1. Potential Energy = mgh
h = U_g / (mg) = 14 / (17 * 9.81) = 0.084 m above the ground.
2. Kinetic Energy = 1/2 mv^2
m = 2K_e / (v^2) = 2.45 kg
3. U_g = mgh = (1200)(9.81)(24) = 282528 J
4. U_g = mgh = (478)(9.81)(150) = 703377 J
5. U_g = mgh = (100)(9.81)(12.5) = 12262.5 J
6. h = U_g / (mg) = 14 / (17 * 9.81) = 0.084 m above the ground.
7. m = U_g / (gh) = 1500 / (9.81 * 35) = 4.37 kg
Evaluate if m = 16 and p = 2. 1/2m + 3p A) 10 B) 14 C) 18 D) 48
Answer:
B) 14
Step-by-step explanation:
We can plug in the values of m and p into the equation:
1/2 m + 3p = 1/2 (16) + 3 (2) = 8 + 6 = 14.
Find the midpoint of the segment with the following endpoints.
(6,4) and (9,1)
Answer:
[tex]=\left(\frac{15}{2},\:\frac{5}{2}\right)[/tex]
Step-by-step explanation:
[tex]\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)\\\\\left(x_1,\:y_1\right)=\left(6,\:4\right),\:\left(x_2,\:y_2\right)=\left(9,\:1\right)\\\\=\left(\frac{9+6}{2},\:\frac{1+4}{2}\right)\\\\=(\frac{15}{2} , \frac{5}{2} )\\\\[/tex]
4x=x+18 solve for x
Answer:
X = 6
Step-by-step explanation:
Subtract 1 x from both sides so the equation will be 3x = 18. Then divide 3x by 3 and 18 by 3 to get 6
Answer: [tex]x=6[/tex]
Subtract x from both sides
[tex]4x-x=x+18-x\\3x=18[/tex]
Divide both sides by 3
[tex]3x=3=18/3\\x=6[/tex]
What are the possible values of x and y for two distinct points, (5, –2) and (x, y), to represent a function? The value of x can be .
Answer:
x ≠ 5
Step-by-step explanation:
For the two points to represent a function, the value of x cannot be repeated. The only restriction on the values of x and y is that x is not 5. (x can be anything but 5.)
Answer:
The value of x can be
✔ any real number except 5
.
The value of y can be
✔ any real number
Step-by-step explanation:
i got it correct on edguinty
1. Find the cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of ₹ 3 per m². 2. Find the area of the isosceles triangle whose perimeter is 11 cm and the base is 5 cm. 3. Find the area of the equilateral triangle whose each side is 8 cm. 4. The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. Find the area of the triangle.
1. Find the cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of ₹ 3 per m².
a = 51 m, b = 37 m, c = 20 m
semiperimeter: p = (51+37+20):2 = 54 m
Area of triangle:
[tex]A=\sqrt{p(p-a)(p-b)(p-c)}\\\\A=\sqrt{54(54-51)(54-37)(54-20)}\\\\A=\sqrt{54\cdot3\cdot17\cdot34}\\\\A=\sqrt{9\cdot2\cdot3\cdot3\cdot17\cdot17\cdot2}\\\\A=3\cdot2\cdot3\cdot17\\\\A=306\,m^2[/tex]
Rate: ₹ 3 per m².
Cost: ₹ 3•306 = ₹ 918
2. Find the area of the isosceles triangle whose perimeter is 11 cm and the base is 5 cm.
a = 5 cm
a+2b = 11 cm ⇒ 2b = 6 cm ⇒ b = 3 cm
p = 11:2 = 5.5
[tex]A=\sqrt{5.5(5.5-3)^2(5.5-5)}\\\\ A=\sqrt{5.5\cdot(2.5)^2\cdot0.5}\\\\ A=\sqrt{11\cdot0.5\cdot(2.5)^2\cdot0.5}\\\\A=0.5\cdot2.5\cdot\sqrt{11}\\\\A=1.25\sqrt{11}\,cm^2\approx4.146\,cm^2[/tex]
3. Find the area of the equilateral triangle whose each side is 8 cm.
a = b = c = 8 cm
p = (8•3):2 = 12 cm
[tex]A=\sqrt{12(12-8)^3}\\\\ A=\sqrt{12\cdot4^3}\\\\ A=\sqrt{3\cdot4\cdot4\cdot4^2}\\\\A=4\cdot4\cdot\sqrt{3}\\\\A=16\sqrt3\ cm^2\approx27.713\ cm^2[/tex]
4. The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. Find the area of the triangle.
a = 2x
b = 3x
2x + 2•3x = 32 cm ⇒ 8x = 32 cm ⇒ x = 4 cm ⇒ a = 8 cm, b = 12 cm
p = 32:2 = 16 cm
[tex]A=\sqrt{16(16-8)(16-12)^2}\\\\ A=\sqrt{16\cdot8\cdot4^2}\\\\ A=\sqrt{2\cdot8\cdot8\cdot4^2}\\\\ A=8\cdot4\cdot\sqrt2\\\\ A=32\sqrt2\ cm^2\approx45.2548\ cm^2[/tex]
Use the properties of logarithms to expand the following expression as much as possible. Simplify any numerical expressions that can be evaluated without a calculator.
