Answer:
-1
Step-by-step explanation:
Vector a=(1,0) if visualized as a line has points (0,0) and (1,0). This means the line is horizontal and has equation y=0.
This means we are looking for a vertical line.
Instead of lambda, I'm going to use u.
So we want a+ub=(1,0)+u(1,1). to vertical. If we visualize this as a line with points (0,0) and (1+u,u). We would need u=-1 so this would be vertical.
So vectors a=(1,0) and a+ub=(1,0)+u(1,1) are perpendicular for u=-1.
So we are saying vectors (1,0) and (0,-1) are perpendicular. If you draw these, you can get a visual confirmation.
The value of λ is -1 and is perpendicular to vector a.
What is Vector?A vector is a number or phenomena with two distinct properties: magnitude and direction. The term can also refer to a quantity's mathematical or geometrical representation. In nature, vectors include velocity, momentum, force, electromagnetic fields, and weight.
We have,
Vector a = (1, 0) and b = (1, 1).
Here the vector is visualized as line is horizontal and has equation y=0.
Now, we have a + λb is perpendicular to vector a.
So, a + λb = (1, 0) + λ(1, 1)
= (1 + λ, 1)
Now, to get the vertical component we must have λ= -1.
Then, a(1, 0) and a+λb= (1,0)+ λ(1, ) are perpendicular to λ=-1.
Learn more about Vector here:
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solve using identities
Answer:
Solution given
Cos[tex]\displaystyle \theta_{1}=\frac{13}{15}[/tex]
consider Pythagorean theorem
[tex]\bold{Sin²\theta+Cos²\theta=1}[/tex]
Subtracting [tex]Cos²\theta[/tex]both side
[tex]\displaystyle Sin²\theta=1-Cos²\theta[/tex]
doing square root on both side we get
[tex]Sin\theta=\sqrt{1-Cos²\theta}[/tex]
Similarly
[tex]Sin\theta_{1}=\sqrt{1-Cos²\theta_{1}}[/tex]
Substituting value of [tex]Cos\theta_{1}[/tex]
we get
[tex]Sin\theta_{1}=\sqrt{1-(\frac{-13}{15})²}[/tex]
Solving numerical
[tex]Sin\theta_{1}=\sqrt{1-(\frac{169}{225})}[/tex]
[tex]Sin\theta_{1}=\sqrt{\frac{56}{225}}[/tex]
[tex]Sin\theta_{1}=\frac{\sqrt{56}}{\sqrt{225}}[/tex]
[tex]Sin\theta_{1}=\frac{\sqrt{2*2*14}}{\sqrt{15*15}}[/tex]
[tex]Sin\theta_{1}=\frac{2\sqrt{14}}{15}[/tex]
Since
In III quadrant sin angle is negative
[tex]\bold{Sin\theta_{1}=-\frac{2\sqrt{14}}{15}}[/tex]Answer:
- 2√14/15Step-by-step explanation:
In the quadrant III both the sine and cosine get negative value.
Use the identity:
sin²θ + cos²θ = 1And consider negative value as mentioned above:
sinθ = - √(1 - cos²θ) sinθ = - √(1 - (-13/15)²) sinθ = - √(1 - 169/225)sinθ = - √(56/225)sinθ = - 2√14/15The polygons in each pair are similar. find the missing side length
If polygons are similar ratio of sides will be same
[tex]\\ \sf\longmapsto \frac{6}{14} = \frac{3}{x} \\ \\ \sf\longmapsto 6x = 14 \times 3 \\ \\ \sf\longmapsto 6x = 42 \\ \\ \sf\longmapsto x = \frac{42}{6} \\ \\ \sf\longmapsto x = 7[/tex]
Plane R and Plane U intersect at which of the following?
Answer:
do you have any images with the questions?
