After solving the algebraic expression a(b-c)-b(a+c)-c(a-b) we get the equivalent answer as ₋2(ab ₊ ac).
What is equivalent of algebraic expression?
Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
Given the expression is a(b₋c)₋b(a₊c)₋c(a₋b)
The first step is to multiply the terms.
⇒(a×b ₋ a×c) ₋ (b×a ₊ b×c) ₋ (c×a - c×b)
= (ab ₋ ac) ₋ (ba ₊ bc) ₋ (ca ₋ cb)
Now open the brackets.
= ab ₋ ac ₋ ba ₋ bc ₋ ca ₊ cb
Now comes main step of combining the like terms.
Put similar terms together on both sides of the equation.The two phrases are equal if each of the terms in both of them is the equivalent.
= ab ₋ ba ₋ ac ₋ ca ₋ bc ₊bc
Since, bc is a like term with opposite sign, therefore bc gets cancelled.
= ab ₋ ba ₋ ac ₋ ca
= ₋2ab ₋ 2ac
Take 2 as a common term from both the terms.
= ₋2(ab ₊ ac)
Hence we get the required equivalent of a(b-c)-b(a+c)-c(a-b) as
₋2(ab ₊ ac)
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Classify the polynomial by its degree and number of terms
n³ - 12n² + 6m² n²
Answer: It’s a trinomial
Step-by-step explanation: It has three terms, so it’s classified as a trinomial. (Tri=three)
Use factoring by grouping to completely factor the following.
4x^3−3x^2−36x+27=
Answer: 3 answers
Step-by-step explanation:
If arc mAD = 103°, and arc mBC = 115°, what is m∠BEC?
Applying the angles of intersecting chords theorem, m∠BEC = 109°.
What is the Angles of Intersecting Chords Theorem?According to the angles of intersecting chords theorem, the measure of angle BEC equals half the sum of the measures of arcs AD and BC.
arc mAD = 103°
arc mBC = 115°
Therefore, we would have:
m∠BEC = 1/2(103 + 115)
m∠BEC = 109°
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Does anyone how to solve this sum? It’s urgent
The required value for the sum is 9580.
[tex]\frac{10000}{(1+\frac{0.115}{4})^2}+68\frac{1-\frac{1}{(1+\frac{0.115}{4})^2}}{\frac{0.115}{4}}[/tex]
Simplification in mathematics to solve the given condition on its operators.
[tex]\frac{10000}{(1+\frac{0.115}{4})^2}+68\frac{1-\frac{1}{(1+\frac{0.115}{4})^2}}{\frac{0.115}{4}}[/tex]
= [tex]\frac{10000}{1.028^2} +68*\frac{1-\frac{1}{1.028^2} }{\frac{0.115}{4} } \\9451+68*\frac{1-0.94}{\frac{0.115}{4} } \\\\9451+68*\frac{0.054}{\frac{0.115}{4} } \\\\\\9451+3.72{\frac{4}{0.115} } \\\\\\9451+129\\[/tex]
= 9580
The required solution is given as 9580.
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a survey of 504 citizens found that 378 of them favor a new bill introduced by the city. We want to find a 95% confidence interval for the true proportion of the population who favor the bill. What is the lower limit of the interval? (Round to 3 decimal digits)
The lower limit of the interval is 0.712 if the survey of 504 citizens found that 378 of them favor a new bill introduced by the city.
What is a confidence interval?It is defined as the sampling distribution following an approximately normal distribution for known standard deviation.
We have:
A survey of 504 citizens found that 378 of them favor a new bill introduced by the city.
Sample proportion = p = 378/504 = 0.75
q = 1 - p = 1 - 0.75 = 0.25
[tex]\rm SD = \sqrt{\dfrac{pq}{n}}[/tex]
[tex]\rm SD = \sqrt{\dfrac{0.75\times0.25}{504}}[/tex]
SD = 0.01928
For 95% confidence interval Z value = 1.96
Lower limit = 0.75 - 1.96(0.01928)
= 0.712
Thus, the lower limit of the interval is 0.712 if the survey of 504 citizens found that 378 of them favor a new bill introduced by the city.
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If m∠B = 14°, and m∠D = 49°, what is m∠BEA?
Answer:
117 degrees
Step-by-step explanation:
The Nutty Professor sells cashews for $7.40 per pound and Brazil nuts for $4.80 per pound. How much of each type should be used to make a 28 pound mixture that sells for $6.19 per pound?
Answer:
cos4B =1-8sin^2(B)+8sin^4(B)
Step-by-step explanation:
cos4B =1-8sin^2(B)+8sin^4(B)
Write a two-column proof.
