Answer:
x = 80°
Step-by-step explanation:
100° and x° are adjacent angles on a straight line and sum to 180° , that is
100° + x = 180° ( subtract 100° from both sides )
x = 80°
Match each expression with its value. −9 7 −2 Undefined h( 3.999 ) h(4) h(4.0001) h(9)
The values are: -9, 7, -2, Undefined, Undefined, 8, Undefined, Undefined.
Let's match each expression with its corresponding value:
Expression: -9
Value: -9
Expression: 7
Value: 7
Expression: -2
Value: -2
Expression: Undefined
Value: Undefined
Expression: h(3.999)
Value: Undefined
Expression: h(4)
Value: 8
Expression: h(4.0001)
Value: Undefined
Expression: h(9)
Value: Undefined
Now let's explain the reasoning behind each value:
The expression -9 represents the number -9, so its value is -9.
Similarly, the expression 7 represents the number 7, so its value is 7.
The expression -2 represents the number -2, so its value is -2.
When an expression is labeled as "Undefined," it means that there is no specific value assigned or that it does not have a defined value.
For the expression h(3.999), its value is undefined because the function h(x) is not defined for the input 3.999.
The expression h(4) has a value of 8, indicating that when we input 4 into the function h(x), it returns 8.
Similarly, the expression h(4.0001) has an undefined value because the function h(x) is not defined for the input 4.0001.
Lastly, the expression h(9) also has an undefined value because the function h(x) is not defined for the input 9.
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Evaluate the function as indicated, and simplify.
g(x) = 2x² - 3x + 1
g(x) = 2x² - 3x + 1 =
-2 = 2\((x+2)^{2}\)+ 3(x+2) - 1
-2 = 2( \(x^{2}\) + 4x + 4) + 3(x+2) - 1
-2 = 2\(x^{2}\) + 8x + 8 + 3x + 6 - 1
-2 = 2\(x^{2}\) + 11x + 13
0 = 2\(x^{2}\) + 11x + 15
0 = ( 2x + 5 )(kx + 3 )
2x + 5 = 0 ---> kx= -5/2
x+3=0 ----> x = -3
Recognize that a function is a particular kind of relation where a rule states that every input must be paired with exactly one output.
one of them sums up a function the best?
Recognize that a function is a particular kind of relation where a rule states that every input must be paired with exactly one output. So, this is the best choice.
The function's type is f/x)= 2x 2 + 3x 1.
Explanation: Since the polynomial f(x)=2x33x+1 is continuous and contains continuous derivatives of all orders for all real x, it unquestionably meets the theorem's hypotheses.
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find the value of 8s-5t when s=3 and t=-2
Answer:
34
Step-by-step explanation:
Substitute the values.
s = 3 and t = -2
8s-5t
8 (3) - 5(-2)
( 8 x 3 ) - ( 5 x -2 )
24 + 10 [ - x - = + ]
= 34
the perimeter of a square piece of cardboard is 56 inches. how long is each side of the piece of cardboard ? PLEASE ANSWER ASAP
Answer:
14 inches
Step-by-step explanation:
To calculate the area of a square, multiply the base by itself, which can be expressed as side × side. If a square has a base of length 8 inches its area will be 8 × 8= 64 square inches. Area of a square is given by: A = a2. where a = length of side. Perimeter of a square = 4a.
14 is the answer
ten days after it was launched toward mars in december 1998, the mars cli- mate orbiter spacecraft (mass 629 kg) was 2.87 x 106km from the earth and traveling at 1.20 x 104km/h relative to the earth
The kinetic energy of the Mars Climate Orbiter spacecraft is approx 3.31 x 10^7 joules.
To determine the kinetic energy of the Mars Climate Orbiter spacecraft, we can use the formula:
Kinetic energy = (1/2) * mass * velocity^2
Given:
Mass of the spacecraft (m) = 629 kg
Velocity of the spacecraft (v) = 1.20 x 10^4 km/h
First, we need to convert the velocity from km/h to m/s:
1 km = 1000 m
1 h = 3600 s
Velocity in m/s = (1.20 x 10^4 km/h) * (1000 m/km) / (3600 s/h) ≈ 333.33 m/s
Now, we can calculate the kinetic energy:
Kinetic energy = (1/2) * (629 kg) * (333.33 m/s)^2
Kinetic energy ≈ 3.31 x 10^7 joules
Therefore, the kinetic energy of the Mars Climate Orbiter spacecraft is approximately 3.31 x 10^7 joules.
