Answer:
[tex]k \approx 5$ units[/tex]
Step-by-step explanation:
In Triangle JKL
[tex]\angle K=120^\circ\\\angle L=40^\circ\\KL=2\\JL=k[/tex]
We want to determine the approximate value of k using the law of sines.
[tex]\angle J+\angle K+\angle L=180^\circ $ (Sum of angles in a \triangle)\\\angle J+120^\circ+40^\circ=180^\circ \\\angle J=180^\circ-(120^\circ+40^\circ)=20^\circ[/tex]
Using Law of Sines
[tex]\dfrac{k}{\sin K} =\dfrac{j}{\sin J} \\\dfrac{k}{\sin 120} =\dfrac{2}{\sin 20} \\k=\sin 120 \times \dfrac{2}{\sin 20}\\k=5.06\\k \approx 5$ units[/tex]
Answer:
5.1
Step-by-step explanation:
Right on EDU
I need help with finding the surface area of the prism
Answer:May be 12
Step-by-step explanation:
Answer: The surface area of the rectangular prism is 114 cm^2.
Step-by-step explanation:
1) Formula: A = 2wl + 2lh + 2hw
( W=width, l= length, h=height)
2) Plug it in: A=2(3)(8) + 2(8)(3) + 2(3)(3)
3) A= 2( 24) + 2(24) + 2(9)
4) A= 48+ 48+ 18= 114
6,666,666×666,666 /1+2+3+4+5+6+5+4+3+2+1 − 777,777×777,777/1+2+3+4+5+6+7+6+5+4+3+2+1
Answer:
111111 [tex]\times[/tex] 1111110 is the simple expression.
Step-by-step explanation:
The expression to be solved:
[tex]\dfrac{6,666,666\times666,666 }{1+2+3+4+5+6+5+4+3+2+1} - \dfrac{777,777\times777,777}{1+2+3+4+5+6+7+6+5+4+3+2+1}[/tex]
First of all, let us solve the first term:
[tex]\dfrac{6,666,666\times666,666 }{1+2+3+4+5+6+5+4+3+2+1}\\\Rightarrow \dfrac{6666666\times666666 }{36}\\\Rightarrow \dfrac{6666666\times666666 }{6\times 6}\\\Rightarrow 1111111\times 111111[/tex]
Now, the right term:
[tex]\dfrac{777777\times777777}{1+2+3+4+5+6+7+6+5+4+3+2+1}\\\Rightarrow \dfrac{777777\times777777}{49}\\\Rightarrow \dfrac{777777\times777777}{7 \times 7}\\\Rightarrow 111111 \times 111111[/tex]
So, the expression to be solved becomes:
[tex]1111111\times 111111-111111\times 111111\\\Rightarrow 111111(1111111-1)\\\Rightarrow 111111\times 1111110[/tex]
help me pls!! Ill so grateful!! TYSM!
Answer:
Hey there!
We want to change the equation for each line into slope intercept form, or y=mx+b form.
Luckily, the first one is already in slope intercept form.
The second line can be converted to: y=-3/4x-7/4.
The third line can be converted to: -8y=-6x+4, or y=3/4x-1/2
Line one and line two are neither perpendicular or parallel.
Line one and line three are perpendicular.
Lines two and three are neither perpendicular or parallel.
This is because parallel lines have same slope, and perpendicular lines have opposite reciprocal slopes.
Hope this helps :)
Answer:
Line 1 and Line 2: Neither
Line 1 and Line 3: Perpendicular
Line 2 and Line 3: Neither
Step-by-step explanation:
To make the answering process easier, begin by converting each formula into the format y = mx +b:
Line 1: y = -4/3x + 1 (already in format)
Line 2:
-4y = 3x + 7
Divide all terms by -4:
y = -3/4x - 7/4
Line 3:
6x - 8y = 4
Subtract both sides by 6x:
-8y = -6x + 4
Divide all terms by -8:
y = 3/4x - 1/2
We can determine the relationships of the lines:
Line 1 and Line 2: Neither. They do not have the same slope, and they are not opposite reciprocals of each other.
Line 1 and Line 3: Perpendicular. The slopes of each line are opposite reciprocals: (-4/3 and 3/4)
Line 2 and Line 3: Neither. The slopes are the same but one is negative.
James is contemplating an investment opportunity represented by the function A(t)=P(1.06)t, where P is the initial amount of the investment, and t is the time in years. If James invests $5000, what is the average rate of change in dollars per year (rounded to the nearest dollar) between years 15 and 20?
Answer:
Average rate of change in dollars per year between years 15 to 20 is:
$5300 per year.
Step-by-step explanation:
Given that:
Initial Investment, P = $5000
Formula:
[tex]A(t) = P(1.06)t[/tex]
To find: If James invests $5000,
average rate of change in dollars per year (rounded to the nearest dollar) between years 15 and 20=?
Solution:
First of all, let us find out A(15) and A(20):
Putting t = 15 first,
[tex]A(15) = 5000(1.06)\times 15 ....... (1)[/tex]
Putting t = 20,
[tex]A(20) = 5000(1.06)\times 20 ....... (2)[/tex]
Average rate of change / year is defined as:
[tex]\dfrac{\text{Change in value of A}}{\text{Number of years}}[/tex]
So, required rate of change:
[tex]\dfrac{A(20)-A(15)}{5}\\\Rightarrow \dfrac{5000 \times 1.06 \times 20-5000 \times 1.06 \times 15}{5}\\\Rightarrow \dfrac{5000 \times 1.06 \times (20-15)}{5}\\\Rightarrow \dfrac{5000 \times 1.06 \times 5}{5}\\\Rightarrow 5000 \times 1.06\\\Rightarrow \$5300\ per \ year[/tex]
So, the answer is:
Average rate of change in dollars per year between years 15 to 20 is:
$5300 per year.
i mark brainliest for all my questions that are answered right :) thx for helping me
A taut string of length 10 inches is plucked at the center. The vibration travels along the string at a constant rate of c inches per millisecond in both directions. If x represents the position on the string from the left-most end, so that 0≤x≤10, which of the following equations can be used to find the location x of the vibration after 0.3 milliseconds? A. | x -5 | =0. 3 B. ∣cx−5∣=0.3 C. | x -0.3 | = 5 D. | x - 10 | =0.3c
Answer:
The correct option is
[tex]A. \ \dfrac{1}{c} \times \left | x - 5 \right | = 0.3[/tex]
Step-by-step explanation:
The parameters given are;
The length of the string = 10 inches
The speed or rate of travel of the wave = c inches per millisecond
The position on the string from the left-most end = x
The time duration of motion of the vibration to reach x= 0.3 milliseconds
The distance covered = Speed × Time = c×0.3
Given that the string is plucked at the middle, with the vibration travelling in both directions, the point after 0.3 millisecond is x where we have;
The location on the string where it is plucked = center of the string = 10/2 = 5 inches
Distance from point of the string being plucked (the center of the string) to the left-most end = 5 inches
Therefore, on the left side of the center of the string we have;
The distance from the location of the vibration x (measured from the left most end) to the center of the string = 5 - x = -(x -5)
On the right side of the center, the distance from x is -(5 - x) = x - 5
Therefore, the the equation that can be used to find the location of the vibration after 0.3 milliseconds is [tex]\dfrac{1}{c} \times \left | x - 5 \right | = 0.3[/tex] or [tex]\left | x - 5 \right | = 0.3 \times c[/tex] which gives the correct option as A
Use the graph to evaluate the function below for specific inputs and outputs.
Answer:
y = G(x) = 6, when x = -4
y = G(x) = -2, when x = 3
Step-by-step explanation:
From the attached graph tracing the first point to the graph and then to x axis.
y = G(x) = 6
as shown on the attachment(by the thick line)
y = G(x) = 6, when x = -4
From the attached graph tracing the second point to the graph and then to x axis.
y = G(x) = -2
as shown on the attachment(by the thin line)
y = G(x) = -2, when x = 3
#1 The area of a rectangular deck, in square meters, is given by the polynomial 40p^2 + 24p.
