After solving the given equation log₃x = 4, the value of x = 81.
What is an equation?A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.So,
Given: log₃x = 4Then,
log₃x = 4logbx = n ⇔ x = bⁿlog₃x = 4 ⇔ 3⁴ = 81Therefore, after solving the given equation log₃x = 4, the value of x = 81.
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plsss helppppp i rlly need this
Write and solve a logarithmic equation.
The value of logarithmic equation log₂ (x+3) + lox₂ (3) = log₂(27) which is taken as an example is x = 6.
How to solve a logarithmic equation?Step 1: Isolate a logarithmic expression (with the same base) on both sides of the equation using exponentiation rules.
Step 2: equalize the arguments.
Step 3: Solve the resultant equation.
Step 4: Verify your responses.
Let us consider an example -
log₂ (x+3) + lox₂ (3) = log₂(27)
using logₐ(m.n) = logₐ(m) + logₐ(n)
log₂(3(x+3)) = log₂(27)
log₂(3x + 9) = log₂(27)
3x+9 = 27
x = 27 - 9 / 3
x = 6
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For her birthday, Carrie has asked her family to donate money to the World Nature Fund. Five of her family members donated $15 each to the cause. Carrie also emptied $21.27 from her piggy bank and donated it all. How much has Carrie and her family donated in all? Video
Answer: $96.27
Step-by-step explanation: 15x5=75, 75+21.27=96.27
Answer: $96.27
Step-by-step explanation:
If five of Carries' family members donated $15 we would have 15x5.
15+15+15+15+15=$75.
Carrie, herself, donated $21.27.
$75+$21.27
75+21=96
Add the .27 to 96.
Answer= $96.27 in total
D. C=15.75h
2.
Dylan is building a model car. The actual length of the car is 12 feet and is represented
by 5 inches in the model.
Which equation represents the relationship between the actual length (a), in feet, and
the length of the model (m), in inches?
A.
B.
C.
D.
a=
m = 2a
a=0.52m
m = 0.52a
The equation that can be use to represent the relationship between the actual length(a) in feet, and the length of the model (m), in inches is a = 2.4m or m = a / 2.4
How to use equation to represent the relationship between actual length and length of the model?The actual length of the car is 12 feet and is represented by 5 inches in the model.
The equation that can be use to represent the relationship between the actual length(a) in feet, and the length of the model (m), in inches is as follows:
12 feet = 5 inches
Hence,
m = 5 / 12 a
a = 2.4m
where
a = actual length in feetm = length of the modelor
m = a / 2.4
Therefore, the equation that can be use to represent the relationship between the actual length(a) in feet, and the length of the model (m), in inches is a = 2.4m or m = a / 2.4
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look at the picture and get an answer
Answer:
The symbol should be equal to.
They are the same when the first expression is multiplied.
Answer:
=
Step-by-step explanation:
6.738 × 10^-11 = 0.00000000006.738
0.00000000006738 = 0.00000000006738
Using your answer(s) for question 3, were there any extraneous answers, and how did you check?
Question 3 was:
(Solve |2(x-5)|+11=17)
The answer is x = 8 and x = 2
Answer:
x = 8 and x = 2 are both valid solutions.
There are no extraneous answers.
Step-by-step explanation:
Given absolute value function:
[tex]|2(x-5)|+11=17[/tex]
To solve an equation containing an absolute value, isolate the absolute value on one side of the equation:
[tex]\implies |2(x-5)|+11=17[/tex]
[tex]\implies |2(x-5)|+11-11=17-11[/tex]
[tex]\implies |2(x-5)|=6[/tex]
Set the contents of the absolute value equal to both the positive and negative value of the number on the other side of the equation, then solve both equations.
