Answer:
y = (C-Ax)/B
Step-by-step explanation:
We first move Ax to the right by subtracting from both sides
Ax+By=C
Ax+By - Ax = C - Ax
By = C - Ax
Now we divide by B
y = (C - Ax)/B
note that it only works if B ≠ 0
Answer:
y = [tex]\frac{C-Ax}{B}[/tex]
Step-by-step explanation:
Ax + By = C ( subtract Ax from both sides )
By = C - Ax ( divide both sides by B )
y = [tex]\frac{C-Ax}{B}[/tex] (B ≠ 0 )
Solve each inequality using a table.
(Hint: For more accurate results, set ΔTbl=0.001 . )
3 log x+log (x+2)>1
After solving the given inequality the answer is 3logx+log₁₀(x+2)>1.
What exactly do we mean by inequality?In mathematics, an inequality is a relationship that involves a non-equal comparison of two numbers or other mathematical expressions.It is most commonly used to compare two numbers' sizes on a number line.So,
Given: 3log x + log(x+2) > 1
3log x + log(x+2) > 1 ⇒ 3logx+log₁₀(x+2)>1
Therefore, after solving the given inequality the answer is 3logx+log₁₀(x+2)>1.
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If KL = 8x - 5 and LM = 6x + 3, what is KL?
KL = LM To find the measures of KL
8x-5 = 6x+3
-6x -6x 8(4) - 5
___ ___ 32 - 5
2x - 5 = 3 27
+5 +5
__ __ To find the measure of LM
2x = 8 6(4) + 3
--- --- 24 + 3
x = 4 27
Use the equation y = -1/2х-3 for questions 1 and 2.
1. What is the form of this linear equation?
2.rewrite this equation in standard form.
1. The given equation is in the slope intercept form.
2. The standard form is x ₊ 2y = ₋6
3. The given equation is in the point slope form.
4. The standard form is 2x ₋ 3y = ₋3
Given,
the equation is y = ₋1/2x ₋ 3
the above equation is in the form of slope intercept form i.e,
y = mx ₊ c
to convert it into standard form i.e, ax ₊ by = c
therefore, 2y = ₋x ₋ 6
x ₊ 2y = ₋6
2. the equation is y ₋ 7 = 2/3 (x ₋ 9)
the above equation is in the form of point slope form.
i.e, y ₋ y₁ = m(x ₋ x₁)
therefore, to convert it into standard form i.e, ax ₊ by =c
y ₋ 7 = 2/3 (x ₋ 9)
3(y ₋ 7) = 2(x ₋ 9)
3y ₋ 21 = 2x ₋ 18
3y ₋ 2x = ₋18 ₊ 21
₋ 2x ₊ 3y = 3
2x ₋ 3y = ₋3
hence we get the required results.
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$750, annual rate:10 1/2% what is the time to double & the amount after 10 years?
well, let's start like the crab, from the back, what would the amount be after 10 years, with a 10.5% annual rate, compounding annually of course.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$750\\ r=rate\to 10.5\%\to \frac{10.5}{100}\dotfill &0.105\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases} \\\\\\ A=750\left(1+\frac{0.105}{1}\right)^{1\cdot 10} \implies A=750(1.105)^{10}\implies \boxed{A \approx 2035.56}[/tex]
when will it double? well, hmmm 750 doubled will be 1500, so
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$1500\\ P=\textit{original amount deposited}\dotfill &\$750\\ r=rate\to 10.5\%\to \frac{10.5}{100}\dotfill &0.105\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years \end{cases}[/tex]
[tex]1500=750\left(1+\frac{0.105}{1}\right)^{1\cdot t} \implies \cfrac{1500}{750}=(1.105)^t\implies 2=1.105^t \\\\\\ \log(2)=\log(1.105^t)\implies \log(2)=t\log(1.105) \\\\\\ \cfrac{\log(2)}{\log(1.105)}=t\implies 6.94\approx t\qquad \textit{about 6 years and 344 days}[/tex]
Please help me with this assignment! Grade 8th math
We need to know about translation, reflection and rotation to solve the problem. (1) We translate a triangle with respect to a horizontal and vertical direction. (2) We rotate a traingle about a given angle. (3) We refelct a triangle about a line of reflection which can be axis or vector.
