Determine the solution for each equation, identify the solution on the graphs in right solution, in terms of their respective differences from the axis of symmetry?
Answers
According to the given question information equation: f(x) =\(x^2\)- 1 the solutions for f(x) are x = -1 and x = 1.
Difference from the axis of symmetry: For x = -1, the difference from the axis of symmetry x = 0 is -1 unit to the left. For x = 1, the difference from the axis of symmetry x = 0 is 1 unit to the right.
Equation: g(x) = \(x^2\) + 3
since\(x^2\) is always non-negative, there are no real solutions for this equation.
The graph of g(x) = \(x^2\) + 3 does not intersect the x-axis.
Difference from the axis of symmetry: Since there are no real solutions for this equation, there are no differences from the axis of symmetry.
Equation: h(x) = \(x^2\)
the solutions for h(x) are x = 0.
Difference from the axis of symmetry: For x = 0, the difference from the axis of symmetry x = 0 is 0 units.
In terms of the graphs, the graph of f(x) =\(x^2\)- 1 will be symmetric with respect to the y-axis, while the graphs of\(g(x) = x^2 + 3 \\ and \\h(x) = x^2\) will be symmetric with respect to the x-axis. The solutions x = -1 and x = 1 for f(x) will be 1 unit away from the axis of symmetry x = 0, on the left and right sides respectively.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=).
For example, the argument "2x + 3 = 9" asserts that the phrase "2x +3" equals the number "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true.
Let's find the solutions for each equation and identify their differences from the axis of symmetry.
Equation: f(x) =\(x^2\)- 1
Axis of symmetry: The axis of symmetry for a parabola in the form \(y = ax^2 + bx + c\)is given by x = -b/2a. In this case, a = 1 and b = 0, so the axis of symmetry is x = 0.
Solution: Setting f(x) = 0, we get\(x^2 - 1 = 0\). Solving for x, we have:
\(x^2 - 1 = 0\\x^2 = 1\)
x = ±√1
So the solutions for f(x) are x = -1 and x = 1.
Difference from the axis of symmetry: For x = -1, the difference from the axis of symmetry x = 0 is -1 unit to the left. For x = 1, the difference from the axis of symmetry x = 0 is 1 unit to the right.
Equation: g(x) = \(x^2\) + 3
Axis of symmetry: Similar to the previous equation, the axis of symmetry is x = 0.
Solution: Setting g(x) = 0, we get\(x^2 + 3 = 0.\)However, since\(x^2\) is always non-negative, there are no real solutions for this equation.
The graph of g(x) = \(x^2\) + 3 does not intersect the x-axis.
Difference from the axis of symmetry: Since there are no real solutions for this equation, there are no differences from the axis of symmetry.
Equation: h(x) = \(x^2\)
Axis of symmetry: Again, the axis of symmetry is x = 0.
Solution: Setting h(x) = 0, we get\(x^2\) = 0. Solving for x, we have:
\(x^2\)= 0
x = ±√0
So the solutions for h(x) are x = 0.
Difference from the axis of symmetry: For x = 0, the difference from the axis of symmetry x = 0 is 0 units.
In terms of the graphs, the graph of f(x) =\(x^2\)- 1 will be symmetric with respect to the y-axis, while the graphs of\(g(x) = x^2 + 3 \\ and \\h(x) = x^2\) will be symmetric with respect to the x-axis. The solutions x = -1 and x = 1 for f(x) will be 1 unit away from the axis of symmetry x = 0, on the left and right sides respectively.
The solutions x = 0 for g(x) and h(x) will be exactly on the axis of symmetry. So, on the graphs, the solutions will be at -1 and 1 units from the axis of symmetry for f(x), and at 0 units from the axis of symmetry for g(x) and h(x).
g(x) does not have any real solutions, as mentioned earlier, so it will not intersect the x-axis on the graph. The graph of h(x) will intersect the x-axis at x = 0, since x = 0 is a solution to the equation h(x) =\(x^2.\)
Overall, the graph of f(x) will be shifted 1 unit to the right of the graph of h(x), with both being symmetric with respect to the y-axis, while the graph of g(x) will be symmetric with respect to the x-axis and not intersect the x-axis.
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Related Questions
Given f(x) = 2x2 − 3x + 7, find f(2.5)
Answers
Answer:
12
Step-by-step explanation:
Given that,
f(x) = 2x² - 3x + 7
To find the value of f ( 2.5 ), replace x with 2.5 and solve the equation.
