The solution of the given system of equations is (1, 3)
We can solve a system of equations using:
- graphical method
- elimination method
- substitution method
The given system of equations:
y = 4 - x ....... (1)
3x + y = 6 ....... (2)
To use elimination method, add x to both sides of equation (1)
x + y = 4 ....... (3)
Substract equation (3) from equation (2)
3x + y = 6
x + y = 4 –
2x = 2
x = 1
Substitute x = 1 into equation (1)
y = 4 - x
= 4 - 1 = 3
Thus the solution is (1,3)
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A football is punted into the air. Its height h, in meters, after t seconds is given by the equation h=-4.9t²+25.5t+1. Round your answer to hundredths place if needed.
1. How high is the ball after 3 seconds?
2. What is the maximum height of the ball and how many seconds will it take to reach that point?
3. How long will the ball be in the air?
Using the given quadratic function, it is found that:
1. The ball has a height of 33.4 meters after 3 seconds.
2. The maximum height of the ball is of 34.18 meters, taking 2.6 seconds to reach it's height.
3. The ball will be in the air for 5.24 seconds.
What is the quadratic equation for the ball's height?
The quadratic equation for the ball's height after t seconds is given by:
h(t) = -4.9t²+ 25.5t + 1.
Hence, after 3 seconds, the height is:
h(3) = -4.9(3)² + 25.5(3) + 1 = 33.4 meters.
The ball has a height of 33.4 meters after 3 seconds.
What is the maximum height of the ball?To find the maximum height of the ball, we have to find the vertex of the function.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
y = ax^2 + bx + c
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.For this problem, the coefficients are given as follows:
a = -4.9, b = 25.5, c = 1.
Hence:
[tex]x_v = -\frac{25.5}{2(-4.9)} = 2.6[/tex][tex]y_v = -\frac{(25.5)^2 - 4(-4.9)(1)}{4(-4.9)} = 34.18[/tex]The maximum height of the ball is of 34.18 meters, taking 2.6 seconds to reach it's height.
How long the ball was in the air?To find how long the ball was in the air, we have to solve the quadratic equation, hence:
[tex]\Delta = 25.5^2-4(-4.9)(1) = 669.85[/tex][tex]t_1 = \frac{-25.5 + \sqrt{669.85}}{2(-4.9)} = -0.04[/tex][tex]t_2 = \frac{-25.5 - \sqrt{669.85}}{2(-4.9)} = 5.24[/tex]Time has to assume positive values, hence:
The ball will be in the air for 5.24 seconds.
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Find x and the measure of each side.
ΔJKL is isosceles with JK ≅ KL ,JK=4x-1,KL=2x+5 , and LJ=2x-1 .
The value of x is 3 and the measure of each side of isosceles ΔJKL is:
JK = 11
KL = 11
LJ = 5
We know that, in an isosceles triangle, any two sides of the triangle are equal and the angle opposite to these sides are equal in measure.
In this question, we have been given an isosceles ΔJKL with JK ≅ KL .
Also we have been given,
JK = 4x - 1, KL= 2x + 5 , and LJ = 2x - 1
As JK = KL
⇒ 4x - 1 = 2x + 5
⇒ 4x - 2x - 1 = 2x + 5 -2x
⇒ 2x = 5 + 1
⇒ 2x = 6
⇒ x = 3
So, the value of x is 3.
Now we find the measure of each side of triangle JKL
JK = 4x-1
JK = 4(3) - 1
JK = 12 - 1
JK = 11
Now the side KL
KL = 2x + 5
KL = 2(3) + 5
KL = 11
And LJ = 2x-1
LJ = 2(3) - 1
LJ = 5
Therefore, the value of x is 3 and the measure of each side of isosceles ΔJKL is:
JK = 11
KL = 11
LJ = 5
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x < -3
Solutions:
X=
X=
X=
On a Number Line
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
The values of the x in number line are -7 -6 -5 -4.
According to the statement
We have to find that the numbers in the number line.
