We have the following system of linear equations:
[tex]\begin{gathered} 2x+y-5z=-2, \\ -4x+4y-6z=3, \\ 6x-3y+z=-7. \end{gathered}[/tex]1) We solve for x the first equation:
[tex]\begin{gathered} 2x+y-5z=-2, \\ 2x=5z-y-2, \\ x=\frac{1}{2}\cdot(5z-y-2)\text{.} \end{gathered}[/tex]2) We replace the last equation in the second and third equations:
[tex]\begin{gathered} -4\cdot\frac{1}{2}\cdot(5z-y-2)+4y-6z=3, \\ 6\cdot\frac{1}{2}\cdot(5z-y-2)-3y+z=-7. \end{gathered}[/tex]Simplifying these equations, we have:
[tex]\begin{gathered} 6y-16z+4=3, \\ -6y+16z-6=-7. \end{gathered}[/tex]3) Multiplying by -1 the last equation, we have:
[tex]\begin{gathered} 6y-16z+4=3, \\ 6y-16z+6=7. \end{gathered}[/tex]4) Isolating the term 6y - 16z in each equation, we have:
[tex]\begin{gathered} 6y-16z=-1, \\ 6y-16z=1. \end{gathered}[/tex]5) Equalling the equations, we get:
[tex]-1=1.[/tex]Which is absurd. So we conclude that the system of equations is incompatible and it has no solutions.
Answer: No Solution
A plant is 6.2cm tall.
The height of the plant increases by 11% each week
Find how tall the plant will be after 2 weeks
If A plant is 6.2cm tall. The height of the plant increases by 11% each week. Then 7.564 cm is the height of plant after two weeks.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
A plant is 6.2cm tall
The height of the plant increases by 11% each week
Let us convert 11% to the decimal value by dividing 11 with 100.
11/100=0.11
Now we have to find height plant will be after 2 weeks.
The increase of plant length in 1 week will be
0.11×6.2=0.682 inches
For 2 weeks it is 2×0.682
=1.364
Now add the initial length with increment of height to find the height after 2 weeks.
6.2cm+1.364m=7.564cm
Hence 7.564 cm tall the plant will be after 2 weeks
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17)
The table shows a linear relationship between x and y.
What is the rate of change of y with respect to x?
A -9/2
B 2/9
C -2/9
D 9/2
Explain in complete sentences why you chose this answer, make sure
to support your answer with the data above.
Answer:
A
Step-by-step explanation:
Slope is defined by [tex]\frac{y_2-y_1}{x_2-x_1} or \frac{rise}{run}[/tex]. Take 2 points from this table and plug into the formula to find the slope.
[tex]\frac{96-60}{-20--12} = \frac{36}{-8} = -9/2[/tex]
From a logical standpoint, since when x increases and y decreases, the slope must be negative, eliminating answering B and D. Because the y value changed more than the x value, the slope must be more than 1, eliminating option C and leaving you with option A.
Find the x-intercepts and y-intercepts1) 3x + y = 3
The equation of a straight line is written as
y = mx + c
Where
m represents slope
c represents y intercept
The given equation is expressed as
3x + y = 3
y = 3 - 3x
y = - 3x + 3
Comparing the above equation with the slope intercept equation,
y intercept = 3
The x intercept is the value of x when y = 0
Putting y = 0 in the equation, it becomes
0 = - 3x + 3
3x = 3
x = 3x/3
x = 1
x intercept = 1
Help find the volume and write in terms of Pi
Answer:
The volume of the cylinder is 3584π cubic yards.
Explanation:
The given figure is a cylinder. The volume of a cylinder, V is calculated using the formula below:
[tex]V=\pi r^2h[/tex]From the diagram:
• The radius of the cylinder, r = a = 8 yd.
,• The height of the cylinder, h = b = 56 yd.
Substitute these values into the formula above:
[tex]\begin{gathered} V=\pi\times8^2\times56 \\ =3584\pi\:cubic\;yards \end{gathered}[/tex]The volume of the cylinder is 3584π cubic yards.
What type of function is the graph?Sqaue RootPiecewiseStepLinearQuadraticExponentialCube RootAbsolute Value
Let's begin by listing out the given information:
The graph is a curve that crossed the y-intercept
It cannot be a quadratic function. The graph does not cross the x-intercept twice
It cannot be a cube root function. The graph does not cross the x-intercept thrice
It cannot be a linear function because it is not a straight line
The graph is the graph of an exponential function (the graph has the x-axis as an asymptote on the left, and increases very fast on the right)
Write the equation of the line that passes through the points (-3,1) and (-5,8).Put your answer in fully reduced point-slope form
Answer:
y - 1 = -7/2 (x + 3 )
Explanation:
The point-slope form of a line is
[tex]y-y_1=m(x-x_1)[/tex]where (x_1, y_1) is a point on the line and m is the slope.
