Answers
Given graph represent the graph of g(x) = [tex]-x^{2} (x -2)[/tex]
Given,
In the question;
The equation is:
g(x) = - [tex]x^{2} (x -2)[/tex] or h(x) = [tex]x^{2} (x -2)[/tex]
To find the is this the graph of g(x) or h(x).
Graph is given in the figure.
Now, According to the question;
g(x) = [tex]-x^{2} (x -2)[/tex] and h(x) = [tex]x^{2} (x -2)[/tex]
g(x) = 0 h(x) = 0
[tex]-x^{2} (x -2) = 0[/tex] [tex]x^{2} (x -2)[/tex] = 0
x = 0, 2 x = 0, 2
If we put x = 1 then,
g(1) = [tex]-(-1)^2(1-2)[/tex] and h(1) = [tex](1)^2(1-2)[/tex]
g(1) = -1 (-1) h(1) = 1(-1)
g(1) = 1 h(1) = -1
But as shown in graph, graph take positive value at x = 1
∴Given graph is the graph of g(x) = [tex]-x^{2} (x -2)[/tex]
Hence, Given graph represent the graph of g(x) = [tex]-x^{2} (x -2)[/tex]
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Related Questions
use eulers method with step size 0.5 to compute the approximate y values y1 y2 y3 and y4 of the solution of the intitial value problem y'=y 2x y(3)=0
Answers
Answer:
[tex]y_1=\boxed{-3}[/tex]
[tex]y_2=\boxed{-8}[/tex]
[tex]y_3=\boxed{-16}[/tex]
[tex]y_4=\boxed{-28.5}[/tex]
Step-by-step explanation:
Given:
[tex]y'=y-2x, \;\;y(3)=0[/tex][tex]h=0.5[/tex]Use Euler’s method with h = 0.5 to find approximate values for the solution of the initial value problem:
[tex]y'=y-2x, \;\;y(3)=0[/tex]
at x = 3.5, 4, 4.5, 5.
Therefore:
[tex]f(x,y)=y-2x, \quad x_0=3 \;\;\text{and}\; \;y_0=0[/tex]
Euler's Method
[tex]\boxed{y_{n+1}=y_n+hf(x_n,y_n)}[/tex]
[tex]\begin{aligned}\implies y_1&=y_0+hf(x_0,y_0)\\&=0+(0.5)f(3,0)\\&=0+0.5[0-2(3)]\\&=0+0.5(-6)\\&=-3\end{aligned}[/tex]
[tex]\begin{aligned}\implies y_2&=y_1+hf(x_1,y_1)\\&=-3+(0.5)f(3.5,-3)\\&=-3+0.5[-3-2(3.5)]\\&=-3+0.5(-10)\\&=-3-5\\&=-8\end{aligned}[/tex]
[tex]\begin{aligned}\implies y_3&=y_2+hf(x_2,y_2)\\&=-8+(0.5)f(4,-8)\\&=-8+0.5[-8-2(4)]\\&=-8+0.5(-16)\\&=-8-8\\&=-16\end{aligned}[/tex]
[tex]\begin{aligned}\implies y_4&=y_3+hf(x_3,y_3)\\&=-16+(0.5)f(4.5,-16)\\&=-16+0.5[-16-2(4.5)]\\&=-16+0.5(-25)\\&=-16-12.5\\&=-28.5\end{aligned}[/tex]
[tex]\begin{array}{|c|c|c|}\cline{1-3} \text{Step}\;(n) & x_n&y_n\\\cline{1-3} 0&3&0\\\cline{1-3} 1&3.5&-3\\\cline{1-3} 2&4&-8\\\cline{1-3} 3&4.5&-16\\\cline{1-3} 4&5&-28.5\\\cline{1-3} \end{array}[/tex]
-1/3v = -7 how do i solve this equation?
Answers
Answer: v=2.33333333333333.........
Step-by-step explanation: What you would want to do is divide both sides by -1/3 and that would get you v=2.333333.......
6 x (2/3 divided by 2) + 0.5
Answers
The given expression has a value of 2.5.
The BODMAS rule is named after the letters in the acronym: B - Brackets, O - Order of powers or roots, D - Division, M - Multiplication. A stands for addition, and S stands for subtraction. According to the BODMAS rule, mathematical statements having several operations must be solved from left to right in the BODMAS order.
