Answer:
[tex]\begin{aligned}\textsf{(a)} \quad y&=-6x^2\\y&=4x^2-2\end{aligned}[/tex]
[tex]\textsf{(b)} \quad x=\dfrac{1}{4}y^2[/tex]
Step-by-step explanation:
Part (a)A graph is 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.
Linear functions are not symmetric with respect to the y-axis.
Quadratic functions are symmetric with respect to the y-axis if the y-axis is their axis of symmetry, so when the variable x is squared.
Cubic functions are not symmetric about the y-axis.
Square root functions are not symmetric about the y-axis.
There are two quadratic functions with x² in the given answer options.
Test to see if they are symmetric with respect to the y-axis.
Test for symmetry
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.
Given function:
[tex]y=-6x^2[/tex]
Replace x with (-x):
[tex]\implies y=-6(-x)^2[/tex]
[tex]\implies y=-6x^2[/tex]
Therefore, as the function is equal to the original function, this function is symmetric with respect to the y-axis.
Given function:
[tex]y=4x^2-2[/tex]
Replace y with (-y) and x with (-x):
[tex]\implies y=4(-x)^2-2[/tex]
[tex]\implies y=4x^2-2[/tex]
Therefore, as the function is equal to the original function, this function is symmetric with respect to the y-axis.
Part (b)A graph is symmetric with respect to the x-axis if for every point (a, b) on the graph, there is also a point (a, -b) on the graph.
Linear functions are not symmetric with respect to the x-axis.
Quadratic functions are symmetric with respect to the x-axis if the x-axis is their axis of symmetry, so when the variable y is squared.
Cubic functions are not symmetric about the x-axis.
Square root functions are not symmetric about the x-axis.
There is one quadratic functions with y² in the given answer options.
Test to see if it is symmetric with respect to the x-axis.
Test for symmetry
To determine if a graph is symmetric with respect to the x-axis, replace all the y's with (−y). If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the x-axis.
Given function:
[tex]x=\dfrac{1}{4}y^2[/tex]
Replace y with (-y):
[tex]\implies x=\dfrac{1}{4}(-y)^2[/tex]
[tex]\implies x=\dfrac{1}{4}y^2[/tex]
Therefore, as the function is equal to the original function, this function is symmetric with respect to the x-axis.
2. Claire is painting some windows that are all the same size. She used gallon of paint to paint 2 windows. How many gallons of paint are needed to paint 1 window?
Answer:3
Step-by-step explanation:
since 7 is a number and b is to u should just put 3 windows cause u need to add them all up i think, not sure but just do that, why not,
I need help on this Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Answer:
{3, 4, 6, 7, 8}
Step-by-step explanation:
For sets U = {1, 2, 3, 4, 5, 6, 7, 8}, A = {1, 2, 5, 6}, and C = {1, 2, 3, 4, 5}, you want the set {A∩C}'.
A∩CThe set A∩C contains the elements that are common to both sets. Those are {1, 2, 5}.
{A∩C}'The set of interest contains the elements of U that are not in A∩C. Those are ...
{3, 4, 6, 7, 8}
__
Additional comment
DeMorgan's theorem tells us the desired set is equivalent to A'∪C', or {3, 4, 7, 8}∪{6, 7, 8}. That, too, is ...
(3, 4, 6, 7, 8}
By rounding each number to the nearest 10, estimate the value of 197 ÷ 10.3
Answer:
20
Step-by-step explanation:
197 rounded to the nearest 10 is 200.
10.3 rounded to the nearest 10 is 10.
So, 200 ÷ 10 = 20
Answer:
20
Step-by-step explanation:
We are rounding to the nearest 10.
197≈200
10.3≈10
After you have rounded the numbers, The equation simplifies a whole bunch.
200/10=20
Please Mark As BrainliestA radioactive compound with mass 380 grams decays at a rate of 12.1% per hour. Which equation represents how many grams of the compound will remain after 4 hours?
