The augmented matrix, however, is a two-by-four matrix because it also contains the constants.
What do you meant by augmented matrix for the linear system?The augmented matrix will always include one additional column for every additional variable, and the same number of rows as there are equations. An easier technique to write a set of linear equations is to utilize enhanced matrices.
In an augmented matrix, two sides of the matrix are separated by a vertical line that serves as a representation of a succession of equal signs. The collection of linear equations, for instance, would be represented by the matrix. There is only ever one pivot in a column.
For (c): Three rows and four columns make up the augmented matrix of this system. As a result, it only has three pivot points at most. Thus, a pivot column cannot be represented by a single variable.
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Answer:
What is the size of the augmented matrix for the linear system?
B) 2x3
Identify the values for the elements in the augmented matrix:
a11 = 3
a12 = 7
a13 = 20
a21 = 1
a22 = -4
a23 = 9
Step-by-step explanation:
A botanist uses the representations below to show the heights in inches, h, of different plants over a period of time, t.
Plant A
Time in weeks, t
60
80
100
120
Height in inches, h
90
120
150
180
Plant B
h = StartFraction 4 t Over 3 EndFraction
A graph has time (in weeks) on the x-axis and height (in inches) on the y-axis. A line goes through points (50, 150) and (120, 360).
If the growth patterns continue, how much taller is the tallest plant than the shortest plant at 120 weeks of growth?
180 inches
200 inches
270 inches
280 inches
Answer:
B- 200
Step-by-step explanation:
ye ye
How do you reflect over Y =- 4?
4. The table gives the height and shoe sizes of six randomly selected men.
Height 67 70 73. 5 75 78 66
Shoe size 8. 5 9. 5 11 12 13 8 CO
a. What is the equation of line of best fit: 4= 42x-19. 81
b. What is the slope, and what does it mean in this problem?
C. What is the y intercept? What does it mean in this problem?
d. Using the equation of the line of best fit, if a man has a shoe size of 10. 5, what would be his predicted height?
The predicted height if the man with shoe-size 10 is 427.09 cm.
We get the answers using the following steps.
a. The equation of the line of best fit is: y = 42x - 19.81
b. The slope, 42, represents the rate of change of the height variable with respect to the shoe size variable. It means that for every 1-unit increase in shoe size, we can expect a 42-unit increase in height.
c. The y-intercept, -19.81, is the point where the line of best fit crosses the y-axis. It represents the height when the shoe size is 0. It means that if a man has 0 shoe size, his height would be -19.81, both of which is impossible.
d. To predict the height of a man with a shoe size of 10.5, we substitute x = 10.5 into the equation of the line of best fit:
y = 42x - 19.81
y = 42(10.5) - 19.81
y = 447.9 - 19.81
y = 427.09
So, a man with a shoe size of 10.5 would have a predicted height of 427.09 cm
It's worth noting that this is just a predicted value and it might not be accurate. The line of best fit is calculated based on the given data set, it might not be accurate for other data points.
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Factor the expression completely.
x^4-17x^2+72
Answer:
It's neither:
x =√ 9.000 = 3.00000 or :
x =√ 9.000 = -3.00000 or :
x =√ 8.000 = 2.82843 or :
x =√ 8.000 = -2.82843
Four solutions
Answer:
x^4 - 17x^2 + 72 = (x^2 - 9)(x^2 - 8)
Step-by-step explanation:
First, we need to find two numbers that multiply to give us 72 and whose sum is -17. We can see that 8 and 9 multiply to give us 72, and their sum is 8 + 9 = 17. Since we want the sum to be negative, we need to change one of the signs. So we write -(8 + 9) = -17.
