Answer: 3u⋅(9u−9v) = 285
Step-by-step explanation:
We can start by using the distributive property for the dot product:
3u⋅(9u−9v) = 3u⋅9u - 3u⋅9v
We also know that the dot product of two vectors u and v is u⋅v = ∥u∥∥v∥cos(θ), where θ is the angle between vectors u and v. Therefore,
u⋅v = 5 = 107cos(θ)
So we can write:
cos(θ) = 5/(10*7) = 1/14
Then we can use this value to find the dot product of u and v.
3u⋅9u = 3 * (10^2) = 300
3u⋅9v = 3 * (10)(7)(1/14) = 15
So the final answer is:
3u⋅(9u−9v) = 300 - 15 = 285
Explanation: By using the distributive property and the dot product definition, it was possible to find the dot product of 3u⋅9u and 3u⋅9v. By subtracting the latter from the former, we obtained the final answer of 285.
If four people are chosen for a team out of a group of seven, how many possible combinations are there (order does
not matter)
$2750 is invested at an interest rate of 3.5% APR compounded quarterly. Determine the amount after 7 years. Round your answer to the nearest hundredth.
The amount that will be realized after 7years is $3459.5
What is compound interest?Compound interest is when you earn interest on both the money you've saved and the interest you earn.
Amount in Compound interest is given as:
A = P(1+r/n)^nt
Where A is the amount
P is the principal
t is the duration and
n is the period of compoundment
r is the rate
n= ¼, r = 3.5/100 = 0.035
therefore A = 2750(1+0.035/0.25)^0.25×7
A = 2750( 1+0.14)^1.75
A= 2750(1.14)^1.75
A = 2750×1.258
A = $3459.5
Therefore the amount after 7 years is $3459.5
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How many times does 11 go into 77
Answer:
7
Step-by-step explanation:
77 divided by 11 is 7
Marc just bought an SUV for 52,000. This is 7,600 less than twice what his wife paid for her car last year. How much did his wife pay (in dollars) for her car
Answer:
Let's call the amount his wife paid for her car "x". We know that:
Marc's car = $52,000
Marc's car = 2x - $7,600
We can substitute the first equation into the second equation
52,000= 2x-7600
52,000+7600=2x
59,600=2x
x=29,800
His wife paid $29,800 for her car.
Answer:
$29,800.00
Step-by-step explanation:
52000 = 2x - 7600 Add 7600 to both sides
52000 + 7600 = 2x
59600 = 2x Divide both sides by 2
29800 = x
Solve for <4. Please help!
Answer:
The answer is 32
Step-by-step explanation:
We solve this by first finding the angle 3. To do this we subtract 180 (the sum of a triangle) and the two known angles. 180-15-17 = 148.
So now we know that the 3rd angle is equal to 148. Now to find the angle 4 we subtract angle 3 from 180, because a straight line is equal to to 180 degrees; 180-148=32
Hope that helps
What is the difference between the Commutative Property and Associative Property of addition?
Answer:
The commutative property of addition states that the order of the numbers being added does not affect the result of the addition. For example, "a + b = b + a" is the commutative property of addition.The associative property of addition states that when three or more numbers are being added, the grouping of the numbers being added does not affect the result. For example, "(a + b) + c = a + (b + c)" is the associative property of addition.In simple terms, the commutative property of addition allows for numbers to be added in any order and still get the same result, while the associative property of addition allows for numbers to be grouped in any way and still get the same result.Hope this helps! Enjoy Learning!:D
Below is the graph of a system of two linear equations.
Answer:
A
Step-by-step explanation:
y + 4 = x is represented in this equation as -3 + 4 = 1
x + y = -6 is represented in this equation as -4 + -2 = -6
"A" fits these equations and the coordinate attached: (-1, -5) matches the point of intersection.
Some students collected the data below. They will graph the data. What is the y-intercept? Your answer should be an ordered pair ( , )
The ordered pair of coordinates is (0, 28)
How to find the Ordered pair ?To answer to the question given, we have to find the point on the line that goes through the points given in the table when the x-axis represents the month of the year and the y-axis represents the average temperature for that month.
We can read out this ordered pair from the attached graph
In conclusion, the graph displays the point on that line which is on the y-axis is (0, 28).
