ANSWER :
(f - g)(x) = x^2 + 8
EXPLANATION :
From the problem, we have :
[tex]\begin{gathered} f(x)=2x^2+1 \\ g(x)=x^2-7 \end{gathered}[/tex](f - g)(x) is the difference between the two functions
That will be :
[tex]\begin{gathered} (f-g)(x)=f(x)-g(x) \\ =2x^2+1-(x^2-7) \\ =2x^2+1-x^2+7 \\ =x^2+8 \end{gathered}[/tex]2x-8=4Wouldn't the answer be 10
We need to sum 8 to both sides of the equation:
[tex]undefined[/tex][tex]f(x) = x + 7[/tex]Substitute the value a. f(5)b. f(-1)c. f(-3)
Answer
a) f(5) = 12
b) f(-1) = 6
c) f(-3) = 4
Explanation
We are given the function
f(x) = x + 7
We are then asked to evaluate a number of valus of x for the function
a) f(5)
f(x) = x + 7
f(5) = 5 + 7 = 12
b) f(-1)
f(x) = x + 7
f(-1) = -1 + 7 = 6
c) f(-3)
f(x) = x + 7
f(-3) = -3 + 7 = 4
Hope this Helps!!!
Choose the term that has the given definition.AngleCircleCollinearCoplanarCongruentLine segmentParallel linesPerpendicular lines
Solution
Circle: The set of all points in a plane that lie the same distance from a single point in the plane.
Perpendicular lines: Intersecting lines that form right angles
Congruent: Having exactly the same shape and size
Angle: A figure formed by two rays that have the same endpoint
Find the slope of the line.
The slope of the line is [tex]-\frac{1}{3}[/tex].
Consider any two points on the graph,
Let A(x1,y1) and B(x2,y2) are the two points on graph as shown in figure.
The two points are A(-2,0) and B(-4,6)
Slope of a line can be calculated using formula,
[tex]Slope=\frac{y2-y1}{x2-x1}\\\\Slope=\frac{-4-(-2)}{6-0}\\ \\Slope=\frac{-4+2}{6}\\ \\Slope=\frac{-2}{6}\\ \\Slope=\frac{-1}{3}[/tex]
Thus, the slope of the line is [tex]-\frac{1}{3}[/tex].
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8.) Rotate 90' clockwise about the orgin:ADEOriginal NewCoordinates CoordinatesA: () A: (___)B: () B: (__)D:() D:(__)E:( _ :) E: (_,_)V:( _,-) V:( _,-)R: (___) R' (_._)RB2
We have six points that fall in a figure
The original coordinates of this points are:
A: ( -3, 2)
B: ( -3, -4)
D: ( 1, 3)
E: (7, 2)
V: ( 4, 8)
R: ( 3, -2)
To find the new coordinates we must bear in mind that the points must be rotated 90° clockwise.
So, we need to use the next formula to find the new points:
[tex]P(x,y)\to-90^{\circ}\to P^{\prime}(y,-x)[/tex]Finally,
The new coordinates of the points are:
A': ( 2, 3)
B': ( -4, 3)
D': ( 3, -1)
E': ( 2, -7)
V': ( 8, -4)
R': ( -2, -3)
Linear function gis shown in the graph. Write the slope-Intercept form of the equation representing this function.
To find the equation of the line in slope intercept form the first step is to find the slope of the given line:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]In this formula, m is the slope of the function, y2 and y1 are the y coordinates of 2 points on the line, and x2 and x1 are the x coordinates of the same 2 points, for example, they can be (-1,3) and (0,1):
[tex]m=\frac{1-3}{0-(-1)}=-\frac{2}{1}=-2[/tex]The slope of the line is -2.
Now, we can use the y intercept of the graph of g, which is 1.
The slope intercept form of the equation follows the following general structure:
[tex]y=mx+b[/tex]Where m is the slope of the line and b is the y intercept. Use the known values to replace them on the equation. The intercept form of the equation is:
[tex]y=-2x+1[/tex]How do I do pi equations?