Next, we write the expression as the product of two binomials. We factor out the common factor x^2 from the first two terms: x^4 - 17x^2 + 72 = x^2(x^2 - 17) + 72
Now, we complete the square in the first binomial. To do this, we need to add and subtract (17/2)^2 = (8.5)^2 = 72.25 inside the bracket:
x^2(x^2 - 17) + 72 = x^2(x^2 - 17 + 72.25 - 72.25) + 72 = x^2(x^2 - 17 + 72.25) - 72.25 + 72
Now we can rewrite the square of a binomial :
x^2(x^2 - 17 + 72.25) = x^2((x-8.5)^2)
Finally, we can combine the two binomials
x^2((x-8.5)^2) + 72 = (x^2(x-8.5)^2) + 8(9)
So the expression x^4 - 17x^2 + 72 factors completely as (x^2 - 9)(x^2 - 8)
Hope this helps!
Evaluate 21/a+4 when a=3
Answer:
11
Step-by-step explanation:
All you have to do is plug in a. In this case, a=3.
21/a+4
21/(3)+4
21/3+4
7+4
11
If this helps please mark as brainliest
Answer:
11
Step-by-step explanation:
Follow the order of operations, PEMDAS.
First, divide, then add. Plug in 3 for a in the given expression:
21/(3) + 4
Divide, then add:
(21/3) + 4
7 + 4 = 11
11 is your answer.
~
find the slope of the line that passes through the points (4,-3) and (7,12)
Answer:
8/10
Step-by-step explanation:
12 - 4 8
-------- = -----
7 - (-3) 10
Answer:
5
Step-by-step explanation:
y2 - y1 / x2 - x1
12 - (-3) / 7 -4
15 / 3
5
Questions:
1. What did you do to the numerators? What did you do too to the denominators?
2. Did you find like terms among the collected terms of the numerator? What did you do
to terms?
3. What factoring techniques did you apply?
4. How did you simplify your sum?
The answers to all the subparts are shown:
(1) The numerator is simply added. The denominator is copied.
(2) Yes, it has; yet, we include them since that is what needs to be done.
What is numerator and denominator?In a fraction, the number above the line is the numerator.
For instance, the numerator of the fraction 3/5 is 3.
A fraction's numerator displays the number of pieces that make up the whole while the denominator, or a number of equal parts, is displayed below the line.
So, we have the equation:
2x² + x/2x - 2 + x - 4/ 2x - 2
Now, answering questions taking the above-given equation into consideration:
(1) The numerator is simply added. The denominator is copied.
(2) Yes, it has; yet, we include them since that is what needs to be done.
(3) We complete the square, but we can also use the straightforward factoring approach.
(4) We eliminate or simply cancel the factors in the numerator that are also present in the denominator to simplify the sum.
Therefore, the answer to all the subparts are shown:
(1) The numerator is simply added. The denominator is copied.
(2) Yes, it has; yet, we include them since that is what needs to be done.
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The width of this rectangle is measured as 19.4mm correct to 1 decimal place.
b) What is the
lower bound for the area of the rectangle?
Answer:
reducing 9.35 to 19.44 is rounded to 19.4
Step-by-step explanation:
9.35 to 19.44 is rounded to 19.4
19.35 = 19.4
19.36 = 19.4
19.37 = 19.4
19.38 = 19.4
19.39 = 19.4
19.40 = 19.4
19.41 = 19.4
19.42 = 19.4
19.43 = 19.4
19.44 = 19.4
Hence Lower bound of of the rectangle = 19.35 mm
the sum of the interior angle of a regular polygon is 1080
find the number of sides of the polygon
Answer:
8 sides
Step-by-step explanation:
(n-2)×180=1080
180n-360=1080
180n=1080+360
180n=1440
n=1440/180
n=8 sides
it's an octagon
Answer:
It has 8 sides
Step-by-step explanation:
This is because the formula is 180(n-2) where n is the amount of sides. An octagon has 8 sides so the sum of the angles is 180(8-2)=180(6)=180×6=1080 degrees
Hope that helps :)
Formulas can be manipulated to solve for missing information.
Ex: A = bh can be written as ? or ?