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PLEAE HELPP WILL MARK BRAINLIEST
Given that my=34°, find the value of the angle b
A 146°
B 56°
C 34°
D 124°
E 68°
Considering the figure the value of angle b is
D 124°How to solve for angle bAccording to the vertical angle theorem, the opposing angles of two crossing lines must have the same value, or be congruent.
hence angle a = angle y
Then from exterior angle of a triangle theorem: If a triangle's side is created, the outside angle that results is equal to the sum of the two opposite internal angles.
angle b = angle a + 90
= 34 + 90
= 124 degrees
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Solving by Factoring
Please explain in detail the strategy, Solving by Factoring, discussed in the lesson Quadratic in Form Polynomials. Include an example with this explanation to clearly explain the process. (If you need to refer back to the lesson it is in the Instruction Video on slide 6.)
Answer:
Solving by Factoring is a strategy used to solve quadratic equations. This strategy involves factoring the quadratic equation. Factoring is breaking an expression down into smaller expressions that when multiplied together will equal the original expression.
Step-by-step explanation:
To solve a quadratic equation by factoring we must first get the equation into the form ax^2 + bx + c = 0. From here we must use a strategy of factoring known as Reverse FOIL. By using reverse FOIL we will break the equation down into smaller parts. The four steps to use in reverse FOIL are:
1. Find two factors of “ac” (the coefficient of x^2) that when added together equal “b” (the coefficient of x).
2. Multiply the two factors you found in step one to produce “ac.”
3. Group the two terms with the “ac” terms in the equation.
4. Factor the two terms with “bx” in them.
For example, if we have an equation such as 9x^2 + 15x + 4 = 0 we would look for two factors of 4 (ac) that when added together equal 15 (b). The two factors of 4 that when added together equal 15 are -1 and -4. Therefore our equation would become: (9x^2 -1x -4x +4) and we can group the terms like this: (9x^2 -1x)(-4x +4).
The fourth step is to factor the two terms with “bx” in them. In our equation, the two terms with “bx” in them are -1x and -4x. Factoring these terms give us: (9x^2 -1x)(-4x +4) = (3x -1)(3x -4).
The final step is to find the two solutions, or the “x” values, that make the equation equal zero. To find these two x values, just set each factor to zero, and solve the resulting equations. In this example, setting the first factor, (3x - 1) equal to zero, we get x = (1/3); setting the second factor, (3x - 4) equal to zero, we get x = (4/3).
Therefore, the two solutions to 9x^2 + 15x + 4 = 0 are x = (1/3) and x = (4/3).
Using the strategy of Factoring, we have been able to successfully solve the equation 9x^2 + 15x + 4 = 0.
answer the image bellow
vvv
1. The number of days is, 21/5
2. The cost of 100 kg rice is, 4520
3. The teachers required are, 120
What is the ratio?A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.
1. Given that,
3 men can complete a work in 7 days
So, we can say magnitude of work is
M = 3 × 7 =21 unit
now, 5 men are working
So, magnitude of work is same
M = 5 × n
21 = 5 × n
n = 21/5 days
2. the cost of 25kg rice is 1130
price for 1 kg = 1130/25 =45.2
price for 100 kg = 45.2 × 100
= 4520
3. 90 teachers required for 1500 students,
1 teacher is expected to handle 1500/90 students,
So, for 2000 students
Teachers required = 2000/(1500/90) = 120
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PLEASE HELP! URGENT!!! ):
Find the greatest common factor of these two expressions.
18w^6u^8 and 30w^2u^5y^7
Answer:
18w^6u^8 = 2 * 3 * 3 * w^6 * u^8
30w^2u^5y^7 = 2 * 3 * 5 * w^2 * u^5 * y^7
The greatest common factor of these two expressions is 2 * 3 * w^2 * u^5
So the greatest common factor of 18w^6u^8 and 30w^2u^5y^7 is
2 * 3 * w^2 * u^5
toddler triplets whose names are red, green and blue each have a coat whose colour is given by their name, but they aren't clear on which coat belongs to which of them. when they go out, red chooses a coat at random among the three coats, green chooses a coat at random among the remaining two coats and blue is left to take the remaining coat. how many ways are there for exactly one of the toddler triplets to end up with their coat?
Toddler triplets whose names are red, green and blue each have a coat whose colour is given by their name, There are 6ways it can be selected
What are Toddler triplets' ways to select?Generally, There are 3! = 6 ways for the toddler triplets to choose their coats, but since the question asks for exactly one of them to end up with their coat, we need to consider the 3 cases where exactly one of them chooses their coat.