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if a+b=26 what is the value of 2(a+b)+ a+b/6+(a+b)^2-2
Answer:
730 1/3
Step-by-step explanation:
It should be written as:
2(a+b)+ (a+b)/6+(a+b)^2-2, so that the quantity a + b is divided by 6 and not just b.
Hence, we have that
2(a+b)+ (a+b)/6+(a+b)^2-2 =
2(26) + 26/6 + 26^2 - 2 =
52 + 13/3 + 676 - 2 =
52 + 4 1/3 + 674 =
1/3 + 56 + 674 =
1/3 + 730 =
750 1/3
consider an n × m matrix a of rank n. show that there exists an m × n matrix x such that ax = in. if n < m, how many such matrices x are there?
There are infinitely many such choices of (m - n) linearly independent vectors, so there are infinitely many such matrices X.
What is the rank of the matrix A?Since the rank of the matrix A is n, there exist n linearly independent rows in A. Without loss of generality, we can assume that the first n rows of A are linearly independent.
Let B be the matrix consisting of the first n rows of A. Then, B is an n × m matrix of rank n. By the rank-nullity theorem, the null space of B is of dimension m - n.
We can choose any m - n linearly independent vectors in R^m that are orthogonal to the rows of B. Let these vectors be v_1, v_2, ..., v_{m-n}. Then, we can form an m × n matrix X as follows:
The first n columns of X are the columns of B^(-1), where B^(-1) is the inverse of B.
The remaining m - n columns of X are the vectors v_1, v_2, ..., v_{m-n}.
Then, we have:
AX = [B | V] X = [B^(-1)B | B^(-1)V] = [I | 0] = I_n,
where V is the matrix whose columns are the vectors v_1, v_2, ..., v_{m-n}. Therefore, X is an m × n matrix such that AX = I_n.
If n < m, then there are infinitely many such matrices X. To see this, note that we can choose any (m - n) linearly independent vectors in R^m that are orthogonal to the rows of B, and use them to form the last (m - n) columns of X. There are infinitely many such choices of (m - n) linearly independent vectors, so there are infinitely many such matrices X.
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Can somebody plz help answer these questions correclty (like what each letter equals) thanks :3
WILL MARK BRAINLIEST WHOEVER CAN ANSWER THIS FIRST :DD
Answer:
X=12
y=34
z=45
m=33
n=27
z=27
Step-by-step explanation:
there u go
Answer:
23) x -3 = 9
x=9+3=12
24) y-11=23
y=23+11=34
25) z-8=37
z=37+8=45
26) m-16=17
m=17+16=33
27) n-9=18
n=18+9=27
28) z-14=13
z=13+14=27
12x — 8 = 3x + 64; x =
Answer:
x= 8
Step-by-step explanation:
12x - 8 = 3x + 64
12x - 3x = 64 + 8
9x = 72
x= 72÷9
x = 8
Answer:
x=8
Step-by-step explanation:
12x-8=3x+64 ( collect like terms)
=12x-3x=64+8 (add or subs like terms)
=9x=72 (divided both sign by 9)
=9x/9=72/9=8
x=8
The results of a paired-difference test are shown below to the right. d = 5.6
a. Construct and interpret a 99% confidence interval estimate for the paired difference Sd =0.25 in mean values.
b. Construct and interpret a 90% confidence interval estimate for the paired difference n=16 in mean values_ (Round to two decimal places as needed:) Choose the correct answer below:
OA This interval will contain the true population mean 90% of the time_
OB. There is a 90% chance that the true population mean is contained in the interval.
Oc: If many random samples of this size were taken and intervals constructed, 90% of them would contain the true population mean: 0
D. Approximately 90% of the differences will be contained in the interval.
If many random samples of this size were taken and intervals constructed, 90% of them would contain the true population mean. In repeated sampling, about 90% of the constructed confidence intervals will capture the true population mean difference. The correct answer is C.