Given:
The objective is to explain the method of solving pi equations.
The term with pi can be solved
Perform the matrix operation.2 3Given A =25and B =04-1 6find 2A + B.A4 103 1610]B-3 11D4 142 22
step 1
Find 2A
Multiply by 2 each number of the matrix A
so
2A= 4 6
4 10
step 2
Find out the sum 2A+B
so
2A+B= (4+0) (6+4)
(4-1) (10+6)
2A+B= 4 10
3 16
therefore
the answer is the option A
Are The Ratios 1:2 and 5:14 equivalent?
The ratios are equivalent if:
[tex]\frac{2}{1}\equiv\frac{14}{7}[/tex]For example, given a length of 20cm:
[tex]\begin{gathered} 20\times\frac{2}{1}=20\times2=40\operatorname{cm} \\ 20\times\frac{14}{7}=20\times2=40\operatorname{cm} \end{gathered}[/tex]Since:
[tex]40\operatorname{cm}=40\operatorname{cm}[/tex]We can conclude that they are equivalent
Simplify the given expression below:(1 + 2i) ⋅ (5 − 3i) (2 points) a2 − 15i b3 + 2i c5 − 6i d11 + 7i
Simplification of Algebraic Expression.
[tex]\begin{gathered} (1+2i)(5-3i) \\ \text{First, we clear the brackets. } \\ 1(5-3i)\text{ +2i(5 - 3i)} \\ \text{Multiplying through the brackets, we get} \\ 5\text{ -}3i+10i-6(-1) \\ \text{Note: i}^2=\text{ -1} \\ 5\text{ -3i + 10i +6} \\ C\text{ollecting like terms, we get} \\ 5\text{ + 6 -3i + 10i} \\ 11\text{ +7i} \end{gathered}[/tex]Thus, the correct answer is 11 +7i ( option D )
Mario loaned Juan $21,890 at an interest rate of 14% for 164 days. How much will juan pay Mario at the end of 164 days? Round youranswer to the nearest cent. Note: Assume 365 days in a year and 30 days in a month.
For the interest calculation we shall apply the simple interest formula which is;
[tex]\begin{gathered} I=P\times R\times T \\ \text{Where;} \\ P=\text{Initial amount borrowed} \\ R=\text{rate of interest (expressed as decimal)} \\ T=\text{Time in years} \end{gathered}[/tex]The initial amount is $21890, the rate is 14% (that is 0.14) and the time is 164/365 of a year.
Therefore, the interest calculated would be;
[tex]\begin{gathered} I=P\times R\times T \\ I=21890\times0.14\times\frac{164}{365} \\ I=3064.6\times\frac{164}{365} \\ I=1376.9709589 \\ I\approx1376.9\text{ (rounded to the nearest cent)} \end{gathered}[/tex]The interest payable at the end of 164 days is $1,376.90 (rounded to the nearest cent).
Therefore, the amount Juan would pay back is;
Graph the following function using the techniques of shifting, compressing, stretching and or reflecting.
Answer:
Domain: (-∞, ∞)
Range: (-∞, ∞)
Explanation:
The parenting function of g(x) = (x + 3)³ + 5 is f(x) = x³.
The graph of f(x) = x³ is
Then, if we have a function g(x) = f(x + c), we can say that g(x) is the graph of f(x) shifted c units to the left and if we have a function g(x) = f(x) + c, we can say that g(x) is the graph of f(x) shifted c units up
In this case, g(x) = f(x + 3) + 5 because
g(x) = f(x + 3) + 5
g(x) = (x + 3)³ + 5
So, g(x) has the graph of f(x) shifted 3 units to the left and 5 units up.
Therefore, the graph of g(x) is
Now, the domain is the set of values that x can take and the range is the set of values that y can take, so the domain and range are all the real number.
