The solution to the linear system of equation is x = 3, y = 5, and z = -0.5
What is a linear system of equation?A system of linear equations is a set of linear equations that involve the same variable and which work or are operated (simultaneously) together
The system of linear equation is presented as follows;
2·x - 3·y + 6·z = -12...(1)
5·x + 2·y - 8·z = 29...(2)
7·x + 6·y + 4·z = 49...(3)
Multiplying equation (1) by 5 and equation (2) by 2, we get;
5 × Equation (1) ⇒ 10·x - 15·y + 30·z = -60...(4)
2 × Equation (2) ⇒ 10·x + 4·y - 16·z = 58...(5)
Subtract equation (4) from equation (5), to get;
10·x - 10·x + 4·y - (-15·y) - 16·y - 30·z = 58 - (-60) = 118
19·y - 46·z = 118...(6)
Multiplying equation (1) by 7 and equation (3) by 2, we get;
7 × Equation (1) ⇒ 14·x - 21·y + 42·z = -84...(7)
2 × Equation (3) ⇒ 14·x + 12·y + 8·z = 98...(8)
Subtracting equation (7) from equation (8), we get;
14·x - 14·x + 12·y - (-21·y) + 8·z - 42·z = 98 - (-84) = 182
33·y - 34·z = 182...(9)
Multiplying equation (6) by 33 and equation (9) by 19, we get;
627·y - 1,518·z = 3,894...(10)
627·y - 646·z = 3,458...(11)
Subtracting equation (10) from equation (11), we get;
627·y - 627·y -646·z - (-1,518·z) = 3,458 - 3,894 = -436
872·z = -436
z = -436 ÷ 872 = -0.5
z = -0.5
From equation (6), we have;
19·y - 46·z = 118
19·y - 46 × (-0.5) = 118
19·y - 46 × (-0.5) = 118
19·y = 118 + 46 × (-0.5) = 95
y = 95 ÷ 19 = 5
y = 5
From equation (1), we get;
2·x - 3·y + 6·z = -12
2·x - 3 × 5 + 6 × (-0.5) = -12
2·x = -12 + 3 × 5 - 6 × (-0.5) = 6
x = 6 ÷ 2 = 3
x = 3
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16. Points X, Y, and Z are collinear, and Y is
the midpoint of XZ. Find the value of b.
Answer:
b=11
Step-by-step explanation:
lets set up the equation. we know that both sides equal each other so the equation is
2b+7=3b-4 let's move the 2b to the other side so we get
7=b-4 now add the 4 to the other side
11=b
Answer:
B is 11
Step-by-step explanation:
The ____ of 12 is -12.
Answer; the Negative of 12 is -12
Step-by-step explanation: first of all the reciprocal of 12 is 1 over 12. so that's not it. The absolute value of 12 is still 12 so that's not it. So the only thing that it can be is the Negative of 12 is -12
A small publishing company is releasing a new book. The production costs will include a one-time fixed cost for editing an additional cost for each book printed. The total production cost C (in dollars) is given by the function C=650+17.95N, where N is the number of books.
The total revenue earned (in dollars) from selling the books is given by the function R=31.90N.
Let P be the profit made (in dollars). Write an equation relating P to N. Simplify your answer as much as possible.
P = ?
Homework help lolol
Answer: 67
Step-by-step explanation:
do the math
plsssssssshelpppppppppp
a) The correct equation to represent the given condition is;
⇒ 4 (x + $3) = $36
Where, x represents the amount Pablo parents added in each day.
b) The amount to added by his parents in his account = $6
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
For 4 days, Pablo put $3 into his account.
And, His parent also add the some money to his saving account.
In the end, there was a total $36 in his account.
