Two piecewise functions are shown below. What is the value of 6f * (- 2) + 3g * (1) ?
Answers
To find the value of f(-2), we replace x = -2 into the second piece of the function. Then, we operate.
[tex]\begin{gathered} f(-2)=\frac{1}{3}(-2)^3 \\ f(-2)=\frac{1}{3}(-8) \\ f(-2)=-\frac{8}{3} \end{gathered}[/tex]Second partTo find the value of g(1), we replace x = 1 into the first piece of the function. Then, we operate.
[tex]\begin{gathered} g(1)=2|1-1|+3 \\ g(1)=2|0|+3 \\ g(1)=2\cdot0+3 \\ g(1)=0+3 \\ g(1)=3 \end{gathered}[/tex]Finally, we find the value of the given expression:
[tex]\begin{gathered} 6f(-2)+3g(1)=6\cdot-\frac{8}{3}+3\cdot3 \\ 6f(-2)+3g(1)=-\frac{6\cdot8}{3}+9 \\ 6f(-2)+3g(1)=-\frac{48}{3}+9 \\ 6f(-2)+3g(1)=-16+9 \\ 6f(-2)+3g(1)=-7 \end{gathered}[/tex]Related Questions
7. An internet service provider charges $20 per month plus an initial set-up fee. One customer paid a total of $92 after 2 months of service. Write an equation in point-slope-form modeling this situation. Then, write the equation in slope-intercept form. What does the 52 represent in your slope-intercept form equation?
Answers
The internet service provider charges $20 per month plus an initial set-up fee.
Let "x" represent the number of months that are charged, then the monthly fee can be expressed as 20x
Let "y" represent the cost of the internet service after x months.
If the customer paid y=$92 after x=2 months of service, this information represents a point of the relationship that can be expressed as (2,92)
The point-slope form has the following formula:
[tex]y-y_1=m(x-x_1)[/tex]Where
m is the slope
(x₁,y₁) are the coordinates of one point of the line.
The slope of the line corresponds to the monthly fee for the internet service, so m=$20
The coordinates of the point you have to use is (2,92)
So the equation in point-slope form is
[tex]y-92=20(x-2)[/tex]To write the equation in slope-intercept form, the first step is to distribute the multiplication on the parentheses term:
[tex]\begin{gathered} y-92=20\cdot x-20\cdot2 \\ y-92=20x-40 \end{gathered}[/tex]Then pass "-92" to the right side of the equation by adding it to both sides of the equal sign:
[tex]\begin{gathered} y-92+92=20x-40+92 \\ y=20x+52 \end{gathered}[/tex]The equation in point-slope form is y-92=20(x-2)
The equation in slope-intercept form is y=20x+52
$20 is the slope of the equation and represents the monthly fee for internet service.
$52 is the y-intercept of the equation, it represents the initial set-up fee for the internet service.
The equation P=4s represents the perimeter P of a square with side length s. What is the perimeter of a square with side length 6 mi?
The perimeter is mi.
Answers
Answer:
24mi
Step-by-step explanation:
p=4s=4(6mi)
=24mi
Find the inverse of the function below. When typing your answer use the "^" key (shift+6) to indicate an exponent. For example, if we have x squared (x times x) we would type x^2. f(x)= \frac{5x+1}{2-5x}The numerator of f^{-1}(x) is Answer - AnswerThe denominator of f^{-1}(x) is Answer(Answer + Answer)
Answers
Answer:
[tex]\begin{gathered} \text{ The numerator of f}^{-1}(x)\text{ is 1-2x} \\ \text{ The denominator of f}^{-1}(x)\text{ is -5(x}+1) \end{gathered}[/tex]Step-by-step explanation:
To find the inverse of a function, replace f(x) by ''y'', then replace ''y'' with and x, and every x with a ''y''. Solve for y.