Given expression 6 x (2/3 divided by 2) + 0.5
To solve this expression, we must employ the BODMAS rule.
First 2/3 divided by 2
(2/3)/2
= 1/3
Now multiply 1/3 with 6
= 1/3 x 6
= 2
Now add both 2 and 0.5
= 2 + 0.5
= 2.5
Therefore the value of the given expression is 2.5
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ching and his 4 brothers set up computers at their family company. how many computers did they set up if they each set up the same number of computers?
Answers
There are '5n' computers set up if they each set up the same number of computers.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Ching and his 4 brothers set up computers at their family company.
Now,
Let the number of computers for each person = n
The total number of persons = 5
So, We can formulate;
⇒ The number of computers set up if they each set up the same number of computers = 5n
Thus, There are '5n' computers set up if they each set up the same number of computers.
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You have a budget of $300 to order shirts for a math club. The equation 10x + 12y = 300 models the total cost, where x is the number of short-sleeved shirts and y is the number of long-sleeved shirts.
a. Interpret the terms and coefficients in the equation.
b. Graph the equation. Interpret the intercepts.
c. Find three possible solutions in the context of the problem.
Answers
a) The coefficients are the costs of the respective shirts.
b) The graph can be seen on the image at the end, the intercepts are (0, 25) and (30, 0)
c) 3 solutions are:
(0, 25), (30, 0), (25, 4)
What does each coefficient means?
Here we know that:
x = number of short-sleeved shirtsy = number of long-sleeved shirts.And we have the linear equation:
10x + 12y = 300
The first coefficient is the one in the term "10x"
The coefficient 10 will mean the cost, in dollars, of each short-sleeved shirt.
The second coefficient is on the term "12y"
And 12 means the cost in dollars of each long-sleeved shirt.
b) The graph of the linear equation can be seen on the image at the end.
The y-intercept (when x = 0) is the number of long-sleeved shirts you can buy if you don't buy any short-sleeved one.
The x-intercept is the number of short-sleeved shirts you can buy if you don't buy any long-sleeved one.
c) 3 possible solutions can be seen on the graph, some examples are:
(0, 25), (30, 0), (25, 4)
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Calculate (A) amount to be credited and (B) balance outstanding: (Round your answers to the nearest cent.) Invoice: $3,000; Terms 2/10, n/30 Invoice date: July 5 Payment amount $600 Date paid: July 14
Answers
The amount to be credited, based on the invoice amount and the payment, is $612.24. The balance outstanding is $2, 387.76
How to find the balance outstanding?Credit terms of 2/10, n/30 mean that if a buyer pays their payables in 10 days, they get a 2% discount. If they don't, then they'd have to pay the full thing in 30 days.
The days till the partial payment was made was:
= July 14 - July 5
= 9 days
The discount of 2% would apply on the payment of $600 so the amount to be credited is:
= 600 / (1 - 2%)
= $612.24
The balance would then be:
= Invoice amount - credited amount
= 3, 000 - 612.24
= $2, 387.76
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how should i explain this please help???
Answers
Answer:
An arithmetic sequence occurs when the difference between each term and the next is constant. Therefore, only addition or subtraction is possible. Also, the amount (4, in this case) must remain the same when added to each successive term.
Please help I need to find X
Answers
Answer:
x=17
Step-by-step explanation:
8x+20 is equal to 11x-31 because l parallel to m.
8x+20=11x-31
3x=51
x=17
Answer:
[tex]\sf x=17^o[/tex]Step-by-step explanation:
L || m
[tex]\sf (8x+20)^o=(11x-31)^o[/tex]
[ Corresponding angles]
[tex]\sf 8x+20=11x-31[/tex]
[tex]\sf 8x-11x=-31-20[/tex]
[tex]\sf -3x=-51[/tex]
[tex]\sf \cfrac{-3x}{-3}=\cfrac{-51}{-3}[/tex]
[tex]\sf x=17^o[/tex]
__________________
Hope this helps!
Have a great day!
