Answer:
20%
Step-by-step explanation:
You do 3 divided by 15 which is 0.2, or 20 percent.
When 2x^2/y=w+2/4 is solved for w, one equation is w =8x^2/7 -2 Which of the following is an equivalent equation to find w?
w = StartFraction 8 x squared + 2 y Over y EndFraction
w = StartFraction 8 x squared minus 2 y Over y EndFraction
w = 8 x squared minus 3 y
w = 8 x squared minus y
Step-by-step explanation:
To solve an equation for a variable, you can isolate the variable by performing operations that eliminate all other terms.
In this case, the given equation is 2x^2/y = w + 2/4. To solve for w, you can first eliminate the 2/4 term on the right-hand side by multiplying both sides of the equation by 4/2:
4 * (2x^2/y) = 4 * (w + 2/4)
4 * 2x^2/y = 4w + 4 * 2/4
8x^2/y = 4w + 2
Then, you can subtract 2 from both sides to eliminate the 2 on the right-hand side:
8x^2/y - 2 = 4w + 2 - 2
8x^2/y - 2 = 4w
Finally, you can divide both sides of the equation by 4 to eliminate the 4 on the right-hand side:
(8x^2/y - 2) / 4 = (4w) / 4
w = 8x^2/7 - 2
Therefore, the correct answer is w = 8 x squared minus 2 y Over y. This is an equivalent equation to find w, as it gives the same value for w as the original equation when the same values are used for x and y.
The other equations given are not equivalent to the original equation for finding w.
A circular cake has radius 12 cm and height 7 cm. The uniform cross-section of a slice of the cake is a sector with angle 22°. The top and the curved surface of the slice, shaded in the diagram, are covered with chocolate. Calculate the area of the slice which is covered with chocolate.
Therefore, the given area of the slice which is covered with chocolate = 276.57 c[tex]m^{2}[/tex]
What is area ?Area is a mathematical notion that describes the size of a region on a planar or curved surface. A surface area is the area of an open surface or the border of a three-dimensional object, whereas a plane region's or plane's area's refers to a shape's or planar lamina's area.
Here,
Given :
circular cake radius = 12 cm
circular cake height = 7 cm
thus,
the area of the slice which is covered with chocolate = θ/360 *π[tex]r^{2}[/tex]
=> 22/360 * 3.14 *12*12
=> 22/360 * 3.14 *144
=>69.08/360 * 144
=> 276.57 c[tex]m^{2}[/tex]
Therefore the given area of the slice which is covered with chocolate = 276.57 c[tex]m^{2}[/tex]
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Two beetles sit at the top edge of a house roof. The roof has two faces. The first face is such that the horizontal shift by 3cm along this face means 2cm shift vertically. Simultaneously, the beetles start moving downwards, the first beetle by the first face, the second - by the second face of the roof. First beetle moves twice as fast as the second beetle. Find the altitude of the first beetle above the second beetle when they will be 72 cm apart horizontally, if the second face of the roof
has the same incline as the first face or is perpendicular to the base
Answer:
16
mark me brainliest
Step-by-step explanation:
Write the equation of the piecewise function whose graph is shown
Please help will give brainlist only if correct!
Answer:
C.
Step-by-step explanation:
Also what you picked
A four-sided figure with four-right angles
Answer:
Square and Rectangle
(4+ square root3x-2 (4+square root 13x-2)
How do you foil this?
The solution of the expression is ( 4 + √3 / x) ( 4 + √13 / x).
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The given expression is 4 + √(3x⁻²) and 4 + √(13⁻²). The expression will be solved as,
E = {[4 + √(3x⁻²)]} { {4 + √(13x⁻²).]}
E = {4 + [√3 / √x²] { [4 + √13 / √x²]}
E = ( 4 + √3 / x) ( 4 + √13 / x).
Therefore, the solution of the expression is ( 4 + √3 / x) ( 4 + √13 / x).
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During a mathematics test, 18 students answered question 1 correctly, 23 students answered question 2 correctly, 8 students got them both correct and 11 students answered incorrectly on both questions. How many students took the test?(A) 41 (B) 44 (C) 49 (D) 52 (E) 60
Answer:
(D) 52
Step-by-step explanation:
sum up correct answers from questions 1, 2 and both 1 and 2 incorrect this time therefore we have --> 18+23+11=52 students
You could also do a Venn diagram to understand this better with 8 being the intersection of students who goth both 1 and 2 correct and 11 being left out as the number of students who got both questions incorrectly.
