The equation for the functions g₁(x), g₂(x), and g₃(x) are (x + 3)², (x + 3)² + 5, and -[(x + 3)² + 5] respectively.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
f(x) = x²
We have:
g₁(x) which is a transformed function of f(x)
f(x) shifted three units to the left.
Plug x → (x + 3)
g₁(x) = (x + 3)²
Similarly,
Equation for the function whose graph is in the shape of g₁(x), but shifted five units up.
g₂(x) = (x + 3)² + 5
Equation for the function whose graph is in the shape of g₂(x), but reflected in the x-axis.
g₃(x) = -[(x + 3)² + 5]
Thus, the equation for the functions g₁(x), g₂(x), and g₃(x) are (x + 3)², (x + 3)² + 5, and -[(x + 3)² + 5] respectively.
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help mee answer the question
..............................................
What is the value of x in the figure below?
Let's see
[tex]\\ \rm\dashrightarrow \dfrac{9}{x}=\dfrac{24}{12}[/tex]
[tex]\\ \rm\dashrightarrow \dfrac{9}{x}=2[/tex]
[tex]\\ \rm\dashrightarrow x=\dfrac{9}{2}[/tex]
[tex]\\ \rm\dashrightarrow x=4.5[/tex]
Hi if you can give me a clear explanation that would be great! :)
1) segment ab has endpoints a(-3,1) and b(2,-6). suppose that point b is translated to b (-1,-8)
-how far away is point b from point a?
-how far did point b move to get to point b?
The distance of point a from translated b is 9.2 units and the distance of point b from translated b is 3.6 units
What is a line?A line is the distance between two points.
Analysis:
point a( -3,1) point b(2, -6) point translated b(-1, -8)
Distance ab = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }[/tex]
Distance ab = [tex]\sqrt{(-1--3)^{2} + (-8-1)^{2} }[/tex] = 9.21 units
Distance btb = [tex]\sqrt{(-1-2)^{2} + (-8- -6)^{2} }[/tex] = 3.6 units
In conclusion, the distance of b from a is 9.2 units and b from b is 3.6 units.
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Explain step by step how you find the product of 6x^2y^5 and 3x^2 - 8x + 2xy^2 + 4y^3
The final product is 18x⁴y⁵ - 48x²y⁵+12x³y⁷+24x²y⁸
What is a product ?
The product is result obtained when a number or an expression is multiplied by the other number.
The product of the given expression
6x²y⁵ and 3x²-8x+2xy²+4y³
6x²y⁵ (3x²-8x+2xy²+4y³)
Step 1 : To multiply each term in the bracket with the other expression
out of the bracket
6*3*x²*y⁵*x² - 6*8*x²*y⁵ +6x²y⁵ *2*x*y² + 6*4*x²y⁵ *y³
Step 2 : The like variables will be solved
18x⁴y⁵ - 48x²y⁵+12x³y⁷+24x²y⁸
This is the final product
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If f (x) = StartRoot one-half x minus 10 EndRoot + 3, which inequality can be used to find the domain of f(x)?
StartRoot one-half x EndRoot greater-than-or-equal-to 0
One-half x greater-than-or-equal-to 0
One-half x minus 10 greater-than-or-equal-to 0
StartRoot one-half x minus 10 EndRoot + 3 greater-than-or-equal-to 0
The inequality that represents the domain of the function is [tex]\frac 12x - 10 \ge 0[/tex]
How to determine the domain?The function is given as:
[tex]f(x) = \sqrt{\frac 12x - 10} + 3[/tex]
Set the radicand greater than or equal to 0
[tex]\frac 12x - 10 \ge 0[/tex]
Multiply through by 2
x - 20 ≥ 0
Add 20 to both sides
x ≥ 20
Hence, the domain of the function is x ≥ 20
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Can someone answer question 1-6
Answer:
Equation- a statement of the equality of two mathematical expressions Ex: 4 + 2 = 3 + 3Table of value- a set of ordered pairs usually resulting from substituting numbers into an equation (relation)Set of coordinate points- a set of numbers that show an exact point on a graph Ex: (2, -6)Graph- the collection of all points whose coordinates satisfy a given relationPattern- a repeated design of things like; numbers, shapes, colors, etc Ex: O $ X O $ X O $ XWord description- give a verbal description of its elements.Step-by-step explanation:
Hope I did it right, tell me if its wrong.
