Answer:
y+2= -4(x-8)
Step-by-step explanation:
Carefully follow the steps to find the solution to the three equation system.
1.2x+y+3:= 12
2. x-2y+z=-5
3.5.x- y+ 2z = 5
a. Use equations 2 and 3 and eliminate the z by multiplication and addition, creating a new equation with only two variables.
b. Use equations 1 and 2 and eliminate the z by multiplication and addition, creating a second equation with only two variables.
c. Use the two new equations, and eliminate the x-variable by multiplication and addition, finding the value for the y-variable.
d. Substitute y-value in the second new equation and find the x-value.
e. Substitute the z-and y-values into original equation 2 to find the z-value
Answer:
This answer assumes that the first equation is meant to read:
2x + y +3z = 12, and not
1.22x+y+3:= 12
Spoiler Alert: x = 1, y=4, and z=2
Step-by-step explanation:
1. 2x + y +3z = 12
2. x - 2y + z = -5
3. 5x - y+ 2z = 5
==============
Use equations 2 and 3 to eliminate z:
2. x - 2y + z= -5
3. 5x - y+ 2z = 5
-2(x - 2y + z) = -2(-5) [Multiply equation 2 by -2]
5x - y+ 2z = 5
Now subtract this new equation from equation 3:
-2x + 4y - 2z = 10 (Eq 3)
5x - y+ 2z = 5 [
3x +3y = 15 [Equation A]
=================
Use equations 1 and 2 to eliminate z:
2x + y +3z = 12 (Eq. 1)
x - 2y + z = -5 (Eq. 2)
2x + y +3z = 12
(-3)(x - 2y + z = -5) [Multiply Eq. 2 by (-3)]
-3x + 6y -3z = 15
Now add the resulting two equations.
2x + y + 3z = 12 (Eq. 1)
-3x + 6y -3z = 15 (Eq,2 times -3)
-x +7y = 27 [Equation B]
=============
Eliminate x with the 2 resulting equations (from above)
3x +3y = 15 [Equation A]
-x +7y = 27 [Equation B]
----
3x +3y = 15
3*(-x +7y = 27) [Multiply the Equation B by 3]
-3x +21y = 81 [Aha - this equation has a -3x term, exactly what we need to eliminate the x term in Equation A]
---
Now add the two resulting equations:
3x +3y = 15
-3x +21y = 81
24y = 96 [The x term disappears. But we'll "find x" later]
y = 4 [Divide both sides by 24]
Find y and z:
Since y = 4,
-x +7y = 27 (From above, Equation B]
-x = -7y + 27
x = 7y - 27
x = 7(4)-27
x = 1 [Looking good]
=====
Find z: (Use y = 4 and x = 1)
x - 2y + z = -5 [Equation 2]
(1) -2*(4) + z = -5
1 - 8 + z = -5
z = 2
Check:
Do the original equations work when x = 1, y = 4, and z = 2?
Results:
1. 2x + y +3z = 12
(1) + (4) +3(2) YES, this equals 12
2. x - 2y + z = -5
(1) -2*(4) + (2) YES, this equals -5
3. 5x - y+ 2z = 5
5(1) - (4) + 2(2) YES, this equals 5
x = 1, y=4, and z=2
a city's monthly precipitation amounts, in inches, for the last two years are recorded in the table. which histogram corresponds to the table?
Based on the given histograms, and the table on the city's monthly precipitation amounts, the histogram that corresponds to the table is Histogram 1.
Which histogram is the appropriate fit?The number of months with 0 - 1.992 inches is 8 months which means that the first bar on the histogram of between 0 to 2 inches should reach the 8 month mark.
6 months had 1.992 - 3.994 inches so the next bar should stop at the 6th month mark. The next bar should stop at the 4 month mark.
The one after that should stop at the 5 month mark. The last bar would stop at the 1 month mark.
The only histogram that has this is histogram 1 which is not shown clearly but it likely the only one with these qualities as the others don't have it.
Rest of the question:
Amount (inches) 0 - 1.992 - 3.99 4 -5.996 - 7.998 - 9.99
Number of Months 8 6 4 5 1
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The Volume of a cube depends on the length of its sides.This can be written in function notation as v(s).What is the best interpretation of V(3)=27
Answer and Step-by-step explanation:
There is a cube with side length 3. The volume of this cube is 27.
Help please I'll mark you as brainlist if the answer is correct
if (x + q) is a factor of two polynomials x2 + px + q and x2 + mx + n, then prove that a = n-q m-p
If (x + q) is factor of two polynomial [tex]x^2+px+q[/tex] and [tex]x^2+mx+n[/tex] than [tex]a = \frac{n - q}{m- p}[/tex].
x + a is factor of equations [tex]x^2+px+q[/tex] and [tex]x^2+mx+n[/tex]
What is a polynomial equation?Polynomial equation is equation of independent variables.
Putting it in both the equations
[tex]x^2+px+q=0[/tex]
[tex](-a)^2+p(-a)+q=0\\a^2-ap+q=0 ........(1)[/tex]
[tex]x^2+mx=n = 0\\(-a)^2+m(-a)+n=0\\a^2-am+n=0 .....(2)[/tex]
subtracting (2) from (1)
[tex]-am+ap+n-q=0[/tex]
[tex]a=\frac{n-q}{m-p}[/tex]
Thus, the required expression is [tex]a=\frac{n-q}{m-p}[/tex].
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can someone please help and explain these problems ??
Answer:
AAA
Step-by-step explanation:
yesss
what is the ratio 3:1
Answer:
3:1
Step-by-step explanation:
3 and 1 is not divisible by any number
If angle D is an acute angle and its tangent ratio is 1.055, then what is the measure of angle D to the nearest tenth of a degree?
The measure of angle D to the nearest tenth of a degree is 47 degrees
Application of SOH CAH TOAThis theorem is used to determine the measure of sides and angles of a triangle.
According to the theorem
tan theta = opp/adj = 1.055
theta = arctan(1.055)
theta = 46.53 degrees
Hence the measure of angle D to the nearest tenth of a degree is 47 degrees
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Charlie is installing new carpet in his rectangular living room, which is 5 feet longer than it is wide. He has received quotes for the total
installation costs from two different contractors for the same style of carpet.
Contractor A charges an installation fee of $125 plus $2 per square foot for the carpet.
Contractor B charges an installation fee of $75 plus $2.50 per square foot for the carpet.
Based on this information, which system of equations could be used to determine the width of the living room, x, in feet, at which the
quote for the installation costs, y, is the same for both companies?
Considering the area of a rectangle, the equation that could be used to determine the width for which the costs are the same is:
125 + 2(x² + 5x) = 75 + 2.5(x² + 5x)
What is the area of a rectangle?The area of a rectangle of length l and width w is given by the multiplication of dimensions, that is:
A = lw
In this problem, the dimensions are given as follows:
w = x, l = x + 5.
Hence the area in square feet is:
A = x(x + 5) = x² + 5x.
Then the costs are given as follows:
A(x) = 125 + 2(x² + 5x).B(x) = 75 + 2.5(x² + 5x).The costs will be equal when:
A(x) = B(x)
125 + 2(x² + 5x) = 75 + 2.5(x² + 5x)
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Answer:
see photo
Step-by-step explanation:
Plato/Edmentum
inequalities i need help question is in picture
Answer:
19-73 19-73 is fine thanks 70-65-46 024 465 8554 48-57
Golf balls cost $0.90 each at Jerzy’s Club, which has an annual $25 membership fee. At Rick and Tom’s sporting-goods store, the price is $1.35 per ball for the same brand. Where you buy your golf balls depends on how many you wish to buy. Explain, and illustrate your reasoning with a graph.
Answer:
See attached graph.
Step-by-step explanation:
Each situation can be expressed as an equation:
Jerzy: Total Cost (y1) is the $25 membership fee plus $0.80/golf ball (x):
y1 = $25 + $0.90x
Rick and Tom's: Total Cost (y2) is $1.25 per golf ball, x.
y2 = $1.25x
See the attached graphs of these two equations. Jerzy's cost less after 56 balls are purchased.
John has 48 square centimeter tiles he wants to use to create a mosaic. He wants the mosaic to be rectangular with a length that is 2 centimeters longer than the width.
Which equation could John solve to find w, the greatest width in centimeters he can use for the mosaic?
w(w – 2) = 48
w(w + 2) = 48
2w(w – 2) = 48
2w(w + 2) = 48
The equation that could John solve to find w, the greatest width in centimeters he can use for the mosaic is option B: w(w + 2) = 48.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
The mosaic to be formed is rectangular in shape.
Area of a rectangle = length x width
The length is longer than the width by 2,
So, length = w+2
Area of a rectangle = (w+2) x w
The correct equation is B: w(w + 2) = 48
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Answer: B
Step-by-step explanation:
If f(x) = 3x^2 - x, find f(-2).
Answer:
14
Step-by-step explanation:
to find f(value), we plug that x value into the equation
so, if..
f(x)= 3x² -x
f(-2)= 3 · (-2)² - (-2)
f (-2) = 3 · 4 + 2
f (-2) = 12 + 2
f (-2) = 14
Answer:
14
Step-by-step explanation:
f(x) =3x^2-x
here,
f(-2)= 3(-2)^2 -(-2)
=3*4+2
=12+2
=14 Answer.
Find the value of x. Round the length to the nearest tenth.
Answer:
6 m
Step-by-step explanation:
[tex]sin22 = x/16\\x = 16sin22\\x = 6[/tex]
Hurry pleaeeeee show your work
117n + 90=
Answer:
n=-0.769
Step-by-step explanation:
Since there is no number after the equal sign in the equation given, we can put a zero in that place.
117n+90=0
Subtract 90 from both sides.
117n=-90
Divide 117 and -90
n=-0.769
Hope this helps!
If not, I am sorry.
Use the properties of exponents to rewrite this expression. Then evaluate the rewritten expression for the given values to
complete the statement.
(11j³k²) (³4)
When j = -8and k = 7
The value of the expression for the given values is 1294139
Evaluating an expression
From the question, we are to rewrite the expression
(11j⁻³k²) (j³k⁴)
This can be rewritten as
11 × j⁻³ × k² × j³ × k⁴
11 × j⁻³ × j³ × k² × k⁴
11 × j⁻³⁺³ × k²⁺⁴
11 × j⁰× k⁶
= 11 × 1 × k⁶
= 11k⁶
Now we are to evaluate the expression for when j = -8 and k = 7
The expression is
= 11 × k⁶
= 11 × 7⁶
= 1294139
Hence, the value of the expression for the given values is 1294139
Here is the complete question:
Use the properties of exponents to rewrite this expression. Then evaluate the rewritten expression for the given values to
complete the statement.
(11j⁻³k²) (j³k⁴)
When j = -8 and k = 7
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Answer:
539
Step-by-step explanation:
Consider an investment of $6000 that earns 4.5% interest
What is the value of the investment after
15 years if the interest is compounded
annually?
Answer:
$11,611.69
Step-by-step explanation:
Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedGiven:
P = $6,000r = 4.5% = 0.045n = 1 (annually)t = 15 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=6000\left(1+\frac{0.045}{1}\right)^{(1 \times 15)}[/tex]
[tex]\implies \sf A=6000(1.045)^{15}[/tex]
[tex]\implies \sf A=11611.69466...[/tex]
Therefore, the value of the investment after 15 years will be $11,611.69 to the nearest cent.
help help help help help
Answer:
2/3 + 9.26 is rational
:)
Use properties to evaluate 3/4(1/5÷3/5)(-8).
A. 2
OB. 5
O C. -2
OD. -5
Answer:
C. -2
Step-by-step explanation:
Use A-P-E-X
How I solved it:
3/4(1/5÷3/5)(-8)
3/4(1/5×5/3)(-8)
3/4(1/3)(-8)
1/4(-8)=-2
Hope this helps!
If not, I am sorry.
when 7 is subtracted from 3 times a certain number , the result is 28. What is the number
The number will be equal to 11.67.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
The expression will be formed from the given data. Let the number be x so the expression will be:-
3x - 7 = 28
3x = 35
x = 35 / 3
x = 11.67
Therefore the number will be equal to 11.67.
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A ration of two numbers is equal to 3:8 if the smaller number is 14 find the greatest number
Answer:
34 and ⅔
Step-by-step explanation:
added in the picture
Which best describes why the function is nonlinear? the rate of change between 1 and 2 trees is different than the rate of change between 2 and 3 trees. the rate of change between 1 and 2 trees is different than the rate of change between 1 and 3 trees. the rate of change between 2 and 3 trees is different than the rate of change between 3 and 4 trees. the rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.
The function is nonlinear because: D. the rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.
What is a nonlinear function?A nonlinear function can be defined as a type of function whose rate of change (increase or decrease) are not the same i.e they are different.
The rate of change between 2 and 3 trees is given by:
R₂₃ = (180 - 120)/(3-2)
R₂₃ = 60.
Also, the rate of change between 3 and 5 trees is given by:
R₃₅ = (290 - 180)/(5-3)
R₃₅ = 110/2
R₃₅ = 55.
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Complete Question:
A tree company charges a delivery fee for each tree purchased in addition to the cost of the tree. The delivery fee decreases as the number of trees purchased increases. The table below represents the total cost of x trees purchased, including delivery fees. Which best describes why the function is nonlinear?
The function is nonlinear because: D. the rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.
What is a nonlinear function?
A nonlinear function can be defined as a type of function whose rate of change (increase or decrease) are not the same i.e they are different.
The rate of change between 2 and 3 trees is given by:
R₂₃ = (180 - 120)/(3-2)
R₂₃ = 60.
Also, the rate of change between 3 and 5 trees is given by:
R₃₅ = (290 - 180)/(5-3)
R₃₅ = 110/2
R₃₅ = 55.
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Complete Question:
A tree company charges a delivery fee for each tree purchased in addition to the cost of the tree. The delivery fee decreases as the number of trees purchased increases. The table below represents the total cost of x trees purchased, including delivery fees. Which best describes why the function is nonlinear?
In parallelogram MNPQ if m/PQM = 140°
find m/MNP.
Answer: 140
Step-by-step explanation:
A parallelogram means the sides are parallel, so PQM would have the same angle as MNP since they are opposite, just like NPQ and QMN.
Answer: 140°
Detailed Explanation with Figure:
In a Parallelogram, the Opposite Angles are Equal. Therefore, ∠PQM = ∠MNP, which is equal to 140°.
Here’s the Figure :-
PLEASE HELP ME!
3 markers cost $5.79 Which proportion would help determine the cost of 13
markers?
A:
13/5.79=x/3
B:
x/13=3/5.79
C:
3/5.79=13/x
D:
13/x=5.79/3
E:
None of the Above
Answer:
C: 3/5.79=13/x
Step-by-step explanation:
Two ratios are said to be in proportion when the two ratios are equal
3 markers cost $5.79 in which the proportion price is unknown
13 markers cost x
markers / cost = markers / cost
3 / $5.79 = 13 / x
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helen rolls a dice and flips a coin.
calculate the probability
Answer:
1/12
Step-by-step explanation:
dice rolling=1/6
coin flipping=1/2
Hence probability=1/6×1/2
Answer:
Dice roll = 1/6
Coin flip = 1/2
what is the price of a $90 mobile phone after a 30% discount
Answer:
$ 63
Step-by-step explanation:
Let the new price ( price after the discount ) be x.
Old price Discount New price
100 30 70
90 30 x
Now we can make an expression like this to solve this
100 ⇒ 70
90 ⇒ x
Use cross multiplication to solve for x.
100x = 70 × 90
100x = 6300
Divide both sides by 100.
x = $ 63
Answer:
Discount: $27.00
Final Price: $63.00
Step-by-step explanation:
Discount = Original Price x Discount %/100
Discount = 90 × 30/100
Discount = 90 x 0.3
You save = $27.00
Final Price = Original Price - Discount
Final Price = 90 - 27
Final Price = $63.00
a Each exterior angle of a regular polygon measures 20° How many sides
does the polygon have?