The equation that represents how many grams of the compound will remain after 4 hours is A(4) = 380 *(1 - 12.1%)⁴
How to determine the equation?From the question, we have the following parametersa:
Mass = 380 grams
Rate of decay= 12.1% per hour
These parameters can be represented using the following exponential equation
A(n) = A *(1 - r)ⁿ
Where
n = number of hours = 4
A = Initial mass = 380
r = rate of decay = 12.1%
Substitute the known values in the above equation, so, we have the following representation
A(4) = 380 *(1 - 12.1%)⁴
Hence, the equation is A(4) = 380 *(1 - 12.1%)⁴
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The followings are the sys. BP in mmHg of 12 patents
under certain therapy of hypertension
183
144
152
178
157
114
178
152
194
163
118
158
Can we conclude on basis of these data that sample
mean is less than pop mean 165 mmHg
Let a = 0.05
There is no sufficient evidence to support that the population mean is less than 165.
What is mean ?
The average of a set of values is referred to as the mean in statistics and math. The simple arithmetic mean, geometric mean, and harmonic mean are some of the methods that can be used to calculate the mean. The simple arithmetic mean involves adding the numbers together and dividing the result by the number of observations.
From the given data
183, 152, 178 , 157 , 194 , 163 , 144 , 114 , 178 , 152 , 118 , 158
Mean = 157.5833
Standard deviation s = 24.39
n = 12
Null hypothesis [tex]H_{0}[/tex] : μ = 165
Alternative Hypothesis [tex]H_{1}[/tex] = μ < 165
Level of significance ∝ = 0.05
degree of freedom (df) = n - 1
(df) = 12 - 1
(df) = 11
critical value [tex]t_{0.05 , 11}[/tex] = -1.796 (left - tailed)
Test - statistics (t) = ( mean - μ ) / ( s / √n)
(t) = -1.053
p - value = 0.1574
p - value > Significance level (∝)
0.1574 > 0.05
We fail to reject the null hypothesis
Critical value [tex]t_{0.05 , 11}[/tex] = -1.796
|[tex]t_{0.05 , 11}[/tex]| = 1.796
|test - statistics| < |critical value|
1.053 < 1.796
We fail to reject the null hypothesis
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What is the standard form of ( 7 − 5 i ) ( 2 + 3 i ) ?M
The standard form of the complex numbers ( 7 − 5 i ) ( 2 + 3 i ) is
29 + 11iHow to expand the complex numbersComplex numbers are numbers that are represented of the form a + ib
a and b are real numbers. a is the real part and b is in the imaginary part
i = √-1
Opening up the parenthesis by multiplication
( 7 − 5 i ) ( 2 + 3 i )
= 14 +21i - 10i -15i^2
where i^2 = -1
= 14 +21i - 10i -15 * -1
= 14 +21i - 10i +15
= 29 + 11i
The equation is equal to 29 + 11i
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20 is ______times as much as 2
−8×(−10+(−7))
Evaluate the following expression.
Answer:
136
Step-by-step explanation:
solve the inside of the parentheses and you get -17, then multiply by -8
0 x ≤-21
0 x ≤21
0 x ≤-15
0 x ≤15
21. 2z>-28 (I point)
O z>-56
O z>-14
O z<-14
O z<14
Answer: [tex]z > -14[/tex]
Step-by-step explanation:
Divide both sides by 2.
What is the graph of the system of inequality?
Graph of the system of inequality is a solid line and a portion of area is shaded which satisfy the condition of the inequality.
What is inequality?
When left hand side is not exactly equal to the right hand side of an equation then it is known as inequality. For system of inequality, there are four types of inequalities <, >, [tex]\le[/tex], and [tex]\ge[/tex].
Using following steps anyone can graph the inequality:
1. Get y alone on one side of a linear inequality in two variables (like x and y) before graphing it. Then, take into account the associated equation that was created by switching the inequality sign for an equality sign. This equation has a line as its graph.
2. The graph is a dashed line if the inequality is strict ( < or >). The graph is a solid line if the inequality is not strict ([tex]\le[/tex] or [tex]\ge[/tex] ).