Given: 7y = 8x – 14; y = 6
Prove: x = 7
1) [tex]7y=8x-14, y=6[/tex] [given]
2) [tex]7(6)=8x-14[/tex] [substitution]
3) [tex]56=8x[/tex] [addition property of equality]
4) [tex]7=x[/tex] [division property of equality]
5) [tex]x=7[/tex] [symmetric property of equality]
A two columns proof is given in the attached image below as per the concept of solving equations.
A two columns proof is given below:
Statement | Reasons
y = 6 | Given
7y = 8x - 14 | Given
7(6) = 8x - 14 | Substitution (Substitute y with 6 in statement 2)
42 = 8x - 14 | Simplification
42 + 14 = 8x | Addition Property of Equality (Add 14 to both sides)
56 = 8x | Simplification
56/8 = x | Division Property of Equality (Divide both sides by 8)
7 = x | Simplification (Simplify the fraction 56/8)
x = 7 | Symmetric Property of Equality (Rearrange statement 9)
In this two-column proof, we start with the given information that y is equal to 6 (statement 1).
Then, we substitute the value of y into the equation 7y = 8x - 14 (statement 2) to get 42 = 8x - 14 (statement 3).
We simplify the equation to isolate 8x and find that 56 = 8x (statement 6). Dividing both sides of this equation by 8 (statement 7) gives us x = 7 (statement 8).
Finally, we use the symmetric property of equality to rearrange the equation and conclude that x is indeed equal to 7 (statement 9).
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Let [] denote the operation a [] b = a+b - [tex]\frac{ab}{2}[/tex] ....
The only statement that holds for the given operation is Statement II
Operations and numbersGiven the following operartions
a [] b = a+b - ab/2
We need to check the true statement
For the expression x [] (y+z) = x [] y + x [] z
x [] (y+z) = x+y+z - x(y+z)/2
x [] (y+z) = x+y+z - (xy+xz)/2
x [] y +x [] z = x+y - xy/2 +[x+z - xz/2 ]
x [] y +x [] z = x+y+x+z -xy/2 - xz/2
x [] y +x [] z = 2x+y+z - (xy+xz)/2
This shows that the statement I is incorrect
For the second statement
y [] z = y+z - yz/2
x [] (y [] z) = x + (y+z - yz/2) - x(y+z-yz/2)/2
x [] (y [] z) = x+y+z-yz/2 -xy/2 - xz/2+xyz/4
For the other expression
x [] y = x+y - xy/2
(x [] y) [] z = x+y - xy/2 + z - z(x+y - xy/2)/2
(x [] y) [] z = x+y+z- xy/2 -zx/2 - zy/2 + xyz/4
This shows that x [] (y [] z) = (x [] y) [] z is correct (Statement II)
For the third statement
x [] z = x+z - xz/2
y [] z = y+z - yz/2
z [] 0 = z+0 - z(0)/2
z [] 0 = z
x[]z + y[]z - z[]0 = x+z - xz/2 + y+z - yz/2 - z
x[]z + y[]z - z[]0 = x+y+z - xz/2 - yz/2
For the expression (x+y)[] z
(x+y)[] z = (x+y)+z - (xyz)/2
Hence the statement III is not valid
Based on the explanations above, the only statement that holds for the given operation is Statement II
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what is the vertex form of y=2x^2+8x+1
Answer:
So, the vertex form of your function is [tex]y(x)=2*(x+2)^2-7[/tex].
The vertex is at [tex](-2|-7)[/tex]
Step-by-step explanation:
Given function:
[tex]y(x)=2*x^2+8x+1[/tex]
Steps:
[tex]y(x)=2*x^2+8x+1\\[/tex]
[tex]y(x)=2(x^2+4x+\frac{1}{2} )[/tex] (Factor out)
[tex]y(x)=2(x^2+4x+2^2-2^2+\frac{1}{2} )[/tex] (Complete the square)
[tex]y(x)=2((x+2)^2-2^2+\frac{1}{2} )[/tex] (Use the binomial formula)
[tex]y(x)=2((x+2)^2-\frac{7}{2} )[/tex] (Simplify)
[tex]y(x)=2*(x+2)^2-7[/tex] (Expand)
Consider a banking system where the Federal Reserve uses required reserves to control the money supply. (This was the case in the U.S. prior to 2008.) Assume that banks do not hold excess reserves and that households do not hold currency, so the only form of money is demand deposits. To simplify the analysis, suppose the banking system has total reserves of $400. Determine the money multiplier and the money supply for each reserve requirement listed in the following table.
The determination of the money multiplier and the money supply for each reserve requirement listed in the following table are as follows:
Reserve Requirement Simple Money Money Supply
(percent) Multiplier (Dollars)
5 20 $8,000
10 10 $4,000
What is the money multiplier?The money multiplier is the ratio of the reserve to the money supply.
The formula for determining the money multiplier is 1/r where r is the reserve ratio.
What is the money supply?The money supply is the total amount of money circulating in the commercial banking system.
The quantity of the money supply is determined by multiplying the money multiplier by the total reserves.
Data and Calculations:Reserve Requirement Simple Money Money Supply
(percent) Multiplier (Dollars)
5 20 (1/0.05) $8,000 ($400 x 20)
10 10 (1/0.1) $4,000 ($400 x 10)
Question Completion:
Reserve Requirement Simple Money Money Supply
(percent) Multiplier (Dollars)
5
10
Thus, the money multiplier and money supply for the 5% reserve requirement are higher than for the 10% reserve requirement.
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what is the inverse of this function? f(x)=-1/2 square root of x+3, x > -3
The inverse function of [tex]f(x) = -\frac 12\sqrt{x + 3}[/tex] is[tex]f^{-1}(x) = 4x^2- 3[/tex]
How to determine the inverse function?The function is given as:
[tex]f(x) = -\frac 12\sqrt{x + 3}[/tex]
Rewrite as;
[tex]y = -\frac 12\sqrt{x + 3}[/tex]
Swap the positions of x and y
[tex]x = -\frac 12\sqrt{y + 3}[/tex]
Multiply through by -2
[tex]-2x = \sqrt{y + 3}[/tex]
Square both sides
4x^2 = y + 3
Subtract 3 from both sides
y = 4x^2 - 3
Express as an inverse function
[tex]f^{-1}(x) = 4x^2- 3[/tex]
Hence, the inverse function of [tex]f(x) = -\frac 12\sqrt{x + 3}[/tex] is[tex]f^{-1}(x) = 4x^2- 3[/tex]
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z varies directly as x^3 and inversely as y^3. if z=59 when x=8 and y=8, find Z if x=3 and y=4
[tex]z=\dfrac{kx^3}{y^3}\\\\\\59=\dfrac{k\cdot 8^3}{8^3}\\k=59\\\\\\z=\dfrac{59x^3}{y^3}\\\\\\z=\dfrac{59\cdot 3^3}{4^3}=\dfrac{1593}{64}[/tex]
What is the product of the following equation??
Answer:
B
Step-by-step explanation:
1.(5x^3)(xy^4 -2x^3y)
2.5x^4y^4 -10x^6y
Solve
f(x)= 2x -13
g(x) = x^2 - 6x + 3
Answer:
just hey effect me II rieirjttjhg shewtha
Find the following sums ( for letter C)
Each number in the sum is even, so we can remove a factor of 2.
2 + 4 + 6 + 8 + ... + 78 + 80 = 2 (1 + 2 + 3 + 4 + ... + 39 + 40)
Use whatever technique you used in (a) and (b) to compute the sum
1 + 2 + 3 + 4 + ... + 39 + 40
With Gauss's method, for instance, we have
S = 1 + 2 + 3 + ... + 38 + 39 + 40
S = 40 + 39 + 38 + ... + 3 + 2 + 1
2S = (1 + 40) + (2 + 39) + ... + (39 + 2) + (40 + 1) = 40×41
S = 20×21 = 420
Then the sum you want is 2×420 = 840.
Determine the slope of the line that contains the given points
J(-5, -2), K(5, −4)
Answer:
[tex]-\frac15[/tex]
Step-by-step explanation:
Hello!
We can utilize the slope formula to find the slope.
Slope Formula: [tex]S = \frac{y_2-y_1}{x_2-x_1}[/tex]
Remember that a coordinate is written in the form (x,y)
Find the Slope[tex]S = \frac{y_2-y_1}{x_2-x_1}[/tex][tex]S = \frac{-4-(-2)}{5-(-5)}[/tex][tex]S = \frac{-2}{10}[/tex][tex]S = -\frac15[/tex]The slope of the line is [tex]-\frac15[/tex].
Answer:
-1/5
Step-by-step explanation:
To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)
Plug in these values:
(-4 - (-2)) / (5 - (-5))
Simplify the parentheses.
= (-4 + 2) / (5 + 5)
= -2 / 10
Simplify the fraction.
-2/10
= -1/5
This is your slope.
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sin A - sin B - sin C=-4cos A 2 .sin B 2 .sin C 2
sinA+sinB+sinC
=2sin(A+B)/2cos(A-B)/2+sin C
=2sin(pi-C)/2cos(A-B)/2+2sin C/2cosC/2
=2cosC/2(cos(A-B)/2+cos(A+B)/2)
=4 cos A/2 cos B/2 cos C/2
= RHS
8. A school cafeteria
purchased 256
hotdogs, 332 apples,
and 154 cookies. How
many items did they
purchase in all?
the school purchased 742 items in total.
Just add 256+332+154
which equals...742. :)
Answer:
742 items
Step-by-step explanation:
Add up all the items that the cafeteria purchased. 256+332+154=742!
please help me im d-mb
Answer:
5621 years
Step-by-step explanation:
Plug everything in first.
[tex]N=N_0e^{-kt}\\\\\implies 0.57 = e^{-0.0001t}\\\\\implies\ln \left(0.57\right)=-0.0001t\\\\t=-\frac{\ln \left(0.57\right)}{0.0001}[/tex]
Round to closest amount of years = 5621 years
Question 6 of 10
If and
A.D
BD B.C
are rational expressions, then:
OA. True
OB. False
The expression a/b ÷ c/d = ad/bc is A. true.
Given to show that if a/b and c/d are rational expressions, then a/b ÷ c/d = ad/bc.
The ratio of two polynomials is an example of a rational expression. If an expression f is rational, it can be expressed in the form p/q, where p and q are polynomials.
Here we have a ,b ,c and d in the form of p/q form.
We take the reciprocal of the expression on the right side of the division sign when the rational expression a/b is to be divided by the rational expression c/d.
so, L.H.S = a/b ÷ c/d
= a/b × 1/(c/d)
= a/b × d/c
= ad/bc
= R.H.S
since L.H.S = R.H.S
a/b ÷c/d = ad/bc
Hence the expression a/b ÷ c/d = ad/bc is A.true.
Your question was incomplete. Please find the missing content here.
If A/B and C/D are rational expressions, then: A/B ÷C/D
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Enter the correct answer in the box.
The function (x)=7*+1 is transformed to function g through a horizontal compression by a factor of 3. What is the equation of function g?
Substitute a numerical value for k into the function equation.
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The equation of function g is f(x) = 7^3x + 1
How to determine the function g(x)?The function f(x) is given as:
f(x) = 7^x + 1
The rule of horizontal compression by a factor of 3 is represented as
g(x) = f(kx)
Where k = 3
So, we have:
f(x) = 7^3x + 1
Hence, the equation of function g is f(x) = 7^3x + 1
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This is from Khan academy I have to attach a PNG if you can help me solve it! Thank you!
49^2m-m : Not equivalent
7^2m-2m : Not equivalent
7^2m-m : Not equivalent
This is actually a trick question. All of the following are actually false statements. Want to know why? Let me show you.
For exponents, if you are dividing a number to some power (i.e 5^3) by the SAME number to a different power (i.e 5^2), then the expression is 5^3-2 or 5^1 = 5. This is true for any number a such that a^b ÷ a^c = a^b-c.
Since 7 and 49 are not the same number, this rule does not apply and thus cannot be simplified any further.
Let me prove why. 5^3 = 125, and 5^2 = 25, and 125 ÷ 25 = 5. This is also the same as 5^3-2 = 5^1 = 5. We just proved this as so.
But, what about 7 and 49, or 2 different numbers. Well it doesn't apply. 7^3 = 343, and 49^2 = 2401, and 343 ÷ 2401 ≈ 0.14. Thus, this is NOT equal to 7^3-2 which is 7. We just proved that a^y ÷ b^z ≠ a^y-z. Congratulations!
Hope this helped!
−5 = s−9. what is s?
Answer:
S= 4
Step-by-step explanation:
add 9 to -5
= 4
s=4
Which is the equation in slope-intercept form for the line that passes through (−1, 5) and is parallel to 3x + 2y = 4?
y=−23x+72
y=−32x+72
y=32x−72
y=23x+72
Answer:
[tex]y=-\frac{3}{2}x+\frac{7}{2}[/tex]
Step-by-step explanation:
So when two lines are parallel there slopes are the same, but there y-intercepts are different, since if they had the same y-intercept, then they would be the same exact line. To convert an equation into slope-intercept form you simple isolate y by moving everything else to the other side, and then divide by the coefficient of y so the coefficient of y becomes 1. This will give you the equation in the form: y=mx+b where m is the slope and b is the y-intercept (because when the linear equation crosses the y-axis, the x is 0, thus mx will be 0, leaving only b, so the y-intercept is b).
