Answer:38
Step-by-step explanation:
Find the minimum value of the parabola y = x2 − 6.
The minimum value of the parabola is y = -6
An equation of a parabola is given as
y = x²-6
We will find its minimum value using the differentiation method.
For this first we will find the derivative with respect to x and find the value of x at which the derivative becomes zero. The derivative becomes zero only when the parabola has either a maximum or minimum value. We further check whether the parabola has a minimum or maximum at that x by finding the second derivative of the parabola at that x.
So first derivative of y with respect to x is 2x.
So 2x = 0
⇒ x =0
Now take the second derivative of y with respect to x at x = 0,
Second derivative = 2 > 0 at x = 0
Here the second derivative is greater than zero at x = 0. So y has a minimum value at x = 0
The minimum value of the parabola is,
y = 0² - 6
⇒ y = -6
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explain to Elena what her mistake war and what the correct solution is
Alex buys 32oz of yogurt for $2.56. John buys a Goz yogurt for $0.48. Are the unit prices equal? Write an equation using the unit price to represent this relationship if they are equal. options: Yes, y=5.33x . Yes, y=12.5x, No, the ratios are not equivalent . Yes, y=0.08x
Answer:
Yes, y=0.08x
Explanation:
The unit price can be calculated as the price divided by the number of ozs, so the unit prices are:
[tex]\frac{\text{Price}}{\text{Ounces}}=\frac{\text{ \$2.56}}{32\text{ oz}}=\text{ \$0.08 per ounce}[/tex][tex]\frac{Price}{Ounces}=\frac{\text{ \$0.48}}{6\text{ oz}}=\text{ \$0.08 per ounce}[/tex]Therefore, the unit prices are equal, so the equation that represents the relationship is:
y = kx
Where k is the unit price, so replacing k by 0.08, we get:
y = 0.08x
So, the answer is:
Yes, y=0.08x
The table below gives the population of a town (in thousands) from 2000 to 2008. What was the average rate of change of population between 2002 and 2004, and between 2002 and 2006?
The average rate of change in population is -35 between 2002 and 2004, and -2.5 between 2002 and 2006 which represents the decrease in the population.
What is Lagrange mean value theorem?Lagrange mean value theorem states that, if a function f is continuous over the closed interval [a, b] and differentiable over the open interval (a, b), then there must be at least one point c in the interval (a, b) where the slope of the tangent at the point c is equal to the slope of the tangent through the curve's endpoints, resulting in the expression f'(c) = {F(b) -F(a)}/(b-a)
As per the given data in the table, the required solution would be below
The average rate of change in population between 2002 and 2004 as:
⇒ (76-83)/(2004-2002)
⇒ -7/2
⇒ -3.5
The average rate of change in population between 2002 and 2006
⇒ (78-83)/(2006-2002)
⇒ -5/2
⇒ -2.5
This represents the decrease in the population.
Therefore, the average rate of change in population is -35 between 2002 and 2004, and -2.5 between 2002 and 2006.
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There is a new fair coming to town this weekend. Tickets are selling for $10.99 for adults and $5.99 for kids. Each ride is $0.99 cents each. Make an equation for adults tickets and another equations for kids ticket. How much money would each spend if they each ride 5 rides?
Answer:
(a)Adult:10.99+0.99x, Kid: 5.99+0.99x
(b)Adult's Total cost = $15.94, Kid's Total cost =$10.94
Explanation:
Cost of a ride = $0.99
Let x be the number of rides.
Cost of an Adult Ticket = $10.99
An equation for adult tickets will therefore be: 10.99+0.99x
Similarly, the cost of a kid ticket =$5.99
An equation for adult tickets will therefore be: 5.99+0.99x
(b)If they ride 5 tickets each, the amount of money spent will be:
x=5 rides
Total cost for an adult=10.99+0.99(5)
=10.99+4.95
=$15.94
Total cost for a kid = 5.99+0.99(5)
=5.99+4.95
=$10.94
Write the correct inequality for the following statement and then solve for the given number of
guests.
