Answer:
x+y=3
Step-by-step explanation:
For an equation to have no solution, their slope needs to be same and y intercept needs to be different,
so in this case where x+y=2
doing simply, x+y=3 makes a set of equation which has no solution, you can take any real value which is not 2
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].
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]
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)
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]
"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
A 4-pack of plastic flower pots costs $4.08. What is the unit price?
Answer:
If 4 flower pots cost 4.08 dollars, then 1 flower pot costs 4.08/4 dollars.
4.08/4 = 1.02.
So the unit price is $1.02.
Let me know if this helps!
when graphing y=-2x+10, is it a line that shows only one solution to the equation, all solutions, or shows the y-intercept?
Answer:
there is always a y-intercept in all graphs.
Step-by-step explanation:
be it a line graph, quadratic graph or cubic graph. all graphs will definitely have a y-intercept. and in this case, since y=mx + c where c is the y-intercept. the y intercept of this graph is 10
cho tam giác ABC cân tại A trung tuyến AM.Biết BC=6cm,AM=4cm .Tính độ dài các cạnh AB và AC
Vì tam giác ABC cân tại A (gt) mà AM là đg trung tuyến nên AM đồng thời là đg cao của t/giác đó:
AM là trung tuyến của t/giác ABC nên M là trung điểm BC:
=> BM =BC/2 =6:2=3(cm)
Xét tam giác AMB vuông tại M
AB^2 =AM^2+BM^2 ( theo định lý Py-ta -go)
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.
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?
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:
 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.
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")
so i need help with this pls i suck at algebra
Answer:
The 5x^2 vs -5x^2 will reflect over "X" axis
the +1 vs -2 will shift the graph down three units
the first answer is the correct answer
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
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.Simplify and find the perimeter of the triangle
Answer:
2x - 19
Step-by-step explanation:
Perimeter = sum of sides
First let's simplify each side
We can simplify each side by using distributive property. Distributive property is where you multiply the number on the outside of the parenthesis by the numbers on the inside of the parenthesis.
2(x + 5)
Distribute by multiplying x and 5 by 2
2 * x = 2x and 2 * 5 = 10
2x + 10
1/2(4x + 8)
Distribute by multiplying 4x and 8 by 1/2
1/2 * 4x = 2x and 1/2 * 8 = 4
2x + 4
-3(2x + 11)
Distribute by multiplying 2x and 11 by -3
-3 * 2x = -6x
-3 * -33
-6x - 33
Finally add all the simplified expressions ( remember that they represent the side lengths of the triangle )
2x + 10 + 2x + 4 - 6x - 33
Combine like terms
2x + 2x - 6x = -2x
10 + 4 - 33 = -19
Perimeter: -2x - 19
Answer:
Perimeter = - 2x - 19
Step-by-step explanation:
[tex]Perimeter \: of \: a \: triangle \\ = Sum \: of \: the \: length \: of \: all \: sides \\ = [2(x+5)]+[-3(2x+11)]+[ \frac{1}{2} (4x+8)] \\ = [(2 \times x)+(2 \times 5)]+[(-3 \times 2x)+( - 3 \times 11)]+[ (\frac{1}{2} \times 4x) + ( \frac{1}{2} \times 8)] \\ = (2x + 10) + ( - 6x - 33) + (2x + 4) \\ = 2x + 10 - 6x - 33 + 2x + 4 \\ = 2x - 6x + 2x + 10 - 33 + 4 \\ = - 2x - 19[/tex]
So, the perimeter is - 2x - 19.
ײ × ×⁴=ײ+⁴ find the ×
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
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
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Rewrite as a simplified fraction.
3.2 = ?
(Repeating)
Answer:
Step-by-step explanation:
29/9 or 3 2/9
What do you notice about the absolute value of the
difference between the two numbers of -5 and -1
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).
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
The receipt shows the prices of goods that Mr. Baker bought at the store.
The state Mr. Baker lives in has a sales tax rate of 7% on all purchases.
How much money does Mr. Baker pay in sales tax and what is the total amount he must pay for his purchases?
Answer:
The answer is $82.46 sales tax
$1,260.46 Total
Step-by-step explanation:
Since the price before the Sales tax is $1,178.00 and if you add the 7% Sales tax the total is $1,260.46 and the price of the Sales tax is $82.46
Revolve into factor : 2x square + 5xy + 2y square
Answer:
(2x + y) ( x + 2y)
Step-by-step explanation:
John earns $6 per hour for mowing the lawn. If t represents John's total earnings for h hours of mowing, which equations can be used to model the situation
Answer:
h=6
Step-by-step explanation:
An investor has an account with stock from two different companies. Last year, his
stock in Company A was worth $6600 and his stock in Company B was worth $3500.
The stock in Company A has increased 7% since last year and the stock in Company B
has increased 1%. What was the total percentage increase in the investor's stock
account? Round your answer to the nearest tenth (if necessary).
What quantity of parsley would you need to make 5 times as much as the original recipe?
1. The position of a particle moving along a coordinate axis is given by: s(t) = t^2 - 5t + 1. a) Find the speed of the particle b) Find the acceleration of the particle c) Find the velocity of the particle
Answer: [tex]\left | 2t-5\right |,\ 2,\ 2t-5[/tex]
Step-by-step explanation:
Given
Position of the particle moving along the coordinate axis is given by
[tex]s(t)=t^2-5t+1[/tex]
Speed of the particle is given by
[tex]\Rightarrow v=\dfrac{ds}{dt}\\\\\Rightarrow v=\dfrac{d(t^2-5t+1)}{dt}\\\\\Rightarrow v=\left | 2t-5\right |[/tex]
Acceleration of the particle is
[tex]\Rightarrow a=\dfrac{dv}{dt}\\\\\Rightarrow a=2[/tex]
velocity can be negative, but speed cannot
[tex]\Rightarrow v=\dfrac{ds}{dt}\\\\\Rightarrow v=\dfrac{d(t^2-5t+1)}{dt}\\\\\Rightarrow v=2t-5[/tex]