Answer:
18
Step-by-step explanation:
The exterior angles of any regular polygon add to 360°, so the answer is 360/20 = 18
Calculate the following limit:
[tex]\displaystyle \lim_{x \to \infty}{\dfrac{\log(x^8 - 5)}{x^2}}[/tex]
If we evaluate at infinity, we have:
[tex]\bf{\displaystyle L = \lim_{x \to \infty}{\frac{\log(x^8 - 5)}{x^2}} = \frac{\infty}{\infty} }[/tex]
However, the infinity of the denominator has a higher order. Therefore, we can conclude that [tex]\boldsymbol{L = 0.}[/tex]
However, proving that the limit is 0 without using L'Hopital or the "order" criterion is complicated. To do so, let us denote:
[tex]\boldsymbol{\displaystyle f(x) = \frac{\log(x^8 - 5)}{x^2} }[/tex]
To find the limit, we must look for two functions h(x) and g(x) such that h(x)≤ f(x)≤ g(x) and
[tex]\boldsymbol{\displaystyle \lim_{x \to \infty}{h(x)} = 0, \qquad \lim_{x \to \infty}{g(x)} = 0}[/tex]
If we find these functions, then we can conclude that [tex]\bf{\lim_{x \to \infty}{f(x)} = 0.}[/tex]
First, let's note that when x⁸ - 5 > 1, then log(x⁸ - 5) > 0 (and this is true when x is large). Likewise, we have that x² > 0 for x > 0. Therefore, we have:
[tex]\boldsymbol{\displaystyle f(x) = \frac{\log(x^8 - 5)}{x^2} \geq 0}[/tex]
when x "is big enough". Thus, we have h(x) = 0 where it is clear that [tex]\bf{\lim_{x \to \infty}{h(x)} = 0.}[/tex]
To find the second function, let's first note that \log is an increasing function, so since x⁸ ≥ x⁸ - 5, then log(x⁸) ≥ log(x⁸ - 5). So we have to
[tex]\boldsymbol{\displaystyle \frac{\log(x^8 - 5)}{x^2} \leq \frac{\log(x^8)}{x^2} }[/tex]
now, if we take y = e^y, then we can write
[tex]\boldsymbol{\displaystyle \frac{\log(x^8)}{x^2} = \frac{\log(e^{8y})}{e^{2y}} = \frac{8y}{e^{2y}}}[/tex]
A very important property about the exponential function is
[tex]\boldsymbol{\displaystyle e^x > \frac{x^n}{n!}}[/tex]
For any n [tex]\bf{n \in \mathbb{N}}[/tex] and x > 0. If we take n = 2, then we have
[tex]\boldsymbol{\displaystyle e^{2y} > \frac{(2y)^2}{2!} = \frac{4y^2}{2} = 2y^2}[/tex]
From this it follows that
[tex]\boldsymbol{\displaystyle \frac{1}{e^{2y}} < \frac{1}{2y^2} }[/tex]
Therefore, we have to
[tex]\boldsymbol{\displaystyle \frac{\log(x^8 - 5)}{x^2} \leq \frac{\log(x^8)}{x^2} < \frac{8y}{2y^2} = \frac{4}{y} = \frac{4}{\log x} }[/tex]
yes, [tex]\bf{g(x) = 4/\log x}[/tex] where [tex]\bf{\lim_{x \to \infty}{g(x)} = 0}[/tex]. Also, [tex]\bf{h(x) \leq f(x) < g(x)}[/tex]. Therefore, [tex]\bf{\lim_{x \to \infty}{f(x)} = 0}[/tex].
[tex]\red{\boxed{\green{\boxed{\boldsymbol{\sf{\purple{Pisces04}}}}}}}[/tex]
Weiming receives a weekly pocket money of $28. If he decides to save 20% of it, find his saving in a year and spendings in a year
Welming's spending is $1164.8 and his savings is $291.2
How to determine the savings and the spending?The given parameters are:
Weekly pocket = $28
Save = 20%
There are 52 weeks in a year.
So, the yearly pocket is:
Yearly pocket = $28 * 52
Evaluate
Yearly pocket = $1456
He saves 20%.
So, we have:
Savings = 20% * $1456
Evaluate
Savings = $291.2
His spending is then calculated as:
Spending = $1456 - $291.2
Evaluate
Spending = $1164.8
Hence, Welming's spending is $1164.8 and his savings is $291.2
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Which of the following is equivalent to the logarithmic equation below? in x=3
Which point has coordinates (5,-7pi/6)?
Point A
Point B
Point C
Point D