You are in charge of planning your mother's surprise party. You have
found a hall that rents for $225 and a caterer that will charge you $15 per
guest. Write an inequality to calculate your total cost (T) based on the
number of guests (g).
If you have a total budget of $1000 how many guests can you
invite?
Step-by-step explanation:
You are in charge of planning your mother's surprise party. You have found a hall that rents for $225 and a caterer that will charge you $15 per guest. Write an inequality to calculate your total cost (T) based on the number of guests (g).
T = 15g + 225
If you have a total budget of $1000 how many guests can you
invite?
1,000 = 15g + 225
subtract 225 from both sides:
1,000 -225 = 15g + 225 - 225
775 = 15g
divide both sides by 15:
775/15 = 15g/15
g = 51.66
Because you cannot invite part of a guest round down to inviting 51 guests
is the answer 9 im lost can you help me
Solution
Population of the town = 3000
Rate = 4%
Amount = 4700
[tex]A=P(1+r)^n[/tex][tex]\begin{gathered} 4700=3000(1+4\text{ \%\rparen}^n \\ \frac{4700}{3000}=1+0.04)^n \\ 1.567=1.04^n \end{gathered}[/tex]Find log of both side
[tex]\begin{gathered} 1.567=1.04^n \\ ln1.567=ln1.04^n \\ nln1.04=1.567 \\ n=\frac{ln1.567}{ln1.04} \\ n=11.5yrs \end{gathered}[/tex]Therefore the number of years it will take population to reach 4700 = 11.5yrs
A(-6, -2)→ A'(-6, 2) B(-3, -6) →B'(-3, 6) C(-2,-2)→ C'(-2, 2)
A(-6, -2)→ A'(-6, 2) B(-3, -6) →B'(-3, 6) C(-2,-2)→ C'(-2, 2). The y-coordinates are different with the negative sign in the given transformations.
Given that,
A(-6, -2)→ A'(-6, 2) B(-3, -6) →B'(-3, 6) C(-2,-2)→ C'(-2, 2)
We have to find the difference of the transformations.
So,
First take A(-6, -2)→ A'(-6, 2)
We can see the difference is the A of y-coordinates have negative sign of the A'.
Now,
Take B(-3, -6) →B'(-3, 6)
We can see the difference is the B of y-coordinates have negative sign of the B'.
Now,
Take C(-2,-2)→ C'(-2, 2)
We can see the difference is the C of y-coordinates have negative sign of the C'.
Therefore, The y-coordinates are different with the negative sign in the given transformations.
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A rancher has 800 feet of fencing to put around a rectangular field and then subdivide the field into three identical smaller rectangular plot by placing to fence is parallel to the field shorter side. Find the dimensions that maximize the enclosed area. Write your answer as a fraction reduced to lowest term
The diagram of the problem is:
S is the length of the shorter side of the fence. L is the length of the longest side of the field.
We know that the perimeter of the rectangle is 800ft. This means:
[tex]2S+2L=800[/tex]And the area:
[tex]A=SL[/tex]The smaller rectangles will have dimensions:
The area is:
[tex]a=\frac{SL}{3}[/tex]As we can see, if we maximize the area of the bigger rectangle "A", we are also maximizing the area of the smaller rectangles "a".
Then, we have two equations:
[tex]\begin{gathered} 2S+2L=800 \\ A=SL \end{gathered}[/tex]We can solve for L in the first equation:
[tex]\begin{gathered} 2S+2L=800 \\ 2L=800-2S \\ L=400-S \end{gathered}[/tex]Then substitute in the second:
[tex]A=S(400-S)[/tex]Simplify:
[tex]A=400S-S^2[/tex]This is a function of the area depending on the length of the shorter side of the rectangle:
[tex]A(S)=400S-S^2[/tex]We can find the maximum of this function if we find the value where the derivative of this function is 0.
