By using Gauss-Jordan elimination the solution to the linear equation is (3, 2, –3). The correct option is B.
What is Gauss-Jordan's elimination method?
In mathematics, the algorithm known as Gaussian elimination, commonly referred to as row reduction, is used to solve systems of linear equations. It comprises a series of operations carried out on the relevant coefficients matrix.
x – 2z = 9 so x = 2z + 9
6x – 2y – 5z = 29
–5x + 5y + 3z = –14
Substitute x = 2z + 9 into 6x – 2y – 5z = 29 and –5x + 5y + 3z = –14
6(2z + 9) – 2y – 5z = 29
12z + 54 - 2y -5z =29
-2y + 7z = - 25 (1st equation)
–5(2z + 9) + 5y + 3z = –14
-10z - 45 + 5y + 3z = -14
5y - 7z = 31 (2nd equation)
Multiply (1st) equation by 5 and (2nd) equation by 2.
-10y + 35z = - 125
10y - 14z = 62
21z = - 63
z = -3
Substitute z = - 3 into x = 2z + 9
x = 2z + 9
x = 2(-3) + 9
x = 3
Substitute x = 3 and z = 3 into 6x – 2y – 5z = 29
6x – 2y – 5z = 29
6(3) – 2y – 5(-3) = 29
18 - 2y + 15 = 29
-2y + 33 = 29
-2y = -4
y = 2
x = 3, y = 2 and z = -3
Therefore, the solution to the linear equation is (3, 2, –3). The correct option is B.
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Marion is observing the velocity of a cyclist at different times. After two hours, the velocity is 18km/h. After four hours, the velocity of the cyclist is 4km/h.
Part A: write an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times. Show your work and define the variables used.
Part B: how can you graph the equations obtained in part A for the first 8 hours?
To solve this problem,
we assume that velocity is a linear function of time:
v(t) = m t + b
where
v = velocity
t = time
m = slope of line
b = y-intercept of line equation
When t = 2 hours, v =
18 km/h, therefore:
2 m + b = 18 (1)
When t = 4 hours, v = 4 km/h, therefore
4 m + b = 4 (2)
Subtract (1) from (2) to obtain
4 m – 2 m = 4 - 18
2 m = -14
m = -7
From (1), calculate
for b:
b = 18 – 2(-7) = 32
Part A. The
equation in standard form is therefore:
v = -7 t + 32
Part B. To graph
the equation for the first 8 hours, we create a table as shown below. Assign
values of t from 0 to 8 hours then calculate the corresponding velocity.
A heartbeat takes 0.8 seconds.How many sec is his written as a faction?
Evaluate |-a^2|, given a = 5, b = -3, and c = -2.
What is the measure of the hypotenuse of an isosceles right triangle with leg lengths 6?
ohn 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
Answer:
[tex]w(w+2)=48[/tex] can be used by John.
Step-by-step explanation:
John has 48 square centimeter tiles he wants to use to create a mosaic.
We can say that 48 square cm is the area of the rectangle.
Let the width of the mosaic be = w
So, given is, He wants the mosaic to be rectangular with a length that is 2 centimeters longer than the width.
[tex]l=w+2[/tex]
Now area of rectangle is given as = [tex]length\times width[/tex]
[tex]48=l\times w[/tex]
Substituting l= w+2
[tex]48=(w+2)\times w[/tex] square cm
Hence, the equation John can use to solve and find w, the greatest width in centimeters he can use for the mosaic is :
[tex]w(w+2)=48[/tex]
A sphere fits snugly inside a 6-in. cube as shown. what is the volume of the region inside the cube but outside the sphere
The volume of the region inside the cube but outside the sphere is approximately 187.73 in^3.
Explanation:The volume of the region inside the cube but outside the sphere can be calculated by subtracting the volume of the sphere from the volume of the cube.
Volume of the cube = side^3 = 6^3 = 216 in^3
Volume of the sphere = (4/3)πr^3
Since the sphere fits snugly inside the cube, the radius of the sphere is half the length of the side of the cube. So, r = 3/2 in.
Therefore, volume of the region = volume of the cube - volume of the sphere = 216 in^3 - (4/3)π(3/2)^3 in^3 = 216 in^3 - 9π in^3 = 216 in^3 - 28.27 in^3 ≈ 187.73 in^3.
What is the complete factorization of the polynomial below?
x3 - 3x2 + x - 3
Final answer:
The complete factorization of the polynomial x³ - 3x² + x - 3 is (x - 3)(x² + 3)(x + 1).
Explanation:
The complete factorization of the polynomial x³ - 3x² + x - 3 can be found by using the Rational Root Theorem and synthetic division. By trying out the possible rational roots using the Rational Root Theorem, we find that one of the roots is 3. So, we divide the polynomial by (x - 3) to get the quadratic factor and the remaining linear factor.
(x - 3) is a factor, so we divide x³ - 3x² + x - 3 by (x - 3) using synthetic division:
3|1-31-3|3030|1010
The result is x² + 3.
The remaining linear factor is 1x + 1 = x + 1.
Therefore, the complete factorization of the polynomial x³ - 3x² + x - 3 is (x - 3)(x² + 3)(x + 1).
A spinner is separated into 5 equal pieces, as shown below: patrick spins the spinner 9 times. what is the theoretical probability that it stops on the brown sector on the last spin?
To solve this problem, let us first define what probability means in this case. It would be:
Probability = (number of colors to choose from) / (total number of colors)
There are a total of 5 colors on the spinner. The number of colors to choose from spins 1 to 8 would be 5 out of 5, while for the last spin 9 the number of colors to choose from would only be brown so that would be 1 out of 5. The total probability would be the product of the probability of each spins, therefore:
Probability = 1st spin * 2nd spin * 3rd spin * 4th spin * 5th spin * 6th spin * 7th spin * 8th spin * 9th spin
Probability = (5/5) *(5/5) *(5/5) *(5/5) *(5/5) *(5/5) *(5/5) *(5/5) * (1/5)
Probability = 0.2
There is a 20% chance to get brown on the last spin.
Answer:
1/5
Step-by-step explanation:
Think of it like this. If there is five spots it can potentially land on, and only 1 brown spot, the answer would be 20 %, or as a fraction, 1/5.
what is the final step to solving the inequality -2(5-4x)<6x-4
Answer:
x< 3
Step-by-step explanation:
-2(5-4x)<6x-4
multiply -2 inside the parenthesis
-2 * 5 = -10
-2 * -4x= 8x
-2(5-4x)<6x-4
-10 + 8x < 6x -4
To solve for x we need 'x' on the left hand side
Subtract 6x from both sides
-10 + 8x -6x< 6x -6x -4
-10 +2x < -4
Add 10 on both sides
-10 +10 +2x < -4+10
2x < 6
divide by 2 on both sides
x< 3
Joel and Melinda provide the following proofs for vertical angles to be equal:
Joel's proof: angle 2 + angle 3=180° (t is a straight line)
angle 1 + angle 2 = 180° (PQ is a straight line)
Therefore, angle 1 + angle 2 = angle 2 + angle 3 (Transitive Property of Equality)
Hence, angle 1 = angle 3 (Subtraction Property of Equality)
Melinda's proof: angle 1 + angle 2 + angle 3 + angle 4 = 360°
Therefore, angle 1 + angle 4 = 180° (t is a straight line)
Hence, angle 4 = angle 2 (Transitive Property of Equality)
Which statement is correct?
A Joels is correct
B Melindas is correct
C Both Melinda and joels is correct
D Neither is correct
The answer is A! I just did it and gotit right
Perform the operation(s) and write the answer in simplest form.
12 2/5 - 5 1/10
A.) 7 1/5
B.) 7 1/10
C.) 7 3/10
D.) 7 4/10
Use the given information below, find the p-value
a., test statistic z = -1.52
The p value can simply be located given the value of the z statistic by using a standard normal probabilities distribution table.
We are given that the z value of z = - 1.52. Since z is negative this means that we are to look for the proportion or p value located to the left of z. Based on the standard normal probabilities distribution table, this is equivalent to a p value of:
p value = 0.0643
This given p value indicates that 0.0643 or 6.43% of the population is located to the left of z.
Answer:
p value = 0.0643
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The table below represents a function.
heres the table
x 1 2 3 4 5
y 1 16 64 256 1,024
Which statement would best describe the graph of the function?
The graph is a straight line that has a slope of 8.
The graph is a horizontal line at y = 16.
The graph starts flat but curves steeply upward.
The graph is a parabola that opens upward.
Answer:
(c) The graph starts flat but curves steeply upward.
Step-by-step explanation:
(a) The graph is a straight line that has a slope of 8
In the table, the value y increases. there is no constant increase in y
So The graph is not a straight line
(b) The graph is a horizontal line at y = 16
For y=16 graph, the value of y remains the same
The value of y changes in the table
So the graph is not a horizontal line
(c) The graph starts flat but curves steeply upward.
The value of y on the table increases rapidly. So we can say that graph starts flat and curves steeply upward.
(d) The graph is a parabola that opens upward.
There is no vertex mentioned in the table. the y values goes on increasing.
In parabola, the graph increases and then decreases or vice versa .
So the graph of given table is not a parabola
A rhombus, which is a quadrilateral with 44 equal sides, is plotted on the coordinate plane. The coordinates of the vertices are: (5,3)5,3, (2,-1)2,-1, (-3,-1)-3,-1, (0,3)0,3. How long is each side of the rhombus?
Find the zeros of the function.
f(x) = 9x3 - 72x2 + 135x
Lena will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $50 and costs an additional $0.50 per mile driven. The second plan has no initial fee but costs $0.70 per mile driven. For what amount of driving do the two plans cost the same? What is the cost when the two plans cost the same
The two plans cost the same when Lena drives 250 miles, resulting in a cost of $175 for both plans, as per the given linear equation.
A linear equation is a mathematical expression that represents a straight line relationship between variables, typically in the form of ax + b = 0.
The two plans cost the same when the amount of driving satisfies the equation:
50 + 0.50x = 0.70x
Where:
50 represents the initial fee for the first plan,
0.50x represents the cost per mile for the first plan, and
0.70x represents the cost per mile for the second plan.
Now, let's solve for x:
50 + 0.50x = 0.70x
Subtract 0.50x from both sides:
50 = 0.20x
Now, divide both sides by 0.20:
x = 50 / 0.20
x = 250
So, the two plans cost the same when Lena drives 250 miles. To find the cost at this point, plug x = 250 into either plan:
For the first plan:
Cost = 50 (initial fee) + 0.50 (cost per mile) * 250
Cost = $50 + $125
Cost = $175
For the second plan:
Cost = 0.70 (cost per mile) * 250
Cost = $0.70 * $250
Cost = $175
So, when Lena drives 250 miles, both plans cost $175.
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In the figure,(p)parallel(q) and (r)pparallel(s). Match each pair of congruent angles with the reason for their congruency.
Answer:
∠1≅∠5 by Corresponding angles for parallel line p and q cut by traversal r
∠5≅∠13 by Corresponding angles for parallel line r and s cut by traversal q
∠10≅∠14 by Corresponding angles for parallel line p and q cut by traversal s
∠13≅∠16 by Vertical angles theorem
The given pairs of congruent angles can be matched with their reasons as follows:
[tex]5 \angle \cong \angle 13[/tex] is: corresponding angles for lines r and s that is cut by traversal q[tex]10 \angle \cong \angle 14[/tex] is: corresponding angles for lines p and q that is cut by traversal s[tex]13 \angle \cong \angle 16[/tex] is: vertical angles theorem.[tex]1 \angle \cong \angle 5[/tex] is: corresponding angles for lines p and q that is cut by traversal r.Given:
[tex]r \parallel s\\\\p \parallel q[/tex]
From the image,
1. [tex]\angle 5 $ and \angle 13[/tex] share the same corner along transversal q that cuts across lines r and s. Hence, both angles correspond to each other.
The reason for [tex]5 \angle \cong \angle 13[/tex] is: corresponding angles for lines r and s that is cut by traversal q2. [tex]\angle 10 $ and \angle 14[/tex] share the same corner along transversal s that cuts across lines p and q. Hence, both angles correspond to each other.
The reason for [tex]10 \angle \cong \angle 14[/tex] is: corresponding angles for lines p and q that is cut by traversal s3. [tex]\angle 13 $ and \angle 16[/tex] share the same vertex angle and are just directly opposite each other. Thus, they are vertically opposite each other and are therefore equal by the vertical angles theorem.
The reason for [tex]13 \angle \cong \angle 16[/tex] is: vertical angles theorem.
4. [tex]\angle 1 $ and \angle 5[/tex] share the same corner along transversal r that cuts across lines p and q. Hence, both angles correspond to each other.
The reason for [tex]1 \angle \cong \angle 5[/tex] is: corresponding angles for lines p and q that is cut by traversal r.In summary, the given pairs of congruent angles can be matched with their reasons as follows:
[tex]5 \angle \cong \angle 13[/tex] is: corresponding angles for lines r and s that is cut by traversal q[tex]10 \angle \cong \angle 14[/tex] is: corresponding angles for lines p and q that is cut by traversal s[tex]13 \angle \cong \angle 16[/tex] is: vertical angles theorem.[tex]1 \angle \cong \angle 5[/tex] is: corresponding angles for lines p and q that is cut by traversal r.Learn more here:
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What positive number is twice it's own square
Answer: The positive number is [tex]\dfrac{1}{2}.[/tex]
Step-by-step explanation: We are given to find the positive number that is twice it's own square.
Let x denotes the required number.
Then, according to the given information, we have
[tex]x=2x^2\\\\\Rightarrow 2x^2-x=0\\\\\Rightarrow x(2x-1)=0\\\\\Rightarrow x=0,~~2x-1=0\\\\\Rightarrow x=0,~\dfrac{1}{2}.[/tex]
Sine 0 is not considered as a positive number, so the required positive number is [tex]\dfrac{1}{2}.[/tex]
Thus, the positive number is [tex]\dfrac{1}{2}.[/tex]
When critiquing an observational study, which four factors should be analyzed?
A Methodology, Results, Discussion, Conclusion
B Introduction, Results, Discussion, Conclusion
C Introduction, Methodology, Results, Discussion
D Methodology, Causes, Results, Discussion
Answer:
Introduction, Methodology, Results, Discussion.
Step-by-step explanation:
yes
Which of the following is the explicit formula for the geometric sequence 320, 80, 20, 5, ...?
G(n) = 320(¼)n-1
G(n) = 320(4)n-1
G(n) = 320(¼)n
G(n) = ¼(320)n-1
Answer:
The first one hopefully :)
Step-by-step explanation:
What is the name of the shape graphed by the function r^2=9 cos(2 theta)?
The name of the shape graphed by the function r ^ 2 = 9 cos (2 theta) is called the “lemniscate”. A lemniscate is a plane curve with a feature shape which consists of two loops that meet at a central point. The curve is also sometimes called as the lemniscate of Bernoulli.
Explanation:
The period of coskθ is 2π/k. In this case, k = 2 therefore the period is π.
r ^ 2 = 9 cos 2θ ≥0 → cos 2θ ≥0. So easily one period can be chosen as θ ∈ [0, π] wherein cos 2θ ≥0.
As cos(2(−θ)) = cos2θ, the graph is symmetrical about the initial line.
Also, as cos (2(pi-theta) = cos 2theta, the graph is symmetrical about the vertical θ = π/2
A Table for half period [0,π4/] is adequate for the shape in Quarter1
Use symmetry for the other three quarters:
(r, θ) : (0,3)(3/√√2,π/8)(3√2/2,π/6)(0,π/4)
Answer:
lemniscate
Step-by-step explanation:
a p e x
For the values a = 8 which is a leg of a right triangle, and value c = 19, which is the hypotenuse, find the length of the other leg, b, to the nearest tenth.
A. 17.7
B. 20.6
C. 17.2
D. 20.3
What is the difference of 28y - 16y
Jessica purchased items worth $41.23 at the local
grocery store. The cashier made a mistake while
ringing up her items, and Jessica ended up paying
$50.23. How many extra dollars did she pay?
If MNO ~XYZ,then what corresponding parts are congruent
Final answer:
In similar triangles MNO and XYZ, corresponding angles are congruent (M with X, N with Y, O with Z) and corresponding sides are in proportion (MN to XY, NO to YZ, MO to XZ).
Explanation:
If triangles MNO and XYZ are similar (denoted as MNO ~ XYZ), then their corresponding parts are congruent. Corresponding parts include angles and sides that match between the two triangles due to their similarity in shape and proportion. In similar triangles, corresponding angles are congruent, while corresponding sides are in proportion.
The corresponding congruent angles would be angle M and angle X, angle N and angle Y, and angle O and angle Z. For the sides, the lengths are proportional, which means that the ratio of MN to XY is the same as the ratio of NO to YZ, which is also the same as the ratio of MO to XZ.
Final answer:
In similar triangles MNO and XYZ, the corresponding congruent parts are angles M, N, O congruent to angles X, Y, Z respectively and sides MN, NO, OM proportional to sides XY, YZ, ZX respectively.
Explanation:
If triangles MNO and XYZ are similar (denoted as MNO ~ XYZ), it indicates that they have the same shape but not necessarily the same size. This means that their corresponding angles are congruent, and their corresponding sides are in proportion.
The corresponding congruent parts would be:
Angle M is congruent to Angle X
Angle N is congruent to Angle Y
Angle O is congruent to Angle Z
Side MN is proportional to Side XY
Side NO is proportional to Side YZSide OM is proportional to Side ZXRemember, while the angles are congruent, the sides are proportional, which means the length of the sides of one triangle is some multiple or fraction of the lengths of the corresponding sides of the other triangle.
Enrique weighs 5 pounds more than twice Brendan's weight. If their total weight is 225 pounds, how much does Enrique weigh?
To find Enrique's weight, set up a system of equations based on the given information and solve for the weights of both Brendan and Enrique.
Enrique weighs 5 pounds more than twice Brendan's weight.
If their total weight is 225 pounds, you can set up a system of equations.
Let x be Brendan's weight, so Enrique's weight is 2x + 5.
From the given information, x + (2x + 5) = 225.
Solving the equation, x = 70 and Enrique's weight is 2(70) + 5 = 145 pounds.
given the following linear function sketch the graph of the function and find the domain and range f(x) =2/7x-2
By using the concept of function, it can be concluded that-
The domain and range of the given function is the set of real numbers
What is a function
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here the given linear function is
f(x) =[tex]\frac{2}{7}x - 2[/tex]
The graph has been attached here
As the given function is a linear function with a non zero slope, the domain and range is the set of real numbers.
So, the domain and range of the given function is the set of real numbers
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A party was organised for thirty people at which they could have either a hamburger or a pizza. if there were five times as many hamburgers as pizzas, calculate the number of each\
There are 5 pizza and 25 hamburgers.
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;
A party was organized for thirty people.
And, There were five times as many hamburgers as pizzas.
Now,
Let number of pizza = x
Then, Number of hamburgers = 5x
So, We get;
⇒ x + 5x = 30
⇒ 6x = 30
⇒ x = 5
Thus, Number of pizza = x
= 5
Then, Number of hamburgers = 5x
= 5 × 5 = 25
Therefore, There are 5 pizza and 25 hamburgers.
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A tropical punch recipe calls for 300 ml of sugar for every 2 flavor packages.Write an equation that shows the relationship between milliliters of sugar (
c. and number of flavor packages(
f. for this recipe.
The equation showing the relationship between milliliters of sugar (c) and the number of flavor packages (f) is c = 150f, derived from the recipe's ratio.
Explanation:The relationship between milliliters of sugar (c) and the number of flavor packages (f) can be expressed with the equation c = 150f. This equation comes from the ratio provided in the recipe, which states that for every 2 flavor packages, 300 ml of sugar is needed. So, if 1 flavor package corresponds to 150 ml of sugar (since 300 ml is for 2 packages), the equation can be derived by multiplying the number of flavor packages by 150 ml to find the milliliters of sugar.