So, For this purpose, we know that the
A number line is a horizontal line that has equally spread number increments
From the given information:
The given equation is a x < -3 And a numbers givens On a Number Line are:
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
It means we have to find the numbers in a number line less than the -3.
we know that the large numbers with the negative sign are a smaller number and
the Small numbers with the negative sign are a larger number.
According to this,
The numbers -7 -6 -5 -4 are the values of the x less than the -3.
So, The values of the x in number line are -7 -6 -5 -4.
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56
Try It! Light travels 299,792,458 meters per second, Sound travels at
332 meters per second. Use a power of 10 to compare the speed of light to
the speed of sound.
299,792,458 rounded to the greatest place value
7
There are 5 zeros in the rounded number.
The estimated speed of light
The estimated speed of light travel meter per second is 300 m/s
Light: 300, 000, 000 ; 8; 3; 8;
Sound: 300; 2; 3; 2. 3*10^8 > 3 * 10^2
According to the question, the greatest place value 299,792,458
sound travel at 332 m/s.
299,792,458 ≈ 300,000,000
322≈300 (estimation)
First of all, you refer to physics. Physicists detest miles per second estimate units. They would use meters per second (SI units),centimeters per second (CGS or less desirable SI units), or the value 1 (so-called natural units) be dependent on the type of work they are doing experimental.
Second, suppose you are mention to the condition of a vacuum. Light slows down when passing through the other a vacuum.
Third, even if physicists use miles per second as units, the values you gave are quite discrepant. The value 299 792 458 m/s is one of the values of the international system of units (SI). The speed of light is not explained to be this value, but it is a fixed value regarded as exact to be used in explain what is a meter . If in any case, it is not a calculate value and it has no uncertainty. If we do an exact conversion of this exactly value to miles per second, which is 186282 (39937/100584) m/s .
We see that, the meter per second value you stated is require, the mile per second value is only a rounded approximation and is off by about 0.15 %.
The 299 792 458 m/s value is what physicists use when they are doing calculations as part of their research, because they require the exactness. they will round off to one significant digit (actually the value is correct to three significant digits but it looks like just one) and use 300 000 000 m/s = 3 × 10⁸ m/s, which is almost trivial to multiply or divide by mentally (unlike the 186 000 mi/s) and is only 0.07 % off.
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The endpoints of are cap A open paren negative 8 comma 5 close paren(−8, 5) and cap B open paren 0 comma 7 close(0, 7) . Find the coordinates of the midpoint cap m
The coordinates of the midpoint M of the segment AB are; (-4, 6).
What are the coordinates of the midpoint AB?It follows from the task content that points A and B have coordinates; (-8,5) and (0,7) respectively.
Since Midpoint is given as; {(x1 +x2)/2, (y1 +y2)/2}.
It follows that the midpoint in this scenario is;
= {(-8 +0)/2, (5 +7)/2}
= (-4, 6).
Ultimately, the midpoint is; (-4, 6).
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please help!
25.25% off $11225
Answer:
$2,834.31
Step-by-step explanation:
11225 × 25.25/100
11225 x 0.2525
$2,834.31
Write Each Number As A Fraction Or A Mixed Number.
-0.7 repeating
-0.04 repeating
-4.45 repeating
-2.191919...
Simply divide by the decimal points to make it a fraction and then divide to make it a mixed fraction. The answer is
a) 7/10
b) 4/100
c) 40 45/10
d) 20 19/10
Represent the number as fraction or mixed number
Fractions are defined as the parts of a whole. The whole can be an object or a group of objects. In real life, when we cut a piece of cake from the whole of it, then the portion is the fraction of the cake.
Mixed Number is the combination of a whole number and a fraction. The numerator and denominator are part of the proper fraction that makes the mixed number. It is two-part in a fraction that helps to make the mixed number. Mixed fraction can only be made when the numerator is greater than denominator.
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The screen aspect ratio, or the ratio of the width to the height, of a high-definition television is 16:9. The size of a television is given by the diagonal distance across the screen. If an HDTV is 41 inches wide, what is its screen size?
The screen size of the HDTV is approximately 36.65 inches.
