Answers
Axis of Symmetry for a Parabola
The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves.
The axis of symmetry always passes through the vertex of the parabola.
So we only need to find the x-coordinate of the vertex of the parabola.
A parabola is the graph of a quadratic function as follows:
\(y=ax^2+bx+c\)The x-coordinate of the vertex is given by:
\(x_v=-\frac{b}{2a}\)We are given the function:
\(y=x^2-5x\)Here we have the values: a = 1, b = -5, c = 0.
Calculating:
\(\begin{gathered} x_v=-\frac{-5}{2(1)} \\ x_v=\frac{5}{2} \end{gathered}\)Thus, the axis of symmetry of the parabola is x = 5/2
Related Questions
The vertices of figure PQRS are translated to form figure P'Q'R'S'. Select all the statements that describe the two figures. Q S R P' S' Q' 'R
the anawer choices are : A. P Q R S is the preimage of PQRS, B. the two figures are congruent, C. the two figures are in different positions , but have the same orientation, D. the two figures are in different positions and have oppsoite orientation , E. corresponding angles and sides of the figures have the same measures.
Answers
The true statements are:
(B) Both figures are congurent.
(C) The two figures have the same orientation but different positions.
(E) Corresponding angles and sides have the same measures.
What is orientation?In geometry, how an item is positioned in the space it occupies—such as a line, plane, or rigid body—is described in terms of its orientation, angular position, attitude, bearing, and direction.
It refers more particularly to the fictitious rotation required to shift an object from a reference placement to its present location.
To get to the current positioning, a rotation might not be sufficient.
It could be required to include a fictitious translation known as the object's location (or position, or linear position).
Together, the position and orientation completely explain where the object is situated in space.
Therefore, the true statements are:
(B) Both figures are congurent.
(C) The two figures have the same orientation but different positions.
(E) Corresponding angles and sides have the same measures.
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Which expression is equivalent to StartRoot 8 x Superscript 7 Baseline y Superscript 8 Baseline EndRoot? Assume x greater-than-or-equal-to 0.
x y squared StartRoot 8 x cubed EndRoot
2 x cubed y cubed StartRoot x y squared EndRoot
2 x cubed y Superscript 4 Baseline StartRoot 2 x EndRoot
4 x cubed y Superscript 4 Baseline StartRoot x EndRoot
Answers
The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.
To understand why this is the case, let's break down each expression and simplify them step by step:
StartRoot \(8 x^7 y^8\) EndRoot:
We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.
Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.
(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:
Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.
Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.
Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.
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Consider the formula for the slope between two coordinate points, m, shown below.
m
92 – 91
I 2
51
Which of the following equations is equivalent to the slope formula?
Answers
Answer:
y2 = m(x2 - x1) + y1
Step-by-step explanation:
Given the slope formula :
m = (y2 - y1) / (x2 - x1)
To obtain an equivalent expression :
We cross multiply :
m(x2 - x1) = y2 - y1
Making y2 the subject ;
Add y1 to both sides
m(x2 - x1) + y1 = y2 - y1 + y1
m(x2 - x1) + y1 = y2
y2 = m(x2 - x1) + y1
Which situation can be modeled with an exponential function?
A computer downloads 100 kilobytes of data per minute.
A tree grows 8 inches per year.
The number of visits to a website doubles every 24 hours.
The population of bacteria grows by 50 bacteria.
Answers
Answer: the answer is c
Step-by-step explanation:
Answer:
c (The number of visits to a website doubles every 24 hours.)
Step-by-step explanation:
how you do the first one
Answers
I HOPE IT WILL HELP YOU.
Thank you.
Which statement describes a cause of screwed data
Answers
a sample that excludes subjects that are not part of the population being measured.
Sam can ride his bike 4.2 kilometers in 6 minutes. Amanda can ride her bike 3.2 kilometers in 8 minutes. Jesse can ride his bike 3.0 kilometers in 5 minutes.
Which rider might go farther in 1 minute?
Answers
Answer:
jesse or sam i think its sam by a little bit.