Write an equation for the trend line shown on the scatter plot. ASP
Answers
Answer:
y=5x+15
Step-by-step explanation:
the equation of a line is y=mx+b where b is the y-intercept and m is the slope.
if you look at the graph you will see that your line intecpts the y axes at b=15 or that would be your y value where the line touches the edge.
now you just have to find your slope. slope is y/x or rise/run
so by looking at the graph at where our line touches the corner of a square. we just need to find 2 of those. we can use (0,15) and (1,20) the distance from 15 to 20 is 5 so that is our rise or change in y. the distance from 0 to 1 is 1 so that is our change in x or run. now just put rise over run so 5/1 which is just 5.
lastly we fill out our equation y=mx+b
our slop m is 5 and our y-intercept b is 15 so y=5x+15
Teddy and Henry both bought a used car on the same day. Teddy's used car has
4,298 miles on it already, and he drives 426 miles per month. Henry's car has 6,129
miles on it already, and he drives 223 miles per month. After how many months will
each car have the same nulaber of miles on it?
Answers
After 9 months each car will have the same number of miles on it.
What is a linear equation?
Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.
Here,
Let miles per month be x.
then, by a linear equation, we get
4298 + x(426) = 6129 + x(223)
203x = 1831
x = 9 months
Hence, after 9 months each car will have the same number of miles on it.
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Select all of the numbers that are correctly written in scientific notation.
A. 42 times 10 superscript 5 baseline
B. 1.1 times 10 superscript 4 baseline
C. 7.0 times 20 superscript 4 baseline
D. 6.01 times 10 superscript negative 4 baseline
E. 18 point 0 time 10 cubed
Answers
The numbers that are correctly written in scientific notation are:
B) 1.1 x 10⁴D) 6.01 x 10⁻⁴.What is scientific notation?Scientific notation is a shorthand (approximate) manner of writing long or short numbers using decimal forms raised to 10 power a baseline.
The rules for correctly writing a scientific notation include the following:
The base should always be 10. The exponent must be a non-zero integer (either positive, like option B, or negative, like option D). The absolute value of the coefficient is greater than or equal to 1 but should be less than 10.Coefficients can be positive or negative numbers including whole and decimal numbers.Thus, the scientific notation rules are correctly satisfied by Options B and D, unlike Options A, C, and E.
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Answer Options:A) 42 x 10⁵
B) 1.1 x 10⁴
C) 7.0 x 20⁴
D) 6.01 x 10⁻⁴
E) 18.0 x 10³
Given g(x) = −2x^2 + 3x + 20, find g(0), g(−2.5), g(4), g(0.75), g(20)
Answers
The functions g(0) = 20, g(−2.5) = 0, g(4) = 0, g(0.75) = 21.125, g(20) = -720 as a result of the mapping with the function g(x) = −2x² + 3x + 20
What is a function?A function is a mapping whose codomain is the set of real numbers. It can also be defined as a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
From the function g given as g(x) = −2x² + 3x + 20, by careful mapping we have the following;
put 0 for values of x
g(0) = -2(0)² + 3(0) + 20
g(0) = 20.
put -25 for values of x
g(-25) = -2(-25)² + 3(-25) + 20
g(-25) = -12.5 - 7.5 + 20
g(-25) = 0
put 4 for values of x
g(4) = -2(4)² + 3(4) + 20
g(4) = -32 + 12 + 20
g(4) = 0
put 0.75 for values of x
g(0.75) = -2(0.75)² + 3(0.75) + 20
g(0.75) = -1.25 + 2.25 + 20
g(0.75) = 21.125
put 20 for values of x
g(20) = -2(20)² + 3(20) + 20
g(20) = -800 + 60 + 20
g(20) = -720
Therefore, by proper mapping of the function g(x) = −2x² + 3x + 20, we derived g(0) = 20, g(−2.5) = 0, g(4) = 0, g(0.75) = 21.125, and g(20) = -720.
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Answer:
g(0) = 20
g(-2.5) = 0
g(4) = 0
g(0.75) = 21.125
g(20) = -720
Step-by-step explanation:
Hello!
We can evaluate each value by plugging the value inside the parenthesis into x in the equation [tex]-2x^2 + 3x + 20[/tex].
