Answer:
A.) gf(x) = 3x^2 + 12x + 9
B.) g'(x) = 2
Step-by-step explanation:
A.) The two given functions are:
f(x) = (x + 2)^2 and g(x) = 3(x - 1)
Open the bracket of the two functions
f(x) = (x + 2)^2
f(x) = x^2 + 2x + 2x + 4
f(x) = x^2 + 4x + 4
and
g(x) = 3(x - 1)
g(x) = 3x - 3
To find gf(x), substitute f(x) for x in g(x)
gf(x) = 3( x^2 + 4x + 4 ) - 3
gf(x) = 3x^2 + 12x + 12 - 3
gf(x) = 3x^2 + 12x + 9
Where
a = 3, b = 12, c = 9
B.) To find g '(12), you must first find the inverse function of g(x) that is g'(x)
To find g'(x), let g(x) be equal to y. Then, interchange y and x for each other and make y the subject of formula
Y = 3x + 3
X = 3y + 3
Make y the subject of formula
3y = x - 3
Y = x/3 - 3/3
Y = x/3 - 1
Therefore, g'(x) = x/3 - 1
For g'(12), substitute 12 for x in g' (x)
g'(x) = 12/4 - 1
g'(x) = 3 - 1
g'(x) = 2.
Find the distance between the points (–15, 3) and (–9, 8). A) units B) units C) units D) units
Answer:
√61
Step-by-step explanation:
d=√(x2 - x1)^2 + (y2 - y1)^2
√(-9-(-15))^2 + (8-3)^2
√61
The distance between points P(-15, 3) and Q(-9, 8) is √61 units.
What is algebra?Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.
The given points are,
P(-15, 3) and Q(-9, 8).
The distance between two points A(x₁, y₁) and B(x₂, y₂)
Distance
= √(x₂ - x₁)² + (y₂ - y₁)²
To find the distance between points PQ,
Use formula
PQ = √(-9 - (-15))²+(8 - 3)²
= √(-9 + 15) ²+(5)²
= √(6) ²+(5)²
= √36 + 25
= √61
The required distance between given points is √61 units.
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La densidad de un líquido es de 1.5 gr/cm3 su masa es de 7 libras Determina la cantidad de litros que ocupan dichos líquidos
Answer:
La cantidad de litros que ocupa dicho líquido es:
2,12 LitrosStep-by-step explanation:
El volumen de un líquido puede obtenerse al tener tanto su densidad como su masa usando la siguiente fórmula:
Densidad = masa / volumenAl despejar volumen se obtiene:
Volumen = masa / densidadPor lo cual, si se reemplazara la fórmula quedaría:
Volumen = 7 Lb / 1.5 gr/cm^3Sin embargo, para operar, las unidades en las que se expresa la masa deben coincidir con las unidades de la densidad, por lo cual vamos a convertir las libras en gramos teniendo en cuenta el siguiente factor de conversión:
1 libra = 453,592 gramos
Entonces:
7 lb = 453,592 gr * 7 = 3175,144 gr
Ahora este valor reemplaza la masa en la fórmula y calculamos:
Volumen del líquido = 3175,144 gr / 1.5 gr/cm^3Volumen del líquido = 2116,762667 cm^3 (He utilizado todos los decimales para obtener el resultado exacto).A simple vista ya se tiene el volumen del líquido en cuestión, sin embargo, el ejercicio pide que sea expresado en litros, por lo cual vamos a convertir los centímetros cúbicos en litros teniendo en cuenta el siguiente factor de conversión:
1 litro = 1000 centímetros cúbicos.
Ahora podemos aplicar una regla de tres simple, si:
1000 cm^3 = 1 L2116,762667 cm^3 = xY operamos:
x = (2116,762667 cm^3 * 1 L) / 1000 cm^3x = 2,116762667 LO si quieres un valor aproximado:
x = 2,12 Litros.Entonces, la cantidad de litros teniendo en cuenta la densidad y la masa brindadas es 2,12 litros.
Answer ASAP PLEASE WILL MARK BRAINLIEST
Answer:
Answer should be A
Step-by-step explanation:
-7/2 divided by 49/4
Change in temperature per hour would be found by dividing the change in temperature by the amount of time.
