The function for the reflection across the y-axis can be written as: f(x,y)=(−x,y)
To reflect a point across the y-axis, we multiply its x-coordinate by -1. This means that if a point has coordinates (x,y), its reflection across the y-axis will have coordinates (−x,y).
We can use this to define a function for the reflection across the y-axis. Let f(x,y) be the function that reflects a point across the y-axis. Then, for any point (x,y), we have:
f(x,y)=(−x,y)
In other words, f(x,y) takes a point (x,y) and returns its reflection across the y-axis.
We can also write this function in terms of components. Let x and y be the coordinates of a point. Then, the reflection of this point across the y-axis has coordinates (−x,y). Therefore, the function for the reflection across the y-axis can be written as:
f(x,y)=(−x,y)
This function takes the coordinates of a point as input and returns the coordinates of its reflection across the y-axis as output.
Factor this polynomial completely x^2-64
Answer:
(x + 8)(x - 8)
Step-by-step explanation:
Difference of squares
a^2 - b^2 = (a + b)(a - b)
In this case
x^2 - 64
= x^2 - 8^2
= (x + 8)(x - 8)
The equation x² - 64 is a difference of two squares and can be factored using the formula for the difference of squares, which leads to (x - 8)(x + 8).
Explanation:The equation given is x² - 64, which is a difference of two squares. In mathematics, the difference of two squares is any expression that can be rewritten as the square of a number or expression, subtracted from the square of another number or expression. To factor this expression, we can use the formula a² - b² = (a - b)(a + b).
So, we have
x² - 64
= (x)² - (8)². Applying the formula, this factors to (x - 8)(x + 8).
Learn more about Factoring Polynomials here:https://brainly.com/question/28315959
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What is the relationship between angles A and B
Answer:
They are complementary
Step-by-step explanation:
Complementary angles sun to 90°
∠A + ∠B = 59° + 31° = 90° ← complementary
Describe the graph of the function.
y =Square root of
x-1 + 4
Answer: Square root of x+3
Step-by-step explanation:
Insert the denominator to 3
ANSWER
The graph of the function starts from (1,4) and moves up right.
EXPLANATION
The given rational function is
[tex]y = \sqrt{x - 1} + 4[/tex]
The base of this function is
[tex]y = \sqrt{x} [/tex]
The -1 under radical sign means the graph of the base function is shifted 1 unit right.
The +4 shows that base function is shifted up by 4 units.
The graph of the function therefore starts from (1,4) and moves up right.
Find the length of the missing side. Round answers to the nearest tenth (one decimal).
Right triangle with base=6.3 mi and hypotenuse=15.4 mi
Answer:
14.1 mi
Step-by-step explanation:
Use pythagorean theorem (a^2 + b^2 = c^2)
a = base
b = side
c = hypontenuse
then just plug the numbers into the formula -----> 6.3^2 + b^2 = 15.4^2
then subtract 6.3^2 from both sides ----> b^2 = 15.4^2 - 6.3^2
solve ------> b^2 = 197.47
Square root both sides and you get b = 14.1 mi as your answer
Answer:
14.1
Step-by-step explanation:
If f(x)=0. 5(3-x), what is the value of f(-3)?
3
1. 5
0. 5
0
[tex]
f(x)=0.5(3-x) \\
f(-3)=0.5(3-(-3)) \\
f(-3)=0.5\cdot6 \\
f(-3)=3
[/tex]
Hope this helps.
r3t40
Factor completely 9x2 + 9x -28
Answer:
Your answer is (3x - 4) (3x + 7)
Step-by-step explanation:
Hope my answer has helped you and if not i'm sorry.
