Answers
In order to solve this, the first thing we have to do is to determine the value of g(-2), this is possible by evaluating -2 for x in g(x), like this:
g(-2) = 3(-2)²= 3×4 = 12
Now that we know the value of g(-2), we can determine the value of f(g(-2)) by evaluating g(-2) = 12 in f(x), like this:
f(g(-2)) = f(12) = 5(g(-2)) + 3 = 5(12) + 3 = 60 + 3 = 63
Then, f(g(-2)) = 63
Related Questions
Ally bought 4 liters of lemonade, 3,000 milliliters of iced tea, and 2,500 milliliters of fruit punch. How many liters of drinks in total did she buy?
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Answer:
9.5 liters
Explanation:
The volume of each drink that Ally bought is:
• Lemonade: 4 liters
,• Iced tea: 3,000 milliliters
,• Fruit Punch: 2,500 milliliters
Since we are required to find the total in liters, convert the volumes given in milliliters to liters.
[tex]\begin{gathered} 1000\text{ milliliters}=1\text{ liters} \\ \implies1\text{ milliliter}=\frac{1}{1000}\text{ liter} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} 3000\text{ milliliter}=\frac{3000}{1000}=3\text{ liter} \\ 2500\text{ m}\imaginaryI\text{ll}\imaginaryI\text{l}\imaginaryI\text{ter}=\frac{2500}{1,000}=2.5\text{ l}\imaginaryI\text{ter} \end{gathered}[/tex]Therefore, the total volume in liters will be:
[tex]4+3+2.5=9.5\text{ liters}[/tex]Ally bought 9.5 liters of drinks in total.
Hey can you pleas help me on this math problem thank you
Answers
Given:
Nolan wraps 36 presents in 12 hours on Saturday
And wraps 42 presents in 14 hours on Friday
If y = number of gifts, and x = number of hours
So, the proportional equation will be as follows:
[tex]y=kx[/tex]Where k is the constant of proportionality
Total gifts = y = 36 + 42 = 78
Total hours = x = 12 + 14 = 26
So, subtitute into the euation to find k
[tex]\begin{gathered} 78=k\cdot26 \\ k=\frac{78}{26}=3 \end{gathered}[/tex]So, the answer will be the constant = 3
The triangle ABC pictured below is a right, isosceles triangle. If the length of side AC is 3, give the lengths of the other two sides and the measures of angle A and angle B.
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From the statement, we know that we have a right triangle that:
0. has an angle ∠C = 90°,
,1. is also an isosceles triangle,
,2. has a side AC = 3.
1) From points 2 and 3, we know that:
[tex]AC=BC=3.[/tex]Because we have a right triangle, we can use Pitagoras Theorem, which states that:
[tex]c^2=a^2+b^2.[/tex]Where:
• c = AB = hypotenuse,
,• a = BC = 3,
,• b = AC = 3.
Replacing these data in the equation above, we get:
[tex]c^2=3^2+3^2=9+9=18\Rightarrow AB=c=\sqrt{18}.[/tex]2) From point 2 we know that angles A and B must be equal:
[tex]\angle A=\angle B.[/tex]From geometry, we know that the inner angles of a triangle sum up to 180°, so we have:
[tex]\angle A+\angle B+\angle C=180\degree\Rightarrow2\angle A+\angle C=180\degree\Rightarrow\angle A=\frac{180\degree-\angle C}{2}=\frac{180\degree-90\degree}{2}=45\degree.[/tex]Where we have used point 1.
AnswerThe sides of the triangle are:
• AB = √18,,
,• AC = 3,
,• BC = 3.
The angles of the triangle are:
• ∠A = 45°,,
,• ∠B = 45°,,
,• ∠C = 90°.