Let's differentiate:
[tex]A^{\prime}(S)=400-2S[/tex]And now we find where A'(S) = 0:
[tex]\begin{gathered} 0=400-2S \\ 2S=400 \\ S=200 \end{gathered}[/tex]We have found that the shorter side must have a length of 200ft to maximize the area. Let's find the length of the larger side:
[tex]L=400-200=200[/tex]As expected, the quadrilateral which maximizes the area is the square. Thus, the dimensions of the field are 200ft x 200ft
The abc one is my question could I please get sum help
For this problem, we are given two sides and one angle of a triangle. We need to determine the length of the side that is opposite to the known angle.
To solve this problem, we need to use the law of cosines.
[tex]a=\sqrt{b^2+c^2-2bc\cdot\cos(m\angle A)}[/tex]Applying the given data, we have:
[tex]\begin{gathered} a=\sqrt{13^2+21^2-2\cdot13\cdot21\cdot\cos(105)}\\ \\ a=\sqrt{169+441-546\cdot(-0.2588)}\\ \\ a=\sqrt{610+141.3048}\\ \\ a=\sqrt{751.3048}=27.41 \end{gathered}[/tex]The correct answer is 27.4.
I need help with this question
The coordinates of B after the translation is ( 3 , -2)
What is coordinates in maths?
Coordinates are a pair of integers (also known as Cartesian coordinates), or occasionally a letter and a number, that identify a specific point on a grid, also known as a coordinate plane. The x axis (horizontal) and y axis are the two axes that make up a coordinate plane (vertical).Transformation involves changing the position of a shape.
The coordinates of B after the translation is (-4,-2)
A = ( 1, 1)
B = ( 3 , 4)
C = ( -1 , 8 )
The translation rule is given as ( x , y-6)
So, the coordinates of B' is calculated using
( x , y ) ⇒ ( x , y-6)
This gives
B = ( 3 , 4) ⇒ ( 3 , 4 - 6 )
( 3 , 4) ⇒ ( 3, -2 )
Rewrite as
B' = ( 3, -2 )
Hence, the coordinates of B after the translation is ( 3 , -2)
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Triangle ABC is similar to triangle DEFwhich proportion can be used to find the length of DE in centimeters?A. 4/3 = DE/9B. 5/15 = DE/4C. 4/DE = 9/3D. 9/DE = 3/5
In the given figure, Triangle ABC is similar to triangle DEF.
Applying the Similar Triangle Formula, the proportion to be used to find the length of DE is:
[tex]\frac{4\text{ cm}}{3\text{ cm}}\text{ = }\frac{DE}{9\text{ cm}}[/tex]Therefore, the answer is A.
Hidden Hollow Mining Co. acquired mineral rights for $49,500,000. The mineral deposit is estimated at 55,000,000 tons. During the current year, 17,050,000 tons were mined and sold.
A. Determine the depletion rate.B. Determine the amount of depletion expense for the current year.C. Journalize the adjusting entry on December 31 to recognize the depletion expense. Refer to the Chart of Accounts for exact wording of account titles.
A. The depletion rate is $0.90 per ton.
B. The amount of depletion expense that Hidden Hollow Mining Co. should recognize for the current year is $15,345,000.
C. The adjusting journal entry to recognize the depletion expense is as follows:
Adjusting Journal Entry:Debit Depletion Expenses $15,345,000
Credit Accumulated Depletion $15,345,000
To recognize the depletion expense for the current year.What is an adjusting entry?Adjusting entries are the journal entries made at the end of the accounting period to recognize unrecorded expenses, revenue, and other gains or losses.
An example of an adjusting entry is the entry to recognize depreciation, amortization, or depletion expenses.
The value of the mineral rights = $49,500,000
The estimated mineral deposit = 55,000,000 tons
Depletion rate = $0.90 per ton ($49,500,000/55,000,000)
The current year's tons mined and sold = 17,050,000 tons
Amount of depletion expense for the current year = $15,345,000 (17,050,000 x $0.90)
Adjusting Entry Analysis:Depletion Expenses $15,345,000 Accumulated Depletion $15,345,000
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9-3 2 = (x) 6 what is the function family.
a. G(x) = 1/4x - 5 Since it's similar to the equation f(x)=mx + b, which is a linear
function, g(x) is a linear function.
b. f(x) = 2*(x - 1)^2 - 5 Since the degree of the polynomial is 2, we deduce it is a cuadratic function.
c. f(x) = 7 Since the degree of x is zero ( there is no x) , we deduce it is a constant function.