(1) Translation of a triangle means changing it's position without changing the shape or size of the triangle. We translate a triangle with respect to a horizontal and vertical direction. We get the new triangle by adding the horizontal translation value to the x-coordinate and the vertical translation value to the y-coordinate.
(2) Rotation of a triangle is turning the triangle by an angle around a center point. When a triangle is rotated by 90° clockwise then (x,y) becomes (y,-x), when rotated by 90° anticlockwise (x,y) becomes (-y,x), when rotated by 180° clockwise or anticlockwise (x,y) becomes (-x,-y).
(3)Reflection of a triangle is finding a mirror like image of the triangle about a line of reflection. The line of reflection may be either of the axes, a vector. To find the image we have to find the coordinates of the triangle that are of same distance from the line of reflection on the opposite side like they are from the original triangle.
Therefore we learnt about translation, reflection and rotation and saw that (1) Translation needs a horizontal and vertical direction for translating, (2) Rotation needs an angle of rotation and a center point and (3) Reflection needs a line of reflection.
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What is the area of the parallelogram shown above?
Hint : The area of a parallelogram is
A = b x h.
Area = [?]ft^2
Answer: 299^2 ft
Step-by-step explanation: Literally all you have to do is Base X Hight and you get the answer. The base is basically just the length.
Hope this helps!
11. How many dots are in the nth term of the following sequence? term: 3,5,7,9 n+2 n²+2 2n+1 n+3
The nth term of the sequence is 2n + 1
The formula known as the nth term allows us to locate any term in a series. The letter n stands for number. By changing the term number's value, we can create a series that uses the nth term (n).
The sequence 3,5,7,9.....
n =1
3 = 1 + 2
3 = 1 + (2×1)
n = 2
5 = 1 + 4
5 = 1 + (2×2)
n = 3
7 = 1 + 6
5 = 1 + (2×3)
n = 4
9 = 1 + 8
9 = 1 + (2×4)
9 = 1 + 8
Therefore, the expression for the Nth is 1+ 2n or 2n + 1
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We can go to the amusement park or the library. the amusement park is too expensive, so we must go to the library.
Based on the logical fallacy given by saying that they can either go to the amusement park or the library, the category is False dilemma.
What is a false dilemma?A False dilemma is a logical fallacy where the speaker makes it seem as though there are no other options to be considered. The possibility of there being other options is therefore ignored.
In the above thought, the speaker says that they can either go to the amusement part or to the library. They then pick the library because the amusement park is too expensive.
This is a logical fallacy because there were other places they could have gone to that were not even considered.
In conclusion, the statement above that presents only two choices of places to go which were the library or the amusement park is an example of a false dilemma.
Rest of the question:
Identify the logical fallacy in the given statement.
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Choose the answer that represents the product below as a exponential
expression.
(-8) (-8) (-8) (-8) (-8) (-8) (-8)
OA. (-8)5
OB. (-8)-8
C. 7. (-8)
Answer:
[tex](-8)^7[/tex]
Step-by-step explanation:
You are multiplying (-8) 7 times. Therefore, it can be simplified down to [tex](-8)^7[/tex].
Which statement is true of this function?
ƒ(x) = (²) — 2
O A. As the value of x increases, the value
B. The domain of the function is (-2, 00).
OC. The function has a y-intercept at (0,-2).
OD. The function is increasing.
The statement "As the value of x increases, the value of f(x) moves toward a constant." is true. Option A
What is the function?A relation between a collection of inputs and one output for each of those inputs is the definition of a function.
The given function is;
F(x)=(1/5)^x-2
The statement that is true of this function is as follows;
As the value of x increases, the value of f(x) moves toward a constant.
The domain of the function is (-∞, ∞).The function has a y-intercept at (0,-1).The function is decreasing.Therefore, the assertion that is true about this function is that when the value of x rises, the value of f(x) advances toward a constant. This is because of the way that the function works.
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CQ
Select the correct answer. Which statement is true of this function?
f(x)=(1/5)^x-2
A.
As the value of x increases, the value of f(x) moves toward a constant.
B.
The domain of the function is (-2, ∞).
C.
The function has a y-intercept at (0,-2).
D.
The function is increasing.
Decide whether each claim is based on science or bias.