An arithmetic sequence has this recursive formula:
{ A1=5
{An= An-1-4
What is the explicit formula for this sequence?
A. an= (-1) + (n - 5)(-4)
B. an=5+ (n − 1)(-4)
C. an= 5+ (n-4)(-1)
D. an= (-4) + (n − 1)5
An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference. The correct option is B.
What is an arithmetic sequence?An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.
The explicit formula for any arithmetic series is given by the formula,
aₙ = a₁ + (n-1)d
where d is the difference and a₁ is the first term of the sequence.
Given A₁=5 and An= A₍ₙ₋₁₎-4, therefore we can write,
aₙ = a₁ + (n-1)d
Aₙ= 5+(n-1)(-4)
Hence, the correct option is B.
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The figure shows two identical metal bars are different temperatures. What is the
coefficient of linear expansion for the metal from which the bars are made?
(A) 1.6 × 10 (*C).¹
(B) 1.4 x 10
(*C)-¹
L₁ - 1.000 m
42-1.001 m
(C) 1.2 x 10-5 (°C)-¹
(D) 1.1 x 10 (C)-¹
T₁=0.0°C
T₂-70.0°C
ut.
luce
The coefficient of thermal expansion of the metal will be 1.4 x 10⁻⁵ °c.
What is thermal expansion?Every material has its property of contraction or expansion by the change of temperature. The expansion and contraction of any material are indicated by a coefficient this coefficient is called the coefficient of thermal expansion.
Here we have the following data:-
l₁= 1.000 m
l₂ = 1.001 m
Δ = 70° C
The formula for calculating the coefficient of linear expansion will be:-
[tex]\alpha =\dfrac{\Delta l}{\Delta t\times l}[/tex]
By putting the values we will get the answer.
[tex]\alpha=\dfrac{0.0001}{70\times 1}= 1.4\times 10^{-5}[/tex]
Therefore the coefficient of thermal expansion of the metal will be 1.4 x 10⁻⁵ °c.
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What does x= please help
The value of x is 8
This question is a proportion. To solve it, let's assemble it as follows:5 = 4
10 x
Now, just multiply in the form of a cross. Then, let's split the terms:5 . x = 10 . 4
5x = 40
x = 40 ÷ 5
x = 8
So, the result of x will be 8
(08.05 LC)The histogram shows the number of prizes won by different numbers of students at a sports competition. Which of the following statements is correct regarding the number of students and the number of prizes won? A histogram titled Prizes Won is shown. The horizontal axis is labeled Number of Prizes with bins 0 to 3, 4 to 7, 8 to 11, and 12 to 15. The vertical axis labeled Students with values from 0 to 10 at intervals of 1. The first bin goes to 3, the second goes to 6, the third goes to 1, and the last goes to 9.
Answer:
It is C.
Step-by-step explanation:
First thing you would do is go through all the information and read the options then what you would do is see the labels and its will try to throw you off at A. saying that its Prizes instead of students that has won the prizes so there for
C. Six prizes were won by 4, 5, 6, or 7 students.
is your answer
The inverse of f(x)= 2x + 3 is written:
Answer:
It should be x-3/2 (also written as "(x-3)÷2")
Step-by-step explanation:
y=2x+3
switch the y and x
x=2y+3
solve for y
x/2=y+3
x-3/2=y
If you graph these two functions you will see that y=2x+3 give the points (-1.5,0) and (0,3) and x-3/2 give (0,-1.5) and (3,0). because you've switched the x number to the y number you've "inversed" it
Find the value of each variable.
Please help
Step-by-step explanation:
a is the interior angle of the 2 opposing arc angles. the interior angle is the mean value between the 2 arc angles.
a = (145 + 45)/2 = 190/2 = 95°
b is the simply the supplementary angle to a (meaning together they are 180°, because the sum of all angles around a single point on one side of a line is 180°).
b = 180 - 95 = 85°
You owe 3 of your friends $15 dollars each. Before you pay your friends back, you
have $52. How much money do you have after paying your friends back?