Consider the following compound inequality. 7
a)The solution of the inequality is 3 < x ≤ 5
c) The solution in interval notation is (3, 5]
Step - by - Step Explanation:
What to find?
• The solution of the inequality.
,• The graph of the inequality.
,• The solution in interval notation.
Given:
7 < x +4 ≤ 9
Re-write the above inequality.
x + 4 > 7 or x + 4 ≤ 9
Solve for x in each case.
x + 4 > 7
Subtract 4 from both-side of the inequality.
x > 7 - 4
x > 3
x + 4 ≤ 9
Subtract 4 from both-side of the inequality.
x ≤ 9 - 4
x≤ 5
Combine the two solutions.
3Hence, the solution to the inequality is 3 < x ≤ 5
b) We can proceed to graph the inequality.
c) The solution in interval notation is (3, 5]
What the are of this parallelogram?
Mr. Knox's garden is in the shape of a triangle. What is the area of Mr. Knox’s garden? __ square feet
Using the area of a triangle, the area of Mr. Knox's garden is: 58 square feet.
How to Find the Area of a Triangular Shape?The area of any triangular shape can be calculated using the formula for the area of a triangle.
The area of a triangle = 1/2(base)(height).
The shape of Mr. Knox's garden is triangular. The parameters of his triangular garden are:
Length of the base of the triangular garden = 24½ ft
Height of the triangular garden = 8 ft.
Area of the garden = 1/2(24½)(8)
Area of the garden = 1/2(29/2)(8)
Area of the garden = 1/2(232/2)
Area of the garden = 232/4
Area of the garden = 58 square feet.
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If n ∥ m, which of the following statements are true? Select all that apply. Line m and n are parallel lines. Point B is lies on line m. Point A and C are lies on line n. There are two lines started from point B and one line passes through point A and one line passes through point B. So there is a triangle ABC. The angle ACB is denoted by 1. The angle ABC is denoted by 3. There is an angle with line m and line AB is denoted by 2 and an angle with line m and line BC is denoted by 4. Angle 1 is alternate interior angle of angle 4. The opposite angle of angle 1 is 60 degree. Also the corresponding angle of angle 2 is 20 degree. A. m∠2 = 60° B. m∠3 = 100° C. m∠2 + m∠4 = 80° D. m∠2 + m∠3 = 80°
Based on the angle relationships formed by the parallel lines, the statements that are true are:
B. m∠3 = 100°
C. m∠2 + m∠4 = 80°
How to Apply the Angle Relationship Formed by Parallel Lines?Some of the angle relationship that applies when two parallel lines are crossed by a transversal are:
Corresponding angels that are congruent.Vertical angles that are congruent.Given the image attached below, where m and n are parallel lines, we can deduce the following measures of the numbered angles based on the angle relationships:
Measure of angle 1 = 60° [vertical angles]
Measure of angle 2 = 20° [corresponding angles]
Using the triangle sum theorem, we also have:
Measure of angle 3 = 180 - m∠CAB - m∠1
Measure of angle 3 = 180 - 20 - 60 = 100°
m∠4 = 60° [corresponding angles]
m∠2 + m∠4 = 20 + 60 = 80°
From the above, we can conclude that the statements are:
B. m∠3 = 100°
C. m∠2 + m∠4 = 80°
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Parallel lines are those straight lines that are always the same distance apart from each other.
B m∠3 = 100°
C. m∠2 + m∠4 = 80° are true
What are parallel lines?Parallel lines are those straight lines that are always the same distance apart from each other. · Parallel lines never meet no matter how much they are extended.
Given that, n||m
Point B is lies on line m.
Point A and C are lies on line n.
There are two lines started from point B and one line passes through point A and one line passes through point B forms a triangle ABC.
