[tex]\\ \rm\Rrightarrow \sqrt{x²-10x+25}[/tex]
[tex]\\ \rm\Rrightarrow \sqrt{x²-5x-5x+25}[/tex]
[tex]\\ \rm\Rrightarrow \sqrt{x(x-5)-5(x-5)}[/tex]
[tex]\\ \rm\Rrightarrow \sqrt{(x-5)(x-5)}[/tex]
[tex]\\ \rm\Rrightarrow \sqrt{(x-5)^2}[/tex]
[tex]\\ \rm\Rrightarrow\pm (x-5)[/tex]
Solution set(for x-5)
{-10,-9,-8,-7,-4,-3,-2,-1,0}for 5-x
{0,-1,-2,-3,-4,-5,-6,-7,-8,-9,-10}Answer:
First, simplify the expression under the square root sign by factoring:
[tex]\implies x^2-10x+25[/tex]
[tex]\implies x^2-5x-5x+25[/tex]
[tex]\implies x(x-5)-5(x-5)[/tex]
[tex]\implies (x-5)(x-5)[/tex]
[tex]\implies (x-5)^2[/tex]
Therefore:
[tex]\implies \sqrt{x^2-10x+25}=\sqrt{(x-5)^2}[/tex]
[tex]\implies \sqrt{x^2-10x+25}=\pm(x-5)[/tex]
[tex]\implies \sqrt{x^2-10x+25}=|x-5|[/tex]
As the domain is -5 ≤ x < 5, then:
[tex]\implies y=-x+5[/tex]
and the range is 0 < y ≤ 10
Kindly help me solve this questions
a) 3/X+2-2=1/1/2
b) 3(4-7x)/5-0.7=x-6/2
Answer:
a) x=6
b) x= 498/463
hope this helps!!
Which number sentence is not true?
A. | -1 | > 1/2
B. | -1 | = -1
C. | 1/2 | < | -1 |
D. | -1/2 | < | -1 |
Answer:
Option B
Step-by-step explanation:
|-1| [tex]\neq[/tex] -1
|-1| = 1
Answer:b
Step-by-step explanation: bc it’s right
helpppppopppppoppppppp
The invers of 10/4 is
Answer:
4/10
Step-by-step explanation:
What is the approximate circumference of the circle that has a center (3, 1) and passes through the point (3, 4)?
Step-by-step explanation:
You use the Distance Formula
d= √( x2 - x1 )^2 + ( y2 - y1 )^2
substitute
r= √(3-3)^2 + (4-1)^2
√0^2 + 3^2
r = √9
r = 3
Now you can use the equation for finding the circumference
2πr
2π3
≈ 6π or 18.85
Two players, A and B, are playing an asymmetrical game. There are n points on the game board. Each turn player A targets a pair of points and player B says whether those two points are connected or unconnected. A can target each pair only once and the game ends when all pairs have been targeted. Player B wins iff a point is connected with all other points on the very last turn, while player A wins if any point is connected with all other points on any turn but the very last one OR if no point is connected to all other points after the last turn. For what values of n does either player have a winning strategy?
The values of n does either player have a winning strategy is; Player B has a winning strategy for all n ≥ 2.
How to predict winning probability?Let us use an example to solve this question. The game is played on the complete graph Kₙ (n ≥ 2), which consists of n vertices, each pair of vertices joined by an edge.
Now, Initially all edges are unpainted. At each turn, A chooses an edge, which B paints blue or red. Now, B will win if, after the last edge is painted, there is a vertex which is joined to all other vertices by blue edges. If that doesn't happen, then A wins.
The winning strategy of B is described by 3 rules which are;
Rule 1; Paint the last edge blue.Rule 2. Never paint an edge red if that would result in two red vertices being joined by an unpainted edge.Rule 3. Use red paint whenever permitted by Rules 1 and 2.Thus, if n >2, the first edge will always be painted red, the second will always be painted blue.
In conclusion, when we apply that same scenario to our question it is the same result and as such Player B has a winning strategy for all n ≥ 2.
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You have a biased coin, where the probability of flipping a heads is 70%. You flip once, and the coin comes up tails. What is the expected number of flips from that point (so counting that as flip #0) until the number of heads flipped in total equals the number of tails?