Rewrite the numbers as improper fractions and the answer would be d.
-49/4 / 7/2
A student can get paid $12 per hour to run a three-hour economics tutoring session, or he can take a five-hour shift helping at his mom’s store that pays $15 per hour. What is the opportunity cost of working at the store? $12 $75 $36 $45 $60
Answer: C. $36
Step-by-step explanation:
Opportunity cost refers to the best economic alternative so in this case, it would be referring to the student tutoring for three hours. $12x3=$36
The weights of professional wrestlers are approximately normally distributed with a mean of 220 pounds and a standard deviation of 7 pounds. Using the normalcdf function on your graphing calculator, approximately what percent of wrestlers have weights less than 205 pounds?
Answer:
1.6%
Step-by-step explanation:
The cumulative distribution function (CDF) of a random variable X is denoted by F(x), and is defined as
F(x) = P(X ≤ x). where x is the largest possible value of X that is less than or equal to x
z = (x-μ)/σ,
where:
x is the raw score = 205
μ is the population mean, = 220 pounds
σ is the population standard deviation = 7 pounds
205 -220/7
z = -15/7
z = -2.1428571429
Using the normal cdf function on your graphing calculator,the cumulative distribution is
normalcdf( -2.1428571429, 100)
= 0.01606229
In percent form = 0.01606229 × 100
= 1.6%
Find the volume of a pyramid with a square base, where the perimeter of the base is
12.8 m and the height of the pyramid is 12.5 m. Round your answer to the nearest.
tenth of a cubic meter.
Answer:
42.7 cm ^2
Step-by-step explanation:
What is being constructed based on the markings in the following diagram?
-Inscribed regular hexagon
-Inscribed equilateral triangle
-Parallel lines
-Perpendicular lines
Parallel lines are being constructed based on the markings in the following diagram.
What are parallel lines?When two lines never meet each other even after extending them on the either side are called parallel lines.
What are the steps to draw parallel lines?1. First we have to draw a straight line and then any point of it draw any angle.
2. After that, on the second line take a point. Copy the first angle on it.
3. Draw the line to complete the copied angle and there you have parallel lines.
Hence, the construction indicated in the diagram is of parallel lines.
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Q1: Which pairs of expressions are equivalent (Choose all that apply.) *
14 - 9 and 14 + (-9)
18-6 and -18 + 6
-7-22 and 22-(-7)
3-30 and 3 + (-30)
10 - 5 and 5 - 10
Answer:
#'s 1 and 4
Step-by-step explanation:
1.) 14-9=5 and 14+(-9)=5
2.) 18-6=12 and -18+6=-12
3.) -7-22=-29 and 22-(-7)=29
4.) 3-30=-27 and 3+(-30)=-27
5.) 10-5=5 and 5-10=-5
The graph of f(x) shown below resembles the graph of g(x)=x^3, but it has been vertically stretched. Which of the following could be the equation of f(x)?
Answer: it’s b
Step-by-step explanation:
Solve for x by finding the missing side of the triangle. Round your answer to the nearest tenth.
Answer:
x≈14.28
Step-by-step explanation:
cos32° = 12/x
so : x= 12/cos32° = 12/0.84 = 14.28
I need helpppppppppppppo
Answer:
25%, -2x + 3
Step-by-step explanation:
8/24 = 1/4 =.25 = .25%
plug in numbers
PLEASE MARK ME BRAINIEST
WILL MARK BRAINLIEST! Identify and explain each example as Newton’s First, Second, or Third law of motion. I pull on the Earth because Earth pulls on me. Answer 1 Choose... The velocity of a falling object isn’t constant because Earth’s gravity exerts a force on it. Answer 2 Choose... If air resistance is ignored, the acceleration of a falling object is equal to the ratio of the force of gravity to mass. HELP PLZ!!!
Answer:
1.) Newton 3rd law
2.) Newton 1st law
3.) Newton 2nd law.
Step-by-step explanation:
1.) I pull on the Earth because Earth pulls on me. This can be identified as Newton 3rd law of motion. The law state that, in every action, there must be equal and opposite reaction.
