Answers
Answer:
k = 9
Step-by-step explanation:
For this, we can factor the top expression to look like the bottom expression.
So, first we have to find the gcf of 18 and \(x^{2}\) and add up to 11x.
18\(x^{2}\) 11x
1 and 18 19 - No
2 and 9 11 - Yes
3 and 6 9 - No
So, the numbers are 2 and 9. The expression should now look like this:
\(x^{2}\) + 2x + 9x + 18
Now, undistribute the terms.
x(x + 2) + 9(x + 2)
(x+2)(x+9)
This matches up with the bottom expression.
The value of k is 9.
Related Questions
\(\begin{bmatrix}\sf x+y=7\\ \sf x+2y=11\end{bmatrix}\)
Answers
x + y
1+ 6
2+5
3+4
x +2y
3+ (2x4)
3+8
=11
x=3
y=4
Answer:
x = 3y = 4Step-by-step explanation:
The equations are,
→ x + y = 7
→ x + 2y = 11
Forming the equation for y,
→ x + 2y = 11
→ 2y = 11 - x
→ y = (11 - x)/2
Now the value of x will be,
→ x + y = 7
→ x + (11 - x)/2 = 7
→ (2x + 11 - x)/2 = 7
→ x + 11 = 7 × 2
→ x = 14 - 11
→ [ x = 3 ]
Then the value of y will be,
→ y = (11 - x)/2
→ y = (11 - 3)/2
→ y = 8/2
→ [ y = 4 ]
Hence, the value of y is 4.
If EF = 117 , FG = 100, EG = 94, IJ = 40 , and HJ = 37.6 , find the perimeter of HIJ. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale.
Answers
Answer:
124.4
Step-by-step explanation:
Perimeter of ∆HIJ = IJ + HJ + HI
IJ = 40
HJ = 37.6
HI = ?
Let's find HI
∆HIJ and ∆EFG are similar. Since they have equal corresponding angles. Therefore, the ratio of their corresponding sides would be equal.
Thus:
EF/HI = FG/IJ
EF = 117 (given)
HI = ?
FG = 100 (given)
IJ = 40 (given)
Plug in the values
117/HI = 100/40
117/HI = 2.5
117 = HI*2.5
117/2.5 = HI
HI = 46.8
✔️Perimeter of ∆HIJ = IJ + HJ + HI
= 40 + 37.6 + 46.8
= 124.4
What is the total area of the top surface of all 16 solar panels? Describe the process you used to solve the problem. (4 points)
Answers
To find the total area of the top surface of all 16 solar panels, we need to know the dimensions of each individual panel and then multiply the area of one panel by the total number of panels.
To solve the problem, we first need to determine the dimensions of a single solar panel. Let's assume the length of a panel is L and the width is W. The area of one panel can be calculated by multiplying the length and width: A = L * W.
Once we have the area of one panel, we can calculate the total area of all 16 panels by multiplying the area of one panel by the total number of panels: Total Area = A * 16.
By knowing the specific dimensions of a single solar panel, we can substitute the values into the equation and calculate the total area of the top surface of all 16 panels.
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Need help with Geometry proof please!!!
Answers
Step-by-step explanation:
QR is parallel to TU | Given
S is the midpoint of QT | Given
QS = ST | Definition of midpoint
<QSR = <TSU | definition of vertical angles
<QRS = <STU | Definition of Alternate Interior Angles
QSR = TSU | ASA
Pretty sure that's right :D
Also, wherever it says "=", I mean congruency symbol
Explanation of how we can make (a) subject
Answers
Answer:
Step-by-step explanation:
A speed camera takes 2 photos of a car photo 2 was taken 0. 5 seconds after photo 1 marks on the road are 0. 8 metres apart calculate the average speed of the car in m/s
Answers
The average speed of the car while taking photos in m/s is 1.6 m/s
Total photos taken = 2
Time taken = 0.5 seconds
Distance = 0.8m
Thus, this can be noted as -
Distance = Marks on the road between the two photos = 0.8 meters
Time = Time between the two photos = 0.5 seconds
Speed is defined as the rate at which a distance travelled or a height reached changes. It has a time component. In the given case, the speed camera is taking photos and we are required to calculate the average speed of the car
Calculating the speed -
Average Speed = Distance ÷ Time
Substituting the values -
= 0.8 /0.5
= 1.6
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A car is purchased for 20,000. After each year, the resale value decreases by 30%. What will the resale value be after 4 years?