log4(2x2 - 20x + 12y)
Answer:
[tex]f(x,y) = \log_{4} (x-5-\sqrt{25-6\cdot y})+\log_{4} (x-5+\sqrt{25-6\cdot y})[/tex]
Step-by-step explanation:
Let be [tex]f(x,y) = \log_{4}(2\cdot x^{2}-20\cdot x +12\cdot y)[/tex], this expression is simplified by algebraic and trascendental means. As first step, the second order polynomial is simplified. Its roots are determined by the Quadratic Formula, that is to say:
[tex]r_{1,2} = \frac{20\pm \sqrt{(-20)^{2}-4\cdot (2)\cdot (12\cdot y)}}{2\cdot (2)}[/tex]
[tex]r_{1,2} = 5\pm \sqrt{25-6\cdot y}[/tex]
The polynomial in factorized form is:
[tex](x-5-\sqrt{25-6\cdot y})\cdot (x-5+\sqrt{25-6\cdot y})[/tex]
The function can be rewritten and simplified as follows:
[tex]f(x,y) = \log_{4} [(x-5-\sqrt{25-6\cdot y})\cdot (x-5+\sqrt{25-6\cdot y})][/tex]
[tex]f(x,y) = \log_{4} (x-5-\sqrt{25-6\cdot y})+\log_{4} (x-5+\sqrt{25-6\cdot y})[/tex]
What is the solution set to the inequality 1 + 7x + 5x< 13?
Answer:
[tex]x<1[/tex]
Step-by-step explanation:
So we have the inequality:
[tex]1+7x+5x<13[/tex]
First, combine like terms:
[tex]1+12x<13[/tex]
Subtract 1 from both sides:
[tex]12x<12[/tex]
Divide both sides by 12:
[tex]x<1[/tex]
And that's our answer :)
Answer:
Step-by-step explanation:
12x + 1 < 13
12x < 12
x < 1
A second number is 9 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 760, find the numbers. The three numbers are (Use a comma to separate answers as needed.)
Express 0.2 degrees without decimals
Write 100 as a product of prime factors
Prime factorization of 100 is 2 * 2 * 5 * 5
100 as a product of prime factors will be 2 ×2×5×5 .
Given,
Number = 100
Now,
To write 100 as prime factor product ,
Take LCM of 100
LCM 100 = 2 ×2×5×5
Thus the factors obtained in the LCM is prime factors only .
So we can write 100 as the product of prime factors:
100 = 2 ×2×5×5
Know more about prime factors,
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A bulb after certain testing had a life of 25 months. The standard deviation based on this sample of size one is
Answer:
25 monthsStep-by-step explanation:
Using the formula for calculating the standard error of the mean to get the standard deviation. The standard error of the mean is expressed as;
SE = S/√n where;
S is the standard deviation
n is the sample size
Given SE = 25 months and n = 1, on substituting this parameters into the formula, we will have;
25 = S/√1
25 = S/1
cross multiply
S = 25*1
S = 25 months
Hence the standard deviation based on the sample is 25 months
What is the domain of the function? f(x)=[tex]\frac{x-3}{2x^{2}+x-21 }[/tex] (−∞,3)∪(3,∞) (−∞,−3)∪(−3,72)∪(72,∞) (−∞,−72)∪(−72,∞) (−∞,−72)∪(−72,3)∪(3,∞)
Answer:
(−∞,−7/2)∪(−7/2,3)∪(3,∞)
Step-by-step explanation:
(x-3)
----------------
2x^2 +x -21
First factor the denominator
(x-3)
----------------
( 2x +7) (x-3)
The domain is restricted when the denominator goes to zero
2x+7 =0 x-3 =0
2x = -7 x-3=0
x = -7/2 x =3
This two points are not in the domain
(−∞,−7/2)∪(−7/2,3)∪(3,∞)
If a student is selected at random, what is the
probability that the student is a graduate
(rounded to the nearest percent)? [? ]%
Answer: 24%
Step-by-step explanation:
There are a total of 2610 graduates and if that is the divided by the total which is 10730 you will get 0.2432 which is about 24%
Answer:
24%
Step-by-step explanation:
I checked it on the test to make sure, I have acellus too.