Now,
Let the amount Pablo parents added in each day = x
So, We can formulate;
⇒ 4 (x + $3) = $36
Solve for x as;
⇒ 4x + $12 = $36
⇒ 4 x = $36 - $12
⇒ 4x = $24
Divide by 4 both side, we get;
⇒ x = $6
Thus,
a) The correct equation to represent the given condition is;
⇒ 4 (x + $3) = $36
Where, x represents the amount Pablo parents added in each day.
b) The amount to added by his parents in his account = $6
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Answer Asap
Thank u
Angle are ,x = 45 and y = 45
What are angles?When two straight lines or rays intersect at a single endpoint, an angle is created.The vertex of an angle is the location where two points come together.The Latin word "angulus," which means "corner," is where the term "angle" originates.Vertex: The intersection of two lines or sides at an angle is called a vertex. In the diagram, O is the vertex.Arms: The angle's two sides linked at a single end. The arms of an angle are OA and OB.Initial Side: A straight line from which an angle is drawn, sometimes referred to as the reference line. The reference line is OB.The side that the angle measurement is done up to is known as the terminal side. OA is the terminal side in the diagram that is shown below.acc to our question-
x + 45= 90x = 90-45x=45as x and y are alternate interior anglesy = 45Hence,Angle are ,x = 45 and y = 45
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a sample of 900 computer chips revealed that 34% of the chips do not fail in the first 1000 hours of their use. the company's promotional literature states that 31% of the chips do not fail in the first 1000 hours of their use. the quality control manager wants to test the claim that the actual percentage that do not fail is different from the stated percentage. determine the decision rule for rejecting the null hypothesis, h0, at the 0.10 level.
The alternative hypothesis and null are:
H₀ : p = 0.31 vs H₁ : p > 0.31
Given that;
A sample of 900 computer chips revealed that 34% of the chips do not fail in the first 1000 hours of their use. the company's promotional literature states that 31% of the chips do not fail in the first 1000 hours of their use. the quality control manager wants to test the claim that the actual percentage that do not fail is different from the stated percentage.
To get decision rule for rejecting the null hypothesis, h0, at the 0.10 level;
n = 900
P = 0.34
p = 0.31
α = 0.10
Claim: More than 31% do not malfunction within the first 1000 hours of operation.
The null and alternative hypothesis must be stated.
This is a right-tailed test because the claim is directional to the right side (> type).
Therefore, the alternative hypothesis and null are:
H₀ : p = 0.31 vs H₁ : p > 0.31
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an old-model machine can stamp 1000 parts in four hours. a newmodel machine can stamp 1000 parts in just two hours. how long will it take one old-model and one new-model machine to stamp 1000 parts working together?
It will take 1 hour 20 mins for one old-model and one new-model machine to stamp 1000 parts working together.
Given that;
Finding the hourly cost of stamping parts for each machine is one way to approach this issue.
In 4 hours, the outdated equipment can stamp 1000 pieces. That means that it produces 250 parts per hour (1000 divided by 4). The new machine produces 1000 parts in two hours, which translates to 500 components every hour of stamping (1000 divided by 2).
If t is the amount of time that both machines are simultaneously stamping, then to determine the output, which must be 1000 parts, we simply multiply the rates of the two machines by t.
By multiplying the unknown time, t, by each of the two machines' rates and setting the result equal to 1000, it is possible to determine the precise amount of time required. Equation form of this is;
250t + 500t = 1000
750t = 1000
t = 1000/750
t = 1.333
It will take 1 hour 20 mins for one old-model and one new-model machine to stamp 1000 parts working together.
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Is x + 1/y = 7 a linear equation?
[tex]x + \frac{1}{y} = 7[/tex]
The equation ; x + 1/y = 7 as given in the task content is a linear equation.
What are linear equations?It follows from the task content that the equation given in the task content is to be identified as linear or not.
Since the given equation is; x + 1/y = 7;
It is noteworthy to know that a linear equation is one in which case, the greatest exponent of the variable is; 1.
Therefore, since the greatest exponent of a variable in the given equation is 1; it follows that the equation is a linear equation.
Hence, the equation given in the task content; x + 1/y = 7 is a linear equation.
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Need help asap
Solve by using elimination. Express your answer as an ordered pair.
3x−2y=11
3x−y=7
The solution to the given set of systems of equations is (x, y) = (1, -4).