Answer:
$7
Step-by-step explanation:
Since you have to pay 3 of your friends $15 each, you would multiply 15 by 3 and get 45. Then you would subtract that from 52 and you would get $7.
True or False?
A square can be similar to a triangle since a square is composed of two triangles.
When Ronald goes to BIG Burgers, he orders a sandwich and a side order. For the
Answer:
true is the answer not hard question
Which list correctly orders A, B, and C from least to greatest when A=171, B = -6, and C=1-51?
A, B, C
B, C, A
C, B, A
A, C, B
In 1997 the U.S. population was approxiamately 266,667,000 people. At the rate of 440 prisoners per 100,000 population, about how many prisoners were inthe system
Answer:
Around 1.2 million
Step-by-step explanation:
If we multiply 266,667,000 by 440/100,000 we get about 1,173,334 which we can round to about 1.2 million
X^2-6x+5=0 solve with quadratic formula
Answer: x1 = 5
x2 = 1
Step-by-step explanation:
1. Identify the coefficients
2. Move the constant to the right side of the equation and combine
3. Complete the square
4. Solve for x
Answer:
x = 5 and 1
Step-by-step explanation:
[tex]x^2-6x+5=0\\x_{1,\:2}=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:1\cdot \:5}}{2\cdot \:1}\\x_{1,\:2}=\frac{-\left(-6\right)\pm \:4}{2\cdot \:1}\\\rightarrow x_1=\frac{-\left(-6\right)+4}{2\cdot \:1},\:x_2=\frac{-\left(-6\right)-4}{2\cdot \:1}\\\\\frac{-\left(-6\right)+4}{2\cdot \:1}\\\\=\frac{6+4}{2\cdot \:1}\\\\=\frac{10}{2\cdot \:1}\\\\=\frac{10}{2}\\\\=5\\\\\\\frac{-\left(-6\right)-4}{2\cdot \:1}\\\\=\frac{6-4}{2\cdot \:1}\\\\=\frac{2}{2\cdot \:1}\\\\=\frac{2}{2}\\\\=1[/tex]
the length of nicks garden is equal to its width. Nick is going to enlarge his garden by making each side 20% longer.How much will the area of the garden increase
Answer:
44%
Step-by-step explanation:
Existing garden: L*W, where L and W are the length and width (We'll assume meters, but it can be any other linear measurement, such as miles, cm, or feet, etc.).
Area, A1 = L*W
New Area, A2 = (1.2L)*(1.2W)
A2 = (1.2)*(1.2)*(L*W)
Since L*W = A1, we can write A2 = 1.44*A1
New Area = 1.44 the original area, a 44% increase.
PLEASE HELP ASAP
What is the missing statement for the sixth step in the proof below?
Answer:
C
Step-by-step explanation:
The last reasoning is the side angle side theorem. In the whole proof, there is no mention of an angle. So the answer has to involve prooving that the angle in between the two sides that have been proven similar is the same in both traingles. This is best accomplished by statement C.
8. Which of these is the primary reason for the extinction of a species?
loss of habitat
overhunting
O pollution
Osudden environmental changes
Answer:
my bet would be d)
Step-by-step explanation:
ur asking math students btw
What is the x and y intercept of y=1/3x-2, y=12-6x, and y=3x-7? Please show work!
Answer:
y = 1/3x - 2:
y - intercept: - 2x - intercept: 6y = 12 - 6x:
y - intercept: 12x - intercept: 2y = 3x - 7:
y - intercept: -7x - intercept: 7/3Step-by-step explanation:
Hello!
Slope Intercept FormThe slope-intercept form of a line is [tex]y = mx + b[/tex]
y = output, ordinatem = slopex = input, abscissab = y-intercepty = 1/3x - 2The y-intercept is the "b" value of the line, given as -2.
To find the x-intercept, we simply replace the y-value with 0:
0 = 1/3x - 22 = 1/3x6 = xy - intercept: - 2
x - intercept: 6
____________________________________________________
y = 12 - 6x
You can rearrange the equation, y = -6x + 12, to find the y-intercept: 12.