3. The last step is to choose a point that is not on either line (typically (0, 0) is the simplest) and determine whether or not these coordinates fulfil the inequality. If so, shade the portion of the half-plane that contains that point. If not, shade the opposite half-plane.
Hence, the graph of the system of inequality is a solid line and a portion of area is shaded which satisfy the condition of the inequality.
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If −2≤f(x)≤5 on [−1,3] then find upper and lower bounds for ∫−13f(x)dx
Answer:
Answer is attached as a photo. I will be honest I am not familiar with a calculus problem being set up that way. I am guessing that is what they are looking for...
Step-by-step explanation:
The upper bound of the given function is 20 while the lower bound of the given function is -8.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.
As per the given function,
-2 ≤ f(x) ≤ 5
At the upper bond, f(x) = 5
[tex]\int\limits^{3}_{-1} {f(x)} \, dx[/tex] = [tex]\int\limits^{3}_{-1} {5} \, dx[/tex]
⇒ 5(3 + 1) = 20
At the lower bond f(x) = -2
[tex]\int\limits^{3}_{-1} {f(x)} \, dx=\int\limits^{3}_{-1} {-2} \, dx[/tex]
⇒ -2(3 + 1) = -8
Hence "The upper bound of the given function is 20 while the lower bound of the given function is -8".
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write -1/2x + 4 = 10 in slope intercept form
Answer: y=-1/2x+4
Step-by-step explanation:
Raven and Tyler are selling their cups of hot chocolate for $2.25. They sold 11 cups. They are also sold 9 candy canes on the side for $0.75 each. They spent $7.50 on supplies that they will have to pay back to the bank.
How much did they earn from candy canes?
The amount they earn from the sale of candy canes as required is; $6.75.
How much did they earn from candy canes?It follows from the task content that the amount earned by Raven and Tyler as in the task content is to be determined.
Since they sell their cups of hot chocolate for $2.25 in which case they sold 11 cups.
However, the question requires that the amount which they earn from the sale of candy canes is to be determined.
Therefore, since each candy cane is sold for $0.75, it follows that the amount earned on 9 candy cones is;
= 9 × $0.75
= $6.75
Ultimately, the amount earned from the candy canes is; $6.75.
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The ratio of flour to sugar is 2 cups to 3 cups. If there are 5 cups of flour, how many cups of sugar are there?
Question 3: Multiply: 0.33.10⁵
330
330000
33000
3300
Answer:
33,000
Step-by-step explanation:
0.33 x 10^5 is 33,000
help!! i’ve been stuck on this problem!
Answer:
x less than or equal to -2
Step-by-step explanation:
I believe that's the answer
Answer:
x < -2
Step-by-step explanation:
You want the domain of a function graphed as a curve with an open circle at x=-2, which is the right end of the curve.
DomainThe domain is the horizontal extent of the graph. It is the set of values for which the relation is defined.
ApplicationThe open circle at (x, y) = (-2, 0) means that point is not part of the graph. All x-values to the left of that point have corresponding y-values, so the extent of the graph can be said to be ...
x < -2
The domain of the relation is x < -2.
What are the 7 types of triangles?
The 7 names of triangles:
Scalene, Isosceles, Equilateral, Equiangular triangle, Acute triangle,
Right triangle, Obtuse triangle
What are triangles?
Three vertices make up a triangle, a three-sided polygon. The triangle's angles are formed by a point where the three sides are joined end to end. The triangle's three angles add up to a total of 180 degrees.
Equiangular triangle: All angles are equal.
Acute triangle . . . all three angles are less than 90°
Right triangle . . . one angle is 90°
Obtuse triangle . . . one angle is greater than 90°
Equilateral triangle . . . all three sides are the same length
Isosceles triangle . . . two sides are the same length
Scalene triangle . . . all three sides are different lengths
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cards and chips are being created for a board game by company the number of cards produced is proportional to the number of chips that are produced over a short period of time the company produced 32 cards and four chips what is the ratio of cars the chips produce State and simplest form as a unit rate in cards per chip (I NEED ANSWERS FAST)
Answer:
8 cards per chip
Step-by-step explanation:
So 32:4 is the ratio.