[tex]\begin{gathered} f(x)=\frac{5x+1}{2-5x} \\ Replace\colon\text{ f(x)}\rightarrow y \\ y=\frac{5x+1}{2-5x} \\ Replace\colon\text{ y}\rightarrow x\text{ x}\rightarrow y \\ x=\frac{5y+1}{2-5y} \\ \text{ Solve for y.} \\ x(2-5y)=5y+1 \\ 2x-5yx=5y+1 \\ -5yx=5y+1-2x \\ -5yx-5y=1-2x \\ y(-5x-5)=1-2x \\ y=-\frac{1-2x}{5x+5} \\ y=-\frac{1-2x}{5(x+1)} \end{gathered}[/tex][tex]\begin{gathered} Replacey\colon f^{-1}(x) \\ f^{-1}(x)=-\frac{1-2x}{5(x+1)} \end{gathered}[/tex]Select the equation of a circle with a center at the origin and a radius 7.
Answers
The Solution.
The circle with a center at the origin implies that (a,b) = (0,0).
The equation of a circle is given by;
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ \text{Where a=0, b=0 and r=7 units.} \end{gathered}[/tex]Substituting the values above into the formula, we get
[tex]\begin{gathered} (x-0)^2+(y-0)^2=7^2 \\ x^2+y^2=49 \end{gathered}[/tex]Step 3:
Presentation of the Answer.
Thus, the correct answer is option C / third option.
[tex]x^2+y^2=49[/tex]What is the range of the function
Answers
Answer:
[tex]\{ y\; |\; 0 \leq y < 9 \}[/tex]
Step-by-step explanation:
The range of a function is the set of all possible output values (y-values).
From inspection of the given graph:
Minimum value of y = 0Maximum value of y = 9As there is an open circle where y = 9, this means the value is not included in the range.
Therefore, the range of the function is:
[tex]\{ y\; |\; 0 \leq y < 9 \}[/tex]
Type the correct answer in the box.
Find the value of x in the figure.
Answers
Answer:
x = 35
Step-by-step explanation:
An hexagon has 6 sides, so (n-2) is 4, and the internal angles add up to 180° × 4 = 720°
so
4x - 5 + 117 + 3x - 3 + 3x + 6 + 118 + 4x - 3 = 720
14x + 230 = 720
14x = 720 - 230
14x = 490
x = 490 : 14
x = 35
Answer:
x=35
Step-by-step explanation:
In ΔCDE, m∠C = 86° and m∠D = 58°. Which statement about the sides of ΔCDE must be true?
Answers
ANSWER
DE > EC > CD
EXPLANATION
Let us make a sketch of triangle CDE:
Let us first find the measure of angle E.
The sum of angles in a triangle is 180 degrees. This means that:
58 + 86 + 144 + =>
The sine of the angle of a triangle and side opposite that triangle is proportional for every angle and side of a triangle.
That is, the ratio of the sine of an angle and the side opposite that angle is constant for a triangle. This is known as the Sine Law.
This law implies that the bigger an angle of a triangle is, the larger the side opposite it and vice versa.
Therefore, since DE > EC > CD
That is the answer.
100 POINTS PLEASE HELP
Lisa is saving for college. The account is modeled by the function: F (x) = 250(1.25)^x , when x represents how many years she has saved.
Xavier is also saving for college. His account is modeled by this table:
x 0 1 2 3
g(x) 200 270 364.5 492.08
Answer the following questions:
A. After 5 years, how much does Lisa's account have in it?
B. After 5 years, how much does Xaviers account have in it?
C. What is the positive difference in their accounts after 5 years?
Show your work. (this does not have to be done by hand, but just show what you would enter into the calculator)
Answers
Answer:
A. $762.94
B. $896.81
C. $133.87
Step-by-step explanation:
Given function modelling Lisa's saving account:
[tex]\boxed{f(x)=250(1.25)^x}[/tex]
where x is the number of years.
