The solution of the matrix in vector form is [-13 3 -3 4]
The given matrix equation is Ax = b, where A is a matrix with 1 row and 4 columns, and b is a matrix with 1 row and 3 columns
In this case, the augmented matrix is a 5x4 matrix, with the first 4 columns being A and the last column being b. The augmented matrix for this system is then:
=> [tex]\left[\begin{array}{ccc}1&2& 3\\3& 5 &2 \\-4 &2 &5 \\-13 &11 &8\end{array}\right][/tex]
To solve the system, we can use Gaussian elimination, which is a method of solving a system of linear equations by transforming the augmented matrix into a row-echelon form.
After applying Gaussian elimination to the augmented matrix, we get the following row-echelon form:
=> [tex]\left[\begin{array}{ccc}1& 0& 0 \\-1& 0 &-3 \\-3& 0& 4 \end{array}\right][/tex]
We can then find the solution of the system by back-substitution:
=> x₁ = -13, x₂ = 3, x₃ = -3, and x₄ = 4.
Therefore, the solution of the linear system is x = [-13 3 -3 4]
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six upright dominos of increasing height are lined up to be knocked down.The dominos sre numbered 0 to 5.The smallest domino number 0 is 5.00 cm tall and will be toppled by a person to start the chain reaction.Each subsequent domino 13% taller than the one before what is the height of domino number 5?
Answer:
Approximately 9.23 cm
Step-by-step explanation:
We can start by finding the height of each domino in the chain, starting with domino 0, which is 5.00 cm tall.
Let h be the height of domino 5. Then we can express the height of each domino in terms of h as follows:
Domino 0: 5.00 cm
Domino 1: 1.13 * 5.00 = 5.65 cm
Domino 2: 1.13 * 5.65 = 6.38 cm
Domino 3: 1.13 * 6.38 = 7.21 cm
Domino 4: 1.13 * 7.21 = 8.16 cm
Domino 5: 1.13 * 8.16 = h cm
Since we know that domino 5 is the tallest domino and is number 5 in the sequence, we can set the height of domino 5 equal to h and solve for h:
h = 1.13 * 8.16
h ≈ 9.23 cm
Therefore, the height of domino 5 is approximately 9.23 cm.
write the solution set of the given homogeneous system in parametric vector form.3x1+3x2+6x3=0−6x1−6x2−12x3=0 −4x2+4x3=0where the solution set is x =[x1 x2 x3]
The solution set of the system of equations in this problem is defined as follows:
[-3x3 x3 x3]
How to solve the system of equations?The system of equations for this problem is defined as follows:
3x1+3x2+6x3=0.−6x1−6x2−12x3=0.−4x2+4x3=0.From the third equation, we write x2 as a function of x3, as follows:
4x2 = 4x3
x2 = x3.
Replacing into the first equation, we can write x1 as a function of x3, hence:
3x1+3x2+6x3=0.
3x1 + 3x3 + 6x3=0.
3x1 = -9x3
x1 = -3x3.
Hence the vector solution of the system is given as follows:
[-3x3 x3 x3]
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Complete the follow two column proof
(Best answer gets Brainly!)
The two column proof showing that ΔFHK ~ ΔGHJ is as detailed below.
How to write the two column proof?A two-column proof is defined as a geometric proof that consists of a list of statements, and the reasons that we know those statements are true.
Statement 1: FG/FH = KJ/KH
Reason 1: Ratio of similar sides of a triangle
Statement 2: ∠H ≅ ∠H
Reason 2: Reflexive Property of Congruence
Statement 3: ΔFHK ~ ΔGHJ
Reason 3: SAS Similarity Theorem
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100 POINTS AND BRAINLIEST
Answer:0.67<1(top part)
3x - y < 1
3/3 1/3=0.33...
0.33..-y < 1
-0.33=0 1-0.33..=0.67<1
i only know the top art sorry
Answer:
its 0.67
Step-by-step explanation:
Will give Brainly please
The value of the mean excluding the outlier is 130. 5
What is an outlier?An outlier can be defined as a data point that differs significantly or greatly from other observations.
It occurs as a result of;
variability in the measurement indication of novel dataexperimental errorFrom the information given, we have that;
121, 89, 410, 203, 55, 230, 182, 148, 135, 233, 11, 219, 108, 192
Since, the outlier is 410
The mean is given as;
= 121 + 89+ 203+ 55 + 230+182 + 148 + 135 + 233+ 11+ 219 + 108 + 192/13
Add the values
= 1696/13
= 130. 5
Hence, the value is 130. 5
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A cheetah ran 196 meters in 8 seconds. How long will it take for the cheetah to run 147 meters?
Answer:
Step-by-step explanation
1. 196:8=147:x
2. you multiply the outisde numbers with the inner numbers
196*x=147*8
196x=1176
then find x
x=1176/196
x=6seconds
Answer:
We can use the ratio of distance to time for the cheetah's first run to find how long it will take to run 147 meters.
The speed of the cheetah is given by:
Speed = distance/time
In the first run, the cheetah ran 196 meters in 8 seconds, so its speed was:
Speed = 196/8 = 24.5 meters per second
To find out how long it will take for the cheetah to run 147 meters, we can use the speed we just calculated and the distance we want to find:
Speed = distance/time
24.5 = 147/time
Solving for time:
time = 147/24.5
time = 6 seconds
Therefore, it will take the cheetah 6 seconds to run 147 meters.
Does this graph represent a function?Explain
Check the picture below.
A chord which passes through the centre is called · A. radius · B. diameter · C. arc · D. none
Answer:
It would be a diameter
Step-by-step explanation:
The diameter is also a chord.
If i had 1 apple and another apple how many apples would i have?
Answer:
Two
Step-by-step explanation:
It's just- 1+1
Answer: 1 + 1 = 2
Step-by-step explanation:
what is the square root of 4761
The square root of 4761 is found to be 69.
If there is a number a, and there is another number b. Now, if we multiply a with a and we get the number b, then we say that the number a is the square root of the number b.
It can be written as,
a = √b
This sign "√" is called the sign on under root. So, now we ae to find the square root of the number 4761,
First we will find the factor of the number 4761 and then make the pair of two each and then multiply to find the root.
4761 = 3 x 3 x 23 x 23
Now, 3 x 23
So, the square root of 4761 is 69.
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Federico makes 60% of the free throw shots he takes in basketball. Federico is fouled, and he is in a one-and-one shooting situation meaning that he only gets a second free throw shot if he makes his first one. Each free throw shot is worth one point. What is the probability that Federico scores one point in this situation?
Based on the question given, the probability that Federico scores one point in this situation is 0.24, or 24%
Calculating the Probability of Scoring One Point in a One-and-One Free Throw Situation in BasketballSince Federico makes 60% of his free throws, the probability that he makes his first free throw is 0.6. If he makes his first free throw, he will get a second free throw, and the probability that he makes his second free throw is also 0.6.
If he misses his first free throw, he will not get a second free throw, and he will score zero points in this situation.
So, to find the probability that Federico scores one point in this situation, we need to find the probability that he makes his first free throw and misses his second free throw:
P(score 1 point) = P(makes 1st free throw) * P(misses 2nd free throw)
= 0.6 * (1 - 0.6) [since the probability of missing a free throw is 1 minus the probability of making it]
= 0.6 * 0.4
= 0.24
Therefore, the probability that Federico scores one point in this situation is 0.24, or 24%
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Triangle FGH is similar to triangle ABC.
Solve for x.
Answer:
PLEASE MARK BRAINLIEST.
Step-by-step explanation:
Notice how the triangle's side lengths are scaled up by a factor of 2. This means that FH*2=x. Solving for x, we get that x=6*2= 12 units.
Need help with this work sheet
1) Note that it can be concluded that Rishi is not doing well with his budget. The actual overshot the by 5%. See attached Spreadsheet.
2) If the driver who hit Rishi does not have Insurance and neither does Rishi (according to the budget) then Rish will have to save up for a new car because he didn't include the cost of insurance in his budget.
What is a budget and why is it important?A budget is a financial plan that outlines expected income and expenses for a specific period, typically a month or a year.
It helps individuals and organizations to manage their finances by ensuring that they do not spend more money than they earn, and that they allocate their funds in a way that aligns with their goals and priorities.
A budget is important because it enables people to make informed financial decisions, avoid debt, and save money for future expenses.
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Please help integrate Cos^3 x + ( tan^2 5x - Sec 2x )/7 x
Answer:
Step-by-step explanation:
Nora bought a motorcycle for $12,000. One year later, she looked online and found that the value of her motorcycle had decreased to about $10,560. Based on this online research, she expects the motorcycle to continue decreasing in value each year.
Answer:y=12000(0.88)^x
$6,330
Step-by-step explanation: I got it wrong and saw the answer
Find the volume of the composite solid below. Round to the nearest tenth.
a
310.7 inches cubed
b
315 inches cubed
c
320.7 inches cubed
d
204.1 cubic inches
The volume of the composite solid is 320.7 cubic inches.
What is a composite solid?A composite solid is a three-dimensional object that is created by combining or "composing" two or simpler three-dimensional shapes, such as prisms, cylinders, pyramids, cones, or spheres. The combined shape may be more complicated or asymmetrical than the sum of its parts, yet it may still be measured and examined using the same geometrical rules and formulas. Cones with a frustum or truncated bases, pyramids with rectangular or triangular bases, and structures created by fusing together cylinders, prisms, or spheres are a few examples of composite solids. In order to build and create complicated structures and objects, composite solids are frequently utilized in architecture, engineering, and manufacturing.
To find the volume of the composite solid, we need to find the volumes of each of its components and add them together.
The volume of a hemisphere with a radius of 5 inches is given by:
V_hemisphere = [tex]\frac{2}{3}\pi r^{3}[/tex] = [tex]\frac{2}{3}\pi 5^{3}[/tex] = 523.6 cubic inches
Since there are two hemispheres, the total volume of the hemispheres is:
V_total_hemispheres = 2V_hemisphere = 2(523.6) = 1047.2 cubic inches
The cylinder has a radius of 5 inches and a length of 13 inches. The volume of a cylinder is given by:
V_cylinder = [tex]\pi r^2h[/tex] = [tex]\pi 5^2(13)[/tex] = 1025.0 cubic inches
The total volume of the composite solid is:
V_total = V_total_hemispheres + V_cylinder = 1047.2 + 1025.0 = 2072.2 cubic inches
Rounding to the nearest tenth, we get:
V_total ≈ 320.7 cubic inches
Therefore, the answer is option (c) 320.7 cubic inches.
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How do you do 3 + 4?
7
We can solve it by using a fractional part of a component of your body known as brain... which you might not have considering you asked such an high end mathematical question... This can be solved using the concept of Addition...
During lunch, Dasia drinks 2 3/4 cups of milk. Taniya drinks 1 1/6 cups of milk, Calixte drinks 8/8 cups of milk. How much milk do the 3 students drink?
The amount of milk the 3 students drink is 4 11/12 cups of milk
How much milk do the 3 students drink?From the question, we have the following parameters that can be used in our computation:
Dasia = 2 3/4
Taniya = 1 1/6
Calixte = 8/8
The amount of milk the 3 students drink is calculated as
Total = 2 3/4 + 1 1/6 + 8/8
Evaluate the sum
Total = 4 11/12
Hence, the total is 4 11/12 cups of milk
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what is the secant in trigonometry?
Secant can be defined as the reciprocal of cosine. Secant of angle A will be hypotenuse/adjacent.
There are three basic trigonometric ratios. Sin, Cos and Tan.
Sin = opposite side/ hypotenuse
Cos = adjacent side/ hypotenuse
Tan = opposite side/ adjacent side
Here in the give image, Sin(A) = a/c
Cos(A) = b/c
Tan(A) = a/b
There are reciprocals for each trigonometric functions
Cosecant is the reciprocal of sine. Cosec(A) = c/a
Secant is the reciprocal of Cosine. Sec(A) = c/b
Cotangent is the reciprocal of Tangent . Cot(A) = b/a
So secant is one of inverse trigonometric functions.
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True or false : A pure monopoly involves a very large number of firms producing a single unique product.
The solution is, a single firm producing a product for which there are no close substitutes.
What is pure monopoly ?A pure monopoly has been characterized mostly as individual manufacturer sellers, i.e., 100 percent of the market share. Throughout the UK, a corporation can be considered and has monopolistic control if someone has a market penetration of further above 25 percent.
here, we have,
A pure monopoly is a single supplier having a market or industry i.e. defined.
The firm should be considered as an industry also in this there is no competitor or any subsitution existed.
It can be arise at the time when the market share of the one firm is more than 90%
So as per the given situation, the above represent the answer
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A tessellation is a ____ pattern that completely covers a plane with no gaps or overlaps.
Proportional
Repeating
Reflection
Transformation
Answer:
Repeating
Step-by-step explanation:
A Tessellation is when you cover a surface with a pattern of flat shapes, so there are no gaps. So, the answer is Repeating.
How to convert 100 ml to l?
The conversion of the milliliters to liters the value of 100 milliliters is equal to ( 0.1 ) liters .
Converting milliliters to liters we have ,
Milliliters and liters are the units which is required to measure volume of the liquid .1 liters is equal to 1000 milliliters
⇒ 1000 milliliters = 1 liters
⇒ 1 milliliters = ( 1 / 1000 ) liters
⇒ 100 milliliters = ( 100 / 1000 ) liters
⇒ 100 milliliters = ( 1 / 10 ) liters
⇒ 100 milliliters = ( 0.1 ) liters
Therefore, the value of the converting the 100 milliliters to liters is equal to ( 0.1 ) liters .
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8 6 4 2 ... next three integers
you need to subtract 2
ok so write about the chapter 1- 12 travellers question and answer
where's the question tho
Answer:
without question how am i suppsed to answer..............
12. When 3a2-7a+6 is subtracted from 4a²-3a +4, the result is
(1) a² +4a-2
(2) a²-10a-2
(3)-a²-4a+2
(4) 7a²-10a+10
Answer:
(1) a² +4a-2
Step-by-step explanation:
[tex]4a^2-3a\:+4\:-\:\left(3a^2-7a+6\right)\\\\= 4a^2-3a\:+4\:- 3a^2 + 7a -6[/tex]
Grouping like terms
[tex](4a^2 -3a^2) +(-3a + 7a) +(4 - 6)\\\\= a^2 +4a - 2[/tex]
PLEASE HELP ME!
Question in image. Thank you huh
The end behavior of the polynomial is defined by:
NEG/EVENas x goes to ∞, f(x) goes to -∞as x goes to -∞, f(x) goes to -∞How to identify the end behavior of the polynomial?Here we want to find the end behavior of a polynomial, to do it, we need to look at the degree and the sign of the leading coefficient.
Remember that the degree is the largest exponent of the polynomial.
Here we can see that the degree is 12 (on the fourth term), so it is even.
And the leading coefficient (the coefficient in the term with the largest exponent) is -10, so it is negative.
Then the first correct option is:
NEG/EVENEven means that both ends tend to the same value, and in this case, a negative leading coefficient means that both ends tend to negative infinity, then:
as x goes to ∞, f(x) goes to -∞as x goes to -∞, f(x) goes to -∞Learn more about end behavior at:
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f c(x) = 4x – 2 and d(x) = x2 + 5x, what is (c circle d) (x)?
Answer:
[tex]16x^2-24x+9[/tex]
Step-by-step explanation:
To find (c circle d)(x), we need to first find d(c(x)) and then simplify.
First, we need to find c(x) and substitute it into d(x), as follows:
d(c(x)) = d(4x - 2) = (4x - 2)^2 + 5(4x - 2)
Expanding the square and simplifying, we get:
d(c(x)) = 16x^2 - 24x + 9
Now, we have (c circle d)(x) = d(c(x)) = 16x^2 - 24x + 9.
Helpppppp
It’s about finding the missing angle it’s easy but I forgot how too
Angle number 2, represents measures the ∠SXU.
What is a transversal?We know when a transversal intersects two parallel lines at two distinct points,
Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.
Given, Are three lines RS, TU, and VW and TU intersects RS and VW at
X and Y respectively.
We know when we write an ∠ABC we measure the angle of 'B'.
Given, An ∠SXU, in which we are measuring the angle of X with respect to S and U.
Therefore, 2 is the number that represents ∠SXU.
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Suppose two bicyclists start at the same location.
The first bicyclist rides due south and the other rides due east. Find the speed that each bicyclist rode in miles per hour if they are 12√2 miles apart after riding for 1.5 hours at the same speed.
Answer:
8 Mph
Step-by-step explanation:
We can solve this problem by using the Pythagorean theorem, which relates the lengths of the sides of a right triangle. Let's call the speed of the first bicyclist "v1" and the speed of the second bicyclist "v2". After 1.5 hours of riding, the first bicyclist has traveled 1.5v1 miles to the south, and the second bicyclist has traveled 1.5v2 miles to the east. The distance between them is the hypotenuse of a right triangle with legs of length 1.5v1 and 1.5v2:
c^2 = (1.5v1)^2 + (1.5v2)^2
where c is the distance between the two bicyclists, which is given as 12√2 miles. Substituting and simplifying, we get:
(12√2)^2 = (1.5v1)^2 + (1.5v2)^2
288 = 2.25v1^2 + 2.25v2^2
128 = v1^2 + v2^2
We also know that the two bicyclists are traveling at the same speed, so v1 = v2. Substituting this into the equation above, we get:
128 = 2v1^2
v1^2 = 64
v1 = √64 = 8
Therefore, each bicyclist is traveling at a speed of 8 miles per hour.
Refer to the image attached.
What is 5/9 as a percent?.l