Answer:
Brainliestgive o020201000
The vector (a) is a multiple of the vector (2i +3j) and (b) is a multiple of (2i+5j) The sum (a+b) is a multiple of the vector (8i +15j). Given that /a+b/= 34 and the scaler multiple of (8i+15j) is positive, Find the magnitude of a and b.
Answer:
[tex]\|a\| = 5\sqrt{13}[/tex].
[tex]\|b\| = 3\sqrt{29}[/tex].
Step-by-step explanation:
Let [tex]m[/tex],[tex]n[/tex], and [tex]k[/tex] be scalars such that:
[tex]\displaystyle a = m\, (2\, \vec{i} + 3\, \vec{j}) = m\, \begin{bmatrix}2 \\ 3\end{bmatrix}[/tex].
[tex]\displaystyle b = n\, (2\, \vec{i} + 5\, \vec{j}) = n\, \begin{bmatrix}2 \\ 5\end{bmatrix}[/tex].
[tex]\displaystyle (a + b) = k\, (8\, \vec{i} + 15\, \vec{j}) = k\, \begin{bmatrix}8 \\ 15\end{bmatrix}[/tex].
The question states that [tex]\| a + b \| = 34[/tex]. In other words:
[tex]k\, \sqrt{8^{2} + 15^{2}} = 34[/tex].
[tex]k^{2} \, (8^{2} + 15^{2}) = 34^{2}[/tex].
[tex]289\, k^{2} = 34^{2}[/tex].
Make use of the fact that [tex]289 = 17^{2}[/tex] whereas [tex]34 = 2 \times 17[/tex].
[tex]\begin{aligned}17^{2}\, k^{2} &= 34^{2}\\ &= (2 \times 17)^{2} \\ &= 2^{2} \times 17^{2} \end{aligned}[/tex].
[tex]k^{2} = 2^{2}[/tex].
The question also states that the scalar multiple here is positive. Hence, [tex]k = 2[/tex].
Therefore:
[tex]\begin{aligned} (a + b) &= k\, (8\, \vec{i} + 15\, \vec{j}) \\ &= 2\, (8\, \vec{i} + 15\, \vec{j}) \\ &= 16\, \vec{i} + 30\, \vec{j}\\ &= \begin{bmatrix}16 \\ 30 \end{bmatrix}\end{aligned}[/tex].
[tex](a + b)[/tex] could also be expressed in terms of [tex]m[/tex] and [tex]n[/tex]:
[tex]\begin{aligned} a + b &= m\, (2\, \vec{i} + 3\, \vec{j}) + n\, (2\, \vec{i} + 5\, \vec{j}) \\ &= (2\, m + 2\, n) \, \vec{i} + (3\, m + 5\, n) \, \vec{j} \end{aligned}[/tex].
[tex]\begin{aligned} a + b &= m\, \begin{bmatrix}2\\ 3 \end{bmatrix} + n\, \begin{bmatrix} 2\\ 5 \end{bmatrix} \\ &= \begin{bmatrix}2\, m + 2\, n \\ 3\, m + 5\, n\end{bmatrix}\end{aligned}[/tex].
Equate the two expressions and solve for [tex]m[/tex] and [tex]n[/tex]:
[tex]\begin{cases}2\, m + 2\, n = 16 \\ 3\, m + 5\, n = 30\end{cases}[/tex].
[tex]\begin{cases}m = 5 \\ n = 3\end{cases}[/tex].
Hence:
[tex]\begin{aligned} \| a \| &= \| m\, (2\, \vec{i} + 3\, \vec{j})\| \\ &= m\, \| (2\, \vec{i} + 3\, \vec{j}) \| \\ &= 5\, \sqrt{2^{2} + 3^{2}} = 5 \sqrt{13}\end{aligned}[/tex].
[tex]\begin{aligned} \| b \| &= \| n\, (2\, \vec{i} + 5\, \vec{j})\| \\ &= n\, \| (2\, \vec{i} + 5\, \vec{j}) \| \\ &= 3\, \sqrt{2^{2} + 5^{2}} = 3 \sqrt{29}\end{aligned}[/tex].