Evaluateg(0)g(0) = -2(0)² + 3(0) + 20g(0) = -2(0) + 0 + 20g(0) = 0 + 0 + 20g(0) = 20g(-2.5)g(-2.5) = -2(-2.5)² + 3(-2.5) + 20g(-2.5) = -2(6.25) - 7.5 + 20g(-2.5) = -12.5 - 7.5 + 20g(-2.5) = -20 + 20g(-2.5) = 0g(4)g(4) = -2(4)² + 3(4) + 20g(4) = -2(16) + 12 + 20g(4) = -32 + 12 + 20g(4) = -20 + 20g(4) = 0g(0.75)g(0.75) = -2(0.75)² + 3(0.75) + 20g(0.75) = -2(0.5625) + 3(0.75) + 20g(0.75) = -1.125 + 2.25 + 20g(0.75) = 1.125 + 20g(0.75) = 21.125g(20) g(20) = -2(20)² + 3(20) + 20g(20) = -2(400) + 60 + 20g(20) = -800 + 60 + 20g(20) = -740 + 20g(20) = -720The values are, in order, 20, 0, 0, 21.125, and -720.
Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
g(x) = square root 49 - x squared
Answers
The critical number are 0, 7 , -7.
Given function:
g(x) = [tex]\sqrt{49-x^{2} }[/tex]
first derivative is,
= -x/([tex]\sqrt{49-x^{2} }[/tex] )
-x = 0 or x = 0
[tex]\sqrt{49-x^{2} }[/tex] = 0
49 - [tex]x^{2} =0[/tex]
49 = [tex]x^{2}[/tex]
x = 7 , -7.
Therefore the critical number are 0, 7 , -7.
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Use the order of operations to simplify this expression (1/4 + 7/8)x 1/2
Answers
Order of operation to simplify this expression as follows:
[tex]((1\div4+7\div 8)\times 1)\div 2[/tex]
⇒ [tex]((0.25+7\div 8)\times 1)\div 2[/tex]
⇒ [tex]((0.25+0.875)\times 1)\div2[/tex]
⇒ [tex](1.125\times 1)\div2[/tex]
⇒ [tex]1.125\div 2[/tex]
⇒ [tex]0.5625[/tex]
What is order of operation?
The best way to solve an expression is from left to right if all the operations are the same (for instance, only addition, only subtraction, only multiplication, or only division). However, we must adhere to the order of operations for expressions including several operations.
The rule that dictates how to solve an expression involving numerous operations is known as the order of operations.
PEMDAS can help you remember that sequence. In PEMDAS, each letter denotes a mathematical operation.
Given Expression is ; [tex]((1\div4+7\div 8)\times 1)\div 2[/tex]
Firstly we calculate the highest priority between(+,-, x, and [tex]\div[/tex])
Here, division is the highest priority ,
[tex]((0.25+7\div 8)\times 1)\div 2[/tex]
[tex]((0.25+0.875)\times 1)\div2[/tex]
and then we solve parathesis,
[tex](1.125\times 1)\div2[/tex]
now we do multiply,
[tex]1.125\div 2[/tex]
and the final answer will be [tex]0.5625[/tex]
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A teacher covered the exterior of a rectangular prism-shaped box that measured 8 inches by 9 inches by 10 inches using one sheet of rectangular-shaped wrapping paper that measured 2 feet by 3 feet. There were no gaps or overlapping paper. How many square inches of wrapping paper were left over?
Answers
The number of square inches of the wrapping paper left over is 380 square inches
How to determine the amount of square inches left?From the question, we have the following parameters that can be used in our computation:
Box:
Dimension = 8 inches by 9 inches by 10 inches
Rectangular-shaped wrapping paper
Dimension = 2 feet by 3 feet.
The surface area of the box is
Box = 2(lw + lh + wh)
So, we have
Box = 2 * (8 * 9 + 8 * 10 + 9 * 10)
Evaluate
Box = 484 square inches
The surface area of the wrapping paper is
Wrapper = lw
So, we have
Wrapper = 2 * 3
Evaluate
Wrapper = 6 square feet
Convert to square inches
Wrapper = 864 square inches
The amount of square inches left is
Amount left = Wrapper - Box
Amount left = 864 square inches - 484 square inches
This gives
Amount left = 380 square inches
Hence, the amount left is 380 square inches
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The expression $25 + $10h gives the amount of money that Stephanie earns per day, where h is the number of hours she works. How much does she earn if she works 4 hours?
