Answer:
Step-by-step explanation:
\(d^2=x^2+y^2\\ \\ d^2=15^2+8^2\\ \\ d^2=225+64\\ \\ d=\sqrt{289}m\\ \\ d=17m\)
find the zeros of the function f(x)=8x^2 +32
Answer: no solution
Step-by-step explanation:
\(8x^{2} +32=0\)
Factor out 8
\(8(x^{2} +4)=0\)
no solution
Why?
Think about the graph, \(x^{2}\) shifted up 4 has no zeros, even with a vertical stretch of 8.
Is 8/9 the multiplicative inverse of -1⅛? why or why not?
Answer:
-8/9
Step-by-step explanation:
-1 1/8
=> - 9/8
=> Multiplicative inverse of 9/8 is:
=> - 8/9 [Sign does not change only the numerator goes to the denominator and denominator to the numerator]
=> -8/9 is the multiplicative inverse of -1 1/8
When the mortgage is completely paid off for Mark and Lynne’s house, it will be 6 times as old as it is now. If they have 25 years left on the mortgage, how old is the house right now?
Let us take the age of the house currently as x.
The second statement says that the house will be 6 times as old as it is now after payment is completed.
If the mortgage will be completed in 25 years, we can write that mathematically as
\(6x=x+25\)Therefore, the age of the house, x, can be calculated as
\(\begin{gathered} 6x-x=25 \\ 5x=25 \\ x=\frac{25}{5} \\ x=5 \end{gathered}\)Hence, the house is 5 years old now.
37% of 6.3=
pls answer youll make my day
37% of 6.3 is 2.331.
37/100 = x/6.3. 100x = 233.1. x = 2.331
A ticket for the train costs $6.23. If Barbara has $32, does she have enough money to buy 5 tickets? Explain your reasoning.
what is the place value of 2 in 842567
Answer:
842567
the answer is thousands
7 is ones
6 is tens
5 is hundreth
2 is thousands
4 is ten thousands
8 is hundred thousands
Hope This Helps!!!
The minute hand of a clock is 6 inches long. How far does the tip of the minute hand move in 20 minutes? Round to two decimal places.
Book club A charges $20 for membership and $2 per book rental. Book club B charges $10 for membership and $3 per book rental. For how many movie rentals will the cost be the same at both book clubs? What does that cost?
Given:
Book club A charges $20 for membership and $2 per book rental.
Book club B charges $10 for membership and $3 per book rental.
To find:
The number of books for which the cost be the same at both book clubs.
Solution:
Let x be the number of books.
Book club A charges $20 for membership and $2 per book rental. So, the total cost is
\(C_1=20+2x\) ...(i)
Book club B charges $10 for membership and $3 per book rental. So, the total cost is
\(C_2=10+3x\) ...(ii)
Equating (i) and (ii), we get
\(10+3x=20+2x\)
\(3x-2x=20-10\)
\(x=10\)
The total cost is
\(C_1=20+2(10)\)
\(C_1=20+20\)
\(C_1=40\)
Therefore, the total cost at both book clubs are same for 10 rental books and that cost is $40.
What is 23% of 56.28 rounded to the nearest cent
Solve the matrix equation for the unknown matrix X. (If not possible, enter IMPOSSIBLE in any cell of the matrix.) A = [7 3 4 3] B = [7 2 7 2] C = [3 3 4 0 0 8] D = [10 30 30 30 30 0] 5(X - C) = D x = []
After solving the equation 5(X - C) = D , for the given matrices , we get , the unknown matrix X is = \(\left[\begin{array}{ccc}5&9\\10&6\\6&8\end{array}\right]\) .
In the question ,
it is given that , the matrices are
A = \(\left[\begin{array}{ccc}7&3\\4&3\end{array}\right]\) B = \(\left[\begin{array}{ccc}7&2\\7&2\end{array}\right]\) C = \(\left[\begin{array}{ccc}3&3\\4&0\\0&8\end{array}\right]\) and D = \(\left[\begin{array}{ccc}10&30\\30&30\\30&0\end{array}\right]\) .
and the equation is given as 5(X - C) = D ,
and we have to find the value of unknown matrix X .
let the matrix X be = \(\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right]\)
Substituting , the given matrices A , B , C and D in the equation 5(X - C) = D ,
we get ,
5(X - C) = D ,
5X - 5C = D ,
5\(\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right]\) - 5\(\left[\begin{array}{ccc}3&3\\4&0\\0&8\end{array}\right]\) = \(\left[\begin{array}{ccc}10&30\\30&30\\30&0\end{array}\right]\)
5\(\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right]\) = \(\left[\begin{array}{ccc}10&30\\30&30\\30&0\end{array}\right]\) - \(\left[\begin{array}{ccc}15&15\\20&0\\0&40\end{array}\right]\)
Simplifying further ,
we get ,
5\(\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right]\) = \(\left[\begin{array}{ccc}25&45\\50&30\\30&40\end{array}\right]\)
Dividing both sides by 5 ,
we get ,
X = \(\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right]\) = \(\left[\begin{array}{ccc}5&9\\10&6\\6&8\end{array}\right]\)
Therefore , the matrix X is = \(\left[\begin{array}{ccc}5&9\\10&6\\6&8\end{array}\right]\) .
The given question is incomplete , the complete question is
Solve the matrix equation for the unknown matrix X.
A = \(\left[\begin{array}{ccc}7&3\\4&3\end{array}\right]\) B = \(\left[\begin{array}{ccc}7&2\\7&2\end{array}\right]\) C = \(\left[\begin{array}{ccc}3&3\\4&0\\0&8\end{array}\right]\) and D = \(\left[\begin{array}{ccc}10&30\\30&30\\30&0\end{array}\right]\) . the equation is
5(X - C) = D .
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suppose a soup can has a height of 6 inches and a radius of 2 inches. in terms of π, how much material is needed to make each can?
The amount of material needed to make a can can be calculated by finding the surface area of the can. In this case, we have a soup can with a height of 6 inches and a radius of 2 inches.
To calculate the surface area, we need to find the area of the circular top and bottom, as well as the area of the curved side. The area of each circular top or bottom is given by the formula A = πr^2, where r is the radius. So, the total area of the circular tops and bottoms is 2π(2^2) = 8π.
The area of the curved side can be found using the formula for the lateral surface area of a cylinder, which is given by A = 2πrh, where r is the radius and h is the height. In this case, the curved side of the can forms a rectangle when it is unrolled, so the height of the rectangle is the same as the height of the can, which is 6 inches. Therefore, the area of the curved side is 2π(2)(6) = 24π.
To find the total amount of material needed, we add the areas of the circular tops and bottoms to the area of the curved side. So, the total surface area of the can is 8π + 24π = 32π square inches.
Therefore, in terms of π, the amount of material needed to make each can is 32π square inches.
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Sketch the region enclosed by y = 3 x and y = 6 x 2 . find the area of the region.
The area of the region enclosed by the curves: Y = 3X and Y = 6X² is
1/8 sq. unit.
What are Linear Equation and Quadratic Equation?Linear equation are those in which power is 1 or maximum degree is 1. For example: x + y = 3 here the maximum degree is 1.
Quadratics equation are those in which power is 2 or maximum degree is 2. For example: X² + 6X + 3 = 0. here the maximum degree is 2.
Here, we have given two equation:
Y = 3X
Y = 6X²
To find the limit we will equate the both equation:
3X = 6X²
6X² - 3X = 0
3X ( 2X - 1 ) = 0
here we get two values of X, X = 0 and X = 1/2
so, Lower limit = 0 and Upper limit = 1/2.
Area = \(\int\limits^ \frac{1}{2} _0 {(3x - 6x^{2} ) } \, dx\)
Area = ( 3/2 ( x ⁸ ) - 2 ( x³ ) ) --- Limit from: 0 to 1/2
Area = (3/2 ( 1/2 ² ) - 2 ( 1/2 ³) ) - ( 3/2 ( 0² ) - 2 ( 0³) )
Area = 3/8 - 1/4 - 0 + 0
Area = 1/8 sq. unit
Hence,
The area of the region enclosed by the curves: Y = 3X and Y = 6X² is
1/8 sq. unit. For graph See the attached image.
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neep help with iready
Answer:
I can help you.
Step-by-step explanation:
Explain how to solve 5x − 2 = 8 using the change of base formula . include the solution for x in your answer. round your answer to the nearest thousandth.
x = 2 is the solution to the equation 5x - 2 = 8.
What is the logarithm?
A logarithm is a power to which a number must be raised in order to get some other number. For example, the base ten logarithms of 100 is 2, because ten raised to the power of two is 100: log 100 = 2. because. 102 = 100.
The change of base formula for logarithms allows us to change the base of a logarithm without changing the value of the logarithm.
The formula is: logb(x) = (logc(x)) / (logc(b))
To solve 5x - 2 = 8 using the change of base formula, we will first bring the equation to one side and get 2 = 5x - 8.
Then we will add 8 to both sides of the equation to get 2 + 8 = 5x, which gives us 10 = 5x.
Finally, we will divide both sides of the equation by 5 to get x = 2.
x = 2
Therefore, x = 2 is the solution to the equation 5x - 2 = 8.
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(a) A cyclit rode hi bike for 169 min at an average velocity of 3. 53 m/ on a bearing of 450. Find hi total diplacement in km a a vector in the form i and j (3 mark)
The total displacement in km and vector form in the form of i and j is 35.8 a[x] km + 0 a[y] km.
According to the question,
We have the following information:
A cyclist rode his bike for 169 min at an average velocity of 3. 53 m/s on a bearing of 450.
Now, we know that the following formula is used to find the velocity:
Velocity = displacement/time
(We will convert time from minutes into seconds.)
Displacement = 3.53*(169*60)
Displacement = 35794.2 m
Now, the displacement in km will be 35.8 km approximately.
Now, let's take that the bike is moving along the positive x-axis. So, it would be written in the following expression:
Displacement = 35.8 a[x] km + 0 a[y] km
Hence, the total displacement in km and vector form in the form of i and j is 35.8 a[x] km + 0 a[y] km.
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Find the equation of this line.
[?]
y = -
x + ]
Answer:
y = -1/2x + 1
Step-by-step explanation:
The y-intercept can be determined since the line touches the y-axis at the point (0,1), making it 1. The slope can be determined since the line is going down negatively, down one half and right one, making it -1/2
HELP PLS Explain why each statement might be true or might be untrue. Tell if each is an example of inductive or deductive reasoning? Justify your answers.
1. All men are mortal. Joe is a man. Therefore Joe is mortal. If the first two statementsare true, then the conclusion must be true.
2. To get a high school diploma from The Ogburn School, a student must have 24 credits. Cindy has more than 24 credits. Therefore, Cindy must have a high school diploma.
3. This cat is black. That cat is black A third cat is black. Therefore all cats are black.
4. This marble from the bag is black. That marble from the bag is black. A third marble from the bag is black. Therefore all the marbles in the bag are black.
5. For problems A-E, write the converse, inverse, and contrapositive statements based on the given conditional statement.
A. If I own a dog, then I own an animal.
Converse:
Inverse:
Contrapositive:
B. If I go to be early, then I sleep well.
Converse:
Inverse:
Contrapositive:
C. If this is Thursday, then I do not go to church.
Converse:
Inverse:
Contrapositive:
D. If today is Wednesday, the yesterday was Tuesday.
Converse:
Inverse:
Contrapositive:
E. If 5x = 10, then x = 2.
Converse:
Inverse:
Contrapositive:
1. The statement is an example of deductive reasoning. It is true because it follows a logical syllogism.
2. The statement is an example of inductive reasoning. It is not necessarily true that Cindy must have a high school diploma based solely on having more than 24 credits.
3. The statement is an example of inductive reasoning. While it is true that the described cats are black, it does not logically follow that all cats are black.
4. The statement is an example of inductive reasoning. The conclusion is not necessarily true.
1. The first premise states that all men are mortal, the second premise states that Joe is a man, and the conclusion logically follows that Joe must be mortal based on the given premises. This argument is deductive because the conclusion necessarily follows from the premises.
2. While it is a requirement to have 24 credits to obtain a diploma from The Ogburn School, it is possible for Cindy to have accumulated more credits without fulfilling other requirements for graduation. Therefore, the conclusion is not guaranteed to be true based on the given information. This argument is inductive because the conclusion is based on probability rather than strict logical inference.
3. The conclusion is an overgeneralization based on a limited sample. There could be cats of different colors that have not been observed. Therefore, the conclusion cannot be considered universally true. This argument is inductive because the conclusion extends beyond the observed instances.
4. Similar to the previous example, the conclusion that all marbles in the bag are black is an overgeneralization based on a limited sample. Even if multiple marbles have been observed to be black, it is possible that there are marbles of different colors in the bag that have not been drawn yet. Therefore, the conclusion is not necessarily true. This argument is inductive because the conclusion goes beyond the observed instances.
A. Converse: If I own an animal, then I own a dog.
Inverse: If I don't own a dog, then I don't own an animal.
Contrapositive: If I don't own an animal, then I don't own a dog.
B. Converse: If I sleep well, then I go to bed early.
Inverse: If I don't sleep well, then I don't go to bed early.
Contrapositive: If I don't go to bed early, then I don't sleep well.
C. Converse: If I don't go to church, then this is not Thursday.
Inverse: If I go to church, then this is Thursday.
Contrapositive: If this is not Thursday, then I go to church.
D. Converse: If yesterday was Tuesday, then today is Wednesday.
Inverse: If yesterday was not Tuesday, then today is not Wednesday.
Contrapositive: If today is not Wednesday, then yesterday was not Tuesday.
E. Converse: If x = 2, then 5x = 10.
Inverse: If x is not equal to 2, then 5x is not equal to 10.
Contrapositive: If 5x is not equal to 10, then x is not equal to 2.
In each case, the converse switches the order of the conditional statement, the inverse negates both the hypothesis and conclusion, and the contrapositive swaps and negates both the hypothesis and conclusion.
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solve for x -6x+14 <-28 or 9x+15 equal to -12
Answer:
i think the answer is D. there are no solutions
Answer:
A. x ≤ -3 or x > 7
Step-by-step explanation:
Solve the first equation.
-6x + 14 < -28
Subtract 14 from both sides.
-6x < -42
Divide both sides by -6. REMEMBER: when dividing an inequality by a negative number, flip the sign.
x > 7.
Solve the second equation.
9x + 15 ≤ -12
Subtract 15 from both sides.
9x ≤ -27
Divide both sides by 9.
x ≤ -3.
Your answer is A.
What do we call to the number system that we always used?
The decimal positional number system is the one that is most frequently used.
What is number system?The consistent representation of numbers using digits and other symbols is known as a number system.
Some key features of number system are-
Any number in a number can have its value determined by that digit, its place with in number, and the number system's base. The numbers are uniquely represented, enabling us to perform operations such addition, subtraction, and division.It's a way of expressing numbers. It also establishes a set of numbers to represent a quantity and is referred to as the system of numeration. The most widely used digits among these are the binary numbers 0 or 1, that are employed to represent them. Other sorts of data are represented by the digits 0 to 9.To know more about number system, here
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what is the probability that in a particular crossing, there are total 10 pedestrian and they are all crossing from left to right?
The probability of having exactly 10 pedestrians crossing from left to right during a 2-minute period is extremely low, at approximately 0.00118%.
We can approach this problem by using the Poisson distribution, which describes the probability of a certain number of events occurring within a given time period, given a known rate of occurrence.
Let X be the number of pedestrians crossing from left to right during a 2-minute period. Since the arrival processes from the left and right sides are independent Poisson processes with rates λL and λR, respectively, we can model X as a Poisson random variable with rate λ = λL + λR = 6.
Therefore, the probability of having exactly k pedestrians crossing from left to right during a 2-minute period is given by the Poisson distribution:
P(X = k) = (e^(-λ) * λ^k) / k!
Now we want to find the probability that in a particular crossing, there are a total of 10 pedestrians crossing from left to right. Let Y be the total number of pedestrians crossing in both directions during a 2-minute period.
Since the arrival processes from the left and right sides are independent, we can model Y as a Poisson random variable with rate 2λ = 12.
Since we know that there are 10 pedestrians crossing from left to right, there must be a total of 10 pedestrians crossing in both directions. Therefore, we want to find the probability that out of the 10 pedestrians, exactly 10 of them are crossing from left to right.
We can use the binomial distribution to calculate this probability. Let Z be the number of pedestrians crossing from left to right out of the 10 pedestrians. Since each pedestrian has an independent probability of crossing from left to right of 1/2, we have:
P(Z = 10) = (10 choose 10) * (1/2)^10
= 1/1024
Therefore, the probability that in a particular crossing, there are a total of 10 pedestrians and they are all crossing from left to right is:
P(X = 10, Y = 10) = P(X = 10) * P(Z = 10)
= (e^(-6) * 6^10 / 10!) * (1/1024)
≈ 0.0000118
Writing this probability in percentage gives = 0.0000118 x 100% = 0.00118%
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Complete question is:
Pedestrians approach a crossing from the left and right sides following independent Poisson processes with average arrival rates of λL = 5 and λR = 1 arrivals per minute. Each pedestrian then waits until a light is flashed, at which time all waiting pedestrians must cross to the opposite side (either from left to right or from right to left). Assume that the left and right arrival processes are independent, that the light flashes every T = 2 minutes, and that crossing takes zero time – it is instantaneous.
1. What is the probability that in a particular crossing, there are total 10 pedestrian and they are all crossing from left to right?
describe the figure EFGH that result from a dilation using center A and scale factor 1/2.
Select all that are true about the polygon ABCD and EFGH
1. C’(4,10)
2. C’D is half of CD
3. Measure A is 60 degrees therefore A’ is 30 degrees
4. Polygon ABCD is similar to polygon EFGH
5. D’ is (3,5)
6. Polygon ABCD is congruent to polygon EFGH
Answer:
6.polygon ABCD is congruent to polygon EFGH
⚠️ARE YOU A PRO AT ALGEBRA⁉️❓? I NEED HELP. BE SURE TO EXPLAIN WHAT METHOD YOU USED (GRAPHING, ALGEBRAIC, NUMERIC) TO DETERMINE WHETHER THEY ARE INVERSE OR NOT AND EXPLAIN HOW YOU KNOW YOU ARE CORRECT ⚠️
I used the Algebraic Method to solve the questions
The First functions are inverses but the Second set aren't
PLEASE ANSWER THIS FOR ME!!!!!!!!!!!!
Answer:
It's the option on the bottom right corner.
Step-by-step explanation:
5,000,000,000 has 9 zeros. so look at the option that has 9 zeros.
Find all values of $x$ such that 9+27/x+8/(x^2)=0
Answer:
Step-by-step explanation:
Multiply by x^2 on both sides
9x^2+27x+8=0
Factor.
The answers are -1/3, -8/3
What are three ways in which stereotypical views of gender could negatively affect progressive growth of society
Please help!!
Review the diagram.
Select the best angle property to solve for the measure of D
Answer:
d = 122°
Step-by-step explanation:
d and 58° are a linear pair and sum to 180° , that is
d + 58° = 180° ( subtract 58° from both sides )
d = 122°
Solve the system of
equation using the
elimination method.
2x + y = 4
x - y = 2
Answer:
x=2
y=0
Step-by-step explanation:
I use symbolab it helps
May I please receive help?
Answer:
what u will recieve
Step-by-step explanation:
please telle
phil is randomly drawing cards from a deck of 52. he first draws a queen, places it back in the deck, shuffles the deck, and then draws another card. what is the probability of drawing a queen, placing it back in the deck, and drawing any face card? answer choices are in the form of a percentage, rounded to the nearest whole number. 31% 25% 7% 2%
The probability of drawing a queen and then any face card is 7%. To understand this, let's examine the odds. There are 4 queens in a standard 52-card deck, so the odds of selecting a queen on the first draw are 4/52, or 7.7%.
To illustrate, if you were to draw a queen on the first draw, it would reduce the number of queens remaining in the deck to three. When you place the queen back in the deck and shuffle, the odds of selecting a queen on the second draw are now 3/51, or 5.9%. This means that the probability of selecting any face card on the second draw is 94.1% (100 - 5.9% = 94.1%).
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Answer:
2%
Step-by-step explanation:
Got it right on the test.
The perimeter of a rectangular garden is 24. If the length is half the width, what is
the width?
Let length be x
Width be 2xATQ
\(\\ \sf\longmapsto 2(L+B)=24\)
\(\\ \sf\longmapsto 2(x+2x)=2=\)
\(\\ \sf\longmapsto 2(3x)=24\)
\(\\ \sf\longmapsto 6x=24\)
\(\\ \sf\longmapsto x=\dfrac{24}{6}\)
\(\\ \sf\longmapsto x=4\)
Step-by-step explanation:
let the length be X and breadth be 2x
p=2(l+b)
24=2(X+2x)
24=2x+4x
24=6x
24÷6=x
4=X
so,we know that
X=4 and 2x=2 X 4= 8
therefore the value of breadth or width is 8