find the products AB and BA to determine whether B is the multiplicative inverse of A.
Answers
B is not the multiplicative inverse of A.
Multiplicative inverse matrix:The multiplicative inverse matrix, also known as the inverse matrix or simply the inverse, is a matrix that when multiplied by a given matrix, results in the identity matrix. The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere.
Here we have
[tex]A = \left[\begin{array}{cc}3&-2&\\0&-3&\end{array}\right][/tex] [tex]B = \left[\begin{array}{cc}-1&2&\\0&-4&\end{array}\right][/tex]
Product of A and B
[tex]AB = \left[\begin{array}{cc}3&-2&\\0&-3&\end{array}\right] \times \left[\begin{array}{cc}-1&2&\\0&-4&\end{array}\right][/tex]
[tex]AB = \left[\begin{array}{cc}3(-1) + (-2)(0) &3(2) + (-2)(-4)&\\0 + 0 &0 +(-3)(-4)&\end{array}\right][/tex]
[tex]AB = \left[\begin{array}{cc}-3 &14&\\0 &12&\end{array}\right][/tex]
Product of B and A
[tex]BA = \left[\begin{array}{cc}-1&2&\\0&-4&\end{array}\right] \times \left[\begin{array}{cc}3&-2&\\0&-3&\end{array}\right][/tex]
[tex]BA = \left[\begin{array}{cc}1(3) + 2(0)&-1(-2)+2(-3)\\0(3)+0 &0(-2)+(-4)(-3) \end{array}\right][/tex]
[tex]BA = \left[\begin{array}{cc}-3&-4\\0&12\end{array}\right][/tex]
Here AB ≠ BA ≠ I
Therefore,
B is not the multiplicative inverse of A.
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Complete Question given in the picture
Related Questions
Solve for the roots in simplest form by completing the square:
Answers
Answer:
3rd degree
3
-4
-(1/2)x³
-1/2
Step-by-step explanation:
1st blank: The largest exponent tells you the degree of the polynomial.
2nd blank: Count how many "parts" (terms) are separated by + or -
3rd: The term without variables is the constant term. Include the sign in front of it!!
4th: The term that includes the highest degree variable. Include the sign in front of it!!
5th: The number preceding the variable in the leading term. Again, include the sign...!!
Ken stopped for gas after driving 65% of the way to his grandparents' house. If he had already driven 262 miles, how far is it to his grandparents?
Answers
Answer:
about 403.1 miles
Step-by-step explanation:
262 miles is 65% of the distance to the grandmother's house. Let d be that distance.
[tex].65d = 262[/tex]
[tex]d = 403.1[/tex]
The distance from Ken's house to his grandmother's house is about 403.1 miles.
Please help! Thank you!
7. Out of the total of 213 students selected for an award at the school banquet, 115 of
them won awards for mathematics and 42 of them won awards for science. There
were 21 students who won awards for both mathematics and science. A student was
selected randomly for an on-site interview to celebrate their success. What's the
probability that the student won an award for mathematics or for science?
Answers
the probability that the student won an award for mathematics or for science is 0.6385 or approximately 64%.
How to solve probability?
To find the probability that the student won an award for mathematics or for science, we need to use the concept of set theory and the inclusion-exclusion principle.
Let A be the set of students who won awards for mathematics, and B be the set of students who won awards for science. We are interested in finding the probability of A union B, which represents the set of students who won awards for either mathematics or science or both.
From the given information, we know that |A| = 115, |B| = 42, and |A intersect B| = 21, where |X| denotes the cardinality of the set X, i.e., the number of elements in the set X.
Using the inclusion-exclusion principle, we can write:
|A union B| = |A| + |B| - |A intersect B|
Substituting the values, we get:
|A union B| = 115 + 42 - 21 = 136
Therefore, there are 136 students who won awards for either mathematics or science or both.
To find the probability of selecting a student who won an award for mathematics or for science, we divide the cardinality of A union B by the total number of students, which is given as 213:
P(A union B) = |A union B| / 213 = 136 / 213 = 0.6385 (rounded to four decimal places)
Therefore, the probability that the student won an award for mathematics or for science is 0.6385 or approximately 64%.
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I need help with this problem
Answers
The area of the region enclosed by the curves can be found to be 1/6 square units.
How to find the area of the region ?To find the area enclosed by the curves y = x, y = 5x, and y = -x + 2, we first need to find the points where these curves intersect.
Intersection points of y = x and y = 5x: (0, 0)
Intersection points of y = x and y = -x + 2: Intersection point: (1, 1)
Intersection points of y = 5x and y = -x + 2: Intersection point: (1/3, 5/3)
Now we have the three intersection points: (0, 0), (1, 1), and (1/3, 5/3). The area enclosed by the curves is a triangle with vertices at these points.
To find the area of the triangle, we can use the Shoelace Formula:
Area = (1/2)|x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
Area = (1/2)|0(1 - 5/3) + 1(5/3 - 0) + (1/3)(0 - 1)|
Area = 1 / 6 square units
The area enclosed by the curves is 1/6 square units.
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Simplify the expression. (4.57u − 14) − (−6 + 7.6u) −3.03u + (−20) −3.03u + (−8) 12.17u + (−20)
Answers
After simplification of the given expression, the resultant answer is (B) −3.03u + (−8).
What are expressions?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
It's possible to multiply, divide, add, or subtract with this mathematical operation.
Keep in mind that terms can be coefficients, constants, or variables. So, 1+1 is a straightforward example of an expression.
This equation has one operation, two constant terms, and (addition). x3 is another illustration.
So, the given expression is:
(4.57u − 14) − (−6 + 7.6u)
Then, solve as follows:
4.57u - 14 - ( -6 + 7.6u)
4.57u - 14 + 6 - 7.6u
4.57u - 7.6u = -3.03u AND -14 + 6 = -8
-3.03u - 8 (or -3.03u + (-8) )
Therefore, after simplification of the given expression, the resultant answer is (B) −3.03u + (−8).
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Correct question:
Simplify the expression.
(4.57u − 14) − (−6 + 7.6u)
A. −3.03u + (−20)
B. −3.03u + (−8)
C. 12.17u + (−20)
D. 12.17u + (−8)
use Euler's method with step size 0.2 to estimate y(0.6), where y(x) is the solution of the initial value problem y'= cos (x+y), y(0)=0
Answers
Using Euler's method with step size 0.2, we estimate that y(0.6) ≈ 0.6024.
What is Euler's method ?
Euler's method is a simple numerical method used to approximate the solution of a first-order ordinary differential equation (ODE) with a given initial value. The method is based on the idea of approximating the solution by taking small steps along the direction of the derivative of the solution.
To use Euler's method, we need to take steps of size 0.2 from x=0 up to x=0.6, and use the derivative y' = cos(x + y) to approximate the value of y at each step.
We start by setting up a table:
x y y' = cos(x+y) y(i+1) = y(i) + h*y'
0.0 0.0 cos(0) = 1 0.2 * 1 + 0 = 0.2
0.2 0.2 cos(0.2+0.2) 0.2 * 1.981 = 0.3962
0.4 0.3962 cos(0.4+0.3962) 0.2 * 1.9774 = 0.3955
0.6 0.7919 cos(0.6+0.7919)
To estimate y(0.6), we need to complete the last row of the table. We have:
y(0.2) = 0.21 + 0 = 0.2
y(0.4) = 0.21.981 + 0.2 = 0.3962
y(0.6) ≈ 0.3955 + 0.2*cos(0.6+0.7919) ≈ 0.6024
Therefore, using Euler's method with step size 0.2, we estimate that y(0.6) ≈ 0.6024.
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It costs $7.80 to manufacture screen printed t-shirts. Marcos wants to sell the t-shirts he makes at a mark-up, selling each for 110% of its manufacturing cost. What is the price of each t-shirt to customers?
Answers
Step-by-step explanation:
If it costs $7.80 to manufacture the t-shirt, then a 110% markup would mean selling it for 1.1 times the manufacturing cost:
Price = 1.1 x $7.80 = $8.58
So Marcos should sell each t-shirt for $8.58 to customers.
A company starts to track the number of phone calls received each month.Information about the number of phone calls the company received the first three months of tracking is listed below.
-During the first month,the company received 4,265 phone calls.
-During the second month,the company received 25% more phone calls than in the first month.
-During the third month,the company received 6,396 phone calls
What was the percent increase in the number of phone calls from the second month to the third month
Answers
Answer:
20%
Step-by-step explanation:
Number of phone calls received second month = 4265 + 25% of 4265
= 4265 + 0.25 * 4265
= 4265 ( 1 + 0.25)
= 4265 * 1.25
= 5331.25
Number of calls in third month = 6396
Increased calls than second month = 6396 - 5331.25
= 1034.75
[tex]Increased \ percentage = \dfrac{Increased \ calls}{second \ month \ calls}*100[/tex]
[tex]=\dfrac{1064.75}{5331.25}*100\\\\=19.97 \%\\\\= 20\%[/tex]
An experiment consists of recording, in order of their births, the sex composition of a four-child family in which the children were born at different times. (Let b represent the birth of a boy and g represent the birth of a girl. Enter your answers using letter combinations separated by commas. Example: bgbg, gggg, ...)
(a) Describe an appropriate sample space S for this experiment.
(b) Describe the event E that there are three boys and a girl in the family.
Answers
(a) An appropriate sample space S for this experiment is the set of all possible sequences of four children, where each child can be either a boy (b) or a girl (g). So, the sample space S is:
S = {bbbb, bbbg, bbgb, bgbb, gbbb, bggg, bgbg, gbgg, ggbb, gbgb, bggg, gbgg, gggg, gggb, gggg}
There are 2^4 = 16 possible outcomes in the sample space.
(b) The event E that there are three boys and a girl in the family can be represented by the set of all sequences in the sample space S that have three b's and one g. So, the event E is:
E = {bbbg, bbgb, bgbb, gbbb}
There are 4 possible outcomes in the event E.
Over what interval is the graph of f(x) = -(x + 3)? - 1 decreasing?
Answers
the interval over which the graph of f(x) = -(x + 3) - 1 is decreasing is (-∞, +∞).
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
The given function is:
f(x) = -(x + 3) - 1
To find the interval over which the function is decreasing, we need to find the values of x where the function's derivative is negative.
The derivative of the function is:
f'(x) = -1
The derivative is a constant, which means the function has a constant slope of -1. Since the slope is negative, the function is decreasing over its entire domain.
Therefore, the interval over which the graph of f(x) = -(x + 3) - 1 is decreasing is (-∞, +∞).
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Javier's home has assessed for $234,000. The millage rate for the school district is 6.3 mills. The millage rate for the city is 6.9 mills. The millage rate for the county is 7.1 mills. What is his total property tax bill? Round to the nearest dollar.
Answers
Javier's total property tax bill is $4,750.06. By solving the question.
How to solve the question?
To calculate Javier's property tax bill, we need to use the assessed value of his home and the millage rates for each tax district.
First, we need to convert the millage rates to decimal form. To do this, we divide each millage rate by 1,000:
School district millage rate = 6.3 / 1,000 = 0.0063
City millage rate = 6.9 / 1,000 = 0.0069
County millage rate = 7.1 / 1,000 = 0.0071
Next, we need to calculate the tax for each district by multiplying the assessed value of Javier's home by the millage rate for that district:
School district tax = $234,000 x 0.0063 = $1,475.20
City tax = $234,000 x 0.0069 = $1,615.46
County tax = $234,000 x 0.0071 = $1,659.40
Finally, we add up the tax for each district to get Javier's total property tax bill:
Total property tax bill = $1,475.20 + $1,615.46 + $1,659.40 = $4,750.06
Therefore, Javier's total property tax bill is $4,750.06.
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Part 3. Describe the transformations of the following functions in complete sentences.
11. y = -ln(x + 3) + 7
12. 3*+5 - 2
Answers
The function y = -ln(x + 3) + 7 is a logarithmic function that has undergone multiple transformations like horizontal and vertical shift and reflection and any transformations can not be described for second expression.
What is transformation?
A transformation is a process or operation that changes the position, shape, or orientation of a geometric figure or an object in space.
11. The function y = -ln(x + 3) + 7 is a logarithmic function that has undergone multiple transformations. We can describe these transformations as follows:
Horizontal shift: The argument of the logarithm has been shifted horizontally to the left by 3 units. This means that the graph of the function has been shifted to the left by 3 units relative to the parent function y = -ln(x).
Vertical shift: The entire graph of the function has been shifted vertically upwards by 7 units. This means that the minimum point of the graph has been shifted from y = -∞ to y = 7.
Reflection: The function has been reflected across the x-axis. This means that the values of y will be negative for all positive values of x.
12. The expression 3*+5 - 2 is not a valid mathematical expression or function. It appears to be incomplete, as there is no variable or operation specified. Without additional information, we cannot describe any transformations of this expression.
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Which can be represented using the product (50) × (-5) ?
O saving $5 each day for 50 days
O a submarine rising by 50 feet each hour for 5 hours
O earning $50 each month for 5 months
O an airplane losing altitude by 5 feet each second for 50 seconds
Answers
Answer: D
Step-by-step explanation:
564 ÷ 18 as a fraction
Answers
Answer: The simplest form of 564/18 is 94/3.
Step-by-step explanation: Hope this helps
A fair coin tossed 3 times. What is the probability tossing at least 1 head
Answers
Answer:
[tex]\frac{7}{8}[/tex]
Step-by-step explanation:
Can somebody please help Me?
Answers
The examples of monomial, binomial, and polynomial expressions are as follows:
2x³ + 5x = Binomial
3 = Monomial
9x³ - 4y = Binomial
5x - 7y = Binomial
3x + 3y - 2 = Polynomial
8x^6 + 3x - 2 = Polynomial
2x + 4y = Binomial
2x² = Monomial
How to classify the expressionsTo classify these expressions, you can first start by noting that mono means 1, so a monomial expression has just one term. So, the number 3 is a monomial expression.
Also, a binomial expression has two terms as sen in the expression, 2x + 4y. Finally, a polynomial expression has three terms and the expression, 3x + 3y - 2 is an example.
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A CBS News/New York Times poll of 1,000 adults in the United States asked the question, "Do you think global warming will have an impact on you during your lifetime?" (CBS News website). Consider the responses by age groups shown below.
Answers
Given the information, the probability that a response is between the ages of 18 and 29 and 30 or older is, respectively, 0.536 and 0.654. There is a 0.265 percent chance that they will say yes—that global warming will affect them over their lifetime. Concern over global warming also seems to vary across people aged 18 to 29 and those over 30.
Define probability?Probability is the ratio of favourable events to all other potential outcomes in a circumstance. The symbol x can be used to denote how many successful outcomes there were in an experiment with 'n' outcomes. The formula below can be used to determine a given event's probability.
Positive Results/Total Results = x/n = Probability (Event)
The likelihood that a respondent between the ages of 18 and 29 believes that there will be no significant threat from global warming in his or her lifetime is:
P (18-29 and no) = 293/(134 + 293 + 117) = 0.536
The likelihood that a respondent who is 30 years of age or older believes that there will be no significant threat from global warming in his or her lifetime is:
P (30+ and no) = 432/(131 + 432 + 178) = 0.654
The likelihood that a randomly chosen respondent will select "yes"—that is, that they will experience the effects of global warming throughout their lifetimes—is:
P(Yes) = (134 + 131)/(134 + 131 + 293 + 432 + 117 + 178) = 0.265
Yeah, it does seem that younger people (18–29) are less concerned about global warming than older people (30+). In comparison to respondents aged 18 to 29, the likelihood that a respondent aged 30 or older believes that global warming will not constitute a severe hazard during their lifetime is higher (0.654). (0.536). According to this, respondents who are older are less concerned about global warming than respondents who are younger. To confirm this difference, a formal statistical test would be required.
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The complete question is:
Do you think global warming will have an impact on you during your lifetime? A CBS News/New York Times poll of 1000 adults in the United States asked this ques- tion (CBS News website, December, 2014). Consider the responses by age groups shown below Response Age 18-29 30+Yes 134 131No 293 432Unsure a. What is the probability that a respondent 18-29 years of age thinks that global warming will not pose a serious threat during his/her lifetime?b. What is the probability that a respondent 30+ years of age thinks that global warming will not pose a serious threat during his/her lifetime? c. For a randomly selected respondent, what is the probability that a respondent answers yes? d. Based on the survey results, does there appear to be a difference between ages 18-29 and 30+ regarding concern over global warming?
Suppose that $9000 is placed in an account that pays 9% interest compounded each yea
Assume that no withdrawals are made from the account
Answers
Answer:
1). $9810
2). $10,620
Step-by-step explanation:
9000 x .09= 810
9000 + 810= 9810
810 x 2= 1620
9000 + 1620= 10,620
Answer: A : 810 B : 1620
Step-by-step explanation: 9000 x 9% x 1
9000 x 9% x 2
P x R x T
Principle (Money started with) x Rate ( Interest Rate) x Time (Years)
During a test drive, a self-driving car travels a distance of 50 miles in 80 minutes. How many miles will the car travel after 320 minutes?
Answers
So, after 320 minutes, the car will have covered 200 miles.
MILE DEFINITION?In both the US customary and British imperial systems of measurement, a mile is a unit of length or distance. It is measured in yards or 5,280 feet. Approximately 1.609 km make up one mile.
IMPERIAL SYSTEM: WHAT IS IT?A method of measurement known as the imperial system was created in England in the 12th century and afterwards adopted by other nations. It is often referred to as the Imperial Units or the British Imperial System. The system comprises units for weight, such as ounces, pounds, and tons, volume, and length (such as inches, feet, and miles). (such as fluid ounces, pints, quarts, and gallons). Despite the fact that many other nations have switched to the metric system, the imperial system is still in use in some nations, including the United States and the United Kingdom.
The autonomous vehicle covers **0.625 miles per minute**. (50 miles in 80 minutes).
After 320 minutes, we may multiply the rate by the time to get how many miles the car will have travelled:
0.625 miles/minute × 320 minutes = **200 miles**
0.625 miles per minute divided by 320 minutes equals 200 miles.
So, after 320 minutes, the car will have covered **200 miles**.
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Is differentiating 8c to the fourth power equal to four times 8c to the 4-1 power?
Answers
Differentiating 8c to the fourth power gives 32c³, not 4 times 8c to the 4-1 power.
What is differentiation?
Differentiation is a mathematical operation that involves finding the derivative of a function with respect to one of its variables.
No, differentiating 8c to the fourth power is not equal to four times 8c to the 4-1 power.
To differentiate a term with a power, we use the power rule of differentiation, which states that:
d/dx [xⁿ] = n*x⁽ⁿ⁻¹⁾
where d/dx denotes differentiation with respect to x, n is the power of x, and x⁽ⁿ⁻¹⁾ is the derivative of xⁿ.
Applying this rule to 8c to the fourth power, we get:
d/dc [8c⁴] = 4*8c³
Notice that the power of c decreased by 1 after differentiation, not by 4 as suggested in the question.
Therefore, differentiating 8c to the fourth power gives 32c³, not 4 times 8c to the 4-1 power.
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Alleen wants to make a representation that will show the weekly high temperatures in Bartow, Florida for the past six months. Select all the graphical representations that will best display the data.
Answers
The graphical representations that would best display the data are:
Line graphBar graphScatter plotHeat mapWhat is graph?A graph is a visual representation or diagram that organises facts or values. The points on the graph frequently reflect the relationship between two or more objects.
To display the weekly high temperatures in Bartow, Florida for the past six months, the following graphical representations could be used:
Line graph: A line graph would be a good choice for showing the trend of temperature over time. The x-axis could represent time (e.g. weeks) and the y-axis could represent temperature (in degrees Fahrenheit or Celsius).Bar graph: A bar graph could be used to show the average temperature for each month. The x-axis could represent the months and the y-axis could represent the average temperature.Scatter plot: A scatter plot could be used to show the relationship between temperature and some other variable (e.g. humidity, precipitation, etc.). The x-axis could represent temperature and the y-axis could represent the other variable.Heat map: A heat map could be used to show the distribution of high temperatures across the weeks and months. The x-axis could represent the weeks and the y-axis could represent the months. The colors could represent the high temperatures, with red indicating the highest temperatures and blue indicating the lowest temperatures.Therefore, the graphical representations that would best display the data are:
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Q2. Evaluate: (a) \( j^{12} \); (b) \( -\frac{1}{j^{9}} \); (c) \( \frac{5}{2 j^{13}} \)
Answers
the evaluated expressions are: (a) j¹² = 1 ,(b) -1/j⁹ = j ,(c) 5/(2j¹³) = (5/2)j
to solve this use the properties of the imaginary unit.
what is imaginary unit ?
The imaginary unit is a mathematical concept denoted by i or j (in electrical engineering) that represents the square root of -1. It is called an "imaginary" unit because it does not have a real number counterpart.
In the given question,
To evaluate these expressions, we need to recall the properties of the imaginary unit, j, which is defined as the square root of -1. Specifically, we need to remember that:
j² = -1
j³ = -j
j⁴ = 1
Using these properties, we can simplify the given expressions:
(a) j¹² = (j⁴)³ = 1³ = 1
(b) -1/j⁹ = -1/(j³)³= -1/(-j)³ = -1/(-j³) = -1/(-(-j)) = -1/j = -j/j² = -j/-1 = j
(c) 5/(2j¹³) = 5/(2(j⁴)³*j) = 5/(2*1*j) = 5/(2j) = (5/2) * (1/j) = (5/2) * (-j³/j⁴) = -(5/2)j³ = (5/2)j
Therefore, the evaluated expressions are:
(a) j¹² = 1
(b) -1/j⁹ = j
(c) 5/(2j¹³) = (5/2)j
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. Evaluate the following expression to simplest form \( j^{12} \); (b) \( -\frac{1}{j^{9}} \); (c) \( \frac{5}{2 j^{13}} \)
Lose sold her bicycle for 88.50 she sold her bicycle helmet for 8.75 she brought a basketball for 35.82 how much money does Louis have now
Answers
Answer:61.43
Step-by-step explanation:
yes
Answer:
Louis $61.43 now.
Step-by-step explanation:
Louis sells her bike and helmet for $88.50 and $8.75. Add these together and it gives you the total amount of money she has earned.
[tex]88.50+8.75= 97.25[/tex]
Louis now has $97.25. She then buys something for $35.82, so, subtract the amount of the basketball by the amount of money she earned to find out how much money she has left.
[tex]$97.25- 35.82=61.43[/tex]
Louis now has $61.43.
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Find the Area of the figure?
please an explanation!
Answers
The total area is 1570 square units.
Explain area
Area refers to the measurement of the size of a two-dimensional surface. It is typically expressed in square units, such as square meters or square feet. The area of a shape can be calculated by multiplying its length by its width, or by using specific formulas for more complex shapes. Area is an important concept in geometry and is used in many real-life applications, such as calculating the area of a room or a piece of land.
According to the given information
Here the base of the right triangle is 20 and the hypotenuse is 29, so we can set up the equation:
29² = 20² + h²
where h is the height of the triangle(length of dotted line) that we want to find.
Simplifying and solving for h, we get:
h² = 29² - 20²
h² = 841 - 400
h² = 441
h = √(441)
h = 21
Therefore, the length of the dotted line is 21 units
Now,
The area of a right triangle is given by the formula A = (1/2)bh, where b is the base and h is the height. So, the area of the right triangle with base 20 and height 21 is:
A_triangle = (1/2)(20)(21) = 210
The area of a right trapezium is given by the formula A = (1/2)(a+b)h, where a and b are the parallel sides and h is the height. So, the area of the right trapezium with a longer side of 55, smaller side of 21, and height of 40 is:
A_trapezium = (1/2)(55+21)(40) = 1360
Therefore, the total area of the right triangle and right trapezium is:
A_total = A_triangle + A_trapezium = 210 + 1360 = 1570
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Find the perimeter of the shaded region. Round your answer to the near seat hundredth
Answers
The perimeter of the shaded region is 30.72 units
How to find the perimeter of the shaded region?
To find the perimeter of the shaded region, the arc length at three corners is calculated and then added up with the length of the shape given.
Length of the shape excluding three arcs = 5 + 5 + 5 = 15 units
Radius of the arc = 5/2 = 2.5 units
arc length = 120/360 * 2 * π * 2.5
arc length = 120/360 * 2 * 22/7 * 2.5
arc length = 5.24 units
perimeter of the shaded region = length of shapes excluding three arcs + three times arc length
perimeter of the shaded region = 15 + 3(5.24)
perimeter of the shaded region = 30.72 units
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A number sequence begins 18,27,36,45,…The sequence continues by adding 9 every time. What is the 20 th term of the sequence?
Answers
Reason:
A company wants to lay cable across a lake. To determine the distance across the lake it took the following measurements and created this diagram. To the nearest tenth of a kilometer, what is the approximate distance across the lake?
Answers
The approximate distance across the lake is 6.7 kilometers, which is closest to option D.
What is Pythagorean theorem?
The Pythagorean theorem is a fundamental concept in mathematics that relates to the lengths of the sides of a right triangle.
To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the distance across the lake is the hypotenuse of a right triangle, and the distances 6 km and 3 km are the lengths of the other two sides. Therefore, we can write:
distance across the lake = √(6 km)² + (3 km)²
distance across the lake = √(36 km² + 9 km²)
distance across the lake = √45 km²
distance across the lake ≈ 6.7 km
Therefore, the approximate distance across the lake is 6.7 kilometers, which is closest to option D.
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What are the y-values of the quadraticquation y = x² + 3x + 1, if x =
{1,2,3,4}?
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The y-values of the quadratic equation for x = {1, 2, 3, 4} are {5, 11, 19, 29}.
What is quadratic equation?
A quadratic equation is a type of polynomial equation of degree 2, which means it contains a variable raised to the second power (i.e., x²). It has the standard form of ax² + bx + c = 0, where a, b, and c are constants and x is the variable. The coefficient a cannot be equal to zero, as this would result in a linear equation.
Quadratic equations can have one or two real solutions, depending on the discriminant (b² - 4ac) of the equation. If the discriminant is greater than zero, the equation has two real solutions. If the discriminant is equal to zero, the equation has one real solution. If the discriminant is less than zero, the equation has no real solutions (but has two complex solutions).
To find the y-values of the quadratic equation y = x² + 3x + 1 for x = {1, 2, 3, 4}, we simply substitute each value of x into the equation and evaluate.
For x = 1, y = 1² + 3(1) + 1 = 5.
For x = 2, y = 2² + 3(2) + 1 = 11.
For x = 3, y = 3² + 3(3) + 1 = 19.
For x = 4, y = 4² + 3(4) + 1 = 29.
Therefore, the y-values of the quadratic equation for x = {1, 2, 3, 4} are {5, 11, 19, 29}.
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What is the area of this figure? 7 cm 9 cm 11 cm square centimeters 2 cm 2 cm 5 cm
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Total area = 63 cm² + 33 cm² + 4 cm² + 4 cm² = 104 cm²
What is area of Trapezoid ?The area of a trapezoid is given by the formula:
A = (a + b)h/2
where a and b are the lengths of the parallel sides of the trapezoid and h is the height (the perpendicular distance between the parallel sides).
To use this formula, simply plug in the values of a, b, and h and then solve for A. Note that all measurements must be in the same unit (such as centimeters or inches) for the formula to work correctly.
First, we can find the area of the rectangle with sides 7 cm and 9 cm:
Area of rectangle = length × width = 7 cm × 9 cm = 63 cm²
Next, we can find the area of the trapezoid with bases 2 cm and 5 cm and height 11 cm:
Area of trapezoid = (sum of bases × height) / 2 = ((2 cm + 5 cm) × 11 cm) / 2 = 33 cm²
Finally, we can find the area of the two squares with side lengths 2 cm and 2 cm:
Area of square 1 = side × side = 2 cm × 2 cm = 4 cm²
Area of square 2 = side × side = 2 cm × 2 cm = 4 cm²
Adding up the areas of all the shapes, we get:
Total area = 63 cm² + 33 cm² + 4 cm² + 4 cm² = 104 cm²
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What fraction can we use to rename
19
20
as hundredths? PLEASE HELP
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Answer:
0,95
Step-by-step explanation:
[tex] \frac{19}{20} [/tex]
Multiply the fraction by 5, so that the denominator would be equal to 100:
[tex] \frac{19 \times 5}{20 \times 5} = \frac{95}{100} = 0.95[/tex]
I don't know if I got it right, though...
