Given:
The equation is
[tex]y=5x^3-6x^2-4x+8[/tex]
To find:
The coordinates of the turning point.
Solution:
We have,
[tex]y=5x^3-6x^2-4x+8[/tex]
Differentiate with respect to x.
[tex]\dfrac{dy}{dx}=5(3x^2)-6(2x)-4(1)+(0)[/tex]
[tex]\dfrac{dy}{dx}=15x^2-12x-4[/tex]
For the turning points [tex]\dfrac{dy}{dx}=0[/tex].
[tex]15x^2-12x-4=0[/tex]
Using quadratic formula:
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\dfrac{-(-12)\pm \sqrt{(-12)^2-4(15)(-4)}}{2(15)}[/tex]
[tex]x=\dfrac{12\pm \sqrt{144+240}}{30}[/tex]
[tex]x=\dfrac{12\pm \sqrt{384}}{30}[/tex]
Now,
[tex]x=\dfrac{12+\sqrt{384}}{30}\text{ and }x=\dfrac{12-\sqrt{384}}{30}[/tex]
[tex]x\approx 1.053\text{ and }x\approx-0.253[/tex]
Putting x=1.053 in the given equation, we get
[tex]y=5(1.053)^3-6(1.053)^2-4(1.053)+8[/tex]
[tex]y\approx 2.973[/tex]
Putting x=−0.253 in the given equation, we get
[tex]y=5(-0.253)^3-6(-0.253)^2-4(-0.253)+8[/tex]
[tex]y\approx 8.547[/tex]
Therefore, the turning points are (1.053,2.973) and (-0.253, 8.547).
A store sells about 30 pants each week for Nu 800 each. The owner expects to lose one sale each week for every increase in price of Nu 40. a) Write an expression to represent the i) new price of a pant after n Nu 40 price increases. ii) expected number of pants that will be sold weekly after n price increases. b) Write a function to represent the expected weekly sales as a function of the number of price increases of Nu 40. c) Use the function to determine the price that will maximize totally sales.
The new price after the price increase of Nu 40 will be Nu 840.
How to calculate the price?The price of a pant after n Nu 40 price increases will be:
= 800 + 40
= 840
The expected weekly sales as a function of the number of price increases will be:
= n - 1) × 800
= (30 - 1) × 800
= 29 × 800
= 23200
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Find the term that must be added to the equation x2+6x=7 to make it into a perfect square.
To make x² + 6x = 7 a perfect square, we add 16 to the equation.
In the question, we are asked for the term that must be added to the equation x² + 6x = 7, to make it into a perfect square.
The given equation can be shown as:
x² + 6x = 7,
or, x² + 6x - 7 = 0.
To make it a perfect square, we need to find the b² term as per the 2ab term for the formula, (a + b)² = a² + 2ab + b², where a is x.
This can be shown as:
x² + 6x - 7 = 0,
or, x² + 2(x)(3) - 7 = 0, where we get b = 3.
Thus, b² = 3² = 9, can be obtained by adding 16 to the equation, as -7 + 16 = 9.
Thus, we add 16 to both sides of the equation, to get:
x² + 2(x)(3) - 7 + 16 = 16,
or, x² + 2(x)(3) + 9 = 16,
or, (x + 3)² = 16, which gives us the required perfect square.
Thus, to make x² + 6x = 7 a perfect square, we add 16 to the equation.
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The table gives an inequality and a number to multiply both sides of the inequality by. Identify the new, true inequality.
A: (-16 > -4) (-16 < -4) (-16 = -4)
B: (40 > 8) (40 < 8) (40 = 8
C: (-45 > 15) (-45 < 15) (-45 =15)
D: (35 > -20) (35 < -20) (35 = -20)
Multiplying both sides of an inequality by a negative number (does not change) (reverses) the inequality symbol.
Multiplying both sides of an inequality by a negative number reverses the inequality symbol.
How to determine the true inequalities?The table of values is given as:
A: (-16 > -4) (-16 < -4) (-16 = -4)
B: (40 > 8) (40 < 8) (40 = 8
C: (-45 > 15) (-45 < 15) (-45 =15)
D: (35 > -20) (35 < -20) (35 = -20)
In the above list of inequalities, the true inequalities are
-16 < -4 --- because -16 is less than -4
40 > 8 --- because 40 is greater than 8
-45 < 15 --- because -45 is less than 15
35 > -20 --- because 35 is greater than -20
Lastly, when an inequality is multiplied or divided by a negative number, the inequality sign changes
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Answer:
-16 < -4
40 > 8
-45 < 15
35 > -20
Reverses
Step-by-step explanation:
hope this helps
help please its khan academy
What expression is equivalent to (square root)
Answer:
C.) [tex]x^{\frac{3}{2} } y^{\frac{19}{2} }[/tex]
Step-by-step explanation:
To simplify the expression, you need to:
1.) Rewrite [tex]\sqrt{xy^{3} }[/tex]
-----> [tex]\sqrt{x} = x^{\frac{1}{2} }[/tex]
2.) Distribute the exponents
-----> When an exponent is raised to another exponent, they should be multiplied
3.) Create common denominators
4.) Combine the variables
-----> When two variables with exponents are being multiplied, the exponents should be added
What is the solution of StartFraction negative 8 Over 2 y minus 8 EndFraction = StartFraction 5 Over y + 4 EndFraction minus StartFraction 7 y + 8 Over y squared minus 16 EndFraction?
The solution of the fraction given as -8/(2y - 8) = 5/(y + 4) - (7y + 8)/(y² - 16) is determined as 4 or - 0.25.
What is fraction?A fraction represents a part of a whole or, more generally, any number of equal parts.
A fraction can also be described as how many parts of a certain size there are, in a given whole.
Solution of the fractionThe fraction given can be written as follows;
-8/(2y - 8) = 5/(y + 4) - (7y + 8)/(y² - 16)
simplify as follows;-8/(2y - 8) = 5/(y + 4) - (7y + 8)/(y - 4)(y+4)
-8/(2y - 8) = [5(y - 4) - (7y + 8)] /(y-4)(y + 4)
-8/(2y - 8) = (5y - 20 + 7y + 8)/(y-4)(y + 4)
-8/(2y - 8) = (12y - 12)/(y-4)(y + 4)
cross and multiply both sides of the equation;
-8((y-4)(y + 4)) = (12y - 12)(2y - 8)
-8(y² - 16) = 24y² - 96y - 24y + 96
-8y² + 128 = 24y² - 120y + 96
0 = 32y² - 120y - 32
solve the quadratic equation using formula method;
a = 32, b = -120, c = - 32
y = 4 or -0.25
Thus, the solution of the fraction given as -8/(2y - 8) = 5/(y + 4) - (7y + 8)/(y² - 16) is determined as 4 or - 0.25.
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y=6
for the eqution
[tex]\frac{-8}{2y-8} =\frac{5}{y+4} -\frac{7y+8}{y^{2}-16 } \\[/tex]
Solve the equation below by factorising.
2m^2- 11m + 5 = 0
Answer:
[tex]m_{1} =1/2\\m_{2} =5[/tex]
Step-by-step explanation:
[tex]2m^{2} -11m+5=0[/tex]
[tex](2m-1)(m-5)=0[/tex]
[tex]2m-1=0\\2m=1\\m_{1} =1/2[/tex]
[tex]m-5=0\\m_{2} =5[/tex]
Hope this helps
A solid lies between planes perpendicular to the x-axis at x0 and x. The cross-sections perpendicular to the axis on the interval 0x are squares with diagonals that run from the parabola to the parabola. Find the volume of the solid.
The volume of the solid is 900 cubic unit given that the solid lies between planes perpendicular to the x-axis at x = 0 and x = 19, the cross sections perpendicular to the x-axis on the interval 0 ≤ x ≤ 15 are squares with diagonals that run from the parabola y = - 2√x to the parabola y = 2√x. This can be obtained by finding the area of the square using the length of the diagonal.
What is the volume of the solid?