Find C.Round to the nearest tenth.20 ft\22 ftAB18 ftC = [? ]°Law of Cosines: c2 = a2 + b2 - 2ab cos C=Enter
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The given triangle is shown below
From the triangle
[tex]a=22ft,b=20ft,c=18ft,C=\text{?}[/tex]Using the law of Cosines
[tex]c^2=a^2+b^2-2ab\cos C[/tex]Substitute the values of a, b, c into the formula
This gives
[tex]18^2=22^2+20^2-2(22)(20)\cos C[/tex]Simplifying the expression
[tex]\begin{gathered} 324=484+400-880\cos C \\ 324=884-880\cos C \end{gathered}[/tex]Collect like terms
[tex]\begin{gathered} 324-884=-880\cos C \\ -560=-880\cos C \end{gathered}[/tex]Divide both sides by -880
[tex]\begin{gathered} \frac{-560}{-880}=\cos C \\ \cos C=0.6364 \end{gathered}[/tex]Find the value of C
[tex]\begin{gathered} C=\cos ^{-1}(0.6364) \\ C=50.5^{\circ} \end{gathered}[/tex]Helps ASAP just 6 and 7 please and thank you
Answers
Using a calculator, we calculate the following
[tex]\begin{gathered} 1.41^2=1.9881 \\ 1.42^2=2.0164 \end{gathered}[/tex]Based on these calculations, the square root of 2 is between 1 and 2.
I need some help with this problem. Thanks.
Answers
Answer:
Natural:G
Whole number: B
Integer: H,D,J
Rational: A,F,E,I
Irrational: C,K
Step-by-step explanation:
The figure below is the graph of the dimensions of a rectangle whoseadjacent side lengths exhibit direct variation.
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Concept
What is a direct variation? A direct variation is a direct relationship between two variables in which increase in one variable lead to increase in the other variable and decrease in one variable lead to decrease in the other variable.
Hence, the relationship fron the graph between Height and Width of the rectangle is not a direct variation.
Therefore,
The relationship is not a direct variation.
Final answer
Option B = False
Consider a trebuchet launching a flaming stone over a castle wall. It is mounted on a small hill and has a parabolic trajectory (neglecting air resistance). Once it crashes into the ground on the other side of the castle wall, it comes to rest. This motion is described by the function below, where x, measured in meters, represents horizontal displacement from the launch position and y = f(x) represents vertical distance from the ground, measured in meters.
f(x) = -0.25x2 + 3.15x + 5
Determine the contextual domain and range and justify your answers. What is the peak height of the flaming stone?
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The domain of function f(x) is the set of all real numbers.
the range of function f(x) is, f ≤ 14.9225
And the peak height of the flaming stone would be, 14.9 meters
In this question, we have been given a trebuchet launching a flaming stone over a castle wall. It is mounted on a small hill and has a parabolic trajectory. Once it crashes into the ground on the other side of the castle wall, it comes to rest. This motion is described by the function f(x) = -0.25x² + 3.15x + 5, where x, measured in meters, represents horizontal displacement from the launch position and y = f(x) represents vertical distance from the ground, measured in meters.
We need to determine the contextual domain and range and justify your answers.
The domain of function f(x) is the set of all real numbers.
The range of function f(x) is, f ≤ 14.9225
From the range of the function, the peak height of the flaming stone would be, 14.9 meters
Therefore, the domain of function f(x) is the set of all real numbers.
the range of function f(x) is, f ≤ 14.9225
And the peak height of the flaming stone would be, 14.9 meters
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help;aaefefdsfsd fnujyhvbnmhgf rfdgtrbtg get it?
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The value of the expression [tex]\frac{-4[5(7-13)-19]}{2(-1)}[/tex] is - 98.
The abbreviation BODMAS rule is used to assist kids to recall the proper order of operations when performing mathematics. Operations are essentially the various mathematic operations we can do on numbers. "Brackets, Order, Division, Multiplication, Addition, Subtraction" is what it stands for.
A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression. Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Consider the expression,
[tex]\frac{-4[5(7-13)-19]}{2(-1)}[/tex]
Using the BODMAS rule,
We will first solve the parenthesis.
[tex]\frac{-4[5(7-13)-19]}{2(-1)}=\frac{-4[35-65-19]}{-2}[/tex]
[tex]\frac{-4[5(7-13)-19]}{2(-1)}=\frac{-140+260+76}{-2}[/tex]
Now, the next step is to divide the expression.
[tex]\frac{-4[5(7-13)-19]}{2(-1)}=\frac{-140}{-2}+\frac{260}{-2}+\frac{76}{-2}[/tex]
[tex]\frac{-4[5(7-13)-19]}{2(-1)}=70-130-38[/tex]
Subtracting the expression,
[tex]\frac{-4[5(7-13)-19]}{2(-1)}=-98[/tex]
Hence, the value of the expression is - 98.