Divide by 4 to get 8 cards per chip.
HURRY PLS!!
Kevin took $45 with him to spend on snack for himself and his friends at the movie theater. The price for each bucket of popcorn was $4. The price of each drink was half the price of a bucket of popcorn.
A. Sketch the graph that represents the situation and label the intercepts. Use one axis to represent the number of buckets of popcorn and the other axis to represent the number of drinks.
Explain your graph.
B. Graph the absolute value function.
C. (a) Graph a linear function of your choice. On the same graph, graph a linear function transformed 2 units up and 3 units down.
(b) What was the equation of your linear function in slope-intercept form?
(c) What was the equation of the transformed function in slope-intercept form?
The equation of Kevin's scenario is 4x + 2y = 45
The absolute equation is y = 2|x - 3| + 5The equation of the linear function in slope-intercept form is y = 2x + 3The equation of the transformed function in slope-intercept form is y = 2x - 1How to determine Kevin's equationFrom the question, we have the following parameters
Amount = $45Bucket of popcorn = $4Bucket of each drink= Half the bucket of popcorn = $2Represent the buckets of popcorn with x and the number of drinks with y
So, we have the following equation
4x + 2y = total amount
This gives
4x + 2y = 45
See attachment for the graph
The graph of an absolute functionAn absolute function is represented as
y = a|x - h| + k
Where the vertex is (h, k)
So, we make use of the following function
y = 2|x - 3| + 5
See attachment 2 for the graph
The graph of a linear functionHere, we are to make use of any equation
A linear equation is represented as
y = mx + b
Where
slope = m
y-intercept = b
So, we make use of
m = 2 and b = 3
This gives
y = 2x + 3
When transformed 2 units up and 3 units down, the resulting equation is
y = 2x + 2 - 3
Evaluate
y = 2x - 1
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Please help will mark Brainly
Answer: Horizontal Translation
Step-by-step explanation:
Annika is comparing two companies based on the costs for renting a bike for the . Company A charges a $20 rental fee plus $4.50 the bike is rented. Company B charges a 9 rental fee plus $6.50 per hour the bike is rented.
Answer:
depends on how long u need it for
Step-by-step explanation:
In, a city had a population of 310,000 people. Each year since 2007, the population has grown by 4.8%.
Let t be the number of years since. Let y be the city's population.
Write an exponential function showing the relationship between t and y.
The exponential function showing the relationship between t and y is y = 310000(1.048)⁺
How to determine the exponential function?From the question, we have the following parameters that can be used in our computation:
Initial population = 310000
Rate of growth = 4.8%
These parameters can be represeted as
a = 310000 and r = 4.8%
An exponential function is represented as
y = a(1 + r)⁺
Substitute the known values in the above equation, so, we have the following representation
y = 310000 (1 + 4.8%)⁺
Evaluate
y = 310000(1.048)⁺
Hence, the function is y = 310000(1.048)⁺
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The sum of two numbers is 66. Two times the lesser number is 15 more than the greater number. What are the numbers
If x is a lesser number, the equation is
Answer:
See below!
Step-by-step explanation:
Let the two numbers be x and y
Condition # 1:x + y = 66 ----------------(1)
Condition # 2:2x = y + 15
2x - y = 15 ---------------(2)
Add both equations
x + y + 2x - y = 66 + 15
x + 2x = 66 + 15
3x = 81
Divide both sides by 3
x = 27Put x = 27 in Eq. 1
27 + y = 66
Subtract 27 to both sides
y = 66 - 27
y = 39[tex]\rule[225]{225}{2}[/tex]
Shivani and Yamini have certain amounts of
money with them. If Shivani gives 60 to Yamini, the
amounts with both will be equal. Instead, if Yamini
gives 20 to Shivani, the amount with Shivani would
become twice the amount left with Yamini. What is
the amount with Shivani?