Original Equation:
3x + 2y = 4
Subtract 3x from both sides
2y = -3x + 4
Divide both sides by 2
y = -3/2x + 2
Generally any parallel line will be in the form:
[tex]y=-\frac{3}{2}x + b\ \ \ \ \ b\ne2[/tex]. Since as stated before if two lines have the same slope and y-intercept, they're the same line, which is not the same as parallel, since parallel lines never intersect.
So since we're given a point in the parallel line (-1, 5) we can plug those values into the equation to find the value of b
[tex]5=-\frac{3}{2}(-1) + b[/tex]
Multiply and
[tex]5=\frac{3}{2}+ b[/tex]
Convert 5 into a fraction with a denominator of 2
[tex]\frac{5}{1} * \frac{2}{2} = \frac{10}{2}[/tex]
Write equation using this form of 5:
[tex]\frac{10}{2}=\frac{3}{2}+b[/tex]
Subtract 3/2 from both sides
[tex]\frac{7}{2}=b[/tex]
Now take this value and input it into the slope-intercept form to finish the equation: [tex]y=-\frac{3}{2}x+\frac{7}{2}[/tex]
You’re involved in the design of a new facility. It is important for people to move between work stations quickly. Based on the figure below, how many feet would a person need to walk to get from Work Station 1 to Work Station 3?
Answer:
13 feet
Step-by-step explanation:
A^2 + B^2 = C^2
A=5 ^2 = 25
B=12 ^2 = 144
144 +25 = 169
C=13
There are red and blue files in a box. The ratio of red to blue tiles is 3:5. There are 12 more blue tiles than red tiles in the box. How many red tiles are in the box? There are red and blue files in a box . The ratio of red to blue tiles is 3 : 5 . There are 12 more blue tiles than red tiles in the box . How many red tiles are in the box ?
The number of red tiles in the box given the chance ratio of red to blue tiles is 18
RatioNumber of red tiles = xNumber of blue tiles = 12 + xTotal tiles = x + 12 + x= 12 + 2x
Ratio of red = 3Ratio of blue = 5Total ratio = 3 + 5 = 8Number of red tiles = 3 / 8 × 12+2x
x = 3(12 + 2x) / 8
x = (36 + 6x) / 8
8x = 36 + 6x
8x - 6x = 36
2x = 36
x = 36/2
x = 18 tiles
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Answer: 28
Step-by-step explanation:
If there are 3 liquids in a Density column, which liquid would be the least dense?
The liquid on the bottom of the column.
The liquid floating on the top.
The liquid in between the liquid on the top of the column and the liquid on the bottom layer of the column.
The liquid that will be the least dense liquid in the density column is; The liquid floating on the top.
How to identify least dense liquid?
The formula for density is;
Density = Mass/Volume
Thus, the greater the mass, the more the density. Thus, it means that heavier objects will sink while lighter ones will float.
Thus, this means that the liquid that is most dense will be at the bottom of the liquid.
The liquid that is least dense will be at the top of the liquid.
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Sin (5x-25) = COS (3x)
X=?
Answer:
x=23
Step-by-step explanation:
put it in desmos and was right
need help with this question
Answer:
[tex]f(x) = a(x^2+4)(x-3)^2[/tex]
Step-by-step explanation:
So I'm assuming it means that one of the zeros is at x=3 with a multiplicity of 2 and it has an imaginary solution of 4i. Anyways, imaginary solutions come in conjugate pairs meaning if you have a complex solution of [tex]a-bi[/tex] there is another complex solution which is the conjugate of that which is [tex]a+bi[/tex] but since the imaginary solution is 4i, the complex number is just [tex]0+4i[/tex] so the conjugate is [tex]0-4i[/tex] or [tex]-4i[/tex]. So since you have x=3 as a zero that can be represented as [tex](x-3)^2[/tex] since 3 would make it 0 and it has a multiplicity of 2. As for the other factors, you won't just have ([tex](x-4i)(x+4i)[/tex], you'll have a factor that is set up in a way that the solutions are: [tex]x=\pm\sqrt{-4}[/tex]. That means it'll be a quadratic. So it'll be in the form [tex]x^2+b[/tex]. Since you're moving b to the other side and it's negative. that means it has to be positive and since the value is 4, you'll have the factor [tex](x^2+4)[/tex] which when set equal to zero has the solutions sqrt(-4). So this gives you the equation
[tex]f(x) = a(x^2+4)(x-3)^2[/tex]