Answers
We are looking for the functions which are symmetric with respect to the y-axis.
This should be an even function with the vertex on the y-axis.
All functions of odd degree or restricted domain or range are excluded:
Lines, cubic functions, square root or exponent functions.Possible symmetric functions:
Quadratic, 4th degree etc., absolute value, circles with center on the y-axis.See the attached. Those with red cross are excluded, with green mark are correct choices.
Answer:
[tex]y=-7x^2[/tex]
[tex]y=8x^2-3[/tex]
Step-by-step explanation:
Functions are symmetric with respect to the y-axis if for every point (a, b) on the graph, there is also a point (-a, b) on the graph:
f(x, y) = f(-x, y)To determine if a graph is symmetric with respect to the y-axis, replace all the x's with (−x). If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the y-axis.
Therefore, any function that includes the term x² will be symmetric with respect to the x-axis since (-x)² = x².
[tex]\begin{aligned}&\textsf{Given}: \quad& y&=-7x^2\\&\textsf{Replace $x$ for $(-x)$}: \quad& y&=-7(-x)^2\\&\textsf{Simplify}: \quad &y&=-7x^2\\\end{aligned}[/tex]
Therefore, since the resultant expression is equivalent to the original expression, it is symmetric with respect to the y-axis.
[tex]\begin{aligned}&\textsf{Given}: \quad& y&=8x^2-3\\&\textsf{Replace $x$ for $(-x)$}: \quad& y&=8(-x)^2-3\\&\textsf{Simplify}: \quad &y&=8x^2-3\\\end{aligned}[/tex]
Therefore, since the resultant expression is equivalent to the original expression, it is symmetric with respect to the y-axis.
Related Questions
A scientist invents a car that can travel for many hours without stopping for fuel. The
car travels around a track at 54 miles an hour for 24 hours. At the end of the 24
hours, how far has the car traveled?
o 1,286 miles
o 1, 296 miles
• 78 miles
• 1, 080 miles
Answers
Answer:
1,296 miles
Step-by-step explanation:
to answer this question, we have to apply the next formula:
Distance = Speed rate x time
speed rate = 54 miles per hour
time = 24 hours
Replacing with the values given and solving for D (distance)
D = 54 mph x 24 h = 1,296 m
The car traveled 1,296 miles
Hope this helped! :)
Please help I was sick and missed out on class.Thank you
Answers
Answer: [tex]\frac{0}{24}[/tex]
Step-by-step explanation:
The slope is [tex]\frac{y_{1}-y_{2}}{x_{1}-x_{2}}[/tex], or reverse: [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
If we substitute, we get that [tex]\frac{2-2}{6-(-18)}[/tex].
Simplify to get [tex]\frac{0}{24}[/tex].
Question 2(Multiple Choice Worth 2 points)
(Scientific Notation LC)
Write 2,850,000,000 in scientific notation.
A. 2.85 x 109
B. 285 x 107
C.285 x 10-7
D. 2.85 x 10-9
Answers
The value of 2,850,000,000 in scientific notation is 2.85*[tex]10^{9}[/tex], so option A is correct.
Given:
= 2,850,000,000
= 2850,000 * [tex]10^{3}[/tex]
= 2850 * [tex]10^{3}[/tex] * [tex]10^{3}[/tex]
= 2850 * [tex]10^{6}[/tex]
= 285*[tex]10^{7}[/tex]
= 28.5*[tex]10^{8}[/tex]
= 2.85*[tex]10^{9}[/tex]
Therefore the value of 2,850,000,000 in scientific notation is 2.85*[tex]10^{9}[/tex], so option A is correct.
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The equation y=2x represents a proportional relationship.
Select the true statement.
The graph is a curve
The y-intercept is 2
The slope is 2
The slope is 0
Answers
The slope of the line is 2 whose equation is given by y = 2x.
The given equation is y = 2x
The general equation of the line is given by
y = mx +c where m is the slope and c is the intercept of the line.
The slope of line a line's steepness can be determined by looking at its slope. The slope is calculated mathematically as "rise over run."
