Answers
Answer:
(-9, 14)
Step-by-step explanation:
Let the column vector be represented as a = (3, 4) and b = (5, -2)
2a = 2(3,4)
2a = (6,8)
3b = 3(5, -2)
3b = (15, -6)
Take the difference 2a - 3b
2a - 3b = (6,8) - (15, -6)
2a - 3b = (6-15, 8 -(-6))
2a - 3b = (-9, 14)
Hence the column vector is (-9, 14)
We want to find 2a - 3b as a column vector, we will get:
[tex]2a - 3b = \left[\begin{array}{ccc}-9\\14\end{array}\right][/tex]
So we want to perform a sum (difference actually) of vectors, we have that:
[tex]a = \left[\begin{array}{ccc}3\\4\end{array}\right] \\\\\\b= \left[\begin{array}{ccc}5\\-2\end{array}\right][/tex]
Remember that when we multiply a vector by a scalar, each component gets multiplied by that scalar, so we have:
[tex]2a = \left[\begin{array}{ccc}2*3\\2*4\end{array}\right] = \left[\begin{array}{ccc}6\\8\end{array}\right] \\\\\\3b= \left[\begin{array}{ccc}3*5\\3*-2\end{array}\right] = \left[\begin{array}{ccc}15\\-6\end{array}\right][/tex]
Now we just perform the direct difference:
[tex]2a - 3b = \left[\begin{array}{ccc}6\\8\end{array}\right] - \left[\begin{array}{ccc}15\\-6\end{array}\right] = \left[\begin{array}{ccc}6 - 15\\8 + 6\end{array}\right] = \left[\begin{array}{ccc}-9\\14\end{array}\right][/tex]
If you want to learn more, you can read:
https://brainly.com/question/10435343
Related Questions
A true/false test has 30 questions. A passing grade is 78% or more correct answers.
a. What is the probability that a person will guess correctly on one true/false question?
Answers
Answer:
50%
Step-by-step explanation:
one question has 2 possible answers and 1/2 is 50%
You have only quarters and dimes in your pocket. In total, you have 15 coins. The total value of all of these coins is $3.00. How many quarters and how many dimes do you have?
Answers
Answer: 10 quarters, 5 dimes.
Explanation:
10 x .25 = 2.50
5 x .10 = .50
2.50 + .50 = 3.00
Find the x- and y-intercepts of the graph of x + 3y = 33. State your answers as
whole numbers or as improper fractions in simplest form.
Answers
Answer:
x intercept is (33,0)
y intercept is (0, 11)
Step-by-step explanation:
x-intercepts are found when y=0
x + 3(0)=33,,, x=33
y-intercepts are found when x=0
0 + 3y= 33,,, y=11
Which system of equations is inconsistent?
Answer Choices Listed Below
Answers
Answer:
B
Step-by-step explanation:
just took the test
omg help plsssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss
Answers
Answer:
the image isn't clear
can you type the numbers???
Step-by-step explanation:
The table below shows the number of people, y, who ride a roller coaster at a theme park over a certain number of hours, x, during a day. Write an equation that represents the relationship between the number of people that ride a roller coaster in terms of the time, in hours, as shown in the table. Use the on-screen keyboard to type the correct equation in the box.
Answers
Answer:
y = 350x
Step-by-step explanation:
To find the equation of the chart, we simply find the slope and then follow the slope-intercept equation.
Points on the chart: (0, 0) and (1.5, 525)
Slope:
m=(y2-y1)/(x2-x1)
m=(525-0)/(1.5-0)
m=525/1.5
m = 350
Slope-intercept:
y - y1 = m(x - x1)
y - 0 = 350(x - 0)
y - 0 = 350x
y = 350x
which expression is equivalent to (2x ^2 +6)(x-2)
Answers
Answer:
B
Step-by-step explanation:
Answer:
D.
Step-by-step explanation: First multiply 2x^2 to x - 2 to get 2x^3 - 4x^2
and then multiply 6 to x - 2 to get 6x - 12. Then put the equation together:
2x^3 - 4x^2 + x - 2
A philosophy professor assigns letter grades on a test according to the following scheme. A: Top 10% of scores B: Scores below the top 10% and above the bottom 58% C: Scores below the top 42% and above the bottom 20% D: Scores below the top 80% and above the bottom 9% F: Bottom 9% of scores Scores on the test are normally distributed with a mean of 67.3 and a standard deviation of 7.3. Find the numerical limits for a D grade. Round your answers to the nearest whole number, if necessary.
Answers
Answer:
The numerical limits for a D grade are 58(lower limit) and 61(upper limit).
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Scores on the test are normally distributed with a mean of 67.3 and a standard deviation of 7.3.
This means that [tex]\mu = 67.3, \sigma = 7.3[/tex]
D: Scores below the top 80% and above the bottom 9%
This means that lower bound is the 9th percentile and the upper bound is the 100 - 80 = 20th percentile.
9th percentile:
This is X when Z has a pvalue of 0.09. So X when Z = -1.34.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.34 = \frac{X - 67.3}{7.3}[/tex]
[tex]X - 67.3 = -1.34*7.3[/tex]
[tex]X = 57.52[/tex]
Rounding to the nearest whole number, 58.
20th percentile:
This is X when Z has a pvalue of 0.2. So X when Z = -0.84
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.84 = \frac{X - 67.3}{7.3}[/tex]
[tex]X - 67.3 = -0.84*7.3[/tex]
[tex]X = 61.17[/tex]
Rounding to the nearest whole number, 61.
The numerical limits for a D grade are 58(lower limit) and 61(upper limit).
A circular mirror has a diameter of 12 inches. And a circular frame that is 3 inches wide surrounds the mirror. What is the combined area, in square inches, of the circular mirror and the frame? *
Answers
Answer:
254.5 in.^2
Step-by-step explanation:
diameter of mirror = 12 in.
radius of mirror = diameter/2 = 13 in. / 2 = 6 in.
frame width = 3 in.
radius if combined mirror and frame = 6 in. + 3 in. = 9 in.
A = (pi)(r^2)
A = 3.14159 * (9 in.)^2
A = 3.14159 * 81 in.^2
A = 254.5 in.^2
PLZZZ Help I need to hurry I got all the other questions right except this one. I dont understand it.
One of the terms in the summation is _______.
Answers
I think its B because i did this in class before and it looks familiar. (branliest will be appreciated as well) Thanks
One of the terms in the summation is(1,3)
Use the partial quotients algorithm to find the value of 966 +23
Answers
Evaluate The expression 3•2^t when t is 1
Answers
Answer:
6
Step-by-step explanation:
[tex]2^{1}[/tex] = 2
3 × 2 = 6
GIVING OUT BRAINLIEST TO WHOEVER CAN PROVIDE THE CORRECT ANSWER !! Asap
Answers
Kelly jarred 30 liters of jam after 8 days. What is the unit rate? Pleasee help
Answers
Answer:
3.75 liters a day
Step-by-step explanation:
Write an equation to model the situation
Jack works at a t-shirt store. Jack earns $150 a week plus $2 for every t-shirt (T) that
he sells. If Jack's gross pay at the end of the week is $320, how many t-shirts did he sell?
Answers
David averaged 12 points per game during his 7th grade basketball season. As a result of practicing all summer, he averaged 20 points per game during his 8th-grade season. By what percent did his average change?
Answers
Answer:
20-12=8 the answer is 8 I did the math
Answer:
8 is right
Step-by-step explanation:
because 20-12=8
A group of 25 people are going to run a race. The top 8 finishers advance to the finals.
Answers
Kelly purchased a t-shirt
for 9.99 and a pair of
jeans for $21.50. The
sales tax rate is 8.25%.
What was the total cost
of Kelly's purchase
(including sales tax)?
PLEASE HELP
Answers
Answer:
34.09
Step-by-step explanation:
Answer: $34.09
Step-by-step explanation:
Is the point (-4, 1/2) on the graph of y= 1\2 x-4 ? How do you know? Show your work/thinking.
Answers
9514 1404 393
Answer:
no, when x is even, y will be an integer, not a fraction
Step-by-step explanation:
We observe that the coefficient of x is 1/2, so the x-term will be an integer only if x is a multiple of 2 (even). If the x-term is an integer, y will be an integer.
The given point has x even (-4), so we expect y to be an integer. The given point has y=1/2, not an integer, so the point will NOT be on the graph.
5 rubber stamps cost $9.70.
Which equation would help determine the cost of 11 rubber stamps?
A: x/11 = 5/9.70
B: 11\$9.70 = x/5
C: 5/11 = x/9.70
D: 11/5 = 9.70/x
E: None of the above
Answers
Last year, Lien earned $1,600 more than her husband. Together they earned $51,000. How much did each of them earn?
Answers
Answer:
Lien: $26300 Her husband: $24700
Step-by-step explanation:
x+(x+1600)=51000
2x+1600=51000
2x=49400
x=24700
Her husband earned 24700
24700+1600=26300
Lien earned 26300
GIVING OUT BRAINLIEST ANSWER !! PLS HELP ME OUT !! (last minute)
Answers
Answer:
A, 32 degrees, hope this helps !! :D
Step-by-step explanation:
Need help fast please
Answers
Answer:
1. 53 97 159
2 6 and 6.1
3. 1 1/3
Estimate the product 28 2/3 x 4/5
Answers
Answer:
23.2, exact is 22.9333334
Step-by-step explanation:
28 2/3 is around 28.5 ,4/5 is .75
28.5 * .75 = 21.375
HELP ME PLS I NEED HELP ALSO I NEED A SHOW YOUR WORK BUT PLS HELP
Answers
Step-by-step explanation:
6 y = mx + b
7. m
8. b
9a m = 4 (slope), b = 12(yintercept)
9b -1. 4
9c 8. 21
9d 12. 9
which dimensions describe a rectangular prism with a volume of
Answers
Answer:
Square ⬛ ormmmfjdixxjx
How do I solve this problem?And if a bot puts a link on my question,then what i'm going to do is report the bot.
Answers
So Chris borrowed $88.00
Then from those $88 he had to give his grandparents $31.78 so you can do :
88 - 31.78
Which would give you 56.22 and that is the amount he owes them.
If $18 is 45% what is 100%
Answers
Answer:
$40Step-by-step explanation:
45% = 45/100 = 0.45
0.45x = 18x = 18/0.45x = 40100% is $40
Answer:
solution given;
let total be X
45% of X=$18
X=$18×100/45=$40
So.100% is $40.
What is the surface area?
5 yards
5 yards
5 yards
Answers
Answer:
150 yards^2
Step-by-step explanation:
If all lengths are equal (assuming that the question refers to 5 yds x 5 yds x 5 yds) that means that it is a cube.
A cube has 6 faces and each face is 25 yds^2 (because of the 5 x 5 lenght sides)
If you multiply 25 by 6 (the amount of faces) you would get 150 yds^2
Answer:
usbdkhfjdnbdjdkfdbdbdnkccndndkckcjd. endkcn
A snowstorm dropped three and two-fifths inches of snow. The next day one and four-fifths inches melted, how much snow was left?
Answers
Answer:
After the melting there were one and three fifths of snow left.
Step-by-step explanation:
Given that a snowstorm dropped three and two-fifths inches of snow, and the next day one and four-fifths inches melted, the following calculation must be performed to determine how much snow was left:
2/5 = 0.40
4/5 = 0.80
3.40 - 1.80 = X
1.60 = X
0.60 = 3/5
Thus, after the melting there were one and three fifths of snow left.