Step-by-step explanation:
Answer:
Sam
Step-by-step explanation:
Find all of their speeds to find how far they will go in 1 minute, by dividing the number of kilometers by the number of minutes:
Sam
4.2/6
= 0.7 km/min
Amanda
3.2/8
= 0.4 km/min
Jesse
3/5
= 0.6 km/min
Since 0.7 is the greatest number, that means Sam is the rider that will go the farthest in one minute.
(m? - 5 m +6 )
÷(m - 2)
Answers
Answer:
(m? - 5 m +6 ) ÷ (m - 2) = \(\frac{m}{-5m+6} / (m - 2)\)
Step-by-step explanation:
Divide the first expression by the second expression.
\(\frac{m}{-5m+6} / (m - 2)\)
I hope this helps.
The cube of the product of 4 and a number
Answers
hi
if you call the number "n" you have : ( 4n)³
The cube formed by the product of 4 and a number is (4 * n)^3.
What are cubes?A number's third power, or the outcome of multiplying three occurrences of the number n together, is known as the cube In mathematics and algebra. A superscript 3 represents the cube of a number or any other mathematical expression.The name comes from the fact that the volume of a geometric cube is equal to the cube of its side length.According to our question ,
Let n be any number on any integer.The cube of the product of and any number will be = (4 * n)^3.Hence we can say that the cube formed by the product of 4 and a number is (4 * n)^3.
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HELP ON THESE TWOOO.....it’s for mathhhhhh
Answers
Answer:
6-2I hope this helps!
1. If AACB AEDF, what is the measure of ZEFD.
Answers
Answer:
Step-by-step explanation:
110
What is the weight of a 32 kg child
Answers
Answer:
32000 grams
Step-by-step explanation:
The weight of a 32 kg child in pounds is 70.56 pounds.
What is Measurement unit?
A measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.
Given that;
The weight of baby = 32 kg
Now,
Since, 1 kg = 2.205 pounds
So, We convert the weight of baby from kg to pounds as;
1 kg = 2.205 pounds
32 kg = 32 x 2.205 pounds
= 70.56 pounds.
Thus, The weight of a 32 kg child in pounds is 70.56 pounds.
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least common multiple of 5/12 and 7/16
Answers
The least common multiple LCM of 5/12 and 7/16 is 35/16 or 2 whole number 3/16 expressed as a mixed fraction.
Least Common MultipleThe least common multiple also called LCM of two numbers is the smallest positive integer that is divisible by both numbers.
5/12 = 1/2 × 1/2 × 1/3 × 5 {expressed as product of its prime factors}
7/16 = 1/2 × 1/2 × 1/2 × 1/2 × 7 {expressed as product of its prime factors}
so their least common multiple is calculated as;
LCM = 1/2 × 1/2 × 1/2 × 1/2 × 5 × 7
LCM = 35/16
Therefore, the LCM of 5/12 and 7/16 is the fraction 35/16 or expressed as 2 whole number 3/16.
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when the function f(x) = 2x^n + ax² - 6 is divided by (x+3), the remainder is 129.
calculate the value of "a" and "n" and hence write the complete polynomial function.
Answers
The complete polynomial is f(x) = 2x³ + 15x² - 6 if n = 3 and a = 15
Given is polynomial f(x) = 2xⁿ + ax² - 6, when divided by (x+3), the remainder is 129,
Calculating the values of a and n :-
From the question, we have the following parameters that can be used in our computation:
f(x) = 2xⁿ + ax² - 6 is divided by (x+3), the remainder is 129
This means that,
f(-3) = 129
So, we have
f(-3) = 2(-3)ⁿ + a(-3)² - 6
f(-3) = 2(-3)ⁿ + 9a - 6
2(-3)ⁿ + 9a - 6 = 129
2(-3)ⁿ + 9a = 135
Assume n = 3
So, we have
2(-3)³ + 9a = 135
2/27 + 9a = 135
9a = 135 - 2/27
9a = 3643/27
a = 3643/243
a = 15
Therefore,
n = 3 and a = 15
So, the complete polynomial is f(x) = 2x³ + 15x² - 6
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which of the following 5-digit numbers can be rounded to 20,000?