The intercept of the line is a point on the y-axis known as an intercept is where the line's slope passes.
On Comparing the given equation with the general equation, we have:
m = slope = 2
Thus the slope of the line is 2.
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The following data are for Jay Robert Company. Breakeven sales revenue $250,000 Fixed costs $150,000 Calculate the sales revenue necessary to generate net income of $100,000. $618,667 $533,333 $625,000 $400,000 $416,667
Answers
The sales revenue necessary to generate net income of $100,000 is: $416,667.
How to find the sales revenue?Using this formula to find the sales revenue
Sales revenue = Sales revenue + (Sales revenue × Net income / Fixed costs)
Let plug in the formula
Sales revenue = $250,000 + ($250,000 × $100,000 /$150,000)
Sales revenue = $250,000 + ($250,000 ×0.6666666)
Sales revenue = $250,000 + $166,666.65
Sales revenue = $416,666.65
Sales revenue = $416,667 (Approximately)
Therefore the correct option is E.
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A 35-tooth gear on a motor shaft drives a larger gear having 63 teeth. If the motor shaft rotated at 900 rpm, what is the speed of the larger gear
Answers
If the motor shaft rotated at 900 rpm, the speed of the larger gear will be 100 rpm.
What is the ratio?
It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
it is given that, A 35-tooth gear on a motor shaft drives a larger gear having 63 teeth and the motor shaft rotated at 900 rpm.
The number of teeth on the smaller gear,n₂ = 35
The number of teeth on the larger gear,n₁ = 63
The gear ratio is obtained as,
n₁/n₂=63/35
n₁/n₂=9:5
If the motor shaft rotated at 900 rpm, The speed of the larger gear is,
=900 rpm / 9
=100 rpm
Thus, if the motor shaft rotated at 900 rpm, the speed of the larger gear will be 100 rpm.
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NO LINKS!! Please assist me with this problem Part 3m
If a and h are real numbers, find the following values for the given function
Answers
[ 9(a + h) - 3 - 9a + 3]/h =
9h /h = 9
Answer:
[tex]\textsf{(d)} \quad \boxed{9a+9h-3}[/tex]
[tex]\textsf{(e)} \quad \boxed{9a+9h-6}[/tex]
[tex]\textsf{(f)} \quad \boxed{9}[/tex]
Step-by-step explanation:
Given function:
[tex]f(x) = 9x - 3[/tex]
Part (d)
To find f(a + h), substitute x = a + h into the function:
[tex]\begin{aligned}\implies f(a+h)&=9(a+h)-3\\&=9a+9h-3\end{aligned}[/tex]
Part (e)
Find f(a) by substituting x = a into the function:
[tex]\implies f(a)=9a-3[/tex]
Find f(h) by substituting x = h into the function:
[tex]\implies f(h)=9h-3[/tex]
Therefore:
[tex]\begin{aligned}\implies f(a)+f(h)&=(9a-3)+(9h-3)\\&=9a-3+9h-3\\&=9a+9h-6\end{aligned}[/tex]
Part (f)
[tex]\begin{aligned}\implies \dfrac{f(a+h)-f(a)}{h}&=\dfrac{(9(a+h)-3)-(9a-3)}{h}\\\\&=\dfrac{9a+9h-3-9a+3}{h}\\\\&=\dfrac{9h}{h}\\\\&=9\end{aligned}[/tex]
please help this is due tomorrow
Write an equation that represents the difference in seed yield between beans without treatment and beans with treatment.
Answers
The equation that represents the difference in seed yield between beans without treatment and beans with treatment is (seed yield with treatments-seed yield without treatment) whose value will be 340.
According to the question,
We have the following information:
We have a diagram where seed yield is given.
Now, the required equation represents the difference in seed yield between beans without treatment and beans with treatment will be:
(seed yield with treatments-seed yield without treatment)
(300+310-270)
(610-270)
340
Hence, the equation that represents the difference in seed yield between beans without treatment and beans with treatment is (seed yield with treatments-seed yield without treatment) whose value will be 340.
