Answers
For the given systems of equations, we have that:
1) The infinite solutions have the following format: (3y - 12, y, 10y - 31).
2) There is one solution: (1.58, -3.45, 3.89).
3) There is one solution: (3, 2, 4).
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For item 1, the system is:
3x + y - z = -5.-4x + 2y + z = 17.-2x - 4y + z = -7.From the first equation, we have that:
z = 3x + y + 5.
Replacing on the second equation, we have that:
-4x + 2y + 3x + y + 5 = 17
-x + 3y = 12
x = 3y - 12.
Replacing on the third equation, we have that:
-2x - 4y + 3x + y + 5 = -7
x - 3y = -12
Since x = 3y - 12:
3y - 12 - 3y = -12
0 = 0.
Free variable, hence:
x = 3y - 12.y = y.z = 3x + y + 5 = 9y - 36 + y + 5 = 10y - 31.The infinite solutions have the following format: (3y - 12, y, 10y - 31).
For item 2, the system is:
x + 5y + 3z = -4.x + 2y - 3z = 8.-3x + 2y + 3z = -12.From the first equation:
x = -4 - 5y - 3z.
Replacing on the second equation:
-4 - 5y - 3z + 2y - 3z = 9.
-3y -6z = 13.
3y + 6z = 13.
Replacing on the third equation:
-3(-4 - 5y - 3z) + 2y + 3z = -12
12 + 15y + 9z + 2y + 3z = -12
17y + 12z = -14.
From the second equation, we have that:
z = (13 - 3y)/6.
Hence, replacing on the third again:
17y + 2(12 - 3y) = -14
11y + 24 = -14.
y = -3.45.
z = (13 - 3 x (-3.45))/6 = 3.89.
x = -4 - 5(-3.45) - 3(3.89) = 1.58.
Hence:
There is one solution: (1.58, -3.45, 3.89).
For item 3, the system is:
-4x - 2y + 5z = 4.5x + 2y - z = 15.5x - 2y - 3z = -1.From the second equation:
z = 5x + 2y - 15.
Replacing on the first:
-4x - 2y + 5(5x + 2y - 15) = 4
-4x - 2y + 25x + 10y - 75 = 4
21x + 8y = 79.
Replacing on the third:
5x - 2y - 3(5x + 2y - 15) = -1
5x - 2y - 15x - 6y + 45 = -1.
-10x - 8y = -46.
Adding both resulting equations, we have that:
11x = 33.
x = 3.
Then
21x + 8y = 79.
63 + 8y = 79
8y = 16
y = 2.
z = 5x + 2y - 15 = 5(3) + 2(2) - 15 = 4.
There is one solution: (3, 2, 4).
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Related Questions
Joel, Ben, and Luke are each wearing a hat with a number on it. Each person adds the two numbers on the other two hats, giving totals of 11, 17, and 22. What is the largest number on a hat?
Answers
Solving a system of equations, we conclude that the largest number on a hat is 14.
What is the largest number on a hat?
We have 3 hats, each one with a number that we will define as:
x, y, and z.
We know that by adding pairs of these numbers we get 11, 17 and 22, then we can write a system of equations:
x + y = 11
x + z = 17
y + z = 22
Clearly z is the largest number, so we want to find z.
First, we can isolate x on the first equation so we get:
x = 11 - y
Replacing that in the second equation giveS:
x + z = 17
(11 - y) + z = 17
Now our system is:
y + z = 22
(11 - y) + z = 17
Isolating y in the first one we get:
y = 22 - z
Now we can replace that in the other equation:
(11 - (22 - z)) + z = 17
Now we can solve this for z.
11 - 22 + z + z = 17
-11 + 2z = 17
2z = 17 + 11 = 28
z = 28/2 = 14
z = 14
We conclude that the largest number on a hat is 14.
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can someone help me really quick
Answers
Shawn earn 11 per hour.
Hannah travel 25 miles in one gallon of gas.
What is graph?A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
given:
According to the graph the y- axis shows the earnings.
So, we have the coordinates are
(1, 11), (2, 22) and (3, 33)
So, Shawn earn = 22 - 11 / 2 -1 = 11 per hour.
Now, in second case
The coordinates are
(3, 75), (5, 125), (6, 150), (10, 250)
So, m= (125 - 75) / (5-3)
m= 50/2
m=25
So, Hannah travel 25 miles in one gallon of gas.
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The longest side of a triangle is a cm.
The second side is bcm shorter than the first side.
The third side is half as long as the second side.