Given table modelling Xavier's savings account:
[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5} x & 0 & 1 & 2 & 3\\\cline{1-5} g(x) & 200 & 270 & 364.5 & 492.08\\\cline{1-5}\end{array}[/tex]
Part ATo find the amount in Lisa's savings account after 5 years, substitute x=5 into the function:
[tex]\begin{aligned}\implies f(5)&=250(1.25)^5\\&=250(3.051757...)\\&=762.939453...\end{aligned}[/tex]
Therefore, the amount in Lisa's savings account after 5 years is $762.94 (nearest cent).
Part BFirst, create an exponential function to model Xavier's savings account.
General form of an exponential function:
[tex]y=ab^x[/tex]
where:
a is the initial value (y-intercept).b is the base (growth/decay factor) in decimal form.From inspection of the given table, the initial value (a) is 200.
[tex]\implies g(x)=200b^x[/tex]
To find the value of b, substitute point (1, 270) into the function:
[tex]\begin{aligned}\implies g(1)=200b&=270\\b&=\dfrac{270}{200}\\b&=1.35\end{aligned}[/tex]
Therefore. the function that models Xavier's savings account is:
[tex]\boxed{g(x)=200(1.35)^x}[/tex]
To find the amount in Xavier's savings account after 5 years, substitute x=5 into the found function:
[tex]\begin{aligned}\implies g(5)&=200(1.35)^5\\&=200(4.4840334...)\\&=896.806687...\end{aligned}[/tex]
Therefore, the amount in Xavier's savings account after 5 years is $896.81 (nearest cent).
Part CTo find the positive difference in their accounts after 5 years, subtract Lisa's balance from Xavier's balance:
[tex]\implies 896.81-762.94 =133.87[/tex]
3.Ronald loves to compete in triathlons. At a race a few months ago, hefinished in 290 minutes. At a race yesterday, he took 10% more time tofinish. What was his time at yesterday's race?
Answers
Explanation:
First we have to get 10% of 290 minutes:
[tex]290\times\frac{10}{100}=290\times0.1=29[/tex]If yesterday took him 10% MORE time to finish the race, it means that it took him 290min as a few months ago plus another 29 minutes
Answer:
Ronald's time at yesterday's race was 319 minutes
indicate the maximum or minimum of value of f(x) whichever exists.
Answers
The given function is
[tex]f(x)=x^2-2x-5[/tex]All quadratic functions represent a parabola. If the quadratic term is positive, the parabola opens up, if the quadratic term is negative, the parabola opens down.
In this case, we observe a positive quadratic term, so the parabola opens up, which means the function has a minimum.
To find the minimum of the function, we need to find its vertex (h,k), where
[tex]h=-\frac{b}{2a}[/tex]a = 1 and b = -2.
[tex]h=-\frac{-2}{2(1)}=\frac{2}{2}=1[/tex]Then, evaluate the function to find k.
[tex]f(1)=(1)^2-2(1)-5=1-2-5=1-7=-6[/tex]The k-coordinate of the vertex refers to the minimum value.
Therefore, the answer is -6.
Find the surface area. Leave your answers in terms of T.9 mi
Answers
Given:
The shape is
Find-:
The surface area of the cylinder
Explanation-:
The surface area of the cylinder
[tex]A=2\pi rh+2\pi r^2[/tex]Where,
[tex]\begin{gathered} r=\text{ Radius} \\ \\ h=\text{ Height} \end{gathered}[/tex]The radius and height of the cylinder
[tex]\begin{gathered} r=\frac{\text{ Diameter}}{2} \\ \\ r=\frac{12}{2} \\ \\ r=6\text{ mi} \\ \\ h=9\text{ mi} \end{gathered}[/tex]The surface area of the shape is:
[tex]\begin{gathered} A=2\pi rh+2\pi r^2 \\ \\ A=2\pi(6)(9)+2\pi(6)^2 \\ \\ A=108\pi+72\pi \\ \\ A=180\pi\text{ mi}^2 \end{gathered}[/tex]The surface area is 180π mi²
Find the value if n in improper fraction.
Answers
The value of n will be equal to -7/2 or [tex]-4\frac{1}{2}[/tex].