Let us first find the slope.
[tex]m=\frac{\text{rise}}{\text{run}}=\frac{8-1}{-5-(-3)}[/tex][tex]m=-\frac{7}{2}[/tex]A point on the line we are told is (-3, 1); thereofore, (x_1, y_1) = (-3, 1); hence
[tex]y-1=-\frac{7}{2}(x+3)[/tex]The question is : what number makes this equation true
Given
[tex]\frac{2}{3}\div\frac{\placeholder{⬚}}{7}=\frac{14}{21}[/tex]Find
what makes the equation true
Explanation
Let the number be x.
so , the equation becomes
[tex]\frac{2}{3}\div\frac{x}{7}=\frac{14}{17}[/tex]then , by solving this
[tex]\begin{gathered} \frac{2}{3}\div\frac{x}{7}=\frac{14}{21} \\ \\ \frac{2}{3}\times\frac{7}{x}=\frac{14}{21} \\ \\ \frac{14}{3x}=\frac{14}{21} \\ \\ x=7 \end{gathered}[/tex]Final Answer
Therefore ,
[tex]\frac{2}{3}\div\frac{7}{7}=\frac{14}{21}[/tex]4. In 2002, Sam invested $115,000 in high risk stocks. The following is an exponential function to represent the value of the stocks at a specific time period. y = 115000(.82)18 Please enter the appropriate blanks: What is the initial value Is this growth or decay What is the growth or decay Rate What is the time period listed in the exponential function listed above years What is the value of the exponential function listed above Round your answer 2 decimal places.
Solution
[tex]y=115000(0.82)^{18}[/tex]What is the initial value
Initial value = 115000
Is this growth or decay
Since 0.82 <1 , decay
What is the growth or decay Rate
The decay rate is 0.82
What is the time period listed in the exponential function listed above years
t = 18
What is the value of the exponential function listed above
[tex]y=115000(0.82)^{18}=3231.08[/tex]Round your answer 2 decimal places.
A professional baseball diamond is a square. Thedistance from base to base is 90 ft. To the nearest foot,how far does a catcher standing at home plate throwthe ball across the diagonal of the square to secondbase?
We have this diagram:
We have to calculate D, using the Pythagorean theorem:
[tex]\begin{gathered} D^2=A^2+A^2=2A^2 \\ D=\sqrt{2A^2}=\sqrt{2}\cdot A \\ D\approx1.414\cdot90=127.26\approx127 \end{gathered}[/tex]A catcher standing at home plate is at 127 ft across the diagonal from second base.
y A functionf (x) is graphed on the coordinate plane. 4 What is the function rule in slope-intercept form? 3 2 11 Enter your answer in the box. -5 -4 -3 -2 -1 1 2 3 4 5 f(x) = = -27 -3 Basic -5+ 7 8 9 -- X Y 22 0 X 4 5 6 х PO 1 2 3 < V + $ 0 % (0)
ANSWER
f(x) = -4x - 2
EXPLANATION
The slope-intercept form of the equation of a line is:
[tex]f(x)=mx+b[/tex]Where m is the slope and b is the y-intercept.
The first thing we can get from the graph is the y-intercept - which is the point where the line crosses the y-axis:
The y-intercept is -2.
To find the slope we can select another point on the line and use the formula:
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]The slope is:
[tex]m=\frac{2-(-2)}{-1-0}=\frac{2+2}{-1}=\frac{4}{-1}=-4[/tex]So the equation of the line is:
[tex]f(x)=-4x-2[/tex]Expand: (m + 4) 0 m2 + 8m + 16 0 m2 + 4m + 16 O mp + m +- 8
we have the next squared binomial
[tex](m+4)^2[/tex]we have the next formula in order to expand a squared binomial
[tex](a+b)^2=a^2+2ab+b^2[/tex]So we can expand
[tex](m+4)^2=m^2+2(4)(m)+4^2=m^2+8m+16[/tex]so the correct answer is the first one
What is the amount in the account after 4 yrs , rounded to the nearest dollar
We have the next formula
[tex]f(x)=350(1+0.03)^x[/tex]where x us the number of years, in this case x= 4
[tex]f(4)=350(1+0.03)^4=393.92[/tex]rounded to the nearest dollar is $394 is the amount in the account after 4 years.
what is the function of matrices in Algebra 1?