Step-by-step explanation:
find the measure of y.
options:
86°
102°
130°
122°
Answer:
B
Step-by-step explanation:
It's a 4 sided polygon, so it's sum of interior angle will be 360. 120+y+85+53=360. y=102
[tex]2 \sqrt{75} - \sqrt{108} + 5 \sqrt{48}[/tex]
[tex]\\ \sf\longmapsto 2 \sqrt{75} - \sqrt{108} + 5 \sqrt{48} \\\\ \sf\longmapsto 2 \sqrt{25 \times 3} - \sqrt{36 \times 3} + 5 \sqrt{16 \times 3} \\ \\ \sf\longmapsto 2 \times 5 \sqrt{3} - 6 \sqrt{3} + 5 \times 4 \sqrt{3} \\ \\ \sf\longmapsto 10 \sqrt{3} - 6 \sqrt{3} + 20 \sqrt{3} \\ \\ \sf\longmapsto (10 - 6 + 20) \sqrt{3} \\ \\ \sf\longmapsto 24 \sqrt{3} [/tex]
Answer:
24aprtment3
Step-by-step explanation:
Find the measurement of the angle diagonal indicated in the following parallelogram
Answer:
24units
Step-by-step explanation:
From the parallelogram given, we can see that the line FH bisects EG at V. Hence;
GE = 2GV.
Given that
GV = 12
GE = 2(12)
GE = 24
Hence the measure of the length GE is 24units
A survey was conducted by asking 120 students in a town how they traveled to school.
The following pie chart shows the result of the survey
Car 30%
Cycle 25%
Walk 10%
Bus ?
What are the number of students that travel to school by bus
Answer:
42
Step-by-step explanation:
30+25+10=65%
bus=35%
35/100×120=42
BUS=42
Find the area of sector TOP in (O using the given information. Leave your
answer in terms of π.
13. r = 5 m, m = 90 degrees
Answer:
Pls give me the answers as soon as possible and make sure that the answers are correct.
Alex wants to test the reliability of “lie detector tests,” or polygraph tests. He performs a polygraph test on a random sample of 12 individuals. If there is more than a 50% chance that the tests result in no false positives (that is, the test does not result in a true statement being recorded as a lie), Alex will conclude that the tests are reliable. If the probability of a lie detector test resulting in a false positive is 5.5%, what will Alex conclude? Use Excel to find the probability, rounding to three decimal places.
The correct statement is test is reliable and authentic as the probability of no false positives is more than 0.5
Given that
[tex]H_o:P= 0.50\\\\H_1:P>0.50[/tex]
Now following calculations to be done to reach the conclusion:
There is no false positive as
= 100 - 5.5
= 94.5%
[tex]\hat P =0.945, n = 12[/tex]
Now
[tex]z = \frac{\hat P - P}{\sqrt\frac{P(1-P)}{n} }\\\\=\frac{0.945-0.5}{\sqrt\frac{0.5\times0.5}{12} } \\\\= 3.08[/tex]
So
P value = P(z >3.08) = 0.0010
Therefore we can conclude that test is reliable and authentic as the probability of no false positives is more than 0.5
Learn more about the polygraph test here:
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The number 804 is divisible by what numbers?
Answer: 804 is divisible by 1, 2, 3, 4, 6, 12 ,67 ,134 ,201, 268, 402 ,804
Answer:
The factors of 804 are: 1, 2, 3, 4, 6, 12, 67, 134, 201, 268, 402,804.
Step-by-step explanation:
How do I find x and y?
Answer:
x = 20
y = 70
Step-by-step explanation:
Since B and D are parallel :
6x - 10 + 3x + 10 = 180 add/subtract like terms
9x = 180 divide both sides by 9
x = 20
angle represented by y and 6x - 10 are supplementary and their sum is 180
y + 6x - 10 = 180 replace x with 20
y + 6*20 - 10 = 180
y + 120 - 10 = 180
y + 110 = 180 subtract 110 from both sides
y = 70
Given that x : 3 : 9/2 = 15/4 : 4 1/2 : y, find the value of x and y.
Answer:
x = [tex]\frac{5}{2}[/tex] , y = [tex]\frac{27}{4}[/tex]
Step-by-step explanation:
Equate the first 2 parts of the ratios on both sides of the equation and solve for x.