Answers
from the given graph: state it's
a) amplitude
b) period
c) function of the graph:
Answers
Step-by-step explanation:
The amplitude is 2. Amplitude means height from the x-axis to the crest/trough.
The period is 2pi. It is from crest to crest (next crest) or trough to trough (next trough).
Note that crest are the highest points of a wave, and that troughs are the lowest points of a wave. (we are talking about transverse waves, but this is more of a physics thing).
Function of graph:
By playing around in a graphing calculator, I got the equation to be
2 (cos (x + pi/2)).
the 2 changes the amplitude, and the + pi/2 shifts the graph by pi/2 to the left.
A hot air balloon descended 3240 feet in an hour. Find the change in altitude per minute?
Answers
3,240 / 60 = 54
Therefore, the change in altitude per minute is 54 feet.
Unit analysis is a tool that we can use to convert units. It involves multiplying the original number by a fraction to cancel out units.
Solving the QuestionWe're given:
\(\dfrac{3240\hspace{4}feet}{hour}\)
We also know that:
\(\dfrac{hour}{60\hspace{4}minutes}\)
Multiply the two to cancel out the hour:
\(\dfrac{3240\hspace{4}feet}{hour}\times\dfrac{hour}{60\hspace{4}minutes}\\\\=\dfrac{3240\hspace{4}feet}{60 minutes}\)
Simplify:
\(=\dfrac{54\hspace{4}feet}{minute}\)
Answer\(\dfrac{54\hspace{4}feet}{minute}\)
John wishes to choose a combination of two types of cereals for breakfast - Cereal A and Cereal B. A small box (one serving) of Cereal A costs $0.50 and contains 10 units of vitamins, 5 units of minerals, and 15 calories. A small box (one serving) of Cereal B costs $0.40 and contains 5 units of vitamins, 10 units of minerals, and 15 calories. John wants to buy enough boxes to have at least 500 units of vitamins, 600 units of minerals, and 1200 calories. How many boxes of each cereal should he buy to minimize his cost?
Answers
Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:
10x + 5y ≥ 500 (minimum 500 units of vitamins)
5x + 10y ≥ 600 (minimum 600 units of minerals)
15x + 15y ≥ 1200 (minimum 1200 calories)
We want to minimize the cost, which is given by:
0.5x + 0.4y
This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:
10x + 5y = 500
5x + 10y = 600
15x + 15y = 1200
Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.
Next, we can calculate the value of the cost function at each corner point of the feasible region:
Corner point A: (20, 40) -> Cost = 20
Corner point B: (40, 25) -> Cost = 25
Corner point C: (60, 0) -> Cost = 30
Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.
I invested $1585 for 5 years and
earned $475.50 in interest. What was
the interest rate?
Answers
Answer:
6%
Step-by-step explanation:
Given data
Principal= $1585
Time = 5 years
Interest = $475.50
Rate =???
The expression for the interest is given as
SI=PRT/100
substitute
475.50=1585*R*5/100
Cross multiply
475.50*100= 7925R
47550=7925R
R= 47550/7925
R= 6%
Hence the rate is 6%
different equation dy÷dx+ytanx=secx
Answers
Answer:
First, we rearrange the equation to isolate the y-term on one side:
dy/dx + ytanx = secx
Then, we multiply both sides by the integrating factor, which is e^(∫tanx dx) = e^(ln|secx|) = |secx|: | secx| dy/dx + ysecx tanx = 1
Next, we can write this as the derivative of a product using the product rule: d/dx (y |secx|) = 1
Integrating both sides with respect to x, we get: y |secx| = x + C
where C is the constant of integration. Solving for y, we have:
y = (x + C)/|secx|
Note that there is a singularity at x = (2n + 1)π/2, where the denominator |secx| is zero. At these points, the solution is not defined
Consider the following figure.
(Note that the figure is not drawn to scale.)
20°
L
47°
89°
Order the side lengths IK, KL, IJ, IL, and LJ from least to greatest.