Answers
Answer:
25+10(4)= 65
Step-by-step explanation:
think of it as she makes 10 dollars an hour plus then she gets a 25 dollar bonus so you multiply the number of hours by 10 then and the bonus
Answer: $65
Step-by-step explanation:
25+10h h=4
25+10x4=
25+40=
65
Adam has a goal to hike
70 miles. If he hikes 8
miles per day, how
long will it take him to
hike all 70 miles?
Answers
Answer:
9 days (round up)
Step-by-step explanation:
70 ÷ 8 = 8.75
≈ 9 (round up)
Right now you have 8 times X = 70.
To solve this, you’re going to divide both sides by 8.
So you have X = 70/8
Now, assuming you’re not wanting that big of a fraction, we can simplify to 35/4 or put it in decimal format with 8.75.
Then your answers is 8.75!
convert the following percents to a decimal. show steps. help fast pls
10%
15%
17.5%
0.125%
113%
202.125%
Answers
Answer:
below
Step-by-step explanation:
0.1
0.15
0.175
0.00125
1.13
2.02125
A bag contains 35 coins, some dimes and some quarters. The total amount of money in the bag is $4.85. How many dimes and how many quarters are in the bag?
Answers
Answer:
9 quarters and 26 dimes
Step-by-step explanation:
your welcome :)
Write the fraction 45/54 in simplest form
Answers
Answer:5/6
Step-by-step explanation:
Use the diagram to complete the statement.
Answers
The value of the side CB in the right angled triangle is found as 4√2 units.
Describe the Pythagorean theorem?The Pythagoras theorem, commonly known as the Pythagorean theorem, says that if a triangle has a right angle (90 degrees), the square of the hypotenuse equals equal to the sum of a squares of the opposite two sides.It describes the connection between the three sides of such a right-angled triangle.For the given question,
The diagram is given;
AB = 7 units.
AG = 3 units.
GB = 7 - 3 = 4 units.
GC = 4 units.
In right angled triangle GCB, apply Pythagorean theorem.
CB² = GB² + GC²
CB² = 4² + 4²
CB² = 2(4)²
Taking square root both side.
CB = 4√2
Thus, the value of the side CB in the right angled triangle is found as 4√2 units.
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For each ordered pair, determine whether it is a solution to the system of equations.
Answers
Answer:
no, no, yes, yes
Step-by-step explanation:
You want to know which of the ordered pairs are solutions to the given system of equations: 6x -3y = 9, y = 2x -3.
GraphThe attached graph shows that the two equations describe the same line. The given points are plotted on the same graph. The ones on the line are solutions.
(4, -5) . . . not a solution
(-1, 8) . . . not a solution
(7, 11) is a solution
(0, -3) is a solution
Different liquids freeze at different temperatures, called their freezing points. Liquid acetone, used in nail polish remover, has a freezing point of – 137°F. Water has a freezing point of 32°F. How much warmer is the freezing point of water than the freezing point of acetone? °F
Answers
The freezing point of water in relation to the freezing point of acetone, is 169 °F
How to find the difference in freezing points?The difference between the freezing point of water (how much warmer the freezing point of water is) and the freezing point of acetone can be found by the formula:
= Freezing point of water - Freezing point of acetone
Freezing point of water = 32°F
Freezing point of Acetone = – 137°F
In relation to the freezing point of acetone, the degrees warmer that the freezing point of water is:
= 32 - (- 137)
= 32 + 137
= 169 °F
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Write the equation of the line with a slope of 3/2that contains the point ( — 4, − 2).
Answers
The equation of line with a slope of 3/2 which passes through point (-4,-2) is y = (3/2)x + 4.
What is the equation of line with the given point and slope?
The equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the data in the question;
Point (-4, -2 )
x = -4y = -2Slope m = 3/2First, we determine the y-intercept 'b'.
Plug the point and slope slope into the equation of line formula and solve for b.
y = mx + b
-2 = (3/2)(-4) + b
-2 = (3)(-2) + b
-2 = -6 + b
b = -2 + 6
b = 4
Now, plug the slope and y-intercept into y = mx + b to determine the equation of the line.
y = mx + b
y = (3/2)x + 4
Therefore, the equation of the line is y = (3/2)x + 4.
