Which is the logarithmic form of 25 = 52? log25 = 25 log252 = 5 log525 = 2 log52 = 25.
The value of the logarithm function log₅25 is 2. Then the correct option is C.
What is a logarithm?Logarithms are another way of writing exponent. A logarithm with a number base is equal to the other number. It is just the opposite of the exponent function.
The logarithmic form of 25 will be
We know that if the base of the logarithm is the same as the number then the value of the logarithm will be 1 one that is given as
[tex]\rm log_a a = 1[/tex]
Then take the log with the base value of 5.
log₅25 = log₅5²
log₅25 = 2 × log₅5
log₅25 = 2
The value of the logarithm function log₅25 is 2. Then the correct option is C.
More about the logarithm link is given below.
https://brainly.com/question/7302008
Answer:
c
Step-by-step explanation:
Find cot and cos
If sec = -3 and sin 0 > 0
Answer:
Second answer
Step-by-step explanation:
We are given [tex]\displaystyle \large{\sec \theta = -3}[/tex] and [tex]\displaystyle \large{\sin \theta > 0}[/tex]. What we have to find are [tex]\displaystyle \large{\cot \theta}[/tex] and [tex]\displaystyle \large{\cos \theta}[/tex].
First, convert [tex]\displaystyle \large{\sec \theta}[/tex] to [tex]\displaystyle \large{\frac{1}{\cos \theta}}[/tex] via trigonometric identity. That gives us a new equation in form of [tex]\displaystyle \large{\cos \theta}[/tex]:
[tex]\displaystyle \large{\frac{1}{\cos \theta} = -3}[/tex]
Multiply [tex]\displaystyle \large{\cos \theta}[/tex] both sides to get rid of the denominator.
[tex]\displaystyle \large{\frac{1}{\cos \theta} \cdot \cos \theta = -3 \cos \theta}\\\displaystyle \large{1=-3 \cos \theta}[/tex]
Then divide both sides by -3 to get [tex]\displaystyle \large{\cos \theta}[/tex].
Hence, [tex]\displaystyle \large{\boxed{\cos \theta = - \frac{1}{3}}}[/tex]
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Next, to find [tex]\displaystyle \large{\cot \theta}[/tex], convert it to [tex]\displaystyle \large{\frac{1}{\tan \theta}}[/tex] via trigonometric identity. Then we have to convert [tex]\displaystyle \large{\tan \theta}[/tex] to [tex]\displaystyle \large{\frac{\sin \theta}{\cos \theta}}[/tex] via another trigonometric identity. That gives us:
[tex]\displaystyle \large{\frac{1}{\frac{\sin \theta}{\cos \theta}}}\\\displaystyle \large{\frac{\cos \theta}{\sin \theta}[/tex]
It seems that we do not know what [tex]\displaystyle \large{\sin \theta}[/tex] is but we can find it by using the identity [tex]\displaystyle \large{\sin \theta = \sqrt{1-\cos ^2 \theta}}[/tex] for [tex]\displaystyle \large{\sin \theta > 0}[/tex].
From [tex]\displaystyle \large{\cos \theta = -\frac{1}{3}}[/tex] then [tex]\displaystyle \large{\cos ^2 \theta = \frac{1}{9}}[/tex].
Therefore:
[tex]\displaystyle \large{\sin \theta=\sqrt{1-\frac{1}{9}}}\\\displaystyle \large{\sin \theta = \sqrt{\frac{9}{9}-\frac{1}{9}}}\\\displaystyle \large{\sin \theta = \sqrt{\frac{8}{9}}}[/tex]
Then use the surd property to evaluate the square root.
Hence, [tex]\displaystyle \large{\boxed{\sin \theta=\frac{2\sqrt{2}}{3}}}[/tex]
Now that we know what [tex]\displaystyle \large{\sin \theta}[/tex] is. We can evaluate [tex]\displaystyle \large{\frac{\cos \theta}{\sin \theta}}[/tex] which is another form or identity of [tex]\displaystyle \large{\cot \theta}[/tex].
From the boxed values of [tex]\displaystyle \large{\cos \theta}[/tex] and [tex]\displaystyle \large{\sin \theta}[/tex]:-
[tex]\displaystyle \large{\cot \theta = \frac{\cos \theta}{\sin \theta}}\\\displaystyle \large{\cot \theta = \frac{-\frac{1}{3}}{\frac{2\sqrt{2}}{3}}}\\\displaystyle \large{\cot \theta=-\frac{1}{3} \cdot \frac{3}{2\sqrt{2}}}\\\displaystyle \large{\cot \theta=-\frac{1}{2\sqrt{2}}[/tex]
Then rationalize the value by multiplying both numerator and denominator with the denominator.
