Both 3 is an extraneous solution.
We have the equation x - 6 = [tex]\sqrt{3x}[/tex]
To find the value of x we need to square on both side of the equation
[tex](x-6)^{2}[/tex] = [tex](\sqrt3{x} )^{2}[/tex]
[tex]x^{2}[/tex] - 12x + 36 = 3x
[tex]x^{2}[/tex] -15x + 36 = 0
[tex]x^{2}[/tex] - 12x - 3x + 36 = 0
x ( x- 12 ) - 3( x - 12) = 0
(x -12 ) ( x - 3) = 0
Therefore we get x = 12 , 3
Now we will put both the value of x in the equation
x - 6 = [tex]\sqrt{3x}[/tex]
Let put 12 first
12 - 6 = [tex]\sqrt{3 * 12}[/tex]
6 = 6
Now put 3
3 - 6 =[tex]\sqrt{3 * 3}[/tex]
- 3 [tex]\neq[/tex] 3
Therefore 3 is an extraneous solution .
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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]
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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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
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]
Ian has a loyalty card good for a discount at his local grocery store. The item he wants
to buy is priced at $34, before discount and tax. After the discount, and before tax,
the price is $30.60. Find the percent discount.
Ian got a discount of 3.4 and percent discount is 10% after buying the items he wants in the local grocery store
How to find the percent discount
Given data
price before tax and discount = $34
price after discount = $30.60
solving for discount
$34 - $30.60 = $3.4
percent discount
= 3.4 / 34 * 100 / 1
= 0.1 * 100
= 10%
Therefore we can say that Ian got a discount of 3.4 and percent discount is 10% after buying the items he wants in the local grocery store
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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."
||
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
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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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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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
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
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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62+41+(2)+(4) what is the answer to this
Answer:
109.
Step-by-step explanation:
62+41+(2)+(4) we can remove the brackets:
= 62 + 41 + 2 + 4
= 109.
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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Please help! I will mark brainliest! :)
Answer:
The measure of angle 3 is 30 (C).
Step-by-step explanation:
m<1, m<2, and m<3 have a sum of 180 Linear Pair Postulate
So 2x + 3x - 20 + x - 4 = 180
6x - 24 = 180
6x = 204
x = 34
Then you substitute and get 34 - 4 for angle 3 which = 4
Hope this helps!
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:
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!
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 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°.
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
Which pair of expressions below or equivalent?
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.
**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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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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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.
• 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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plsss helppppp i rlly need this
i need help really quick..
Answer: i feel like all of them but dont go by my word
Step-by-step explanation:
What is the measure of the missing angle? show your work.
The measure of the missing angle is 112°.
Sum of Interior AngleWhen you need to find some interior angle of polygons, you can apply the formula for the sum of interior angle. This formula relate the number of sides of the polygon with the sum of interior angle. The formula is presented below.
S = (n – 2 )*180º, where:
S= sum of interior angles
n= number of sides of the given polygon
The given figure shows:
a polygon with 5 sides ;the angles of polygon are: 105°,118°,75°, 130° and x°.Applying the formula, S = (n – 2 )*180º, you find:
S=(5-2) * 180
S=3*180
S=540°
Now that you know the sum of the interior angles for the given polygon, thus:
x+105+118+75+130=540
x+428=540
x=540-428
x=112°
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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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