When we construct a confidence interval, it is important to understand its interpretation. In this case, the correct answer (Oc) states that if we were to take many random samples of the same size and construct confidence intervals for each sample, approximately 90% of these intervals would contain the true population mean difference.
This interpretation is based on the concept of sampling variability. Due to random sampling, different samples from the same population will yield slightly different sample means.
The confidence interval accounts for this variability by providing a range of values within which we can reasonably expect the true population mean difference to fall a certain percentage of the time.
In the given scenario, when constructing a 90% confidence interval for the paired difference, it means that 90% of the intervals we construct from repeated samples will successfully capture the true population mean difference, while 10% of the intervals may not contain the true value.
It's important to note that this interpretation does not imply a probability or chance for an individual interval to capture the true population mean. Once the interval is constructed, it either does or does not contain the true value. The confidence level refers to the long-term behavior of the intervals when repeated sampling is considered.
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At a restaurant, Julio's bill totals $37.60 (before tip). He leaves a 15% tip. Find the amount Julio left for tip.
Answer:
$5.64 is left for tip.
Step-by-step explanation:
Given that,
The total bill of Julio = $37.60
He leaves a 15% tip.
We need to find the amount Julio left for the tip.
The left amount can be calculated as follows :
\(L=15\%\ of\ 37.60\\\\=\dfrac{15}{100}\times 37.60\\\\=\$5.64\)
So, Julio left $5.64 for tip.
Out of all the readers who visit a blog, 11% click on an advertisement. Predict how many readers will click on an advertisement if 500 people visit the blog in one day.
ميز هذا السؤال Suppose that the daily salaries in JD of workers in the Hashemite University are normally distributed with a mean of 70 JD and a standard deviation of 10 JD. Determine the value of the daily salary (X) such that 25% of the daily salaries are greater than X? 1. 071.3 JD 2. 073.9 JD 3. 76.7 JD 4. 80.4 JD
To find the value of the daily salary (X) such that 25% of the daily salaries are greater than X, we need to find the corresponding z-score using the standard normal distribution.
First, we convert the given percentage to a z-score. Since we want the upper 25% (greater than X), the corresponding z-score is the value that leaves 25% in the lower tail. Using a standard normal distribution table or a calculator, the z-score corresponding to 25% is approximately 0.674.
Next, we use the formula for z-score conversion: z = (X - μ) / σ, where μ is the mean and σ is the standard deviation. Plugging in the given values, we have 0.674 = (X - 70) / 10.
Solving for X, we get X = 0.674 * 10 + 70 = 6.74 + 70 = 76.74.
Rounding to one decimal place, the value of the daily salary X is approximately 76.7 JD. Therefore, option 3, 76.7 JD, is the correct answer.
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The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answer:
x=17 degrees
Step-by-step explanation:
All 3 angles = 180 degrees
So 90 + 54 + (x+19) = 180
Combine like terms
163 + x = 180
Subtract 163 from both sides
x = 180-163
x = 17
write one problem statement for each subject area that stactistics can solve
Answer:
look in explanation
Step-by-step explanation:
what is the probability of the ball hitting u in dodge ball in pe
what is the ratio of your computer to everyone else's in comp science
how much of your essay did you finish (in a fraction)
how many people are there in psychology class for every notebook?
Find the nominal rate of interest convertible monthly at which the accumulated value of $1000 at the end of 11 years is $4000. A. 15.203% B. 13,431% C. 15.836% D. 161,175% E. 12.669%
The correct answer is A. 15.203%.The nominal rate of interest convertible monthly, at which the accumulated value of $1000 at the end of 11 years is $4000, can be determined using the formula for compound interest.
To find the nominal rate of interest convertible monthly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the accumulated value, P is the principal amount, r is the nominal interest rate, n is the number of compounding periods per year, and t is the number of years.
In this case, we have:
A = $4000
P = $1000
n = 12 (since it is compounded monthly)
t = 11
Substituting these values into the formula, we get:
$4000 = $1000(1 + r/12)^(12*11)
To solve for r, we need to isolate it in the equation. However, this involves a complex calculation that cannot be easily solved algebraically. Therefore, we can use numerical methods or financial calculators to find the value of r.
Using these methods, we find that the nominal rate of interest convertible monthly is approximately 15.203% (rounded to three decimal places). Therefore, option A is the correct answer.
