Answer:
Given the functions:
[tex]f(x) = 3x^2+2[/tex]
[tex]g(x) = x-8[/tex]
we have to find [tex](f \cdot g)(2)[/tex]
[tex](f \cdot g)(2) = f(2) \cdot g(2)[/tex] ....[1]
Substitute the value of x = 2 in f(x) and g(x) we have;
[tex]f(2) = 3(2)^2+2 =12+2 = 14[/tex] and
[tex]g(2) = 2-8 = -6[/tex]
Substitute these in [1] we have;
[tex](f \cdot g)(2) = 14 \cdot -6 = -84[/tex]
Therefore, the value of [tex](f \cdot g)(2)[/tex] is, -84
I don't get how to do it i have tried but I can't I think that it might be 20 i think
How do i solve
3(x+3)=18
If a four-sided figure has four congruent sides, then it has four right angles. Prove this wrong
Please Help!
1. Define an example of a function – this could be distance traveled vs. time, the cost
of a turkey vs. weight, ect.
2. Show this relation as a set of correctly determined ordered pairs -- you will need
at least 5 ordered pairs in set notation -- remember that set notation will look
like: {(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)} with the { } around the ordered pairs.
Can you please explain how you did it. I want to understand. (30pts)
Question 2 (multiple answer)
Which simplifications of the powers of i are correct?
There is more than one correct answer. Select all correct answers.
i7=i4⋅i3=−1⋅−i=i
i6=i4⋅i2=1⋅−1=−1
i6=i4⋅i2=−1⋅−1=1
i7=i4⋅i3=1⋅−i=−i
i8=i4⋅i4=−1⋅−1=1
i5=i3⋅i2=−i⋅−1=i
i5=i3⋅i2=i⋅−1=−i
i8=i4⋅i4=1⋅1=1
Suppose you are walking home from the skating ring , you have to walk 6 miles east and 9 miles north , use the Pythagorean theorem how far is the skating ring from where u are.
plzzzzz!!!!!help
this forms a right triangle where you need to calculate the length of the hypotenuse by using the Pythagorean theorem
a^ + b^2 = c^2
6^2 = 36
9^2 = 81
36+81 = 117
sqrt(117) = 10.816
10.8 miles
Avani went to the grocery store and bought home a cardboard box that was covered with a sealed top Two end face of the box are squares The area of the face on either end is 64 square inches what is the length of the side of a square face? Plz help me plz
HELP PLEASE !!!!
Solve rt-3f=12 for f
SHOW STEPS !!!! And explain how to get answer please
Hey!
Hope this helps...
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
If you have any questions on how I did this, please ask!
rt - 3f = 12
-3f = 12 - rt
f = (12 - rt) / 3
Because we do not know what r nor t equal, we cannot find the exact value of f...
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Myles can ride his bike 24 miles in 6 hours. How many miles can he travel in 1 hour? (Unit rate)
How many miles can Myles travel in 5 hours?
Suppose that (x1, y1) and (x2, y2) are two points on a linear function. Write the formula to find the function’s rate of change for the interval [x1, x2].
Final answer:
The rate of change for a linear function on the interval [x1, x2] is the slope of the line m, calculated by dividing the difference in y-values by the difference in x-values: m = (y2 - y1) / (x2 - x1).
Explanation:
To find the rate of change of a linear function for the interval [x1, x2], we need to calculate the slope of the line connecting the points (x1, y1) and (x2, y2). This is done using the formula:
m = (y2 - y1) / (x2 - x1)
where m represents the slope, which is the ratio between the change in y-values (rise) and the change in x-values (run). When graphing the function, if you plotted these two points, you'd be able to draw a straight line between them, and by finding the slope, you determine how steep the line is. The slope, or rate of change, indicates how much y increases or decreases for each unit increase in x. This rate of change is constant along the entire length of a straight line.
The land ares of Florida is 1×100,000+3×10,000+9×1,000+8×100+5×10+2×1 square kilometers. Write in standard form and word form
What is the ratio of the circumferences for two circles with areas 6π m and 150π m?
The ratio of the circumferences equals the ratio of the radii.
so we need to find their radii
first circle's radius:
pir^2 = 6pi
r = √6
second circle's radius:
pir^2 = 150pi
r = √150
Their ratio is
√6 : √150 =
√6 : √6√25 =
√6 : 5√6 =
1 : 5
The ratio of the circumferences of two circles with areas of 6π m² and 150π m² is 5:1.
To find the ratio of the circumferences of two circles given their areas, we first recall the formula for the area of a circle, A = πr², where A is the area and r is the radius. Knowing the area, we can solve for the radius of each circle. The areas given are 6π m² and 150π m².