Equation 1 (positive)
[tex]\implies 2(x-5)=6[/tex]
[tex]\implies \dfrac{2(x-5)}{2}=\dfrac{6}{2}[/tex]
[tex]\implies x-5=3[/tex]
[tex]\implies x-5+5=3+5[/tex]
[tex]\implies x=8[/tex]
Equation 2 (negative)
[tex]\implies 2(x-5)=-6[/tex]
[tex]\implies \dfrac{2(x-5)}{2}=\dfrac{-6}{2}[/tex]
[tex]\implies x-5=-3[/tex]
[tex]\implies x-5+5=-3+5[/tex]
[tex]\implies x=2[/tex]
Therefore, the solutions are x = 8 and x = 2.
Check if the solutions are valid by substituting them into the original equation:
[tex]\begin{aligned}x=8 \implies |2(8-5)|+11 & =17\\|2(3)|+11 & =17\\|6|+11 & =17\\6+11 & =17\\ 17 & = 17\end{aligned}[/tex]
[tex]\begin{aligned}x=2 \implies |2(2-5)|+11 & =17\\|2(-3)|+11 & =17\\|-6|+11 & =17\\6+11 & =17\\ 17 & = 17\end{aligned}[/tex]
Therefore, both solutions are valid and there are no extraneous answers.
Note: An extraneous solution is a solution that is produced by solving the problem, but is not a valid solution to the problem.
S
R
Q
Name the vertex of the angle.
The vertex (the common end point for the two rays) in the angle SRQ is the point R as it is in the middle and common.
The angle is SRQ with sides SR and RQ. The common point is R.
A vertex of an angle is the endpoint where two line or rays come together. The vertex of an angle is the point where two rays begin or meet, where two line segments join or meet, where two lines intersect (cross), or any appropriate combination of rays, segments and lines that result in two straight "sides" meeting at one place.
Here two sides are SR and RQ the end point to both the sides is common which is R. So the vertex to the angle SRQ is R.
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What is the solution of log (3-2 x)=-1 ?
Solution of logarithmic eq. log (3 - 2x) = -1 is , [tex]x = \frac{29}{20}[/tex]
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as [tex]log_{a}x[/tex] .
where, a is the base of function or equation
x is expression equation
Mathematically, if [tex]a^x = N[/tex] is an exponential function then, this can be converted to logarithmic function as [tex]log_aN = x[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms :
[tex]log a + log b = log a.b[/tex][tex]log a - log b = log \frac{a}{b}[/tex][tex]log a^x = x loga[/tex][tex]log_aa=1[/tex][tex]log_a1=0[/tex]According to given statement,
log (3 - 2 x)= -1
now convert this equation to exponential form
=> 3 - 2x = 10^-1
=> 3 - 2x = 1/ 10
=> x = 29 / 10
Thus solution for this equation is x =29/20.
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Which pair of expressions below or equivalent?
The area of a room is 32m^2 . What is the area of the room in mm^2?
Answer:
Steps below.
Step-by-step explanation:
Unit Conversion is definitely needed in this question. Therefote, we will do some conversions first.
[tex]1m = 1000 mm \\ 1 {m}^{2} = {(1000)}^{2} {mm}^{2} \\ 1 {m}^{2} = 1000000 {mm}^{2} [/tex]
Now we can use the above converted unit to solve for the question.
[tex]32 {m}^{2} = 32 \times 1000000 \\ = 32000000 {mm}^{2} [/tex]
x less than or equal to 25
Answer:
[tex]x\leq 25[/tex]
Step-by-step explanation:
Since x can equal anything 25 and lower, here are some of the possibilities x can be.
x = 25, 24, 23, 22, 21, 20, etc.
X could also be a decimal and doesn't have to be an integer.
x = 24.7, -20.4, 24 5/7
So to put these numbers in one equation, we can use the [tex]\leq[/tex] symbol.
Therefore, [tex]x\leq 25[/tex].
Hope this helped! Have a great day!
Accrotime is a company that manufactures quartzcrystal watches. Accrotime researchers have shown that the watches have an average life of 28 months before certain electronic componentsdeteriorate, causing the watch to become unreliable. The standard deviation of watch lifetimes is 5 months, and the distribution of lifetimes is normal.
if Acro time does not want to make refunds for more than 12% of the watches it makes how long should the guarantee period be to the nearest month
if acro time guarantees a full refund on any defective watch for two years after purchase what percentage of total production should the company expect to replace
The guarantee period of the electronic components by Accrotime manufactures is 38 months.