[tex]\displaystyle \large{\cot \theta = -\frac{1 \cdot 2\sqrt{2}}{2\sqrt{2} \cdot 2\sqrt{2}}}\\\displaystyle \large{\cot \theta = -\frac{2\sqrt{2}}{8}}\\\displaystyle \large{\cot \theta = -\frac{\sqrt{2}}{4}}[/tex]
Hence, [tex]\displaystyle \large{\boxed{\cot \theta = -\frac{\sqrt{2}}{4}}}[/tex]
Therefore, the second choice is the answer.
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Summary
Trigonometric Identity[tex]\displaystyle \large{\sec \theta = \frac{1}{\cos \theta}}\\ \displaystyle \large{\cot \theta = \frac{1}{\tan \theta} = \frac{\cos \theta}{\sin \theta}}\\ \displaystyle \large{\sin \theta = \sqrt{1-\cos ^2 \theta} \ \ \ (\sin \theta > 0)}\\ \displaystyle \large{\tan \theta = \frac{\sin \theta}{\cos \theta}}[/tex]
Surd Property[tex]\displaystyle \large{\sqrt{\frac{x}{y}} = \frac{\sqrt{x}}{\sqrt{y}}}[/tex]
Let me know in the comment if you have any questions regarding this question or for clarification! Hope this helps as well.
Jacinta drove her car from the mountains into the desert. She travelled from
an altitude of 4,450 feet above sea level to an altitude of 150 feet below sea level.
Jacinta drove at a constant speed and the trip took her five hours. Which
statement is true about her rate of change in elevation?
A She descended at a rate of 920 feet per hour.
B She ascended at a rate of 860 feet per hour.
C She ascended at a rate of 920 feet per hour.
D She descended at a rate of 860 feet per hour.
The statement that is true about her rate of change in elevation is She descended at a rate of 920 feet per hour.
How to calculate the rate of changeFrom the question, Jacinta traveled from an altitude of 4,450 feet above sea level to an altitude of 150 feet below sea level, then the total distance traveled will be
D = 4450 + 150
D = 4600 feet
If Jacinta drove at a constant speed and the trip took her five hours, her rate will be expressed as:
Rate = Total distance/Time
Rate = 4600/5
Rate = 920 feet perhour
Hence the statement that is true about her rate of change in elevation is She descended at a rate of 920 feet per hour.
learn more on rate of change here: https://brainly.com/question/8728504
1. If the measure of angle D=162º and
angle C=122° Angle A= B=
2. If the measure of angle D=171° and
angle C =128° Angle A= B=
3. If the measure of angle A=22° and
angle B =35° Angle C= D=
4. If the measure of angle A= 20° and
angle B =29° Angle C= D=
Answer:
1.= 178 2.= 165 3.= 93 4.= 46
Step-by-step explanation: If you read the letter coordations and minus the orbs and graphs then you would get your first answer then you would multiply it by the same number. hope this helps :)
solve and simplify 6 2/3 x 3 1 /2
[tex]6 \frac{2}{3} = \frac{2}{18} = 9[/tex]
[tex]3 \times \frac{1}{2} = \frac{1}{6} = 6[/tex]
6×9=54
It is well-documented that watching TV, working on a computer, or any other activity involving artificial light can be harmful to sleep patterns. Researchers wanted to determine if the artificial light from e-Readers also disrupted sleep. In the study, 12 young adults were given either an iPad or printed book for four hours before bedtime. Then, they switched reading devices. Whether the individual received the iPad or book first was determined randomly. Bedtime was 10 P.M. and the time to fall asleep was measured each evening. It was found that participant took an average of 10 minute s longer to fall asleep after reading on an iPad. The P-value for the test was 0.009.
(a) What is the research objective?
(b) What is the response variable? It is quantitative or qualitative?
(c) What is the treatment?
(d) Is this a designed experiment or observational study? What type?
(e) The null hypothesis for this test would be that there is no difference in time to fa ll asleep with an e-Reader and print ed book. The alternative is that there is a difference. Interpret the P-value.