To find the radius for the first circle, we set up the equation:
6π = πr²
We solve for r, yielding:
r = √6.
Similarly, for the second circle:
150π = πr²
This gives us:
r = √150.
Next, we use the formula for the circumference C = 2πr. We calculate the circumferences of the circles using their respective radii:
First circle's circumference: C1 = 2π(√6)
Second circle's circumference: C2 = 2π(√150)
Finally, to find the ratio of the circumferences, we divide C2 by C1 and simplify:
Ratio = C2÷C1 = (2π(√150))÷(2π(√6)) = √(150÷6) = √25 = 5.
Therefore, the ratio of the circumferences of the two circles is 5:1.
Which is true? A 10.59 > 10.60 B 10.590 = 10.59 C 10.43 < 10.24 D 9.0005 = 9.0050
A) 10.59 > 10.60: True, because 10.59 is greater than 10.60.
B) 10.590 = 10.59: True, as they have the same value.
C) 10.43 < 10.24: False, as 10.43 is greater than 10.24.
D) 9.0005 = 9.0050: False, as they are not equal.
Use the concept of mathematical expression defined as:
Using operations like addition, subtraction, multiplication, and division, a mathematical expression is defined as a group of numerical variables and functions.
A) 10.59 > 10.60: This statement is true.
In decimal numbers, the higher the number, the greater its value.
Since 10.59 is greater than 10.60 (because 59 is greater than 60), this statement holds true.
B) 10.590 = 10.59: This statement is also true.
When two decimal numbers have the same digits after the decimal point, they are considered equal.
In this case, 10.590 and 10.59 have the same value.
C) 10.43 < 10.24: This statement is false.
Similar to the first option, the higher the number, the greater its value.
In this case, 10.43 is greater than 10.24,
So the statement is not true.
D) 9.0005 = 9.0050: This statement is also false.
Although the numbers are very close, they are not equal.
When comparing decimal numbers, each digit after the decimal point matters.
In this case, the numbers differ after the fourth decimal place, making them unequal.
Hence, the given expressions:
A) 10.59 > 10.60: True,
B) 10.590 = 10.59: True,
C) 10.43 < 10.24: False,
D) 9.0005 = 9.0050: False.
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a metallurgist has an alloy with 10% titanium and an alloy with 20% titanium. he needs 100 grams of an alloy with 17% titanium. how much of each alloy should be mixed to attain the 100 grams of alloy with 17% titanium?
Let us say that:
x = mass of 10% titanium alloy required
y = mass of 20% titanium alloy required
To solve this problem, we set-up two mass balances or equations.
Overall mass balance: x + y = 100
x = 100 – y ---> 1
Titanium mass balance: 0.10 x + 0.20 y = 0.17 (100)
0.10 x + 0.20 y = 17 ---> 2
Now we combine equations 1 and 2:
0.10 (100 – y) + 0.20 y = 17
10 – 0.10 y + 0.20 y = 17
0.10 y = 7
y = 70 g
Calculating for x using equation 1:
x = 100 – y
x = 100 – 70
x = 30 g
Answer:
x = 30 g of 10% titanium alloy required
y = 70 g of 20% titanium alloy required
PLEASE HELP WITH THESE TWO IM VWRY CONFUSED AND SIPER DUMD !!
3 hours worked for$12;9 hours worked for $36
This answer explains the concept of Labor Economics and Wages by calculating the hourly rate from given total pay and total hours worked.
Explanation:The subject of this question involves Labor Economics and Wages.
In this scenario, the wage for working 3 hours is $12, while for working 9 hours, the pay is $36. To determine the hourly rate, we can use the formula: Hourly Rate = Total Pay / Total Hours Worked. Applying this formula, we find the hourly rate to be $4 per hour.
Example:
3 hours worked for $12 -> Hourly rate = $12 / 3 hours = $4 per hour9 hours worked for $36 -> Hourly rate = $36 / 9 hours = $4 per hourJason and Jenny are out on a lunch date. Jason gives Jenny a bouquet that has 4 roses, 3 carnations, and 4 orchids. They decide that Jenny gets to choose their lunch order if the flower she randomly picks from the bouquet is a carnation or a rose. What is the probability that Jenny gets to choose lunch?
Max has more than 5 carrots (number of carrots Max has = c
A large planetarium in the shape of a dome is being built. When it is complete, the base of the dome will have a circumference of 87 kilometers. What area of land was required for this planetarium?