Solving for the x-intercept (remember, replace y with 0):
0 = -6x + 12-12 = -6x2 = xy - intercept: 12
x - intercept: 2
____________________________________________________
y = 3x - 7Simply take the "b" value, -7, to find the y-intercept of -7.
Solve for the x-intercept:
0 = 3x - 77 = 3xx = 7/3y - intercept: -7
x - intercept: 7/3
Additional Note:
You can also solve for the y-intercept by replacing x with 0. This method can be used for any interests, just plug in the opposite variable from what you are solving for with 0.
The proof is that the x-intercept is the value when the y = 0, the x-axis. You can plug in 0 for y to solve for x. Similarly, when solving for the y-intercept, you plug 0 for x as the y-axis is at x = 0.
Please help and thanks
Choose the correct answer
2x>12x and 7x<14
Answer:
C - x < -6 and x < 2
Step-by-step explanation:
2x ">" -12 and 7x < 14. with negative numbers, the bigger the number the less it is. -12 < -6 because negative numbers work the opposite way that positive numbers do. I hope this helps you!!!!
Find the area and volume of a 11 inch cube (pls write do the equation in steps)
Answer:
1331 inches cubed
Step-by-step explanation:
V=LHW
since it is a cube, the length, height, and width will all be the same; 11 inches. You have to multiply 11 by 11 by 11, which equals 1331.
Hope this helped!
A flower pot hangs from a brace. △MNQ and △MNP form the brace what is the value of x?
The value of x from the given triangle formed by the pot hanging from a brace is; x = 50°
How to find the missing angle in a triangle?
We are given from the diagram that;
∠NMP = 110° and ∠NPM = 30°
Sum of angles in a triangle is 180°.
Thus;
∠MNP = 180 - (110 + 30)
∠MNP = 40°
Thus;
x = 90 - 40
x = 50°
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AMSWER ASAP PLEASE PLEASE PLEASE
Answer:
(2,14)
Step-by-step explanation:
so i solved this with substitution but there are other methods to solve this!
equation 1 : y = -x + 16
equation 2 : y = x + 12
solve for y in equation 1 !!
y = -x + 16
(add x on both sides)
y + x = 16
(subtract y on both sides)
x = -y + 16
equation 1 now equals : x = -y + 16
substitute equation 1 into equation 2 :)
y = (-y + 16) + 12
(add 16 + 12)
y = -y + 28
(add y on both sides)
2y = 28
(divide 2 on both sides)
y = 14
now to solve for x you can insert y !
you can use equation 1 or equation 2 to solve for x.
i'm using equation 2 :
y = x + 12
(14) = x + 12
(subtract 12 on both sides)
x = 2
therefore, the answer is (2, 14).
hope this helps :p
Susan and five of her friends enjoyed dinner at her favorite restaurant. They
split the bill evenly among themselves, and each person paid $11.75. How
much was the total bill?
$= 0.1
Answer here
Factor 60-36w60−36w60, minus, 36, w to identify the equivalent expressions.
Answer: 60( 1 - 72)
Step-by-step explanation: i think it might be right so heres a proof
Solve the inequality
x² + 6x + 8 <0
Answer:
look above
Step-by-step explanation:
hope it hepls
Probability and statistics please help me out
Answer:
first option
Step-by-step explanation:
1/7
I hope this is correct...
Simplify 4 + (-3) - 2 times (-6)
Step-by-step explanation:
[tex] = 4 + ( - 3) - 2 ( - 6)[/tex]
here ( + ) × ( - ) = ( - )
[tex] = 4 - 3 + 12[/tex]
[tex] = 4 + 12 - 3[/tex]
[tex] = 16 - 3[/tex]
[tex] = 13[/tex]
The correct result of this simplification is 13
To solve this question, we'll just apply the rule of signs - and then we'll calculate the operations.
- In the sign rule - when both signs are equal, the result will be positive. If the signs are different, the result is negative.
- ( - ) = ++ ( + ) = +- ( + ) = -+ ( - ) = -Resolution4 + ( - 3 ) - 2 · ( - 6 )
4 - 3 - ( - 12 )
4 - 3 + 12
1 + 12
13
Therefore, the alternative value will be 13