Find the perimeter of a circle with radius 35 cm
[tex](take \pi = 22 7 \div 7[/tex]
Answer:
[tex]here \: is \: your \: solution... \\ \\ radius \: of \: circle = 35 \: cm \\ \\ perimeter \:of \: circle = \pi \: r {}^{2} \\ \\ perimeter \: of \: circle = (22 \div 7)35 \times 35 \\ \\ perimeter \: of \: circle = 3846.5 \: cm \\ \\ \huge\mathfrak\purple{hope \: it \: helps...}[/tex]
Answer:
Index or vertex are 77 so context and factors are already divided each 5..so i think radio and centimeter are 45/95 take ADF from fraction and multiplyit!! as a exactly answer!! and perimeter are revolved!!
Step-by-step explanation:
HOPE IT HELPS!!
(NO LINKKKKKKKKKKS)
Pls help me if your good at math I’ll mark brainliest if correct <3333
Answer:
I think its C
Step-by-step explanation:
Find the derivative of the function.
F(x) =
x2 integral et7dt
x
The requried derivative of the given function is [tex]F'(x) = 2xe^{x^{14}} - e^{x^7}[/tex].
What is implicit differentiation?The method of determining the derivative of an implicit function by differentiating each term separately, expressing the derivative of the dependent variable as a symbol, and solving the resulting expression for the symbol
here,
Given expression,
[tex]F(x) = \int\limits^{x^2}_x {e^{t^7}} \, dx[/tex]
Following the Leibniz rule
[tex]F'(x) = \frac{d}{dx}[ \int\limits^{x^2}_x {e^{t^7}} \, dx]\\F'(x) = \int\limits^{x^2}_x \delta/\delta x (e^{t^7}) + (e^{(x^2)^7}) d/dx (x^2) - e^{x^7}d/dx [x] \\F'(x) = 0 + 2xe^{x^{14}} - e^{x^7}\\F'(x) = 2xe^{x^{14}} - e^{x^7}[/tex]
Thus, the requried derivative of the given function is [tex]F'(x) = 2xe^{x^{14}} - e^{x^7}[/tex].
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What would an 18% increase of 90 be?
Answer:
106.2
Step-by-step explanation:
A 18% increase of a number is the same as multiplying it by 1.18.
If we multiply 90 by 1.18 we get:
90 * 1.18
106.2
Can someone please answer // Find the central angle given that the measure of the arc is 200°
Answer:
The central angle of a circle is measured in either degrees or radians. It is measured with the help of length of the arc and length of the radius of the circle. The formula to measure central angle (in radians) = (Length of the arc)/(Length of the radius).
Step-by-step explanation:
Select the correct answer
A geneticist needs to grow a stock of fruit flies for her experiments. She currently has a stock of 200 fruit flies and predicts the stock will grow by
38% each day. Which function could she use to calculate f(n), the number of days required for her stock to grow to n fruit flies?
200
A f(n) = 1081. 38
OB. F(n) = 1080. 88
OC f(n) = log1. 38(260)
OD. F(n) = logo. 38
198(260)
(200)
Reset
Next
For her research, a geneticist has to raise a stock of fruit flies. She presently has 200 fruit flies in stock;
The mathematical function she may use to calculate is given as
f(n)=log1.38(n/200)
Which function could she use to calculate, the number of days required for her stock to grow to n fruit flies?
Generally, the equation for the final value is mathematically given as
A=Ao(1+u)^t
Therefore
n=200(1+0.38)*t
log(1.38^t)=log(n/200)
t=log1.38(n/200)
In conclusion, The function she could use to calculate is
f(n)=log1.38(n/200)
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Factor Completely 4q^6+8q^3
Answer:
4[tex]q^{3}[/tex]( q³ + 2)
Step-by-step explanation:
4[tex]q^{6}[/tex] + 8q³ ← factor out 4q³ from each term
= 4q³ (q³ + 2)
Answer:
4q^3(q^3 + 2)
Step-by-step explanation:
The GCF of the exponents is 3, and the GCF of the bases is 4q. So divide both numbers by 4q ^ 3 and get
4q ^ 6 / 4q ^ 3 = q ^ 3
8q ^ 3 / 4q ^ 3 = 2
so you get
4q^3 (q ^ 3 + 2)
the swim team trains 4 days every week. Mon, Tues, and Thurs, the swim tea spends 1/2h in the gym followed by 1 1/4 in the pool. On Saturday there is no gym work but double the swim team time. how many hours per week does the team train?