Expressing the ratios in fractional form, then
[tex]\frac{x}{3}[/tex] = [tex]\frac{\frac{15}{4} }{\frac{9}{2} }[/tex] = [tex]\frac{15}{4}[/tex] × [tex]\frac{2}{9}[/tex] = [tex]\frac{5}{6}[/tex] ( cross- multiply )
6x = 15 ( divide both sides by 6 )
x = [tex]\frac{15}{6}[/tex] = [tex]\frac{5}{2}[/tex]
-----------------------------------------------------------------------------------
Equate the last 2 parts of the ratios on both sides and solve for y
[tex]\frac{\frac{9}{2} }{y}[/tex] = [tex]\frac{3}{\frac{9}{2} }[/tex] = 3 × [tex]\frac{2}{9}[/tex] = [tex]\frac{2}{3}[/tex] ( cross- multiply )
2y = [tex]\frac{9}{2}[/tex] × 3 = [tex]\frac{27}{2}[/tex] ( divide both sides by 2 )
y = [tex]\frac{27}{4}[/tex]
Write an equation of the line that is parallel to the given line and passes through the given point.
1. y=2x+1; (0,4)
2. y= -x-3; (0,7)
3. y=-8x +9; (0,-2)
On a piece of paper, graph y+ 2[tex]\leq[/tex] 1/4 x-1. Then determine which answer choice matches the graph you drew.
Answer:
Graph A
Step-by-step explanation:
find the measure of the indicated angle to the nearest degree
[tex]\boxed{\sf sin\Theta=\dfrac{P}{H}}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=\dfrac{16}{26}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=\dfrac{8}{13}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=0.5[/tex]
Convert to p/q form[tex]\\ \sf\longmapsto sin\Theta=\dfrac{5}{10}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=\dfrac{1}{2}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=sin30[/tex]
[tex]\\ \sf\longmapsto \Theta\approx30°[/tex]
It’s 11 but I need help
A,12/15=4/5
B,20/25=4/5
C,25/30=5/6
D,28/35=4/5
=> C
Rewrite the following fractions with a denominator of 24.
1/3
2/8
1/2
5/12
5/6
5/1
3/4
7/8
Answer:
or,
3/4×2/3=6/8
or, 3/4×3/3=9/12
Answer:
1/3, 2/81/2,5/125/6,3/4Step-by-step explanation:
1/3×2/8=2/24
1/2×5/12=5/42
5/6×3/4=15/24
Hope it is helpful to you
I neeeddddd helppppp it’s urgenttttttt!!!!!!!!
Answer:
x=7
Step-by-step explanation:
The sum of the arc of a circle is 360 degrees
85+5x+5+10x+5+-7+6x+6+17x = 360
Combine like terms
38x+94=360
Subtract 94 from each side
38x+94-94 = 360-94
38x = 266
Divide each side by 38
38x/28 = 266/38
x = 7
a teacher writes the following product on the board (3x) (x^2+6) = 3x^3 + 18x Eduardo says that 3x^3 + 18x is a factor of 3x
Your answer is attached above. hope it helps
7. Which dimensions result in the minimum perimeter for a rectangle with area 42.0 cm2?
a. l = 9.00 cm, w = 4.67 cm c. l = 1.00 cm, w = 42.00 cm
b. l = 5.00 cm, w = 8.40 cm d. l = 6.48 cm, w = 6.48 cm
8. The minimum perimeter occurs when the rectangle is a _____.
a. quadrilateral c. parallelogram
b. triangle d. square
9514 1404 393
Answer:
7. d. l = 6.48 cm, w = 6.48 cm
8. d. square
Step-by-step explanation:
For a given area, the perimeter can always be shortened by reducing the length of the long side and increasing the length of the short side. When you get to the point where you can't do that, then you have the minimum perimeter. You will reach that point when the sides are the same length: the rectangle is a square.