The deck is 8p meters wide
a) Find the polynomial that represents the length of the deck.
b) Find the polynomial that represents the perimeter of the deck.
#2 A cylinder has a volume of 200 mm^3 and a height of 17mm.
a) The volume formula for a cylinder is the equals v=(pi)r^2h. Isolate the variable for r in this formula.
b) using the equation where are you isolated r for part a, find the radius of the cylinder round your answer to the nearest hundredth.
PLEASE HELP even if you just answer #1 or #2 it would help i don’t have very much time.
Answer:
1.
a. 5p + 3
b. 26p + 6
2.
a r = (v ÷(pi)h)½
b. r = 3.74 to the nearest hundredth
Step-by-step explanation:
1.
Area of deck = 40p² + 24p
Width of deck = 8p
Area = length × width(breadth)
a. Area = length × width
40p² + 24p = length × 8p
Factorise out 8p from the left hand side
8p(5p + 3) = length × 8p
Divide both sides by 8p
5p + 3 = length
b Perimeter of deck = 2 (length + width)
"" = 2(5p+3 + 8p)
"" = 2 (13p + 3)
"" = 26p + 6
2.
Volume = 200 mm³
Height = 17mm
a. isolate the r in the equation v = (pi)r²h
v = (pi)r²h
Divide both sides by (pi)h
v ÷ (pi)h = r²
Take the square roots of both sides
(v ÷ (pi)h)½ = r
b. find r using your answer in a.
r = (v ÷ (pi)h)½
r = (200 ÷ ( 22/7 × 17))½
r = (200 ÷ 53.4286)
r = 3.7433
r = 3.74 to the nearest hundredth
78÷4 68÷7 98÷6
Answer me fast
Answer:
78/4=19.5, 68/7=9.71, 98/6=16.3
Step-by-step explanation:
Q2:
Which expression is equivalent to 4(x + 1) – 7(x + 3)?
A
11x + 25
B
11x – 17
C
–3x – 17
D
–3x + 25
Answer:
The expression equivalent to the given equation is -3x - 17
Step-by-step explanation:
4(x + 1) - 7(x + 3)
Distribute 4 to (x + 1) and distribute 7 to (x + 3).
4x + 4 - 7x - 21
Combine like terms.
-3x - 17
What does x(x - 2) equal?
Answer:
x^2 - 2x
Step-by-step explanation:
Distribute the x to every term in the parenthesis.
Answer:
x^2 -2x
Step-by-step explanation:
x(x - 2)
Distribute
x*x - 2*x
x^2 -2x
Solve the inequality 5(2h + 8) < 60
Step-by-step explanation:
5(2h+8) <60
10h +40< 60
10h + 40-40 < 60-40
10h < 20
10h/10 < 20/10
h < 2
What value of x is in the solution set of 2x-3> 11 - 5x?
-3
2
Answer:
x >2
Step-by-step explanation:
2x-3> 11 - 5x
Add 5x to each side
2x+5x-3> 11 - 5x+5x
7x -3 > 11
Add 3 to each side
7x-3+3 > 11+3
7x >14
Divide by 7
7x/7 > 14/7
x >2
A hiker is climbing down a valley. He stops for a water break 4 times. Between each break, he descends 15 meters. How many meters did he descend? Ju Chan answered the question by writing the following: 4(−15) meters = −60 meters. Which word in the problem indicates that a negative number should be used?
Answer:
"descends"
Step-by-step explanation:
(just had the same question).
I will mark brainiest if correct Let f(x)=5x−7 and g(x)=x+3. Find f(g(x)) and g(f(x)).
Step-by-step explanation:
f(g(x))= 5(g(x))- 7 = 5(x+3) - 7 = 5x +8
g(f(x)) = f(x) +3 = 5x -7 +3= 5x -4
5. Solve 2(1 - x) > 2x.
a. x > 2
b. x < 2
c. x < 0.5
d. x > 0.5
Answer:
I do not know for sure but i think it might be B.