This question can be solved using the Laws of exponents. We have the expression 1/8 ÷ √2 = 2ⁿ. We can rearrange this expression as follows
1/(8×√2) = 2ⁿ
We can also write this as
1/(2³·2^1/2) = 2ⁿ
From laws of exponents if bases are same then the powers get add up that is
1/(2^7/2) = 2ⁿ
2^-7/2 = 2ⁿ
From laws of exponents, we compare that the bases are same so the powers will also be same. So, we find that n = -7/2 which can be written in improper fraction as [tex]-4\frac{1}{2}[/tex].
Learn more about Exponents at:
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Graph 8x - 4y = 16, then find its x-intercept & y-intercept.
Answers
The y-intercept of an equation is where its graph intersects the y-axis - this happens at x = 0; therefore, putting in x =0 should give us the y-intercept.
Putting in x = 0 gives
[tex]8(0)-4y=16[/tex][tex]\rightarrow-4y=16[/tex][tex]\therefore y=-4.[/tex]Hence, the y-intercept is y = -4.
The x-intercept of an equation is where its graph intersects the x-axis - this happens where y = 0; therefore, the x-intercept is found by putting in y =0:
[tex]8x-4(0)=16[/tex][tex]\rightarrow8x=16[/tex][tex]\therefore x=2.[/tex]Hence, the x-intercept is x = 2.
The graph is attached below.
4) Find the area of each composite figure. 2.5 in 2.5 in 6 in in? 4.2 in А = square A trapezoid ina А figure 1/1
Answers
The figure is a combination of a square and a trapezoid;
Thus, we first look for the area of a square using the formula below;
[tex]\begin{gathered} A_{square}=length\times length \\ \text{Where the length of the square is 2.5in} \\ A_{square}=2.5\times2.5 \\ A_{square}=6.25in^2 \end{gathered}[/tex]Answer: The area of the square is 6.25 square inches.
Also, we find the area of the trapezoid using the formula below;
[tex]\begin{gathered} A_{trapezoid}=\frac{1}{2}(a+b)h \\ \text{Where a and b are the upper length and the bottom length respectively } \\ a\text{ is the length of the square = 2.5in} \\ b=\text{ 4.2in} \\ \text{h is the height = 6in} \\ A_{trapezoid}=\frac{1}{2}(2.5+4.2)6 \\ A_{trapezoid}=3(6.7) \\ A_{trapezoid}=20.1in^2 \end{gathered}[/tex]Answer: The area of the trapezoid is 20.1 square inches.
[tex]\begin{gathered} A_{figure}=A_{square}+A_{trapezoid} \\ A_{figure}=6.25in^2+20.1in^2 \\ A_{figure}=26.35in^2 \end{gathered}[/tex]Answer: The area of the figure is 26.35 square inches.
Find the are of the circle below.
Answers
To find the area of the circle with diameter = 18 cm
We will use the formula:
[tex]\text{Area of a cirlce = }\pi r^2[/tex]where r= radius of the circle
From the quesion diameter = 18 cm
radius = diameter/2
radius = 18cm/2 = 9 cm
substituting r = 9cm into the formula
[tex]Area\text{ of a circle = }\pi(9)^2[/tex][tex]A\text{rea of the circle }=\text{ 81}\pi cm^2[/tex]The above answer is when we are to leave the answer in terms of π
Otherwise if π is given to be 3.14 or 22/7 , we will simply substitute into the formula
That is given that π= 3.14
[tex]\text{Area of the circle = 81 }\times3.14=254.34cm^2[/tex]
There are 13 candidates for homecoming king and 14 candidates for homecoming queen. How many possible outcomes are there for homecoming king and queen ?