What is defined as the normal distribution?A normal distribution is a data set arrangement in which the majority of values cluster inside the middle of the range and the remainder trimmed off symmetrically toward any extreme.It happens whenever a normal random variable does have a mean of zero and a standard deviation of one.mean = μ = 24 months
standard deviation = σ = 5 months
2 years = 24 months
a) P(x < 24)
= P[(x - μ ) / σ < (24 - 28) / 5]
= P[(x - μ ) / σ < -0.8
= P(z < -0.8 )
Using z table,
= 0.212
Percentage = 21.2%
b) Use standard normal table,
Refund percentage = 12%
P(Z > z) = 12%
= 1 - P(Z < z) = 0.12
= P(Z < z) = 1 - 0.12
= P(Z < z ) = 0.88
= P(Z < 0.174 ) = 0.94
z = 0.174
Using z-score formula,
x = z ×σ + μ
x = 1.74 × 5 + 28
x = 36.7
The guarantee period = 38 month
Thus, the guarantee period of the electronic components by Accrotime manufactures is 38 months.
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help please
Which expression is equivalent to −3(b − 7)?
−3b − 21
−3b + 21
−3b − 7
3b + 7
Answer:
- 3b + 21
Step-by-step explanation:
- 3(b - 7) ← multiply each term in the parenthesis by - 3
= - 3b + 21
If José's present age is 3 n, how old will he be in 5 years?
Answer:
3n+5
Step-by-step explanation:
you don’t know the official age, all you know is that his age is 3 times whatever number
Sep 14, 8:22:40 AM
A bakery sold 26 vanilla cupcakes in a day, which was 13% of the total number of
cupcakes sold that day. How many total cupcakes did the bakery sell that day?
The total number of cupcakes sold by the bakery on that day were 200.
Here, we are given that a bakery sold 26 vanilla cupcakes in a day.
This was 13% of the total number of cupcakes sold that day.
Let the total number of cupcakes sold that day be x
Then 13% of x is given to be 26. Mathematically this can be represented as-
(13/100)x = 26
solving the equation to find the value of x, we get-
x = 26 × 100/ 13
x = 26/13 × 100
x = 2 × 100
x = 200
Thus, the total number of cupcakes sold by the bakery on that day were 200.
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Easy points !! WILL GIVE BRAINLIST TO BEST ANSWER A
VIEW PHOTO
Answer:
6
Step-by-step explanation:
Terms are what is separated by addition and subtraction.
Help me pls with this question I will give you points,
Answer:
64
Step-by-step explanation:
Angles DBF and EBF form a linear pair, so:
[tex]5x+6+3x-2=180 \\ \\ 8x+4=180 \\ \\ 8x=176 \\ \\ x=22 \\ \\ \implies m\angle DBF=116^{\circ}[/tex]
Similarly, because angles DBF and DBC form a linear pair, the answer is 64°.
Juna noticed that easter fell on april 1st in 2018, april 21st in 2019, and april 12* in 2020, and april 4th in 2021. she conjectured that easter always falls in the first 22 days in april. can you find a counterexample that disproves her conjecture?
A counterexample that disproves her conjecture is that Easter date fell outside the first 22 days in April in the year 2024, 2027, 2032 and 2038.
Easter Sunday might come between March 22 and April 25. Easter is always celebrated on the Sunday immediately following the Paschal Full Moon date of the year. The Paschal Full Moon is the first Ecclesiastical Full Moon date after March 20. So, in Western Christianity, Easter is always celebrated on the Sunday immediately following the Paschal Full Moon.
Her conjecture over 2018 to 2021 is not a full reflection of the changes that occurs in these dates. To draw a more concrete assumptions, a wider range of year would need to be considered. Hence, the date variations between 2018 and 2021 is not enough for such conjectures.