Step-by-step explanation:
Im not the smartest so yeah hopefully that is the answer you are looking for tho :D
geometry question please help
Answer:
see below
Step-by-step explanation:
Alright, geometric probability.
We need to find
the area of the rectanglethe area of the equilateral triangle the area of the square the area of the part of the circle that does not include the squareand the area of the part of the rectangle that does not include the square, circle, or triangle.To find those, we need to find the areas of:
the outer rectanglethe circlethe equilateral trianglethe squareLet's start off with the easiest figure. The circle.
The circle has a radius of 10. Therefore, its area is is π[tex]r^2[/tex]. 100π is roughly 314.159265.
The circle has an area of around 314.159265.
Half of the diagonal of the square is 10m. That means that the full diagonal of the square is 20 m.
Formula for side of square using diagonal:
a = q / √2
20/√2 = 14.142135623731
The area of a square is a^2
14.142135623731^2= 200
The area of the square is 200 m^2. (28)
Using this, and the area of the circle, we can find the area of the part of the circle that does not include the square.
314.159265 - 200= 114.159265
The area of the part of the circle that does not include the square is 114.159265.
Now, the most important calculation (because it lets us find the total area of the rectangle); the equiangular triangle.
The height of this triangle is 30m. Therefore, the area is 519.6152422706632.
The area of the equiangular triangle is 519.6152422706632.
The side length of the equiangular triangle is 34.64101615137755.
The area of the rectangle= l times w.
l = 34.64101615137755
w= 30
30 times 34.64101615137755= 1039.23048454133
The total area is 1039.23048454133.
Now that we have the denominator of our fraction (total area), lets go back to our questions.
We need to find
the area of the equilateral triangle the area of the square the area of the part of the circle that does not include the squareand the area of the part of the rectangle that does not include the square, circle, or triangle.The area of the equilateral triangle = 519.6152422706632
519.6152422706632/1039.23048454133 = .5
The geometric probability that a point chosen randomly inside the rectangle is inside the equilateral triangle is .5
The area of the square = 200
200/1039.23048454133 = 0.19245008973
The geometric probability that a point chosen randomly inside the rectangle is inside the square is 0.19245008973
The area of the part of the circle that doesn't include the square: 114.159265
114.159265/1039.23048454133= 0.10984980396
The geometric probability that a point chosen randomly inside the rectangle is inside the part of the circle that doesn't include the square is 0.10984980396
The part of the rectangle that doesn't include the square, circle or triangle.
Area of triangle = 519.6152422706632
(The triangle contains the circle and square).
1039.23048454133- 519.6152422706632 = 519.61524227067
519.61524227067 /1039.23048454133 = 0.5
The geometric probability that a point chosen randomly inside the rectangle is inside the part of the circle doesn't include the square, circle, or triangle is 0.5
Hope this helped! Let me know if I made an errors, or if my answers are incorrect.
Solve the system of equations by substituion,
-5x + y = 3
7.5x - 1.5y = 3
simplify 1/2 -1/4+1 1/2
Answer: 1 3/4
Step-by-step explanation:
Step 1: Subtraction
1/4+1 1/2
Step 2: Addition
1 3/4
Hope it helps <3
Answer:
1 3/4
Step-by-step explanation:
Simplify 1/2 -1/4+1 1/2
1/2 - 1/4 + 1 1/2 =
= 2/4 - 1/4 + 1 2/4
= 1/4 + 1 2/4
= 1 3/4
what is a other name for the set of all x-values
Answer:
its domain
Step-by-step explanation:
Answer:
i believe it is A- range.
Step-by-step explanation:
i took the quiz
Help!!!!! please!!!!!
If 3x-5=10x+9, what is 4(x+7)?
Answer: not sure
Step-by-step explanation:
Answer:
Hey there!