Answers
Answer:
welll
Step-by-step explanation:
Well we know theres only gonna be one king and one queen so the outcome can be that the other people will obviously not get to be king or queen and the other people will get jealous (im not really sure if im right sory)
√-144
Real number or not real number
Answers
Answer:
not a real number
Step-by-step explanation:
Non-real numbers are also called imaginary numbers. Imaginary numbers possess an imaginary component, which exists after taking the square root (or any even root) of a negative number
Muffins $1.75
Cookies $1.25
Cakes
$1.00
For the bake sale, your principal would like to sell each baked good for $4.00. He also mentions that each baked good that is sold needs
at least a 60% profit. Based on this information, which of the baked goods could be sold at the bake sale? Explain how you know whether
each baked good meets or does not meet the criteria for being sold at the bake sale.
Answers
Answer:
rat
Step-by-step explanation:
This year Apple has launched iPhone 14. There are 4 different colors (Silver, gold, space
black, purple) of iPhone 14 Pro Max and iPhone 14 Pro. Also, there are 5 different colors
(Midnight, blue, starlight, purple, red) available for iPhone 14 plus and iPhone 14. How many different types of phones are available this year?
Answers
There are 18 different types of phones are available this year.
What is Addition?The process or skill of calculating the total of two or more numbers or amounts.
There are 4 different colors (Silver, gold, space black, purple) for,
iPhone 14 Pro Max → 4
iPhone 14 Pro → 4
There are 5 different colors (Midnight, blue, starlight, purple, red) for,
iPhone 14 plus → 5
iPhone 14 → 5
Add all of them = 4 + 4 + 5 + 5
we get, = 18
Hence, There are 18 different types of phones are available this year.
To read more about Addition.
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1. Which of the following expressions are monomials with degree 2?i) 2x² + 2xii) 2x²iii) x²iv) 2xa. ii and iiib. ii and ivC.iii and iv
Answers
Answer
a. ii and iii
Step-by-step explanation
A monomial is a polynomial with only one term.
A binomial is a polynomial with two terms.
The degree of a polynomial is determined by the highest exponent of the x-variable.
i) 2x² + 2x
type: binomial
degree: 2
ii) 2x²
type: monomial
degree: 2
iii) x²
type: monomial
degree: 2
iv) 2x
type: monomial
degree: 1
Then, choices ii and iii are monomials with degree 2
. Ross has a spinner that is split into eight equal sections numbered 1 through 8. He spun the spinner 1120 times. Which of the following would be a good estimate of the number of times the spinner landed on number 6?
Answers
The probability of the spinner landing on number 6 is calculated as follows:
[tex]\begin{gathered} p=\frac{\text{ number of favorable outcomes}}{\text{ total possible outcomes}} \\ p=\frac{1}{8} \end{gathered}[/tex]Given that he spun the spinner 1120 times
8 This graph shows how fast Heidi ran on a track. Heidi says she was
running 1.5 laps per minute because 3/2= 1.5. What mistake did
she make? How fast was Heidi running?
Answers
The speed :3/2
So , hedi ran 2/3 laps per minute
help meeeeeeeeeeeeeeeeeeeeeee
thank you
Answers
Answer:
x = -1
y = 3
Step-by-step explanation:
.............
Factorise2rs-4rt-6t+3s
Answers
Given expression:
[tex]2rs\text{ - 4rt - 6t + 3s}[/tex]Collect like terms:
[tex]=\text{ 2rs - 4rt - 6t + 3s}[/tex]Next, we bring the common terms:
[tex]=\text{ 2r(s - 2t) -3(2t - s)}[/tex]Re-writing the expression:
[tex]=\text{ -2r(2t - s) -3(2t -s)}[/tex]Since we have a common term on either side of the negative sign, we can write:
[tex]=\text{ (-2r -3)(2t-s)}[/tex]Answer:
[tex]=\text{ (-2r-3)(2t -s)}[/tex]Let us verify the answer:
[tex]\begin{gathered} (-2r\text{ -3)(2t-s)} \\ =-2r(2t\text{ -s) -3(2t -s)} \\ =\text{ -4rt + 2rs -6t + 3s} \end{gathered}[/tex]the table displays the scores of students on a recent exam find the mean of the scores to the nearest tenth
Answers
In this case, the number of students refers to frequencies.