It's important to note that in real-world scenarios, interest rates are typically expressed as annual rates. However, the question specifically asks for the nominal rate of interest convertible monthly, which is why the answer is given as a monthly percentage.
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The standard deviation is the blank______ of the variance.
a) square
b) square root
c) inverse exponent
Standard deviation is the square root of variance .
So,
It is used in measuring any deviation or shift from the calculated mean.
From a data set, the mean of the data can be determined with which the standard deviation can be measure.
Therefore, Standard deviation is use to measure variation that exist in an individual data set. There are different type of data set from which variation is measured.
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What does this mean?
Suggested to look at picture
Linear functions: Y = mx + b
m = slope (rate of change) ***when it is linear, the slope is constant.
b = y-intercept (starting point)
x = input
y = output
y = 8 - 1.25x
Answer:
Step-by-step explanation:
You need to find out if the equation is linear or not. A linear equation will have a constant change. So as x increases by 1, y decreases by 1.25. You would check every line given and see if it continues the same. If so then it is a linear equation. Your slope is the rate of change, meaning how much does x and y increase or decrease. Your b is where the equation starts. You would find b at the top of the table. The first # on this is 0. 8 is your b. x is the input that is multiplied to the slope to receive the output:y.
2.5.7. Write the general solution to the following linear systems in the form (2.27). Clearly identify the particular solution x* and the element z of the kernel. (a) -y +32 = 1, 1 - 1 0 1 -2 (b y 3 1 (c) 2 0 -4 -6 2 - 1 -2 1 2 2 (d) -1 2 2 2 - 4 y (e) 0 1 -3 6 3 3 1 0 -1 1 -3 2 2 -2 1 3 -1 5 1 1 3 (g) 0 y 5 2 - 2 -8 1 2 -3 4 1 1 -8 -1 90 S
It seems that your question is about finding the general solution to a system of linear equations. However, the given equations are not properly formatted and contain typos. Please provide the correct equations, and I'll be happy to help you find the general solution in the form of x* and z.
(a) -y + 32 = 1, 1 -1 0 1 -2
To write the general solution in the form (2.27), we first need to convert the system to an augmented matrix:
[1 -1 0 1 | -2]
[0 -1 0 -1 | 31]
We can solve this matrix using elementary row operations:
[1 -1 0 1 | -2] [1 -1 0 1 | -2]
[0 1 0 1 | -31] => [0 1 0 1 | -31]
----------------- -----------------
[1 0 0 2 | -29] [1 0 0 2 | -29]
[0 1 0 1 | -31] [0 1 0 1 | -31]
From this, we can see that the general solution is:
x1 = -2x4 - 29
x2 = -x4 - 31
y = y
z = [1, 0, 0, 0]
Therefore, the particular solution is x* = [-29, -31, y, 0] and the element z of the kernel is [1, 0, 0, 0].
(b) y + 3x1 = 1, x2 - 2x3 = -3
To write the general solution in the form (2.27), we can convert the system to an augmented matrix:
[3 1 0 | 1]
[0 1 -2 | -3]
We can solve this matrix using elementary row operations:
[3 1 0 | 1] [3 1 0 | 1]
[0 1 -2 | -3] => [0 1 -2 | -3]
-------------- -------------
[3 0 2 | -2] [1 0 2/3 | -2/3]
[0 1 -2 | -3] [0 1 -2 | -3]
From this, we can see that the general solution is:
x1 = -2/3x3 - 2/3
x2 = -2x3 - 3
y = y
z = [2/3, -2, 1]
Therefore, the particular solution is x* = [-2/3, -3, y, 0] and the element z of the kernel is [2/3, -2, 1].
(c) 2x1 - 4x2 - 6x3 = 2, x1 - 2x3 = -1, -2x2 + x3 = 2
To write the general solution in the form (2.27), we can convert the system to an augmented matrix:
[2 -4 -6 | 2]
[1 0 -2 | -1]
[0 -2 1 | 2]
We can solve this matrix using elementary row operations:
[2 -4 -6 | 2] [1 -2 -3 | 1]
[1 0 -2 | -1] => [0 1 -2 | 1/2]
[0 -2 1 | 2] [0 0 -3 | 0]
From this, we can see that the general solution is:
x1 = -3x3 + 1
x2 = 2x3 + 1/2
x3 = x3
z = [3/2, 1/4, 1]
Therefore, the particular solution is x* = [1, 1/2, 0, 0] and the element z of the kernel is [3/2, 1/4, 1].