EXPLANATION
The major application of matrices is to represent linear transformations, that is, generalization of linear functions.
A home is on the market for $315,00, After 90 days, the seller reduces the price by 8%. What is the new price of the home Whats the anwser
For a project in statistics class, a pair of students decided to invest in two companies, one that produces software and one that does biotechnology research. Kendall purchased 86 shares in the software company and 11 shares in the biotech firm, which cost a total of $2,056. At the same time, Audrey invested a total of $1,937 in 79 shares in the software company and 11 shares in the biotech firm. How much did each share cost?Each share in the software company cost $? and each share in the biotech firm cost $?
Answer:
[tex]\begin{gathered} \text{ Each share in the software company cost \$17.} \\ \text{ Each share in the biotech firm cost \$54.} \end{gathered}[/tex]Step-by-step explanation:
Use a system of linear equations to solve the situation. If Kendall purchased 86 shares in the software company and 11 shares in the biotech firm, which cost a total of $2,056.
[tex]86x+11y=2056[/tex]At the same time, Audrey invested a total of $1,937 in 79 shares in the software company and 11 shares in the biotech firm.
[tex]79x+11y=1937[/tex]Let x be the cost of each share in the software company cost.
Let y be the cost of each share in the biotech firm cost.
Solve using the substitution method, isolate one of the variables on one of the equations and plug it into the other equation;
[tex]\begin{gathered} x=\frac{1937}{79}-\frac{11}{79}y \\ Plug\text{ it into the first one:} \\ 86(\frac{1937}{79}-\frac{11}{79}y)+11y=2056 \\ \frac{166582}{79}-\frac{946}{79}y+11y=2056 \\ -\frac{77}{79}y=-\frac{4158}{79} \\ y=\frac{4158*79}{77*79} \\ y=\text{ \$54} \end{gathered}[/tex]Then, the cost of a share in the biotech firm cost $54. Substitute into the isolated ''x'' equation, and solve for x.
[tex]\begin{gathered} x=\frac{1937}{79}-\frac{11}{79}(54) \\ x=\text{ \$17} \end{gathered}[/tex]Can I get some help on this i got stuck
Given:
Given that
[tex]\tan\theta=\sqrt{5}[/tex]Required:
To find the other five trig ratio.
Explanation:
[tex]\begin{gathered} \tan\theta=\frac{opp}{adj} \\ \\ =\frac{\sqrt{5}}{1} \end{gathered}[/tex]Now the hypotenuse is,
[tex]\begin{gathered} hyp^2=opp^2+adj^2 \\ \\ hyp^2=5+1 \\ \\ =5+1 \\ \\ =6 \\ \\ hyp=\sqrt{6} \end{gathered}[/tex]Now,
[tex]\begin{gathered} \sin\theta=\frac{opp}{hyp} \\ \\ =\frac{\sqrt{5}}{\sqrt{6}} \end{gathered}[/tex][tex]\begin{gathered} \cos\theta=\frac{adj}{hyp} \\ \\ =\frac{1}{\sqrt{6}} \end{gathered}[/tex][tex]\begin{gathered} cot\theta=\frac{adj}{opp} \\ \\ =\frac{1}{\sqrt{5}} \end{gathered}[/tex][tex]\begin{gathered} sec\theta=\frac{hyp}{adj} \\ \\ =\frac{\sqrt{6}}{1} \end{gathered}[/tex][tex]\begin{gathered} cosec\theta=\frac{hyp}{opp} \\ \\ =\frac{\sqrt{6}}{\sqrt{5}} \end{gathered}[/tex]Final Answer:
The six trig ratio are
[tex]\begin{gathered} \sin\theta=\sqrt{\frac{5}{6}} \\ \cos\theta=\frac{1}{\sqrt{6}} \\ cot\theta=\frac{1}{\sqrt{5}} \\ sec\theta=\sqrt{6} \\ cosec\theta=\frac{\sqrt{6}}{\sqrt{5}} \end{gathered}[/tex]Graph 2x+y<1Y>1/2x+2
We need to graph the next given inequalities:
[tex]\begin{gathered} 2x+y<1 \\ \text{and} \\ y>1/2x+2 \end{gathered}[/tex]For 2x+y<1.