The number of hours that the team trians per week is 17 hours.
How to illustrate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
Since the the swim tea spends 1/2h in the gym followed by 1 1/4 in the pool. On Saturday there is no gym work but double the swim team time. The number of hours will be:
( 1 1/4 + 1/2 + 2 1/2) × 4
= 4.25 × 4
= 17 hours.
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Suppose a consumer product researcher wanted to find out whether a highlighter lasted less than the manufacturer's claim that their highlighters could write continuously for 14 hours. The researcher tested 40 highlighters and recorded the number of continuous hours each highlighter wrote before dying. Test the hypothesis that the highlighters wrote for less than 14 continuous hours. X = 13.6 hours, s = 1.3 hours. Report the test statistic, p-value, null hypothesis, conclusion and round to nearest thousandth.
Answer:
The null hypothesis is [tex]H_0: \mu = 14[/tex]
The alternate hypothesis is [tex]H_a: \mu < 14[/tex]
The test statistic is t = -1.95.
The p-value is of 0.0292. This means that for a level of significance of 0.0292 and higher, there is sufficient evidence to conclude that the highlighters wrote for less than 14 continuous hours.
Step-by-step explanation:
Suppose a consumer product researcher wanted to find out whether a highlighter lasted less than the manufacturer's claim that their highlighters could write continuously for 14 hours.
At the null hypothesis, we test if the mean is 14 hours, that is:
[tex]H_0: \mu = 14[/tex]
At the alternate hypothesis, we test if the mean is less than 14 hours, that is:
[tex]H_a: \mu < 14[/tex]
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.
14 is tested at the null hypothesis:
This means that [tex]\mu = 14[/tex]
X = 13.6 hours, s = 1.3 hours. Sample of 40:
In addition to the values of X and s given, we have that [tex]n = 40[/tex]
Test statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{13.6 - 14}{\frac{1.3}{\sqrt{40}}}[/tex]
[tex]t = -1.95[/tex]
The test statistic is t = -1.95.
P-value:
The p-value of the test is the probability of finding a sample mean lower than 13.6, which is a left tailed test, with t = -1.95 and 40 - 1 = 39 degrees of freedom.
Using a calculator, the p-value is of 0.0292. This means that for a level of significance of 0.0292 and higher, there is sufficient evidence to conclude that the highlighters wrote for less than 14 continuous hours.
If x = 34, y = 53, and the measure
of AC = 4 units, what is the difference in length between
segments AB and AD? Round your answer to
the nearest
hundredth.
A- 0.74
B- 1.17
C- 1.64
D- 2.14
9514 1404 393
Answer:
D 2.14
Step-by-step explanation:
The lengths of interest are the hypotenuses of the respective triangles. We are given the angle and the opposite side, so the sine relation is of interest.
Sin = Opposite/Hypotenuse
sin(34°) = AC/AB ⇒ AB = AC/sin(34°)
sin(53°) = AC/AD ⇒ AD = AC/sin(53°)
The desired difference in lengths is ...
AB -AD = AC(1/sin(34°) -1/sin(53°)) = 4(1.78829 -1.25214) ≈ 2.1446
The difference in lengths is about 2.14 units.
Name three pairs of parallel segments below.
Answer:
hypotenuse,adjacent and opposite
For each situation, make a tree diagram to show the sample space. Then give the total number of outcomes.
tossing a coin and choosing a consonant from the word ALGEBRA
a. 2
c. 6
b. 4
d. 8
HELP PLEASE
Answer:
I would go with D, 8.