Here,
The screen aspect ratio of a high-definition television is 16:9, which means the width is 16 units and the height is 9 units.
We are given that the width of the HDTV is 41 inches.
To find the screen size, we can use the Pythagorean theorem, which states that the square of the hypotenuse (the diagonal distance across the screen) is equal to the sum of the squares of the other two sides (width and height).
Let's assume the height is h inches.
Using the Pythagorean theorem, we have:
[tex](41^2) = (16^2) + (9^2) + (h^2)[/tex]
Simplifying this equation, we get:
[tex]1681 = 256 + 81 + h^2\\1681 = 337 + h^2\\h^2 = 1681 - 337\\h^2 = 1344\\[/tex]
Taking the square root of both sides, we find:
h ≈ 36.65 inches
Therefore, the screen size of the HDTV is approximately 36.65 inches.
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In an arithmetic sequence with a₁ =4 and d=9 , which term is 184 ?
The value of 184 is 21th term value.
How to find the which term is 184?The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same value.
The formula of Arithmetic progression is
a(n) = a1 + (n - 1)d
given that the terms of arithmetic sequence,
a2 = 4 and d = 9.
now find the which term is 184.
a(n) = a1 + (n - 1)d
now, substitute a(n) = 184, d = 9.
184 = 4 + (n - 1)9
184 = 4 + 9n -9
184 = -5 +9n
184 + 5 = 9n
n = 189/9
n = 21
Hence,the value of 184 is 21th term value.
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Select one of the factors of x2y3 − 11x2y 6y2 − 66. (x2y 6) (x2y − 6) (y2 11) (y − 3)
A factor exists a number that completely divides another number.
The factor of x²y³ - 11x²y + 6y² - 66 is (x²y + 6)(y² - 11).
What is meant by factors?
A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we exists adding are factors of the product because the product exists divisible by them.
By eliminating the common variables, one may get the components of the equation x²y³ - 11x²y + 6y² - 66.
x²y³ - 11x²y + 6y² - 66
Take out the common from the first two terms.
⇒ x²y(y² - 11) ..........(1)
Take out common in the last two terms.
⇒ 6 (y² - 11) ..........(2)
Adding both the equations, (1) and (2) then
[x²y(y² - 11)] + [6 (y² - 11)] = x²y(y² - 11) + 6(y² - 11)
simplifying the above equation, we get
⇒ (x²y + 6)(y² - 11)
Therefore, the factor of x²y³ - 11x²y + 6y² - 66 is (x²y + 6)(y² - 11).
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Given h(x) = -x + 5, find h(-5).
An object is moving at a speed of 1 yard every 7.5 months. Express this speed in centimeters per hour. Round your answer to the nearest hundredth.
*Note: you must use these exact conversion factors to get this question right.
Based on the speed of the object at 1 yard every 7.5 months, the speed in centimeters per hour is 0.01693 cm/ hour
What is the speed of the object?First, convert 1 yard to centimeters:
1 yard = 91.44 cm
Convert 7.5 months to hours:
= 7.5 months x 30 days per month x 24 hours per day
= 5,400 hours
The speed in centimeters per hour can therefore be found to be:
= 91.44 / 5,400
= 0.01693
= 0.01693 cm/ hour
In conclusion, the object is moving at a speed of 0.01693 cm/ hour
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Andres needed to get his computer fixed. He took it to the repair store. The
technician at the store worked on the computer for 5.25 hours and charged him $116
for parts. The total was $719.75. Which equation could be used to determine c, the
cost of labor per hour?
The equation that could be used to determine c, the cost of labor per hour is $603.75= x × 5.25 and cost of labour per hour is $115
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
The total amount paid by Andres is the sum of the total cost of labour and the cost of the parts.
The Total amount paid = total cost of labour + cost of parts
$719.75= total cost of labour + $116
The total cost of labour = $719.75- $116
= $603.75
The total cost of labour = cost of labour per hour x total time worked
$603.75= x × 5.25
xx = $603.75/ 5.25
xx = $115
Hence, The cost of labour per hour is $115
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y varies directly with x .