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What is the slope of the points (19, -2), (-11, 10)?
Answers
Answer:
-2/5
Step-by-step explanation:
the slope is change in y over change in x
formula for slope is
(y2-y1)/(x2-x1), so if you input the coordinates, (10-(-2))/(-11-19) = 12/30 = 2/5
Riley wants to find the smallest of the fractions One-sixth, Eleven-twelfths, Five-sixths, and Ten-twelfths. She uses 0 and 1 as benchmarks. Which fraction is closest to 0?
Answers
Answer: 1/6
Step-by-step explanation: Make all of the denominators the same. The least common multiple of 6 and 12 is 12. 1/6 gets multiplied by 2/2 to the equivalent fraction 2/12. 11/12 stays the same. 5/6 is multiplied by 2/2 to get 10/12. 10/12 stays the same. 1/6 is the smallest fraction so it is the closest to 0.
The formula for simple interest is I=Prt,I=Prt, where II is the interest earned, PP is the principal, rr is the interest rate and tt is the number of years. Solve the formula for PP in terms of r,r, II and t.t.
Answers
Answer:
[tex]P=\cfrac{I}{rt}[/tex]----------------------------
GivenI = PrtSolve for P[tex]I = Prt[/tex][tex]\cfrac{I}{rt} = \cfrac{Prt}{rt}[/tex][tex]\cfrac{I}{rt} =P[/tex][tex]P=\cfrac{I}{rt}[/tex]ou get an auto loan at 6% interest for 5 years; please answer the following. You can afford a $350 per month car payment; how expensive a car can you afford? (Round to two decimal places and do not include a dollar symbol)
Answers
You can afford a car at a price of 13,016.79
What is the monthly payment formula?
The monthly payments are given by the equation presented as follows:
[tex]A=P\frac{R(1+R)^{n} }{(1+R)^{n}-1 }[/tex]
where R = r / 12
P is the initial amount , r is the interest rate , n is the number of payments.
Given data ,
A = $ 350
R = 6 %
r = 6 / 12 %
= 0.5 %
= 0.005
n = 5 years
= 5 x 12 months
= 60
Therefore , the maximum value of the car is calculated as
[tex]A=P\frac{R(1+R)^{n} }{(1+R)^{n}-1 }[/tex]
[tex]250=P\frac{0.005(1+0.005)^{60} }{(1+0.005)^{60}-1 }[/tex]
[tex]250=P\frac{0.0067}{1.3488501-1}[/tex]
[tex]P = \frac{250*0.348850}{0.0067}[/tex]
[tex]P=\frac{87.2125}{0.0067}[/tex]
P = 13016.79
Hence , you can afford a car at a price of 13,016.79
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Solve for x if log(x - 1) + log(x + 1) = log21
Answers
Answer: [tex]x=\pm \sqrt{22}[/tex]
Step-by-step explanation:
[tex]\log(x-1)+\log(x+1)=\log 21\\\\\log((x-1)(x+1))=\log 21\\\\\log(x^2-1)=\log 21\\\\x^2-1=21\\\\x^2=22\\\\x=\pm \sqrt{22}[/tex]
Answer:
sqrt(22) = [tex]\sqrt{22}[/tex]
Step-by-step explanation:
we can use the logarithm rule, "log x + log y = log(xy)" to solve this problem
log(x-1) + log(x+1) = = [tex]log((x-1)(x+1))[/tex] = log(21)
this means that x^2 - 1 equals 21
xx-1 = 21
xx=22
x=sqrt(22)
Brett tallies up the transactions in his check register and comes up with a total balance of $248.53, but his bank statement says that his balance is $257.72. Which of the following are still outstanding?
Answers
The amount that is outstanding when Brett tallies up the transactions in his check.is $9.19.
How to calculate the value?From the information, Brett tallies up the transactions in his check register and comes up with a total balance of $248.53, but his bank statement says that his balance is $257.72.
The amount that is outstanding will be the difference between the amount given. This will be:
= Bank statement - Total balance
= $257.72 - $248.53
= $9.19
This is the outstanding amount.
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