"A parabola has the equation = ^ + − . What are the coordinates of the vertex? (You must solve by factoring)!!!!!" I NEED THE ANSWER TO THIS FAST WITH STEPS I'm a grade 10 academic student by the way
Answer:
1
Step-by-step explanation:
1
Please help solve both due soon
Answer:
x is 7
EF is 10
FG is 12
Step-by-step explanation:
[tex]EF + FG = EG \\ (4x - 18) + (3x - 9) = 22 \\ 7x - 27 = 22 \\ 7x = 49 \\ x = 7[/tex]
then substitute:
[tex]EF = 4x - 18 \\ EF = 4(7) - 18 \\EF = 28 - 18 \\ EF = 10[/tex]
[tex]FG = 3x - 9 \\ FG = 3(7) - 9 \\FG = 21 - 9 \\ FG = 12[/tex]
First question:
BC + BA = CA
BC = CA - BA
BC = 36 - 9
BC = 27
HELP PLEASE!!! I DONT UNDERSTAND
Answer:
20 miles
Step-by-step explanation:
She ran 20miles, at the same point she passed her friend
The temperature of a 24-hour period ranged between -6°F and 35°F, inclusive. What was the range in Celsius degrees? (Use F = 9/5C + 32)
Roger bought some tins and decided to fill them with brownies to give to his friends. Roger baked 278 brownies. He put 4 brownies in each tin and made sure to fill as many tins as he could. How many brownies did Roger have left over?
Answer:
Divide 278 by 4 and the remainder value is the amount of leftover brownies.
278 ÷ 4 = 69, remainder of 2
Therefore, he had 2 brownies left.
find A={a,b,c} then find A*A.
Assuming you want to do a cartesian product, then you basically form items (x,y) such that x is in set A, and y is in set A
More generally, A * B will consist of items of the form (x,y) such that x is in A and y is in B. However, we have B = A.
So,
A * A = {
(a,a), (a,b), (a,c)
(b,a), (b,b), (b,c)
(c,a), (c,b), (c,c)
}
I broke things up into separate rows to show that we can form a 3x3 table. Each row is a different x value from the set {a,b,c}. Each column is a different y value from the set {a,b,c}
In my opinion, this helps organize things much better than rather have it all on one single line like this
A * A = { (a,a), (a,b), (a,c), (b,a), (b,b), (b,c), (c,a), (c,b), (c,c) }
which in all honesty looks like a bit of a cluttered mess.
Answer:
Step-by-step explanation:
A={a,b,c}
A×A={a×a,a×b,a×c,b×a,b×b,b×c,c×a,c×b,c×c}
help please :) try to explain and answer math coordinates
Tell whether each order pair is a solution of the equation.
1. 2x+y=5 (2,1)
2. 4x-3y=10 (4,3)
helppp pls i don’t understand thisssss
Answer:
1.) (2,1) is a solution
2.) (4,3) is NOT a solution
Step-by-step explanation:
1.) (2,1)
These are these mean (x,y)
2=x and 1=y
You want to substitute the numbers for the letters in the equation.
so.
2(2)+1=5
4+1=5
5=5, This statement is true so (2,1) is a solution.
2.) Same as above. 4=x and 3=y
4(4)-3(3)=10
16-9=10
7 Does Not Equal 10, Therefore, (4,3) is Not a solution to the equation.
Revolve into factor : 2x square + 5xy + 2y square
Answer:
(2x + y) ( x + 2y)
Step-by-step explanation:
The expression.1*e^0.0347t models.The balance in thousand of dollars where t represents time.In years after the account was opened. What does the 0.034 represent in this context? Write an expression for the number of years after which there will be 15,000 Dollars in the account?
Answer:
0.0347 = constant of proportionality
[tex]1 * e^{0.0347t} = 15000[/tex]
Step-by-step explanation:
Given
[tex]1*e^{0.0347t}[/tex]
Solving (a): what does 0.0347 represent?