Find the soultion(s) to the system of equations. Select all that apply
Answer:
(0,-3)
(3,0)
Step-by-step explanation:
The solutions to the system of equations are where the two graphs cross
The first is at x=0 and y=-3
The second is at x=3 and y=0
What is the slope of a line that is perpendicular to the line represented by the equation y=-2/5x+4/5
Answer:
[tex]\frac{5}{2}[/tex]
Step-by-step explanation:
recall for a line whose equation is
y = mx + b,
the slope of this line is m
the slope of a line that is perpendicular to this line is -[tex]\frac{1}{m}[/tex]
in this case,
m = -[tex]\frac{2}{5}[/tex]
hence -[tex]\frac{1}{m}[/tex]=[tex]\frac{5}{2}[/tex]
The slope of a line that is perpendicular to the line represented by the equation y = -2/5x + 4/5 is 5/2 .
What is the slope of a line perpendicular to a given line ?The slope of a line perpendicular to a given line is equal to the negative reciprocal of the slope of the given line.
Let the given line is y = mx + c , where the slope of the line is m and the y-intercept is c .
The slope of the line perpendicular to this given line is equal to -1/m .
How to find the slope of the given line ?Given equation of line is y = -2/5x + 4/5 .
The slope of the given line is -2/5 .
Thus, the slope of the line perpendicular to this given line is equal to
= -(-5/2) = 5/2 .
Therefore, the slope of a line that is perpendicular to the line represented by the equation y = -2/5x + 4/5 is 5/2 .
To learn more about slope of perpendicular line, refer -
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What is the change due if a $50 bill is tendered for a charge of $9.76?
Answer:$40.24
Step-by-step explanation:
Answer:
$40.24
Step-by-step explanation:
You just have to do $50.00 - $9.76= $40.26
The border line of the linear inequality 4x+7y<5 is dotted. True or false
Answer:
True
Step-by-step explanation:
The region defined by the following inequality
[tex]4x+7y<5[/tex]
is delimited by the line: [tex]4x+7y=5[/tex]
Therefore the points that are on the line that delimits the region are those where [tex]4x+7y=5[/tex]
Since the symbol "<" represents only the values that are smaller and excludes those that are greater or equal, then the points where [tex]4x+7y=5[/tex] are not included in the region. This is represented by drawing a dotted line
The statement is true; the border line of the inequality 4x+7y<5 is drawn as a dotted line because it does not include the boundary points as part of the solution set.
The statement that the border line of the linear inequality 4x+7y<5 is dotted is true. When graphing a linear inequality, the border line is typically solid if the inequality includes the equality (≤ or ≥), which indicates that the points on the line are included in the solution set. However, when the inequality does not include equality ( < or > without the line underneath), as in 4x+7y<5, the border line is drawn as a dotted line, signifying that points on the line are not part of the solution set. Therefore, the given statement is correct and the border line should indeed be dotted.
Which of the following functions grows at the same rate as ((x^4)+x)^(1/2)
A. X
B. X^2
C. X^3
D. X^4
Answer:
B
Step-by-step explanation:
(x⁴ + x)^½
As x approaches infinity, x⁴ becomes much larger than x. So:
(x⁴ + x)^½ ≈ (x⁴)^½ = x²
So x² grows at the same rate as (x⁴ + x)^½.
If g(x) = 4(x - 2)2 - 4, complete the following statements.
The axis of symmetry of function f is x =
. The axis of symmetry of function g is x =
Answer:
x = 10
Step-by-step explanation:
Please, use " ^ " to denote exponentiation: g(x) = 4(x - 2)^2 - 4
The vertex is located at (2, -4) which numbers come directly from the '2' in (x - 2) and the "-4" at the end of the equation.
Where is the function f(x) that you mentioned?
The axis of symmetry here is the vertical line that passes through the vertex. Its equation is x = 10.
The axis of symmetry for the function g(x) is x = 2, determined by the standard form of a quadratic equation, which tells us the axis of symmetry is at x = h, where g(x) is in the form a(x - h)^2 + k.
The question asks for the axis of symmetry for function g(x) which is given as g(x) = 4(x - 2)2 - 4. The axis of symmetry for a parabolic function in the form f(x) = a(x - h)2 + k is given by x = h. Thus, in the function g(x), the axis of symmetry is x = 2. If f(x) was provided in a similar quadratic form, its axis of symmetry would similarly be derived from its formula. However, since f(x) was not given in the question, we can't determine its axis of symmetry.