Answers
The side lengths from least to greatest as follows:
IK < KL < IJ < IL < LJ
To order the side lengths IK, KL, IJ, IL, and LJ from least to greatest, we can analyze the given figure.
Since the figure is not drawn to scale, we cannot determine the exact lengths of the sides. However, we can make some observations based on the given angles.
Let's analyze the angles:
Angle L: Since angle L is marked as 47°, we know that side KL is the shortest side, as it is opposite to the smallest angle in a triangle.
Angle I: Since angle I is marked as 20°, we can infer that side IJ is longer than side IK, as it is opposite to a larger angle.
Angle LJ: Since angle LJ is marked as 89°, we can conclude that side LJ is the longest side, as it is opposite to the largest angle in the triangle.
Based on these observations, we can order the side lengths from least to greatest as follows:
IK < KL < IJ < IL < LJ
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A particular restaurant can legally have only 150 people in it at one time. The tables in the restaurant can seat 4 people at a time. The number of tables, t, in the restaurant can be represented by the inequality 4t < 150. What is the maximum number of tables the restaurant can have?
Answers
Answer:
The correct answer would be 37.5, but since you cant have half a table, its rounds up to A., 37. Hope you found this helpful, and if so, please mark as Brainliest! (:
A couple bought some stock for RM30 per share that pays an annual dividend of
RM0.90 per share. After 1 year, the price of the stock was RM33. Find the simple
interest rate on the growth of their investment.
Answers
Answer:
The answer is "13%".
Step-by-step explanation:
\(P_0 = 30\\\\D_1 = 0.90\\\\P_1 = 33\\\\\)
\(Increase = 33 - 30 + 0.90\\\\\)
\(= 3+0.90\\\\=3.90\)
\(\text{Calculating increasing }\% :\)
\(= \frac{3.90}{30} \times 100 \\\\= \frac{390}{30} \\\\= \frac{39}{3} \\\\= 13\%\)
Translate each phrase into a variable expression. Use n for the variable.
Nine increased by twice a number
Answers
The expression of the phrase " Nine increased by twice a number " is 2n + 9
The given phrase is
Nine increased by twice a number
We have to convert the the phrase to the expression
The expression is the mathematical statement that consist of different variables, numbers and mathematical operators. The mathematical operators are addition, subtraction, division and multiplication. The equal sign and inequality will not be the part of expression.
Consider the number as n
Twice the number = 2n
nine increased by twice a number = 2n + 9
Hence, the expression of the phrase " Nine increased by twice a number " is 2n + 9
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Is 3/5 A.irrational, B.rational, C.natural and whole, or D.natural, whole integer and rational
Answers
Answer:
B
Step-by-step explanation:
3/5 is a fraction, meaning it isn't irrational, natural, whole or an integer, therefore the answer is rational (B).
Answer:
B.rational
Step-by-step explanation:
3/5 is written as a fraction so it is a rational number
It is not a whole number since it is a reduced fraction that is less than 1
plzzzzzzzzzzzz i need help
Answers
Answer:
27
Step-by-step explanation:
-5a-b
-5(-6)-3
30-3
2
-5a - b
a = -6
b = 3
(-5 * -6) - 3
30 - 3 = 27
Which expression below represents the average wages the company pays per employee each week?
Answers
According to the given data we have the following:
19 employees that earn $360
18 employees that earn $400
8 employyes that earn $480
5 employees that earn $600
The total employees would be=19+18+8+5=50
Therefore, to find the average we have to put at the numerator the amount of wages times of what correspond to each employee, and at the denominator the total of employees which are 50. Therefore, the expression that represents the average wages the company pays per employee each week would be 2.
Estimate 6,976 + 3,983 + 13,560 by first rounding each number to the nearest thousand.
Answers
Answer:
Step-by-step explanation:
The thousand mark is the 4th number when going from right to left. So it would be the {6},976. When it comes to rounding, you go "5 and above, give it a shove, 4 and below, let it go. 6,976 rounded to the nearest thousand is 7,000, 3,983 rounded to the nearest thousand is 4,000, 13,560 rounded is 14,000.