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The school that ming goes to is selling tickets to the annual talent show. on the first day of
ticket sales the school sold 8 senior citizen tickets and 4 student tickets for a total of $84. the
school took in $66 on the second day by selling 8 senior citizen tickets and 2 student tickets.
find the price of a senior citizen ticket and the price of a student ticket.
The school that Ming goes to sell their tickets as follows: price of a senior citizen ticket is $6 and the price of a student ticket is $9
How to find the price of a senior citizen ticket and the price of a student ticket
Given data
first day 8 senior citizen tickets and 4 student tickets for a total of $84
second dat 8 senior citizen tickets and 2 student tickets for a total of $66
let the price of a senior citizen ticket be x and the price of a student ticket be y. The equation is written as:
8x + 4y = $84 equation 1
8x + 2y = $66 equation 2
subtracting equation 2 from equation 1
( 8x - 8x ) + 4y - 2y = 84 - 66
0 + 2y = 18
2y = 18
y = 9
substituting y = 9 into equation 1
8x + 4y = 84
8x + 4 * 9 = 84
8x + 36 = 84
8x = 84 - 36
8x = 48
x = 6
Hence the price of a senior citizen ticket is $6 and the price of a student ticket is $9
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**HELP*
-5 - 2
6 - (-5)
The solutions of the expression are;
a. - 5 - 2 = -7
b. 6 - (-5) = 11
What is Addition?
A process of combining two or more numbers are called Addition.
The given expression are;
a. -5 - 2
b. 6 - (-5)
Now, Solve the expression as;
-5 - 2 = - 7
And, 6 - (-5) = 6 + 5 = 11
So, The solutions of the expression are;
- 5 - 2 = -7
6 - (-5) = 11
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Simplify y to the negative eighth power over x to the negative fifth power.
pls pls help!!
Answer:
[tex] \dfrac{x^{5}}{y^{8}} [/tex]
Step-by-step explanation:
[tex] \dfrac{y^{-8}}{x^{-5}} = [/tex]
[tex] = \dfrac{x^{5}}{y^{8}} [/tex]
The expression is simplified to give y⁻⁸x⁵
How to simply the index formsFirst, it is important to note that index forms are described as mathematical forms that are used to represent numbers of variables that are too large or that are too small in more convenient forms.
These index forms are also known as scientific notations or standard forms
From the information given, we have that;
y to the negative eighth power over x to the negative fifth power
This is represented as;
y⁻⁸/x⁻⁵
Since the forms are not of the same bases, we cannot add the exponents
y⁻⁸x⁵
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SOMEONE PLEASE HELP ME
Answer:
A) "If q, then p."
B) "If not p, then (not) q."
C) "If (not) q, then not p."
Henry has a total of 39 cards to play a game.
Every player must get 8 cards.
How many players can play this game?
Answer: 4 players can play and still have 8 cards each.
39÷8=4.875
Answer:
4 people
Step-by-step explanation:
39 cards / 8 cards = 4.87500
each person must have 8 cards, so only 4 people can play
What is the equation of a line perpendicular to y=1/4x-3 that passes through point (-2,4)?
Step-by-step explanation:
To find a line perpendicular to one another and passing through the point we take the slope of the original line and apply its reciprocal in point slope form.
Reciprocal of [tex]\frac{1}{4}[/tex] is [tex]\frac{-4}{1}=-4[/tex]
Now plug the slope into point-slope form with the known x and y values:
[tex]x-(-2)=-4(y-4)\\x+2=-4(y-4)\\x+2=-4y+16\\x+2+4y=16\\4y=16-x-2\\y=4-\frac{x}{4}-\frac{2}{4}\\y=3.5-\frac{x}{4}[/tex]
• For software that really has a virus, the test says "Yes" 97% of the time
• For software that is really virus-free, the test says "Yes" 2% of the time ("false
positive")
If 1% of all software has a virus and the virus test for a randomly selected software says
"Yes", what are the chances that the software really has a virus?