(d) -x1 + 2x2 + 2x3 = 2, 2x1 - 4x2 - 4x3 = -4, y = y
To write the general solution in the form (2.27), we can convert the system to an augmented matrix:
[-1 2 2 | 2]
[2 -4 -4 | -4]
[0 0 0 | y]
We can solve this matrix using elementary row operations:
[-1 2 2 | 2] [1 -2 -2 | -2]
[2 -4 -4 | -4] => [0 0 0 | 0]
[0 0 0 | y] [0 0 0 | y]
From this, we can see that the general solution is:
x1 = -2x2 - 2x3 - 2
x2 = x2
x3 = x3
y = y
z = [2, 1, 0]
Therefore, the particular solution is x* = [-2, 0, 0, y] and the element z of the kernel is [2, 1, 0].
(e) x2 - 3x3 + 6x4 = 5, x2 + 3x3 - x4 = 1, 3x2 - x3 + 5x4 = 1
To write the general solution in the form (2.27), we can convert the system to an augmented matrix:
[0 1 -3 6 | 5]
[0 1 3 -1 | 1]
[0 3 -1 5 | 1]
We can solve this matrix using elementary row operations:
[0 1 -3 6 | 5] [0 1 -3 6 | 5]
[0 1 3 -1 | 1] => [0 1 3 -1 | 1]
[0 3 -1 5 | 1] [0 0 10 -17 | -2]
From this, we can see that the general solution is:
x1 = -2x3 + 3/5x4 - 1/5
x2 = -3x4 + 2/5
x3 = x3
x4 = x4
z = [-3/5, 0, 1, 0], [-2/5, -3, 0, 1]
Therefore, the particular solution is x* = [-1/5, 2/5, 0, 0] and the elements z of the kernel are [-3/5, 0, 1, 0] and [-2/5, -3, 0, 1].
(g) y + 5x2 = 2, 2x2 - 2x3 - 8x4 = -1, 4x2 - 3x3 + 90x4 = 3
To write the general solution in the form (2.27), we can convert the system to an augmented matrix:
[0 1 0 0 | 2]
[0 2 -2 -8 | -1]
[0 4 -3 90 | 3]
We can solve this matrix using elementary row operations:
[0 1 0 0 | 2] [0 1 0 0 | 2]
[0 2 -2 -8 | -1] => [0 1 -1/2 -4 | -1/2]
[0 4 -3 90 | 3] [0 0 1/2 -49/8 | -5/8]
From this, we can see that the general solution is:
x1 = -1/2x3 + 49/16x4 + 1/16
x2 = 2 - x3/2 + 2x4
x3 = x3
x4 = x4
z = [-49/8, 2, 1/2, 0], [-5/8, 0, 0, 1]
Therefore, the particular solution is x* = [1/16, 2, 0, 0] and the elements z of the kernel are [-49/8, 2, 1/2, 0] and [-5/8, 0, 0, 1].
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Complete a Fish-bone
diagram for the following problem:
a. Problem
statement: My microwave cooked
popcorn burned.
The Fishbone diagram identifies possible causes for the problem of burned microwave popcorn, including equipment condition, popcorn quality, timing, temperature control, popcorn bag or container, kernel distribution, popcorn quantity, microwave maintenance, popcorn storage, and power fluctuations.
Problem: My microwave cooked popcorn burned.
1. Equipment: Check the microwave's condition, age, and power settings.
2. Popcorn: Examine the popcorn brand, quality, and packaging instructions.
3. Timing: Analyze the cooking time set for the popcorn.
4. Temperature: Assess the microwave's heating consistency and temperature control.
5. Popcorn bag/material: Investigate the type of bag or container used for the popcorn.
6. Kernel distribution: Consider the distribution of kernels within the bag.
7. Popcorn quantity: Evaluate the amount of popcorn used for cooking.
8. Microwave maintenance: Check if the microwave is clean and free from residue.
9. Popcorn storage: Consider the storage conditions and age of the popcorn.
10. Power fluctuations: Investigate if there were any power surges or fluctuations during cooking.
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the interpretation of the slope is different in a multiple linear regression model as compared to a simple linear regression model. t or f
True. the interpretation of the slope is different in a multiple linear regression model as compared to a simple linear regression model.
what is slope in statistics?The slope and intercept of a line reveal the steepness of the line and the location in which it intersects an axis. The slope and intercept of the logistic relationship of the two variables can be utilized to get the average change rate. The ratio of a change in the variable y to the rise in the x component is known as the the line's slope.