An exponential model is represented as:
[tex]f(t) = a * e^{kt}[/tex]
Where:
[tex]k \to[/tex] constant of proportionality
So, by comparison:
[tex]k = 0.0347[/tex]
Hence:
[tex]0.0347 \to[/tex] constant of proportionality
Solving (b): Formula to calculate when balance equals 15000
To do this, we simply equate the formula to 15000.
So, we have:
[tex]1 * e^{0.0347t} = 15000[/tex]
Please help explanation if possible
Step-by-step explanation:
Y=
[tex]y = 10 - 8x \\ put \: this \: in \: the \: second \: equation \\ 2(10 - 8x) - 4x = 40 \\ 20 - 16x - 4x = 40 \\ 20 - 20x = 40 \\ - 20 = 20x \\ x = - 1 \\ put \: the \: value \: of \: x \: in \: th \: first \: equation \\ y = 10 - 8( - 1) \\ y = 10 + 8 \\ y = 18[/tex]
Hence, x=-1 and y=18
Answer:
(- 1, 18 )
Step-by-step explanation:
Given the equations
y + 8x = 10 ( subtract 8x from both sides )
y = 10 - 8x → (1)
2y - 4x = 40 → (2)
Substitute y = 10 - 8x into (2)
2(10 - 8x) - 4x = 40 ← distribute and simplify left side
20 - 16x - 4x = 40
20 - 20x = 40 ( subtract 20 from both sides )
- 20x = 20 ( divide both sides by - 20 )
x = - 1
Substitute x = - 1 into (1) for corresponding value of y
y = 10 - 8(- 1) = 10 + 8 = 18
solution is (- 1, 18 )
Make a histogram, using a bin width of ten, to display the bowling scores for these 31 players: 87, 104, 79, 94, 117, 82, 72, 116, 105, 95, 88, 93, 109, 119, 75, 103, 112, 97, 73, 85, 91, 86, 102, 99, 106, 84, 98, 83, 81, 96, 92.
Step-by-step explanation:
Using R, I used the following code to create a histogram:
bowling.scores <- c(87, 104, 79, 94, 117, 82, 72, 116, 105, 95, 88, 93, 109, 119, 75,
103, 112, 97, 73, 85, 91, 86, 102, 99, 106, 84, 98, 83, 81, 96, 92)
data.frame(bowling.scores)
ggplot(data.frame(bowling.scores), aes(x=bowling.scores)) +
xlim(c(70, 120)) +
scale_y_continuous(breaks = seq(0, 10, by=1), "Frequency") +
geom_histogram(breaks=seq(70, 120, by=10), color="black", fill="grey60") +
labs(title="Histogram of Bowling Scores", x="Bowling Scores", y="Frequency")
calculate the square of 31
Answer:
square of 31 is 961
Step-by-step explanation:
31^2
31×31
=961
What is 4,327 rounded to the nearest thousand?
Answer: 4,000
Step-by-step explanation: To round 4,327 to the nearest thousand, we first find the digit in the rounding place, which in this case is the 4 in the thousands place. Next, we look at the digit to the right of the 4, which is 3.
According to the rules of rounding, since the digit to
the right of the rounding place is less than 5, we round down.
So the 4 in the rounding place stays the same
and all digits to the right of the 4 become 0.
So 4,327 rounded to the nearest thousand is 4,000.
how many metres of wire is needed to fence a circular pond of radius 7.7m if the fence is to have three strands of wire all the way around .Give your answer correct to one decimal place. (Take pi is 3.14)
Find the circumference of the pond:
Circumference = 2 x pi x radius
Circumference = 2 x 3.14 x 7.7 = 48.356 m
You want to go around 3 times so multiply the circumference by 3:
48.356 x 3 = 145.068m
Rounded to 1 decimal = 145.1m
 A study found that healthy eating can help to cut the risk of heart disease. Therefore, a person can conclude that if they eat healthy they definitely will not have any heart issues.