Answer:
$300
Step-by-step explanation:
S = amount of $$ Shivani currently has
Y = ... Yamini currently has
1. If Shivani gives 60 to Yamini, the amounts with both will be equal:
S - 60 = Y + 60
2. if Yamini gives 20 to Shivani, the amount with Shivani would become twice the amount left with Yamini: 2(Y-20) = S+20
3. Simplify both equations and solve the system:
S = Y + 120
S = 2Y - 60
Y + 120 = 2Y - 60 ⇒ Y = 180
S = 180 + 120 = 300
The ratio of flour to sugar is 2 cups to 3 cups. If there are 5 cups of flour, how many cups of sugar are there?
The number of sugar cups will be equal to 7.5 cups.
What are ratios and proportions?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.
Given that the ratio of flour to sugar is 2 cups to 3 cups. The number of cops for flour is 5.
The number of sugar cups will be calculated as,
F / S = 2 / 3
5 / S = 2 / 3
S = ( 5 x 3 ) / 2
S = 7.5 cups
Therefore, the number of sugar cups will be equal to 7.5 cups.
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After a 20% discount, you purchase a television for $240. What was the television's
price before the reduction? (Define a variable, create an equation, solve using algebra,
and answer in a sentence.)
===========================================
Work Shown:
x = price of the TV before the discount
20% of x = 0.20x = discount, aka amount saved
x - 0.20x = 0.80x = price after discount
0.80x = 240
x = 240/0.80
x = 300
The TV was $300 before the discount.
-------------
Check:
20% of 300 = 0.20*300 = 60 dollars is the amount saved
300-60 = 240 is the price after the discount, which matches the given info. The answer is confirmed.
Please help asap!!!!!!
How do you isolate the variable by dividing each side by factors that don't contain the variable?
We isolate the variable in an equation by dividing both sides of the equation in which one side does not contain any variable.
According to the question,
We have the following information:
Isolating a variable by dividing each side of the equation in which one side does not contain any variable.
Now, in this case, it is clearly stated that the first step to isolate the variable from the equation is to perform division.
Now, this can be done as follows in the given equation:
2x = 14
Now, the variable x can be isolated by dividing both sides of the equation by 2:
x = 14/2
x = 7
Hence, we isolate the variable in an equation by dividing both sides of the equation in which one side does not contain any variable.
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What are rational roots Class 10?
The rational root theorem, as its name suggests, is used to find the rational solutions of a polynomial equation (or zeros or roots of a polynomial function). The solutions derived at the end of any polynomial equation are known as roots or zeros of polynomials. A polynomial doesn't need to have rational zeros.
Rational root theorem, also called rational root test, in algebra, theorem that for a polynomial equation in one variable with integer coefficients to have a solution (root) that is a rational number, the leading coefficient (the coefficient of the highest power) must be divisible by the denominator of the fraction and the constant term (the one without a variable) must be divisible by the numerator.
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what is the solution a b to this system of linear equations 3a6b45 2a 2b 12
Solution of the system of linear equation 3a + 6b = 45 , 2a -2b = -12 is equal to a = 1 and b =7.
As given in the question,
System of linear equation are:
3a + 6b = 45 __( 1 )
2a - 2b = -12 __(2 )
Solution of the linear equation by elimination method is given by:
Multiply ( 2 ) by 3 and add it to (1) we get,
3a + 6b = 45
6a - 6b = -36
9a = 9
⇒ a = 1
Substitute the value of a = 1 in (1) we get,
3( 1 ) + 6b = 45
⇒ 6b = 42
⇒ b = 7
Therefore, the solution of the system of linear equation is a = 1 and
b =7.
The complete question is :
What is the solution (a, b) to this system of linear equations?
3a+6b = 45 , 2a-2b = -12
a. (-27, 6)
b. (-1, 7)
c. (1, 7)
d. (27, -6)
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