Briefing:Y = a + bX, where X seems to be the mediating variable and Y is the response variable, is the equation of a linear regression line. A is the intersection (the result of y for x = 0), and b is the line's slope.
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Please please help me with this question and show your steps nooooooow
Answer:
\(y = mx + c \\ - 3 = 2m + c \\ - 2 = 4m + c \\ subtract \: (2) - (1) \\ 1 = 2m \\ m = \frac{1}{2} \\ - 3 = 2( \frac{1}{2} ) + c \\ c = - 4 \\ y = \frac{1}{2}x - 4 \)
alternative method
\(\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}\)
This net consists of a square and 4 identical triangles. What is the surface area of the solid this net can form?
144 square inches
184 square inches
224 square inches
264 square inches
Answer: C, 224 inches squared
Step-by-step explanation:
When formed into a solid, the triangles are folded upwards to make a pyramid. You can find the surface area by finding the areas of the individual shapes.
There are four triangles with a height of 10 inches and a base of 8 inches.
There is one square with a side length of 8 inches.
Triangle area formula : A = (b * h) / 2
Square area formula: A = s^2
(10 * 8) / 2 = 40
8 ^ 2 = 64
There are four triangles with area of 40 and one square with area of 64.
40 + 40 + 40 + 40 + 64 = 224 inches squared. The correct answer choice is C.
The surface area of the pyramid is 224 in².
What is surface area?The surface area of a solid object is a measure of the total area that the surface of the object occupies.
Given net will form a square pyramid, so we will find the surface area of the square pyramid.
Therefore,
The area of the pyramid = side² + 2 × side × height
= 8² + 2 × 8 × 10
= 64 + 160
= 224
Hence the surface area of the pyramid is 224 in².
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1
A line segment has the endpoints (-7,-4) and (9,8). What are the coordinates of the
midpoint of this line segment?
Find the most general real-valued solution to the linear system of differential equations vector x = [\begin{array}{cc}-5&-4\\1&-5\end{array}\right] vector x.[\begin{array}{c}x1(t)\\x2(t)\end{array}\right] = C1 [\begin{array}{c} \\ \end{array}\right] + C2 [\begin{array}{c} \\ \end{array}\right]
The condition that ensures a solution for the mentioned equation is :
1. b₂ = 2b₁ and 6b₁-3b₃ +b₄ = 0.
In mathematics, an equation is a formula that connects two expressions with the equal sign = to indicate that they are equal. An equation consists of two expressions joined by an equal sign ("="). Expressions for both sides of the equals sign are called the "left side" and the "right side" of the equation. Usually the right side of the equation is assumed to be zero. If this is accepted, it does not reduce the generality, since it can be done by subtracting the right side from the two sides.
According to the Question:
Given that:
x₁+ 2x₂= b₁ ------------------------- (1)
2x₁ + 4x₂ = b₂ ------------------------- (2)
3x₁ + 7x₂ = b₃ ------------------------ (3)
3x₁ + 9x₂ = b₄ ------------------------ (4)
From equation (1) and (2), we get:
b₂ = 2b₁
After analysis equation (1), we have:
6b₁-3b₃ +b₄ = 0
Using equation (1), (3) and (4), we get:
3(x₁+2x₂) -6(3x₁+7x₂) + 3x₁ + 9x₂ ≠ 0
Putting the value from equation (1),(3) and (4), we get:
6(x₁+2x₂) -3(3x₁+7x₂) + 3x₁ + 9x₂ = 0
Hence option (1) is correct.
Complete Question:
Consider the following system of linear equations:
x₁+ 2x₂= b₁
2x₁ + 4x₂ = b₂
3x₁ + 7x₂ = b₃
3x₁ + 9x₂ = b₄
which one of the following conditions ensures that a solution exists for the above system.