The distance around the lake is 2 kilometers. If
Elena wants to run 14 kilometers this week, how
many laps must she run around the lake
Answer:
7 laps
Step-by-step explanation:
Take the total distance and divide by the distance around the lake to determine how many laps she must run
14 km/2 km
7
She must run 7 laps
According to the Ruler Postulate, what does the set of points on any line correspond to?
Answer:
Points on the Real number line correspond to Real numbers.The distance between two points is the absolute value of the difference of the corresponding numbers. ... The set of points on any line corresponds to the coordinate .
Step-by-step explanation:
Please mark brainliest and have a great day!
PLEASE HELPPPP ME ASAP and here are the answer choices :>
27
33
60
93
Answer:
The answer is 60
Step-by-step explanation:
Drag each description to the correct location on the table. Each description can be used more than once.
Classify each polynomial based on its degree and number of terms.
Answer:
-6 - x^5+3x^2 is cubic, and trinomial
5x^3 - 8x is cubic, and binomial
1/3x^4 is quartic, and monomial
6/7x + 1 is linear, and binomial
-0.7x^2 is quadratic, and monomial
Step-by-step explanation:
Monomial is 1 term
Binomial is 2 terms
Trinomial is 3 terms
- Exponents don't count as terms btw
Answer:
Step-by-step explanation:
why is 3 meals a day a unit rate
It tells how many of one thing corresponds to only one of another thing.
Explanation:In this example, it is shown how the number of meals corresponds to one day: [tex]\frac{\text{3 meals}}{\text{day}}[/tex].
1.) 2x + y = 3
2.) x - 2y = -1
If equation 1 is multiplied by 2 and then the equations are added, the result is
A.3x = 2
B.3x = 5
C.5x = 5
Answer: C is correct, 5x=5
Step-by-step explanation:
1. When equation 1 is multiplied by 2 it becomes 4x+2y=6
2. Now we have...
4x+2y=6 and x - 2y = -1
Add those together and you have your answer! 5x=5 (simplified is x=1)
The perimeter of the scalene triangle is 60 cm. The length
of the longest side is 4 times that of the shortest side.
Which statements about the possible measures of the
sides are reasonable? Check all that apply.
The value of x can equal 40.
The longest side can equal 30 cm.
The shortest side can equal 7 cm.
The value of x can equal 25.
The shortest side can equal 5.
Answer:
Step-by-step explanation:
Perimeter = 60 cm
longest side = 4* shortest side (x)
longest side = 4x
shortest side = x
third (intermediate side=y= 60 -x -4x = 60-5x
The triangle inequality specifies that the sum of the two shorter sides must be greater than the longest side to form a triangle. Hence
x + y > 4x
x + 60-5x > 4x
60 - 4x > 4x
8x < 60
x < 60/8 = 7.5, or
x < 7.5
Therefore to form a triangle, x must be less than 7.5 cm.
Now if we look at the options both 7 and 5 are less than 7.5 cm.
40, 30 and 25 all have a problem because the longest side (4 times longer) will exceed the perimeter of 60.
Now also examine cases where 4x is not the longest side, in which case we need
4x>=y
or
4x >= 60-5x
9x >=60
x >= 6.67
so x=5 will not qualify, because 4x will no longer be the longest side.
The only valid option is x=7 cm
The side lengths for x=7 and x=5 are, respectively,
(7, 25, 28)....
Sal is trying to determine which cell phone and service plan to buy for his mother. The first phone costs $100 and $55 per month for unlimited usage. The second phone costs $150 and $51 per month for unlimited usage. How many months will it take for the second phone to be less expensive than the first phone?
The inequality that will determine the number of months, x, that are required for the second phone to be less expensive is 100 + 55x > 150 + 51x100 + 55x < 150 + 51x100x+ 55 > 150x+ 51100x+ 55 < 150x+ 51.
The solution to the inequality is x > 2.4x < 2.4x < 12.5x > 12.5.
