The question is missing parts. Here is the complete question.
Let M = [tex]\left[\begin{array}{cc}6&5\\-1&-4\end{array}\right][/tex]. Find [tex]c_{1}[/tex] and [tex]c_{2}[/tex] such that [tex]M^{2}+c_{1}M+c_{2}I_{2}=0[/tex], where [tex]I_{2}[/tex] is the identity 2x2 matrix and 0 is the zero matrix of appropriate dimension.
Answer: [tex]c_{1} = \frac{-16}{10}[/tex]
[tex]c_{2}=\frac{-214}{10}[/tex]
Step-by-step explanation: Identity matrix is a sqaure matrix that has 1's along the main diagonal and 0 everywhere else. So, a 2x2 identity matrix is:
[tex]\left[\begin{array}{cc}1&0\\0&1\end{array}\right][/tex]
[tex]M^{2} = \left[\begin{array}{cc}6&5\\-1&-4\end{array}\right]\left[\begin{array}{cc}6&5\\-1&-4\end{array}\right][/tex]
[tex]M^{2}=\left[\begin{array}{cc}31&10\\-2&15\end{array}\right][/tex]
Solving equation:
[tex]\left[\begin{array}{cc}31&10\\-2&15\end{array}\right]+c_{1}\left[\begin{array}{cc}6&5\\-1&-4\end{array}\right] +c_{2}\left[\begin{array}{cc}1&0\\0&1\end{array}\right] =\left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex]
Multiplying a matrix and a scalar results in all the terms of the matrix multiplied by the scalar. You can only add matrices of the same dimensions.
So, the equation is:
[tex]\left[\begin{array}{cc}31&10\\-2&15\end{array}\right]+\left[\begin{array}{cc}6c_{1}&5c_{1}\\-1c_{1}&-4c_{1}\end{array}\right] +\left[\begin{array}{cc}c_{2}&0\\0&c_{2}\end{array}\right] =\left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex]
And the system of equations is:
[tex]6c_{1}+c_{2} = -31\\-4c_{1}+c_{2} = -15[/tex]
There are several methods to solve this system. One of them is to multiply the second equation to -1 and add both equations:
[tex]6c_{1}+c_{2} = -31\\(-1)*-4c_{1}+c_{2} = -15*(-1)[/tex]
[tex]6c_{1}+c_{2} = -31\\4c_{1}-c_{2} = 15[/tex]
[tex]10c_{1} = -16[/tex]
[tex]c_{1} = \frac{-16}{10}[/tex]
With [tex]c_{1}[/tex], substitute in one of the equations and find [tex]c_{2}[/tex]:
[tex]6c_{1}+c_{2}=-31[/tex]
[tex]c_{2}=-31-6(\frac{-16}{10} )[/tex]
[tex]c_{2}=-31+(\frac{96}{10} )[/tex]
[tex]c_{2}=\frac{-310+96}{10}[/tex]
[tex]c_{2}=\frac{-214}{10}[/tex]
For the equation, [tex]c_{1} = \frac{-16}{10}[/tex] and [tex]c_{2}=\frac{-214}{10}[/tex]
Which set of points are collinear? P, T, Y D, S, Y H, T, S Y, D, H
Answer: P, T, Y
This is because the points on the line are straight
Option - A is the correct answer.
We have a geometrical figure given in the question.
We have to determine which set of points are collinear.
What are Collinear points?Three or more points are said to be collinear if they lie on a single straight line.
According to question -
It can be seen that only one set of points - (P, T, Y) lie on the same straight line. Of the options mentioned, one is - (P, T, Y)
Hence, the correct option is Option - A.
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Suppose Q is the midpoint of PR. Use the information to find the missing value.
11) PQ = 3x + 14 and QR = 7x - 10 x =
Answer:
x = 6
Step-by-step explanation:
Given that PQ = 3x + 14, QR = 7x - 10, and Q is the midpoint of PR, it means Q is equidistant from both endpoints of P and Q. In order words, the distance from P to Q is the same as the distance from Q to R.
Therefore, PQ = QR. Which is:
[tex] 3x + 14 = 7x - 10 [/tex]
Solve for x. Collect like terms
[tex] 3x -7x = - 14 - 10 [/tex]
[tex] -4x = -24 [/tex]
Divide both sides by -4x
[tex] x = 6 [/tex]
In what quadrant is cosine negative and cotangent negative?
Answer:
Step-by-step explanation:
cosine is negative in 2nd and 3rd quadrant.
cotangent is negative in 2nd and 4th quadrant.
In the second quadrant, both cosine and cotangent are negative.
What are the signs of each trig function in four quadrants?In the first quadrant all trig functions are positive, In the second quadrant sine and sec are positive in the third quadrant tan and cot are positive, and in the fourth quadrant cos and cosec are positive.
We know there are four quadrants in an XY plane.
We also know that sine is positive on 1st and second quadrants and cosine is positive on the first and fourth quadrants.
tan = (sin/cos).
So, cot = 1/tan = cos/sing.
∴ cotangent is negative if any one of sine and cosine is negative which is in the second and fourth quadrants because in the third quadrant both sine and cosine are negative making cotangent positive.
∴ In the second quadrant cosine and cotangent, both are negative.
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How many solutions does the equation have |r-6|=0
Answer:
Only one solution
Step-by-step explanation:
[tex] |r - 6| = 0 \\ r - 6 = \pm \: 0 \\ r - 6 = 0 \\ r = 6[/tex]
Which operation would you do third in the following problem?
8 (10-4)
6
addition
subtraction
multiplication
division
Answer:
multiplication
Step-by-step explanation:
it seems the best
what is the surface area of a tent 5ft height. 7ft length, 6ft width
Does anyone know the answer to this? Needed asap
Answer:
t=r/d; t=0.2
Step-by-step explanation:
If d=r/t, then multiple both sides by t, to get td=r, then divide both sides by d, to get t=r/d. So t=8/40 t=0.2
if f(x) = x^2 + 1
and g(x) = 5-x then what is
(f+g)(x) =
Answer: x²-x+6
Step-by-step explanation:
(f+g)(x) means f(x)+g(x). Since we are given the values of f(x) and g(x), we can directly subtract them.
x²+1+(5-x) [distribute +1]
x²+1+5-x [combine like terms]
x²-x+6
Answer:
[tex]\huge\boxed{(f+g)(x) = x^2 - x+ 6}[/tex]
Step-by-step explanation:
[tex]\sf f(x) = x^2 + 1\\g(x) = 5-x[/tex]
Adding both functions
[tex]\sf (f+g)(x) = x^2 + 1+ 5 - x\\(f+g)(x) = x^2 - x+ 6[/tex]
On average, a bird visits 1,170 flowers per day for nectar.
Part A: How many flowers does the bird visit in an hour? Round your answer to the nearest whole flower.
Part B: How many flowers does the bird visit in a year?
Given h(p)=p^2+2p, Solve h(p)=3
We have [tex]h(p)=p^2+2p[/tex] and [tex]h(p)=3[/tex] which means we can equate:
[tex]p^2+2p=3[/tex].
Subtract 3 from both sides:
[tex]p^2+2p-3=0[/tex].
Then solve for p:
[tex]p^2+2p-3=0[/tex].
[tex](p-1)(p+3)=0[/tex].
So the product of two factors (p-1) and (p+3) is 0 which means at least one of the factors must be 0:
[tex]p-1=0\implies p_1=1[/tex].
Or
[tex]p+3=0\implies p_2=-3[/tex].
Hope this helps.
please help me with this question!!!! it’s due in 20 minutes
Answer:
3^12
Step-by-step explanation:
(3^3/4(2) - 3/8) ^4/9
(3^6/8-3/8)^4/9
(3^3/8)^4/9
3^3/8(4/9)
3^27/72(32/72)
3^864/72
3^12
Sorry if it's hard to read...
Which net below represents the given figure?
Ο Α.
O B.
B or C (both are correct just choose one)
B or C (both are correct).
A bank manager is interested in the average length of time that customers are willing to wait in line before they give up
Note. The original question with options given on the bottom
Answer:
F - 1, B -2, A - 3, D - 4, C - 5, E - 6
Step-by-step explanation:
F. Sample
The 25 customers that the manager observed leaveB. Population
All of the bank's customersA. Statistic
The average length of time that the 25 customers waited before leaving the bankD. Parameter
The average length of time that all customers will wait before leaving the bankC. Data
The list of times for the 25 customers who left the bankE. Variable
The length of time a customer waits before leaving the bank========================================================
Question
A bank manager is interested in the average length of time that customers are willing to wait in line before they give up and leave the bank. Match the vocabulary word with its corresponding example.
---------------------
1. The 25 customers that the manager observed leave
2. All of the bank's customers
3. The average length of time that the 25 customers waited before leaving the bank
4. The average length of time that all customers will wait before leaving the bank
5. The list of times for the 25 customers who left the bank
6. The length of time a customer waits before leaving the bank
---------------------
A. Statistic B. Population C. DataD. Param eter E. Variable F. SampleS. Determine which is the best buy. Show calculations and explain your answer Ed's Bagels 4 for $.89 Best Bagels Only $1.39 for 6
Answer:
eds bageles are $.22 per bagel and best bagels are $.23 per bagel.
Step-by-step explanation:
Marlena places a square rug on her living room floor, which is also a square. What area of her floor is NOT covered by the rug? A. 9 square ft B. 12 square ft C. 63 square ft D. 81 square ft
Answer:
B. 12 square ft C. 63 square ft
Step-by-step explanation:
Marlena places a square rug on her living room floor, which is also a square.
Now if a square rug is placed in her room, the area of the floor will definitely be the area if the square rug..
And area of a square it = length ²
The result will give s a perfect square for an integer number.
A. 9 square ft = perfect square
B. 12 square ft = not perfect square
C. 63 square ft =not perfect square
D. 81 square ft= perfect square
So the ones that are not perfect squares Is the answer to the question
The area of her floor is NOT covered by the rug is 12 square ft and 81 square ft.
It is required to find the area of her floor is NOT covered by the rug.
What is square?A square is a four-sided polygon, whose all its sides are equal in length and opposite sides are parallel to each other. Also, each vertices of square have angle equal to 90 degrees.
Given:
Marlena places a square rug on her living room floor, which is also a square.
Now if a square rug is placed in her room, the area of the floor will definitely be the area if the square rug..
If the length of each side of the rug is equal to the length of each side of the room, there will be no area not covered.
According to given question we have,
And area of a square it = length ²
The result will give s a perfect square for an integer number.
A. 9 square ft = perfect square
B. 12 square ft = not perfect square
C. 63 square ft =not perfect square
D. 81 square ft= perfect square
Therefore, the area of her floor is NOT covered by the rug is 12 square ft and 81 square ft.
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Nate has 6 3/5 of fabric. He uses 3 1/2 yards of fabric to make a pillow. How much fabric dose he left
Answer:
3 and 1/2 minus 2/3 minus 1/3 =
7/2 minus 2/3 minus 1/3 =
21/6 minus 4/6 minus 2/6 =
17/6 - 2/6 =
15/6 = 5/2 = 2 and 1/2
Optionally, you can think of it this way:
He used 2/3 yards for the pillow and 1/3 yard for the scarf.
So he used 1 yard
3 and 1/2 minus 1 = 2 and 1/2 = 5/2
Step-by-step explanation:
Find the equation of the line perpendicular to y=2x-6 that passes through the point (1,5). If possible, write the equation in slope-intercept form.
Answer:
[tex]y=-0.5x+4.5[/tex]
Step-by-step explanation:
The slope of [tex]y=2x-6[/tex] is:
[tex]2[/tex]The negative reciprocal of that slope is:
[tex]m=-\frac{1}{2}[/tex]So the perpendicular line will have a slope of [tex]-1/2[/tex]:
[tex]y - y_1 = (-\frac{1}{2} )(x - x_1)[/tex]And now put in the point [tex](1,5)[/tex]:
[tex]y-5=(-\frac{1}{2})(x-1)[/tex]And that answer is OK, but let's also put it in [tex]y=mx+b[/tex] form:
[tex]y-5=-\frac{x}{2}+\frac{1}{2}[/tex][tex]y=-\frac{x}{2}+\frac{11}{2}[/tex][tex]y=-0.5x+4.5[/tex]A door with width 4.20 has an arc as shown in the diagram. Find: a the radius of the arc, to the nearest cm b the length of the arc, to the nearest cm. 225° is the central angle
Answer:
The arc length is 4 cm to the nearest cmStep-by-step explanation:
The diagram is not given in this question, but we can proceed anyways.
from the problem statement we can observe that the radius of the arc is same as the width of the door
a. the radius is 4.2 cm
b. the length of the arc given that the central angle is 25° can be gotten using the formula stated bellow
arc length = 2 π r *(∅/360)
substituting we have
arc length = 2*3.142*(225/360)
arc length= 6.284*0.625
arc length=3.92 cm
Approximately the arc length is 4 cma bathtub is filled with 38 1/3 gallons of water. if 2 3/5 gallons splash out, how much water is left in the tub?
Answer:
3/5^3
3/5^3 = 27
125
= 0.216
Step-by-step explanation:
Rules for expressions with fractions:
Fractions - use the slash “/” between the numerator and denominator, i.e. for five-hundredths enter 5/100. If you are using mixed numbers be sure to leave a single space between the whole number and fraction part.
The slash separates the numerator (number above a fraction line) and denominator (number below).
Mixed numerals (mixed fractions or mixed numbers) write as non-zero integer separated by one space and fraction i.e., 1 2/3 (having the same sign). An example of a negative mixed fraction: -5 1/2.
Because slash is both signs for fraction line and division, we recommended use colon (:) as operator of division fractions i.e., 1/2 : 3.
Decimals (decimal numbers) enter with a decimal point . and they are automatically converted to fractions - i.e. 1.45.
Colon : and slash / is the symbol of division. Can be used to divide mixed numbers 1 2/3 : 4 3/8 or can be used for write complex fractions i.e. 1/2 : 1/3.
An asterisk * or × is the symbol for multiplication.
Plus + is addition, minus sign - is subtraction and ()[] is mathematical parentheses.
The exponentiation/power symbol is ^ - for example: (7/8-4/5)^2 = (7/8-4/5)2
Calculator follows well-known rules for order of operations. Most common mnemonics for remembering this order of operations are:
PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
BEDMAS - Brackets, Exponents, Division, Multiplication, Addition, Subtraction
BODMAS - Brackets, Of or Order, Division, Multiplication, Addition, Subtraction.
GEMDAS - Grouping Symbols - brackets (){}, Exponents, Multiplication, Division, Addition, Subtraction.
Be careful, always do multiplication and division before addition and subtraction. Some operators (+ and -) and (* and /) has the same priority and then must evaluate from left to right.
Answer:
[tex]\frac{536}{15}[/tex] or [tex]35\frac{11}{15}[/tex] (they're the same)
Step-by-step explanation:
[tex]38\frac{1}{3} - 2\frac{3}{5} = \frac{536}{15} = 35.7333 = 35\frac{11}{15}[/tex]what is the smallest angle of a right triangle with sides 9, 40, and 41? Round your answer to the nearest degree.
Answer:
13°
Step-by-step explanation:
The smallest angle in a triangle is the angle opposite the shortest side.
In this case the angle opposite side 9
let the angle be x, then using the tangent ratio in the right triangle
tan x = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{9}{40}[/tex] , thus
x = [tex]tan^{-1}[/tex] ([tex]\frac{9}{40}[/tex] ) ≈ 13° ( to the nearest degree )
Which rule describes this transformation?
Answer:
[tex](x+4,y-5)[/tex]
Step-by-step explanation:
Studying the figures ABCD and A'B'C'D', we can look at just one point and figure out the transformation from that.
Point A is at (-7, 8)
Point A' is at (-3, 3)
If we look at the x values, -7 and -3, we can see that the value changed by 4. So [tex]x+4[/tex] will be what the x becomes.
Also looking at the y values, we can see that the values were 8 and 3 - that's a change of -5, so our y is [tex]y-5[/tex].
Combining these, we get [tex](x+4, y-5)[/tex].
Hope this helped!
Answer: A. (x,y) → ( x+4,y-5)
Step-by-step explanation:
This a rigid transformation and is being translated to find the transformation you could use any vertex.
Using the image of B and to get to B prime we have to move 4 units to the right and 5 units down.
So we could describe the whole transformation as (x,y) → ( x+4,x-5)
The sum of the angle measures of a quadrilateral is 360°. Write and solve an equation to find the value of .
76°
to
122°
92°
The equation is
360
let the unknown no.be x
therefore, 76+122+92+x = 360
= 198+92+x = 360
= 290+x = 360
x=360-290
x= 70degree
hope this is helpful,
^_^
Total employment for metal workers in 2019 is projected to be 210,000. If this is a 5% increase from 2009, approximately what was the total employment in 2009?
Answer:
200,000
Step-by-step explanation:
To solve this, you can divide the 2019 total projected employment (210,000) by 1 + the growth rate (.05) to find the 2009 total employment.
210,000 / (1 + .05) = 200,000
I hope this helps!
-TheBusinessMan
In a particular class of 34 students, 16 are men. What fraction of the students in the class are women?
The value of β is:
60º
45º
90º
30º
75º
Answer:
60°
Step-by-step explanation:
The definition of cosine tells you ...
cos(β) = 3/6 = 1/2
β = arccos(1/2) . . . . use the inverse cosine function to find the angle
β = 60°
_____
The ratio of side lengths in a 30°-60°-90° triangle (one of the "special" triangles), is ...
1 : √3 : 2
The 2 : 1 ratio of longest to shortest side in this right triangle is a clue that the largest acute angle is 60°. It also tells you that x = √3 times the short side length, so is x = 3√3.
(-2)^-3 without exponent
Answer:
-1/8
Step-by-step explanation:
[tex](-2)^-3 \\=\frac{-1}{2}^{3}\\=\frac{-1}{8}[/tex]
Answer:
-1/8
Step-by-step explanation:
[tex]\left(-2\right)^{-3}\\\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}\\\left(-2\right)^{-3}=\frac{1}{\left(-2\right)^3}\\\\=\frac{1}{\left(-2\right)^3}\\\\\left(-2\right)^3=-8\\\\=\frac{1}{-8}\\\\=-\frac{1}{8} \\\\\left(\mathrm{Decimal:\quad }\:-0.125\right)[/tex]
Anais
30°
In the triangle above, what is sin A?
A. sin A x 0.707
B. sin A = 0.5
C. sin A = 30
D. cannot be determined without side lengths
Answer:
The answer is B. sin A = 0.5
Step-by-step explanation:
What is the slope of the line?
Answer:
7/4 = 1.75
Step-by-step explanation:
step 1: pick two points on the line that have nice integer coordinates.
--> (3,4) and (-1,-3)
step 2: calculate the y difference and the x difference
--> y difference: 4 - -3 = 7
x difference: 3 - -1 = 4
step 3: the slope is y difference / x difference
--> slope = 7/4
Traffic police monitor the speed of vehicles as they travel over a new bridge. The average speed for a sample of 41 vehicles was 81.35 km/h, with the sample standard deviation being 4.52km/h. We will assume that the speeds are Normally distributed, and the police are interested in the mean speed.
Part a) Since the variance of the underlying Normal distribution is not known, inference here would involve the t distribution. How many degrees of freedom would the relevant t distribution have?
Part b) Create a 95 % confidence interval for the mean speed of vehicles crossing the bridge. Give the upper and lower bounds to your interval, each to 2 decimal places. ( ,)
Part c) The police hypothesized that the mean speed of vehicles over the bridge would be the speed limit, 80 km/h. Taking a significance level of 5 %, what should infer about this hypothesis?
A. We should reject the hypothesis since 80 km/h is in the interval found in (b).
B. We should reject the hypothesis since 80 km/h is not in the interval found in (b).
C. We should not reject the hypothesis since the sample mean is in the interval found in (b).
D. We should reject the hypothesis since the sample mean was not 80 km/h.
E. We should not reject the hypothesis since 80 km/h is in the interval found in (b).
Part d) Decreasing the significance level of the hypothesis test above would (select all that apply)
A. not change the Type II error probability.
B. decrease the Type I error probability.
C. either increase or decrease the Type I error probability.
D. not change the Type I error probability.
E. increase the Type I error probability.
Answer:
(a) The degrees of freedom; the relevant t distribution would have = n - 1 = 41 - 1 = 40.
(b) A 95% confidence interval for the mean speed of vehicles crossing the bridge is [79.92 km/hr, 82.78 km/hr] .
(c) We should not reject the hypothesis since 80 km/h is in the interval found in (b).
(d) Decrease the Type I error probability.
Step-by-step explanation:
We are given that the average speed for a sample of 41 vehicles was 81.35 km/h, with the sample standard deviation being 4.52km/h.
(a) Since here we don't know about population standard deviation, so the distribution that will be used here is t-distribution as the data also follows the normal distribution.
The degrees of freedom; the relevant t distribution would have = n - 1 = 41 - 1 = 40.
(b) Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample average speed of vehichles = 81.35 km/h
s = sample standard deviation = 4.52 km/h
n = sample of vehicles = 541
[tex]\mu[/tex] = population mean
Here for constructing a 95% confidence interval we have used a One-sample t-test statistics as we don't know about population standard deviation.
So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-2.021 < [tex]t_4_0[/tex] < 2.021) = 0.95 {As the critical value of t at 40 degrees of
freedom are -2.021 & 2.021 with P = 2.5%}
P(-2.021 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.021) = 0.95
P( [tex]-2.021 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.021 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
P( [tex]\bar X-2.021 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.021 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.021 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.021 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]81.35-2.021 \times {\frac{4.52}{\sqrt{41} } }[/tex] , [tex]81.35+2.021 \times {\frac{4.52}{\sqrt{41} } }[/tex] ]
= [79.92 km/hr, 82.78 km/hr]
Therefore, a 95% confidence interval for the mean speed of vehicles crossing the bridge is [79.92 km/hr, 82.78 km/hr] .
(c) The hypothesis given to us is;
Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 80 km/hr {means that the mean speed of vehicles over the bridge would be the speed limit of 80 km/h}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 80 km/hr {means that the mean speed of vehicles over the bridge would be the speed limit of different from 80 km/h}
Here, we should not reject the null hypothesis since 80 km/h is in the interval found in (b) which means that we are 95% confident that the mean speed of vehicles over the bridge would be the speed limit of 80 km/h.
(d) Decreasing the significance level of the hypothesis test above would decrease the Type I error probability because Type I error probability is represented by the significance level.
A total of 438 tickets were sold for the school play. They were either adult tickets or student tickets. There were 62 fewer student tickets sold than adult tickets. How many adult tickets were sold?
Answer:
a + s = 394 total tickets sold is 394 s = a - 56 56 fewer student tickets than adult substitute a-56 in place of s in 1st equation and solve for a a + (a - 56) = 394 2a - 56 = 394 2a = 450 a = 225 adult tickets sold s = a-56 = 169 student tickets sold
Hoped I helped