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with work please 2x -42 = -8x + 28
Answers
We first need to
{x+3y=7 -9x+2y=8 elimination or addition method
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The solution to the system of equations is (-10/29, 71/29).
We are given a system of linear equations in two variables.We have two equations and two variables.The first equation is x+3y = 7.The second equation is -9x+2y = 8.We will use the elimination method to solve the equations.x + 3y = 7-9x + 2y = 8Multiply both sides of the first equation by -9.-9x -27y = -63Subtract this newly generated equation from the second equation.(-9x + 2y) - (-9x -27y) = 8 - (-63)-9x + 2y + 9x + 27y = 8 + 6329y = 71y = 71/29Use this value in the first equation to find the value of "x".x + 3y = 7x + 3(71/29) = 7x + 213/29 = 7x = 7 - (213/29)x = -10/29To learn more about equations, visit :
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A chemical company mixes pure water with their premium antifreeze solution to create an inexpensive antifreeze mixture. The premium antifreeze solutioncontains 80% pure antifreeze. The company wants to obtain 320 gallons of a mixture that contains 15% pure antifreeze. How many gallons of water and howmany gallons of the premium antifreeze solution must be mixed?
Answers
Amount of water = 260 gallons
Amount of antifreeze = 60 gallons
Explanation:let the amount of water = w
amount of water + amount of antifreeze will give 320 gallons of mixture
w + amount of antifreeze = 320
amount of antifreeze = 320 - w ...(1)
The concentration for the antifreeze = 80% = 0.8
The concentration of the mixture = 15% = 0.15
From our question, we are mixing antifreeze with pure water (two different things). In our calculation, we can write the concentration in terms of water or in terms of antifreeze.
Writing the concentration in terms of amount of antifreeze
0.8(amount of antifreeze) + percent of antifreeze (amount of water) = concentraton of the mixture
The mixture contains 15% antifreeze
water contains no antifreeze, percent = 0
0.8(320 - w) + 0(w) = 0.15(amount of mixture)
0.8(320 - w) + 0 = 0.15(320)
256 - 0.8w + 0 = 48
256 - 0.8w = 48
collect like terms:
256 - 48 = 0.8w
208 = 0.8w
divide both sides by 0.8:
208/0.8 = w
w = 260
substitute for w in equation (1)
amount of antifreeze = 320 - 260 = 60
Amount of water = 260 gallons
Amount of antifreeze = 60 gallons
Write a linear function that represents the depth of the pond at a given time
Answers
Let x represent the number of days
Let f(x) represent water depth
We can see that the water depth is a function of the number of days.
Water depth, f(x) is the dependent variable and number of days, x is the independent variable.
As the days go by, the water depth changes.
The function is therefore:
[tex]f(x)=54-0.5x[/tex]The domain is the set of values (number of days) for which the pond will have a valid depth, i.e. between 54'' and 0.
[tex]0\le x\le108[/tex]Because at 0 days,
[tex]f(x)=54-0.5(0)=54^{\doubleprime}[/tex]And at 108 days,
[tex]f\mleft(x\mright)=54-0.5\mleft(108\mright)=0[/tex]Try this: Find "y." How does CPCTC help? A ABC EA ADC. Find y. A (3y) 21° D C С B. DO Pear Deck Interacti Do nove Students, enter a number!
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AS ACD and ACBare congruent triangles, we have that
[tex]\begin{gathered} 3y=21\rightarrow \\ y=\frac{21}{3}=7 \end{gathered}[/tex]so the answer is y=7
For a particular nature trail, the amounts of time that hikers take to walk the trail are normally distributed.The mean of the times is 30.1 minutes,and the standard deviation is 3.6 minutes.For a sample of 4 hikers,what is the probability that the mean time for the sample is less than 28 minutes?
Answers
Let X be the normally distributed random variable representing the time hiker takes to walk the trail.