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Can you help me please and explain I don’t get this. *slope*
Answers
Answer:-5/1
Step-by-step explanation:
down 5 and over 1
to get the slope, find a spot on the graph and then go 1 to the right and read how much the graph went up or down.
on 5) you see it did neither, so m=0
when the graph goes up, m is positive, when it goes down, m is negative.
so on graph 1, you have 2 dots.
you go 2 right, and 4 down. when the dots are not 1 apart (counting going right) then divide by the steps you went right.
4 divided by 2 is 2.
-> graph went down, slope for 1) is m = -2
graph 2) you go 2 right and 2 up, 2/2 = 1. you went up, so m is positive and m = 1 for this graph.
3) is undefined because it doesn't go anywhere when you go right, it's 100% vertical
4) m = -5 because you went 1 right and 5 down
5) you go 6 right between the dots and 4 down. m is negative because it went down, not up. so m = -(4/6)
A small town has two local high schools. High School A currently has 900 students and is projected to grow by 30 students each year. High School B currently has 750 students and is projected to grow by 45 students each year. Let AA represent the number of students in High School A in tt years, and let BB represent the number of students in High School B after tt years. Write an equation for each situation, in terms of t,t, and determine how many students would be in each high school in the year they are projected to have the same number of students.
Answers
After 10 years students in both schools are same.
Algebra is a branch of mathematics that uses mathematical expressions to represent problems. To form a meaningful mathematical expression, variables such as x, y, and z are combined with mathematical operations such as addition, subtraction, multiplication, and division. It teaches you how to solve a problem by following a logical path. As a result, you will have a better understanding of how numbers function and interact in an equation. You will be able to do any type of math better if you have a better understanding of numbers.
There are two high schools in a small town.
High school A has currently 900 students and is projects to grow by 30 students each year
Similarly
High school B has currently 750 students and is projected to grow by 45 students each year.
To find the equation for each situation in terms of t years.
also in how many years t' the number of students in both high schools would be same?
Given
The initial strength of school A = 900
the increasing rate of students = 30 students per year
i.e students in 1 year = 30
students in t years = 30t
Total students of school A after 't' years = 900+ 30t
⇒ A = 600+ 65t
The initial strength of school B = 750
increasing rate of students = 45 per year
i.e. student in 1 year = 45
⇒ student in 't' years = 45t
Total students of school B in 't' years = 950 + 30t
=> B=950+30t
Now to find no. of years 't' when students in both schools are the same i.e. A =B
⇒ 900+ 30t = 750 + 45t
⇒ 45t-30t = 900-750
⇒ 15t = 150
⇒t= 150 /15
⇒t=10
Therefore after 10 years, students in both schools are the same.
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What is the slope of a line perpendicular to the line whose equation is 5x-y=-7. Fully simplify your answer.
Answers
Answer:
-1/5
Step-b-1/5y-step explanation:
The rule for a perpendicular slope of a line is -1/s
In this case, we find the slope of the line first.
5x - y = -7
-y = -5x - 7
y = 5x + 7
The slope is 5, so -1/(5) is the slope of the perpendicular line.
select all coordinate pairs that could represent a solution to 3x - 2y = 12
Answers
The coordinate pairs that could represent the equation 3x - 2y = 12 are
( x₁ , y₁ ) = ( 2 , -3 )
( x₂ , y₂ ) = ( 4 , 0 )
( x₃ , y₃ ) = ( 0 , -6 )
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be A
3x - 2y = 12
Now , Substituting the values of x and y in the above equation , we get
a)
The coordinate pair ( 2 , -3 )
So , the equation becomes
3 ( 2 ) - 2 ( -3 ) = 12
6 + 6 = 12
12 = 12
Therefore , the coordinate pair satisfies the given equation
b)
The coordinate pair ( 4 , 0 )
So , the equation becomes
3 ( 4 ) - 2 ( 0 ) = 12
12 = 12
Therefore , the coordinate pair satisfies the given equation
c)
The coordinate pair ( 0 , -6 )
So , the equation becomes
3 ( 0 ) - 2 ( -6 ) = 12
12 = 12
Therefore , the coordinate pair satisfies the given equation
Hence , the coordinate pairs that satisfies the the equation 3x - 2y = 12 are
( 2 , -3 ) , ( 4 , 0 ) and ( 0 , -6 )
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Kaitlyn has a least five purses (how to i solve that with signs and number?)