Let us solve it now.
f(2.5) = 2(2.5)² - 3×2.5 + 7
f(2.5) = 12.5 - 7.5 + 7
f(2.5) = 12
Answer:
\(f(x) = 2 {x}^{2} - 3x + 7 \\ f(2.5) = 2 {(2.5)}^{2} - 3(2.5) + 7 \\ f(2.5) = 12.5 - 7.5 + 7 \\ \boxed{f(2.5) = 12}\)
f(2.5) = 12 is the right answer.Enter the number that belongs in the green box
Answers
The angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.
To find the measure of the angle between the sides measuring 4 and 5 in an obtuse triangle with side lengths 4, 5, and 7, we can use the Law of Cosines. The Law of Cosines states that in a triangle with side lengths a, b, and c, and an angle opposite to side c, the following equation holds:
\(c^2 = a^2 + b^2 - 2ab*cos(C)\)
In this case, we have side lengths a = 4, b = 5, and c = 7. We want to find the angle C, which is opposite to side c. Substituting these values into the Law of Cosines, we get:
\(7^2 = 4^2 + 5^2\)- 2(4)(5)*cos(C)
49 = 16 + 25 - 40*cos(C)
49 = 41 - 40*cos(C)
40*cos(C) = 41 - 49
40*cos(C) = -8
cos(C) = -8/40
cos(C) = -0.2
To find the measure of angle C, we can take the inverse cosine (arccos) of -0.2:
C = arccos(-0.2)
Using a calculator, we find that C ≈ 101.54 degrees.
Therefore, the measure of the angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.
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30% of what number is 7.5??
Answers
30% of a number is 7.5 can be written as an equation.
30% can be rewritten as 0.30, or even 0.3.
a number can be written as "x".
So far, we have 0.3x.
"is" is a keyword for "equal".
0.3x=
It says "is 7.5".
0.3x=7.5
We can solve this equation.
0.3x=7.5
/0.3 /0.3
x=25
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hope it helps
I REALLY NEED HELP MY GRADES GO IN TONIGHT AND I CANT SOLVE THIS I NEED A REAL ANSWER I WILL CHECK BEFORE GIVING POINTS!!!!!!!!!!!!!!!!!
Answers
Answer:
it's "whats shaking"
Step-by-step explanation:
Answer:
k=8.
n=12
a=29
h=5
i=297
g=89
Find the measure of the angle indicated in bold.
16)
x + 142
x + 62
Answers
Answer:
pls attatch a pic so i can help u out :)
Step-by-step explanation:
Hans is performing an experiment examining how salt affects the speed at which water freezes. He fills four equally sized containers with the same amounts of water. Then, in three of the containers, he stirs in varying amounts of salt. The fourth container remains plain water.
Hans places all four of the containers in the same freezer and checks the containers every five minutes, recording when the water in each container freezes solid.
In this situation, what do Hans’s time measurements represent?
A.
the response variable
B.
the control group
C.
the response group
D.
the explanatory variable
Answers
Answer:
Answer B.
Because we know He's checking the experiment every 5 minutes.
In a controlled lab environment some organisms exhibit growth over a specific period. Suppose a certain organism starts out weighing 16 mg and grows to 46 mg over a 5 hour period.
Find a linear model (equation of line) that describes the growth of the organism for the time period given.
Hint x is the number of hours and y is the weight
Answers
A linear model (equation of line) that describes the growth of the organism for the time period given is y = 46/5(x) + 16.
What is the slope-intercept form?Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.Based on the information provided, we have the following equation that represents the relationship between the number of hours and the weight;
y = mx + c
y = 46/5(x) + 16
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i need help on these please
Answers
The cost of gas is proportional to the volume of gas because a constant rate of $3.15 to 1 gallon of gas.
How to calculate the constant rate of gas?From the given table;
The volume of the first gas Layla bought = 3 gallons.
The cost of the 3 gallons = 9.45
Therefore the cost of 1 gallon = ?
That is:
3 gallons = $9.45
1 gallon = X
Make X the subject of formula:
X = 9.45/3 = $3.15
Therefore, the cost of 11 gallons of gas would be = 11×3.15 = $34.65. This is because the cost of 1 gallon would be = $3.15.
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Please help solve this for me
Answers
Answer:
i believe the answer would be option D
Step-by-step explanation:
find two whole numbers that are closest to v42. explain your reasoning
Answers
Answer:
The numbers are 6 and 7.
Step-by-step explanation:
4² = 16
5² = 25
6² = 36
7² = 49
√36 = 6
√42 = ?
√49 = 7
The numbers are 6 and 7.
Define fraction (in your own words)
Think back to the last time you needed to use fractions, for example a ruler or measuring tape. Discuss how you used it.
Explain the steps of adding or subtracting unlike fractions. Using a ruler, measure the heights of two different-size cans of food and show how to calculate the difference in heights
Answers
A number that is divided by another, like 1 divided by 2 is one half, it is a fraction of a number.