Domain: (-∞, ∞)
Range: (-∞, ∞)
Suppose that the dollar value v(t) of a certain car that is t years old is given by the following exponential function. v(t) = 21, 300 * (1.24) ^ t
Given:-
[tex]v(t)=21300(1.24)^t[/tex]To find the initial value, does the fucnction represent growth or decay.
Here the value of a is 21300.
So we get,
[tex]1+r=1.24[/tex]So the value of r is,
[tex]r=0.24[/tex]So now we get percentage is,
[tex]24\%[/tex]Rate of change is 24%.
So the required solution is,
[tex]initial\text{ value =21300}[/tex]So the percentage range is,
[tex]24\%[/tex]
I am struggling on figuring out how to do this. Please help me
Given:-
[tex]f(x)=13x+2[/tex]To find the inverse of the function.
So now we change the value of x in the given function as y and find the value of y. so we get,
[tex]x=13y+2[/tex]Now we find the value of y. so we get,
[tex]\begin{gathered} 13y+2=x \\ 13y=x-2 \\ y=\frac{x-2}{13} \end{gathered}[/tex]So the required solution is,
[tex]y=\frac{x-2}{13}[/tex]Twice a number, decreased by 4, is at least 12. Which of the following is a solution?8576
Answer:
8
Explanation:
Let the number = n
Twice the number decreased by 4:
[tex]2n-4[/tex]The phrase 'at least' means the expression above can either be equal to or greater than 12.
Thus, the given statement as inequality is:
[tex]2n-4\geq12[/tex]We then solve the inequality for n.
[tex]\begin{gathered} \text{ Add 4 to both sides} \\ 2n-4+4\geq12+4 \\ 2n\geq16 \\ \text{ Divide both sides by 2} \\ \frac{2n}{2}\geq\frac{16}{2} \\ n\geq8 \\ \implies n=(8,9,10,\cdots) \end{gathered}[/tex]The number that is a solution is 8.
View the tables:How are the values in each table growing?Which table shows common differences? Explain your reasoning.Which one shows common factors? Explain your reasoning.
In first table, where the height of the water is considered, every minute the water rises by 3 cm.
In second table, where possible outcome is considered, for increase in one coin the outcome increases by a factor of two.
The first table, where the height of the water is considered, shows common difference. As it increases equally every minute.
The second table, where possible outcome is considered,shows a common factor as all the values are divisible by 2. So the common factor is 2.
Given any triangle ABC labeled as shown, the law of sines states:BaсССAСAbbsin Asin BsincΟ Α.сasin Asin BB.sincsincbaсsincsin BO c.sin Abaсsin Asin BsincD.aС
Simply, the law of sine states that the ratio of the lenght of a side of a triangle to the sine of the angle opposite that side is the same for all side and angles in a given triangle. In other words,
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]which corresponds to option D
PLEASE ANSWER QUICK WILL GIVE Brain
n73=8.76
Answer:
n=639.48
Step-by-step explanation:
i love my life
Answer: 8.33--
Step-by-step explanation:
73/8.76
Which economic system has no government involvement in the market? a. capitalism b. communism c. socialism d. No economic system is free from government involvement.
Answer Is D
The economic system that has no government involvement in the market is d. No economic system is free from government involvement.
Why there is no economic system is free from government involvement?In reality there is no government intervention because at some point the government will comes in , this could actually be mininmal, only in the free market is where there is no government intervention.
It should be noted that in this free market, there is an unregulated system of economic exchange, where the act of taxes collection as well as quality controls, has no economic interventions which can be attributed to government .
Therefore option D is correct.
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Please help me with this problem for my son to understand thank you.Factor completely.36x^4+18x^3+40x^2Enter your answer in the box.
The expression is given to be:
[tex]36x^4+18x^3+40x^2[/tex]Rewrite the terms so that we can factorize the common terms out:
[tex]\begin{gathered} 36x^4\Rightarrow2x^2\cdot18x^2 \\ 18x^3\Rightarrow2x^2\cdot9x \\ 40x^2\Rightarrow2x^2\cdot20 \end{gathered}[/tex]Therefore, the expression can be rewritten to be:
[tex]2x^2\cdot18x^2+2x^2\cdot9x+2x^2\cdot20[/tex]Since there is a common term, 2x², we can factorize to give:
[tex]\Rightarrow2x^2(18x^2+9x+20)[/tex]The quadratic function in the parentheses cannot be factored further.