Answers
The solution when Kaitlyn has at least five purses using signs and number is N ≥ 5
How to write expressions with inequalities?Equations and inequalities are both mathematical sentences formed by relating two expressions to each other.
When two expressions are equal, we use the equal sign ( = ). But when we are trying to compare two values or expressions, we use the inequality signs like greater than (>), less than (<), greater than or equal to ( ≥ ) and less than or equal to (≤)
Given that: Kaitlyn has at least five purses
In order to solve this problem with signs and number, you will make use of the inequality that explains the situation:
Let the number of purses be N
Kaitlyn having at least five purses means she has 5 purses or more. Using inequality, the number of purses is greater than or equal to 5. Thus:
N ≥ 5
Therefore, the solution using signs and number is N ≥ 5
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Which represents Newton's second law?
Ov=d/t
a = F/m
OF=0
OF = m/v
Answers
a = F/m
because F = ma
if Jonny had 674
appes he gave away 379 how much does he have now?
Answers
Answer:
295
Step-by-step explanation:
he has 379 less apples now so you have to subtract 379 from 674
674 - 379 = 295
Write an equation that has the given solutions. 1, -1
Answers
Answer:
(x+1)(x-1)
Step-by-step explanation:
The solutions 1 and - 1 is given when
x = 1 or x = - 1
hence; (x - 1) = 0 or (x + 1) = 0
(x - 1)(x + 1) = 0
x² -1 = 0
Mark as brainliest answer please. Thanks
it takes Barry 634 hours to detail a car. If he worked 81 hours during the week, how many cars did he detail?
Answers
Answer:
He would have detailed 16 cars.
Step-by-step explanation:
912/57=16
" I hoped I helped you matey : - ) "
Which parts of the triangles are congruent in the image?
Answers
Answer:
B, C, E
Step-by-step explanation:
B is correct because it is written to the side and also because of the Definition of midpoint.
C is correct because HL and KI H and I are congruent just like L and K because of alternate interior angles.
E is correct because of the verticle angle theorum.
14. Four friends decide to share
equally 7 packs of baseball cards.
There are 8 cards in each pack.
Part A
How many cards does each
friend get?
Part B
Explain your strategy.
Answers
Answer:
Each gets 14 cards.
Step-by-step explanation:
7*8=56
56 Is the total amount of cards
56/4 equals 14
We divide 56 by 4 since 4 is the total number of friends.
Consider the equation equation v + 4 + v = 8. What is the resulting equation after the first step in the solution? Age Erde Sade IME 5 -y+4= 8 1 V 10-1950 LEIL DIE 35 Las 12 he will 1913DF0 HIS AG pale au vopse FINE E
Answers
The resulting equation after the first step in the solution is: 2v + 4 = 8.
What is an equation?In Mathematics, an equation is sometimes referred to as an expression and it can be defined as a mathematical expression which shows that two (2) or more thing are equal.
In this exercise, you're required to describe the steps that should be taken to find a solution to the given equation by solving for v. Therefore, the appropriate and required steps that should be used include the following:
Step 1: Rearrange the equation by collecting like terms.
(v + v) + 4 = 8
Step 2: Add the like terms together.
2v + 4 = 8
Step 3: Subtract 4 from both sides of the equation.
2v + 4 - 4 = 8 - 4
2v = 4
Step 4: Divide both sides of the equation by 2.
v = 4/2
v = 2.
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Complete Question:
Consider the equation v + 4 + v = 8. What is the resulting equation after the first step in the solution?
v +4 = 8 – v
v +4 = 8
4 + v = 8 – v
2v + 4 = 8
ahmad bought 2 books for 120 at a book fair. Another time he bought 4 books for 280 .wwrite an equation in standard form that represents. Ahmad spending with respect to the number of books purchased.