There is 0.329 probability or chance that the software really has a virus.
The calculation will be based on Bayes' theorem which relates the probability and statistics, as is mentioned in the given question. The values provided are True positive = 97%, False positive = 2% and Prevalence = 1%.
Probability = (True positive × user) ÷ (True positive × user) + (false positive × non user)
Keep the values in formula to find the probability
Probability = (0.97 × 0.01) ÷ (0.97 × 0.01) + (0.02 × 0.99)
Probability = 0.0097 ÷ (0.0097 + 0.0198)
Probability = 0.0097 ÷ 0.0295
Probability = 0.329
Thus, there is 0.329 chance that the software really has a virus.
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i need help really quick..
Answer: i feel like all of them but dont go by my word
Step-by-step explanation:
How is graphing a two-variable inequality similar to graphing a one-variable inequality on the number line? HURRY PLEASE
Answer: “The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥.”
- https://www.mathplanet.com
Step-by-step explanation:
||
Evaluating a formula
Use the equation below to find T, if w=72, m=8, and a = 2.
T=w-ma
Answer: its 56
Step-by-step explanation:
plug #'s in
t=72-8x2
t=56
In triangle $ABC,$ $M$ is the midpoint of $\overline{AB}.$ Let $D$ be the point on $\overline{BC}$ such that $\overline{AD}$ bisects $\angle BAC,$ and let the perpendicular bisector of $\overline{AB}$ intersect $\overline{AD}$ at $E.$ If $AB = 44,$ $AC = 30,$ and $ME = 10,$ then find the area of triangle $ACE.$
please help with this, it will truly be appreciated
Using the description, area of triangle ACE is solved to be 150 square units
How to find angle ACEfrom the given data we fine AE using Pythagoras rule, as AE is the hypotenuse of the triangle AEM. So we solve as:
AE^2 = ME^2 + AM^2
AE^2 = 10^2 + 22^2
AE = √(100 + 484)
AE = √584
note AM is half of AB which is 44, it was given that M is the mid point of line AB, this makes AM = AB / 2 = 22
Area of triangle ACE
area of triangle when two sides and one angle is given is solved by the formula
= a b sin ∅ / 2
angle at A/2 = arc tan (10/22) = 24.44
= AC * AE * sin A/2 / 2
= 30 * √584 * sin 24.44 / 2
= 299.95 / 2
= 149.98 ≅ 150
Hence area of triangle ACE is solved to be 150 square units
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from a window 35 meters high, the angle of depression to the top of a nearby streetlight is 55.. the angle of depression to the base of the streelight is 57.8. how tall is the streelight/?
The height of the street light is approx. 3.5m.
Angle of depression is defined as the angle formed between the horizontal line and the line of sight when the observer looks down .
In the given question
let h be the height of the street light
let d be the distance from the base of building to the street light .
form the figure given below.
In ΔADE
[tex]tan(57.8)=\frac{AD}{DE}[/tex]
Substituting the value of AD and DE from the figure
[tex]tan (57.8)=\frac{35}{d} \\ \\ d=\frac{35}{tan(57.8)} \\ \\ d=\frac{35}{1.5879}[/tex]....substituting the value of tan (57.8)
d=22.04 m ...(i)
In ΔABC
[tex]tan(55)=\frac{AB}{BC}[/tex]
Substituting the value of AB and BC from the figure
since AD=AB+BD
35=AB+h
AB=35-h
[tex]tan (55)=\frac{35-h}{d}[/tex]
Substituting the value of d from (i)
[tex]tan (55)=\frac{35-h}{22.04}\\ \\ 35-h=tan(55)*22.04\\ \\ 35-h=1.428*22.04[/tex]( substituting the value of tan(55) )
[tex]35-h=31.47[/tex]
[tex]h=35-31.47\\h=3.53\\[/tex]
h≅3.5
Therefore , the height of the streetlight is approx. 3.5m .
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