Write an expression, in its simplest form, for the perimeter of
the triangle
Answers
Answer:
P = 2.5a - 1.5bStep-by-step explanation:
The sides of the triangle are:
a cm,a - b cm,(a - b)/2 cm.Its perimeter is the sum of the three sides:
P = a + a - b + (a - b)/2 = 2a - b + 0.5a - 0.5b = 2.5a - 1.5bGiven , find the average rate of change of f(x)=[tex]f(x)=\frac{1}{x+5}[/tex] on the interval
[1,1+h]. Your answer will be an expression involving h.
Pls halp
Answers
The average rate of change of function f(x)= [tex]\frac{1}{x+5}[/tex] on the interval [1,1+h] is [tex]-\frac{1}{36+6h}[/tex]
Given,
The function = [tex]\frac{1}{x+5}[/tex]
We know the average rate of change of the function is [tex]\frac{f(b)-f(a)}{b-a}[/tex]
Where a and b are the intervals
a= 1
b=1+h
f(a) =f(1)= [tex]\frac{1}{1+5}[/tex]
=[tex]\frac{1}{6}[/tex]
f(b)= f(1+h)
=[tex]\frac{1}{1+h+5}[/tex]
=[tex]\frac{1}{6+h}[/tex]
f(b)-f(a)= [tex]\frac{1}{6+h}-\frac{1}{6}[/tex]
[tex]=\frac{6-(6+h)}{6(6+h)} \\=\frac{6-6-h}{36+6h}\\ =-\frac{h}{36+6h}[/tex]
Then,
[tex]\frac{f(b)-f(a)}{b-a} =\frac{-\frac{h}{36+6h} }{1+h-1}[/tex]
[tex]=\frac{-\frac{h}{36+6h} }{h} \\=-\frac{1}{36+6h}[/tex]
Hence, the average rate of change of function f(x)= [tex]\frac{1}{x+5}[/tex] on the interval [1,1+h] is [tex]-\frac{1}{36+6h}[/tex]
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Question 2 (1 point)
Given the following points, are lines CD and EF parallel, perpendicular, or neithe
A(1,2) B(3,4) C(5,2) D(8,3) E(3,8) F(-6,5)
a
b
C
parallel
perpendicular
neither?
Answers
Given lines CD and EF are parallel. Therefore answer is (a)
How to find slope of two lines and check whether they are parallel or perpendicular
Given are two points P (x₁, y₁) and Q ( x₂, y₂)
Then slope of the line PQ is given by (y₂-y₁)/(x₂-x₁)
If two lines have slopes m₁ and m₂ respectively
Then the lines are parallel when their slopes are equal i.e. m₁=m₂
and the lines are perpendicular when m₁*m₂= -1
Given C(5,2), D(8,3),E(3,8) F(-6,5)
Then,
Slope of CD = (3-2)/(8-5)= 1/3
Slope of EF = (5-8) / (-6-3) = 1/3
Slope of CD=Slope of EF
Therefore CD and EF are parallel
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Solve the system of equations. -5a + 7b = 2 -15a + 21b = 6
Answers
It should be noted that solving the system of equations. -5a + 7b = 2 -15a + 21b = 6 will give 0 and this implies that it has no solution
How to illustrate the information?It should be noted that we simply want to solve the equations given:
-5a + 7b = 2 ................ i
-15a + 21b = 6 ............. ii
Divide equation ii through by 3. This will give:
-5a + 7b = 6
Therefore, the equations will be:
5a + 7b = 2 ................ i
5a + 7b = 2 ................ ii
Subtract equation ii from i
This will be (5a + 7b = 2) - (5a + 7b = 2) = 0
Therefore, it should be noted that solving the system of equations. -5a + 7b = 2 -15a + 21b = 6 will give 0 and this implies that it has no solution
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the perimeters of two squares are in the ratio 2 : 7. What is the ratio of the area of the smaller square to the area of the larger square
Answers
The ratio of the area of the smaller square to the area of the larger square = 4 : 49
Finding the area of a square from the perimeterLet the perimeter of the small square be [tex]P_1[/tex]
Lethe the perimeter of the large square be [tex]P_2[/tex]
Perimeter of a square = 4 Length
[tex]P_1=4L_1\\\\P_2=4L_2[/tex]
The ratio of the perimeters = 2:7
[tex]\frac{4L_1}{4L_2} =\frac{2}{7} \\\\\frac{L_1}{L_2} =\frac{2}{7}[/tex]
The area of a square = L^2
[tex](\frac{L_1}{L_2} )^2=(\frac{2}{7} )^2\\\\\frac{L_{1} ^{2} }{L_{2} ^{2}} =\frac{2^2}{7^2} \\\\\frac{L_{1} ^{2} }{L_{2} ^{2}} =\frac{4}{49}[/tex]
Therefore, the ratio of the area of the smaller square to the area of the larger square = 4 : 49
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Altogether, tom and sarah have 32 baseball cards. if sarah has three times as many baseball cards as tom, how many does each of them have
Answers
tom has 8 cards and sarah has 24 cards .