All you need the photo
Answers
The average rate of change of h(t) = -16t ² + 40t + 4 between t = 0 and t = 2 is
(h (2) - h (0)) / (2 - 0) = ((-16×2² + 40×2 + 4) - (-16×0² + 40×0 + 4)) / 2
… = ((-64 + 80 + 4) - 4) / 2
… = 16 / 2
… = 8
h(t) is measured in feet, so the average rate of change is measured in feet per second, so it's 8 feet per second.
If the area of a square inscribed in a circle is
25, what is the area of the circle?
Answers
The area of a square inscribed in a circle is 25, then the area of the circle is 25π/2 or approximately 39.27 square units.
To solve this problem, we can use the relationship between the area of a square inscribed in a circle and the area of the circle itself.
When a square is inscribed in a circle, the diagonal of the square is equal to the diameter of the circle. Let's assume that the side length of the square is 's' and the radius of the circle is 'r'.
We are given that the area of the square is 25, so we can find the side length of the square:
Area of square = \(s^2 = 25\)
Taking the square root of both sides, we get:
s = √25 = 5
Since the diagonal of the square is equal to the diameter of the circle, we can find the diameter of the circle:
Diagonal = Diameter = s√2 = 5√2
The radius of the circle is half the diameter, so:
Radius = 5√2 / 2 = (5√2)/2
Now, we can calculate the area of the circle using the formula:
Area of circle = \(\pi r^2\)
Substituting the value of the radius, we get:
Area of circle = π((5√2)/\(2)^2\) = π(25/2) = 25π/2
Therefore, the area of the circle is 25π/2 or approximately 39.27 square units.
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Find the measure of the supplement of a 10° angle.
Answers
Answer:
170°
Step-by-step explanation:
180 - 10 = 170
Which expressions are equivalent to 6 + 12x?
Select each equivalent expression.
Answers
Answer:
2 (3 + 6x), 3 (2 + 4x) and 6 (1 + 2x)
Step-by-step explanation:
Given the expression 6 + 12x.
The following functions are equivalent;
Factoring out common number;
For 2;
2(3) + 2(6x)
2 (3 + 6x)
Factoring out 3;
3(2) + 3(4x)
3 (2 + 4x)
Factoring out 6;
6(1) + 6(2x)
6 (1 + 2x)
Hence the possible equivalent expressions are 2 (3 + 6x), 3 (2 + 4x) and 6 (1 + 2x)
Pls help this is for a grade and don’t give the wrong answers
Answers
Answer:
1. B
2. A
3. E
4. C
5. D
Step-by-step explanation:
yes sure, ??
2:C
3:A
4:E
5:B
I’m a math teacher here you go , Glad i could help
3. Choose the item that has measurable volume,. answer choices are.
Answers
right option is water bottle, because we always find the volume for solid objects or objects that can be containers
Sketch the function of f(x)=x^(3)-5x^(2)
Answers
The cubic function can be graphed using the function behavior and the points.
x 0 1 2 3 4
y 0 −4 −12 −18 −16
How to estimate the function of \($f(x)=x^{3}-5x^{2}\)?Put x = 0.
Replace the variable x with 0 in the expression.
\(f(0)=(0)^3-5(0)^2\)
Raising 0 to any positive power yields 0.
f(0) = 0 − 5⋅0
f(0) = 0
y = 0
Put x = 1.
Replace the variable x with 1 in the expression.
\(f(1)=(1)^3-5(1)^2\)
f(1) = 1− 5⋅1
f(1) = −4
y = −4
Put x = 2.
Replace the variable x with 2 in the expression.
\(f(2)=(2)^3-5(2)^2\)
\(f(2)=8-5(2)^2\)
f(2) = 8 − 5⋅4
f(2) = −12
y = −12
Put x = 3.
Replace the variable x with 3 in the expression.
\(f(3)=(3)^3-5(3)^2\)
f(3) = 27 − 45
f(3) = −18
y = −18
Put x = 4.
Replace the variable x with 4 in the expression.
\(f(4)=(4)^3-5(4)^2\)
\(f(4)=64-5(4)^2\)
f(4) = 64 − 5 ⋅16
f(4) = 64 − 80
f(4) = −16
y = −16
The cubic function can be graphed using the function behavior and the points.
x 0 1 2 3 4
y 0 −4 −12 −18 −16
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Determine if the sequence below is arithmetic or geometric and
determine the common difference / ratio in simplest form.
11, 6, 1, ...
This is
sequence and the
is
equal to
Answers
The sequence 11, 6, 1 .... is an example of an Arithmetic Sequence. The common difference in this sequence will be d = -5.