We need to find the x-intercept and y-intercept
To find the y-intercept, set x=0
[tex]\begin{gathered} 2(0)+y<1 \\ \text{Then} \\ y<1 \\ \text{The y-intercept is the point (0,1)} \end{gathered}[/tex]To find the x-intercept, set y=0
[tex]\begin{gathered} 2x+0<1 \\ \text{solve for x} \\ x<\frac{1}{2} \end{gathered}[/tex]The symbol "<" means less than, so we get the next graph:
For the second inequality y>1/2x+2
To find the y-intercept, set x=0
The function table below is intended to represent the relationship y = 5x-1. However, one of the entries for y does not correctly fit the relationship with x.
Solution
We have the following info:
x y
1 4
2 8
3 14
4 19
The relationship is:
y= 5x-1
If we look for the second row we have this:
y= 5*2 -1 = 10 -1= 9
Then we can conclude that the incorrect value is:
x=2
The volume of this cube is 125 cubic meters. What is the value of d?
EXPLANATION
The volume of a cube is equal to:
V= side*side*side
Let's call to the side: "d"
V = d*d*d = d^3
If the volume is equal to 125 m^3, then the value of d will be:
[tex]125=d^3[/tex]Isolating d:
[tex]\sqrt[3]{125}=5m^3[/tex]Answer: the value of d is 5 cubic meters.
A tree service company put logs in the shape of a rectangular prism.However, it is supposed to snow, and the owner wants to cover the logs tokeep them dry. If the pile of logs creates a rectangular prism with thesemeasurements: 30 cm long, 12 cm wide, and 40 cm high, what is theminimum amount of material needed to cover the pile of logs? *
An example of a rectangular prism is given below
To get the minimum amount of material needed to cover the pile of logs, we will get the volume of the rectangular prism
The volume is calculated as:
[tex]\text{Volume of prism = length}\times breadth\times height[/tex]Thus, the minimum amount of material will be
[tex]\begin{gathered} \text{Volume}=30\operatorname{cm}\times12\operatorname{cm}\times40\operatorname{cm} \\ \text{Volume}=14400\operatorname{cm}^3 \end{gathered}[/tex]The minimum amount of material needed to cover the pile of logs will be 14400cm³
I need help with math
Frank's Hardware's store has a rectangular logo with a width of 3.4m
and area 13 square meters, we are to obtain the length,
[tex]\begin{gathered} \sin ce\text{ Area=L}\times B \\ The\text{ equation becomes;} \\ L=\frac{13}{3.4} \end{gathered}[/tex]In the figure, KM is perpendicular to JL Point Pis the midpoint of JL.KMGiven AJPKALPK and AJPM - ALPM, which criterion can be directly applied to show that AKIM AKLM?CAGReview progres
In this problem we have that
JK=KL
JM=LM
and
KM is a common side
therefore
triangle KJM and triangle KLM are congruent by SSS
The equation F = 9/5 C + 32 is used to convert Celsius temperature to Fahrenheittemperatures. C is the temperature in degrees Celsius. What is the temperature indegrees Fahrenheit when the temperature in 35 in Celsius?76596795Music offADdu1256 PM12/11/2020ORIeType here to search
The formula for converting from fahrenheit to celsius is given as
F = 9/5C + 32
Where
C represents Celsius
F represents Fahrenheit
If C = 35, then the temperature in fahrenheit is
F = 9/5 * 35 + 32
F = 63 + 32
F = 95
The correct option is 95
The cost of a taxi ride is $1.451.45 for the first mile and $1.251.25for each additional mile or part thereof. Find the maximum distance we can ride if we have $42.742.7. Enter your answer as an integer or a decimal. If needed, round to the nearest tenths of miles.
The maximum distance is 34.4 miles
Explanation:Given that:
The ride costs $1.45 for the first ride, and $1.25 for each additional mile or part thereof.
Having $42.7, the maximum distance we can ride is given as:
[tex]\begin{gathered} 42.7=1.45+1.25x \\ \\ 1.25x=42.7-1.45 \\ x=\frac{42.7-1.45}{1.25}=34.4 \end{gathered}[/tex]The maximum distance is 34.4 miles
4472^73+10008×273÷6382
If c(x) = 4x-2 and d(x) = x2 + 5x, what is (c.d)(x)?
O 4x³ + 18x² - 10x
O x² +9x-2
O 16x² + 4x - 6
O4x² + 20x - 2
In a case whereby c(x) = 4x-2 and d(x) = x2 + 5x, is two different equation, then the value of c(d(x)) is 4x2 + 20x - 2.