Sal’s mother would have to keep the second cell phone plan for at least 231213 months in order for it to be less expensive
Answer:
a) The first inequality 100+55x>150+51x;
b) The last inequality x>12.5
c) 13 months
Step-by-step explanation:
a) Let x be the number of months.
1. The first phone costs $100 and $55 per month for unlimited usage, then for x months it will cost $55x and in total
$(100+55x)
2. The second phone costs $150 and $51 per month for unlimited usage, then for x months it will cost %51x and in total
$(150+51x)
3. If the second phone must be less expensive than the first phone, then
150+51x<100+55x
or
100+55x>150+51x
b) Solve this inequality:
55x-51x>150-100
4x>50
x>12.5
c) Sal's mother has to keep the second cell phone for at least 13 months (because x>12.5).
Part 1:
The first phone costs $100 and $55 per month for unlimited usage.
Let f(x) be the cost of the first phone and x be the number of months.
Equation forms:
[tex]f(x)=55x+100[/tex]
The second phone costs $150 and $51 per month for unlimited usage.
Let g(x) be the cost of the second phone and x be the number of months.
Equation forms:
[tex]g(x)=51x+150[/tex]
We have to find the inequality that will determine the number of months, x, that are required for the second phone to be less expensive, it is given by:
[tex]g(x)<f(x)[/tex]
[tex]51x+150<55x+100[/tex]
Part 2:
The solution to the inequality is:
[tex]51x+150<55x+100[/tex]
=> [tex]51x-55x<100-150[/tex]
=> [tex]-4x<-50[/tex]
=> [tex]-x<-12.5[/tex]
=> [tex]x>12.5[/tex]
Or rounding off to 13.
Part 3:
Sal’s mother would have to keep the second cell phone plan for at least 13 months in order for it to be less expensive.
Use the discriminant to describe the roots of each equation. Then select the best description. 2m2 + 3 = m double root real and rational roots real and irrational roots non-real roots
Answer:
The roots of the equation 2m²+3=m are non-real roots.
Step-by-step explanation:
Given equation:
2m²+3=m
2m²-m+3=0
Here, from the equation we can obtain the following values:
a = 2, b = -1, c = 3
Discriminant of an equation is given as:
D = b²-4ac
= (-1)²-4(2)(3)
= 1 - 21
= -20
Discriminant can tell what kinds of roots the equation have.
In our case, the discriminant is less than 0.
When D < 0, the roots of the equation are complex conjugates.(non-real)
Answer:
Imaginary root
Step-by-step explanation:
-1^2-4(2*3)
1-4*6
1-24
-23
-23 has no square root or it will be a decimal.
What is the surface area of the cube below?
Answer:
96 units squared
Step-by-step explanation:
Answer:
B. 96 Units^2.
Step-by-step explanation:
Got Correct On Assist.
A brownie recipe asks for two and one third times as much sugar as chocolate chips. If three and one half cups of sugar is used, what quantity of chocolate chips would then be needed, according to the recipe?
Answer:
1 1/2 cups.
Step-by-step explanation:
If the quantity of chocolate chips is x cups then:
x * 2 1/3 = 3 1/2
x * 7/3 = 7/2
x = 7/2 / 7/3
x = 7/2 * 3/7
x = 3/2 = 1 1/2 cups.
The quantity of chocolate chips needed for the brownie recipe when using three and one half cups of sugar, divide the amount of sugar by the sugar-to-chocolate chips ratio of 2 1/3. The answer is one and one half cups of chocolate chips.
Related to ratios and proportions in a brownie recipe. If a recipe calls for two and one third times as much sugar as chocolate chips, and if three and one half cups of sugar is used, you can calculate the amount of chocolate chips required as follows:
First, it's important to understand the ratio given: 2 1/3 cups of sugar for every 1 cup of chocolate chips.
Next, since we know that 3 1/2 cups of sugar are used, you need to divide the amount of sugar by the ratio to find the amount of chocolate chips needed, which is, 3 1/2 divided by 2 1/3.
To perform the division, you first convert the mixed numbers into improper fractions. 3 1/2 becomes 7/2, and 2 1/3 becomes 7/3.