__
7. In light of the above, the best dimensions are √42 ≈ 6.48 cm for length and width.
__
8. In light of the above, the shape is a square.
_____
The attached graph shows the length of one side (x) and the associated perimeter. The other side is 42/x, which will also be 6.48.
due to Deepavali or TV is sold for rupees 14900 after allowing a discount of 23% what is the Marked price
Answer:
Correct option is
C
Rs.8000
SP=xRs
CP=(0.8x+600)Rs
P%=14
7
2
%
SP=
100
CP(100+P%)
x=
100
(0.8x+600)(100+
7
100
)
x=
7×100
(0.8x+600)(800)
700x=640x+480,000
x=8,000
Lydia runs an experiment to determine if a coin
Please help I will give brainliest to whoever helps
Answer:
A = x + 15
B = 1 + 2
Step-by-step explanation:
x 2 + 17x + 30
x2 + 15 x + 2x + 30
1 ( x + 15 ) + 2 ( x + 15 )
( x + 15 ) ( 1 + 2 )
Hope this answer helps you :)
Have a great day
Mark brainliest
Which of the following is a parent function?
O A. f(x) = e*
O B. f(x) = 2.34
O x
C. f(x) = x4 +3
O D. f(x) = 2e2x
Answer:
[tex]f(x) = e^x[/tex]
Step-by-step explanation:
Given
Options (a) to (d)
Required
Which is a parent function
A parent function is such that has a single term without coefficients
From the list of given options
[tex]f(x) = e^x[/tex] suits the above definition
Other options (b) to (d) either have coefficients, or have multiple terms
I want a simple explanation on how to get the answer to this question not just the answer.
Help!! ASAP!! THANKS AND NO FILES!! It's also on Khan academy!!
Answer: 44
Step-by-step explanation:
Sum of all angles is 180 so it is 103+33+x = 180.
so, it is 136+x = 180
x = 180-136 => 44
câu 1: cho hình chóp S.ABC có đáy là tam giác đều cạnh bằng a, cạnh bên SB vuông góc với mặt phẳng (ABC) , SB =2a. Tính thể tích khối chóp S.ABC
Câu 2: Cho hình chóp S.ABC với SA, SB,SC đôi một vuông góc và SA=SB=SC +a . TÍnh thể tích của khối chóp S.ABC.
Answer:
[tex]\frac{\sqrt{3}}{6} a^{3}[/tex] và [tex]\frac{a^{3} }{6}[/tex]
Step-by-step explanation:
Câu 1: V = 1/3.2a.[tex]\frac{\sqrt{3}}{4}[/tex][tex]a^{2}[/tex] = [tex]\frac{\sqrt{3}}{6} a^{3}[/tex]
câu 2: Theo đề bài ta có SA là chiều cao và tam giác đáy SBC vuông tại S (hình chóp S.ABC đổi thành chóp A.SBC)
=> V = 1/3 SA.(diện tích tam giác SBC) = 1/3a.[tex]\frac{a^{2} }{2}[/tex] = [tex]\frac{a^{3} }{6}[/tex]
the sum of the following algebraic expression 2x + 15, 7-8x and 3x - 41 is 30 find the value of x..
[tex] \\ \tt \longmapsto2x + 15 + 7 - 8x + 3x - 41 = 30 \\ \\ \tt \longmapsto 2x - 8x + 3x + 15 + 7 - 41 = 30 \\ \\ \tt \longmapsto - 3x - 19 = 30 \\ \\ \tt \longmapsto 3x + 19 = - 30 \\ \\ \tt \longmapsto 3x = - 30 -19 \\ \\ \tt \longmapsto 3x = - 49 \\ \\ \tt \longmapsto x = - \frac{49}{3}[/tex]
Answer:
Step-by-step explanation:
2x + 15 + 7 - 8x + 3x - 41 = 30
2x - 8x + 3x + 15 + 7 - 41 = 30
Combine like terms
-3x - 19 = 30
Add 19 to both sides
-3x = 30 + 19
-3x = 49
Divide both sides by (-3)
x = 49/-3
x = -[tex]16\frac{1}{3}[/tex]
With the given information, which of these conclusions is reasonable? A.Town A and Town B had the same low temperatures. B.The temperatures in each town were the same every day. C.The mean low temperatures in Town A and Town B were the same. D.The variability of temperatures in Town A and Town B was the same.
Answer:
A. Town A and Town B had the same low temperatures.
Step-by-step explanation:
The towns both A and B had low temperatures is shown by the same rate of low temperatures.
Find the length of y. Assume the triangles are similar.\
A. 3.6
B. 3.2
C. 3.9
D. 3.4
6,3:y=4,2:2,4
y=3,6
Chọn a