Given that mean and standard deviation are 30.1 and 3.6 minutes, respectively,
[tex]\begin{gathered} \mu=30.1 \\ \sigma=3.6 \end{gathered}[/tex]The sample size is 4,
[tex]n=4[/tex]The z-score corresponding to any value of 'x' is given by,
[tex]z=\frac{x-\mu}{\sigma}[/tex]So the probability that the mean time for the sample is less than 28 minutes is calculated as,
[tex]\begin{gathered} P(X<28)=P(z<\frac{28-30.1}{3.6}) \\ P(X<28)=P(z<-0.58) \\ P(X<28)=P(z>0.58) \\ P(X<28)=P(z>0)-P(0From the Standard Normal Distribution Table,[tex]\varnothing(0.58)=0.2190[/tex]Substitute the value,
[tex]\begin{gathered} P(X<28)=0.5-0.2190 \\ P(X<28)=0.281 \\ P(X<28)=28.1\text{ percent} \end{gathered}[/tex]Thus, there is approximately 28.1% probability that the mean time for the sample is less than 28 minutes.
A company uses a logo shaped like a triangle. The dimensions of the logo are shown in the diagram. What is the area of the logo in square inches?
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Area of triangle shape
Area A = BxH/2 = [ 8 x (5+1/2) ]/2
. = 4 x 5.5
. = 22
Then answer is
Area of logo = 22 inches2
OPTION B)
2 - 2f(x)X + 1g(x) = 18 - 3.2Escreva (fog)(2) como uma expressão em função de 2.(fog)(x) =
Answers
Answer
[tex](f\text{ o g)(x) = }\frac{3x-16}{17-3x}[/tex]Explanation
We are given that
f(x) = (2 - x)/(x + 1)
g(x) = 18 - 3x
We are then asked to find (f o g)(x)
(f o g) (x) is the same as writing the expression for f(x) but instead of x, we will write g(x) in the expression.
[tex]\begin{gathered} f(x)=\frac{2-x}{x+1} \\ (\text{fog)(x) = }\frac{2-g(x)}{g(x)+1} \end{gathered}[/tex]Recall that
g(x) = 18 - 3x
So,
[tex]\begin{gathered} (\text{fog)(x) = }\frac{2-g(x)}{g(x)+1} \\ (\text{f o g)(x) = }\frac{2-(18-3x)}{18-3x+1} \\ (f\text{ o g)(x) = }\frac{2-18+3x}{17-3x} \\ (f\text{ o g)(x) = }\frac{-16+3x}{17-3x} \\ (f\text{ o g)(x) = }\frac{3x-16}{17-3x} \end{gathered}[/tex]Hope this Helps!!!
The length of a rectangle is 4ft less than 3 times width. Perimeter is 54 ft. What equation can be used to find the width of the rectangle
(3w-4)+2w=54
2(3w-4)+2w=54
w(3w-4)=54
2(4w-3)+2w=54
Answers
Answer:
b
Step-by-step explanation:
Here,
The length of a rectangle is 4ft less than 3 times the width
Then,
length=3w-4ft
Now,
2(l+w)=P
2(3w-4+w)=54
6w-8+2w=54
2(3w-4)+2w=54
Equation b can be used to find the width of the rectangle
Due to an economic downturn, a company had to decrease its staff from 48 employees to 24 employees. What was the percentage decrease in staff?
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we get that the decrease percentage is
[tex]\frac{48-24}{48}\cdot100=\frac{24}{48}\cdot100=50\text{ \%}[/tex]so the percentage of decrease is 50%
help me please
thank you
Answers
Answer:
Domain: A, [tex](-\infty, \infty)[/tex]
Range: A, [tex][4, \infty)[/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Hello, I need some assistance with this homework question please for precalculusHW Q44
Answers
SOLUTION:
Case: Logarithms
A logarithm is the opposite of power. In other words, if we take a logarithm of a number, we undo exponentiation.
We consider the log of power law below:
[tex]\begin{gathered} \log_aa^x=x\log_aa \\ =x \end{gathered}[/tex]Given:
[tex]\log_33^{66}[/tex]Required: Without using calculators, use log laws to answer
Method:
Applying the law above,
[tex]\begin{gathered} \log_33^{66} \\ =66\log_33 \\ =66\times1.(Remember\text{ same base law: }\log_33=1 \\ =66 \end{gathered}[/tex]Final answer:
66
3. A data set has six numbers. Four of the numbers are: 4, 3, 8, 12. If the mode is 3, find at least three possibilities for the other two numbers.