Therefore, the answer is:
[tex]2x^2(18x^2+9x+20)[/tex]what is the flying distance between the greenhouse and the stadium
The flying distance between the greenhouse and the stadium = 5 units
Explanations:The coordinates of the greenhouse: (-6, 0)
The coordinates of the stadium: (-2, 3)
The distance between two points of coordinates (x₁, y₁) and (x₂, y₂) is given as:
[tex]D\text{ = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]For the flying distance between the greenhouse and the stadium:
x₁ = -6, y₁ = 0, x₂ = -2, y₂ = 3
Substitute these values into the distance equation given above:
[tex]\begin{gathered} D\text{ = }\sqrt[]{(-2-(-6))^2+(3-0)^2} \\ D\text{ = }\sqrt[]{(-2+6)^2+3^2} \\ D\text{ = }\sqrt[]{4^2+3^2} \\ D\text{ = }\sqrt[]{16+9} \\ D\text{ = }\sqrt[]{25} \\ D\text{ = 5} \end{gathered}[/tex]The flying distance between the greenhouse and the stadium = 5 units
identify the transformation from the pre-made to the image
You can notice that each point of both images are at the same distance of the origin of coordinates. It means that the transfromation is a reflection across the line y = x
answer: reflection across y = x
3.Six Flags charge and entrance fee per person and a fee per every ride that you get on. When 6 teachers went to Six Flags and rode on 20 rides total, they ended up paying $350. When 15 people went to Six Flags and rode on 47 rides they paid $900. Write an expression for this situation.
Answer:
Step-by-step explanation:
Expression:
y = mx + n*b
In which m is the cost per ride and b is the entrance fee.
y is the total cost, x is the number of rides and n is the number of people.
When 6 teachers went to Six Flags and rode on 20 rides total, they ended up paying $350.
This means that:
20m + 6b = 350
When 15 people went to Six Flags and rode on 47 rides they paid $900.
This means that:
47m + 15b = 900
Solving the system:
20m + 6b = 350
47m + 15b = 900
Multiplying the first equation by -5, the second by 2.
-100m - 30b = -1750
94m + 30b = 1800
-6m = 50
Use the given data to make a box-and-whisker plot.5, 4, 16, 21, 10, 6, 15
Given the set of data:
5, 4, 16, 21, 10, 6, 15
Let's create a box-and-whisker plot from the given data.
The box and whisker plot has the following properties:
Let's solve for the following:
• Minimum value or lower extreme:
This is the smallest value in the data set.
Here, the minimum value is 4.
• Maximum value or upper extreme:
This is the greatest number in the data set.
Here, the greatest number is 21.
• Median:
This is the middle value after arranging the data in ascending order(from lowest to greatest).
Arranging in ascending order, we have:
4, 5, 6, 10, 15, 16, 21
The middle number above is = 10
Therefore the median is 10.
• Lower quartile:
The lower quartile is the median of the lower half of the data.
To find the lower quartile, let's list the lower half of data first.
Lower half:
4, 5, 6
The median of the lower half of the data is 5.
Therefore, the lower quartile is 5.
• Upper quartile:
The upper quartile is the median of the upper half of the data set.
Upper half of the data set:
15, 16, 21
The median is 16.
The upper quartile is 16.
Therefore the box and whisker plot created from the given data set is:
Option B is correct.
ANSWER:
B
The width of a rectangle is 5x-4. The perimeter is 14x+4. What is the length
Given:
The width of rectangle is w = 5x - 4.
The perimeter of rectangle P = 14x + 4.
Explanation:
The formula for the perimeter of rectangle is,
[tex]P=2(L+w)[/tex]Substitute the expression in formula to determine the length of rectangle.