7,000 + 4,000+ 14,000 = 25,000
whats answere y+2=-3 (x - 4)
Answers
Answer:
Slope = 6.000/2.000 = 3.000
x-intercept = 10/3 = 3.33333
y-intercept = -10/1 = -10.00000
Step-by-step explanation:
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -10.000 and for x=2.000, the value of y is -4.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -4.000 - (-10.000) = 6.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Answer:
x=10/3
Step-by-step explanation:
0+2=-3x+12
2=-3x+12
3x=12-2
3x=10
1. Find the equation of the image of the circle x² + y2 + 16x-24y + 183 = 0 by rotated the line mirror 4x + 7y + 13 = 0. 2. The image of the circle (x - 3)² + (y-2)² = 1 in the line mirror ax + by = 19 is (x-1)³ + (y-16)2 = 1 then, find the values of (a, b). 3. Find the equation of a line passing through the origin and making an angle with the 4 line y-3x-5. 4. A parabola is drawn with its focus at (3,4) and vertex at the focus of the parabola y²-12x - 4y + 4 = 0. The n find equation of the parabola. 5. If the line ax + by + c = 0 touches the circle x² + y² - 2x = and is normal to the circle x² + y² + 2x - 4y + 1 = 0, then find the value of (a, b). 6. If the line through the points (-2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24). Find the value of x. -3 7.1² 14 231= [] then find the matrix A 8. Find the equation of the ellipse having its center at the point (2,-3), one and one vertex at (4, -3). 3 9. Find the value of x if-1 0 10. Solve the linear system using Cramer's rule a) 2 1 2 4 (6x - 4y = -12 8x - 3y = -2 X = 16 -21 3x + 2y = z = 5 b) x-y+3z = -15 (2x + y +7z = -28 one focus at (3,-3) 11. Find the value of k for which the following system of linear equations has infinite solutions: x + (k+1)y = 5 ((k+1)x + 9y = 8k - 1
Answers
Answer:
-72x - 53y + 287 = 0.
Step-by-step explanation:
To find the equation of the image of the circle, we need to reflect each point on the circle in the given line mirror.
The line mirror equation is given as 4x + 7y + 13 = 0.
The reflection of a point (x, y) in the line mirror can be found using the formula:
x' = (x - 2Ay - 2B(Ax + By + C)) / (A^2 + B^2)
y' = (y - 2Bx + 2A(Ax + By + C)) / (A^2 + B^2)
where A, B, and C are the coefficients of the line mirror equation.
For the given line mirror equation 4x + 7y + 13 = 0, we have A = 4, B = 7, and C = 13.
Now, let's find the equations of the image of the circle.
The original circle equation is x² + y² + 16x - 24y + 183 = 0.
Using the reflection formulas, we substitute the values of x and y in the circle equation to find x' and y':
x' = (x - 2Ay - 2B(Ax + By + C)) / (A^2 + B^2)
= (x - 2(4)y - 2(7)(4x + 7y + 13)) / (4^2 + 7^2)
= (x - 8y - 8(4x + 7y + 13)) / 65
= (x - 8y - 32x - 56y - 104) / 65
= (-31x - 64y - 104) / 65
y' = (y - 2Bx + 2A(Ax + By + C)) / (A^2 + B^2)
= (y - 2(7)x + 2(4)(Ax + By + C)) / (4^2 + 7^2)
= (y - 14x + 8(Ax + By + C)) / 65
= (y - 14x + 8(4x + 7y + 13)) / 65
= (57x + 35y + 104) / 65
Therefore, the equation of the image of the circle is:
(-31x - 64y - 104) / 65 + (-57x + 35y + 104) / 65 + 16x - 24y + 183 = 0
Simplifying the equation, we get:
-31x - 64y - 57x + 35y + 16x - 24y + 183 + 104 = 0
-72x - 53y + 287 = 0
So, the equation of the image of the circle is -72x - 53y + 287 = 0.