As the earth pulls on you, the reaction to that action which is equal and opposite is you pulling back on earth.
2.) The velocity of a falling object isn’t constant because Earth’s gravity exerts a force on it. This can be identified by Newton 1st law of motion which state that: an object will continue to be at rest or in a linear motion except an external force act on it.
The velocity of a falling object suppose to be constant if there is no external force. But it isn’t constant because Earth’s gravity exerts a force on it.
3.) If air resistance is ignored, the acceleration of a falling object is equal to the ratio of the force of gravity to mass. This can be identified by Newton 2nd law of motion which state that: The rate of change in momentum is proportional to the applied force. Or
F = ma
Where F = applied force
M = mass of the object
a = acceleration
If air resistance is ignored,
F = mg
where g = acceleration due to gravity.
Answer:
1. Newton 3rd law
2. Newton 1st law
3. Newton 2nd law.
Step-by-step explanation:
Justin is ordering an ice cream dessert. He must order a size, a flavor of ice cream, and a topping. There are 2 sizes, 2 flavors, and 2 toppings to choose from. How many different ice cream desserts could he order?
Answer:
8
Step-by-step explanation:
because thats the answer
Answer:
It is going to be 8
Step-by-step explanation:
usign a tree diagram
orin simple
2 *2*2 is 8
In a cookie-eating contest, Luke ate 8 cookies in 1 minute and 30 seconds. At this rate, how many cookies will he eat in 3 minutes and 45 seconds?
Answer:
20 cookies
Step-by-step explanation:
Change from minutes and seconds to seconds
1 minute 30 seconds = 90 seconds
3 minutes 45 seconds = 3 *60 +45 = 180+45 = 225 seconds
Now we can use ratios to solve
8 cookies x cookies
------------- = -----------------
90 seconds 225 seconds
Using cross products
8 * 225 = 90x
Divide each side by 90
1800/90 = 90x/90
20 =x
which statement is not always true for a parallelogram PLZ HELP QUICK
A consecutive angles are congruent, B opposite angles are congruent, C diagonals bisect each other, D opposite sides are congruent
Answer:
I think option a is correct answer because consecutive angles are supplementary.
Answer:
The correct answer is A
Step-by-step explanation:
PLEASE SOLVE! FIST CORRECT ANSWER GETS BRAINLIEST! Simplify using the distributive property: -0.1·(100a+10b-c)
Answer:
-10a - b + 0.1c
Step-by-step explanation:
We can distribute the -0.1 to 100a, 10b and -c.
-10a - b + 0.1c
That's all!
Hope this helps
Answer: -10a - b + 0.1c
Step-by-step explanation:
simplify 0.1 * 10b * -c
10a - b - 0.1 * -c
regroup terms.
-10a - b - ( - 0.1 * c )
remove parentheses
-10a - b + 0.1 * c
Help me pllzzzzzzz help help
Answer:
0.75
Step-by-step explanation:
Out of the 8 tiles, 6 of them are not a blue A so the chance of not drawing a blue A is 6/8 = 0.75.
Answer: 3/4
Step-by-step explanation:
There are 8 choices, 2 of which are blue A's. Thus, 6 out of the eight options are NOT blue A's. Therefore, you have a 6/8, or 3/4 chance of not drawing a blue A.
Hope it helps <3
(-3ab - 8a + 8) - (-5ab +2)
Answer:
2ab - 8a + 6
Step-by-step explanation:
(-3ab - 8a + 8) - (-5ab +2)
(-3ab - 8a + 8) -1(-5ab +2)
Distribute -1 to the brackets.
(-3ab - 8a + 8) + 5ab - 2
Remove the brackets.
-3ab - 8a + 8 + 5ab - 2
Rearrange.
5ab - 3ab - 8a + 8 - 2
Combine like terms.
2ab - 8a + 6
Find the value of x and simplify completely. Just answer needed , not explanation
Answer:
x=(27)^2+y^2
=√729+y^2( root of 729+y^2)
= 27+√y^2
Answer:
x=9√10solution,
[tex] {y}^{2} = 3 \times 27 \\ {y}^{2} = 81 \\ y = \sqrt{81} \\ y = \sqrt{ {9}^{2} } \\ y = 9 \\ \\ {y}^{2} + {27}^{2} = {x}^{2} \\ or \: {9}^{2} + {27}^{2} = {x}^{2} \\ or \: 81 + 729 = {x}^{2} \\ or \: 810 = {x}^{2} \\ or \: x = \sqrt{810} \\x = 9 \sqrt{10} [/tex]
hope this helps...