Claim
Basis of claim
People bred domestic cats from wildcats. They selected cats with desired traits as the parents for each generation. Evidence shows that humans developed many domestic animals and plants in much the same way.
Select ...
Select ...
An ad for a new type of tire describes it as "the best tire ever made." The ad shows pictures of the tire and compares it with an older type of tire. Under the pictures is a caption that states, "Look how much wider our new tire is."
The situations are classified as follows:
Cats... evidence ... : science.Tyre: bias.What is science in a claim?A claim is classified as science if there are experiments, or statistical tests, that prove the claim. In the cats experiment, there is evidence, hence it is science.
What is bias in a claim?A claim is classified as biased when no experiments are made, the observations are made with the "eye test". One example is watching a NFL game and saying that the team that gets the most passing yards generally wins, without making statistical tests to verify this.
For this problem, the ad for the tire is based on bias, as there were no experiments, just the eye test.
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Solve the equation V^3=36
Answer:
V= [tex]\sqrt[3]{36}[/tex]
Alternative Form
V≈3.301927
Evaluate
V
3
=36
Take the 3-th root on both sides of the equation
3
V
3
=
3
36
hope this helps now
Answer:
[tex]\mathrm{V=\sqrt[3]{36}}[/tex]
Step-by-step explanation:
Determine if 36 is a cube root
(a-b)•(a^2+ab+b^2) =
a^3+a^2b+ab^2-ba^2-b^2a-b^3 =
a^3+(a^2b-ba^2)+(ab^2-b^2a)-b^3 =
a^3+0+0-b^3 =
a^3-b^3
→ Using this checker, we can see that 36 is not a cube root because it cannot be factored as the difference between two perfect cubes.
Solve
v^3 - 36 = 0
v^3 = 36
v = ∛36
what is -3 to the -3 power
Answer:
-0.03
Step-by-step explanation:
[tex]3^{-3}=\frac{1}{3^3}\\=-\frac{1}{3^3}\\3^3=27\\=-\frac{1}{27}\\= -0.03[/tex]
please help!. i'll give 50 brainly points
Daniel’s parents were planning a big birthday party for him.
His parents spent $2.29 on each of 8 goodie bags. How much did they spend on goodie bags? Show your work.
They spent $160 to rent a bounce house for 8 hours. How much is the hourly rate for the rental? Show your work.
If the parents spent a total of $209.48 on the party, how much more did they spend than what was spent in parts (a) and (b)? Show your work.
show your work on each questions please!
Answer: A. 18.32
B. 20
C. 31.16
Step-by-step explanation:
2.29 times 8=18.32 dollars spent on goodie bags
160 divided by 8=20 dollars per hour
160+18.32=178.32
1209.48-178.32= 31.16 more than what was spent in parts a and b.
3.18 + 2m = 12.7 how do you do this?
Answer:
Step-by-step explanation:
If you're solving for m:
3.18 + 2m = 12.7
-3.18 -3.18
Therefore making the new equation: 2m = 9.52
Divide- [tex]\frac{2m}{2\\} =\frac{9.52}{2}[/tex]
m = 4.76
I need help solving this problem
((5-3)(2))÷2x2
Answer:
1
Step-by-step explanation:
because (5-3)=2 (2) means multiply the two 2's then divided by (2x2) so, (2x2)/(2x2) would be 4/4 = 1
The number of buckets of paint n needed to paint a fence varies directly with the total area a of the fence and inversely with the amount of paint p in a bucket. It takes three 1 -gallon buckets of paint to paint 72 square feet of fence. How many 1-gallon buckets will be needed to paint 90 square feet of fence?
Approximately 1 gallon of 4 buckets will be needed to paint 90ft²of fences.
Formula used: N = kA / p
Given information:
N = 3 (buckets)k = constantA = area that is72p = components of a bucket (1 gallon in this case)So,
Determine k.
This is something you must work out with the units when solving for k.
3 buckets = k × 72 ft^2/1 gallon3 buckets × 1 gallon = k × 72 ft²3 bucket gallons / 72 ft² = k k = 1/24 bucket gallons / ft² = kThen, we get:
k = 0.04166666666 × bucket gallons / ft² = kNow, solve for 90 ft² as follows:
n = k × Area / pp = 1k = 0.04166666Area = 90So,
n = 0.041666666 × 90 / 1n = 3.75 bucketsAfter rounding off, the answer will be 4 buckets of 1-gallon.