How can the value of the expression c(d(x)) be calculated?the first equation is been given as c(x) = 4x-2
And the second equation is been given as d(x) = x2 + 5x
Then to know the value of c(d(x)) then we will need to find the multiplication of the values that is been associated with c and d and this can be done as:
c(d(x)) = [c(x2 + 5x)]
And this will give us
=[ 4(x2 + 5x) - 2]
then after expansion we will have 4x2 + 20x - 2, going through the solution, we can see that the function that is given is been followed and the values for each of the function is been substituted so that the the value of c(d(x)) can be gotten.
Therefore, option D is correct.
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Draw ALMN with vertices L(3,-1), M(7,-3), and N(6,3). Find the coordinates of the vertices after a 90° rotation about the origin and about each of the points L, M, and N. what are the coordinates of the points after a 90° rotation about the origin? L=? M=? N=?
Answer:
The coordinates of the image are;
[tex]\begin{gathered} L^{\prime}=(-1,-3) \\ M^{\prime}=(-3,-7) \\ N^{\prime}=(3,-6) \end{gathered}[/tex]Explanation:
Given the coordinates of L,M and N as;
[tex]\begin{gathered} L=(3,-1) \\ M=(7,-3) \\ N=(6,3) \end{gathered}[/tex]A 90 degree clockwise rotation can be represented as;
[tex](x,y)\rightarrow(y,-x)[/tex]Applying this rule to the given coordinates we have;
[tex]\begin{gathered} L(3,-1)\rightarrow L^{\prime}(-1,-3) \\ M(7,-3)\rightarrow M^{\prime}(-3,-7) \\ N(6,3)\rightarrow N^{\prime}(3,-6) \end{gathered}[/tex]Therefore, the coordinates of the image are;
[tex]\begin{gathered} L^{\prime}=(-1,-3) \\ M^{\prime}=(-3,-7) \\ N^{\prime}=(3,-6) \end{gathered}[/tex]What is the actual length of the living space if the length of the scale drawing is 16.8 centimeters? Enter your answer in the box4 cmPatio 2 cm4.8 cmLiving Spaceбелеов16.8 cmScale: 2 cm = 2.5 mm
Take into account that the scale of the drawing realted to the actual size is
2 cm = 2.5m
Conisder that the width and length of the living space is 16.8 cm and 4.8 cm respectivley.
Convert the height and length to the actual lengths by using the given scale, as follow:
length = 16.8 cm => 16.8 (2.5 m) = 42 m
height = 4.8 cm => 4.8 (2.5 m) = 12 m
Hence, the actual length of the living space is 42 m
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).14,84,504Find the 6th term.
ANSWER
a6 = 108864
EXPLANATION
First, we have to find the rule to obtain the nth term of the sequence. For that, we have to decide if this sequence is an arithmetic sequence or a geometric sequence. Note that between the first and second term there's a difference of 70, but between the second and third terms the difference is 420. Therefore it can't be an arithmetic sequence.
Let's assume it is a geometric sequence. The formula for the nth term is:
[tex]a_n=a_1\cdot r^{n-1}[/tex]We have a1 = 14 and using the second term we can find r. a2 = 84:
[tex]\begin{gathered} a_2=a_1\cdot r^{2-1} \\ 84=14\cdot r^1 \\ r=\frac{84}{14} \\ r=6 \end{gathered}[/tex]The general formula for the nth term of this sequence is:
[tex]a_n=14\cdot6^{n-1}[/tex]To be sure, let's check if it works for the third term:
[tex]\begin{gathered} a_3=14\cdot6^{3-1} \\ a_3=14\cdot6^2 \\ a_3=14\cdot36 \\ a_3=504 \end{gathered}[/tex]Now, to find the 6th term, we just have to use this formula, with n = 6:
[tex]\begin{gathered} a_6=14\cdot6^{6-1} \\ a_6=14\cdot6^5 \\ a_6=108864 \end{gathered}[/tex]Hence, the 6th term of this sequence is 108864.
Express the set in roster form.The set of natural numbers between and Question content area bottomPart 1Choose the correct answer below.A.B.C.D.E.F.G.
To express a set in roster form, we shall list all the elements of that set separated by comas, and enclosed on either side by braces.
For the set of all natural numbers between 18 and 161, we would have the answer as;
ANSWER:
[tex]\mleft\lbrace18,19,20,21,\ldots,161\mright\rbrace[/tex]The correct answer is option A