Arithmetic Progression
It is a mathematical sequence in which all the consecutive terms in a sequence are separated from each other by a common difference throughout the whole sequence i.e. every term is separated from the previous term by a difference which is called a common difference throughout the sequence.
In the given situation, the sequence is 11, 6, 1....
to find the common difference we need to subtract two consecutive terms to know the difference between them.
In this sequence, a₁ = 11 and a₂ = 6. We know Common differences can be represented by d = a₂ - a₁. Putting values we get :
=> d = 6 - 11 => d = -5
Hence, here is a common difference, d = -5 and it is an example of an Arithmetic Sequence.
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A spinner with 12 equally sized slices is shown below. (The 12 slices are red.) The dial is spun and stops on a slice at random. What is the
probability that the dial stops on a red slice?
Write your answer as a fraction or a whole number.
Answers
Answer:
100/100
Step-by-step explanation:
XD
Find the value of the expression if x=13 and Y = -8
|x+y|=
Answers
Answer:
5
Step-by-step explanation:
13 + (-8) = 5
Determine if the sequence below is arithmetic or geometric and determine the
common difference / ratio in simplest form.
11, 6, 1, ...
Answers
Answer:
Arithmetic, common difference = -5
Step-by-step explanation:
11 - 6 = 5
6 - 1 = 5
Your friend tells you she has 7 coins in her hand (just pennies, nickels, dimes and quarters). If you guess how many of each kind of coin she has, she will give them to you. If you guess randomly, what is the probability that you will be correct?
Provide an explanation for the formula used.
Answers
The probability that the person will be correct based on the information will be 0.00833.
How to solve probabilityIn this case, the total coins are 7 and the types of coins are 4. Therefore, the combination will be:
= 10! / 3!(10 - 3)!
= 10! / 3!7!
= (10 × 9 × 8) / (3 × 2)
= 120
Therefore, the probability will be:
= 1/120 = 0.00833
In conclusion, the correct option is 0.00833.
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how to work this fraction 4/11+5/22+3/44
Answers
Answer:
29/44
Step-by-step explanation:
\(\frac{4}{11} +\frac{5}{22} +\frac{3}{44} =\\\)
-find the common denominator
\(\frac{4*4}{4*11} + \frac{2*5}{2*22} +\frac{3}{44} =\)
\(\frac{16}{44} +\frac{10}{44} +\frac{3}{44} =\)
-add the fractions and solve
\(\frac{16+10+3}{44} =\)
\(\frac{29}{44}\)
Bella needs to paint a logo made using two right triangles. The dimensions of the logo are shown below. What is the area of the two triangles that need to be painted?
Dimensions:
Triangle 1: 6 by 2
Triangle 2 5 by 9
Answers
Answer:
It would be 28.5. First, you would find the area of the smaller triangle by using the formula a=.5bh (area=.5xbasexheight) and then when you get that, you should get 6. Then, you do the same for the larger triangle and you should get 22.5. Then, 22.5 + 6 = 28.5, giving you that answer.
Step-by-step explanation:
4. For his garden, Clay has a mixture of 12
white corn seeds, 24 yellow corn seeds, and
16 bicolor corn seeds. If he reaches for a
seed without looking, what is the probability
that Clay will plant a bicolor corn seed first?
Answers
Answer:
I believe about 30.8%
Find the length of the line joining A (3,5) and B (1,3)
Answers
Answer:
2√2 units.
Step-by-step explanation:
To find the length of the line joining points A(3, 5) and B(1, 3), we can use the distance formula. The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Substituting the coordinates of points A and B into the formula, we have:
d = sqrt((1 - 3)^2 + (3 - 5)^2)
= sqrt((-2)^2 + (-2)^2)
= sqrt(4 + 4)
= sqrt(8)
= 2sqrt(2)
Therefore, the length of the line joining points A and B is 2√2 units.
Measurement of angle q
Answers
Answer:
34º
Step-by-step explanation:
The sum of the angles in a triangle is 180º
m∠Q = 180 - 90 - 56
m∠Q = 34º
Three apples (x) plus two
oranges (y) costs $16.
Five apples plus two
oranges costs $24. Hov
muon do each apples and
oranges cost?
Answers
Identify any angles of rotation that create symmetry
Answers
The angle of rotation that create symmetry in the image is 120°.
We are given an image.
We need to find the angles of rotation that creates this symmetry.
We know that the whole plane is divided into 12 parts.
That is 360° is divided into 12 parts.
So, we get that:
1 part = 360° / 12 = 30°
Now, we can also see that, from rotation to one quadrant to another, the image travels 4 parts of the plane.
So, angle of rotation will be = 4 × 30°
angle of rotation = 120°
Therefore, we get that, the angle of rotation that create symmetry in the image is 120°.
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