Good luck on your assignment..
Last week Fred had 47 dollars. He washed cars over the weekend and
now has 50 dollars. How much money did he make washing cars?
Answer:
fred made 3 dollars
Step-by-step explanation:
47+3=50
The table shows the distances and times between stops on a trolley line. Between which two stops did the trolley go
the slowest?
Stops
From Stop A to Stop B
From Stop B to Stop C
From Stop C to Stop D
From Stop D to Stop E
Data for a Trolley
Distance
150 meters
200 meters
360 meters
280 meters
Time
50 seconds
50 seconds
60 seconds
40 seconds
Stop A and Stop B
Stop B and Stop C
Stop C and Stop D
Stop D and Stop E
Answer:
Stop A and Stop B
Step-by-step explanation:
Data for a Trolley
Stops Distance Time
From Stop A to Stop B 150 meters 50 seconds
From Stop B to Stop C 200 meters 50 seconds
From Stop C to Stop D 360 meters 60 seconds
From Stop D to Stop E 280 meters 40 seconds
From definition: speed = distance/time
Speed From Stop A to Stop B : 150/50 = 3 m/sSpeed From Stop B to Stop C : 200/50 = 4 m/sSpeed From Stop C to Stop D : 360/60 = 6 m/sSpeed From Stop D to Stop E : 280/40 = 7 m/s1) sqrt x^+6x+9 if x≥3
2) sqrt x^2+6x+9 if −3≤x<3
3) sqrt x^2−6x+9 if x<−3
will give brainliest
Answer:
Step-by-step explanation:
first one:
[tex]x^{2}+6x+9={(x+3)}^{2} \\\sqrt{{(x+3)}^{2} }=x+3[/tex]
second one:
[tex]x^{2}+6x+9=(x+3)^{2} \\\sqrt{(x+3)^{2} } = x+3[/tex]
third one:
[tex]x^{2} -6x+9=(x-3)^{2} \\\sqrt{(x-3)^{2} } =|x-3| \ \ (because \ x<-3)[/tex]
(-2,-11);slope=4 write the equation of the line
Answer: y = 4x-3
slope = 4, y intercept = -3
=================================================
m = 4 is the slope
[tex](x_1,y_1) = (-2,-11)[/tex] is the point the line goes through
Using point slope form, we can say,
[tex]y - y_1 = m(x - x_1)\\\\y - (-11) = 4(x - (-2))\\\\y + 11 = 4(x + 2)\\\\y + 11 = 4x + 8\\\\y + 11-11 = 4x + 8-11\\\\y = 4x - 3\\\\[/tex]
The equation is in slope intercept form y = mx+b
m = 4 = slope
b = -3 = y intercept
------------------------
As an alternative, you can use y = mx+b to get the same answer. We'll plug in m = 4 and (x,y) = (-2,-11) to solve for b
y = mx+b
-11 = 4(-2)+b
-11 = -8+b
-11+8 = -8+b+8
-3 = b
b = -3 we get the same y intercept value as above
------------------------
To check the answer, plug x = -2 into the equation. We should get y = -11
y = 4x-3
y = 4(-2)-3
y = -8-3
y = -11 we get the proper y value. The answer is confirmed.
Answer:
y = 4x-3
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b
The slope is 4
y = 4x+b
Substitute the point into the equation
-11 = 4(-2)+b
-11 = -8+b
Add 8 to each side
-11+8 = b
-3 = b
y = 4x-3
Which statement is the most appropriate comparison of the spreads?