3x-5=10x+9
-5=7x+9
-14=7x
x=-2
4(x+7)
4(-2+7)
4(5)
20
Hope this helps :)
help me solve this please
Answer:
Center : (-2, 7)
Radius : 6
Step-by-step explanation:
If you use desmos (graphing website), you're able to plug in the the equation to find the radius and center.
Select the correct answer. What is the average rate of change of f(x), represented by the graph, over the interval [-1, 1]? A. 2 B. 3 C. 5 D. 6
Answer:
C
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [ a, b ] = [- 1, 1 ] , thus
f(b) = f(1) = 5 ← from graph
f(a) = f(- 1) = - 5 ← from graph , thus
average rate of change = [tex]\frac{5-(-5)}{1-(-1)}[/tex] = [tex]\frac{10}{2}[/tex] = 5 → C
Please answer this question now in two minutes
Answer: x=6, y=20
Step-by-step explanation:
Since ΔBCD and ΔTUS are congruent triangles, we can set the sides equal to each other.
y=2y-20 [subtract both sides by 2y]
-y=-20 [divide both sides by -1]
y=20
--------------------------------------------------------------------------------------
3x+32=9x-4 [add both sides by 4, and subtract both sides by 3x]
36=6x [divide both sides by 6]
x=6
Determine the solution to f(x) = g(x) using the following system of equations: (5 points) f(x) = 3x − 23 g(x) = −4.5x + 7
Answer:
(The solution is (4, -11).
Step-by-stp explanation:
Let f(x) = g(x) = y:
y = 3x − 23
y = -4.5x + 7 Subtract the second equation from the first to eliminate y:
0 = 7.5x - 30
7.5x = 30
x = 4
Plug this into the first equation:
y = 3(4) - 23
y = -11.
I have two U.S. coins that total 30 cents. One is not a nickel. What are the two coins?
To solve the given problem, we need to know the types of US coins. The given problem is one of the tricky problems. So lets find out
In the united states, there are six types of coins produced. Penny- 1 cent, nickel- 5 cents, dime- 10 cents, quarter- 25 cents, half dollar- 50 cents and dollar- 100 cents. So u should know these types to slove this know lets move on to the :
Answer and Explanation:
The given problem is a kind of a riddle. It is given that the total of two US coins is
30
cents.
One is not a nickel, But the other one can be a nickel=
5
cents. So, the first one coin is a quarter=
25
cents. Which gives the total
30
cents.
Therefore, the two coins are a nickel and a quarter.
Hope you understood it!!!Some one HELP PLEASE
THE ANSWER IS NOT 40,5 20 -20
Answer:
x = 20
Step-by-step explanation:
If AE is a bisector then it divides the angle in half
BAE = EAC
x+30 = 3x-10
Subtract x from each side
30 = 2x-10
Add 10 to each side
40 = 2x
Divide by 2
40/2 =2x/2
20 =x
Please help ! ;v; A coordinate plane is shown. A line passes through the point (-4,1) and through the y-axis at 4. What is the y-intercept of the line shown?
Answer:
(0, 4)
Step-by-step explanation:
The y-intercept is where the graph crosses the y-axis when x = 0. Since you are given the graph, you can see that when x = 0, the graph crosses y = 4, so our y-int is (0, 4).
HELP ME PLEASE PLEASE IM BEGGING
Answer:
The solution is the triplet: (a, b, c) = (-3, 0, 0)
Step-by-step explanation:
Let's start with the second equation, and solving for "a":
a - b = -3
a = b - 3
Now replace this expression for a in the third equation:
2 a + b = -6
2 (b - 3) +b = -6
2 b - 6 +b = -6
3 b = -6 +6
3 b = 0
b = 0
So if b = 0 then a = 0 - 3 = -3
now we can replace a= -3, and b = 0 in the first equation and solve for c:
2 a - b + c = -6
2 ( -3) - 0 + c = -6
-6+ c = -6
c = -6 + 6
c = 0
Our solution is a = -3, b= 0 , and c = 0 which can be expressed as (-3, 0, 0)