The diagram below shows a cylinder with diameter 6 cm and height 20 cm. The
Volume, in cm³, of the cylinder is
-6 cm
20 cm
The volume of the cylinder is 180π cm³.
What is volume ?
Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
Volume is a measurement of three-dimensional space that is occupied. Numerous imperial or US customary units, as well as SI-derived units (such the cubic meter and liter), are frequently used to quantify it numerically (such as the gallon, quart, cubic inch). Volume and length (cubed) have a symbiotic relationship.
As diameter = 6cm
We know that radius is half of diameter
∴ radius = 3 cm
height = 20 cm
Volume = π r² h
= π (3)²×20
= π × 9 × 20
= 180 π cm³
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The table shows the transportation method of employees at a certain company. What percent of the employees walk to work?
A. 0.5 %
B. 1 %
C. 5 %
D. 7 %
We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100. 0.5% of employees walk to work.
What percent of the employees walk to work?A % is a quantity or ratio that, in mathematics, represents a portion of one hundred.
A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.
The symbol "%" is frequently written after the number to indicate percentages.
We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.
Given,Employees who use;
Car: 758
Bus: 530
Walk: 7
Other: 105
Total = 758+530+7+105 = 1400
Employees percentage who walk to work
=No of employees who walk /Total number*100
Percentage =700/1400 =0.5%
0.5% of employees walk to work.
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Is there a transformation that maps shape I onto shape IV? Explain your answer.
Yes, there is a transformation that maps shape I onto shape IV. If the figure I is reflected over the x-axis, we get figure IV.
What is a transformation in math?In mathematics, a transformation is a function or a mapping that takes a set of inputs and produces a new set of outputs.
Transformations can be applied to geometric shapes, functions, and other mathematical objects to change their properties or positions.
There are various types of transformations that can be performed in mathematics, including translation, rotation, reflection, dilation, and more. Each type of transformation has its own specific rules and properties that dictate how it affects the original object.
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Full Question:
See the attached Image
How many miles are in 54.74 kilometers? Round to the nearest whole
number, if necessary.
Answer:
To convert kilometers to miles, you can use the conversion factor that 1 kilometer is equal to 0.621371 miles.
So to convert 54.74 kilometers to miles, you can multiply 54.74 by 0.621371:
54.74 kilometers * 0.621371 miles/kilometer = 34.09 miles
Rounded to the nearest whole number, this is 34 miles.
Step-by-step explanation:
Answer:
To convert kilometers to miles, you can use the conversion factor that 1 kilometer is equal to 0.621371 miles. To convert 54.74 kilometers to miles, you can multiply the number of kilometers by the conversion factor:
[tex]54.74 kilometers * 0.621371 miles/kilometer = 34.08 miles[/tex]
Rounded to the nearest whole number, there are approximately 34 miles in 54.74 kilometers.
Step-by-step explanation:
FILL IN THE BLANK alona is examining the impact of the 2011 penn state scandal on student morale and school spirit by distributing number-scaled surveys in her introduction to sociology class. alona is employing a______research method.
Alona is using a quantitative approach to her studies.
What is Quantitative research?The goal of quantitative research is to quantify the data collection and processing process.
It is based on a deductive method that emphasizes the validation of the hypothesis and is influenced by positivist and empiricist theories.
This research technique, which is related to the natural, applied, formal, and social sciences, encourages the unbiased empirical exploration of observable phenomena to test and comprehend correlations.
This is accomplished using a variety of quantification techniques and procedures, demonstrating the wide application of this approach as a research strategy across numerous academic fields.
So, in the given situation, Alona is using the quantitative research method.
Therefore, Alona is using a quantitative approach to her studies.
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Circles P and Q are externally tangent to each other and have radii 18 meters
and 32 meters, respectively. As shown, circles P and Q are externally tangent
to a line segment at points X and Y, respectively. What is XY?
Answer:
48 m
Step-by-step explanation:
You want to know the distance XY between tangent points on a segment tangent to two circles that are externally tangent to each other. The circles have radii 18 m and 32 m.
Pythagorean theoremAs shown in the attachment, a segment parallel to XY joining segments PX and QY can form a right triangle whose hypotenuse is the sum of the radii, and whose short leg is the difference of the two radii. The length of XY is the unknown leg of the right triangle, and can be found using the Pythagorean theorem.
a² +b² = c²
14² +b² = 50²
b² = 50² -14² = 2304
b = √2304 = 48
The length of XY is 48 meters.
__
Additional comment
In this geometry, the length XY is twice the geometric mean of the two radii. XY = 2√(18·32) = 48.
Jerry flew a total of 4,320 miles over 3 months.
• He flew 6 flights each month.
• He flew the same distance each flight.
How many miles was each of Jerry’s flights?
The number of miles was each of Jerry’s flights travel is 240 miles.
Explain distance in miles.A mile is characterized as the unit of length, which is precisely equivalent to 5280 feet, or 1760 yards, and normalized as precisely 1609.344 meters by the Peaceful accord in 1959. The biggest unit is generally used to quantify the distance between places that are not even close to one another.
According to question:Jerry flew 6 flights each month.
Total flights in 3 months = 3(6) = 18 flights
Let distance traveled in each flight be x
Then,
18x = 4320 miles
x = 4320/18
x = 240 miles
Thus, each flight flow 240 miles.
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Russell is going to hire a makeup artist for a fashion show and is comparing prices. Martha charges $10 as a booking fee and an additional $40 per hour. Jackie charges $35 per hour, plus a booking fee of $20. Depending on the length of the show, the cost could end up being the same for either artist. Write the system of equations for this scenario and define the variables.
After solving the equation, the number of hours obtained is that after 2 hours, the cost ends up being the same for either artist.
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the given information in the question,
Booking fee of Martha = $10
Additional hourly charge of Martha = $40
Then, the equation will be,
y = $10 + $40x (i)
Here, y is the total cost and x is the number of hours.
Booking fee of Jackie = $20
Additional hourly charge of Jackie = $35
Then, the equation for this will be,
y = $20 + $35x (ii)
Here, y is the total cost and x is the number of hours.
Then, depending on the length of the show, the cost could end up being the same for either artist.
So,
From equations (i) and (ii)
$20 + $35x = $10 + $40x
20 - 10 = 40x - 35x
5x = 10
x = 2 hours
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What fraction is equal to 75% of 1/2
Answer:
3/8
Step-by-step explanation:
75% of 1/2
3/4 of 1/2
3/4x1/2
3/8
People at an airport can pass through security on one of two levels: level A or level B. Suppose that, on average, it takes people
22
2222 minutes to pass through security on level A with a standard deviation of
7
77 minutes. On level B, the mean and standard deviation are
20
2020 and
6
66 minutes, respectively.
Every day, the airport looks at an SRS of
100
100100 people who use level A, and an independent SRS of
150
150150 people who use level B. They calculate the mean time for each sample, then look at the difference
(
A
−
B
)
(A−B)left parenthesis, start text, A, end text, minus, start text, B, end text, right parenthesis between the sample means.
What are the mean and standard deviation (in minutes) of the sampling distribution of the difference in sample means?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
μ
x
ˉ
A
−
x
ˉ
B
=
2
σ
x
ˉ
A
−
x
ˉ
B
=
7
2
+
6
2
250
μ
x
ˉ
A
−
x
ˉ
B
σ
x
ˉ
A
−
x
ˉ
B
=2
=
250
7
2
+6
2
(Choice B)
B
μ
x
ˉ
A
−
x
ˉ
B
=
2
σ
x
ˉ
A
−
x
ˉ
B
=
7
2
100
+
6
2
150
μ
x
ˉ
A
−
x
ˉ
B
σ
x
ˉ
A
−
x
ˉ
B
=2
=
100
7
2
+
150
6
2
(Choice C)
C
μ
x
ˉ
A
−
x
ˉ
B
=
21
σ
x
ˉ
A
−
x
ˉ
B
=
7
2
+
6
2
250
μ
x
ˉ
A
−
x
ˉ
B
σ
x
ˉ
A
−
x
ˉ
B
=21
=
250
7
2
+6
2
(Choice D)
D
μ
x
ˉ
A
−
x
ˉ
B
=
21
σ
x
ˉ
A
−
x
ˉ
B
=
7
2
100
+
6
2
150
μ
x
ˉ
A
−
x
ˉ
B
σ
x
ˉ
A
−
x
ˉ
B
=21
=
100
7
2
+
150
6
2
The mean and standard deviation (in ) of the sampling distribution of the difference in sample means [tex]\sigma_1[/tex] - [tex]\sigma_2[/tex] = (7)² ÷100+ 6² /150.