∠ACB=1
∠ABC=2
There is an angle with line m and line AB is denoted by 2.
Using the triangle sum theorem, we also have:
Measure of angle 3 = 180 - m∠CAB - m∠1
Measure of angle 3 = 180 - 20 - 60 = 100°
m∠4 = 60° [corresponding angles]
m∠2 + m∠4 = 20 + 60 = 80°
Hence From the above, we can conclude that the statements are:
B. m∠3 = 100°
C. m∠2 + m∠4 = 80°
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Passing through (-4,-5) and parallel to the line whose equation is y= -3x+4
For the given values the equation of new line is y = -3x - 17
What is a line equation example?The formula for these lines is y = mx + b, where m denotes the slope and b the y-intercept. Our line has a slope of 3 and a y-intercept of -5, which we know from the question. By entering these numbers, we obtain the equation of our line as y = 3x - 5.
Given,
The equation of line is y= -3x+4
as the lines are parallel,
slope of lines will be same,
∴ Slope of new line = -3
The equation of line is:
y - y1 = m(x - x1)
Where x1, y1 are the given coordinates and m is the slope
⇒ y -(-5) = -3 (x - (-4))
⇒ y + 5 = -3 (x + 4)
⇒ y + 5 = -3x - 12
⇒ y = -3x - 17
∴ The equation of the line is y = -3x - 17
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see attached graph photo
Given: The square STUV
To Determine: The coordinate of the image after reflection over the y-axis
Solution
The reflection over the y-axis rule is
[tex](x,y)\rightarrow(-x,y)[/tex]Locate the coordinates of STUV
Let us apply the rule to get the coordinate of the image
[tex]\begin{gathered} S(-10,-10)\rightarrow S^{\prime}(10,-10) \\ T(0,-10)\rightarrow T^{\prime}(0,-10) \\ U(0,0)\rightarrow U^{\prime}(0,0) \\ V(-10,0)\rightarrow V^{\prime}(10,0) \end{gathered}[/tex]Hence, the coordinate of the image after a reflection over the y-axis is
S'(10, - 10)
T'(0, - 10)
U'(0, 0)
V'(10, 0)
Please help with math ! These are due tomorrow.
3) Alex had 20 video games at the beginning.
2) The strategy to solve the problem backward is:
The number of games Alex has now is 16 games.
The number of games he gave to his brother is 2, so add 2 to the current number of video games, 16 + 2 = 18
Now add the games he sold, which are given as 3
18 + 3 = 21
Subtract the games he traded with Hector,i.e. 6 video games
21 - 6 = 15
This obtained number is 3/4 of his games,
3/4 of the total video games = 15
Therefore, the total video games were = (15×4)/3 = 20
4) Yes the answer makes sense.
Operations in reverse order are:
The number of video games given by Alex to hector is = 1/4 of 20 = 5
Remaining video games = 20 - 5 = 15
Number of games after adding exchanged 6 video games = 15+6 = 21
Number of games after Alex sold 3 video games = 21 -3 = 18
Number of games after Alex gave 2 to his brother = 18 - 2 = 16 video games
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The graph below represents the number of miles, y, that Jacob can drive his car for every x gallons of gas. Find the rate of change.
The slope (rate of change) of the graph shown is 31.3 miles per gallon.
What is an equation?An equation is an expression that shows the relationship between two variables and expressions.
Slope is the ratio of vertical rise to horizontal run. It is given by:
Slope = rise / run
The point passes through (10, 313) and (20, 626), hence:
Slope = rise/run
Slope = (626 - 313) / (20 - 10) = 31.3
The graph's slope is 31.3 miles per gallon.
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I need help with this and please get this one right
There is a 0.765 percent chance that the flight will leave on time when it is not raining.
What is probability?Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is. In the probability scale, 0 indicates an impossibility and 1 indicates a certainty.
Given a 0.1 delay probability, the probability of the airplane departing on time is 1-0.1 = 0.9.
The likelihood that it won't rain is 1-0.15 = 0.85.