Answer:
602.32 km²
Step-by-step explanation:
First, find the radius of the circle using the circumference formula
C = 2π*r
87 = 2π*r
∴ r = 13.8465 km
Second, using the radius, calculate the area:
A = π * r²
A = π * 13.8465²
A = 602.32 km ²
Robbie did a survey of four butterfly parks and wrote the following observations: Butterfly Park SurveyPark Number of White Butterflies Total Number of Butterflies A 24 86 B 43 92 C 12 68 D 32 52 Based on the survey, which park had the greatest percentage of white butterflies?
Answer:
A = 24 / 86 = 28%
B = 43 / 92 = 47%
C = 12 / 68 = 18 %
D = 32 / 52 = 62%
Answer D
Step-by-step explanation:
Dan bought a truck for $29,800. The value of the truck depreciated at a constant rate per year. The table below shows the value of the truck after the first and second years: Year 1 2 Value (in dollars) 26,522 23,604.58 Which function best represents the value of the truck after t years?
A.F(T)=29,800(0.89)^t
B.F(T)=26,522(0.89)^t
C.F(T)=29,800(0.11)^t
D.F(T)=26,522(0.11)^t
Answer:
A
Step-by-step explanation:
did the test
find the obtuse angle the line y-2x=7 makes with the x- axis
Identify the equation of the line that has a y-intercept of 7 and is parallel to the graph of y = 5x - 3
A cylinder has its height doubled and its radius cut to one third. What is the ratio of the volumes of the modified cylinder to the original cylinder?
Final answer:
The ratio of the volumes of the modified cylinder (height doubled and radius cut to one third) to the original cylinder is 2:9.
Explanation:
To find the ratio of the volumes of the modified cylinder to the original cylinder, we need to use the formula V = πr²h.
Let the original radius be 'r' and the original height be 'h'. The volume of the original cylinder V1 is given by:
V1 = πr²h
After doubling the height and cutting the radius to one third, the new radius is 'r/3' and the new height is '2h'. The volume of the modified cylinder V2 is:
V2 = π(r/3)²(2h) = π(r²/9)(2h) = (2/9)πr²h
The ratio of the volumes is then:
Volume Ratio (V2/V1) = (2/9)πr²h / πr²h = 2/9
So, the ratio of the volumes of the modified cylinder to the original cylinder is 2:9.
What is the ratio of 2.5 million to 1.5 million
Travis traveled 320 miles in 5 hours. What is his unit rate of speed in miles per hour? _____ miles per hour
The unit rate of speed in miles per hour is 64 miles per hour if Travis traveled 320 miles in 5 hours.
What is the distance?Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.
We have:
Travis traveled 320 miles in 5 hours.
The distance d = 320 miles
Time is taken t = 5 hours
As we know, the change in values of a dependent variable with respect to the independent variables.
The unit rate of speed in miles per hour = 320/5
The unit rate of speed in miles per hour = 64 miles per hour
Thus, the unit rate of speed in miles per hour is 64 miles per hour if Travis traveled 320 miles in 5 hours.
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A pre-image point is rotated 90° clockwise. If the pre-image point had the coordinates (3, -5), what are the coordinates of its image point?
(-5, -3)
(5, 3)
(-3, 5)
(-3, -5)
Answer:
(-5,-3)
Step-by-step explanation:
Assume that the sales of a certain appliance dealer are approximated by a linear function. Suppose that sales were $14,500 in 1982 and $65,500 in 1987. Let x = 0 represent 1982. Find the equation giving yearly sales S
Final answer:
To articulate the linear equation for yearly sales S, we calculate the slope from the two provided data points and use the slope-intercept form, ultimately deriving the equation S = 10200x + 14500.
Explanation:
To find the equation giving yearly sales S, we can use the two data points: sales were $14,500 in 1982 and $65,500 in 1987. With x = 0 representing 1982, the two points are (0, 14500) and (5, 65500). We can calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1), which is the change in sales over the change in time.
So, m = (65500 - 14500) / (5 - 0) = 51000 / 5 = 10200. This means the sales are increasing at a rate of $10,200 per year.
Now, we can use the slope and one point to write the linear equation in the slope-intercept form, which is Y = mx + b, where b is the y-intercept. Since when x = 0, Y = 14500, we know that b = 14500. Therefore, our final equation for yearly sales S is S = 10200x + 14500.
what is 12/20 as a percent?
Answer:
60%
Step-by-step explanation:
show six
ways to add 2,3,4
Answer and Explanation:
Given : Numbers 2,3,4.
To find : Show six ways to add the numbers?
Solution :
As there are three numbers so arrangement of these numbers are as follow by changing there positions,
[tex]2+3+4=9[/tex]
[tex]2+4+3=9[/tex]
[tex]3+2+4=9[/tex]
[tex]3+4+2=9[/tex]
[tex]4+2+3=9[/tex]
[tex]4+3+2=9[/tex]
Above are the ways.