Given that, diagonals that run from the parabola y = - 2√x to the parabola y = 2√x
The length of the diagonal,D = 2√x - (-2√x)
D = 4√x
Using Pythagoras theorem,D² = s² + s², where s is the side of the square
(4√x)² = 2s²
16x = 2s²
s² = 8x
s² is the area
Area A = 8xThus,
volume V = ∫A dx, 0 ≤ x ≤ 15V = [tex]\int\limits^{15}_0 {8x} \, dx[/tex]
V = [tex]8\int\limits^{15}_0 {x} \, dx[/tex]
V = 4 (15² - 0)
V = 4×225
⇒ V = 900 cubic unit
Hence the volume of the solid is 900 cubic unit given that the solid lies between planes perpendicular to the x-axis at x = 0 and x = 19, the cross sections perpendicular to the x-axis on the interval 0 ≤ x ≤ 15 are squares with diagonals that run from the parabola y = - 2√x to the parabola y = 2√x.
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Disclaimer: The question was given incomplete on the portal. Here is the complete question.
Question: A solid lies between planes perpendicular to the x-axis at x = 0 and x = 19. The cross sections perpendicular to the x-axis on the interval 0 ≤x ≤ 15 are squares with diagonals that run from the parabola y = - 2√x to the parabola y = 2√x. Find the volume of the solid.
help me please 10 POINTS
The width of a rectangle is represented by 4x, and its length is represented by (3x+2). Write a polynomial for the perimeter of the rectangle.
Answer:
2(7x + 2)
Step-by-step explanation:
Perimeter of a Rectangle = 2 x Length + 2 x Width.
Given Length = 4x, Width = 3x + 2,
Perimeter of Rectangle = 2(4x) + 2(3x + 2)
= 8x + 6x + 4
= 14x + 4 (Degree one polynomial)
= 2(7x + 2)
The graph of F(x), shown below, resembles the graph of G(x) = x2, but it has
been changed somewhat. Which of the following could be the equation of
F(x)?
F(x)= 2(x-2)^2 + 2 is the correct equation of F(x)
A quadratic function is a polynomial function of the second degree. The general form of a quadratic function is this: f (x) = ax^2 + bx + c, where a, b, and c are real numbers and a≠ 0.
Graphs of quadratic functions
The term "parabola" refers to the graph of a quadratic function. A parabola essentially resembles the letter "U," yet it can be inverted or exactly this shape depending on the situation. The leading coefficient determines whether the graph of a quadratic function opens up or down; if it is more than zero, the parabola opens up; if it is less than zero, the parabola opens down.
It is given that graph of F(x), shown below, resembles the graph of G(x) = x^2, but it has been changed somewhat.
We need to find the equation of F(x)
In the figure, parabola opens up, the leading coefficient is greater than zero ,So option (d) is correct
Hence the equation of F(x) is 2(x-2)^2 + 2
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A prism has volume 100cm^3 and length 8cm. If the cross-section is an equilateral triangle, find the length of a side of the triangle.
Answer:
5.373 cm
Step-by-step explanation:
Divide the volume by the length to find the area of the equilateral triangle
100/8 = 12.5
Area of equilateral triangle = sqrt(3) / 4 * s^2 = 12.5
s^2 = 12.5 *4 / sqrt3
s = 5.373 cm
Which equation represents a population of 250 animals that decreases at an annual rate of 12% ?
Answer:
f(t)=250(1-0.12)^t
or
f(t)=250(0.88)^t
Step-by-step explanation:
Use the formula f(t)=P(1+b)^t
Plug in the information.
f(t)=250(1-0.12)^t
or
f(t)=250(0.88)^t
The only thing I did in the second equation is I subtract 0.12 from 1.
Hope this helps!
(‼️‼️I WILL MARK BRAINLIEST PLEASE HELP‼️‼️)Dilate the figure by the scale factor. Then enter
the new coordinates.
K = 5
(-3,-1)
A
(-1,-4) C
B(2,-2)
A' ([?], [ ])
B' ([ ], [ ])
C' ([ ], [ ])
Answer:
A' (-15, -5)
B' (10, -10)
C' (-5, -20)
Answer:
A ' (-15, -5)
B ' (10, -10)
C ' (-5, -20)
Step-by-step explanation:
The scale factor is [tex]K=5[/tex]. This tells us to multiply each coordinate, of each point, by the scale factor (5) to get the dilated points.