The expected number of flips from that point until the number of heads flipped in total equals the number of tails is 2
How to determine the number of flips?The given parameters are:
P(Head) = 70%
The expected number of flipping a head is:
E(x) = 70% * x
The expected number of flipping a tail is:
E(x) = (1 - 70%) * x + 1
Where 1 represents the first flip
When both values are equal, we have:
70% * x = (1 - 70%) * x + 1
Evaluate
0.7x = 0.3x + 1
Evaluate the like terms
0.4x = 1
Divide both sides by 0.4
x = 2.5
Remove the decimal
x = 2
Hence, the expected number of flips from that point until the number of heads flipped in total equals the number of tails is 2
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My original answer was 18, 1.92, -1, -5.5 but it is wrong on the form so what did i do wrong?
Drag numbers to the table so it shows a proportional relationship between x and y.
PLEASE HELP
Answer:
4 box: 9
5 box:4.5
6 box: 27
Step-by-step explanation:
Do 3/.5= 6 so multiply the numbers by 6
1.5•6=9
4.5•6=27
Hope this helps! ;-)
Which of the following statements is true for a sphere?
A sphere is the set of all points in space equidistant from a line segment called the radius.
Answer A: A sphere is the set of all points in space equidistant from a line segment called the radius.
A
A sphere is the set of all points in space equidistant from a point called the center.
Answer B: A sphere is the set of all points in space equidistant from a point called the center.
B
A sphere is the set of all points in a plane equidistant from a line segment called the radius.
Answer C: A sphere is the set of all points in a plane equidistant from a line segment called the radius.
C
Answer D : A sphere is the set of all points in a plane equidistant from a point called the center.
The answer choice which is true of a sphere; A sphere is the set of all points in space equidistant from a point called the center.
What is a Sphere?A sphere is a geometrical entity that is characterized as a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance from a given point in three-dimensional space. The given point in discuss is the centre of the sphere, and distance, r is the sphere's radius.
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For which inequality would x = 12 be a solution?
12 - x ≥ 4
x + 4 ≤ 12
12 x < 200
12 ÷ x > 12
Answer:
12x < 200
Step-by-step explanation:
12 - x ≥ 4
-x ≥ -8
x ≤ 8
12 is not a solution to this one.
x + 4 ≤ 12
x ≤ 8.
12 is not a solution to this one.
12 x < 200
x < 200/12
x < 16 2/3
12 is a solution.
i need help with v-math
Answer:
Y=p/9
Step-by-step explanation:
Can u see p = 9y?
But there is no option of p = 9y
So try to work a bit on the formula to y = p/9
What’s 5 square root 7n
Answer:
If you are asking what 5[tex]\sqrt{7n}[/tex] is without the radical, it equals to 175n.
Step-by-step explanation:
You square the whole equation first.
5^2 = 25 and [tex]\sqrt{7n}[/tex]^2 =7n
Then you multiply it together.
25 * 7n
175n
322 children came to the summer carnival. if each child was given 3 free ride passes for attending, how many free ride passes were given away?
Answer: 996 free ride passes were given away
Step-by-step explanation:
If each child was given 3 free ride passes, then you have to do 332 x 3 which is 996
Is 23/√3 a rational number? Again is 23 over root 3 a rational or irrational number.
Answer: irrational number
Step-by-step explanation:
Let us write it out.
[tex]\displaystyle \frac{23}{\sqrt{3} }[/tex]
Next, we will define ratoinal and irrational.
A rational number is a number that can be written as a whole number, fraction, or decimal that ends / repeats.
An irrational number is any number that cannot be turned into a fraction.
Let us see which category the number given falls into.
[tex]\displaystyle \frac{23}{\sqrt{3} } = 13.27905619\;\;\;\;\;\;\text {it goes on...}[/tex]
This means [tex]\frac{23}{\sqrt{3} }[/tex] is an irrational number.
what is the measure of angle 7 ?
Answer:
97°
Step-by-step explanation:
Please see attached
A, B and C lie on a straight line.
Given that angle y = 144° and angle z =
92°, work out x.
A
x
Z
The diagram is not drawn accurately.
B
C
PLEASE HELP! WILL GET BRAINLEST
Answer:
See below ~
Step-by-step explanation:
Question 12
Numbers greater than 3 : 5Total numbers : 8P (number > 3) = 5/8Multiply with 4005/8 x 4005 x 50250 timesQuestion 17
Part A
Possible outcomes = {HT, HH, TH, TT}Part B
P (heads at least once) = Outcomes with at least one "H" / TotalP (heads at least once) = 3/4Mrs. Clements has a table with a top that is shaped like the trapezoid shown. Find the area of the table top in square feet? hurry plss
It is to be noted that the area of the Trapezoid is: 28 Feet. See the details of the solution below.