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. 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.
Let's determine the solution using the elimination Method
3x−2y=11 (Equation 1)
3x−y=7(Equation 2)
Multiply the second equation by 2.
6x - 2y = 14 (Equation 3)
Now subtract the first equation from third to eliminate the y.
6x - 2y - (3x - 2y) = 14 - 11
3x = 3
x = 1
Now to find the value of y,
3x−y=7
3(1) − y = 7
y = 7 - 3
y = -4
Therefore, the solution to the given set of systems of equations is (x, y) = (1, -4).
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A family of four goes to a movie theater and spends $26.50. They buy 2 children's tickets at
$3.50 per ticket, 2 adult tickets, and 3 boxes of popcorn at $2.50 per box. What is the cost of
an adult ticket?
(Algebra)
Answer:
$6.50
Step-by-step explanation:
3.50(2)+2x+2.50(3)=26.50
6.00+2x+7.50=26.50
13.50+2x=26.50
2x=13.00
x=6.50
The instructions on a bottle of cough medicine state that the dose for an adult is 20 milliliters. Toms measuring device is marked in teaspoons. How many
teaspoons will Tom take for 2 doses during the day?
(Hint: 1 tsp ≈ 5 mL)
A 4 tsp
B 8 tsp
C 10 tsp
D 40 tsp
Sabrina needs more than 42 ft.³ of soil to top up her raised garden bed. each bag of soil contains 1.75 ft.³. Write and solve any inequality to find how many bags of soil Sabrina needs
The inequality that represents the quantity of bags of soil Sabrina needs is 1.75x > 42
The bags of soil needed is 24 bags
What is inequality?Inequality as used in math refers to relations that are not precisely equal
How to determine the bags of soil Sabrina needsSabrina needs more than 42 ft.³ of soil to top up her raised garden bed
> 42 ft³
each bag of soil contains 1.75 ft.³
let the number of bags of soil be x, such that
1.75x > 42
x > 42 / 1.75
x > 24
Sabrina needs at least 24 bags of soil
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Which of the following equations have exactly one solution?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
6
x
−
6
=
15
x
+
15
6x−6=15x+156, x, minus, 6, equals, 15, x, plus, 15
(Choice B)
B
6
x
+
15
=
6
x
+
15
6x+15=6x+156, x, plus, 15, equals, 6, x, plus, 15
(Choice C)
C
6
x
−
15
=
6
x
+
15
6x−15=6x+156, x, minus, 15, equals, 6, x, plus, 15
(Choice D)
D
6
x
−
6
=
6
x
+
15
6x−6=6x+156
The equation which has exactly one solution is 6x - 6 = 15x + 15.
The correct answer option is option A
Solving equations with one solutionCheck all that applies:
6x - 6 = 15x + 15
6x - 15x = 15 + 6
- 9x = 21
divide both sides by -9
x = 21/-9
x = -2.33
6x + 15 = 6x + 15
6x - 6x = 15 - 15
0 = 0
False
6x - 15 = 6x + 15
6x - 6x = 15 + 15
0 = 30
False
6x - 6 = 6x + 15
6x - 6x = 15 + 6
0 = 21
False
In conclusion, the 6x - 6 = 15x + 15 has only one solution.
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you want to obtain a sample to estimate a population proportion. based on previous evidence, you believe the population proportion is approximately 40%. you would like to be 90% confident that your estimate is within 1.5% of the true population proportion. how large of a sample size is required?
The largest sample size required is 2886.4.
Here we have to calculate how large of a sample size is required.
The formula:
(Z ∝I2/ E)² × P( 1- P)
The given data:
Margin error (E) = 1.5%
=0.015
As it is given that 90% confident that your estimate is within 1.5% of the true population proportion, therefore we have:
The level of significance(∝) = 1 - 0.90
= 0.10
The z value for the 90% confidence is 1.645
Therefore the largest of a sample size is required = ( 1.645/ 0.015)²× ( 0.4)(1- 0.4)
= 2886.4
The largest a sample size required is 2886.4
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Find the total amount given the original price and tax rate. Round to the nearest cent if necessary. $31.69, 6%
The total amount given the original price and tax rate is $33.59
How to determine the total amount?From the question, we have the following parameters:
Original price = $31.69
Sales tax rate = 6%
In order to determine the total sales amount, we make use of the following total sales equation
Total sales = original price + original price * sales tax rate
Substitute the known values in the above equation
So, we have the following equation
Total sales = 31.69 + 31.69 * 6%
Evaluate
Total sales = 33.59
Hence, the total amount is $33.59
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Is -97 prime or composite?
Answer:
Prime
Step-by-step explanation:
Because this number is only divisible by itself and no other number.
I (O,6), J (-1,1)
Help me find the slope please
Answer:
The slope is 5.
Step-by-step explanation:
[tex]m = \frac{1 - 6}{ - 1 - 0} = \frac{ - 5}{ - 1} = 5[/tex]
What does negative 3 over 5 > −2 indicate about the positions of negative 3 over 5 and −2 on the number line? (1 point) a negative 3 over 5 is located on the right of −2 b negative 3 over 5 is located on the left of −2 c negative 3 over 5 is located on the right of 0 and −2 is located on the left of 0 d negative 3 over 5 is located on the left of 0 and −2 is located on the right of 0
This is worth 40 points pls help
Answer:
−2 c negative 3 over 5 is located on the right of 0 and −2 is located on the left of 0 d negative 3 over 5
Step-by-step explanation:
(2sin(x) - 1)(tan(x) - 1) = 0 for 0 ≤ x ≤ 2 pi
Answer: x1=π/6 ,x2 = π/4, x3 = 5π/6, x4 5π/4
Step-by-step explanation:
2sin(x)-1=0
tan(x)-1=0
sin(x)=1/2
tan(x)=1
x=π/6
x=5π/6
x=π/4
x=5π/4
x1=π/6 ,x2 = π/4, x3 = 5π/6, x4 5π/4
Y+4=2(x-7)
In standard form
Answer:
2x-y=18
Step-by-step explanation:
y + 4 = 2(x - 7) (open brackets)
y + 4 = 2x - 14 (re arrange)
4 + 14 = 2x - y
2x - y = 18
Tyler bought a bowling ball for $80. Sales tax is 7%. What is the total cost of the bowling ball?
Answer:
Step-by-step explanation:
first multiply
80* 7% you can also do it as 80* (7/100)
=5.6
then,
add 80 and the ans of 80* (7/100)
80+5.6= 85.6
What is the quotient of 7 over 8 divided by 2 over 5?
Answer:
2 3/16
Step-by-step explanation:
It's simple math :D
NOVEMBER QUOTE!
Ooo! It's fall and thanksgiving time! I gotta get prepared for Thanksgiving and so my friends will come over! Fun! - Ash the Fox
(sorry that ones so long- ;-;)
A construction company is planning the foundation for a house. Stakes have been placed in the ground to mark the corners of the foundation. The four sides formed are measured as 20 feet, 20 feet, 48 feet, and 48 feet. The diagonal of the quadrilateral formed is measured to be 54 feet.
What type of triangle is formed by the diagonal and two sides of the current foundation plan?
Answer:
See below
Step-by-step explanation:
It is NOT a right triangle or the diagonal would measure 52 feet (instead of 54 feet) ....it is an OBTUSE triangle
Solve using proportions: If a 4-pound roast takes 140 minutes to cook, how long should a 5-pound roast take to cook?
Step-by-step explanation:
[tex]4pound \: roast \: = 140 \: minutes \\ 5 \: pounds \: roast \: = {?} \\ then cross multiplication \\ 140 \times 5 \: divide \: by \: 4 \\ 700 \div 4 = 175 \\ 5 \: pound \: roast \: take \: 175 \: minutes[/tex]
5. If f(x)=4x - 1 and f(x)=11, find x.
Answer:
x = 3
Step-by-step explanation:
f(x)=4x - 1
f(x)=11, find x.
We want the value of x that would make 4x-1 equal to 11. Use 11 instead of f(x):
f(x)=4x - 1
11=4x - 1
Solve:
12 = 4x
x = 3
If x were 3, 4x-1 would be 4*3-3 or 11
(jk−1)÷j when j=−4 and k=−0.9
The evaluation of the expression for the given values of j and k is -0.65
Evaluating an ExpressionFrom the question, we are to evaluate the given expression for the given values of j and k.
From the given information,
The given expression is
(jk - 1) ÷ j
and
j = -4 and k = -0.9
Now, substitute the values of j and k into the expression
(jk - 1) ÷ j
((-4)(-0.9) - 1) ÷ -4
= (3.6 - 1) ÷ -4
= 2.6 ÷ -4
= - 0.65
Hence, the value of the expression is -0.65
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Solve for n.
5(n+4)
3
O-24
24
22
O-22
=n-8
The value of n is -22.
What is a variable?
Any traits, figures, or amounts that may be gauged or counted are considered variables.
Given:
5(n+4)/3=n-8
Move 3 to the right
5(n+4)=3(n-8)
5n+20=3n-24
5n-3n= -24-20
2n=-44
n=- 44/2=-22
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Are the following rectangles similar? Show your work pls (yk how teachers are)
No the two rectangles are not similar as the ratios of the sides are not equal.
Two rectangles are said to be similar if the ratio of the sides of the rectangles are equal.
Now let us consider the given rectangles:
In rectangle ABCD:
AB = 18
AD = 36
In rectangle WXYZ :
WX = 25
XY = 45
Now the ratio of the sides of the rectangle are:
AB/AD = 18 / 36 = 1 / 2
WX/XY = 25 / 45 = 5 / 9
Thus we can see that AB : AD ≠ WX : XY
Hence the rectangles are not similar.
If the ratios of the adjacent sides of two rectangles are equal, then they are similar. A rectangle is a quadrilateral in the Euclidean plane because it has four right angles.
Other definitions include a parallelogram with a right angle or a quadrilateral that is equiangular, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides.
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help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Using the velocity, the rocket reaches its maximum height at 3.25 seconds.
In the given question we have to find the maximum height at the rocket reaches.
From the question; a toy rocket is shot vertically into the air from a launching pad 5 feet above the ground with an initial velocity of 104 feet per second.
The height h in feet of the rocket above the ground at t seconds after launch is given by the function h(t)= -16t^2+104t+5.
As we know that at the maximum height, the velocity will be zero.
So the given function of the heigth is
h(t)= -16t^2+104t+5
Velocity(v) = dh(t)/dt = -32t+104
As the maximum height v=0
-32t+104 = 0
Subtract 104 on both side, we get
-32t= -104
Divide by -32 on both side
t= 3.25 seconds
Hence, the rocket reaches its maximum height at 3.25 seconds.
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NEEDS ANSWERING NOW: A carpenter uses 8 1/2 ft of cedar for every 13 2/3 ft of redwood for a construction project. If the carpenter uses 4 1/4 ft of cedar, how much redwood does she need? Use pencil and paper. Is there more than one way to find the amount of redwood? Explain.
The redwood that the carpenter needs is 5 [tex]\frac{5}{6}[/tex] feet.
How to calculate the value?From the information, the carpenter uses 8 [tex]\frac{1}{2}[/tex] ft of cedar for every 13 [tex]\frac{2}{3}[/tex] ft of redwood for a construction project.
Let the redwood needed be illustrated as x.
It's important to note that 4 [tex]\frac{1}{4}[/tex] is half of 8 [tex]\frac{1}{2}[/tex]. Therefore, we will divide the redwoods given earlier by 2. This will be:
= 13 [tex]\frac{2}{3}[/tex] ÷ 2.
= 41 / 3 × 1/2
= 41 / 6.
= 6 [tex]\frac{5}{6}[/tex] ft
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