Explain how many cards sarah and tom has?tom and sarah total baseball cards =32
sarah has three times as many baseball cards as tom
The 2 equations are
1. sarah + tom = 32
2. sarah = [tex]3 \times tom[/tex]
substitute equation 2 in 1.
[tex]3\times tom +tom= 32[/tex]
4 tom = 32
tom = 32/4
tom = 8 cards
sarah = [tex]3\times tom[/tex]
= [tex]3\times 8[/tex]
sarah = 24 cards
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HELP ME PLEASE I need this rn!!!!! SOMEONE ANYONE PLEASEEEEE
question 4
Jeremy is 80 ft from a wall. Each time he moves toward the wall he reduces his distance from the wall by half. Which graph best models the situation?
the four photos are to this question
question 5
Which expressions describe the end behavior of the graph?
the 5 photo is to this one
Select EACH correct answer.
Answers
Using a geometric sequence, we have that:
Graph 1 models the situation.
The end behavior of the graph is given as follows:
As x decreases, y approaches the line y = 2.
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q, hence the second term is the first multiplied by q, the third is the second multiplied by q, and so on.
For item 4, we have that:
The first term is of 80.The common ratio is of 0.5.Hence when x = 2, y = 40, when x = 3, y = 20, and so on.This means that the first graph is correct.
What is the end behavior of a function?The end behavior of a function is given by the limits of the function when x goes to infinity.
Hence, from the final graph, we have that:
As x decreases, y approaches the line y = 2. (lim x -> negative infinity = -2).As x increases, y decreases without bound. (lim x -> infinity = - infinity, not an option but just to explain).More can be learned about geometric sequences at https://brainly.com/question/24643676
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What is the value for
y
in the equation
y
=
x
2
when
x
=
3
?
Answers
y = 2x = 6
HELP...........................! !
Answers
Answer:
[tex] \sf \large( \frac{2}{5} ) {}^{14} [/tex]
Step-by-step explanation:
=((2/5)^4(2/5)^3)^2
=((2/5^4+3))^2
=((2/5^7))^2)
=(2/5)^14
Please help and answer the parts A and B
Answers
A> The equation for the line is y = -0.1x + 2600
B> The value of the car is $16,500
From the table, we know that for every 6000 miles added there is a decrease in the value by $600.
A> So it is the function of one order
y = kx + b
25500 = 5000k + b
24800 = 12000k + b
After equating it we get
b = 26000 and k = -0.1
Now put the value of b and k in the equation, and we get
y = -0.1x + 26000
Therefore the equation is y = -0.1 + 26000
B> When we put the value of x = 95000, we get
y = -0.1 × 95000 + 26000
= 16500
Therefore the cost of the car is $16,500
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Un granjero coloco una cerca al rededor de su parcela. La parcela mide 10 m de cada lado ya que es un cuadrado. Si puso los postes cada 3/4 de metro ¿cuantos postres coloco?
Answers
Greetings from Brasil...
The total length will be: 10+10+10+10 = 40
and
(3/4)m = 0.75m
Then, Rule of 3:
QTD m
1 ------ 3/4
X ------ 40
X = 53.333
Soon 53 posts will be needed
Jillion exercise 5 times a week. She runs 3 miles each morning and bikes in the evening. If she exercises a total of 30 miles for the week, how many miles does she bike each evening?
Answers
If she runs 3 miles each morning, that is 15 miles of running per week. So you subtract that 15 from 30, which means she bikes 15 miles per week. Now divide 15 by 5 and the answer is she bikes 3 miles per evening.
Answer: 3 miles
Step-by-step explanation:
Total = 30 miles per week
Weekly runs in the morning= 3*5 = 15 miles per week
Bikes= 30-15 = 15 miles per week
Bikes each day= 15/5 = 3 miles
Last saturday 16 people worked the at the theater. four people worked the morning shift and 12 worked the evening shift. they earned a total of $1,080.00. what did they earn each?