Point A is at [tex](-3,-1)[/tex] and moves to [tex]A ' (-15, -5)[/tex] after multiplying the x and y coordinates by 5. The same applies to points B and C as well.
Point B moves from [tex](2,-2)[/tex] to [tex]B' (10,-10)[/tex] because [tex]2*5=10[/tex] and [tex]-2*5=-10[/tex]. This also means that Point C moves from [tex](-1,-4)[/tex] to [tex]C' (-5,-20)[/tex] because [tex]-1*5=-5[/tex] and [tex]-4*5=-20[/tex].
The dilation rule can be written as [tex](x, y)[/tex] → [tex](5x, 5y)[/tex]
As a result of the dilation, triangle A'B'C' has sides that are 5 times longer compared to the corresponding sides of triangle ABC.
Which is the equation of the function? f(x) = 3|x| + 1 f(x) = 3|x – 1| f(x) = 1/3|x| + 1 f(x) = 1/3|x – 1|
The equation of the function is −3<x<1. See the explanation below.
What is the solution to the above?Given the graph of function f is a parabola,
Thus, equation of parabola is y=(x+3)(x+1)
⇒y=x² +4x+3
⇒y−3+2²
= x²+2× x ×2+2²
⇒y+1=(x+2)²
We can rewrite this as
(x+2)² =4× (1/4) ×(y+1)
Comparing the above equation to the equation of a parabola, (x−h)² =4a(y−k), where (h,k) is the coordinates of vertex of parabola, we have,
(h,k)≡(−2,−1)
Hence, the x coordinate of the vertex is −2 which lies in the interval −3<x<1
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x/2+y=4/5. x+y/2=7/10
Answer:
x = 2/5
y = 3/5
Step-by-step explanation:
**Disclaimer** Hi there! I assumed the question to be a system of equations. The following answer is a method for solving a system of equations. Thus, if it is not, please let me know and I will modify my answer.
Given information:
[tex]\frac{x}{2}+y=\frac{4}{5}[/tex]
[tex]x+\frac{y}{2} =\frac{7}{10}[/tex]
Eliminate fractions by multiplying 10 on both sides of the first equation:
[tex]10*\frac{x}{2}+10*y=10*\frac{4}{5}[/tex]
[tex]5x+10y=8[/tex]
Eliminate fractions by multiplying 10 on both sides of the second equation:
[tex]10*x+10*\frac{y}{2} =10*\frac{7}{10}[/tex]
[tex]10x+5y=7[/tex]
Current system:
[tex]5x+10y=8[/tex]
[tex]10x+5y=7[/tex]
Multiply the second equation by 2:
[tex]5x+10y=8[/tex]
[tex]20x+10y=14[/tex]
Subtract the first equation from the second equation:
[tex](20x+10y)-(5x+10y)=14-8[/tex]
[tex]20x+10y-5x-10y=6[/tex]
[tex](10y-10y)+20x-5x=6[/tex]
[tex]0+15x=6[/tex]
[tex]\boxed{x=\frac{2}{5} }[/tex]
Substitute the x value back to one of the equations to get the y value:
[tex]x+\frac{y}{2} =\frac{7}{10}[/tex]
[tex](\frac{2}{5}) +\frac{y}{2} =\frac{7}{10}[/tex]
[tex](\frac{2}{5}) +\frac{y}{2}-\frac{2}{5} =\frac{7}{10}-\frac{2}{5}[/tex]
[tex]\frac{y}{2} =\frac{3}{10}[/tex]
[tex]\frac{y}{2}*2 =\frac{3}{10}*2[/tex]
[tex]\boxed{y=\frac{3}{5} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
The answer is x = 2/5, y = 3/5 or (2/5, 3/5)
First, in order to avoid fractional values during calculation, multiply both equations by 10 to simplify.