What is the formula for the area of a Trapezoid?The formula for the area of a regular Trapezoid is:
A = h * ((a+b)/2);
Where
A = Area
a = Short Base
b = Long Base
h = Height
So what is the solution for the above trapezoid?Following the above formula,
A = 4 * ((5+9)/2)
A = 4 * (14/2)
A = 4 * 7
A = 28 Feet.
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help me please this is due tomorrow
well I can say all but a and g are nets according to that explenation
What percentage of the large circle does the small circle take up?
Please please help
Answer:
25 percent.
Step-by-step explanation:
To begin we want to find the area of the small circle. That would be pi(r)^2 or 9pi after plugging in the 3 for the radius. We can only assume that the large circle is double the radius of the smaller circle so it would be 6. Plug 6 in and get 36pi for the area of that circle. 9pi/36pi will equal 0.25 and that will be your percentage. I hope this helped.
Solve for x in -
6(3x-5)-7x=25
Step-by-step explanation:
6 ( 3x - 5 ) - 7x = 25..
18x - 30 - 7x = 25
18x - 7x = 25 + 30
11x = 55
x = 55 / 11
x = 5
[tex]...[/tex]
x=5
Step-by-step explanation:
6(3x-5)-7x=25
18x-30-7x=25
11x-30=25
x=5
How many participants will make 45 handshakes in total
Solve the following equation x2+6x=27 x = and
Answer:
Step-by-step explanation:
Assuming the question is x^2 + 6x = 27x, subtract 6x from both sides. x^2 = 21x. Then, divide both sides by x and you get x= 0, 21
Can the sides of a triangle have lengths 2, 13, and 14?
Answer:
Yes
Step-by-step explanation:
The larger side is smaller than the other sides combined
(2 + 13) > 14
Hope this helps
Is kilobyte bigger than megabyte.
Answer:
no
Step-by-step explanation:
1 kilobyte = 1000 byte
1 megabyte = 1,000,000 byte
1 kilobyte = 1/1000 megabyte
Answer: no
Answer:
NO!!!! Kilobyte isn't BIGGER than MegabyteStep-by-step explanation:
Here's the table:
1 Kilobyte = 1,024 Bytes
1 Megabyte = 1,024 Kilobytes
1 Gigabyte = 1,024 Megabytes
1 Terabyte = 1,024 Gigabytes
From the table, we can see that Megabyte is bigger than Kilobyte
Find the arc length and sectors perimeter of an 85 degree arc of a circle with a finger radius of 4ft
Answer:
Arc length = 5.93 ft
Perimeter = 13.93 ft
Step-by-step explanation:
85/360*2*π*4 = arc length
5.93411946 ft
Perimeter = 4+4+5.93 = 13.93 ft
If f(x) = x2 – 2x and g(x) = 6x 4, for which value of x does (f g)(x) = 0? –4 –2 2 4
The sum of function is a way of adding two or more functions together
The values of x for which f(g(x)) = 0 are -2/3 and -1/3
Sum of functionsThe sum of function is a way of adding two or more functions together
Given the following functions
f(x) = x² - 2x
g(x) = 6x + 4
f(g(x) = f(6x +4))
f(6x+4) = (6x+4)² - 2(6x+4)
(6x+4)² - 2(6x+4) = 0
(6x+4) = 0 and 6x+4-2 = 0
x = -2/3 and -1/3
Hence the values of x for which f(g(x)) = 0 are -2/3 and -1/3
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help with practice problem
Answer:
-5<x<-3
Step-by-step explanation:
Hope this helps! ;-)
Which values of x and y would make the following expression represent a real number? (4 5i)(x yi) x = 4, y = 5 x = –4, y = 0 x = 4, y = –5 x = 0, y = 5
The product will be a real number when x = 4 and y = -5.
Which values of x and y should we use?We have the product of complex numbers:
[tex](4 + 5i)*(x + yi)[/tex]
We want this to be a real number, then the second complex number must be the complex conjugate of the first one, so we must have:
[tex](x + yi) = (4 - 5i)[/tex]
Now, if we take the product, we get:
[tex](4 + 5i)*(4 - 5i)\\\\4*4 - 4*5i + 4*5i - (5*5)*i^2 = 16 + 25 = 41[/tex]
So we can see that the outcome is a real number.
Then we must have x = 4 and y = -5.
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Answer: C
Step-by-step explanation:
