(of a number, quantity, or expression) not expressible as a ratio of two integers, and having an infinite and nonrecurring expansion when expressed as a decimal. Examples of irrational numbers are the number π and the square root of 2."
Find the interest earned and the future value of an annuity with quarterly payments of $600 for 8 years into an account that pays 5% interest per year compounded quarterly.
Answer:
interest earned= 292.878
the future value of an annuity= 892.878
Step-by-step explanation:
Given Data:
Interest rate= 5%
time,t = 8 years
Quarterly payment, P= 600
n= 4 as quarterly
At the end of 8 years, final investment A= ?
As per the interest formula
A= P(1+r/n)^nt
= 600(1+0.05/4)^32
= 892.878
Interest earned = A-P
= 892.878-600
= 292.878 !
Identify the inverse variation and graph in which y = 0.75 when x = 4.
Answer:
[tex]y=3/x[/tex] or [tex]yx=3[/tex]
The graph in the attached figure
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]
so
in this problem we have
y=0.75 when x=4
Find the value of k
[tex]y*x=k[/tex]
[tex]k=0.75*4=3[/tex]
The equation is equal to
[tex]y=3/x[/tex]
using a graphing tool
see the attached figure
Answer:
Y=3/x is the correct answer
24 plzzz I really need help
1. A<10
2. H> or equal to 55
3. D>85
Events A and B are disjointed. P(A) = 4/11; P(B) = 3/11, P(A and B)= 2/11 . Find P(A or B).
Answer:
[tex]P(A\:or\:B)=\frac{7}{11}[/tex]
Step-by-step explanation:
If the two events are disjoint, then P(A or B)=P(A)+P(B).
We were given that:
[tex]P(A)=\frac{4}{11}[/tex]
and
[tex]P(B)=\frac{3}{11}[/tex]
This implies that:
[tex]P(A\:or\:B)=\frac{4}{11}+\frac{3}{11}[/tex]
We simplify the right hand side to obtain:
[tex]P(A\:or\:B)=\frac{4+3}{11}[/tex]
[tex]P(A\:or\:B)=\frac{7}{11}[/tex]
Answer:
5/11
How I got my answer:
For overlapping events, you would subtract P(A and B) from the sum of P(A) and P(B).
In this case, you would do 4/11 + 3/11, which equals 7/11 minus 2/11, which equals 5/11.
True o r False: y = - 5x + 7 is the equation of a line that passes through the point (3,6) and has a slope of - 5.
Answer:
False
Step-by-step explanation:
The equation in slope-intercept form of a line is y=mx+b, where x and y can represent a point on the line by using the coordinates (x,y), m is the slope, and b is the y intercept.
To double check this equation, plug in the coordinates of the point (3,6) to make sure both sides of the equation equal to each other.
6 = -5(3) + 7
6 = -15 + 7
6 = -8
[tex]6 \neq -8[/tex]
Because the equation is invalid, the line does not pass through these points.
The statement is false because the equation y = -5x + 7 does not satisfy the point (3,6).
To determine if the equation y = -5x + 7 is the equation of a line that passes through the point (3,6) and has a slope of -5, we can plug the coordinates of the point into the equation to see if it satisfies the equation.
Substituting x = 3 and y = 6 into the equation gives us:
6 = -5(3) + 7,
which simplifies to:
6 = -15 + 7,
6 = -8, which is not true.
Therefore, the point (3,6) does not lie on the line with the equation y = -5x + 7. The equation y = -5x + 7 does, however, represent a line with a slope of -5, but since it does not pass through the point (3,6), the initial statement is false.
1. A given binomial distribution has a mean of 153.1 and a standard deviation of 18.2. Would a value of 187 be considered usual or
unusual? Why?
A. Unusual, because the result is less than the maximum usual value.
B. Usual, because the result is less than the minimum usual value.
C. Unusual, because the result is greater than the maximum usual value.
D. Usual, because the result is between the minimum and maximum usual values.
Answer:
Usual, because the result is between the minimum and maximum usual values.
Step-by-step explanation:
To identify if the value is usual or unusual we're going to use the Range rule of thumbs which states that most values should lie within 2 standard deviations of the mean. If the value lies outside those limits, we can tell that it's an unusual value.
Therefore:
Maximum usual value: μ + 2σ
Minimum usual value: μ - 2σ
In this case:
μ = 153.1
σ = 18.2
Therefore:
Maximum usual value: 189.5
Minimum usual value: 116.7
Therefore, the value of 187 lies within the limits. Therefore, the correct option is D. Usual, because the result is between the minimum and maximum usual values.