10 (x/2 + y) = 10 (4/5) ⇒ 5x + 10y = 810 (x + y/2) = 10 (7/10) ⇒ 10x + 5y = 7Multiply the 1st equation by 10 and 2nd equation by 5.
3. 10 (5x + 10y) = 10 (8) ⇒ 50x + 100y = 80
4. 5 (10x + 5y) = 5 (7) ⇒ 50x + 25y = 35
Subtract : 3rd equation - 4th equation
50x + 100y - 50x - 25y = 80 - 3575y = 45y = 3/5Now, substitute for x in the 1st equation to find y.
x/2 + 3/5 = 4/5x/2 = 1/5x = 2/5What's a venn diagram, how to draw it and the steps too!
What is a Venn Diagram?
Explain : A Venn diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationships in probability, logic, statistics, linguistics and computer science.
How to draw a Venn Diagram?
Explain : To create an intersecting Venn diagram, draw three circles that overlap in the middle. You'll be able to show which attributes are unique to each circle, which overlap between two, and which are common characteristics of all three groups. Two circles overlapping is a classic venn diagram
What is a venn Diagram mostly used for?
Explain : A Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items. Often, they serve to graphically organize things, highlighting how the items are similar and different.
Set notations: The concepts illustrated in Venn ...
Scaled Venn Diagram: Also called Area Propo...
Reuleaux Triangle: Shape formed from the int...
Intersection: The items that overlap in the sets. ...
Here's some question for Venn Diagrams!
A. What's the first step creating a Venn Diagram? https://www.math-only-math.com/practice-test-on-Venn-diagrams.html
B. What's the last step to create a Venn Diagram? https://www.purplemath.com/modules/venndiag4.htm
C. What does a Venn Diagram looks like?
( Try using those questions to partice more about Venn Diagrams! )
( Also, thank you for the points! )
If light travels at 10,000 km in 3.0 x 10² seconds,
how long will it take light to travel one meter?
(1 km = 1 x 10³ m)
PLEASE HELP ME
Answer:
1000xm
Step-by-step explanation:
1 meter = 3.2808 feet, hence. 9.8424 x 10^8 feet in 1 second. 1 foot in x seconds. hence it takes 1 / (9.8424 x 10^8) = 0.10168 x 10^(-8) seconds. ➡️1km = 1000xm⬅️
It will take light approximately 3.0 x 10⁻⁵ seconds to travel one meter.
To find out how long it will take light to travel one meter, we need to convert the given distance of 10,000 km to meters and the time of 3.0 x 10² seconds to seconds.
Given:
Distance traveled by light = 10,000 km
Time taken by light = 3.0 x 10² seconds
To convert km to meters, we know that 1 km = 1 x 10³ m, so:
10,000 km = 10,000 x 1 x 10³ m = 1 x 10⁷ m
Now, we can find the time taken to travel one meter by dividing the total time by the total distance:
Time taken to travel one meter = Total time / Total distance
Time taken to travel one meter = (3.0 x 10² seconds) / (1 x 10⁷ m)
To simplify the expression, we can cancel out one factor of 10 from the numerator and denominator:
Time taken to travel one meter = (3.0 x 10) / (1 x 10⁶ m)
Now, we get the final answer:
Time taken to travel one meter = 3.0 x 10⁻⁵ seconds
So, it will take light approximately 3.0 x 10⁻⁵ seconds to travel one meter.
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Can someone help? ASAP
Question 4
[tex]\sin 30^{\circ}=\frac{y}{14\sqrt{3}}\\\\\frac{1}{2}=\frac{y}{14\sqrt{3}}\\\\\boxed{y=7\sqrt{3}}\\\\\\\\\cos 30^{\circ}=\frac{x}{14\sqrt{3}}\\\\\frac{\sqrt{3}}{2}=\frac{x}{14\sqrt{3}}\\\\\boxed{x=21}[/tex]
Question 5
[tex]\cos 45^{\circ}=\frac{x}{28}\\\\\frac{1}{\sqrt{2}}=\frac{x}{28}\\\\x=\frac{28}{\sqrt{2}}\\\\\boxed{x=14\sqrt{2}}\\\\\\\\\sin 45^{\circ}=\frac{y}{28}\\\\\frac{1}{\sqrt{2}}=\frac{y}{28}\\\\y=\frac{28}{\sqrt{2}}\\\\\boxed{y=14\sqrt{2}}[/tex]
Can someone help me with this having trouble and show work please!!