True or false?
Answer:
False
Step-by-step explanation:
It only cuts the risk as stated and other factors such as lifestyle, age, bloodpressure and past medical background also have an impact so you can still have heart issues.
Dave solved a quadratic equation. His work is shown below, with Step 111 missing. What could Dave have written as the result from Step 111? \begin{aligned} \dfrac{1}{3}(x+4)^2&=48 \\\\ &&\text{Step }1 \\\\ x+4&=\pm 12&\text{Step }2 \\\\ x=-16&\text{ or }x=8&\text{Step }3 \end{aligned} 3 1 (x+4) 2 x+4 x=−16 =48 =±12 or x=8 Step 1 Step 2 Step 3 Dave solved a quadratic equation. His work is shown below, with Step 111 missing. What could Dave have written as the result from Step 111? \begin{aligned} \dfrac{1}{3}(x+4)^2&=48 \\\\ &&\text{Step }1 \\\\ x+4&=\pm 12&\text{Step }2 \\\\ x=-16&\text{ or }x=8&\text{Step }3 \end{aligned} 3 1 (x+4) 2 x+4 x=−16 =48 =±12 or x=8 Step 1 Step 2 Step 3
From the calculation above, Dave may have jumped the expression
[tex](x+4)^2= 144[/tex]
Given the expression solved by Dave from step 1 as;
[tex]\dfrac{1}{3}(x+4)^2&=48[/tex]
In order to determine what Dave would have written, we will solve the expression above as shown
[tex]\dfrac{1}{3}(x+4)^2&=48\\(x+4)^2 = 3*48\\(x+4)^2 = 144 ..............eqn \ 2\\[/tex]
Take the square root of both sides
[tex]\sqrt{(x+4)^2} =\pm\sqrt{144}\\x+4=\pm12[/tex]
Hence from the calculation above, Dave may have jumped the expression in equation 2 as shown below;
[tex](x+4)^2= 144[/tex]
Learn more on radical equations here: https://brainly.com/question/20931859
Answer:
previous answer is correct
Step-by-step explanation:
HELPPP PLZZZZ DUE SOONnnn
Answer:
x = 7, EF = 10, FG = 12
Step-by-step explanation:
EF = 4x - 18
FG = 3x - 9
EG = 22
EG = 22
EF + FG = 22
4x - 18 + 3x - 9 = 22
4x + 3x - 18 - 9 = 22
7x = 22 + 18 + 9
7x = 49
x = 7
EF = 4x - 18
EF = 4*7 - 18
EF = 28 - 18
EF = 10
FG = 3x - 9
FG = 3*7 - 9
FG = 21 - 9
FG = 12
What do you notice about the absolute value of the
difference between the two numbers of -5 and -1
Find the measure of the third angle of a triangle if the measures of the other two angles are given.
35.5 and 82.6
A. 66.8
B. 58.4
C. 61.9
D. 31.9
9514 1404 393
Answer:
C. 61.9°
Step-by-step explanation:
The sum of angles in a triangle is 180°, so the third angle is ...
180° -35.5° -82.6° = 61.9°
You work for a roofing company and must order the correct number of tiles to complete the final side of the roof. It is in the shape of a trapezoid. The numbers of tiles in each row form a sequence. We know we will have 20 rows to complete the job. The first row has ten tiles. Each row has two more tiles than the previous row. Is this sequence arithmetic or geometric?
Answer:
ljj
Step-by-step explanation:
llk
Yes , the series is an arithmetic sequence of common difference 2
What is Arithmetic Progression?
An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"
The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁
Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
Given data ,
Let the number of terms n = 20
The number of tiles in the first row = 10 tiles
The number of tiles in the second row = 2 more than first row
The number of tiles in the second row = 12 tiles
The number of tiles in the third row = 14 tiles
So , the sequence will be , 10 , 12 , 14 , 16 ...