Answer:
(a) the objective is to determine if the artificial light from e-Readers also disrupted sleep.
sorry thats all i know
FREE
What is the inverse of the function f(x) = 4x + 8?
1
O h(x) = = x-2
4
Oh(x) = x + 2
4
()
ncx) = x + 2
o mw = 3x-2
o ncx) = x+2
O h(x) = 1
D
(
Answer:
f⁻¹(x) = x/4 - 2
Step-by-step explanation:
Interchange the variables.
Solve for y.
Replace
y with f⁻¹ (x) to show the final answer.
Verify if f⁻¹ (x) = x/4 − 2 is the inverse of f(x) = 4x + 8.
The axis of symmetry for the graph of the function f(x)=3x2 bx 4 is x equals three-halves. What is the value of b?.
The axis of symmetry for the graph of the function f(x) = 3x2 + bx + 4 is x = 3/2 , the value of b is -9.
What is an axis of symmetry?
Axis of symmetry is a line that divides an object into two equal halves, thereby creating a mirror-like reflection of either side of the object.
Given
The axis of symmetry for the graph of the function f(x) = 3x2 + bx + 4 is x = 3/2 .
The axis of the symmetry is given by;
[tex]\rm x=\dfrac{-b}{2a}[/tex]
The value of x is 3/2 and a is 3.
Substitute all the values in the formula
[tex]\rm x=\dfrac{-b}{2a}\\\\\dfrac{3}{2}=\dfrac{-b}{2 \times 3}\\\\\dfrac{3}{2}=\dfrac{-b}{6}\\\\ -b = \dfrac{6 \times 3}{2}\\\\ b = \dfrac{=18}{2}\\\\b =-9[/tex]
Hence, the value of b is -9.
To know more about the axis of symmetry click the link given below.
https://brainly.com/question/12896816
A sports club includes 350 members.
200 members play football (F).
130 members play basketball (B).
70 members of those who play basketball DO NOT play football.
a. Fill in the Venn diagram below.
Step-by-step explanation:
You need to find the n( A n B ) and then continue the process, if you have any question revert back to me...
Help see file...............................
Color combinations used in a presentation
2
The overall look of a presentation
4
A typeface without decorative extensions on the ends of the letters
5
The difference between objects
3
A tool used in presentation planning
1
Multiply 34.92 and 0.56 *
1 point
A. 19.5
B. 19.5552
C. 19.55
D. 19.52
Answer:
19.5552
Step-by-step explanation:
34.92 x 0.56
Use calculator or use long multiplication.
3492
×56
20952
+17460
195552
How many numbers are after the point on both of the numbers?
2 each. 2 + 2 = 4
We will take our result 4 points back or divide it by 10^4
195552 / 10000 = 19.5552
hey! im still confused on how 3(x+4)=36 can be solved with the distributive property... can you help me?
The distributive property is basically expanding brackets.
So if you take 3(x + 4) = 36 and remove the brackets (so multiplying out the 3), you get:
3x + 12 = 36
And from there you simplify :)
3x + 12 = 36
3x = 24
x = 8
The distributive property was used to multiply the 3 through the brackets, thus making the equation easier to solve I guess
Step-by-step explanation:
You are taking a class in which your grade is determined from: Quizzes: 15%
Exam (3): 15% for each
Homework: 10%
Final: 30%
Your scores are: Average quiz mean = 85 Exam = 78,81, 92 Homeworks mean = 85 Your final = 89
If the minimum average for B + is 87, did you get B + at the end of the semester. (Show your working.)
Answer:
No, you did not get a B+, you got an 85.6% for the class
Step-by-step explanation:
So, let's split the grades into different parts:
Quiz: 15%
Exam1: 15%
Exam2: 15%
Exam3: 15%
Homework: 10%
Final: 30%
Each part of the grade adds up together to be 100%, so here, we are going to multiply each weighting of the grade with the average amount of points you got for each assignment then add it all up.
(Notice how I convert the percentages to decimals to make it easier to multiply)
Quiz: 0.15(85) = 12.75
Exam1: 0.15(78) = 11.70
Exam2: 0.15(81) = 12.15
Exam3: 0.15(92) = 13.80
Homework: 0.10(85) = 8.50
Final: 0.3(89) = 26.70
Adding these all up:
12.75 + 11.70 + 12.15 + 13.80 + 8.50 + 26.70 = 85.6
You got an 85.6% for the class, which is not a B+
Feel free to ask any questions you may have in the comments! :D
Khan Academyyyyyyyyyyyyyyyy
Answer:
(© 105 + 90 = (52 - 70)
Step-by-step explanation:
What is the value of P ? 45/20= 40.5/P?