Answer:
7a + b
Step-by-step explanation:
5a + 2a + 3b - 2b
= 7a + 3b - 2b
= 7a + b
There are 20 red and blue marbles in a bag. s marbles are red how many are blue?
Answer:
Step-by-step explanation:
Step-by-step explanation:
15 r blue marbles
20- 5 = 15
Simplify 7 1/5 5 A B C D
Answer:
C. 7
Step-by-step explanation:
The answer is 7. Use the power of a power property. To use it you have to multiply the power inside the parenthesis to the one outside of the parenthesis. 1/5 * 5 = 1. Since the power is 1, you do not need to write the power.
Hope this helps!
When given an inverse variation, how do you find k?
can someone please help me?
answer choices:
A. sin (0)
B. cos (0)
C. sin (3/2)
D. cos (3/2)
E. sin ()
F. cos ()
Answer:
B, cos(0)=1
Step-by-step explanation:
cos(0)=1
Coordinate A is at point (1,0)
provide the answer by sketching the graph on the image below
The attached graph is the graph of the function f(x) = -2sin(x)
How to sketch the graph?The function is given as:
f(x) = -2sin(x)
The above function is a sine function that has an amplitude of 2
Next, we plot the graph of the sine function f(x) = -2sin(x) using a graphing calculator
See attachment for the graph of f(x) = -2sin(x)
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urgent please help!!!!! will give brainliest
Answer: Read the explanation
Step-by-step explanation:
If the points of a figure are all moved the same, they are congruent.
Point A is moved 9 points right, and 7 points down.
Point B is moved 9 points right, and 7 points down.
Point C is moved 9 points right, and 7 points down.
So, they are congruent.
12.) tan L
A)
C)
√6
2
√6
w
L
√
V10
B)
D)
2
√6
√10
2
√10
M
N
Answer: [tex]\frac{\sqrt{6}}{2}[/tex]
Step-by-step explanation:
By the Pythagorean theorem,
[tex]2^2 + (MN)^2 = (\sqrt{10})^2\\\\4+(MN)^2 = 10\\\\(MN)^2 = 6\\\\MN=\sqrt{6}\\\\\implies \tan L=\frac{\sqrt{6}}{2}[/tex]
Which table represents a linear function? Which quadratic function is represented by the graph?
The first table is a quadratic function while the second table is a linear function.
How to Interpret Function Tables?
1) For the first table, we have;
x y
0 5
1 0
2 -3
3 -4
4 -3
x = 2 and x = 4 have same value of y = -3 and as such it will be a Quadratic Function.
y = x² - 6x + 5
2) For the second table, we have;
x y
2 5
5 14
6 17
8 23
10 29
This table is a Linear function because slope is same and equal to 3 all through. Thus, the equation is y = 3x - 1
3) For the third table, we have;
x y
-3 8
-2 4
-1 2
0 1
1 0.5
This is an exponential function because equation can be modelled by;
y = 2⁻ˣ
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Solve the equation by completing the square
Answer:
Below.
Step-by-step explanation:
x^2 + 4x = 18
x^2 + 4x + (2)^2 = 15 + 2^2
x^2 + 4x + 4 = 18 + 4
(x + 2)^2 = 22
x + 2 = +/- √22
x = -2 + √22 and x = -2 + √22
x = 2.7 and -6.7 to nearest tenth.
Can someone help me please
The simplified form of the expression is x-4 + 2/x-2
Synthetic division of equationGiven the following fraction below
f(x) = x^2 + 2x - 6/x-2
Using the long division as shown below;
x + 4
x-2 | x^2 + 2x - 6
x^2 - 2x
_________________
4x - 6
4x - 8
___________________
2
Hence the simplified form of the expression is x-4 + 2/x-2
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