Answer:
The slope is 1/2. The x-intercept is (2,0). The y-intercept is (0,-1)
Answer:
The slope is 1/2x and -1 is the (y) intercept
Step-by-step explanation:
Since y= 1/2x - 1 is already a linear equation (y=mx+b) you can use y=mx+b to find the slope and (y) intercept.m is the slope and b is the intercept
A particle P of weight 20 N is suspended by two strings AP and BP. The tension in string AP is (ai+8j)
and the tension in string BP is (6i+bj)
The value of a is?
And the value of b is?
The magnitude of the tension in string AP is?
The angle that string BP makes with the vertical is?
Give your answers as exact whole numbers or as decimals to 3 s.f.
Answer:
i. a = -6 ii. b = 12 iii. 100 iv. 26.6°
Step-by-step explanation:
Since the weight of the object is 20 N and directed downwards, its vector is -20j. Now, since the particle is in suspension, AP + BP = -20j
So, since AP = ai + 8j and BP = 6i + bj,
AP + BP = -20j
ai + 8j + 6i + bj = -20j
ai + 6i + 8j + bj = -20j
(a + 6)i + (8 + b)j = -20j
(a + 6)i + (8 + b)j = 0i - 20j
equating the components on both sids,
a + 6 = 0 and 8 + b = 20
a = -6 and b = 20 - 8 = 12
i. The value of a is -6
ii. The value of b is 12
iii. The magnitude of the tension in string AP is?
since AP = ai + 8j = -6i + 8j
magnitude of AP = √[-6² + 8²] = √[36 + 64] = √100 = 10
iv. The angle that string BP makes with the vertical is?
Since BP = 6i + bj = 6i + 12j, the angle it makes with the horizontal is Ф = tan⁻¹(12/6) = tan⁻¹(2) = 63.44°.
Thus, the angle it makes with the vertical is thus 90° - 63.44° = 26.56° (complementary angles) ≅ 26.6° to 3 s.f
1) The values of a and b of the given vectors are respectively; -6 and 12
2) The magnitude of the tension in string AP is; 10
3) The angle that string BP makes with the vertical is; 26.6°
What is the magnitude of the tension?
We are told that the weight of the particle P is 20 N. Since the particle is suspended by two strings, then its' direction is downwards and as such its vector is -20j.
By equilibrium;
AP + BP = -20j
1) We are given the tension vectors;
AP = ai + 8j and BP = 6i + bj,
Thus;
ai + 8j + 6i + bj = -20j
(ai + 6i) + (8j + bj) = -20j
(a + 6)i + (8 + b)j = -20j
(a + 6)i + (8 + b)j = 0i - 20j
Equating the components of both sides gives;
a + 6 = 0 and 8 + b = 20
Solving gives;
a = -6 and b = 20 - 8 = 12
Thus, the values of a and b are -6 and 12
2) The magnitude of the tension in string AP is gotten from resolution of the tension vector AP;
AP = ai + 8j = -6i + 8j
Thus, magnitude of AP = √(-6² + 8²) = √(36 + 64) = √100 = 10
3) The angle that string BP makes with the vertical is gotten from;
BP = 6i + bj = 6i + 12j
Thus, the angle it makes with the horizontal;
θ = tan⁻¹(12/6) = tan⁻¹(2) = 63.44°.
Angle it makes with the vertical = 90° - 63.44° = 26.56° ≈ 26.6°
Read more about Magnitude of Tension at; https://brainly.com/question/13370981
please help will mark right answer brianlyist
Answer:
y=5/4x+10
Have a nice day.
Answer:
5/4x + 10
Step-by-step explanation:
If it's parallel, the slope will remain the same.
To find the y-intercept, you have to plug in the coordinates into the equation which is, y = 5/4x + b.
y = 5/4x + b
0 = 5/4 (-8) + b
0 = -10 + b
10 = b
The equation is 5/4x + 10.
A right rectangular prism in the shape of a shoebox is cut parallel to its bottom face. Describe the shape of its cross section.