Answer:
D. Usual, because the result is between the minimum and maximum usual values
Step-by-step explanation:
Please help I’m very confused
I will mark brainliest :)
Answer:
volume is 15 in cubed
Surface area is 43 in squares
Which point lies on the line described by the equation below?
y+ 8 = 4(x - 5)
O A. (-5, -8)
O B. (5,0)
O C. (4,5)
O D. (4,-8)
O E. (5,-8)
O F. (5,8)
Answer:
E
Step-by-step explanation:
[tex]
y+8=4(x-5)
[/tex]
Put the the E coordinates.
[tex]
-8+8=4(5-5) \\
0 = 4\cdot 0 \\
\boxed{0=0\Longrightarrow E\in y+8=4x-20}
[/tex]
Hope this helps.
r3t40
By simplifying the given equation y + 8 = 4(x - 5) to y = 4x - 28 and substituting the points' coordinates, it is determined that Point B (5, 0) is the correct point that lies on the line described by the equation.
Explanation:To determine which point lies on the line described by the equation y + 8 = 4(x - 5), we need to verify which of the given options, when substituted into the equation, will satisfy it. First, we will simplify the equation to its standard line equation form y = mx + b (where m is the slope and b is the y-intercept):
y + 8 = 4(x - 5)y = 4x - 20 - 8y = 4x - 28Now we can substitute the x and y values from each of the points into this equation and check which one holds true.
Point A (-5, -8): Substitute x = -5 and y = -8.-8 = 4(-5) - 28-8 = -20 - 28 (Does not hold true)Point B (5, 0): Substitute x = 5 and y = 0.0 = 4(5) - 280 = 20 - 28 (Does hold true)Thus, Point B (5, 0) is the point that lies on the line described by the equation.
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There are only 7 days left until the launch of our new product and we only have 668.00 left in our promotion budget. We need to spend 85.00 on the last day. Can you please calculate how many dollars a day we can send on the remaining days?
Answer:
83.28
Step-by-step explanation:
i did 668-85 and got 583 and i / it by 7
Answer:
Step-by-step explanation:
Given that there are only 7 days left until the launch of our new product and we only have 668.00 left in our promotion budget. We need to spend 85.00 on the last day.
Hence amount left for remaining 6 days = [tex]668-85 = 583[/tex]
This can be spent for the remaining 6 days
If equal amount to be sent then we get
[tex]\frac{583}{6} =97.17[/tex]
But we can round off and send in integral values means we can spread as
each day 100 dollars for first 5 days and on 6th day 83 dollars.
Please help!!!! A modern art museum has the dimensions shown in the figure what is the total amount of space inside museum
ANSWER
[tex] 3840 {m}^{3} [/tex]
EXPLANATION
The total amount of space is the volume of the composite solid.
We find the volume of the rectangular prism and add it to the volume of the triangular prism.
The total amount of space inside the museum is:
[tex] =l \times b \times h + \frac{1}{2} \times base \times height \times height \: of \: triangular \: prism [/tex]
[tex] = 30 \times 12 \times1 0 + 0.5 \times 12 \times 4 \times 10[/tex]
[tex]= 360 0 + 240[/tex]
[tex] = 3840 {m}^{3} [/tex]
Therefore,the total amount of space inside the museum is 3,840 cubic meters.
Answer:
Step-by-step explanation:
An MP3 player has a playlist up with 12 songs you select the shop or option which plays each song in random order without reputation for the playlist and how many different orders can the song to be played
There are 479,001,600 different combinations of songs that can be played without repeating a song
An MP3 player with a playlist of 12 songs can be played in 479,001,600 different orders.
Explanation:An MP3 player with a playlist of 12 songs can play each song in random order without repetition.
To calculate the number of different orders the songs can be played, we can use the concept of permutations.
In this case, we have 12 songs and want to find the number of different ways they can be arranged.
The formula for permutations is n! / (n - r)!, where n is the total number of items and r is the number of items being arranged.
In this case, n is 12 and r is also 12 (since we want to arrange all the songs).
So the formula becomes 12! / (12 - 12)!. Since 12 - 12 is 0, the denominator becomes 0!.
The value of 0! is defined as 1, so we can simplify the formula to just 12!.
Using a calculator or factorial table, we can calculate that 12! (12 factorial) is equal to 479,001,600.