Answers
Earning of each = $33.75
Let's take the earnings of each person to be x.
Total person working at the theater = 16 + 4 + 12
= 32
Now the total earnings of the people = 32x
Which is given = $1080
So we get an equation
32x = 1080
x = $33.75
Hence we get the earnings of each person = $33.75
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the volume of right circular cylinder a is 22 cubic centimeters. what is the volume, in cubic centimeters, of a right circular cylinder with twice the radius and half the height of cylinder a?
Answers
The new volume of the right circular cylinder is 44 cubic centimeter.
The formula for the volume of the cylinder is given as
V = Πr^2h (1)
We have been given that, V = 22 cubic centimeters
Now we need to find the volume of the cylinder which is denoted by V’ whose,
r = 2r
and, h = h/2
Now putting the required values in equation (1) we get
V’ = Π(2r)^2(h/2)
V’ = Π4r^2(h/2)
V’ = 4/2(Πr^2h)
V’ = 2V [as V = Πr^2h]
V’ = 2*22 cubic centimeter
V’ = 44 cubic centimeter
Hence the new volume of the right circular cylinder is 44 cubic centimeter
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Mother, who went to the market with Rs 500 in hand, spent Rs 300 to buy vegetables and Rs 150 to buy fruits. (i) What fraction of the money in hand did she spend on vegetables?
Answers
Answer:
3/5
Step-by-step explanation:
500 is the money she started with if you put that over the money she spent on vegetables it would be 300/500 when simplified it's 3/5
You place the following shapes in a bag 5 circles 3 triangles 7 squares and 5 rectangles if you reach in the bag what is the probability you will grab a shape
Answers
Answer:
theres a 25% you will grab an apple (work shape is suppose to be circle)
Step-by-step explanation:
Hope this helps
a measurement that can be repeated is said to be and one that is close to the accepted or actual value is
Answers
A measurement that can be repeated is said to be precise and one that is close to the accepted or actual value is approximate.
Given that,
The incomplete statement is given we have to complete the statement.
All over the world, most things are in use as of common quantity, so people all over the world agree that they have to follow a common system of measurement and that the common system of measurement is called standard measurement.
Here,
A measurement that can be repeated is said to be precise values
A measurement that is close to the accepted or actual value is approximate.
Thus, the required words are precise and approximate.
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Ashley is constructing CD such that CD intersects AB at C and is the segment bisector of AB. Select the relationship that must be true.
A) Point C is equidistant from A and B.
B) Point D is equidistant from A and B.
C) Point A is equidistant from C and D.
D) Point B is equidistant from C and D
Answers
Answer:
Step-by-step explanation:
a,d
Answer:ad
Step-by-step explanation:
ad
What does pin stand for? a. principal investment number b. permission initiating number c. percent increase number d. personal identification number please select the best answer from the choices provided a b c d
Answers
Answer:
The answer is D.
Step-by-step explanation:
Answer:
in this case the answer is D
Step-by-step explanation:
your welcome
can someone please anwser (5z+y)/7 (the number values of z and y are in the picture)
Answers
Answer:
2
Step-by-step explanation:
First substitute the values of z and y in the expression.
Use PEDMAS. We have to multiply 5 and 3, which gives 15. Subtract 1 from 15 and then divide the result by 7.
[tex]\sf \dfrac{5z + y}{7}= \dfrac{5*3 + (-1)}{7}\\\\[/tex]
[tex]\sf = \dfrac{15 - 1}{7}\\\\ = \dfrac{14}{7}\\\\= 2[/tex]
1 < x + 4 ≤ 4
please help me it’s due at 3:30
Answers
Answer:
−3 < x ≤ 0
Step-by-step explanation:
1 < x + 4 ≤ 4
Add -4 to all parts
1 + −4< x + 4 + −4 ≤ 4 + −4
Put pairs in bracket to avoid confusion
(1 + −4) < x (+ 4 + −4) ≤ (4 + −4)
−3 < x ≤ 0
(2am³n) (-3am⁴)
pa sagot. thanks
Answers
Answer:
if you just want to simplify, -6a^2 m^7 n
Step-by-step explanation:
I cant find my answer please help!