Answer:
Step-by-step explanation:
Rectangle
Which equation, when graphed, has x-intercepts at (8,0) and (-2, 0) and a y-intercept at (0, -48)?
f(x) = -3(x – 8)(x + 2)
f(x) = -3(X + 8)(x - 2)
f(x) = 3(x-8)(x + 2)
O f(x) = 3(X + 8)(- 2)
Answer:
f(x)=-3(x-8)(x+2)
Step-by-step explanation:
f(8)=-3(8-8)(8+2)=-3×0×10=0
f(-2)=-3(-2-8)(-2+2)=-3×(-10)×0=0
f(0)=-3×(0+8)×(0+2)=-3×8×2=-48
what are the coordinates of the midpoint of segment AB with the endpoint A(-3,4) and (5,6)
Answer:
(1,5)
Step-by-step explanation:
You use the midpoint formula to solve this problem
The midpoint formula:
To solve for x: (x1+x2)÷2
To solve for y: (y1+y2)÷2
George says that an account that earns 4% interest compounded annually and an account that earns 2% interest compounded semi-annually will be worth the same if the principals are the same
Answer:
the account won't yield the same amount despite the same principal amount.
Step-by-step explanation:
To test this assertion :
Let principal = $1000
t = 1 year
Compound interest formula :
A = P(1 + r/n)^nt
P = principal ; r = rate, n = number of times interest is compounded per period ; t = time
Account A :
Rate = 4% annually
A = 1000(1 + 0.04/1)^1
A = 1000 * 1.04 = $1040
Account B:
Rate = 2% compounded semianually ; n = 12 /6 = 2
A = 1000(1 + 0.02/2)^1*2
A = 1000(1.01)^2
A = 1000 * 1.0201
A = $1020.1
From the result, the account won't yield the same amount despite the same principal amount.
5/2 divided by -1/3 PLEASE ANSWER!!
Answer:
−7 1/2
Step-by-step explanation:
1
-7 2
Answer: -0.83333333333
Step-by-step explanation:
Line L is mapped onto line M by a dilation centered at the origin with a scale factor of 3. The equation of line is 3x−y=4. Determine and state an equation for line M.
there are websites such as
mathpapa
algebra tiger - favorite
and many more that will give you the CORRECT answer and will give u a step by step explanation on how it was answered
You know the length of the garden is 12 feet. You also know that the area of the garden is 60 ft2. Write and solve an equation to determine what is the width of the garden?
Answer:
Width is 5
Step-by-step explanation:
Set up an equation
12x=60
divided both sides by 12
answer is 5
The width is 5
to check your answer multiply it by the length
12*5=60
Check Check
Answer:
60÷12=5 so the width is 5 if the length is 12.
How do I know that these are not a function?
0,-1
2,3
0,4
2,5
0,6
2,7
Answer:
there are multiple 0's in the same area, and multiple 2's.
Step-by-step explanation:
$4.00 + $2.00=
answer
If Fx) = 7x-6, which of the following is the inverse of Ax)?
O A. F'(x) = **?
0 B. F'(x) =
C. F'(x) = **
O D. F'(x) = *7
Answer:
It's C
Step-by-step explanation:
Write f(x)=7x−6f(x)=7x-6 as an equation.
Interchange the variables.
Solve for y.
man in barbados invest $12 000 into an account that pays 8.5% interest per year, compounded annually. calculate the amount of money that he will have after 3 years.
What is the constant of proportionality, y/x
Answer:
1/2
Step-by-step explanation:
Answer:
k = 0.5Step-by-step explanation:
Proportional relationship:
y = kx, where k- constant of proportionalityUsing point on the graph (1, 0.5) to find the value of k:
0.5 = k*10.5 = kk = 0.5A ship is 40 miles east and 25 miles south of port. The captain wants to sail directly to port. What bearing should be taken?
Answer:
N58°W
Step-by-step explanation:
The trigonometry diagram has been attached below :
To obtain the angle θ ;
Tan θ = opposite / Adjacent
Tan θ = 40 / 25
Tan θ = 1.6
θ = tan^-1(1.6)
θ = 57.99°
Henve, bearing directly to Port is :
N58°W
Write as a decimal: 1%
Answer:
0.01
Step-by-step explanation:
0.01×100=1
hope this helps
Answer:
0.01
Step-by-step explanation:
0.01 is the same as 1/100, and 1% is also the same as 1/100
75% of b is 12. what is b?
Answer:
16
Step-by-step explanation:
same explanation as last time accept its 3/4 into 4/3
Simplify each ratio. Remember to include the UNITS in your final answer.
1) 10 bags to 15 coats
2) 16 apples to 40 oranges
Answer:
2:3
2:5
Step-by-step explanation:
10:15
divide both sides by 5 or gcf
2:3
16:40
divide both sides by 8 or gcf
2:5
HELPPP ON GEOMETRY PLZZ!!! No links i will report.
Answer:
J) is multiplied by 4
Step-by-step explanation:
Suzy is planning to
carpet her room. Her
room measures 12
feet by 15 feet. How
many square yards of
carpeting will she
need?
I'm running out of pointssssssssss
Answer: Question 1 is m=3
Question 2 is, 6 is the intercept for the y axis. And (-4,7) is the other intercept.
Step-by-step explanation:
x² - 6x - 8
I’m confused.... help???
Answer:
(x - 2) (x - 4)
Step-by-step explanation:
-2 & -4 are a factor of -8 and a sum of -6
-2 x -4 = -8
-2 + -4 = -6
Therefore the answer is (x - 2) (x - 4)
#5 need help asap will give brainly
This might help
total surface area Stot = 42.5 ft2
lateral surface area Slat = 30 ft2
top surface area Stop = 6.25 ft2
bottom surface area Sbot = 6.25 ft2
but im thinking they would need 113.7 ft of rapping paper i many be totally wrong tho
Answer:
42.5
Step-by-step explanation:
To find how many square inches of wrapping paper he will need you need to find the area of each face of the box and add them all together.
Top and bottom face:
First, 2.5 times 2.5 equals 6.25. Multiply 6.25 times 2 since there is one for the top and bottom to get 12.5
Left, Right, front, and back face:
Multiply 2.5 by 3 to get 7.5, and multiply 7.5 by 4 to get 30 since there are four faces with the same area.
Final Step:
Now, just add all the areas of the faces calculated to recieve the answer of 42.5
30 + 12.5 = 42.5
A and B are independent events. Find P(A and B). P(A)=1/5, P(B)=3/7
Answer:
Step-by-step explanation:
help pleaseee i’ll give 100 points ❤️
Answer:
C: Translation and dilation.
Step-by-step explanation:
C: Translation and dilation.
The translation moves it to the same space while the dilation retains the shape but makes it larger/smaller.
the answer to your question is C
Paul needs to buy 5_8pound of peanuts. The scale at the store measures parts of a pound in sixteenths. What measure is equivalent to 5_8pound?
Answer:
10 ÷ 16
Step-by-step explanation:
The computation is shown below
Given that
Paul required to buy 5 by 8 pound of peanuts
And, the scale at the store is in sixteenths
So, the measure that should be equivalent is
Here the denominator should be 16 so it should be multiplied by 2
= 5 ÷ 8 × 2 ÷ 2
= 10 ÷ 16
HELP ASAP WILL MARK BRAINLIEST
The circumference of a circle is 19π m. What is the area, in square meters? Express your answer in terms of \piπ.
Answer:
90.25π
Step-by-step explanation:
The circumference of circle is 2πr, or in other words the diameter times π.
The area of a circle is πr^2.
19π is the circumference of this circle.
So, 19 is the diameter, and 9.5 the radius.
The area if (9.5^2)π.
9.5^2=90.25
So, in terms of π, the area of the circle is 90.25π.
Find the surface area of each figure. Round your answers to the nearest hundredth, if necessary
Answer:
506π ft^2
Step-by-step explanation:
here's your solution
=> height of cylinder = 12 ft
=> radius of cylinder = 11 ft
=> surface area of cylinder = 2πr(h+r)
=> SA = 2*11(12+11)*π
=> SA = 22*23π
=> SA = 506π ft^2
hope it helps
An item is regularly priced at $90. It is on sale for 40% off the regular price. How much (in dollars) is discounted from the regular price?
Answer: $36 is discounted from the regular price
Step-by-step explanation:
First, we need to take our given numbers
Originally $90
On sale for %40
Let's now use this equation
90(n)
n will equal 0.40 due to it being %40 off
90(0.40)
$36