Step-by-step explanation:
Tossing a coin, but not saying heads or tails is accepting both (2 outcome branches)
There are 4 consonants in ALGEBRA (each of the two branches above have 4 outcomes that match)
2 x 4 = 8
I don't like how the question is written, because the "total number of outcomes" usually includes the ones you don't want, which would be 14. But since that's not an option, I would chose D.
can y’all help me solve for n?
Answer:
Sure mate, n is equal to 27
Step-by-step explanation:
side ab is similar side pq. This is given.
12/4=3 therefore your scale factor from small to large is 3
side cb is similar to rq. This is given.
the length of cb is equal to 9 multiplying this by 3 will give you the length of line segment rq. and therefore the value of N.
9*3=27
which expression is equivalent to
The provided expression can be simplified in the form 2y4/x4 option ( B) Using the integer exponent characteristics, = [x[tex]^\frac{1}{8}[/tex] . y⁸] is the right answer.
What is defined as an integer exponent?In mathematics, integer exponents are exponents that fall under the integer category. It's possible for the number to be either positive or undesirable. The positive integer exponents in this example dictate how many times that base number must be multiplied by itself.
It's possible for the number to be either positive or undesirable. The positive integer exponents in this example dictate how many instances the base number must be multiplied by itself.
According to the given information:= [x[tex]^\frac{1}{4}[/tex] . y¹⁶][tex]^\frac{1}{2}[/tex]
= [x[tex]^\frac{1}{8}[/tex] . y⁸]
The provided expression can be simplified in the form 2y4/x4 option ( B) Using the integer exponent characteristics, = [x[tex]^\frac{1}{8}[/tex] . y⁸] is the right answer.
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hello please help i’ll give brainliest
Answer:
number 3
Step-by-step explanation:
it helped us try to learn hieroglyphics
Consider your construction of pentagon ABCED.
What segments, if any, are parallel? Explain how you made your
determination.
Therefore , the solution of the given problem of pentagonal comes out to be Nadia has created a pentagonal prism as a result.
Define pentagonal.Pentagons are two-dimensional polygons having five sides and fifth angles. When we mix the Greek terms "penta" and "gon," which mean "five" and "angles," respectively, we have the word "pentagon."
Here,
we know that a pentagonal prism has five rectangular sides in addition to two pentagonal bases at the top and bottom.
Pentagonal prisms are pentagon-shaped if we look at them from the bottom.
When viewed from the side, a pentagonal prism would have a rectangular shape.
If we were to look at the pentagonal prism from the front, it would appear rectangular.
Therefore , the solution of the given problem of pentagonal comes out to be Nadia has created a pentagonal prism as a result.
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Someone please help
Answer:
50 pages per hour
Step-by-step explanation:
Which function best represents the sequence 10, 13, 16, 19, 22..., where n is a positive whole number?
a(n) = 7+3n
Ob(n) = 10 + 3n
Oc(n) = 7+3
Od(n) = 10 +3"
Answer:
first function
Step-by-step explanation:
there is a common difference between consecutive terms , that is
13 - 10 = 16 - 13 = 19 - 16 = 22 - 19 = 3
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 10 and d = 3 , then
[tex]a_{n}[/tex] = 10 + 3(n - 1) = 10 + 3n - 3 = 7 + 3n
A triangle has vertices at (1, 3), (2, -3), and ( -1, -1). What is the approximate perimeter of the triangle?
Answer choices
15
10
14
16
Answer:14
Step-by-step explanation:You can use distance formula to find the length of each side, and then add them together to approximate the perimeter.
What is the perimeter?
Help plz....And no links!! I repeat No links!!!
Answer:
48 cm
Step-by-step explanation:
Answer:48 cm
Step-by-step explanation:
a^2+b^2=c^2
a^2+16^2=20^2
a^2+256=400
a^2= 144
a = 12
12+16+20=48