To find the mean, we have to use the following formula
[tex]\begin{gathered} \bar{x}=\frac{\Sigma(x\cdot f)}{N}=\frac{65\cdot4+70\cdot1+75\cdot7+80\cdot5+85\cdot8+90\cdot3+95\cdot4+100\cdot1}{33} \\ \bar{x}=\frac{260+70+525+400+680+270+380+100}{33} \\ \bar{x}=\frac{2685}{33} \\ \bar{x}\approx81.4 \end{gathered}[/tex]Hence, the mean is 81.4.Can you guys please help me on this question ?
Answers
Solution
Therefore, the correct option is D.
The following table shows the cost of apples. Number of 3 5 8 11 Apples (2) $2.37 Cost (y) $3.95 $6.32 $8.69 Assume the cost of apples is a linear function of the number of apples purchased. 39 www Wwwwwwwwwwwwwwww B Part A www Write a linear equation that describes the cost of apples, y, in dollars, as a linear function of the number of apples purchased, I.
Answers
We will calculate the linear equation, first we need to find the slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where
3=x1
5=x2
2.37=y1
3.95=y2
[tex]m=\frac{3.95-2.37}{5-3}=\frac{1.58}{2}=0.79[/tex]then we will substitute in the next formula
[tex]y-y_1=m(x-x_1)[/tex][tex]\begin{gathered} y-2.37=0.79(x-3) \\ y-2.37=0.79x-2.37 \\ y=0.79x \end{gathered}[/tex]the linear equation is
y=0.79x
What is the length of AB? round your answer to the nearest hundred.
Answers
In order to calculate the length of the line AB, you use the following formula for the distance between points in the coordinate plane:
d = √((x2-x1)²-(y2-y1)²)
That is, it is only necessary to have a pair of points with coordinates (x1,y1) and (x2,y2). In this case you have two points A=(-5,-4)=(x1,y1) and B=(-3,3)=(x2,y2), then, by replacing these values into the formula for the distance you have:
d = √((3-(-3))²-(-5-4)²)
d = √((3+3)²+(-9)²)
d = √(36+81) = √(117) = 10.8166 ≈ 10.82
Hence, the length of the line AB is 10.82
in susan graduating class the ration of girls to boys is 3:2 and the total number of students is 250. what is the total number of girls and boys iin susan's graduating class?
Answers
Explanation:
The ratio of girls to boys = 3:2
Total number of students = 250
Sum of ratio = 3 + 2 = 5
The total number of girls = 3/5 * 250
Would just like to make sure that my answer is correct.
Answers
Answer:
[tex]\text{ -2sin(}\frac{11\pi}{24})\cos (\frac{\pi}{24})[/tex]Explanation:
Here, we want to simplify the given expression
The basic rule we will be using here is:
[tex]\sin (A\text{ + B})\text{ = SinACosB + CosASinB}[/tex]Thus, we have it that:
[tex]\begin{gathered} \text{ sin(}\frac{\pi}{6}+\frac{\pi}{4})\text{ + sin(}\frac{\pi}{8}+\frac{3\pi}{8}) \\ \\ \sin (\frac{5\pi}{12})\text{ + sin(}\frac{\pi}{2}) \end{gathered}[/tex]We use the sine addition formula as follows:
[tex]\sin \text{ A + sin B = 2sin(}\frac{A+B}{2})\cos (\frac{A-B}{2})[/tex]Now, we substitute the last expression into the given addition formula above:
[tex]\begin{gathered} \text{ sin(}\frac{5\pi}{12})\text{ + sin(}\frac{\pi}{2})\text{ =2sin(}\frac{\frac{5\pi}{12}+\frac{\pi}{2}}{2})\cos (\frac{\frac{5\pi}{12}-\frac{\pi}{2}}{2}) \\ \\ =\text{ 2sin(}\frac{11\pi}{24})\cos (\frac{-\pi}{24})\text{ = -2sin(}\frac{11\pi}{24})\cos (\frac{\pi}{24}) \end{gathered}[/tex]