The number of terms n = 20
The first term a = 10
The common difference d = second term - first term
The common difference d = 12 - 10 = 2
The series is an arithmetic sequence and the 20th term of the sequence will be
a₂₀ = a + ( n - 1 )d
a₂₀ = 10 + ( 19 ) 2
a₂₀ = 10 + 38
a₂₀ = 48 tiles
Hence , the series is an arithmetic sequence
To learn more about arithmetic progression click :
https://brainly.com/question/1522572
#SPJ5
41
Ivan has just opened a small coffee shop. He paid a copy store 50.10 percopy to make
1,428 copies of the flyer to announce the opening of the shop an is having 14
distribute all 1 428 flyers, and he is paying them 50.25 tot sath Syer shey der He suure
each friend the same number of flyers
What is the total amount Ivan is paying each friend to
disor
Show your work
Answers
Answer:
41
Ivan has just opened a small coffee shop. He paid a copy store 50.10 percopy to make
1,428 copies of the flyer to announce the opening of the shop an is having 14
distribute all 1 428 flyers, and he is paying them 50.25 tot sath Syer shey der He suure
each friend the same number of flyers
What is the total amount Ivan is paying each friend to
disor
Show your work
Answers
what is the lcm of two numbers if one number is a multiple of the other
If one number is the multiple of another number, then the L.C.M. will be the smaller number (the number whose multiple the other number is).
The sampling distribution of a statistic _________. Group of answer choices gives all the values a statistic can take gives the probability of getting each value of a statistic under the assumption it had resulted due to chance alone is a probability distribution all of the options
Answer:
all of the options
Step-by-step explanation:
A sampling distribution is a probability distribution, gives the probability of getting each value and all values a statics can take. It is arrived out through a repeated sampling form of a large population. It truly exists as a population.suppose that this decade begins on 1 january 2020 which is wednesday and the next decade begins on 1 january 2030. how many Wednesday are there in this decade?
Answer:
521
365 *10 = 3650
365/7 = 521.4
Step-by-step explanation:
If f(x) = 2x + 1 and g(x) = x2 - 2, find f(g(3)).
Answer:
15
Step-by-step explanation:
g(3)=(3)^2-2=7
f(g(3))=f(7)=2*7+1=15
Answer:
9?
Step-by-step explanation:
f(3*2-2)
=4
then
2*4+1
=9 is the answer
3. If bº = 110°, what is the value of gº?
Answer:
hello mate <3
u see here its a quadrialteral
with 4 angles b , d , 70 , g
so b + d + 70 + g = 360
now u see 60 + d = 180 (straight line)
d = 120 and b = 110 ( given)
so
110 + 120 + 70 + g = 360
g + 300 = 360
g = 360 - 300 = 60 degrees option c
brainliest?
Given that h(x) = 5-2x, find the value(s) of x when h(x) =3
Answer:
x=1
Step-by-step explanation:
We have,
h(x) = 5-2x
h(x)=3
Now,
h(x)=5-2x=3
or,5-2x=3
or,5-3=2x
or,2/2=x
Therefore, x=1 when h(x)=3
Answer:
x = 1
Step-by-step explanation:
h(x) = 3
5 - 2x = 3
2x = 2
x = 1
According to the Centers for Disease Control and Prevention, the proportion of U.S. adults age 25 or older who smoke is .22. A researcher suspects that the rate is lower among U.S. adults 25 or older who have a bachelor's degree or higher education level.What is the null hypothesis in this case
Answer:
The null hypothesis is [tex]H_0: p = 0.22[/tex]
Step-by-step explanation:
According to the Centers for Disease Control and Prevention, the proportion of U.S. adults age 25 or older who smoke is .22
This means that at the null hypothesis, it is tested if the proportion is in fact 0.22, that is:
[tex]H_0: p = 0.22[/tex]
A researcher suspects that the rate is lower among U.S. adults 25 or older who have a bachelor's degree or higher education level.
At the alternative hypothesis, it is tested if the proportion is lower than 0.22, that is:
[tex]H_1: p < 0.22[/tex]