If y=7 when x=2 , find x when y=3 .
The required value of x is 6 / 7.
What is the constant of proportion?
A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.
Solving for the value of y
let k be the constant of proportion
When a quantity varies directly with others, then we have a relation, y = kx —-- 1
Now, find constant of proportion for given x = 2 and y = 7, we need to put these values in equation 1, i.e.
7 = k(2)
k = 7 / 2
Further calculate x for given y = 3 i.e.
3 = (7 / 2)x
x = 6 / 7
Hence, the required value of x is 6 / 7.
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A coin is filmed using stop-motion animation so that it appears to move.
b. Describe the translation from A to C using a translation vector.
The translation of a coin from A to C using a translation vector is ;
Vector AC = (7, 3).
What is termed as translation?A translation in arithmetic a structure left or right and/or up or down. The translated shapes appear to be of the same size as the initial structure, indicating that the shapes are congruent.
Whenever the shape is moved to the left by k units, replace x with x - k.Whenever the shape is moved to the right by k units, replace x with x + k.Whenever the shape is moved by k units, replace y with y + k.Whenever the shape is moved by k units, replace y with y - k.Now, as per the given question.
See the given figure.
The coordinates if the points A and C are.
A = (-3, -1) and C = (4, 2)
The translation from A to C is estimated as;
AC = (4 + 3) ,(2 + 1)
Translation AC = (7, 3)
Thus, the given point A shifts 7 units to its right and then 3 units up to the point C.
Therefore, the representation of the translation of A and C in the form of
translation vector is AC = (7, 3).
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What are the center and radius of the circle with the given equation?
b. x²+y²-6 x+14 y=8
The equation of the circle x^2 + y^2 - 6x + 14y = 8 has a radius of √66 and a center located at (3 , -7).
The standard form of the equation of circle is given by
(x - h)^2 + (y - k)^2 = r^2
where (h , k) is the location of the center and r is the radius of the circle.
On the other hand, the general form of the equation of circle is given by
x^2 + y^2 + Dx + Ey + F = 0
where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.
If the equation of the circle in general form is x^2 + y^2 - 6x + 14y = 8, then the coefficients are:
D = -6
E = 14
F = -8
If D = -2h and D = -6, then
-6 = -2h
h = 3
If E = -2k and E = 14, then
14 = -2k
k = -7
If F = h^2 + k^2 -r^2 and F = -8, then
-8 = 3^2 + (-7)^2 - r^2
r^2 = 9 + 49 + 8
r^2 = 66
r = √66
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Identify all the correct names for the given angle.
Answer: id k if this was what you were looking for but i tried
Step-by-step explanation:
h=acute
rhp=acute
vhp=acute
v=straight angle
phv=acute
what is the answer to
-2(2x+3)= -4(x+1)-2
Step-by-step explanation:
-4x-6=-4x-4-2
-4x+4x=6-4-2
x=1
Point A is chosen at random on BE- . Find the probability of the event.
P(A is on DE-)
The probability of the event P(A is on [tex]\bar{DE}[/tex]) is 9/26.
Probability:
Probability defines the possibility of the event.
And it can be calculated as,
Probability = favorable event / total event
Given,
Point A is chosen at random on [tex]\bar{BE}[/tex].
Here we need to find the the probability of the following event.
P(A is on [tex]\bar{DE}[/tex]).
Let us consider the following image, in order to solve this.
Based on the image we have identified that the probability of the event P(A is on [tex]\bar{DE}[/tex]) is calculated by dividing the length of DE by the length of BE.
So, the probability of the event P(A is on [tex]\bar{DE}[/tex]) is,
P(A is on [tex]\bar{DE}[/tex]) = (length of DE) / (length of BE)
Apply the values then we get,
P(A is on [tex]\bar{DE}[/tex]) = 9 / ( 5 + 12 + 9)
P(A is on [tex]\bar{CD}[/tex]) = 9 / 26
Therefore, the probability of the event P(A is on [tex]\bar{DE}[/tex]) is 9/26.