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The possibility of the other two numbers in the given data set is 3.
What do we mean by a number?An object that can be counted, measured, and given a name is a number. The initial examples are the natural numbers 1, 2, 3, 4, and so forth. In language, numbers can be expressed using number words. The symbols referred to as numerals can be used to represent specific numbers in a more general way; for instance, the numeral "5" stands for the number five. Due to the limited amount of symbols that can be learned, fundamental numbers are typically arranged in a numeral system, which is a systematic manner of representing any number. The Hindu-Arabic numeral system, which enables any number to be expressed using a combination of 10 fundamental numeric symbols known as digits, is the most widely used numeral system.So, by observing the data, we can simply conclude that:
As the mode is 3, the remaining two numbers are 3.Therefore, the possibility of the other two numbers in the given data set is 3.
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For right triangle find the missing quantity indicated below express the angle in degrees and minutes not just degrees please and round your answer
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To find the angle we will use the sine theorem, but first we will find the measure of the missing side:
[tex]x^2=1325^2+2569^2[/tex][tex]x=\sqrt[]{1325^2+2569^2}[/tex][tex]x=\sqrt[]{8355386}^{\prime}\text{ }[/tex]measure of angle B must be:
[tex]\frac{sin\text{(B)}}{2569}=\frac{\sin (90^{\circ})}{\sqrt[]{8355386}}[/tex][tex]\sin (B)=\frac{2569}{\sqrt[]{8355386}}[/tex][tex]B=62.72^{\circ}[/tex]Finally convert B to degrees and minutes:
[tex]\frac{1^{\circ}}{60^{\prime}}=\frac{0.72^{\circ}}{m^{\prime}}[/tex][tex]m^{\prime}=0.72\cdot60=43.2^{\prime}[/tex][tex]B=62^{\circ}43.2^{\prime}\text{ }[/tex]Gina has a box of red,blue,and green markers.The ratio of the number of red markers to the number of blue markers is 5:2.The ratio to the number of blue markers to the number of green markers is 3:5.What is the ratio of the number of red markers to the number of green markers?
Answers
Answer: 5:5
Step-by-step explanation:
Use the information to figure out how much you have of each color, then put in ratio.
A hexagonal prism whose base has area 25.6 square centimeters and who’s height is 8.9 centimeters
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We are given the following information about a hexagonal prism.
Base area = 25.6 cm²
Height = 8.9 cm
Recall that the volume is given by
[tex]V=B\cdot h[/tex]Where B is the area of the base and h is the height of the hexagonal prism.
Let us substitute the given values into the above formula
[tex]\begin{gathered} V=B\cdot h \\ V=25.6\cdot8.9 \\ V=227.84\: cm^3 \end{gathered}[/tex]Therefore, the volume of the given hexagonal prism is 227.84 cubic centimeters.
what is the length of AB, if A (-3,-3) and B (5,-9)?
Answers
Answer:
The distance of the line would be 10 units.
hello would you mind checking if this is correct ?
Answers
we will use here pythagoras theorem here,
5^2 + 12^2 = C^2
25 + 144 = C^2
C = root 169
c = 13
Rewrite 0 = 1-2y+14x. As a linear equation
Answers
Answer:
y = 7x + 1/2
Step-by-step explanation:
0 = 1 - 2y + 14x
+2y +2y
2y = 1 + 14x
/2 /2 /2
y = 1/2 + 7x
y = 7x + 1/2
0= 1 - 2y +14x
+2y +2y
Stephanie practiced the piano for 1 hour 15 min per day. If she practiced for 8 days, what was her total practice time?
Answers
convert 1 hour and 15 minutes into minutes, you should get 75 minutes.
multiply 75 by 8 (because 75 minutes for 8 days) and you should get 600 minutes
600 minutes is a fine answer, but if you want to simplify it, divided 600 minutes by 60 (because we’re converting it into hours and there are 60 minutes in an hour)
600/60 = 10
so she practiced for 10 hours in 8 days
Answer:
10 hours
Step-by-step explanation:
1 hour 15 mins = 75 minutes
75 minutes x 8 days = 600 total in minutes
600 minutes/ 60 minutes = 10 hours
The quotient of 4 times X and 2 more than Y
Answers
Answer:4x(y+2)
Step-by-step explanation:
