[tex]f(x) = \log_b(x)[/tex] is a decreasing function when [tex]0 < b < 1[/tex]
This is because we can use the change of base formula to say
[tex]\log_b(x) = \frac{\log(x)}{\log(b)}[/tex]
If b is between 0 and 1, not including either endpoint, notice how the log(b) term is negative.
For example, if b = 0.5, then log(b) = log(0.5) = -0.301 approximately. I'm using log base 10 to get log(0.5) = -0.301
So for b = 0.5, we have,
[tex]\log_{0.5}(x) = \frac{\log(x)}{\log(0.5)} \approx \frac{\log(x)}{-0.301} \approx -3.322\log(x)[/tex]
The log(x) part on its own is always increasing. The negative coefficient out front flips it to always decreasing.
By applying the behavior rules we notice that the expression [tex]F(x) = \log_{b} x[/tex]decreasing function if the base of the logarithm is 0 < b < 1. (Correct choice: D) #SPJ5
How to define the behavior of a logarithmLogarithms are trascendent functions whose form is defined by the following expression:
[tex]\log _{b} x[/tex] such that [tex]x = b^{a}[/tex], where b > 0.
Where b is the base of the power.
Whose rules are described below:
The logarithm is an increasing function if its base is less than 1.The logarithm is a decreasing function if its base is greater than 1.By applying the behavior rules we notice that the expression [tex]F(x) = \log_{b} x[/tex] is a decreasing function if the base of the logarithm is 0 < b < 1. (Correct choice: D)
RemarkThe statement is poorly formatted and reports several mistakes. Correct form is shown below:
For what values of b will [tex]F(x) = \log_{b} x[/tex] be a decreasing function?
A. b > 0
B. 0
C. b < 0
D. 0 < b < 1
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Which Greek mathematician wrote the most definitive text on geometry, one that is still referred to today?
A.
Thales
B.
Pythagoras
C.
Euclid
D.
Archimedes
E.
Hippocrates
How would you find out how many sixth through eighth grade students are interested in joining a running club?
The question is incomplete. The complete question is :
How would you find out how many sixth through eighth grade students are interested in joining a running club? Explain how to choose a sample that will give you a good representation of a whole population.
Answer :
the sample should be random
Explanation :
We have to find the number of student from 6th through 8th grade students those who wanted to join a running club by choosing a sample of population. So in order to choose a sample which will provide a good representation for the whole population is that the sample must be a [tex]\text{random sample}[/tex] from [tex]\text{entire set of students }[/tex] and it should also include enough students to be reliable. The smaller samples have a more variation that lead to a lesser reliable inference.
Luca works at an appliance store. He recently sold 12 appliances, 6 of which were
dishwashers. What is the experimental probability that the next appliance Luca sells will be a
dishwasher?
Write your answer as a fraction or whole number.
Answer:
1/2
Step-by-step explanation:
Answer:
0.50
Step-by-step explanation:
6 out of the total 12 appliances sold were dishwashers, so the experimental probability that the next appliance sold will be a dishwasher is 6/12, or 1/2, or 0.50.
ABC is a triangle. AC = 9 cm, BC = 7 cm and angle BAC = 30°
Calculate the size of angle ABC.
9514 1404 393
Answer:
∠B = 40° or 140°
Step-by-step explanation:
The given angle is opposite the shortest of the given sides, so there are two possible solutions.
From the law of sines, ...
B = arcsin(b/a·sin(A)) = arcsin(9/7·sin(30°)) = arcsin(9/14)
Possible values for angle B are ...
B = arcsin(9/14) ≈ 40.0°
B = 180° -arcsin(9/14) ≈ 140.0°
Find angle C!!!!! See the image below! I need this answer fast
Answer:
55
Angle C is a inscribed angle of the of Arc Ba.
CA is the diameter so that means Arc BA equal 110 becuase
110+70=180.
Angle C is half of Arc BA so Angle C is
[tex]55[/tex]
Adam builds model rockets. Where he lives, his backyard is 12 feet below sea level. When he ignites his rocket, it flies a maximum of 350 feet straight up into the air before releasing its parachute. What is the altitude of Adam’s rocket at its highest point, as measured from sea level
Answer:
338 feet
Step-by-step explanation:
350 - 12 = 338
Sandy made an origami dog. What is the area of the parallelogram highlighted in the origami figure?
Answer:
the area = base × height = 2 × 3.32 = 6.64 ft²
Answer:
incorrect answer
Step-by-step explanation:
-78 + (-30)=
HINT = - + = -
Answer:
-108 is the answer to the question..
Answer:
-108
Step-by-step explanation:
Solve 7+7a=7(2-b) for b
Answer:
b = 1 - a
Step-by-step explanation:
Given
7 + 7a = 7(2 - b) ← divide both sides by 7
1 + a = 2 - b ( subtract 2 from both sides )
- 1 + a = - b ( multiply through by - 1 )
1 - a = b
Answer:
[tex]b = (a - 1)[/tex]
Step-by-step explanation:
Question[tex]7 + 7a = 7(2 - b)[/tex]
First Solve the brackets
[tex]7 + 7a = 7(2 - b) \\ 7 + 7a = 14 - 7b[/tex]
Then Make the b as the Subject
[tex]7 + 7a = 14 - 7b \\7 + 7a - 14 = 7b \\ 7a - 7 = 7b \\ 7(a - 1) = 7b \\ \frac{7(a - 1)}{7} = \frac{7b}{7} \\ a - 1 = b[/tex]
hope this helps you.
Have a nice day!
Does this graph show a function? Explain how you know.
Answer:
Option C, functions can only have one y-value at any given x-place
Cynthia has $2.15 worth of change in her pocket. She has three more nickels than quarters and twice as many dimes as quarters. How many of each type coin has she?
Answer:
7 nickles
8 dimes
4 quarters
Step-by-step explanation:
q
d = 2q
n = q+3
25q + 10d + 5n = 215
25q + 10(2q) + 5(q + 3) = 215
25q + 20q + 5q - 15 = 215
50q = 200
q = 4
d = 2q = 8
n = q + 3 = 7
Mustafa is flying his kite, and Ana is watching from 20 m away, as shown. From Ana's perspective there is an
angle of 109 between Mustafa and his kite. The length of the string between Mustafa and the kite is 46 m.
Kite
46 m
109
?
Mustafa
Ana
20 m
From Mustafa's perspective, what is the angle between Ana and the kite?
Do not round during your calculations. Round your final answer to the nearest degree.
Answer: From Mustafa's perspective, there is a 47\degree47°47, degree angle between Ana and the kite.
Step-by-step explanation: Khan Academy
Cam can't figure out what to eat. He is going to randomly select a piece of fruit from his pantry. There are 444 apples and 555 bananas in his pantry.
What is \text{P(select an apple})P(select an apple)start text, P, left parenthesis, s, e, l, e, c, t, space, a, n, space, a, p, p, l, e, end text, right parenthesis?
If necessary, round your answer to 222 decimal places.
Answer:
0.45
Step-by-step explanation:
no. of outcomes = 4+5 = 9
favourable outcomes = 4
P(an apple) = 4/9
= 0.4444... or 0.45
What is the solution to the system of equations graphed below? Pls Quick
The point (1,−1) satisfies the inequality 40x−22y≤50.
Không thảo mãn vì
44.1-22.(-1)=66
No, the point (1,-1) does not the satisfy the inequality 40x-22y<=50.
What is an inequality?
It is a type of equation in which greater than less than or equal to are used instead of only equal to.
How to solve an inequality?
To check whether whether a point satisfies an inequality or not we need to just put it in the inequality. So,
40x-22y<=50
40(1)-22(-1)=40+22=62
62 is not less than and not equal to 50. So it does not satisfies the inequality.
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Help pls!! this is a presentation I’m doing in class and I NEED this completed rn, ASAP!!! . What I need is just the answers for the picture below and I NEED the explanation to all of them, and if you can pls try to give a similar example to these and solve it or what did u use to solve it. (Only 1 example that is similar) Thank you so much!
Answer:
Step-by-step explanation:
∠ADC = 90°
∠ADB + ∠BDC = 90
20 + ∠BDC = 90
∠BDC = 90 - 20 = 70
∠BDC = 70°
16) ∠PSR = ∠PSQ +∠QSR
= 60 + 10
= 70
18) ∠PSR = 130
∠PSQ + ∠QSR = 130
90+ ∠QSR = 130
∠QSR = 130 - 90
∠QSR = 40
19)∠ADC = ∠ADB + ∠BDC
= 120 +20
= 140
20) ∠PSR = 125
15. 70° because a right angle is 90° and we have the angle of ADB which is 20°. So 90°-20°=70°.
16. 70° because angle PSQ is 60° and angle QSR is 10°. So 60°+10°=70°.
17. 55° because it says it in the explanation. I assume this is a typo and they meant to ask the measurement of ADC and in that case it would be 130° because angle ADB is 75° and angle BDC is 55°. 75°+55°=130°.
18. 40° because angle PSQ is a right angle which means it's 90°. So 130°-90°=40°.
19. 140° because angle ADB is 120° and angle BDC is 20° so 120°+20°=140°.
20. 125° because again it's in the explanation. But if it's a typo and they meant what is the measurement of PSQ then it is 50° because PSR is 125° and QSR is 75° so 125°-75°=50°.
Hope this helps! :)
‼️‼️HELP HELP ILL MARK YOU BRAINLEST ‼️‼️
your parents took your family out to dinner. your parents wanted to give the waiter a 15% tip. if the total amount of the dinner was $82.00 what should be paid to the waiter as a tip?
a)$12.30
b)$8.00
c)12.03
d)$13.00
Answer:
A = $12.30
Step-by-step explanation:
15 × 82 = 12.3
100
It takes a train 8 hours to travel a distance of 216 km. What is the average speed of the train?
(S=D/T)S=216KM, T=8HOURS : 216/8=27KM/HOUR
The average speed of the train is 27 km/hour if It takes a train 8 hours to travel a distance of 216 km.
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:
It takes a train 8 hours to travel a distance of 216 km.
As we know,
Average speed = distance/time
Average speed = 216/8 = 27 km/hour
Thus, the average speed of the train is 27 km/hour if It takes a train 8 hours to travel a distance of 216 km.
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Pls help me I don’t get it
Answer:
15.71cm
Step-by-step explanation:
perimeter of a semi circle=1/2(πdiameter)
1/2(3.142×10cm)
1/2(31.42cm)
15.71cm
Answer:
15.71 cm
Step-by-step explanation:
remember the formula for the circumference of a circle but make it half since it's a semi-circle
the perimeter of a circle is diameter x pi
since
the diameter is 10 and pi is 3.142
its 10 x 3.142
and that equals
31.42
that's a FULL circle so half of that
divide it by 2
31.42/2=15.71
so the diamater of the semi-circle is 15.71
hope this helps!
dont forget is centimeters
What is the circumference of the circle in terms of pi 30 in?
Step-by-step explanation:
Given radius = 30 in.
Circumference is given by 2πr
= 2 × π × 30
= 60π in
Solve for x. Leave your answer in simplest radical form.
There are two Right angled triangles in the given figure, with two missing sides, let's name the other missing side be " y "
According to Pythagoras theorem,
[tex] \boxed{ \large \boxed{h {}^{2} = {b}^{2} + p{}^{2} }}[/tex]
note :
p = perpendicular / opposite sideb = base / adjacent sideh = hypotenuselet's solve for " y² " first ( square of other missing side )
[tex]➢ \: \: {y}^{2} = {8}^{2} + 3 {}^{2} [/tex]
[tex]➢ \: \: {y}^{2} = 64 + 9[/tex]
[tex]➢ \: \: {y}^{2} = 73[/tex]
now let's solve for " x " , by using pythagorous theorem
[tex]➢ \: \: {x}^{2} = {y}^{2} + {6}^{2} [/tex]
[tex]➢ \: \: {x}^{2} = 73 + 36[/tex]
[tex]➢ \: \:x {}^{2} = 109[/tex]
[tex]➢ \: \: x = \sqrt{109} [/tex]
Approximate :
[tex]➢ \: \: 10.44 \: \: units[/tex]
[tex] \mathrm{✌TeeNForeveR✌}[/tex]
Each figure shows a triangle with one of its angle bisectors.
12) 22 - 38°. Find mZTRS.
Answer:
76 degrees
Step-by-step explanation:
this special line is an angle bisected.
that means it splits the angle at its starting point in 2 halves. as these names indicate, both parts are of equal size (half of the general angle).
we know one part (2) of this split angle : 38 degrees.
the other part (1) had to be equally sized : 38 degrees.
so, the total angle at point R is the sum of both split angles:
TRS = 38+38 = 76 degrees.
Please helppppppp meeee
Answer:
angle K is 30 degrees
Step-by-step explanation:
A triangle adds up to 180 degrees. since LM and KM are congruent angle L and M are both 75 degrees each you subtract from 180 and you get 30 degrees
In this addition problem, each letter stands for a different digit.
A
A
+ B B
-------------------
C C C
Find the value of A + B + C?
Using the right triangle below. What is the name for side BC?
A) Hypotenuse
B) Adjacent
C) Opposite
D) None of the above
Answer:
C) Opposite
Step-by-step explanation:
For angle x, the 2 sides that it lies between are either adjacent or hypotenuse. The one the angle doesn't touch is the opposite.
Ahhh please help I’m having a hard time with this(￣^￣)ゞ
Answer:
A x+y
B x+0 + (y+0)
Step-by-step explanation:
(x+0) + y+0
Adding 0
x+y
Changing the order of the parentheses
x+0 + (y+0)
is still the same
list the set of ordered pairs that had a domain that consists of multiples of 3 from -3 to 15
Answer:
Multiple of 3 from -3 to 15 are:-
3, 6, 9, 12 , 15
hope it is helpful to you ☺️
Line p is parallel to line q
Which set of statements about the angles is true ?
PERFORMANCE TASK : “TRANSVERSAL CITY MAP”
This project will help you to demonstrate your knowledge of parallel lines, transversals and the angles that are created by them. You will be designing a city map using the guidelines listed below. Your map must be drawn on construction paper or poster board. Use a ruler to make your streets straight! Have a title for your map, and make it neat and organized! You will be graded on accuracy, creativity and neatness.
Guidelines:
1) There must be a title for your map.
2) Your city must have three streets that are parallel to each other and one street that intersects all three of the parallel streets. You must name all of these streets.
3) Your city has a hospital that is alternate exterior to the school that is in your city. Draw and name the hospital and the school.
4) The school and the drugstore are at corresponding locations. Draw and name the drugstore.
5) The drugstore and the pet shop are at vertical locations. Draw and name the pet shop.
6) The pet shop and the gas station are at alternate interior locations. Draw and name the gas station.
7) The hospital and the park are at same side exterior locations. Draw and name the park.
8) The gas station and the grocery store are at same side interior locations. Draw and name the grocery store.
9) The grocery store and the nail salon are at vertical locations. Draw and name the salon.
10) The nail salon and bank are at corresponding locations. Draw Target.
11) The bank and a fast food restaurant are at same side interior locations. Draw and name the fast food restaurant.
12) Your city has a mall that is in a corresponding location to the bookstore that is in your city. Draw and name the mall and the bookstore. (If you did all of the others correctly, then the bookstore and the mall only have one place to be located)
In constructing a transversal city map by applying the knowledge of transversal and parallel lines, a map named California City Map has been drawn as shown in the image attached below.
(See attachment).
Recall:
Parallel lines are straight lines that do not meet each other.Transversal line is a that run through two or more straight lines that are parallel.Special angles are formed when transversal intersects parallel lines, which are: corresponding angles, same-side interior angles, same-side exterior angles, alternate exterior and alternate interior angles, and vertical angles.Using the knowledge of all these, an map named, "California City Map" has been drawn as shown in the image attached below.
The details are as follows:
1. Title for the map is:
California City Map.2. The three streets that are parallel are:
Adams BoulevardBeverly DriveCarroll AvenueThe street (transversal) that intersects the three is:
Darlin Way3. St. Michael Hospital is alternate exterior to Baptist Model School
4. Baptist Model School and Living Well Drug Store are in corresponding locations to each other.
5. Living Well Drug Store and Vik Pet Store are at vertical locations.
6. Vik Pet Store and Elite Gas-station are at alternate interior locations.
7. St. Michael Hospital and Livingstone Park are at same-side exterior locations.
8. Elite Gas-station and Richie Grocery Store are at same-side interior locations.
9. Richie Grocery Store and Beautyjay Nail salon are at vertical locations.
10. Beautyjay Nail salon and Retro Bank Plc are at corresponding locations.
11. Retro Bank Plc and Tessy's Fast Food Restaurant are at same-side interior locations.
12. California City Mall and Remis Bookstore are at corresponding locations.
In summary, in constructing a transversal city map by applying the knowledge of transversal and parallel lines, a map named California City Map has been drawn as shown in the image attached below.
(See attachment).
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a) vẽ đồ thị hàm số y=2x-3(d1)
b) tìm toạ độ giao điểm B của (d1) với (P):y=x^2
c)tìm m để đường thẳng (d2):y=(m-1)x-m-3 đi qua B
Answer:
Step-by-step explanation: