Answer:
Given system of linear equations are
2x+3y+3z=5
x−2y+z=−4
3x−y−2z=3.
Represent it in matrix form
⎣
⎢
⎢
⎡
2
1
3
3
−2
−1
3
1
−2
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
x
y
z
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
5
−4
3
⎦
⎥
⎥
⎤
which is in the form of AX=B
A=
⎣
⎢
⎢
⎡
2
1
3
3
−2
−1
3
1
−2
⎦
⎥
⎥
⎤
∣A∣=10+15+15=40
=0
∴ A
−1
exists
To find adjoint of A
A
11
=5,A
12
=5,A
13
=5
A
21
=3,A
22
=−13,A
23
=11
A
31
=9,A
32
=1,A
33
=−7
Adj(A)=co-factor
⎣
⎢
⎢
⎡
5
3
9
5
−13
1
5
11
−7
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
5
5
5
3
−13
11
9
1
−7
⎦
⎥
⎥
⎤
A
−1
=
∣A∣
1
Adj(A)
=
40
1
⎣
⎢
⎢
⎡
5
5
5
3
−13
11
9
1
−7
⎦
⎥
⎥
⎤
X=A
−1
B
=
40
1
⎣
⎢
⎢
⎡
5
5
5
3
−13
11
9
1
−7
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
5
−4
3
⎦
⎥
⎥
⎤
X=
40
1
⎣
⎢
⎢
⎡
25−12+27
25+52+3
25−44−21
⎦
⎥
⎥
⎤
X=
40
1
⎣
⎢
⎢
⎡
40
80
−40
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
x
y
z
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
1
2
−1
⎦
⎥
⎥
⎤
Hence, x=1,y=2 and z=−1
The solution to the system of equations is
x = 3
y = 2
z = 2
How to solve the simultaneous linear equation?To solve for x, y, and z, we can use the elimination method or substitution method. Here, we will use the elimination method.
First, we will eliminate y from the equations by multiplying the first equation by 3 and the second equation by 1, and then adding them:
(3) (2x – y + 3z = 10)
6x – 3y + 9z = 30
(1) (x + 3y – 2z = 5)
x + 3y – 2z = 5
Adding the two equations gives:
7x + 7z = 35
Simplifying, we get
x + z = 5 (Equation 1)
Next, we will eliminate y again by multiplying the second equation by 2 and the third equation by 3, and then adding them:
(2) (x + 3y – 2z = 5)
2x + 6y – 4z = 10
(3) (3x – 2y + 4z = 12)
9x – 6y + 12z = 36
Adding the two equations gives:
11x + 8z = 46
Substituting x + z = 5 from Equation 1 into the above equation, we get:
11(x + z) + 8z = 46
11x + 19z = 46
Solving for z, we get:
z = 2
Substituting z = 2 into x + z = 5 from Equation 1, we get:
x + 2 = 5
x = 3
Finally, substituting x = 3 and z = 2 into any of the original equations, we can solve for y:
2x – y + 3z = 10
2(3) – y + 3(2) = 10
6 – y + 6 = 10
y = 2
Therefore, the solution to the system of equations is:
x = 3
y = 2
z = 2
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(Time limit)
Tell me the domain
Tell me the range
Tell me whether the graph is a function or not
The answer choices are below
A relation represents a function when each input value is mapped to a single output value.
On a graph, a function is represented if the graph contains no vertical aligned points, that is, if there are no values of x at which we could trace a vertical line that would cross the graph of the function more than once.
Tracing a vertical line for any x > -3, the vertical line would cross the graph at two points, meaning that the relation is not a function.
As for the domain and the range, we have that:
The domain is: x ≥ -3 -> values of x on the graph.The range is: all real numbers -> values of y on the graph.More can be learned about relations and functions at brainly.com/question/10283950
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So I think that this is a continuation of question 5. Thank you for the help.
b) By basing on the findings in part (a), we rejected the null hypothesis. This implies that a Type I error – which is the mistake of disregarding a validly-true null supposition – could have potentially been made.
(c) Since the confidence interval holds both negative and positive values, we are not able to confirm that leastwise some dissimilarity might exist between these two proportions.
d) Raising the power of the test may be achievable by lessening the significance level.
How to explain the hypothesisIn this state, it would indicate that we concluded that there exists a considerable divergence between the proportion of men and women intending to vote for Trump when factually there is no distinction.
Raising the power of the test may be achievable by lessening the significance level. Doing so will penalize us with being more lenient towards taking up the alternate assumption, consequently reducing the likelihood of having a Type II error.
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PLEASE HELP (WILL GIVE BRAINLIEST
Answer:
V = 62.8 m[tex]^{3}[/tex]
Step-by-step explanation:
V = pi × (radius)[tex]^{2}[/tex] × height
V = [tex]\pi[/tex] × [tex]r^{2}[/tex] × h
V = (3.14 × [[tex]2^{2}[/tex]]) × 5
V = (3.14 × 4) × 5
V = 12.56 × 5
V = 62.8 m[tex]^{3}[/tex]
I need help with this pre calculus question , i understand how to find the period i just don’t understand this graph
The period of the function in the graph is 2π
What is period of a function?Period represents the distance across horizontally located between successive duplicates of an equivalent outline within a graphed function.
In other words, we can say that period is the distance to complete an oscillation where this distance is counted in time. Hence period is measured is seconds
In the graph, the period can be calculated using the points
2π and 0 OR -π and πThese points shows a complete oscillation.
Using from 2π to 0
= 2π - 0
= 2π
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Find the volume of rectangular prism. (You should have at least 2 steps shows in your work!)(show all decimal places or a fraction)
Answer:
[tex]3 \frac{3}{4} \times 4 \frac{1}{2} \times 5 = \frac{15}{4} \times \frac{9}{2} \times 5 = \frac{675}{8} = 84\frac{3}{8} [/tex]
The volume is 84 3/8 cubic meters = 84.375 cubic meters.
If angle N is vertical to angle M, and m angle M 98° and m angle N = (6x + 2), the x must be
If the "angle M" measures 98° and "angle N" measures (6x + 2)°, then value of "x" must be 16.
When the "two lines" intersect, the opposite angles formed are equal in measure, which means that vertical angles are congruent. So, we have:
⇒ Angle M = Angle N
Using the given values, we can write an equation:
⇒ Angle M = 98° and Angle N = (6x + 2)°,
Setting them equal,
We get,
⇒ 98 = 6x + 2,
Solving for x, we subtract 2 from both sides and then divide by 6:
⇒ 96 = 6x,
⇒ x = 16,
Therefore, the variable "x" must be 16 for "angle N" to be vertical to "angle M".
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The given question is incomplete, the complete question is
If an "angle N" is vertical to "angle M", and measure of "angle M" is 98° and the measure of angle N is (6x + 2)°, the x must be.
Please help with my geometry.
Find the area of the shaded region.
Answer:
192pie
Step-by-step explanation:
To find the area of a circle, it is pie (3.14) times r². The radius is 24, so it is 24² times pie. The area is 576 pie. Now to find the area of the shaded, you would do 1/3 times the area. 1/3 of 576 is 192. The answer is 192pie
Nora is going to invest in an account paying an interest rate of 6.4% compounded
daily. How much would Nora need to invest, to the nearest hundred dollars, for the
value of the account to reach $72,000 in 16 years?
The amount of money that Nora would need to invest is $25913.
How to determine the value of P?In Mathematics and Financial accounting, compound interest can be calculated by using the following mathematical equation (formula):
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where:
A represents the future value.n represents the number of times compounded.P represents the principal.r represents the interest rate.T represents the time measured in years.By substituting the given parameters into the formula for compound interest, we have the following;
[tex]72,000 = P(1 + \frac{0.064}{365})^{365 \times 16}\\\\72,000 = P(1 + 1.75 \times 10^{-4})^{5,840}\\\\72,000 = P(1.000175)^{5,840}[/tex]
P = 72,000/2.77849825425152
Principal, P = $25913.28 ≈ $25913
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The first text message was sent on December 3, 1992. Two decades later, texting has become one of the most popular methods of communication. The number, in millions, of SMS messages sent per year in the United Kingdom is given in the table below. In 2012, the first decrease occurred in the number of SMS messages in the UK and was attributed to the unveiling of Apple’s iMessage on June 6, 2011. Find an exponential model for the number of SMS messages sent annually for years before 2012.
Year 2003 2005 2007 2009 2010 2011
SMS 24086 39751 66331 104358 128462 150651
in
millions
An exponential model for the number of SMS messages sent annually for years before 2012 is [tex]y = 12421e^{0.2325x}[/tex].
How to determine the equation of line of best fit?In this scenario, the year would be plotted on the x-axis (x-coordinate) of the scatter plot while the SMS messages would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.
On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an exponential equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the year and SMS messages, an exponential equation for the line of best fit is given by
[tex]y = 12421e^{0.2325x}[/tex]
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Question 10(Multiple Choice Worth 10 points) (04.05 MC) Davenport University claims to accept 63% of applicants. In a random sample of 1,000 Davenport University applicants, 602 were accepted. Calculate the 95% confidence interval and evaluate whether Davenport's claim seems accurate.
The confidence interval using the 95 percent level of significance is given as CI = (0.57, 0.63)
How to solve for the confidence levelSolve for the sample proportion
= 602/1000 = 0.602
z* is the critical value from the standard normal distribution at the 95% confidence level = (1.96)
n = sample size (1000)
CI = 0.602 ± 1.96√((0.602(1-0.602))/1000)
CI = 0.602 ± 0.032
0.602 - 0.032 , 0.602 + 0.032
CI = (0.57, 0.63)
Hence the confidence interval using the 95 percent level of significance is given as CI = (0.57, 0.63)
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math hw for tonight
help solve this problem! Thank you!
ap cal bc
Answer:
[tex]\sqrt{2}[/tex]
Step-by-step explanation:
When t = 0, the velocity is:
[tex]\begin{aligned}\vec{v}(t)&=3^t \vec{i}+e^{6t} \vec{j}\\\\t=0 \implies \vec{v}(0)&=3^0 \vec{i}+e^{(6 \cdot 0)} \vec{j}\\ &=1 \vec{i}+1 \vec{j} \end{aligned}[/tex]
Speed is the magnitude of the velocity of the object.
[tex]\boxed{\text{A vector $\binom{x}{y}$ has magnitude $\sqrt{x^2+y^2}$}}[/tex]
Therefore, the particle's speed at time t = 0 is:
[tex]\begin{aligned}\implies |v|&=\sqrt{1^2+1^2}\\&=\sqrt{1+1}\\&=\sqrt{2}\end{aligned}[/tex]
Brainliest and points if answered correct!!!!
The amount of laps remaining, y, in a swimmer's race after x minutes can be represented by the graph shown.
coordinate grid with the x axis labeled time in minutes and the y axis labeled number of laps remaining with a line from 0 comma 24 and 6 comma 0
Determine the slope of the line and explain its meaning in terms of the real-world scenario.
The slope of the line is 6, which means that the swimmer will finish the race after 6 minutes.
The slope of the line is 24, which means that the swimmer must complete 24 laps in the race.
The slope of the line is −4, which means that the swimmer will complete 4 laps every minute.
The slope of the line is negative one fourth, which means that the swimmer completes a lap in one fourth of a minute.
since i don't see the graph ill go with... B The slope of the line is 24, which means that the swimmer must complete 24 laps in the race.
-24/6 = -4
Step-by-step explanation:
The slope of the line can be found using the formula:
slope = (change in y) / (change in x)
In this case, we can use the two given points on the line: (0, 24) and (6, 0).
Change in y = 0 - 24 = -24
Change in x = 6 - 0 = 6
Therefore, slope = -24/6 = -4
This means that for every minute that passes, the swimmer completes four laps. The swimmer's pace is steady and consistent throughout the race, gradually decreasing the number of laps remaining until they finish at 0 after six minutes.
Answer:
The slope of the line represents the rate of change in the number of laps remaining per unit of time (in this case, per minute). In other words, it tells us how quickly the swimmer is completing laps.
Since the slope of the line is -4, this means that the swimmer is completing 4 laps every minute. This could be interpreted as the swimmer's pace or speed in the race. The negative sign indicates that the number of laps remaining is decreasing over time, which is expected as the swimmer completes more and more laps.
It's worth noting that the slope is constant throughout the race, meaning that the swimmer is maintaining a consistent pace. This information could be useful for the swimmer and their coach in terms of planning and pacing the race.
I am a little lost and seeking help with this
There is a remarkable discrepancy in perceived organization support amongst female and male employees: women garnered a superior mean score (M=4.65, SD=0.58) as opposed to males (M=4.42, SD=0.70), t(198)=2.51, p<0.05.
How to explain the hypothesisConsequently, we recommend that the committee delve into the source of this divide and take steps to ensure that both sexes receive the same level of solidarity.
It was established that there was no distinct disparity in distributive justice perceptions between female and male employees: females earned a mean score of 4.16 (SD=0.64), while men attained a mean score of 4.14 (SD=0.61), t(198)=0.23, p>0.05.
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The die shown below is a perfect cube with sides of length s.
What is the distance from point A to point B?
Responses
s√2
s √ 2
s√3
s √ 3
2s
2 s
s√5
The distance from the point A to point B is s√3
What is the distance from point A to point B?From the question, we have the following parameters that can be used in our computation:
Perfect cube with sides of length s.
The distance from point A to point B is calculated as
Distance^2 = s^2 + s^2 + s^2
When evaluated, we have
Distance^2 = 3s^2
Take the square roots of both sides
Distance = s√3
Hence, the distance = s√3
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A bottle of water has a diameter of 3 inches and a height of 8 inches, and a mass of 1250 g. What is the volume and density?
The volume of the bottle is 56.52 cubic inches, and the density is 22.12 g/in³.
What is the volume and density of the bootle water?The volume of a cylinder is expressed as;
V = π × r² × h
Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 ).
Density is expressed mathematically as;
p = m / v
Where m is mass and v is volume.
Given that:
Diameter = 3 in
Radius r = diameter/2 = 3/2 = 1.5 in
Height h = 8 in
Mass m = 1250 g
Find the volume:
V = π × r² × h
V = 3.14 × (1.5 in )² × 8in
V = 56.52 in³
Find the density:
p = m / v
p = 1250g / 56.52 in³
p = 22.12 g/in³
Therefore, the density is 22.12 g/in³.
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Solve two shapes below shown in photo:
Answer:
1. 69.73 is the Area of the Rectangle. 50.27 is the Area of the Circle. 2. 120 is the area of the parallelogram, 25.13 is the area of the semi-circle
Step-by-step explanation:
For #1, We can to 15 * 8 to get area of what would be the whole rectangle. It is 120. Then, calculate area of the circle, pi * 4^2(4 because the 8 is a diameter. That totals to 50.27 for the circle. Subtract the two, 120-50.27 and you get 69.73 as the area of the shape excluding the circular portion.
For #2, We can apply the same formula for the circle, and divide it by two this time for 25.13 as the circle area. We can use the paralellogram formula of b*h (6*20) and we get 120 for that area. The total for the whole figure on #2 is 145.13 square units.
Note: unit for both is square units, as it is not specified.
I REALLY NEED HELP LIKE ASAP PLS PLS I HAVE A LOT OF HOMEWORK TO DO PLS ANSWER
5(3n+4n+3) = -125
solve for the value of n pls.
Answer:
n=-4
Step-by-step explanation:
5(3n+4n+3) = -125
First, combine like terms:
5(7n+3) = -125
Then, distribute the 5:
35n+15 = -125
Then, get n by itself:
35n= -140
Then, divide by 35 to get n by itself:
n = -140/35
Simplify
n = -4
Muriel translated the phrase below into an algebraic expression and then evaluated it for n = 4.
the product of a number and 8
Which of the following contains the correct expression and value?
Answer:
[tex]8n=32[/tex]
Step-by-step explanation:
Muriel's algebraic expression for the phrase "the product of a number and 8" would be 8n, where n represents the number. When n = 4, the value of 8n would be 8 times 4, which is 32. Therefore, the correct expression and value is 8n = 32 when n = 4.
Answer:
8n=32
Step-by-step explanation:
got it right on homework
Find the value of $x$ . Write your answer in simplest form. 9 squared 2
The value of the expression 9 squared will be 81.
How to explain the expressionIn Mathematics, it is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.
In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.
The value will be:
= 9²
= 9 × 9.
= 81
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In △ABC, we are told that a=17, ∡B=70∘, and ∡C=48∘. Solve for b and c.
Answer: b=18.1 and c=14.3
Step-by-step explanation:o solve for the lengths of the sides b and c in triangle ABC, we can use the law of sines, which relates the lengths of the sides of a triangle to the sines of the angles opposite those sides. Specifically, the law of sines states that:
a/sin(A) = b/sin(B) = c/sin(C)
where A, B, and C are the angles of the triangle opposite sides a, b, and c, respectively.
Given that a = 17, B = 70°, and C = 48°, we can write:
b/sin(70°) = 17/sin(A)
c/sin(48°) = 17/sin(A)
To solve for b and c, we need to find sin(A). We can do this by using the fact that the angles of a triangle sum to 180°:
A + B + C = 180°
A = 180° - B - C
A = 180° - 70° - 48°
A = 62°
Now we can substitute sin(A) = sin(62°) into the equations above and solve for b and c:
please help me with this. I know the answer for the first one, but I'm just confused about the second one.
Answer: 20
Step-by-step explanation:
because Juanita has a aquarium that is 5 feet LONG, 4 feet WIDE, and 2 feet DEEP, in part b it asks what if the water is 1 foot DEEP so what they're trying to say is what if you replace the original 2 feet DEEP with 1 foot DEEP?
so it would be length x width x depth
5x4x1=20
so the volume is 20ft^3
The letters of "EAGLES" should be evenly spaced across a 63 inch wide banner, with no margins. Each letter is 8 inches wide. How many inches (x) should exist between each pair of letter?
Answer:
1 inch
Step-by-step explanation:
125-foot redwood tree is leaning 20° off vertical. How long will its shadow be when the angle the sunlight makes with the ground is 68°?
Answer:
To solve this problem, we can use trigonometry. Let's call the length of the shadow "s" and the height of the tree "h". Since the tree is leaning, we can't just use the height of the tree directly as one leg of a right triangle. Instead, let's draw a diagram of the situation and see if we can find a way to use trigonometry.
|\
| \
| \ h
|20\
| \
| \
________|____\
s
In this diagram, the angle between the ground and the sunlight is 68 degrees, and the angle between the tree and the ground is 70 degrees (since the tree is leaning 20 degrees off vertical). We can use the tangent function to relate these angles to the lengths of the sides of the triangle:
tan(68) = h / s
tan(70) = h / (s + 125)
We can solve for "h" in terms of "s" using the second equation:
h = (s + 125) * tan(70)
Then we can substitute this expression for "h" into the first equation and solve for "s":
tan(68) = [(s + 125) * tan(70)] / s
s * tan(68) = (s + 125) * tan(70)
s * tan(68) = s * tan(70) + 125 * tan(70)
s = 125 * tan(70) / [tan(68) - tan(70)]
s ≈ 318.8 ft
Therefore , the shadow will be approximately 318.8 feet long.
Step-by-step explanation:
I needed help with this one can some help me
A graph of quadrilateral M'N'O'P' after a vertical translation is shown below.
What is a translation?In Mathematics and Geometry, the translation of a graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.
By translating the pre-image of quadrilateral MNOP vertically downward 4 units, the coordinates of quadrilateral M'N'O'P' include the following:
(x, y) → (x, y - 4)
M (-2, 5) → (-2, 5 - 4) = M' (-2, 1).
N (-3, 2) → (-3, 2 - 4) = N' (-3, -2).
O (-5, 2) → (-5, 2 - 4) = O' (-5, -2).
P (-6, 5) → (-6, 5 - 4) = P' (-6, 1).
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I need help finding 1=cos(8π)+isin(8π) but it has to be divided by 6. I will give 20 points to whoever answers it.
Answer: 1/6 = cos(8π)/6 + i*sin(8π)/6
Step-by-step explanation: In the context of complex numbers, the division of 1 by 6 can be accomplished by employing a straightforward procedure that involves dividing both the real and imaginary components by 6.
The mathematical expression 1/6 may be represented in academic prose via the complex number format (cos(8π)/6 + i*sin(8π)/6).
In a paddock of goats and chickens, there are 67 heads and 166 legs. How many goats are there?
Find the missing exponent 82/256=3/4
The missing exponent of the expression is determined as 4.
What is the value of the missing exponent?The value of the missing exponent is calculated as follows;
The given function is;
81/256 = (3/4)ˣ
To determine the value of the missing exponent, we will apply the power law of indicial equation as follows;
From base of the exponential function, we will determine the value of x;
3⁴/4⁴ = (3/4)x
(3/4)⁴ = (3/4)ˣ
4 = x
Thus, the missing value of the exponential function is determined by applying rules of exponent.
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The complete question is below:
Find the missing exponent 81/256 = (3/4)ˣ
A radioactive element has decayed to 1/32 of its original concentration in 10 yrs. What is the half-life of this element?
The half-life of this radioactive element is approximately 2 years.
We have,
The decay of a radioactive element follows an exponential decay model of the form:
[tex]N = N_0 e^{-kt}[/tex]
where:
N0 is the initial concentration of the radioactive element
N is the concentration after time t
k is the decay constant
We are given that the element has decayed to 1/32 of its original concentration, which means that its current concentration is 1/32 times its initial concentration:
N/N0 = 1/32
Taking the natural logarithm of both sides and rearranging, we get:
ln(N/N0) = ln(1/32) = -3.465
Now we can use the formula for half-life, which relates the decay constant to the half-life t1/2:
t1/2 = ln(2) / k
We can solve for the decay constant k by using the information that the element has decayed to 1/32 of its original concentration in 10 years:
ln(N/N0) = -kt
-3.465 = -k x 10
k = 0.3465
Substituting this value of k into the formula for half-life, we get:
t1/2 = ln(2) / k = ln(2) / 0.3465 = 2.0 x 10^0 years = 2 years.
Therefore,
The half-life of this radioactive element is approximately 2 years.
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Rewrite the equation in Ax+By=C form. Use integers for A,B,and C. y+5=5(x-4)
As per the given details, the equation in Ax + By = C form is -5x + y = -25, where A = -5, B = 1, and C = -25.
To rewrite the equation y+5=5(x-4) in Ax+By=C form, we need to simplify and rearrange the equation to isolate y on one side:
y + 5 = 5(x - 4)
y + 5 = 5x - 20 (Distribute 5 on the right side)
y = 5x - 20 - 5 (Subtract 5 from both sides)
y = 5x - 25
Now the equation is in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. To rewrite it in Ax + By = C form, we need to rearrange the terms to get the x and y terms on the left side and a constant on the right side:
y = 5x - 25
-5x + y = -25
So the equation in Ax + By = C form is -5x + y = -25, where A = -5, B = 1, and C = -25.
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Answer:
second one
the y intercept is 8, the slope is -6/8, reduced -3/4
Step-by-step explanation:
equation if a line in slope intercept form is y=mx+