Answer:
D The IQR for town A is less than the IQR for town B
Step-by-step explanation:
A small IQR indicates that the points are closer together, while a larger IQR means that the points are scattered and that the plot is skewed in a certain direction. As you can see, town A's plot looks fairly balanced, while town B's plot is skewing to the left. Hope this helps :)
a baker used three fourths lb flour for rolls , five eights for donuts, and two thirds for cookies. How many pounds of flour was used total
Answer:
2 1/24
Step-by-step explanation:
you first need to convert them to the same least common denominator
the common denominator is 24
so 18/24 plus 15/24 plus 16/24
which is 49/24 which is 2 1/24
hope this helps
−5+(−5r)+10 answer plz
Answer:
-5r + 5
Step-by-step explanation:
We simply simplify by adding like terms. Only thing we can combine are the constants -5 and 10, which we get 5. So then our answer is -5r + 5.
Answer:
5(1-r)
Simplified expression 5-5r
Step-by-step explanation:
Solve 2(x + 1) = 2x + 5.
Answer: No real solutions
Step-by-step explanation:
2(x-1) = 2x +5
Step 1: Distribute the 2 to the parenthesees
2x - 2 = 2x + 5
Step 2: Put the variables on one side and the constants on the other. (add/subtract)
0x = 7
Now, because 0 does not equal 7, there are no real solutions to this problem.
Which of the following shows the graph of y = 2 l n x On a coordinate plane, a curve starts at (0, negative 2) in quadrant 4 and then increases into quadrant 1 and approaches y = 3. On a coordinate plane, a curve starts in quadrant 4 and then curves up into quadrant 1 and approaches y = 5. It crosses the x-axis at (1, 0). On a coordinate plane, a curve approaches the y-axis in quadrant 2 and then increases into quadrant 1. It crosses the y-axis at (0, 1). On a coordinate plane, a curve approaches the y-axis in quadrant 2 and then increases into quadrant 1. It crosses the y-axis at (0, 2).
Answer:
The answer to this question can be defined as follows:
Step-by-step explanation:
Given:
[tex]f(x)= 2^{-x}=\frac{1}{2^x}[/tex]
In the above choices it is clearly defined from the above equation that output rises in the first quadrant, the value of f(x) tends to be zero and increases into another second quadrant. For x = 0, y, once again, has become 1, that is the function passes the y platform at (0,1). Therefore an exponential function reaches y = 0 in quadrant 1 on a coordinate plane and rises into quadrant 2. (0,1) stage is the temperature at which the y-axis intersects.The graph of y = 2ln(x) is (b) on a coordinate plane, a curve starts in quadrant 4 and then curves up into quadrant 1 and approaches y = 5. It crosses the x-axis at (1, 0).
How to determine the graph of the equation?The equation of the graph is given as:
[tex]y = 2\ln(x)[/tex]
Start by plotting the graph of [tex]y = 2\ln(x)[/tex] .
From the graph (see attachment), we have the following highlights
The curve of the graph starts at the 4th quadrantIt moves up to the 1st quadrantIt crosses the x-axis at x = 1, and it approaches y = 5From the list of given options, only option (b) describes the above highlights
Hence, the graph of y = 2ln(x) is (b)
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Express 3*(4*5) as a common fraction given a*b= ab/a+b .
Answer:3 ⋅ ( 4 ⋅ 5 ) = 23 a ⋅ b = a ( b a ) + b = a = 2
Step-by-step explanation:
The common fraction for the given expression is 60/47.
What is a fraction?A fraction represents part of a whole. When something is broken up into a number of parts, the fraction shows how many of those parts you have.
Given that an expression, 3*(4*5) such that, a*b= ab/a+b
Solving the expression as per the given formula,
4*5 = 4×5/(4+5) = 20/9
Now,
3*(4*5) can be written as, 3*20/9
Therefore,
3*20/9 = 3×20/9/(3+20/9)
= 20/3×9/47
= 60/47
Hence, the common fraction for the given expression is 60/47.
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Which of the following is the appropriate notation when calculating
conditional probabilities?
P(
AB)
A. P(
AB) =
P(A)
o
B. P(AUB) = P(A) + P(B) - P(AB)
C. P(AB) =
P(
AB)
P(B)
D. P(
AB) = PC
PCB+ P(B) - P(AUD)
SUBMIT
PREVIOUS
Answer: P(AB) = 3/8
Step-by-step explanation:
You simply multiply P(AuB) by P(B)
3/7 * 7/8 = 3/8