Therefore, approximately 1 gallon of 4 buckets will be needed to paint 90ft²of fences.
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99999999999999999999999999999999999999999999999999999999999999999999999x0
Answer:
Stop please. You use brainly for answering and asking questions.
What is the value of each logarithm?
c. log₆₄1/32
The value of given logarithm log₂⁶(1/32) is -5/6
The properties of log square measure wont to expand one log into multiple logs (or) compress multiple logarithms into one logarithm.A log is simply in a different way of writing exponents. Thus, the properties of logarithms square measure derived from the properties of exponents.There square measure four necessary index properties that square measure listed below:logₐ mn = logₐ m + logₐ n (product property)logₐ m/n = logₐ m - logₐ n (quotient property)logₐ mn = n logₐ m (power property)We have given a logarithm log₂⁶(1/32) .
Using base change property which is given by
[tex]log_b^na^m=\frac{m}{n} log_ba[/tex]
The given logarithm becomes -
log₂⁶(1/32) = 1/6 log₂(1/32)
Using quotient property which is given by
logₐ m/n = logₐ m - logₐ n
The given logarithm becomes -
1/6 log₂(1/32) = 1/6 [ log₂1 - log₂32]
= 1/6 [ 0 - 5 ]
= -5/6
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Expand:-
100x+10y+z
Please tell the answer and process too.
Answer:
−100x +10y+z
Step-by-step explanation:
I use the Expand Using Sum/Difference Formulas. When I plug in -100x + 10y +z it gives out the same thing.
The table shows the starting and ending elevations of a hiking trail starting point 180 ft below sea level ending point 260 above sea levelhow much greater is the elevation of the ending point than the starting point
The difference on the change of elevation is 440 feet.
How to illustrate the information?From the information, it was stated that the hiking trail starting point is 180 ft below sea level and that the ending point is 260 above sea level.
Therefore, the difference in the change will be:
= Ending level - Starting level
= 260 - (-180)
= 260 + 180
= 440 feet
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10. Justin goes to the mall with $120. He spends $54.67 on clothes. $13.49 on school supplies, and $8.14 on lunch. How much does he have left?
Answer:$43.70
Step-by-step explanation:
120−54.67−13.49−8.14
=$43.70
Answer:
43.7
Step-by-step explanation:
120-54.67-13.49-8.14=43.7$
What is the simplified value of (1/64)⁻¹/₆ ?
Express 64 as a product of its prime factors. The indices rule states
a^-n= 1/a^n. Apply the power rule (a^m)^-n= a^(-mn).
64 = 2x2x2x2x2x2 = 2^6
(1/2^6) = 2^-6
2^(-6x-1/6) = 2^(6x1/6) = 2^1
2^1 = 2
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The telephone company offers two billing plans for local calls. Plan 1 charges $33 per month for unlimited calls and Plan 2 charges $16 per month plus $0.05 per call.
A use an inequality to find the number of monthly calls for which Plan 1 is more economical than plan 2
B. Explain the meaning of the answer to part A
Answer:
Part A
Plan 1
33
Plan 2
0.05x+16
0.05x+16=33
0.05x=17
17/0.05=340
341 calls would be enough.
Part B
AN easy way of doing this is by setting the equations equal to each other and then adding a variable to one side that would be the amount of calls made on plan B. Once you get rid of the initial price of 16 dollars, then you have 17 dollars to be set equal to plan B. You divide 17 by 0.05, which gives you 340, meaning that to make both plans equal to each other, you would have to make 340 calls. To make Plan 1 more economical, you would have to add 1 more call to set plan 2 0.05 cents more than Plan 2.
Step-by-step explanation:
Solve each equation. 2log x=-4
The value of x for the given logarithmic equation 2㏒x = -4 is x = 0.01.
What is logarithmic equation?A logarithmic equation contains the log of a variable-containing representation. To begin dealing with exponential equations, check to see if both sides of a equation can be described as powers of a exact number.