In the case where Red chooses their own coat, there are 2! = 2 ways for Green and Blue to choose their coats. In the case where Green chooses their own coat, there are 2! = 2 ways for Red and Blue to choose their coats. In the case where Blue chooses their own coat, there are 2! = 2 ways for Red and Green to choose their coats.
So in total, there are 2 + 2 + 2 = 6 ways for exactly one of the toddler triplets to end up with their coat.
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8 minus the product of 9 and r in algebraic expression
The algebraic expression of 8 minus the product of 9 and r is 8 - 9r
How to determine the algebraic expressionFrom the question, we have the following parameters that can be used in our computation:
8 minus the product of 9 and r
The product of 9 and r can be represented as 9r
So, we have the following representation
8 minus 9r
Minus means -
So, we have
8 - 9r
Hence, the expression is 8 - 9r
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PLEASE ANSWER ASAP !!
You buy shirts and pairs of pants for . Your friend buys shirt and pairs of pants for . What is the cost of each shirt? What is the cost of each pair of pants? use elimination to solve .
The cost of both the shirt and pants each is $10, solved using elimination method.
How to solve cost?Let s stand for shirt and p for trousers.
Then we may solve the following equations:
1st Equation:
2s + 3p = 50
2nd Equation:
3s +1p = 40
Our initial aim is to determine the cost of one shirt. To get rid of the pants, we might artificially multiply the second equation by -3. This is what it would look like:
2s + 3p = 50
-3(3s +1p) = -3(40) (40)
———————————————
2s + 3p = 50
-9s - 3p = -120 We can obviously remove the pants (p) now.
—————————————
-7s = -70
Divide both sides by -7 to isolate s, and we get:
s = 10 -> As a result, one shirt costs $10.
Pants = 2(10) + 3p = 50
p = $10
Let us calculate the cost of 5 shirts.
As a result, we will perform 5 x $10 = $50.
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Complete question:
You buy 2 shirts and 3 pairs of pants for $50. Your friend buys 3 shirts and 1 pair of pants for $40. how much does the shirts cost?
What is the Y intercept of this line?
How much would you need to invest in a money market account if you would like to have $5,000 in the account at the end of 3 years? The account provides an APR of 5% compounded monthly.
Answer:
To calculate the amount you would need to invest in a money market account to have $5,000 at the end of 3 years, we can use the formula for future value of an investment:
FV = PV(1+r)^n
where FV is the future value of the investment, PV is the present value of the investment, r is the interest rate (expressed as a decimal), and n is the number of compounding periods.
In this case,
FV = $5,000 (future value)
r = 5% (APR) = 0.05 (as a decimal)
n = 3 years * 12 (months) = 36
So we can use the formula:
PV = FV / (1 + r)^n
PV = $5,000 / (1 + 0.05)^36
PV ≈ $3,716.76
So you would need to invest $3,716.76 in the money market account to have $5,000 in the account at the end of 3 years.
(Look at picture) Ty for the help
Answer:
Inequalities:
x + y ≤ 3515x + 10y ≥ 400[tex]\begin{array}{|l|c|c|}\cline{1-3} \vphantom{\dfrac12} & \sf Viable & \sf Nonviable\\\cline{1-3} \vphantom{\dfrac12} (10,25)& \checkmark & \\\cline{1-3} \vphantom{\dfrac12} (10,20)&&\checkmark \\\cline{1-3} \vphantom{\dfrac12} (20,12)&\checkmark& \\\cline{1-3} \vphantom{\dfrac12} (35,0)&\checkmark& \\\cline{1-3} \vphantom{\dfrac12} (20,20)&&\checkmark \\\cline{1-3}\end{array}[/tex]
Step-by-step explanation:
Part ADefinition of variables:
Let x = the number of hours cutting grass.Let y = the number of hours tutoring.Given information:
Cutting grass = $15 per hourTutoring reading = $10 per hourSave at least $400Work no more than 35 hoursThe inequality that represents Barrett working no more than 35 hours is:
x + y ≤ 35The inequality that represents Barrett earning at least $400 is:
15x + 10y ≥ 400Part BTo determine if each point is a viable or nonviable solution, substitute each point into the two inequalities. If both inequalities are true, the solution is viable.
[tex]\begin{aligned}(10,25) \implies 10+25 &\leq 35\\35& \leq 35 \leftarrow \sf true\\\\ \implies 15(10)+10(25)&\geq400\\400&\geq 400 \leftarrow \sf true\end{aligned}[/tex]
Therefore, point (10, 25) is a viable solution.
[tex]\begin{aligned}(10,20) \implies 10+20 &\leq 35\\30& \leq 35 \leftarrow \sf true\\\\ \implies 15(10)+10(20)&\geq400\\350&\geq 400 \leftarrow \sf false\end{aligned}[/tex]
Therefore, point (10, 20) is not a viable solution.
[tex]\begin{aligned}(20,12) \implies 20+12 &\leq 35\\32& \leq 35 \leftarrow \sf true\\\\ \implies 15(20)+10(12)&\geq400\\420&\geq 400 \leftarrow \sf true\end{aligned}[/tex]
Therefore, point (20, 12) is a viable solution.
[tex]\begin{aligned}(35,0) \implies 35+0 &\leq 35\\32& \leq 35 \leftarrow \sf true\\\\ \implies 15(35)+10(0)&\geq400\\525&\geq 400 \leftarrow \sf true\end{aligned}[/tex]
Therefore, point (35,0) is a viable solution.
[tex]\begin{aligned}(20,20) \implies 20+20 &\leq 35\\40& \leq 35 \leftarrow \sf false\\\\ \implies 15(20)+10(20)&\geq400\\500&\geq 400 \leftarrow \sf true\end{aligned}[/tex]
Therefore, point (20, 20) is not a viable solution.
[tex]\begin{array}{|l|c|c|}\cline{1-3} \vphantom{\dfrac12} & \sf Viable & \sf Nonviable\\\cline{1-3} \vphantom{\dfrac12} (10,25)& \checkmark & \\\cline{1-3} \vphantom{\dfrac12} (10,20)&&\checkmark \\\cline{1-3} \vphantom{\dfrac12} (20,12)&\checkmark& \\\cline{1-3} \vphantom{\dfrac12} (35,0)&\checkmark& \\\cline{1-3} \vphantom{\dfrac12} (20,20)&&\checkmark \\\cline{1-3}\end{array}[/tex]
The first three terms of an arithmetic sequence are as follows. 17, 25, 33 Find the next two terms of this sequence. 17.25,33. П. П
Answer:
41, 49
Step-by-step explanation
It goes up in 8 if you work out 25-17 or 33-25.
33+8=41, 41+8=49
Tonyas car is not working properly. There is a 70% chance
0.9976 percent of the time, the automobile won't start immediately away.
What is normal distribution?An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range, while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center of the range.
Given that,
X = number of morning car starts right away
X 0 1 2 3 4 5
p(x) 0.0024 0.0283 0.1323 0.3087 0.3601 0.1681
So now we are able to find the given probability
p(x ≥ 1) = 1 - p(0)
1 - 0.024 = 0.9976
Here we used complementary rule to find the answer
p(A') = 1 - p(A)
Therefore, the probability that the car does not start right away is 0.9976.
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Dwight drives 85 km at an average speed of 120 km/h and then 6 km at 90 km/h without stopping. What is the average speed for the whole journey to 1 dp?
The average speed for the whole journey will be 62.33 km per hour.
How to calculate the speed?Speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed. It's a scalar quantity.
Since Dwight drives 85 km at an average speed of 120 km/h and then 6 km at 90 km/h without stopping.
The average speed for the whole journey will be:
= (85 + 6) / (85 / 120) + (90 / 120)
= 91 / (0.71 + 0.75)
= 62.33 km per hour.
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11/14 + 9/14 + 4/14=
Answer: 24/14 or 1 10/14
Step-by-step explanation:
11/14 + 9/14 = 20/14
Add the 11 and nine first.
Then add 20/14 + 4/14 and that = 24/14 or you can turn it into a mixed fraction of 1 10/14.
You're Welcome!
PLEASE HELP I NEED HELP!!!!!!!!!!!!!
Answer:
D. 5
Step-by-step explanation:
You want the constant of proportionality in the relation shown by the graph.
Constant of proportionalityA proportional relation has the equation ...
y = kx . . . . . . . . where k is the constant of proportionality
When x=1, this becomes ...
y = k
The value of y when x=1 is marked on the graph: y = 5 at that point, so ...
k = 5
The value of the constant of proportionality is 5.
Using a ID reader while checking IDs can can make it easier to
Answer:
Using an ID reader while checking IDs can make it easier to quickly and accurately verify the authenticity of the ID and the information it contains
Step-by-step explanation:
When checking IDs, it might be simpler to quickly and precisely confirm the validity of the ID and the information it includes by using an ID reader. RFID (radio frequency identification) or barcode or magnetic stripe scanning technology is used by ID readers to swiftly read and decipher the data on the ID. Since there is no longer a need to manually read and compare the information on an ID to a reference document, doing so can speed up and improve the efficiency of ID verification. By automatically cross-referencing the information with a database to confirm that the ID is legitimate and the person presenting it is the legal owner, ID scanners may also aid in the prevention of mistakes and fraud.
Answer: Identify security features
Step-by-step explanation:
Using an ID reader while checking IDs can make it easier to identify security features that don't appear under regular light. O enlarge the small text of microprinting, display data associated with the ID such as age and other information. spot pinholes, cut marks, and other evidence of tampering.
3/4 divided by 1/2 - using unit rate proportionality
To divide 3/4 by 1/2 using unit rate proportionality, we can set up a proportion with 3/4 as the numerator and 1/2 as the denominator, and then cross-multiply and solve for the unknown value.
3/4 / 1/2 = X
To solve for X, we can cross-multiply to get:
(3/4) * (2/1) = X * (1/2)
Which simplifies to:
3/2 = X
So 3/4 divided by 1/2 is equal to 3/2.
It's important to note that when dividing fractions, we can also simply invert the divisor and multiply the two fractions, 3/4 * 2/1 = 6/4 =3/2.
When you deposit your funds in a financial institution such as a bank, your
money is protected by:
A. Certificate of Deposit Insurance (CDI).
B. the Federal Bank Protection Act (FBPA).
OC. the Federal Deposit Insurance Corporation (FDIC).
OD. the security arrangement with your bank.
When you deposit your funds in a financial institution such as a bank, your money is protected by the Federal Deposit Insurance Corporation (FDIC).
What is deposit in bank ?
deposit in bank nothing but when we want to store the money and by depositing the money in the bank ensures us more security.
Deposit coverage is one of the sizable benefits of getting an account at an FDIC-insured bank—it’s how the FDIC protects your cash within the not going event of a bank failure. the usual insurance amount is $250,000 according to depositor, according to insured bank, for each account possession category. and you don’t need to purchase deposit insurance. in case you open a deposit account in an FDIC-insured bank, you're mechanically blanketed. test out the assets in this page to learn extra about deposit coverage.
Hence, When you deposit your funds in a financial institution such as a bank, your money is protected by the Federal Deposit Insurance Corporation (FDIC).
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Answer:
C. the Federal Deposit Insurance Corporation (FDIC)
Step-by-step explanation:
Laurie won 287 races during seven years while she ran track. She won the same number of races each year.
How many did she win each year?
A. 2,009 races
B. 280 races
C. 72 races
D. 41 races
Answer:
D. 41 races
Step-by-step explanation:
We can use the equation:
Number of races per year = Total number of races / Number of years
In this case, the total number of races is 287 and the number of years is 7.
Plugging in the values:
Number of races per year = 287 / 7
Number of races per year = 41
So, Laurie won 41 races each year. The answer is D) 41 races
List all the multiples of 2
Answer:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, etc.
Step-by-step explanation:
It's counting by two's.
What is the exact value of x?
5.84376
The exact value of x depends on the context of the problem. Without any additional information, it is impossible to answer this question.
John spent 15 minutes developing an estimate for a job. The job itself took 2 hours, 30 minutes to complete. What is the ratio of the time
spent on the job estimate to the total time spent on this job? Submit answer as #:# or fraction.
Answer: The ratio of the time spent on the job estimate to the total time spent on this job is 1/10. Alternatively, it can also be represented as 1:10
Step-by-step explanation:
To find the ratio of the time spent on the job estimate to the total time spent on the job, we need to divide the time spent on the estimate by the total time spent on the job, and then express the result as a fraction.
First, we need to convert both times to minutes.
15 minutes for the job estimate
2 hours = 2*60 = 120 minutes
30 minutes
Total time spent on the job = 120 + 30 = 150 minutes
Now we can divide the time spent on the estimate by the total time spent on the job:
15 minutes / 150 minutes = 1/10
So the ratio of the time spent on the job estimate to the total time spent on this job is 1/10. Alternatively, it can also be represented as 1:10