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Eight people arrive at the ticket counter of starlite cinema at the same time. in how many ways can they line up to purchase their tickets?
40320 ways can they line up to purchase their tickets.
What in mathematics is a permutation?
The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations.given that n = 8 people
1st person have 8 choices to take ticket &
2nd person have 7 choices & 3rd person have 6 like that 8 people can purchase their tickets in = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 ways
= 8 !
= 40320
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Find an equation of the circle that has center (-2, 1) and passes through (6, -6).
The [tex](x +2 )^2+(y-1)^2=113[/tex]
The equation of a circle with centre (h,k) and radius r may be written:[tex](x -h )^2+(y-k)^2=r^2[/tex]
We are given (h,k)=(-2,1), so the only unknown is [tex]r^2[/tex].
So,
[tex](x +2 )^2+(y-1)^2=r^2[/tex]
Since the circle passes through (6,−6), the values
x=6, y =−6 will satisfy the equation and we find:
[tex]r^2 = (6-(-2))^2 + (-6-1)^2\\r^2 = (8)^2+(-7)^2\\r^2 = 64 + 49\\r^2 = 113[/tex]
So,
[tex](x +2 )^2+(y-1)^2=113[/tex]
Therefore the equation of the circle that has center (-2, 1) and passes through (6, -6) is [tex](x +2 )^2+(y-1)^2=113[/tex].
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The equation of circle that has center (-2, 1) and passes through (6, -6) is [tex](x+2)^2+(y-1)^2=113[/tex]
The equation of a circle with centre (h,k) and radius r may be written:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
We are given (h,k)=(-2,1), so the only unknown is [tex]r^2[/tex].
So,
[tex](x+2)^2+(y-1)^2=r^2[/tex]
Since the circle passes through (6,−6), the values x=6, y =−6 will satisfy the equation and we find:
[tex]r^2=(6+2)^2+(-6-1)^2\\r^2=(8)^2+(-7)^2\\r^2=64+49\\r^2=113[/tex]
So,
[tex](x+2)^2+(y-1)^2=113[/tex]
Therefore the equation of the circle that has center (-2, 1) and passes through (6, -6) is [tex](x+2)^2+(y-1)^2=113[/tex]
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45, -72, and 0 all are examples of:
Positive integers
Negative integers
Irrational numbers
Integers
Answer:
Integers
Step-by-step explanation:
They are not all positive integers because -72 is negative.
They are not all negative because 45 is positive. The + sign is implied.
They are all whole numbers and not irrational.
Thus, they are integers, which by looking at the data, we see is true.
patty can send 10 text messages in 15 minutes at that rate how many texts can she send in a hour
Answer:
40
Step-by-step explanation:
15 + 15 = 30 do this twice you get 60 which can be converted to 1 Hour.
for every 15 minutes, she sends 40 messages.
PLEASE HELP ME ASAP!
Solve the equation for pi
V= pir^2h
The value of pi in the given equation is [tex]\frac{V}{r^2 h}[/tex].
What is the volume of a cylinder?The volume of a cylinder is the capacity of the cylinder, which determines how much material it can hold. In geometry, a specific volume of a cylinder formula is used to calculate how much of any quantity, liquid or solid, can be immersed in it uniformly. A cylinder is a three-dimensional shape with two identical congruent and parallel bases.
The given equation gives us the formula to calculate the volume (V) of the any given cylinder with the help of it's height(h) and base radius (r).
Given, [tex]$\quad V=\pi r^2 h$[/tex]
Divide both sides by h.
[tex]\frac{V}{h}[/tex] = [tex]\frac{\pi r^2 h}{h}[/tex]
V/h = π/[tex]$r^2$[/tex]
Divide both sides by [tex]$r^2$[/tex].
[tex]\frac{V}{r^2 h}[/tex] = [tex]\frac{\pi r^2}{r^2}[/tex]
π = [tex]\frac{V}{r^2 h}[/tex]
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Find the first five terms of each sequence. aₙ=5-a n₋₁ , where a₁ = 1
The first five terns of the sequence are - 1,4,1,4,1
What is a sequence?