The ㏒x function has the following properties:
Product Rule : ㏒A + ㏒B = ㏒(AB)Quotient Rule: ㏒(A/B) = ㏒A - ㏒BPower Rule: n㏒A = ㏒AⁿNow, as per the given question;
The given equation is 2㏒x = -4.
Divide both side by 2.
㏒x = -2
Again, rewrite this function ㏒x = -2 in the exponential form by implementing properties of ㏒.
Let x and a be the positive real numbers such that a ≠ 1, then,
㏒ₐx = y is equivalent to [tex]a^{y}[/tex] = x.
Then,
10⁻² = x
Now, solve the value of x.
x = 1/100
x = 0.01 in the decimal form.
Therefore, the obtained value of the logarithmic function 2㏒x = -4 is x = 0.01.
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The area of a rectangle with a length 2 feet less than 3 times its width.
Write a function rule for the area.
What is the area of the rectangle when its width is 2 feet?
The area of the given rectangle is 6ft².
What is a rectangle?A rectangle is a quadrilateral with four right angles in the Euclidean plane. It can also be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides.So, length 2 feet less than 3 times its width:
When the width is 2ft.Then function: L = 3w - 2
L = 3w - 2L = 3(2) - 2L = 6 - 2L = 4 ftNow, the area of the rectangle: l × w
l × w4 × 26ft²Therefore, the area of the given rectangle is 6ft².
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Find the value of a^2+b when a=-2 and b=5
Answer:
answer is 9
Step-by-step explanation:
a*a+b.
-2*-2+5.
4+5=9
The function g(x) shown in the table below is a linear function. Find its slope, y-intercept, and formula in
slope-intercept form.
Answer:
see explanation
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 9, 31) and (x₂, y₂ ) = (15, - 41) ← 2 ordered pairs from the table
m = [tex]\frac{-41-31}{15-(-9)}[/tex] = [tex]\frac{-72}{15+9}[/tex] = [tex]\frac{-72}{24}[/tex] = - 3
the y- intercept is the value of g(x) when x = 0 , then from the table
y- intercept = 4
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept ) , then equation is
y = - 3x + 4
PLEASE HELP!! 20 points
The order of transformation which best describes how to sketch the graph of h(x) = ∛1 - x is: A. Starting with the graph of the basic function y = ∛x, horizontally shift the graph to the left one unit, and then reflect the graph about the y-axis.
The types of transformation.Generally, there are different types of transformation and these include the following:
RotationTranslationDilationReflectionWhat is a reflection?A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.
In this context, we can reasonably infer and logically deduce that the order of transformation which best describes how to sketch the graph of h(x) = ∛1 - x is to start by plotting the graph of the basic function y = ∛x, and then horizontally shift the graph of function y = ∛x to the left one unit, and then reflect the graph about the y-axis.
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Complete Question:
Which of the following order of transformations best describes how to sketch the graph of h(x) = ∛1 - x?
A. Starting with the graph of the basic function y = ∛x, horizontally shift the graph to the left one unit, and then reflect the graph about the y-axis.
B. Starting with the graph of the basic function y = ∛x, vertically shift the graph up one unit, and then reflect the graph about the y-axis.
C. Starting with the graph of the basic function y = ∛x, horizontally shift the graph to the left one unit, and then reflect the graph about the x-axis.
D. Starting with the graph of the basic function y = ∛x, horizontally shift the graph to the right one unit, and then reflect the graph about the y-axis.
f(x)=10 x-10 . Find each value.
(f⁻¹ ⁰ f)(0.2)
An inverse function is one that reverses the action of another function.
The value of this function is y = 0.2.
What is meant by inverse ?Inverse operations are mathematical manipulations in which one operation reverses the action of the other, such as addition and subtraction, multiplication and division. In most cases, the inverse of a number is its reciprocal, i.e. [tex]x ^{- 1[/tex] = 1 / x. A number and its inverse (reciprocal) product equals one.
An inverse function is one that reverses the action of another function. A function g is the inverse of a function f if and only if y = f(x) and x = g. In other words, using f and then g is equivalent to doing nothing.
Let the given function be f(x) = 10x - 10
substitute the value of x = 0.2, then we get
f(0.2) = 10(0.2) - 10
simplifying the above equation be
f(0.2) = -8
y = 1/10(-8) +1
y = 0.2
Therefore, the value of y = 0.2.
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