Therefore, there are 479,001,600 different orders in which the songs can be played on the MP3 player.
write the equation for the exponential function that goes through the points (-2, 0.375) and (7, 192)
Answer:
[tex]y=\dfrac{3}{2}\cdot 2^x[/tex]
Step-by-step explanation:
The general equation of the exponential function is
[tex]y=a\cdot b^x[/tex]
If the graph of the exponential function passes through the points (-2, 0.375) and (7, 192), then their coordinates satisfy the equation:
[tex]0.375=a\cdot b^{-2}\\ \\192=a\cdot b^7[/tex]
Divide the second equation by the first:
[tex]\dfrac{192}{0.375}=\dfrac{a\cdot b^7}{a\cdot b^{-2}}=\dfrac{b^7}{b^{-2}}\\ \\512=b^9\\ \\b=\sqrt[9]{512}=2[/tex]
Substitute it into the second equation:
[tex]192=a\cdot 2^7\\ \\192=a\cdot 128\\ \\a=\dfrac{192}{128}=\dfrac{96}{64}=\dfrac{48}{32}=\dfrac{6}{4}=\dfrac{3}{2}[/tex]
So, the equation of the exponential function is
[tex]y=\dfrac{3}{2}\cdot 2^x[/tex]
Please help me, and explain
Answer:
x=2.4
Step-by-step explanation
Lets take the info already given. 20 is on the larger triangle and 8 is on the smaller. So the side that matches with X is 6. The relationship between 20 and 8 is 2.5. How? 20/8=2.5. then you divide 6 by 2.5. That equals 2.4. So x=2.4. Hope that helps !
Answer:
x=2.4
Step-by-step explanation:
Take the big one and divide it by the small one then you take the answer and divide it by the other side.
I NEED HELP PLEASE AND THANK YOU!!!!
Answer:
1) 9/cos(θ)
2)4[tex]\sqrt{3}[/tex](cos(198) +isin(198))
3)z= cos(π/3) +isin(π/3)
Step-by-step explanation:
x=9
i.e. x= 9 +i0
θ= tan^-1 (0/9)
θ= tan^-1 (0)
=0
hence z= r(cosθ +i sinθ)
= 9(cos 0 + isin 0)
= 9
As cos (0) = 1 hence polar form of x=9 is 9/cos(θ) where θ=0
2)
Given
z1=2[tex]\sqrt{3}[/tex]( cos(116)+isin(116))
z2=2(cos(82)+isin(82))
As per the product formula od complex polar numbers:
z1.z2= r1.r2(cos(θ1+θ2) +isin(θ1+θ2) )
Putting the values
= 4[tex]\sqrt{3}[/tex](cos(198) +isin(198))
3)
z= 1/2 + i[tex]\sqrt{3}[/tex]/2
r= [tex]\sqrt{(1/2)^{2}+(\sqrt{3}/2) ^{2} }[/tex]
r = [tex]\sqrt{1/4 +3/4} \\\sqrt{4/4}\\\sqrt{1}[/tex]
r=1
θ= tan^-1 [tex](\sqrt{3}/2 ) / (1/2)[/tex]
= tan^-1[tex]\sqrt{3}[/tex]
=60
=π/3
hence
z= cos(π/3) +isin(π/3) !
I need help ASAP pls !!
ANSWER
[tex]x = 22 \: \: units[/tex]
EXPLANATION
The line from the center of the circle to the upper chord meets it at right angles, this means that, this line bisects the upper chord.
Hence the length of the upper chord is 2(11)=22 units.
Since the distance from the upper chord to the center is 12 units and the distance from the lower chord to the center is also 12 units, the two chords must be equal.
[tex] \therefore \: x = 22 \: units[/tex]
What is the value of log 13? Use a calculator. Round your answer to the nearest tenth.
㏒[tex]13 = 1.11394335[/tex]
Round.
[tex]1.11[/tex]
The value of log 13 is 1. 11
How to determine the logarithmic valueUsing a calculator, press in the log of 13
Log 13 = 1. 114
Rounding the value to the nearest tenth.
Log 13 = 1. 11
Therefore, the value of log 13 is 1. 11
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What is the volume of a cube whose edges each have a measure of 1.8 inches?
3.24 in³
5.4 in³
5.832 in³
11.664 in³
Answer:
5.832 in³
Step-by-step explanation:
The volume (V) of a cube is
V = s³ ← s is the length of the side
here s = 1.8, thus
V = 1.8³ = 1.8 × 1.8 × 1.8 = 5.832 in³
formula is a^3
a=edge
1.8^3=5.83in^3
volume = 5.832
Please find x in the following problem.
Check the picture below.
so we have two parallel lines, notice, the 115° are corresponding angles and thus equal, the 65° and 55° angles are linear angles to 115° and 125° respectively.
that leaves us with a triangle with 65° and 55°, and since all interior angles in a triangle sum up to 180°, then the last angle must be 60°, which has a twin vertical angle across the junction.
since a full revolution or a full circle go-around is 360°, the other two twin vertical angles next to the green 60° angles must be 360° - 60° - 60° = 240°, and since they're twins, each takes half of 240°.
solve for y in 3(2y-4)=8y+9-9y
3(2y - 4) = 8y + 9 - 9y
Distribute 3:
6y - 12 = 8y + 9 - 9y
Combine like terms:
6y - 12 = -y + 9
Add y to both sides:
7y - 12 = 9
Add 12 to both sides:
7y = 21
Divide both sides by 3:
y = 3
Answer:
Y = 3
Step-by-step explanation:
Nine times the square of a number plus 8 is 44. The number is positive. What’s the number?
Answer:
n = 4Step-by-step explanation:
[tex]n-number,\ n>0\\\\9n^2+8=44\qquad\text{subtract 8 from both sides}\\\\9n^2+8-8=44-8\\\\9n^2=36\qquad\text{divide both sides by 9}\\\\\dfrac{9n^2}{9}=\dfrac{36}{9}\\\\n^2=4\iff n=\pm\sqrt4\\\\n=\pm4[/tex]
A triangle has two sides of lengths 6 and 9. What value could the length of the third side be?
The sum of the lengths of two sides of a triangle must always be less than or equal to the third side. So, if we let the third side be x, we have:
[tex]\begin{cases}6+x\geq9\\x+9\geq6\\6+9\geq x\end{cases} \iff \begin{cases}x\geq3\\x\geq -3\\x\leq 15\end{cases} \iff \begin{cases}x\geq3\\x\leq 15\end{cases}[/tex]
Answer:
anything between 3 and 15 BUT NOT 3 OR 15
they can be
4
5
6
7
8
9
10
11
12
13
14
Which restriction is appropriate for the variable 4a + 12 / a + 3
I'll presume the slash is the fraction bar and the questioner is asking about
[tex]\dfrac{4a+12}{a+3}[/tex]
That always equals 4 except when [tex]a=-3[/tex]
So the restriction is
Answer: a ≠ -3
Answer:
The restriction is at a=-3
Step-by-step explanation:
You need to see if there are like terms. If there are that is a hole. For example you can a 4 out of the equation like so.
4(a+3)/a+3.
since they both have a+3 that is a hole. so a+3=0 so a=-3 is a restriction
Using the numbers 3, 5, and 8, can you write nine proper fractions and nine improper fractions? You may use each number only once within a fraction.
Answer:
9 proper fractions:
3/5,3/8,5/8,3/40,5/24,8/15,3/13,5/11,2/8
9 improper fractions:
8/3,8/5,5/3,24/5,40/3,15/8,11/5,13/3,8/2
Step-by-step explanation:
Proper fraction:
Proper fraction are the fractions in which the numerator is less than the denominator and the value of proper fractions is less than 1.
x/y is proper fraction if x<y and x/y<1
Improper fraction:
Improper fraction are the fractions in which the numerator is greater than the denominator and the value of proper fractions is more than 1.
x/y is improper fraction if x>y and x/y>1
Given numbers: 3,5,8
Making 9 proper and improper fractions with above given numbers with condition to use each number only once within a fraction.
nine proper fractions: (x/y is proper fraction if x<y and x/y<1)
3/5
3/8
5/8
3/(5)(8)= 3/40
5/(3)(8) = 5/24
8/(3)(5) = 8/15
3/(5+8) = 3/13
5/(3+8) = 5/11
(5-3)/8 = 2/8
nine improper fractions: (x/y is improper fraction if x>y and x/y>1)
8/3
8/5
5/3
(8)(3)/5 = 24/5
(8)(5)/3 = 40/3
(5)(3)/8 = 15/8
(3+8)/5 = 11/5
(5+8)/3 = 13/3
8/(5-3) = 8/2 !
Final answer:
To create proper and improper fractions using the numbers 3, 5, and 8, proper fractions must have a smaller numerator than the denominator, and improper fractions must have a larger numerator than the denominator. Nine examples of each type are provided using the given numbers and additional integers as necessary.
Explanation:
When creating proper fractions and improper fractions using the numbers 3, 5, and 8, a proper fraction has a numerator (top number) that is smaller than its denominator (bottom number), whereas an improper fraction has a numerator that is larger than its denominator.
Here are nine proper fractions using 3, 5, and 8:
3/53/85/81/3 (using the number 1 to create the fraction)2/3 (using the number 2 to create the fraction)1/5 (using the number 1 to create the fraction)2/5 (using the number 2 to create the fraction)1/8 (using the number 1 to create the fraction)2/8 or 1/4 after simplification (using the number 2 to create the fraction)Here are nine improper fractions using 3, 5, and 8:
5/38/38/59/5 (using the number 9 to create the fraction)9/8 (using the number 9 to create the fraction)10/3 (using the number 10 to create the fraction)10/5 or 2 after simplification (using the number 10 to create the fraction)11/3 (using the number 11 to create the fraction)11/8 (using the number 11 to create the fraction)