Answers
An equation in standard form is written as y = 80x - 40
How to write equation for books ahmad boughtLet the cost of books Ahmad bought be represented by m
let the flat cost by c (c reduction at the fair)
Information given in the question is interperted as
ahmad bought 2 books for 120 at a book fair
2m + c = 120
Another time he bought 4 books for 280
4m + c = 480
The required equation leads to 2 simultaneous equation with 2 unknown
2m + c = 120
4x + c = 480
solving the 2 equations gives
m = 80 and y = -40
representing the equation as 1 we have
y = mx + c
Definition of variables to suit the problem to be solved
y = Total cost
m = cost per book
x = number of books
c = flat cost
writing the equation
y = 80x - 40
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-5/6 times 1/8 please help
Answers
Answer:
(-5/48)
Step-by-step explanation:
-5 × 1 -5
------- × ------- = -------
6 × 8 48
Multiply the numerators together (top numbers) to get the new numerator
Multiply the denominators together (bottom numbers) to get the denominator.
I hope this helps!
What is the equation of the line?
y=-3x
y=3x
y=3x+1
y=4x
Answers
The equation of the given straight line is y = 3x.
We are given a graph. The graph shows a straight line. Several points are marked on the line in the graph. The coordinates of two such points are (1, 3) and (2, 6). We need to find the equation of the straight line.
The equation of the straight line can be found using the two-point form of a line. The equation is solved below.
(y - y1) = [(y2 - y1)/(x2 - x1)]×(x - x1)
(y - 3) = [(6 - 3)/(2 - 1)]×(x - 1)
y - 3 = 3(x - 1)
y = 3x - 3 + 3
y = 3x
Hence, the equation of the line shown in the graph is y = 3x.
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Simplify this equation:
[tex] {7}^{8} \times {7}^{3} \times {7}^{4} \div {7}^{9} \times {7}^{5} [/tex]
Answers
Answer:
7
Step-by-step explanation:
Exponent law:
[tex]\sf a^m * a^n = a^{m+n}\\\\\dfrac{a^m}{a^n}=a^{m-n}[/tex]
In exponents multiplication, when bases are same add the powers.
In exponents division, if bases are same subtract the powers.
[tex]\sf \dfrac{7^8*7^3*7^4}{7^9*7^5}=\dfrac{7^{8+3+4}}{7^{9+5}}[/tex]
[tex]\sf =\dfrac{7^{15}}{7^{14}}\\\\=7^{15-14}\\\\=7^1\\\\=7[/tex]
The curved surface area, A of a cone of height h and base radius r is π√h²+r².
Make h the subject of the formula.
Find the height of a cone of area 550 cm² and base radius 7 cm
Answers
The height of the cone is 580.36 cm.
The curved surface area of the cone is given by,
[tex]A = \pi \sqrt{h^{2} +r^{2} }[/tex]
Squaring both sides, we get :
[tex]A^{2} =\pi ^{2} (h^{2} +r^{2} )[/tex]
Now, it is given that the height of the cone is h,
The area of the cone = 550 [tex]cm^{2}[/tex]
And the radius of the cone = 7cm,
Putting these values in the given formula, we get,
[tex]A^{2} =\pi ^{2} (h^{2} +r^{2} )[/tex]
[tex]550^{2} = \pi ^{2} * ( h^{2} +7^{2} )\\[/tex]
3,36,875 = [tex]h^{2}+49[/tex]
[tex]h^{2}[/tex] = 3,36,875 - 49 = 3,36,826
h = 580.36 cm
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15 milliliters of pure drug are in 500 mL of solution. What is the percent strength of the solution?
Answers
When 15 milliliters of pure drug are in 500 mL of solution, the percent strength of the solution is
How to find the percent strength of the solution'information from the problem
15 milliliters of pure drug are in 500 mL of solution
the percent strength of the solution = ?