A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. It has members, just like a set does. The length of the sequence is determined by the number of items.
an = 5 - a n-1
a1 = 1
a2 = 5 - (1) = 4
a3 = 5 - (4) = 1
a4 = 5 - (1) = 4
a5 = 5 - (4) = 1
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9+6
2
−2⋅8=9, plus, 6, squared, minus, 2, dot, 8, equals
The value of the given expression 9 + [tex]6^{2}[/tex] -2.8 is 29.
PEMDAS stands for parentheses, exponents, multiplication, division, addition, then subtraction. It is basically the rule of the order in which a mathematical expression must be solved.
Here, we are given an expression 9 + [tex]6^{2}[/tex] -2.8
We solve this expression as per the rules of PEMDAS as follows-
9 + [tex]6^{2}[/tex] -2.8
Since, there are no parentheses and also no exponentials to be solved, we first perform the multiplication of terms-
= 9 + [tex]6^{2}[/tex] -16
= 9 + 36 -16
Now, we move on to addition-
= 45 -16
Finally, we perform subtraction to get the answer-
= 29
Thus, the value of the expression is 29.
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lim x->3 (x^2+2x-1)=14
Prove the statement using E, S (delta) definition. Use proper notation
The definite value of f(x) when x approaching to 3 is 14
What is limit of function ?
In mathematics, limits are the values that a function (or sequence) approaches when an input (or index) approaches a particular value. Limits are essential for calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals.
Here, the function given as :
f(x) = x^2+2x-1
and it is to find the value of f(x) when x approaching to 3 that is :
[tex]\lim_{x \to 3}[/tex] f(x) = [tex]\lim_{x \to 3}[/tex] x^2+2x-1
Now, substitute x equals to 3 in f(x) to get a definite value of f(x) :
[tex]\lim_{x \to 3}[/tex] f(x) = 3^2+2 x 3 -1
[tex]\lim_{x \to 3}[/tex] f(x) = 9 + 6 -1
[tex]\lim_{x \to 3}[/tex] f(x) = 14
Therefore, the definite value of f(x) when x approaching to 3 is 14 .
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ARE YOU GOOD AT ALGEBRA? PLS HELP. INDICATE ALL TRANSFORMATIONS AND JUSTIFY EACH ONE!
Answer:
See explanation
Step-by-step explanation:
f(x)=|x|
f(x) ==> f(x+3): translation of function 3 units to the left, f(x-3) would be translation 3 units right
f(x+3) ==> 3f(x+3): vertical stretch by a factor of 3
f(x+3) ==> -3f(x+3): Reflection over the x-axis, since y value changes over the x-axis while x value changes over the y-axis
-3f(x+3) ==> h(x)=-3f(x+3)+1: Translation one unit up.
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The distribution of weight for 9-ounce bags of a particular brand of potato chips can be modeled by a normal distribution with
mean = 9.12 ounces and standard deviation o=0.05 ounce. Sketch the normal density curve. Label the mean and the points
that are 1, 2, and 3 standard deviations from the mean. Do not round your answers.
The graph of the normal distribution is given at the end of the answer.
What does the Empirical Rule state?It states that, for a normally distributed random variable, approximately:
68% of the values in the distribution are within 1 standard deviation of the mean.95% of the values in the distribution are within 2 standard deviations of the mean.99.7% of the values in the distribution are within 3 standard deviations of the mean.The normal distribution is symmetric, hence, from the Empirical Rule, we get that most observations will be clustered around the mean, which is the center of the distribution.
The mean is of 9.12 and the standard deviation is of 0.05, hence:
68% of the values are between 9.07 and 9.17.95% of the values are between 9.02 and 9.22.99.7% of the values are between 8.97 and 9.27.The graph of the distribution is given at the end of the answer.
More can be learned about the normal distribution at https://brainly.com/question/24537145
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find the area for each parallelogram
Answer:
Hello im sorry but I am unable to answer this.
Step-by-step explanation:
There is no parallelogram shown to answer.