Answer:
P=18
Step-by-step explanation:
45/20= 40.5/P
45p=810
p=18
Which expression represents a way to find the value 4 x 2 x 6?
Answer:
Step-by-step explanation: well the anwser is 48
Identify the area of OK in terms of pi
radius is 7 cm
Answer:
K=49π cm^2
Step-by-step explanation:
Area of a circle: πr^2
r=7
7^2=49
Therefore, the answer is 49πcm^2
a town has a population of 10000 and growns at 2.5% every year what will be the population in 7 years
Answer:
The population after 7 years will be 11887
Step-by-step explanation:
Given
Population = P_0 = 10000
Growth Rate = r = 2.5%
Time = t = 7
The formula for calculating the population after given time at given rate is:
The population after 7 years will be 11887
Step-by-step explanation:
HELP ASAP PWESSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
The volume of a cylinder is given by v, where r is the radius of the cylinder and h is the height. Which expression represents the volume of this can?
Answer:
V= π r2h
is this right
I need help with Rational Functions
Answer: 105 minutes
Step-by-step explanation:
5 – 4 + 7x +1 = __x + __
Fill in the blanks to get no solutions
Answer: 7, 2 in order.
Step-by-step explanation:
We can combine like terms.
5 - 4 + 1 = 2.
Therefore, 5 - 4 + 7x +1 = 7x + 2.
Thus, the blanks are 7, 2 in order.
Answer:
7x + 2
Step-by-step explanation:
5-4 +7x +1
= 7x+1+5-4
= 7x + 2
4. Which is an algebraic expression for the word phrase "8 less than the product of 12 and a
number x?
Answer:
12x-8
Step-by-step explanation:
Answer:
12x-8
Step-by-step explanation:
Is the answer to -341.75 • the square root of 81 rational or irrational !!!!
What is the exact circumference of a circle with a radius of 15 cm?
o 10 pi cm
o 15 pi cm
o 30 pi cm
o 60 pi cm
Answer:
(C) 30πcm
Step-by-step explanation:
In order to find circumference you use the formula C (circumference)=2(pi)(r) in which r is the radius. In this case, two and 15 are thirty so to find the circumference all you have is the equation 30 times pi centimeters is equal to the Circumference.
Relative to the sinusoidal axes (dotted lines) what is the equation of this sinusoid?
Step-by-step explanation:
We know that the function period is 3 so the b value is
[tex] \frac{2\pi}{b} = 3[/tex]
[tex]b = \frac{2\pi}{3} [/tex]
So our b is 2 pi/3.
The midline is -3 and the amplitude is 2.Since this function isn't symmetric about y axis, and looks symmetric about orgin, we trig function will be Sine so we have
[tex]2 \sin ( \frac{2\pi}{3}x ) - 3[/tex]
The function passes through 0,-3 and our function on the graph passes through 1,-3 so we shift one unit to left.
[tex]2 \sin(\frac{2\pi}{3}(x + 1) ) - 3[/tex]
Danny is making hot chocolate. The recipe calls for 1/2 cup of powder to 2 cups of warmed milk. If Danny wants to make 6 cups of hot chocolate, how much powder does he need?
PLEASE HELP
Answer:
3 cups
1/2x6=3
something I recommend for questions like this is the Desmos calculator, it does fractions and decimals.
given right triangle abc with altitude bd drawn to hypotenuse ac.If AB=6 and AD=3 what is the length of AC
Answer:
Step-by-step explanation:
[tex]\frac{6}{3}=\frac{AC}{6}\\AC=12[/tex]
20 points do all thanks
Answer:
so you don't have to give me points but I can explain how to do it
Step-by-step explanation:
so for number 1. it says y=3x-7 and the equation is 5x+4y=6
so basically your plugging in y so
5x+5(3x-7)=6 and you will get your answer
WORTH 50 POINTS FIND THE VALUE OF X
Answer:
D) 10
Step-by-step explanation:
Singe a right triangle has to be 90 degrees, 60+(3*10)=90:)
therefore x=10
Answer:
D
Step-by-step explanation:
the angles 60 and 3x form a right angle , then
60 + 3x = 90 ( subtract 60 from both sides )
3x = 30 ( divide both sides by 3 )
x = 10 → D