What is standard deviation?A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Given:
Level A:
S.D. = 7
Level B: Mean = 20
S.D. = 6
So, [tex]\nu_1[/tex] = 22
[tex]\nu_2[/tex] = 20
Then, [tex]\nu_1[/tex] - [tex]\nu_2[/tex] = 22-20=2
and, [tex]\sigma_1[/tex] - [tex]\sigma_2[/tex]
= (7)² ÷100+ 6² /150
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The data below are the temperatures on randomly chosen days during a summer class and the number of absences on those days: Temperature, x | 72 85 91 90 88 98 75 100 80 No. of absences, y | 3 7 10 10 8 15 4 15 5 a) Find the equation of the regression line for the data. b) Assuming that the variables x and y have a significant correlation, what is the predicted number of absences when the temperature is 91? c) Calculate the correlation coefficient. d) Calculate the standard error for the model.
The equation of the regression line is y=-30.27+0.449x and predicted number of absences when the temperature is 910= 10.589
See table for sum of values.
The regression equation is:
y=α+βx
β = [tex]\frac{Sxx}{Syy}[/tex]=6995-97799779[tex]\frac{6995-9\times\frac{779}{9}\times\frac{77}{9}}{68613-9(\frac{779}{9} )2}[/tex]= 0.449
α=y-βx= 779-(0.449)7799 = =-30.27
The equation is y=-30.27+0.449x
Where y = predicted variable; x = independent variable = 0.449; - 30.27 = intercept/ slope
Constructing a 91% prediction interval for y:
x = 910
Inputting x = 91 into the regression equation : y = 0.449(91) - 30.27
y = 40.859 - 30.27 = 10.589
Prediction interval = y pm error margin
To save computing time, error margin (E) can be obtained using the online error margin calculator.
Obtained error margin (E) value = 2.3398
(10.589- 2.3398, 10.589+ 2.3398)
(8.2492, 12.9288)
(8, 13)
The equation of the regression line is y=-30.27+0.449x and predicted number of absences when the temperature is 910= 10.589
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The question is in the image. Please go through the image.
The best answer will be marked brainliest.
I hope you will explain nicely and step wise.
Step-by-step explanation:
when defined like this, we remember that when the right-angled triangular is inscribed into a circle, sine of an angle is the length of the opposite side of the angle divided by the radius. while cosine of the same angle is the adjacent side divided by the radius.
so, sin(angle) = 12/13 makes us imagine a circle of radius 13, and the side (or leg) opposite of the angle is 12.
now, Pythagoras tells us
c² = a² + b²
c being the Hypotenuse (which is the radius in our scenario), a and b are the legs.
13² = 12² + second leg²
169 = 144 + second leg²
second leg² = 25
second leg = 5
so,
cos(theta) = 5/13
tan(theta) = sin(theta) / cos(theta) =
= 12/13 / 5/13 = (12×13)/(5×13) = 12/5
sin²(theta) + cos²(theta) = (12/13)² + (5/13)² =
= 144/169 + 25/169 =
= 169/169 = 1
sec²(theta) - tan²(theta) =
= (1/cos(theta))² - (12/5)² =
= (1 / 5/13)² - 144/25 = (13/5)² - 144/25 =
= 169/25 - 144/25 = 25/25 = 1
A drama club earns $1040 from a production. It sells a total of 64 adult tickets and 132 student tickets. An adult ticket costs twice as much as a student ticket.
a. Write a system of linear equations that represents this situation. Let x represent the cost of an adult ticket and y represent the cost of a student ticket.
System of equations: x=
x+
y=1040
Question 2
b. What is the cost of each ticket?
The cost of an adult ticket is $
.
The cost of a student ticket is $
.
The system of linear equations, that models the problem is represented as x = 2 and 64x + 132y = 1040 while the cost of adult and student tickets is $8 and $4 respectively.
System of Linear EquationThe system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1.
Let;
x = cost of adult tickety = cost of student ticketa)
x = 2y ...eq(i)
64x + 132y = 1040 ...eq(ii)
b)
From equation (i)
64(2y) + 132y = 1040
y = 4
Put y = 4 into equation (i)
x = 2(4)
x = 8
The cost of adult ticket is $8 and student ticket is $4
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how many shapes are drawn based on the code below? def drawshapes(centerx, centery, radius, points, color): star(centerx, centery, radius, points, fill
6 shapes can be drawn by the given code.
Describe shapes.Shapes in mathematics specify an object's boundaries or contour. Depending on their characteristics, the forms can be divided into many types. The shapes are typically enclosed by an outline or boundary that is composed of points, lines, curves, etc. Geometric figures and figures composed of fixed lines or curves are other names for forms. There are two types of shapes: closed shapes and open shapes. Examples of shapes in daily life are the Sun, Earth, Doors, Windows, Watches, Wall Clocks, and so forth.
Given
Codes are def draw shapes( centerx , centery, radius, points, color): star(centerx, centery, radius, points, fill.
6 shapes can be drawn by the given code.
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when the admission price for a conference is $400, 1000 people will attend. for each $5 reduction in price, an additional 20 peopel will attend. let x be the number of 5 dollar reductions. determine the number of people that will attend as a function of x.
Let y be the number of people that will attend the conference as a function of x. The given information tells us that when x = 0 (the admission price is $400), y = 1000. Additionally, for each $5 reduction in price, an additional 20 people will attend.
We can express this relationship as a function as follows:
y = 1000 + 20xThis function tells us that the number of people that will attend the conference is equal to 1000, plus an additional 20 people for each $5 reduction in price (represented by the variable x).
For example, if the admission price is reduced by $10 (x = 2), the number of people that will attend the conference is given by:
y = 1000 + 20(2)
y = 1000 + 40
y = 1040
So, if the admission price is reduced by $10, 1040 people will attend the conference.
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Use compatible numbers to determine if 455 + 229 455 + 229 is more than 650 650 . Drag the numbers to the table to show each compatible number. Numbers may be used once or not at all. Is it more than one answer for each box or just the one I already selected
The required compatible number of the given two number are 500 and 200 and sum is 700.
What is Compatible Numbers?In math, compatible numbers are the numbers that are not difficult to add, deduct, duplicate, or gap intellectually. compatible number are close in worth to the real numbers that make assessing the response and figuring issues more straightforward. We can adjust the numbers to the closest ten, hundred, thousand or 10,000 to make them viable numbers. For example, in the event that we need to add 493 and 549, we can make the numbers viable by gathering them together to the closest tens or hundreds. 490 and 550 (adjusted to the closest tens) or 500 and 500 (adjusted to the closest hundreds) are a lot simpler to settle.
According to question:So, the compatible number of 455 is 500 and that of 225 is 200.
Then,
Compatible sum = 500 + 200 = 700.
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HELP ASAP!! READ CAREFULLY
Answer:
not true:
3. AD = DC
4. YZ = XW
explanation:
lower base is only congruent to upper base.
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-NO LINKS!!
Find the binomial coefficient
( 11)
(6)
Evaluate using Pascal's Triangle
4_C_1
Answer:
462; 4------------------------------
The binomial coefficients can be found using Pascal's triangle.
Remember the rows are numbered starting from the second one on the top, and the first element is skipped in every row.
For the first one, follow the 11th row and 6th column, it is number 462, and for the second one follow the 4th row and 1st column, this is number 4, see the attached for both.