1. b₂ = 2b₁ and 6b₁-3b₃ +b₄ = 0
2. b₃ = 2b₁ and 6b₁-3b₃ +b₄ = 0
3. b₂ = 2b₁ and 3b₁-6b₃ +b₄ = 0
4. b₃ = 2b₁ and 3b₁-6b₃ +b₄ = 0
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Which expression is equal to the polynomial
below?
2x + 5x38x - 20
Ox³(2x + 5) + 4(2x - 5)
Ox³(2x + 5)- 4(2x + 5)
Ox³(2x-5)-4(2x - 5)
Ox³(2x + 5) + 4(2x + 5)
The expression 2x⁴ + 5x³ - 8x - 20 can be express as follows;
x³(2x + 5) - 4(2x + 5)
How to factorise an expression?2x⁴ + 5x³ - 8x - 20
Therefore,
2x⁴ + 5x³ - 8x - 20
x³(2x + 5) - 4(2x + 5)
Hence, the expression 2x⁴ + 5x³ - 8x - 20 can be express as follows:
2x⁴ + 5x³ - 8x - 20 = x³(2x + 5) - 4(2x + 5)
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Determine the time intervals (in seconds) in which the particle moves in the positive direction and the negative direction. (Enter your answers using interval notation.) positive direction ______. negative direction______.
Given that, the function s(t) describes the motion of a particle along a line. s(t) = t³ − 13t² + 35t − 220
We need to find the time intervals in which the particle moves in the positive direction and the negative direction.
The given equation is s(t) = t³ − 13t² + 35t − 220
Taking the derivative,
v(t) = s'(t) = 3t² -26t + 35 = velocity at time t
s'(t) = 3t² -26t + 35 = 0
(3t -5)(t-7) = 0
t = 5/3 and 7 seconds
Therefore, the velocity > 0 when s'(t) > 0, when t>7 or t < 5/3 seconds
velocity <0 when 5/3 < t < 7 seconds
When moving in a positive direction, the intervals :-
(-∞, 5/3) ∪ (7, ∞)
When moving in a negative direction, the interval :-
(5/3, 7)
Hence, the time intervals are; positive direction (-∞, 5/3) ∪ (7, ∞) and negative direction (5/3, 7)
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The question was incomplete, so I solved for the question;
The function s(t) describes the motion of a particle along a line.
s(t) = t³ − 13t² + 35t − 220
(a) Find the velocity function v(t) of the particle at any time t ≥ 0.
(b) Identify the time interval(s) on which the particle is moving in a positive direction. (Enter your answer using interval notation.)
(c) Identify the time interval(s) on which the particle is moving in a negative direction. (Enter your answer using interval notation.)
true or false let a be a real square matrix. if a is diagonalizable then a is symmetric
False. let a be a real square matrix. if a is diagonalizable then a is symmetric
Explanation: Diagonalizability and symmetry are two different properties of a square matrix. A real square matrix A is diagonalizable if it can be transformed into a diagonal matrix D through a similarity transformation with an invertible matrix P, i.e., A = PDP^(-1). A matrix is symmetric if A = A^T, where A^T is the transpose of A.
While it is true that every symmetric matrix is diagonalizable, the converse is not necessarily true. In other words, not every diagonalizable matrix has to be symmetric.
Conclusion: The statement "if A is diagonalizable then A is symmetric" is false because diagonalizability does not guarantee symmetry.
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What are the 4 steps in graphing linear inequalities?.
The four step to graphing the linear inequalities are: Always begin by separating the variable y from the inequality's left side, Replace the inequality symbol with the equality symbol, In XY plane, graph the boundary line from step 2, The final step is to shade a portion or one side of the border line.
In the given question we have to explain the 4 steps in graphing linear inequalities.
Step 1: Always begin by separating the variable y from the inequality's left side.
Step 2: Replace the inequality symbol with the equality symbol.
Step 3: In XY plane, graph the boundary line from step 2.
Step 4: The final step is to shade a portion or one side of the border line.
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what is -12+6xz equivalent to
Step-by-step explanation:
-12+6xz is equivalent to 6(-2 + xz) or 6(xz - 2)