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Answers
The solution of the matrix product is:
[tex]\left[\begin{array}{ccc}4&0\\-16&-7\\\end{array}\right][/tex]
How to find the product?Remember that the general product between two 2by2 matrices can be written as:
[tex]\left[\begin{array}{ccc}a_{11}&a_{12}\\a_{21}&a_{22}\\\end{array}\right] *\left[\begin{array}{ccc}b_{11}&b_{12}\\b_{21}&b_{22}\\\end{array}\right] = \left[\begin{array}{ccc}a_{11}*b_{11} + a_{12}*b_{21}&a_{11}*b_{12} + a_{12}*b_{22}\\...&...\\\end{array}\right][/tex]
So we multiply the the rows of the first matrix by the columns of the second one, then our product will be:
[tex]\left[\begin{array}{ccc}1&2\\-4&3\\\end{array}\right] *\left[\begin{array}{ccc}4&1\\0&-1\\\end{array}\right] = \left[\begin{array}{ccc}1*4 + 2*0&1*1 + 2*-1\\-4*4 + 3*0&-4*1 + 3*-1\\\end{array}\right]\\\\= \left[\begin{array}{ccc}4&0\\-16&-7\\\end{array}\right][/tex]
That is the solution of the product.
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Related Questions
1. A biconditional statement says, "A polygon is a square if and only if the polygon has
four equal sides and four right angles." Write the hypothesis and condusion.
2. A statement says, "If the measure of 4] equals the measure of K, the angles are congruent." Write the converse, inverse, and contrapositive of this statement.
3. What is the original statement if the converse of the original statement is "If a number is divisible by two, then it is an even number"? What is the inverse of the original statement?
4. Write the biconditional statement if the hypothesis is "This month is November," and the conclusion is "Next month is December."
5. A right triangle is a triangle that contains a right angle. Write the biconditional statement for the statement above. Also write the converse of the statement. Is the converse a true statement? Explain.
Answers
Answer:Hypothesis: A polygon has four equal sides and four right angles.
Conclusion: The polygon is a square.
Converse: If the angles are congruent, then the measure of 4] equals the measure of K.
Inverse: If the measure of 4] does not equal the measure of K, then the angles are not congruent.
Contrapositive: If the angles are not congruent, then the measure of 4] does not equal the measure of K.
Original statement: If a number is even, then it is divisible by two.
Inverse: If a number is not divisible by two, then it is not even.
Biconditional statement: This month is November if and only if next month is December.
Biconditional statement: A triangle is a right triangle if and only if it contains a right angle.
Converse: If a triangle contains a right angle, then it is a right triangle.
The converse is not necessarily a true statement as a triangle can contain a right angle and still not be a right triangle (i.e. it may not meet the requirements of all sides being of equal length).
Step-by-step explanation:
Hypothesis: A polygon has four equal sides and four right angles.
Conclusion: The polygon is a square.
Converse: If the angles are congruent, then the measure of 4] equals the measure of K.
Inverse: If the measure of 4] does not equal the measure of K, then the angles are not congruent.
Contrapositive: If the angles are not congruent, then the measure of 4] does not equal the measure of K.
Original statement: If a number is even, then it is divisible by two.
Inverse: If a number is not divisible by two, then it is not even.
Biconditional statement: This month is November if and only if next month is December.
Biconditional statement: A triangle is a right triangle if and only if it contains a right angle.
Converse: If a triangle contains a right angle, then it is a right triangle.
The converse is not necessarily a true statement as a triangle can contain a right angle and still not be a right triangle (i.e. it may not meet the requirements of all sides being of equal length).
plot the numbers -1.5 3/2, 3/2 and-4/3 on the number line.
Answers
Answer: -1.5, -4/3, 3/2, 3/2
Step-by-step explanation:
First, convert the numbers to decimals or fractions.
-1.5
3/2 = 1.5
3/2 = 1.5
-4/3 = -1.3
Therefore, on a number line, the numbers would be in the following order:
-1.5, -4/3, 3/2, 3/2
Height (in inches)
Class Frequency, f
50-52
5
53-55
8
56-58
12
59-61
13
62-64
11
What is the Sum of the Xm'f Coulumn
Answers
To find the sum of the Xm'f column, we first need to calculate the midpoint (Xm) for each class interval and then multiply it by the frequency (f) for that interval. The midpoint of each class interval can be calculated as the average of the lower and upper bounds of the interval.
For the first class interval 50-52:
Xm = (50 + 52) / 2 = 51
Xm'f = Xm * f = 51 * 5 = 255
For the second class interval 53-55:
Xm = (53 + 55) / 2 = 54
Xm'f = Xm * f = 54 * 8 = 432
For the third class interval 56-58:
Xm = (56 + 58) / 2 = 57
Xm'f = Xm * f = 57 * 12 = 684
For the fourth class interval 59-61:
Xm = (59 + 61) / 2 = 60
Xm'f = Xm * f = 60 * 13 = 780
For the fifth class interval 62-64:
Xm = (62 + 64) / 2 = 63
Xm'f = Xm * f = 63 * 11 = 693
Finally, we can add up the Xm'f values for each interval to get the sum of the Xm'f column:
Sum of Xm'f = 255 + 432 + 684 + 780 + 693 = 2954
So the sum of the Xm'f column is 2954.
find two numbers with a sum of 13 and a difference of 5
Answers
By substituting the second equation into the first, we can find x:
x + y = 13
x = (x + y) - y = 13 - y
x - y = 5
x = (x - y) + y = 5 + y
Setting these two expressions equal to each other, we have:
13 - y = 5 + y
18 = 6 + 2y
12 = 2y
y = 6
Therefore, the two numbers with a sum of 13 and a difference of 5 are x = 5 + 6 = 11 and y = 6.
The quotient of a number and two increased by 2 is 9. What is the number
Answers
Answer:
x = 3.5
Step-by-step explanation:
x/2 + 2 = 9
x/2 = 7
x = 3.5
Which three lengths could be the lengths
of the sides of a triangle?
A. 12 cm, 5 cm, 17 cm
B. 10 cm, 15 cm, 24 cm
C. 9 cm, 22 cm, 11 cm
D. 21 cm, 7 cm, 6 cm
Answers
Answer:
A. 12 cm, 5 cm, 17 cm
Step-by-step explanation:
For any three given lengths to be the sides of a triangle, they must satisfy the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides must be greater than the length of the third side.
Let's check each of the options:
A. 12 cm, 5 cm, 17 cm: 5 + 12 = 17, which is greater than 17, so this is a valid triangle.
B. 10 cm, 15 cm, 24 cm: 10 + 15 = 25, which is greater than 24, so this is a valid triangle.
C. 9 cm, 22 cm, 11 cm: 9 + 11 = 20, which is not greater than 22, so this is not a valid triangle.
D. 21 cm, 7 cm, 6 cm: 7 + 6 = 13, which is not greater than 21, so this is not a valid triangle.
Therefore, the three lengths that could be the sides of a triangle are A (12 cm, 5 cm, 17 cm) and B (10 cm, 15 cm, 24 cm).
Given: f(x) = 2/3x-4 and g(x) = x + 1
Four statements about this system are written
below.
I.f(4) = g(4)
II.When x = 12, f(x) = g(x).
III. The graphs of f(x) and g(x) intersect at
(12,4).
IV. The graphs of f(x) and g(x) intersect at
(4, 12).
Which statement(s) are true?
A. II, only
C. I and IV
B. IV, only
D. II and III
Answers
The statements that are true about the two given functions intersections are; D. II and III
How to find the points of intersection of functions?The functions we are working with are;
f(x) = ²/₃x - 4
g(x) = ¹/₄x + 1
I) f(4) = ²/₃(4) - 4 = -4/3
g(4) = ¹/₄(4) + 1 = 2
II) f(12) = ²/₃(12) - 4
f(12) = 4
g(12) = ¹/₄(12) + 1
g(12) = 4
III) The coordinates of their intersection is; 12, 4
IV) This is incorrect
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This is a Algebra probolem
Answers
Answer:
B=B1B2B3/B1B2+B2B3+B1B3
Step-by-step explanation:
B1 B2 B3=B2B3B+B1B3B+B1B2B
B2B3B+BB1B3B+B1B2B=B1B2B3
(B2B3+B1B3+B1B2)B=B1B2B3
B=B1B2B3/B2B3+B1B3+B1B2
B=B1B2B3/B1B2+B2B3+B1B3
If f(x)=2x-10 and the domain of f(x) is the set of untethers from -1 to 3 which values are elements of the range of f(x) Select all that apply
Answers
Answer:The range is all number greater than -10, so the values that are elements of the range of f(x) are c) -9, d) -6, and e) -2
Step-by-step explanation:
Please help pic is below
Answers
The point (1, 1/2) lie on the equation y(x² + 1) = 1.
What is an ordered pair?An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence.
Pair in Order = (x, y)
x is the abscissa, the distance measure of a point from the primary axis x
y is the ordinate, the distance measure of a point from the secondary axis y
Given, A function y(x² + 1) = 1.
y = 1/(x² + 1).
When x = 1, y = 1/2.
When x = - 1, y = 1/2.
So, The points that lie on the equation y(x² + 1) = 1 is (1, 1/2).
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Write an equation of the line that is parallel to y = 1/2x + 3 and passes through the point (2,-4). A) y = 1/2x-4 - 15 B) y = -2x-4 + 15 C) y = -2x-5 D) y = 1/2x - 5
Answers
Answer:
D
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{1}{2}[/tex] x + 3 ← is in slope- intercept form
with slope m = [tex]\frac{1}{2}[/tex]
• Parallel lines have equal slopes , then
y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
to find c substitute (2, - 4 ) into the partial equation
- 4 = [tex]\frac{1}{2}[/tex] (2) + c = 1 + c ( subtract 1 from both sides )
- 5 = c
y = [tex]\frac{1}{2}[/tex] x - 5 ← equation of parallel line
Sean’s baby brother sleeps about
13 hours a day. If he takes
2 two-hour naps, how long does
he sleep at night?
Answers
Answer:
He sleeps about 9 hours at night.
Step-by-step explanation:
If Sean's baby brother sleeps 13 hours a day, and takes 2 two-hour naps during the day, he sleeps 2 * 2 = 4 hours during the day.
SOOO, he sleeps 13 - 4 = 9 hours at night.
The boiling point of water is 212°F at sea level. Andres lives at an elevation of
7500 ft and finds that water boils at 198°F, What is the percent decrease in
the boiling point of water from sea level to 7,500 ft? Give your answer to the
nearest tenth of a percent. Show your work.
Answers
The percent decrease in the boiling point of water from sea level to 7,500 feet is equal to 18.7%.
What is a percentage?In Mathematics, a percentage simply refers to any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.
In order to determine the percent decrease in the boiling point of water from sea level to 7,500 feet, we would determine the difference in temperature as follows;
Difference in temperature = 212°F - 198°F
Difference in temperature = 14°F
Percentage decrease = 14/7500 × 100
Percentage decrease = 0.00187 × 100
Percentage decrease = 18.7%.
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2/23 divided by 3 1/2
Answers
Answer:
4/161
Step-by-step explanation:
2×2
____
23×7
=4
161
=4
161
To obatin the graph of y=(x-8)^2 shifts the graph of y=x^2
Answers
To obatin the graph of y=(x-8)^2 shifts the graph of y=x^2 8 units right
How to determine the transformationFrom the question, we have the following parameters that can be used in our computation:
y=(x-8)^2
y = x^2
In the above equations, we can see that
The value of 8 is subtracted from x in y = x^2 to get y = (x - 8)^2
This represents a right translation by 8 units
Hence, the translation is 8 units to the right
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On the unit circle the radius of the circle is 1, which means x=
Answers
Answer:
In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane.
Step-by-step explanation:
Work out the following sheet
Answers
x = 112 degrees.
A full triangle is 180 degrees total so do 180 - (39 + 29) = 112.
y = 220 degrees.
The sum of exterior angles are 360 degrees so 360 - 140 = 220.
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Find the surface area if the pyramid
Answers
Answer: [tex]533 yd^{2}[/tex]
Step-by-step explanation:
The surface area of the base is:
(20 x 17.3) / 2
= 346 / 2
= 173
The surface area of one of the three identical triangles is:
(20 x 12) / 2
= 240 / 2
= 120
So in total, your answer would be one base plus three of those identical triangles:
173 + (3 x 120)
= [tex]533 yd^{2}[/tex]
Jared writes a multiplication expression with eight rational factors. Half of the factors are positive and half are negative.
Is the product positive or negative? Why?
Answers
The multiplication expression with eight rational factors are ''positive''.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We have to given that;
Jared writes a multiplication expression with eight rational factors. Half of the factors are positive and half are negative.
Since, Multiplication of four positive numbers are always gives a positive number and multiplication of four negative numbers are always gives a positive number.
Hence, The multiplication expression with eight rational factors are positive.
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Max’s custom lacrosse stringing experienced fixed costs of $750 and variable costs of $15 for each lacrosse stick that was restrung. Write an equation that can be used to determine the total cost when x sticks are restrung. Then determine the total cost of restringing 32 lacrosse sticks.
Answers
The equation representing the total cost is 15x + 750 and the total cost of restringing 32 lacrosse sticks would be $1230.
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
Let, The number of lacrosse sticks be 'x' and the total cost is C(x).
Therefore, The equation representing the context is,
C(x) = 25x + 750.
The total cost of restringing 32 lacrosse sticks would be,
C(32) = 15×32 + 750.
C(32) = 480 + 750.
C(32) = 1230.
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explain a drop of 200 feet
Answers
Answer:-200
Step-by-step explanation:
Mr. Olsen has a computer business in which he sells everything at 44.5% above the wholesale price. If he purchased a printer for $80 wholesale, what will be the retail price?
Answers
If he purchased a printer for $80 wholesale. Then the retail price will be $115.60.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Mr. Olsen has a PC business wherein he sells everything at 44.5% above the wholesale price. On the off chance that he bought a printer for $80 wholesale.
Then the retail price is given as,
⇒ $80 x (1 + 0.445)
⇒ $80 x 1.445
⇒ $115.60
If he purchased a printer for $80 wholesale. Then the retail price will be $115.60.
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wat factor of 26 is between 4 and 26
Answers
Answer:
13
Step-by-step explanation:
cos 13 x 2 = 26
13 is a factor that is more than 4 and less then 26
The factor of the number 26 that is between 4 and 26 is 13. Factors are the numbers that can divide into a number without leaving a remainder. In this case, the factors of 26 are 1, 2, 13, and 26.
Explanation:In mathematics, a factor of a number is a number that divides into another number without leaving a remainder. In the case of the number 26, its factors include 1, 2, 13, and 26. The factor of 26 that is between 4 and 26 is 13.
To find this, you can go through the factors of 26 one by one. The factors are found by dividing 26 by all the numbers up to 26, and the numbers that give a remainder of 0 are the factors. In this case, 1, 2, 13, and 26 divide evenly into 26, and so are the factors of 26. Of these, only 13 lies between 4 and 26.
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1. You have the digits 0-9. How many 6-digit permutations are odd and do not start with 0
Answers
Answer:
We have 10 digits to choose from (0-9), so the total number of 6-digit permutations is 10 × 10 × 10 × 10 × 10 × 10 = 1,000,000.
Of these, the permutations that start with 0 can be eliminated, leaving 9 × 9 × 9 × 9 × 9 × 9 = 729,000.
Now, we need to figure out how many of these are odd. To do this, we note that odd numbers end in 1, 3, 5, 7, or 9. This means that the last digit of an odd 6-digit permutation is always one of these five digits. Since we are choosing the last digit from 5 options, there are 5 × 729,000 = 3,645,000 odd 6-digit permutations that do not start with 0.
Describe each translation in words T(x,y) (x+4,y+9)
Answers
The translation means that the x coordinate is moving 4 units to the right and the y coordinate is moving9 units to the right.
What is translation?A translation in mathematics does not turn a shape; instead, it moves it left, right, up, or down. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They have only changed their direction or directions. The shape just shifts from one place to another, therefore there is no change in the shape.
The translation is T(x,y) (x+4,y+9).
The translation means that the x coordinate is moving 4 units to the right and the y coordinate is moving9 units to the right.
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Write your own expression with coefficient -4 and constant 8.
Answers
Answer: you need to do it on your own
Step-by-step explanation:
Find the difference 800-699
Answers
Answer: The answer is 101
A 2-ft vertical post casts a 10-in shadow at the same time a nearby cell phone tower casts a 115-ft shadow. How tall is the cell phone tower in feet? Your answer
Answers
The height of the cell phone tower in feet is solved to be 23 feet
How to find the height of the cell phone towerThe height of the cell phone tower is calculated using the concept of similar triangle and the equation is as follows
A 2-ft vertical post casts a 10-in shadow
2 / 10
nearby cell phone tower casts a 115-ft shadow
let the height be x
x / 115
equating the proportions
2 / 10 = x / 115
cross multiplying
10x = 2 * 115
x = 2 * 115 / 10
x = 23 ft
The height of the tower is 23 feet
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Pat and Rich drove to the beach
last weekend. It took them twice as
long to get back as it did to drive
there. If they spent 9 hours traveling
to and from the beach, how long
did it take them to drive each way?
Answers
The total time that it took Pat and Rich to get to the beach is given as 3 hours.
How to solve for the total timeLet's call the time it took Pat and Rich to drive to the beach "t".
Since it took them twice as long to get back, it took them 2t to get back.
The total time they spent traveling was 9 hours, so we can set up an equation:
t + 2t = 9
Combining like terms:
3t = 9
Finally, dividing both sides by 3:
t = 3
So it took them 3 hours to drive to the beach, and 6 hours to drive back.
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The average lifetime of smoke detectors that a company manufactures is 5 years, or 60 months, and the standard deviation is 8 months. Find the probability that
sample of 29 smoke detectors will have a mean lifetime
between 57 and 64 months. Assume that the sample is taken from a large population and the correction factor can be ignored.
Round the final answer to at least four decimal places and intermediate z-value calculations to two decimal places.
Answers
The required probability is 0.8945 that a sample of 29 smoke detectors will have a mean lifetime between 57 and 64 months.
To find the probability that a sample mean is between 57 and 64 months, we need to find the standard deviation of the sample mean, which is given by the standard deviation of the population divided by the square root of the sample size.
The standard deviation of the sample mean = standard deviation of the population / square root of sample size = 8 / √(29) = 8 / 5.385 = 1.48
Next, we need to standardize the interval of 57-64 months by subtracting the mean and dividing it by the standard deviation of the sample mean.
z₁ = (57 - 60) / 1.48 = -2.03
z₂ = (64 - 60) / 1.48 = 1.35
Finally, we can use a standard normal table to find the area under the normal curve between z₁ and z₂, which gives us the probability of a sample mean falling in the interval (57, 64).
P(57 < X < 64) = P(-2.03 < Z < 1.35) = 0.9790 - 0.0845 = 0.8945
Therefore, the final answer is 0.8945, rounded to four decimal places.
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