[tex]\begin{gathered} 14x+4=2(L+5x-4) \\ L+5x-4=\frac{14x+4}{2} \\ L=7x+2-5x+4 \\ =2x+6 \end{gathered}[/tex]So length of rectangle is 2x + 6.
Answer: 2x + 6
Write the number as the product of a real number and i[tex] \sqrt{ - 24} [/tex]
An observer stands 400 ft away from a launch pad to observe a rocket launch. The rocket blasts off and maintains a velocity of 300 ft/sec. Assume the scenario can be modeled as a right triangle. How fast is the observer to rocket distance changing when the rocket is 300 ft from the ground?
Let's draw the scenario to understand it better:
From the figure, the information given are:
[tex]\frac{dy}{d\text{t}}=\text{ 300 ft./sec}[/tex]Question:
[tex]\text{What is }\frac{dD}{dt}\text{ at y = }300\text{ ft.}[/tex]Step 1: We write a function that relates the quantities in the diagram using Pythagorean
Theorem.
[tex]\text{ 400}^2\text{ + }y^2=D^2[/tex]Step 2: Differentiate with respect to t.
[tex]2y\frac{dy}{dt}=\text{ }2D\frac{dD}{dt}[/tex]Now we wish to plug in specific numbers for every quantity in the above equation except for dD/dt. However, we notice that we don’t have a specific value for D at y = 400 ft. So first we need to find D at y = 400 ft. using the Pythagorean Theorem.
[tex]400^2\text{ + }300^2=D^2[/tex][tex]D\text{ = }\sqrt[]{400^2+300^2}[/tex][tex]D\text{ = 500 ft.}[/tex]Step 3: Finish the problem by plugging in numbers for every quantity in the equation
containing dD/dt.
[tex]2(300)(300)\text{ = 2(500)}(\frac{dD}{dt})[/tex][tex]\frac{dD}{dt}=\text{ }\frac{2(300)(300)}{2(500)}[/tex][tex]\frac{dD}{dt}=\text{ }\frac{180,000}{1000}[/tex][tex]\frac{dD}{dt}=180[/tex]Conclusion: When the rocket is 300 ft. feet from the ground, the distance between the observer and the rocket is increasing at a rate of 180 ft./sec.
mini lesson[tex]y = - 3x - 10[/tex]math
so we have to replace y. we get
[tex]\begin{gathered} 2x+5=-3x-10 \\ 2x+3x=-10-5 \\ 5x=-15 \\ x=-\frac{15}{5}=-3 \end{gathered}[/tex]if x=-3, we get that y is
[tex]y=2\cdot-3+5=-1[/tex]so the solution is
[tex](-3,1)[/tex]5. What are the zeros of the polynomial function f(x) = x³ - 2x² - 4x + 8? (Select all that apply.)
□ (√2,0)
(2,0)
(0,0)
(-2,0)
Answer:
(2, 0), (-2, 0)
Step-by-step explanation:
f(x) = x³ - 2x² - 4x + 8
(x³ - 2x²) (-4x + 8)
x²(x - 2) - 4(x - 2)
(x² - 4) (x - 2)
(x + 2)(x - 2)(x - 2)
(x + 2) (x - 2)²
x = -2, 2 multiplicity of 2
I hope this helps!
AMAn art teacher has 9 3/5 gallons of paint to pour into containers. If each container holds3/5 gallon, how many containers can they fill?Answer type: Mixed numberSubmit Answerattempt 1 out of
So they can fill 16 containers.
1) If an art Teacher has
9 3/5 gallons
Each container holds
3/5 gallons
2) Firstly, let's turn that mixed number into an improper fraction
9 3/5 = (5 x 9+3) /5 = 48/5
Given that each container holds 3/5, then let's divide
48/5 ÷ 3/5 = 48/5 x 5/3 =16
If we hadn't turned
9 3/5 ÷ 3/5 = 16
3) So they can fill 16 containers.
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