Now, divide 7/2 (the amount of sugar) by 7/3 (the sugar-to-chips ratio) to get the amount of chocolate chips required.
This is the same as multiplying 7/2 by the reciprocal of 7/3, which is 3/7. The sevens cancel out, and the result is 3/2, or one and one half (1 1/2) cups of chocolate chips required for the recipe.
please help asap!!!!
Answer:
B) 0
Step-by-step explanation:
A regular slope-intercept equation would look like this:
y=mx+b
If your equation states y= number, it doesn't have a slope and is graphed as a horizontal line.
Examples:
y=2
y=7
If your equation states x= number, it's slope is going to be undefined and is graphed as a vertical line.
Examples:
x=2
x=7
You have $39 to spend at the music store. Each cassette tape costs $5 and each CD costs $11. Write a linear inequality that represents this situation. Let represent the number of tapes and the number of CDs.
Hello There!
My equation would be 5c + 11d <= 39
C represents cassete tape
D represents disk or the second letter of CD
To solve this I set tapes as X and CDs as Y and then multiplied each variable by the cost, respectively.
Next I set the inequality to be less than or equal to 39, because that is the amount of money you have.
There were 3,982 people at the soccer game on Thursday there were 1,886 more people at the soccer game on Saturday how many people in all attended both games
Answer:
9850
Step-by-step explanation:
3982 + 3982 + 1886 = 9850
Answer:
the answer to your question is 5 868
What is the slope of the line graphed below ? (1,1) (3,2)
Answer:
[tex]m = \frac{1}{2}[/tex]
Step-by-step explanation:
[tex]\frac{y2 - y1}{x2 - x1}[/tex]
[tex]\frac{2-1}{3-1}[/tex]
[tex]2-1 = 1\\ 3-1=2[/tex]
[tex]m = \frac{1}{2}[/tex]
For this case we have that by definition, the slope of a line is given by:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]
We have two points through which the line passes:
[tex](x_ {1}, y_ {1}) :( 1,1)\\(x_ {2}, y_ {2}) :( 3,2)[/tex]
Substituting:
[tex]m = \frac {2-1} {3-1} = \frac {1} {2}[/tex]
Thus, the slope of the line is [tex]\frac {1} {2}[/tex]
Answer:
Option C
what is the explicit formula for this sequence? -7,-3,1,5
Answer:
[tex]a_{n}[/tex] = 4n - 11
Step-by-step explanation:
These are the terms of an arithmetic sequence with n th term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
d = - 3 - (- 7) = 1 - (- 3) = 5 - 1 = 4
and a₁ = - 7, hence
[tex]a_{n}[/tex] = - 7 + 4(n - 1) = - 7 + 4n - 4 = 4n - 11
The explicit formula for the arithmetic sequence -7,-3,1,5 is an = -7 + (n-1)(4), where n is the position of the term in the sequence.
The student is asking for the explicit formula of the sequence -7,-3,1,5. This is an arithmetic sequence, where each term increases by a constant difference. The common difference (d) can be found by subtracting any term from the following term; for instance, -3 - (-7) = 4. To find the explicit formula, we'll denote the first term of the sequence as a1 which is -7. The explicit formula for an arithmetic sequence is an = a1 + (n-1)d. Substituting our values in, we get an = -7 + (n-1)(4).
the radius of the sphere is 10 units .what is the approximate volume of the sphere use π=3.14
Answer:
V≈4188.79
Step-by-step explanation:
The formula of the volume of a sphere is V=4/3πr^3
find the value of x from the equation
[tex]
\dfrac{8^{3x}}{2^{10}}=\dfrac{4^{2x}}{16} \\
\dfrac{2^{3(3x)}}{2^{10}}=\dfrac{4^{2x}}{4^2} \\
2^{9x-10}=4^{2x-2} \\
2^{9x-10}=2^{2(2x-2)} \\
2^{9x-10}=2^{4x-4} \\
9x-10=4x-4 \\
5x-6=0 \\
5x=6 \\
\boxed{x=\dfrac{6}{5}}
[/tex]
Hope this helps.
r3t40