Answers
Answer:a
Step-by-step explanation:
Step-by-step explanation:
A is the value of the car after n years P is the purchase price of the car R is the annual depreciation rate n is the number of years
In this case, we have:
P = 20,000 R = 30 n = 4
So, we can plug these values into the formula and get:
A = 20,000 * (1 - 30/100)^4 A = 20,000 * (0.7)^4 A = 20,000 * 0.2401 A = 4,802
Therefore, the resale value of the car after 4 years will be $4,802.
Question 2 A. Given the matrix R = ( 2 −1 1 3 ),
i. show that R is non-singular. (1 mark)
ii. find R-1 , the inverse of R. (2 marks)
iii. show that RR-1 = I. (2 marks)
B. Use the matrix method or otherwise to solve the following system of simultaneous equations:
i. x + 2y + 3z = – 5
ii. 3x + y – 3z = 4
iii. – 3x + 4y + 7z = – 7
Answers
Part A. R is non-singular. adj(R) is the adjugate matrix of R. RR-1 = I, Part B. the inverse matrix method by multiplying both sides of the equation by A-1 to solve for X, giving the solution X = A-1B.
Part A:
i. To show that the matrix R is non-singular, we need to verify that its determinant is non-zero. Calculate the determinant of R, denoted as det(R), and if det(R) ≠ 0, then R is non-singular.
ii. To find the inverse of matrix R, calculate R-1 using the formula R-1 = (1/det(R)) * adj(R), where adj(R) is the adjugate matrix of R.
iii. To show that RR-1 = I, multiply matrix R with its inverse R-1 and check if the resulting product is the identity matrix I.
Part B:
To solve the system of simultaneous equations, we can represent the system using matrices. Let X be the column matrix of variables (x, y, z), A be the coefficient matrix of the variables, and B be the column matrix of constant terms. The system of equations can be written as AX = B. Use the inverse matrix method by multiplying both sides of the equation by A-1 to solve for X, giving the solution X = A-1B.
Substitute the values of the coefficient matrix A and the constant matrix B into the equation AX = B, find the inverse matrix A-1, and then calculate the product A-1B to obtain the solution matrix X, which represents the values of variables x, y, and z that satisfy the given system of equations.
Therefore, by following the steps described above, we can solve the system of simultaneous equations and find the values of x, y, and z.
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40 is what percent of 54?
Answers
Answer: The answer will be 74.07 percent.
According to the question, let the number be x
Then, x*54/100 = 40
x = 40 × 100 / 54
x = 74.07 (approx)
Davit drives 16.5 miles in 10 minutes. he passes a sign which gives the speed limit as 65 mph. by how much, in mph, did davit's average speed exceed the speed limit?
Answers
Answer:
answer 34
Step-by-step explanation:
16.5x(60÷10)=99
99-65=34. hour= 60 minutes
so the result is 34 mph
7/12 minus 1/6 gggggggggggggggggggg
Answers
Answer:
\( \frac{5}{12} \)
Step-by-step explanation:
\( \frac{7}{12} - \frac{1}{6} \\ \\ = \frac{7}{12} - \frac{2}{12} \\ \\ = \frac{7 - 2}{12} \\ \\ = \frac{5}{12} \)
Answer:
0.41666666666
or
5/12
Step-by-step explanation:
PLEASEE HELP ME IT IS URGENT
Answers
g(x) is basically f(x) but flipped or reflected over or the y-axis. We can achieve this effect by negating f(x), or -f(x).
g(x) = -f(x) = -|x|
when he applied to y combinator (see case exhibit 3), what hypotheses did houston have about dropbox’s strategy? be specific. as of june 2010, which of them turned out to be wrong? be specific.
Answers
He defined quality as a speedy procedure and document security through the use of a web interface, and the data was safely backed up to Amazon S3.
Houston determined that his potential customers, who would be his target demographic, were already technically savvy, but that because of the product's simplicity and the advent of the internet, it could fast increase.
The user-friendly application and product accessibility are important aspects of his business approach. This idea was proven by developing a solution that is simple to use and allows users to work on the most recent version of a particular document via an automated update. Houston wants to ensure that one of the most important aspects of his product is its quality. He defined quality as a speedy procedure and document security through the use of a web interface, and the data was safely backed up to Amazon S3.Houston determined that his potential customers, who would be his target demographic, were already technically savvy, but that because of the product's simplicity and the advent of the internet, it could fast increase. As a result, his next major aspect was the distribution of a single version for all users, as well as the deployment of the "Trojan Horse" technique to expand. Dropbox employed the Freeware model to generate income, which meant that the first 2 GB were provided for free and the remaining GB had to be paid for on a monthly basis.Learn more about data here:
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Harriet thinks of a number.
She squares it and then adds 11.
Harriet's answer is 36.
What was her original number?
Answers
X^2 + 11 = 36
Subtract 11
X^2 = 25
Square root both
X = 5
Solution: her original number is 5
Answer:
5
Step-by-step explanation:
36-11=25
the square root of 25 is 5. you just have to do the problem backwards
My production line creates 3 different widgets. Widget A sells for $12. Widget B sells for $18. Widget C sells for $35. I made a total revenue of $1735 yesterday. I sold a total of 70 widgets. The number of C widgets sold is equal to the total number A and B sold. How many of each type of widgets did I sell?
Answers
9514 1404 393
Answer:
20 A widgets15 B widgets35 C widgetsStep-by-step explanation:
Half the widgets sold were $35 widgets, so the revenue from them was ...
(70/2)($35) = $1225
This means the remaining $1735 -1225 = $510 in revenue came from the sale of a total of 35 A and B widgets.
If we let 'b' represent the number of B widgets sold, then the revenue is ...
12(35 -b) + 18b = 510
6b +420 = 510
6b = 90
b = 15 . . . . . . . number of B widgets sold
35 -b = 20 . . . number of A widgets sold
20 A widgets, 15 B widgets, and 35 C widgets were sold.
__
Check
Total revenue was 20(12) +15(18) +35(35) = 240 +270 +1225 = 1735.
Total widgets were 20 +15 +35 = 70.
The total of A and B was 20 +15 = 35, the same as the number of C.
Your round-trip drive to work is 4 times 3 divided 10 miles. How many miles do you drive to and from work in 3 days?
Answers
Answer:
okay here is what i think see if my explanation will help
Step-by-step explanation:
i think
(4*3/10)*3 get it just follow this work it out and tell me your answer
Solve for x.
42 - 5x = 4x + 15
x = [?]
Answers
Answer:
42-15=4x+5x
27=9x
27/9=x
x=3
Step-by-step explanation:
Solve x2 − 12x + 23 = 0 by completing the square.
a (x − 12)2 = 23; x = −11, x = 35
b (x − 6)2 = 13; x = −7, x = 19
c (x − 12)2 = 23
Answers
Answer:
\( {x}^{2} - 12x + 23 = 0\)
\( {x}^{2} - 12x = - 23\)
\( {x}^{2} - 12x + 36 = 13\)
\( {(x - 6)}^{2} = 13\)
x - 6 = +√13
x = 6 + √13
• write each answer in simplest form.
1. 1/6 +2/6
2. 2/5 - 1/5
Answers
Answer:
1. 1/2
2. 1/5
Step-by-step explanation:
I used a calculator!
Answer:
1.3/6 or 1/2
2.1/5
Step-by-step explanation:
Just write that out, thats all the steps there is, 3/6 simplifies to 1/2 because they're equivalent
An executive is earning $45,000 per year. This is
$15,000 less than twice her salary 4 years ago. Find her
salary 4 years ago.
Answers
If 45,000 is 15,000 less than double her previous salary, we must first add 15,000 to 45,000 to find what double her salary was.
45,000+15,000=60,000.
Since this is twice her salary, we divide this by 2.
60,000/2= 30,000.
So, her salary 4 years ago would have been $30,000.
I hope this helps!
the president of a large company recommends that employees perform, on average, 24 hours of community service each year. the president believes that the mean number of hours of community service performed last year was different from the recommended 24 hours. to estimate the mean number of hours of community service performed last year, the president obtained data from a random sample of employees and used the data to construct the 95 percent confidence interval (20.37, 23.49). if all conditions for inference were met, does the interval provide convincing statistical evidence, at a level of significance of
Answers
If all conditions for inference were met, does the interval provide convincing statistical evidence, at a level of significance of 95%, that the mean number of hours of community service performed last year was indeed different from the recommended 24 hours.
To determine if the 95% confidence interval provides convincing statistical evidence at a level of significance that the mean number of hours of community service performed last year was different from the recommended 24 hours, we'll analyze the constructed interval (20.37, 23.49).
1. First, observe the given confidence interval: (20.37, 23.49)
2. Identify the recommended average of 24 hours by the president.
3. Check if the recommended average is within the confidence interval.
Since 24 hours is not within the interval (20.37, 23.49), it provides convincing statistical evidence, at a level of significance of 95%, that the mean number of hours of community service performed last year was indeed different from the recommended 24 hours.
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find the denominator field for the Perfect loop: a) Z[
2
] bl Z[i] wher i=
−1
Answers
Z[i] satisfies all the properties required for a denominator field, making it the denominator field for the perfect loop. The denominator field for the perfect loop is Z[i], where i is equal to -1.
In the context of algebraic structures, a perfect loop is a set equipped with a binary operation (usually denoted by *) that satisfies the identities of associativity, identity element, and inverse element. The denominator field of a perfect loop is the smallest subfield of the loop's field of fractions that contains the identity element.
In this case, the perfect loop is defined over the integers (Z) with the binary operation of multiplication (*). To find the denominator field, we need to consider the field of fractions of Z, which is the set of all fractions a/b, where a and b are integers and b is nonzero.
Since the identity element for multiplication is 1, the denominator field must contain 1. Additionally, the denominator field should be closed under multiplication and have multiplicative inverses for nonzero elements.
In Z[i], where i is equal to -1, we have the elements of the form a + bi, where a and b are integers. This set is closed under multiplication and contains the identity element 1. It also contains multiplicative inverses, as every nonzero element has an inverse of the form (-a) + (-b)i. Therefore, Z[i] satisfies all the properties required for a denominator field, making it the denominator field for the perfect loop.
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Help needed ASAP will give brainliest! Pls help me
Answers
Answer:
1740 N
Step-by-step explanation:
To find the force, you need to multiply the mass by the acceleration.
(60.0 kg) × (29.0 m/s²) = 1740 N
The force will be 1740 N.
A family wants to make an addition to a deck that extends off the back of their home. The current deck is 400 ft2. The addition will be 18.75 ft in length and 15 ft wide. What will be the total area of the deck once the addition is complete? 681.25 ft2 433.75 ft2 281.25 ft2 118.75 ft2
Answers
Answer:
681.25 ft2.
Step-by-step explanation:
Answer:
Step-by-step explanation: answer is option b
Given h(x)=4x-5 find h(-3)
Answers
Answer:
-17
Step-by-step explanation:
Plug -3 into the function in place of x.
1. h(-3)= 4(-3) - 5
2. h(-3)= -12-5
3. h(-3)= -17
The value of the function h(x) at x = -3 is - 17.
What is a function ?A function can be thought of as the outputs for the given input and input decides the output we get.