Calculation of the binomial coefficient is as follows:
[tex]\[ \binom{11}{6} = _{11}C_6=\cfrac{11!}{6!(11-6)!}=\cfrac{6!*11*10*9*8*7}{6!5!} =\cfrac{11*10*9*8*7}{5*4*3*2} =462[/tex][tex]\[ \binom{4}{1} = _4C_1=\cfrac{4!}{1!(4-1)!} =\cfrac{4!}{3!} =\cfrac{3!*4}{3!} =4[/tex]A large university with over 40,000 students recently took a survey in which 31% of the students claimed to exercise at least 3 times a week. A simple random sample of 250 students was selected. Let p hat = the proportion of students in the sample who claimed to work out at least 3 times a week. What is the standard deviation of the sampling distribution of p hat ? Enter your answer as a decimal rounded to the hundredths place. The standard deviation of the sampling distribution of p hat is
The shape of the sampling distribution of p hat is approximately Normal, because we would expect at least 10 success and 10 failures
What is meant by sampling distribution ?The probability distribution of a statistic that is acquired by repeated sampling of a particular population is called the sampling distribution. It outlines a variety of potential possibilities for a statistic, such as the mean or mode of a population's mean or mode of some variable.
approximately Normal, because we would expect at least 10 success and 10 failures. because they are dividing three times a week
A typical probability distribution in the natural world is the normal distribution, sometimes known as the bell curve. When the sample size is high enough, scientists often assume that a sequence of measurements obtained from a population would be regularly distributed.
The complete question is : A large university with over 40,000 students recently took a survey in which 31% of the students claimed to exercise at least 3 times a week. A simple random sample of 250 students was selected. Let p hat = the proportion of students in the sample who claimed to work out at least 3 times a week. What is the shape of the sampling distribution of p hat and why?
A. approximately Normal, because all sampling distributions are approximately Normal
B. approximately Normal, because we would expect at least 10 success and 10 failures
C. skewed to the right, because 0.31 is lower than 0.5
D. skewed to the left, because 0.31 is lower than 0.5
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Jessica earns 35 for 7 hours of babysitting she is saving to buy a 160 radio how many hours will Jessica have to buysit to have enough money to buy the radio
To have enough money to buy the radio, Jessica will have to babysit for 32 hours
How to determine the number of hours Jessica will have to babysit?From the question, we have the following parameters that can be used in our computation:
Earnings = $35 for 7 hours
This means that the hourly rate can be calculated as
Hourly rate = $35/7 hours
Using the above as a guide, we have the following:
Evaluate the quotients
Hourly rate = $5 per hour
The number of hours Jessica will have to babysit is calculated as
Number of hours = 160/Hourly rate
Substitute the known values in the above equation, so, we have the following representation
Number of hours = 160/5
Evaluate
Number of hours = 32
Hence, the number of hours is 32
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Sebastian has $600 saved for a trip.
He buys an airline ticket for $120 and reserves a hotel room for $55 each night for 4 nights. He wants to use the same amount of spending money each day. If his trip lasts for 5 days, how much mone can he spend each day?
Answer:
$52
Step-by-step explanation:
Sebastian spent $120 on the airline ticket and $55 * 4 = $<<55*4=220>>220 on the hotel.
So, he spent a total of $120 + $220 = $<<120+220=340>>340 on the airline ticket and hotel.
He has $600 - $340 = $<<600-340=260>>260 left to spend.
He plans to be on the trip for 5 days, so he can spend $260 / 5 = $<<260/5=52>>52 per day.
What is equivalent to 1:9
Answer:
2 : 18
Step-by-step explanation:
to find equivalent ratios , multiply or divide each part of the ratio by the same numeric value.
1 : 9 ( multiply both parts by 2 )
= 2 : 18
or
1 : 9 ( multiply both parts by 3 )
= 3 : 27
and so on...
NO LINKS!!
Use the properties of exponents to determine which functions (if any) are the same.
f(x)= 3^x + 11
g(x) = 2^(3x+5)
h(x)= 32(8^x)
a. f(x) = g(x)
b. f(x) = h(x)
c. g(x)=h(x)
d. All three functions are equal
e. None of the functions are equal
Answer:
c. g(x) = h(x)
Step-by-step explanation:
Given functions:
[tex]f(x) = 3^x+11[/tex]
[tex]g(x)=2^{3x+5}[/tex]
[tex]h(x)=32(8^x)[/tex]
Rewrite function g(x) using exponent rules.
[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c:[/tex]
[tex]\implies g(x)=2^{3x} \cdot 2^5[/tex]
[tex]\implies g(x)=2^{3x} \cdot 32[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]
[tex]\implies g(x)=(2^3)^{x} \cdot 32[/tex]
[tex]\implies g(x)=8^{x} \cdot 32[/tex]
[tex]\implies g(x)=32(8^{x})[/tex]
Therefore, g(x) = h(x).