The evaluation of the given functions are as follows;
B. 2•x - 6C. 7C. -8A. 4•x + 4A. 5B. 27B. a² + 2•a•xA. 2•x + aC. x² + 5•x + 1B. 7A. (x + 2)/5(2/x) + 6The inverse of g(x) is f(x)How can the functions be evaluated?1. f(x) = 3 - x
g(x) = -2•x
Therefore;
g(fx) = -2 × f(x)
Which gives;
-2 × (3 - x) = -6 + 2•x = 2•x - 6
g(fx) = 2•x - 6
B. 2•x - 6
2. f(x) = 3 - x
g(x) = -2•x
f(g(x)) = 3 - (-2•x) = 3 + 2•x
f(g(x)) = 3 + 2•x
f(g(2)) = 3 + 2×2 = 7
The correct option is therefore;
C. 7
3. f(x) = 3 - x
g(x) = -2•x
Therefore;
g(fx) = 2•x - 6
g(f-1) = 2×(-1) - 6 = -8
C. -8
4. F(x) = 2•x - 1, G(x) = 3•x + 2, H(x) = x²
F(G(x)) = 2•(3•x + 2) - 1 = 6•x + 3
F(G(x)) - F(x) = 6•x + 3 - (2•x - 1) = 4•x + 4
A. 4•x + 4
5. F(x) = 2•x - 1, G(x) = 3•x + 2, H(x) = x²
G(H(x)) = 3•x² + 2
G(H(1)) = 3×1² + 2 = 5
A. 5
6. F(x) = 2•x - 1, G(x) = 3•x + 2, H(x) = x²
F(G(H(x))) = 2•(3•x² + 2) - 1 = 6•x² + 3
F(G(H(2))) = 6×2² + 3 = 27
B. 27
7. F(x) = 2•x - 1, G(x) = 3•x + 2, H(x) = x²
H(x + a) - H(x) = (x + a)² - x² = 2•a•x + a²
B. a² + 2•a•x
8. (H(x + a) - H(x))/a = (a² + 2•a•x)/a
(a² + 2•a•x)/a = a + 2•x = 2•x + a
A. 2•x + a
9. F(x) = 2•x - 1, G(x) = 3•x + 2, H(x) = x²
F(x) + G(x) + H(x) = 2•x - 1 + 3•x + 2 + x² = x² + 5•x + 1
C. x² + 5•x + 1
10. f(x) = 2•x² - 3•x + 1
f(3) - f(2) = 2×3² - 3×3 + 1 - (2×2² - 3×2 + 1) = 7
B. 7
11. G(x) = 5•x - 2
G^(-1)(x) = (G(x) + 2)/5
Which gives;
G^(-1)(x) = (x + 2)/5
A. (x + 2)/5
12. f(x) = 2/(x - 6)
The inverse is therefore;
(2/f(x)) + 6
The inverse of f(x) is therefore;
(2/x) + 6
13. g(x) = (5•x - 5)/4
(4•g(x) + 5)/5 = (4/5)•g(x) + 1
The inverse of g(x) is therefore;
(4/5)•x + 1 = f(x)
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can someone please help
Answer: a) 4
Step-by-step explanation:
sides should be equal according to the shape.
7x-2=12x-22
Why is the GCF of two prime numbers always one
Answer:
Step-by-step explanation:
A prime number has only two factors (1 and itself). Hence, two prime numbers cannot have any common factor other than 1. Therefore, the greatest common factor of two prime numbers is always 1. For example, the greatest common factor of 5 and 7 is 1.
Nisha likes to make small rectangular paintings of cats. One of her paintings has an area of 33 cm² and a width of 7/1/2 cm. What is the height of this painting?
The height of this painting is 4 2/5 cm.
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
It is given that Nisha likes to make small rectangular paintings of cats. Also One of her paintings has an area of 33 cm² and a width of 7/1/2 cm.
The area of the rectangle = length × Width
Now substitute the values;
Area= L x W
33 cm² = L x 7/1/2 cm
33 divided by 7 1/2
L = 4 2/5
Therefore, the height of this painting is 4 2/5 cm.
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URGENTT PLS ANSWER!!!!!
Mt.Whitney is the highest peak in California at 14,949 feet. The city of El Centro, also in California, is 39 feet below sea level. What is the difference in elevation between in Mt. Whitney’s peak and city of El Centro?
Answer:
14988 feet
Step-by-step explanation:
To find the difference, subtract.
14949 - (-39)
= 14949 + 39
= 14988
Use "add the opposite" to change "minus a negative" to "plus a positive"
A cylinder has a height of 16 yards and a diameter of 14 yards. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth
Answer: it is 14526.72
what is finite sequence
Suppose points P,Q, and R are collinear, with point Q between points P and R . Describe a plan for a proof that the reflection of points P,Q, and R in a line preserves collinearity and betweenness of points.
The points P,Q, and R are collinear points is proved by the property that Congruent Figures' Corresponding Parts are Congruent.
What is meant by collinearity?Collinear points are those that are within the same straight line or on the same plane. In Euclidean geometry, two or more points on a line that are close to or the far from one another are referred to as collinear.
If three items are arranged in a straight line, the things are collinear.More astonishingly, the word collinear has been applied to straightened things, which means something is "in a row" or "in a line."As, per the given question, the description for the reflection of points P,Q, and R to form collinear points are described below.
Draw the points P,Q, and R so they are collinear, with Q between P and R. Connect P to P', Q to Q', as well as R to R' by reflecting P, Q, and R. Display the quadrilateral congruent that results. Congruent Figures' Corresponding Parts are Congruent.If two or more points lie on the same line, they are said to be collinear in geometry. As a result, collinear points are indeed the points that lie on the an one straight line.
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In Δ S Z U, U J=9, V I=3 , and Z T=18 . Find the length.
SJ
In Δ SZU, UJ = 9, VI = 3 , and ZT = 18 then the value of SJ = 6.
What is meant by centroid theorem?The triangle's centroid is the point where the three medians intersect. According to the centroid theorem, the centroid is 23 times the distance from each vertex to the midpoint of the opposite side.
The centroid has the unique property that the distance from a vertex to the centroid is twice that of the distance from the centroid to the midpoint of the side opposite that vertex for each median. In addition, the three medians of a triangle divide the triangle into six equal-area regions.
Given: In Δ SZU, UJ = 9, VI = 3 , and ZT = 18 .
Since ZV ≅ VU, Y is the midpoint of UZ and SV is a median of Δ ZSU. Similarly, points Y and T are also midpoints of SZ and SU, respectively, so YU and ZT are also medians. Therefore, point J is the centroid of
Δ ZSU and, according to the Centroid Theorem, SJ is 2/3 of SV.
SJ = 2/3 (SV)
= 2/3 (SJ + VJ)
simplifying the above equation, we get
(3SJ/2) - SJ = VJ
SJ/2 = 3
SJ = 6
Therefore, the value of SJ = 6.
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.2, .7, .65, 1.15, 1.1,__________
2
Answer: 1.6
Step-by-step explanation:
The pattern occurs for every 2 terms
.65-.2=
.65-.20=.45
1.1-.65=
1.10-.65=.45
1.15-.7=
1.15-.70=.45
?-1.15=.45
.45+1.15=?
?=1.60
?=1.6
You are playing a team card game where a team can get 0 points, 1 point, or 3 points for a hand. The probability of your team getting 1 point for a hand is 60 \% and of getting 3 points for a hand is 5 \% .
b. Design a simulation and estimate your team's average value per hand.
The team's average value per hand is 0.76 and the simulation is shown in the figure.
Average Value:
Average means the ratio of the sum of all given observations to the total number of observations.
Given,
You are playing a team card game where a team can get 0 points, 1 point, or 3 points for a hand.
The probability of your team getting 1 point for a hand is 60% and of getting 3 points for a hand is 5% .
Here we need to design a simulation and estimate your team's average value per hand.
When we use a random number generator to generate integers
1 through 20, where
1–7 represents 0 points,
8–19 represents 1 point, and
20 represents 3 points.
Do 50 trials and record the results in a frequency table.
The table looks like, the following.
Based on the frequency table, The average value is the sum of the product of each point value and its corresponding frequency is calculated as,
=> average = (0 x 16/50) + (1 x 32/50) + (3 x 2/50)
=> average = 0 + 32/50 + 6/50
=> average = 38/50
Which is approximately equal to,
=> average ≈ 0.76
Therefore, team's average value per hand is 0.76
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Find the length of the third side. If necessary, write in simplest radical form. 6 and 6
The length of the third side will be equal to 5.2 units.
What is the Pythagorean theorem?According to the Pythagorean Theorem, the hypotenuse square in a right-angled triangle equals the square of the sum of the other two sides.
This statement states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
This is a right-angled triangle which means that the missing length can be solved using the Pythagorean theorem:
c² = a² + b²
Where c is the hypotenuse, a and b are the other sides.
c = 6
a = 3
b =?
6² = 3² + b²
36 = 9 + b²
b² = 27
b = √27
b = 5.2 units
Therefore, the length of the third side will be equal to 5.2 units.
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Determine the probability of following event, rolling a pair of dice and not getting a 3
According to the question, the probability of the event in which rolling a pair of dice and not getting a 3 is as follows:
What is Probability?
The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.
Probability of not getting 3= 1 - P(getting three)/Total number of events
Probability of not getting 3=1-2/36 = 1-1.18 =17/18
Hence, the probability of not getting three while rolling a pair of dice is 17/18 .
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35000/500
How to do this
Use grouping symbols (parentheses) to make 9 + 3-2 +4 equal 6. Which expression below is true?
O9+(3-2) + 4 = 6
O9+3-(2 + 4) = 6
O (9+3)-2+4=6
O (9+3-2) + 4 = 6
Answer:
the second answer
Step-by-step explanation:
because 19+3 is equal to 12, therefore we substrate by the number we got from 4+2 which is 6, so it will be 12-6 which is equal to 6 ,
write integer for - 2 Feet taller
The integer value of the mathematical statement is -2
How to determine the integer value?The mathematical statement is given as:
- 2 Feet taller
- 2 Feet taller implies that we have a negative integer -2
i.e.
Value = -2
Hence, the integer value of the mathematical statement is -2
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Paula is scuba diving. Her elevation changes by -374 m in 4.5 min. What rational number represents the average change in Paula's elevation each minute? Show your work.
Kelly’s car travels 26 1/4 miles on 5/8 gallon of gas how much Can the car go per gallon
42 miles kelly's car can go if 1 gallon of gas is used .
WHAT IS UNITARY METHOD ?Using the unitary approach, you can solve problems by first figuring out the value of a single unit, then multiplying that value by the number of units you need.
CALCULATIONtotal miles travelled = 26 1/4 miles = 26.25 miles
gas used = 5/8 = 0.625 gallon
distance car can travel in 1 gallon = 26.25 / 0.625
= 42 miles
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22. The mass of Mercury is about
3.3 x 1023 kg. The mass of Jupiter is
about 1.9 x 10²7 kg. About how many
times the mass of Mercury is the mass
of Jupiter?
The mass of the planet Mercury is 1.74 × 10⁻⁴ kg time the mass of the planet Jupiter.
Mass of Mercury = 3.3 × 10²³ kg
Mass of Jupiter = 1.9 × 10²⁷ kg
We need to find that how many times the mass of Mercury is the mass
of Jupiter.
For this, we will divide the mass of mercury with the mass of Jupiter.
So, we get that:
= ( 3.3 × 10²³ kg ) ÷ ( 1.9 × 10²⁷ kg )
Solving the expression by using the properties of exponents, we get that:
= 1.74 × 10⁻⁴ kg.
Therefore, we get that, the mass of the planet Mercury is 1.74 × 10⁻⁴ kg time the mass of the planet Jupiter.
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Please help will give brainliest
A news reporter in a city with several carbon-emitting power plants wanted to see whether local temperatures matched trends in global climate change. She
focused on the four coldest months of the year.
The table shows local temperature data from November through February for the two consecutive cold seasons checked by the reporter.
Average Monthly Temperatures (°F)
2011-2012:
November 61 1
December 51 9
January 53.6
February 56.5
2012-2013:
Nov: 64.2
Dec:56 8
Jan;48.3
Feb: 55.1
How did the mean temperature change between the two cold seasons?
You may use the calculator.
OA.
went down by 1.40
OB.
went up by 0.3°
OC.
went up by 0.9°
OD.
went up by 3.70
The mean temperature change between the two cold seasons is (b) went up by 0.3°
How to compare the mean values of both seasons?The given parameters are:
2011-2012:
November 61 1December 51 9January 53.6February 56.52012-2013:
Nov: 64.2Dec:56 8Jan;48.3Feb: 55.1The mean is calculated as
Mean = Sum/Count
So, we have
2011 - 2012 mean = (61.1 + 51.9 + 53.6 + 56.5)/4
Evaluate
2011 - 2012 mean = 55.8
Also, we have
2012 - 2013 mean = (64.2 + 56.8 + 48.3 + 55.1)/4
Evaluate
2012 - 2013 mean = 56.1
The difference in these mean values are
Difference = 56.1 - 55.8
Evaluate
Difference = 0.3
Hence, the mean temperature change between the two cold seasons is (b) went up by 0.3°
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there are three age groups in a competition.
john wants to do a survey of the competitors.
he uses a stratified sample of exactly 50 competitors according to each age group.
work out the number of competitors in each age group that should be in his stratified sample of 50
There are 10 people in the 16-18 group , 22 people in the 19-24 group and 18 people who are 25+ in the stratified sample.
A method of sampling from a population that can be divided into subpopulations is known as stratified sampling in statistics. When subpopulations within a larger population differ in statistical surveys, it may be desirable to sample each subpopulation separately.
From the given table we can calculate the total of population:
population = 120 + 250 + 200 = 570 people
Now since it is a stratified sample, the ratio of each age group is equal in the sample as in the population.
∴Number of people in the 16-18 group :
[tex]=\frac{120}{570} \times 50\\\\=10.52[/tex]
∴Number of people in the 19-24 group :
[tex]=\frac{250}{570} \times 50\\\\=21.929[/tex]
∴Number of people in the 19-24 group :
[tex]=\frac{200}{570} \times 50\\\\=17.543[/tex]
Now as 10.52 is closer to 10 than 17.54 is closer to 17 , we will round off 10.52 to 10.
Hence there are 10 people in the 16-18 group , 22 people in the 19-24 group and 18 people who are 25+ in the stratified sample.
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Which angles are congruent to each other
Answer:
∠9 and ∠11
Step-by-step explanation:
Vertical angles are congruent, and angles 9 and 11 are vertical.
Find the H.C.F:
a^3+b^3, a^4+a^2.b^2+b^4, a^4-a^2b+ab^2
Answer:
54 sqrt Mr multiple question is whether you are a man or a boy are you ok
determine whether the following graph represents a function
1. Not a function
2. Function, but one to one
3. One to One function
How to simplify arational algebraic expressions
Answer:
To simplify any rational expressions, we apply the following steps:
Factorize both the denominator and numerator of the rational expression. Remember to write each expression in standard form.
Reduce the expression by cancelling out common factors in the numerator and denominator
Rewrite the remaining factors in the numerator and denominator.
Step-by-step explanation:
Example:
Simplify: (x^{2} + 5x + 4) (x + 5)/(x^{2} – 1)
Solution:
Factoring the numerator and denominator to get;
⟹ (x + 1) (x + 4) (x + 5)/(x + 1) (x – 1)
Now cancel the common terms.
⟹ (x + 4) (x + 5)/(x – 1)
13
(4 x 200 ) + (4 x
) + ( 4 × 3 )
x
Answer: 52x^200 + 4x+4x^4
Step-by-step explanation:
At this rate how long would it take for you heart to beat 700,000 times? express your answer in days . now express your answer in days , hours, minutes, & seconds. (example:2 days , 4 hours 21 minutes, 15seconds)
Based on the rate illustrated, the time that it would take for you heart to beat 700,000 times is 8.10 days.
How to calculate the value?It should be noted that the heart beats 86400 tines on a day.
Therefore, when the heart beats 700,000 times, the number of days will be:
Number of times / Number of times the heart beats in a day
= 700000 / 86400
= 8.10 days
Therefore, the time that it would take for your heart to beat 700,000 times is 8.10 days.
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a light flashes every 2 minute, a second light flashes every 3.5 minutes, and a third light flashes every 4 minutes. if all three light flashes together at 8pm whis is the next time of the day they will flash together
You must determine the least common multiple of the three in order to respond to this. 8:28 pm will be the moment when all three lights flash simultaneously next.
Wat is the LCM of 2, 3.5, and 4 in whole numbers?Work with 3.5 now:
3.5 * 1 Equals 3.5 (no, 2 and 4 don't split into 3.5 in an equal manner)
3.5 * 2 = 7 (no, same excuse)
3.5 * 3 = 10.5 (nope) (nope)
3.5 * 4 = 14 (nope) (nope)
3.5 * 5 = 17.5 (nope) (nope)
3.5 * 6 = 21 (nope) (nope)
3.5 * 7 = 24.5 (nope) (nope)
3.5 * 8 = 28 (yes, as 2 and 4 are factors of 28) (yep, since 2 and 4 are factors of 28)
Therefore, 8:28 pm will be the moment when all three lights flash simultaneously next.
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Please help !
- 20 POINTS
Answer:
184
Step-by-step explanation:
My mom is a teacher lol
Find the first differences for each data set, and write an equation to represent the data pattern
The first differences for each data set is 120 120 120 120 120 120, and the equation to represent the data pattern is y = 120
How to find the first differences for each data set, and write an equation to represent the data pattern?The table of values represents the given parameters
On the table of values, we have the following function range
60 180 300 420 540 660 780
Calculate the first differences for each data set
i.e. Difference = Tn - T(n-1) Where n > 1
So, we have
120 120 120 120 120 120
The numbers in the above pattern are the same
So, the equation can be represented as
y = 120
Hence, the first differences for each data set is 120 120 120 120 120 120, and the equation to represent the data pattern is y = 120
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m∠UVX = 76 and m∠XVW = 64, what is the measure of m∠UVW
Based on the angles addition postulate, m∠UVW = 140°.
What is the Angles Addition Postulate?The angles addition postulate says that two smaller angles that is composite of a larger angle can be added together to give the measure of the larger angle.
Based on the angle addition postulate, the following equation that can be used to solve the problem given is derived below:
measure of angle XVW + measure of angle UVX = measure of angle UVW
Given the following:
measure of angle UVX = 76°
measure of angle XVW = 64°
Thus, using the above equation, we have:
64 + 76 = measure of angle UVW
140 = measure of angle UVW
measure of angle UVW = 140°
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the mean is 9.12 and the standard deviation is .05. what percent of the bags weigh less than 9.07?
Answer:
5.1
Step-by-step explanation:
yup i hate math.