If it weren't raining, there is a 0.9 (0.85) = 0.765 percent chance that a flight would leave on time.
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Which of the following functions grows the fastest as x grows without bound?
Answer:
[tex]f(x)=e^x[/tex]Explanation:
First, the function, g(x):
[tex]g(x)=e^{\cos(x)}[/tex]The function g(x) oscillates, thus, it does not increase.
The value of 'e' is approximately 2.7.
[tex]\begin{gathered} f(x)=e^x\approx2.7^x \\ h(x)=(2.5)^x \end{gathered}[/tex]Since 2.7 is greater than 2.5, we can infer that f(x) grows the fastest as x grows without bound.
What equation can be written in a form that shows a proportional relationship using variables
Answer:
y = kx
Step-by-Step explanation:
An equation shows a proportion relationship when it can be written in the following format:
[tex]\frac{y}{x}[/tex]So, in the context of this exercise, we need to pass x to the other side of the equation dividing, by itself.
In this question:
y = k+x
x alone cannot be passed dividing, just k+x
Y = k, there is no x.
The answer is y = kx, because we can also write this as:
[tex]\frac{y}{x}=k[/tex]A cube-shaped box has side lengths of 1.5 m, and it exerts a force of 63 N on the ground. Calculate the pressure, in N/m², that the box exerts on the ground. If your answer is a decimal, give it to 1 d.p.
Answer:
28 N/m²
Step-by-step explanation:
Since you are calculating pressure, you want your question in N/m².
Note that the one side of the box has a length of 1.5m, and so to get the area of the bottom face, you need to square 1.5m::
(1.5m)² = 2.25m²
Then you need to use the formula P=F/A
Where P is pressure, F is force, and A is area, plug in your variables::
P = [tex]\frac{63N}{2.25m^{2} }[/tex]
Then you get an answer of:[tex]28 \frac{N}{m^{2} }[/tex]
You always want to make sure that the answer's units align with what you are told to solve for. In this case, they do, so no further steps are needed.
Hope this helps! :)
Use the properties of exponents to write an equivalent expression for each given expression.
1. 6^4 x 6^3
2. (3^6)^-2
3. 7^3 x 2^3
4. 4^10 divided by 4^4
Please help :)
Answer:
Step-by-step explanation:
The length of a bridge is about 6.3 meters. Which number from the list is closest to 6.3?A. 40B. 748C. 735D. 737Pls help me
The closest number to 6.3 is the number 40, because when we substract 6.3 from 40, we get the smallest number.
40 - 6.3 = 33.7
748 - 6.3 = 741.7
Use a number line to round the number 573 to the nearest 10.
Answer: The answer is 570.
Step-by-step explanation:
So, if you know what numbers are, when you round, this question is easy. If you take a number line and put 570 on the left side and 580 on the right side, and 575 in the middle, you almost got it. Since the number we want to round is 573, we put it in the middle of 570 and 575. And since the number is closer to 570 than 580, the answer is 570. Your welcome!
find a formula for the nth term of the arithmetic sequence the first term is 7 and the common difference is -3
The formula for the nth term of the arithmetic sequence whose first term is 7 and the common difference is -3 is - a[n] = 10 - 3n
What is an Arithmetic progression?An arithmetic progression is a sequence of numbers such that the difference between the consecutive terms is constant. A sequence -
a₁ , a₂, a₃ , a₄ ...... aₙ
will be an arithmetic progression if -
a₂ - a₁ = a₃ - a₂ = a₄ - a₃ = d (constant) is called common difference of A.P. and a₁ = 'a' as the first term.
Given is the the first term equal to 7 and the common difference equal to
- 3.
We can calculate the nth term of an A.P. using the formula -
a[n] = a + (n - 1)d
a[n] = 7 + (n - 1)(- 3)
a[n] = 7 - 3n + 3
a[n] = 10 - 3n
Therefore, the formula for the nth term of the arithmetic sequence whose first term is 7 and the common difference is -3 is -
a[n] = 10 - 3n
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