The set of all inputs are called independent variables and the set of all outputs are called dependent variable.
According to the question a function h(x) = 4x - 5 is given we have to find h(-3).To find h(-3) we have to substitute x = -3 in h(x).
∴ h(-3) = 4(-3) - 5.
h(-3) = -12 - 5
h(-3) = -17.
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PLEASE HELP AS SOON AS POSSIBLE I NEED TO SUBMIT THIS IN 10 MINUTES!!!!
IT GIVES 20 points!!!
Answers
Answer:
1. A. falling asleep
2. D. taking more time to wind down before bedtime
3. B. There is more than one reason that people have trouble sleeping.
4. C. The problem of falling asleep has been around for a long time and affects many people
5. A. why kids have trouble falling asleep and what they can do about it
6. A. something done over and over
Step-by-step explanation:
how many different bracelets have 3 identical orange beads, 3 identical black beads, and 1 teal bead, if rotating or flipping a bracelet does not change it?
Answers
10 different bracelets have 3 identical orange beads, 3 identical black beads, and 1 teal bead, if rotating or flipping a bracelet does not change it
What is permutation and combination?Permutations and combinations are the many methods for picking objects from a set to form subsets, usually without replacing them. When the order of selection is a factor, this selection of subsets is known as a permutation; when the order of selection is not a factor, this selection of subsets is known as a combination.
CalculationI think it is only 10 ways.
Put the teal bead on first. It is the marker bead. This takes care of the rotation aspect.
Then you have 2 lots of 3 identical beads. so that is 6!/(3!3!) ways to place them. Which is 20 ways.
But the bracelet can be flipped so I think this will halve the number of possibilities
For instance TOOOBBB is the same as TBBBOOO
So I think the answer is 10 ways.
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Bonita makes $11.75/ hour and Bruce makes $12.50/hour If Bonita worked 25 hours and Bruce worked 19 hours what was the difference in the amount of money they each earned
Answers
Answer: $56.25
Step-by-step explanation: We know that Bonita makes $11.75 per hour and Bruce makes $12.50 per hour.
To find out how much money Bonita makes if she worked 25 hours, we can multiply the amount she makes per each hour.
$11.75 x 25 hours = $293.75 for 25 hours of work.
We can do the same thing for Bruce.
$12.50 x 19 hours = $237.50 for 19 hours of work.
Now to find the difference in the amount of money they each earned. You can simply subtract $237.50 from $293.75.
$293.75 - $237.50 = $56.25
12.50(19) = 237.5
293.75 - 237.5 = $56.25
The picture shows a triangular island:Which expression shows the value of q?s over sin 55 degreess over cos 55 degreesr sin 55°r cos 55°q?
Answers
A right triangle is a triangle with a right angle. The opposite side to the right angle is called the hypotenuse and the other sides are the legs. Given an angle in a right triangle, the ratio between the leg adjacent to the angle and the hypotenuse is equal to the cosine of the angle.
Using this relation in our problem, we have the following:
\(\cos(55^o)=\frac{s}{q}\)Solving this expression for q, we have:
\(\begin{gathered} \cos(55^o)=\frac{s}{q} \\ q\cos(55^o)=s \\ q=\frac{s}{\cos(55^o)} \end{gathered}\)And this is our answer.
\(\frac{s}{\cos(55^o)}\)Find the sum of each of the following infinite geometric series:
18.9-6.3 +2.1-0.7+..
Answers
The sum to infinity of the geometric sequence is 63
How to determine the sum
The formula for determining the sum of an infinite geometric sequence is expressed as;
\(S = \frac{a}{1 - r}\)
Given that the common ratio is less than 1.
The first term, a = 18. 9common ration, r = -0. 3Now, let's substitute the value into the formula
S = \(\frac{18. 9}{ 1 - (-0. 3)}\)
simplify further
S = \(\frac{18. 9}{1 + 0. 3}\)
S = \(\frac{18. 9}{1. 3}\)
S = 63
Hence, the sum to infinity of the geometric sequence is 63
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