Answers
Step-by-step explanation:
we are calculating miles.
when we have speed, which is mph or miles/hour. what do we have to multiply it with to get miles ? hours !
miles/hour × hour = miles
so, in the function D(x) the speed 60 mph has to be multiplied by the hours spent driving to get the driven miles.
x = hours spent driving
the domain is the interval or set of all valid x (input) values. the range is the interval or set of all valid y (function result) values.
so what are valid x (number of driving hours) values ?
it starts with 0, if course (before actually driving). and it goes up to 4 (after 4 hours the 240 miles are "done").
the domain is
0 <= x <= 4
and the range ? that is all the function result values for the valid x values.
for x = 0 this starts at 240.
and goes down for x = 4 to 0.
the range is
0 <= y (= D(x)) <= 240
If 4 is subtracted from the numerator of a fraction, its value becomes 1/3. If 5 is added to the denominator of the original fraction its value becomes 1/2. What is the original fraction.
Answers
Answer:
79
Step-by-step explanation:
Let the numerator of the original fraction be 'x' and the denominator be 'y'. So, the original fraction becomes xy
According to the question,
Condition I,
If 4 is subtracted from the numerator of a fraction, its value becomes 1/3.
or,x−4y=13
or,3(x−4)=y
or,y=3x−12
Condition II,
If 5 is added to the denominator of the original fraction, the value becomes 1/2.
or,xy+5=12
or,2x=y+5
Put value of y from equation (i) in equation (ii), we get,
or,2x=(3x−12)+5
or,2x=3x−12+5
or,3x−2x−7=0
∴x=7
Put value of x in equation (i), we get,
or,y=3×7−12
or,y=21−12
∴y=9
So, (x,y) = (7,9)
Therefore, the required original fraction is 79.
I dont understand this i pick the right ones but it say im wrong can someone correct me??
Answers
That should be it I’m pretty sure
Answer:
The two in the middle?
Find the quotient of 4 4/5 divided 4/5. Explain how you can use the GCF to write your answer I. Simplest form.
Answers
Answer:
5/4 Quotient[24/5] and 6
Step-by-step explanation:
5/4 Quotient[24/5]
Simplify the following:
(4 + 4/5)/(4/5)
Multiply the numerator of (4 + 4/5)/(4/5) by the reciprocal of the denominator. (4 + 4/5)/(4/5) = ((4 + 4/5)×5)/4:
((4 + 4/5)×5)/4
Put 4 + 4/5 over the common denominator 5. 4 + 4/5 = (5×4)/5 + 4/5:
(((5×4)/5 + 4/5) 5)/4
5×4 = 20:
((20/5 + 4/5)×5)/4
20/5 + 4/5 = (20 + 4)/5:
(((20 + 4)/5)×5)/4
20 + 4 = 24:
(24/5×5)/4
24/5×5 = (24×5)/5:
((24×5)/5)/4
((24×5)/5)/4 = (24×5)/(5×4):
(24×5)/(5×4)
(24×5)/(5×4) = 5/5×24/4 = 24/4:
24/4
The gcd of 24 and 4 is 4, so 24/4 = (4×6)/(4×1) = 4/4×6 = 6:
Answer: 6
1. At 2 p.m., a car is 100 km east of Toronto, driving eastward at 80 km/h. A truck leaves Toronto at 2 p.m. and is driving eastward at 120 km/h. At what time will the truck pass the car? How far east of Toronto will they be when this occurs?
Answers
The time at which the truck will pass the car is 2.5 hours and the distance at which the car and truck meet is 200km.
What is velocity?Velocity is defined as the ratio of the distance moved by the object at a particular time. The velocity is a vector quantity so it needs both the magnitude and the direction.
Given that at 2 p.m., a car is 100 km east of Toronto, driving eastward at 80 km/h. A truck leaves Toronto at 2 p.m. and is driving eastward at 120 km/h.
The time will be calculated as:-
Relative velocity = Distance / Time
Time = Distance / Relative velocity
Time = 100 / 120 - 80
Time = 2.5 Hours
Distance of car = Speed x time = 80 x 2.5
Distance of car = 80 x 2.5
Distance of car = 200 Km
Therefore, the time at which the truck will pass the car is 2.5 hours and the distance at which the car and truck meet is 200km.
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PLSSS HELP ANSWER, THE QUESTION IS IN THE SCREENSHOT
Answers
Let f(x) be the integrand.
[tex]f(-2)=-8 \\ \\ f(0)=0 \\ \\ f(2)=8 \\ \\ f(4)=64 \\ \\ \implies \int^{4}_{-2} x^3 \text{ dx}=\approx \frac{1}{2}(2)[-8+64+2(0+8)] \\ \\ =\boxed{72}[/tex]