The question is a percentage problem, percentage deals with a fraction hundred and used as follows
= volume of pure drug / volume of solution * 100
= 15 milliliters / 500 milliliters * 100
= 0.03
= 3%
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A chemical company makes two brands of antifreeze. The first brand is 70% pure antifreeze, and the second brand is 95% pure antifreeze. In order to obtain 170 gallons of a mixture that contains 80% pure antifreeze, how many gallons of each brand of antifreeze must be used?
first brand: ?
Second brand ?
please dont answer if you dont know it.
Answers
The quantity of first brand is 102 gallons and quantity of second brand is 68 gallons
Given,
The first brand of antifreeze = 70% pure antifreeze
The second brand of antifreeze = 95% pure antifreeze
The quantity of mixture = 170 gallons contains 80% pure antifreeze
We have to find the quantity of each brand of antifreeze must be used;
Now,
The quantity of first brand = x gallons
The quantity of second brand = y gallons
Then,
x + y = 170
x = 170 - y ....(1)
70x / 100 + 95y / 100 = (80 × 170) / 100
70x + 95y = 13600
Now, putting the value of x from equation 1:
70 (170 - y) + 95y = 13600
11900 - 70y + 95y = 13600
11900 + 25y = 13600
25y = 13600 - 11900
25y = 1700
y = 1700/25
y = 68
Now, putting this value of y in equation 1:
x = 170 - 68
x = 102
Therefore,
The quantity of first brand is 102 gallons and quantity of second brand is 68 gallons
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Tara ran to the park and then walked to the store. She ran 4 times as long as she walked. The total time spent walking and running was 25 minutes. Write an equation that can be used to solve for how long it took Tara to walk from the park to the store?
A= x + 4 = 25
B= 1/4x = 25
C= 1/4x + x = 25
D= x + 4x = 25
Answers
The equation of the time that it took Tara to get to the store is; x + 4x = 25
What is the time taken?We know that in this case, the task that we have is to form an equation that would reflect the total time that Tara took in moving to the store. We have to factor in that the variable here is the time.
We are told that she ran 4 times as long as she walked and the total time spent walking and running was 25 minutes. Let us designate the time taken to walk as x. This implies that the time that she ran is 4x.
The equation would now be; x + 4x = 25
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The value of a car is $34535, in 20 years the value will decrease to $500. What is the average amount of depreciation per year?
Answers
Answer:
$1701.75
Step-by-step explanation:
34535-500=34035
34035/20=$1701.75 per year
Write an equation for the line parallel to the line 3/2x= -6 through the point (-6, 5).
Answers
The equation of the line parallel to the line, [tex]y=\frac{3}{2} x-6[/tex] through the point (-6,5) is [tex]3x-2y+28=0[/tex]
What are Parallel Lines?
Parallel lines are a grouping of two or more lines that all lie in the same plane but never cross. Parallel lines have the same slope.What is Point-Slope Equation of Line?
The Point-Slope Equation of a straight line is given as, [tex]y-y_{1}=m(x- x_{1})[/tex].This method is useful in determining the equation of a straight line when the slope (m) of the line and a point [tex](x_{1}, y_{1})[/tex] are known.Here, it is given that the equation of the line parallel to the given straight line is [tex]y=\frac{3}{2} x-6[/tex] ----(1)
We know that the slope of parallel lines is equal.
So, the slope of (1) will be equal to the given line.
Writing (1) in the form of [tex]y=mx+c[/tex], we get
Slope, [tex]m=\frac{3}{2}[/tex]
Using the Point-Slope Equation of the line, we have
[tex]y-y_{1}=m(x- x_{1})[/tex]
Now, substituting the point (-6,5) in the place of [tex](x_{1}, y_{1})[/tex], we get
[tex]y-5=\frac{3}{2} (x- (-6))\\\implies 2(y-5)=3(x+6)\\\implies 2y-10=3x+18[/tex]
Simplifying, we get
[tex]3x-2y+18+10=0\\\implies 3x-2y+28=0[/tex]
Therefore, the equation of the given line is [tex]3x-2y+28=0[/tex]
Correct Question: Write an equation for the line parallel to the line y=3/2x-6 through the point (-6, 5).
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