F(x)=x^2+7x-30
Find the intercepts, domain and range
Answer:
domain (-inf, +inf)
range [-30, +inf)
y-int = -30
x-int = -10, 3
Step-by-step explanation:
A pack of paper costs $3.75, including tax. Mr. Cooper wants to purchase packs of paper for his class and has a $20 budget. Write an inequality to solve for the number of packs of paper Mr. Cooper can purchase.
Answer:
($3.75)n ≤ $20
Step-by-step explanation:
Represent this number by n. Then the total purchase price can be represented by ($3.75)n ≤ $20, which is appropriate because Cooper can't spend more than $20.
The desired inequality is ($3.75)n ≤ $20. If a solution is desired, divide both sides by $3/75):
$20
n ≤ ______ = 5 1/3.
$3.75
Cooper can purchase up to 5 whole packs of paper and have a bit of money left over.
Use back substitution to solve this problem
Answer:
z = -5
y = 1
x = 4
Step-by-step explanation:
2z = -10 ➡ z = -5
4y -(-5) = 9 ➡ 4y = 4 and y = 1
2x + 3 + (-5) = 6 ➡ 2x = 8 and x = 4
Which is equivalent to3/4
Answer:
75%
Step-by-step explanation:
Answer:
6/8
Step-by-step explanation:
An easy way to do this is to draw a giant rectangle. when you do you simply want to stay a line going straight across in the middle. draw 3/4 ontop and 6/8 on the bottom. or another fraction that's close to it. then shade in 3/4 and the same with 6/8. if the shading is the same length, that's how you know it's equivalent
What is the area of a table with a diameter of 28 inches? How did you figure it out? pls help i need the answer asap
Answer:
The answer is 615 inches
Step-by-step explanation:
The formula for solving the area of a circle is :
A= 1/4 π d^2
So since we only know the diameter the formula would be:
A= 1/4 of 3.14 x 28^2
The first thing you need to do is square 28 which is 784Them times 784 by 3.14 which is 2461.76After all that, your equation should look like this: A = 1/4 of 2461.76So then you would times 2461.76 by 1/4 which is 615.75216 or 615.75Hope this helped :)
A drama club has 22 members. Each member pays monthly dues of $18. On the first day of the month, 6 members paid their dues. The remaining members paid their dues on the second day of the month. How much money was collected in dues on the second day of the month?
Answer:
$288
Step-by-step explanation:
Please help........................
Answer:
a. (0,0), (2,0), (4,0)
b. (0,0)
Step-by-step explanation:
To find the x-intercept points, you set the equation equal to 0.
0=x³-6x²+8x [factor out an x]
0=x(x²-6x+8) [factor (x²-6x+8)]
0=x(x-2)(x-4) [set each factor equal to 0]
x=0
x-2=0 [add both sides by 2]
x=2
x-4=0 [add both sides by 4]
x=4
Now, we know our x-intercept points: (0,0), (2,0), (4,0).
To find the y-intercept points, we know that it is located on the y-axis, meaning x=0. We plug in 0 for x, and we will know our y-intercept point.
y=(0)³-6(0)²+8(0) [multiply]
y=0
The y-intercept point is (0,0).
Two lines intersect in a plane in form for angles what are the angles formed fathers intersect is a 53° angle what are the measures of the other three angles explain your answer
Answer:
53°, 127°, 127°
Step-by-step explanation:
Two intersecting lines form two pairs of angles:
Pair of vertical angles. They are opposite to each other and are equalPair of adjacent angles which are supplementary angles and their sum is 180°So if one of the angles is measured 53°, then the other angles are:
53°- vertical angle with the first one180° - 53° = 127°180° - 53° = 127°6. b. In the figure, suppose CD = 11.5 cm, DE = 5.3 cm, and the
perimeter of the figure is 73.8 cm.
What is GE?
Answer:
GE = 11 cm.
Step-by-step explanation:
The figure provided is attached below.
The information given is:
CD = 11.5
DE = 5.3
BC = 8
AH = 11
Perimeter = 73.8
BC = FG = EF
HA = GH
AB = GE
The perimeter of any figure is the sum of all its sides.
The perimeter of the figure provided is:
Perimeter = AB + BC + CD + DE + EF + FG + GH + HA
Perimeter = AB + BC + CD + DE + BC + BC + HA + HA
[tex]73.8=AB+8+11.5+5.3+8+8+11+11[/tex]
[tex]73.8=AB+62.8[/tex]
[tex]AB=11[/tex]
The value of side AB is 11 cm.
Then the value of GE is also 11 cm.
Find the coordinates of the midpoint of a segment with the endpoints M(6, −41) and N(−18, −27). Then find the distance between the points.
Answer:
Midpoint is (-6,-34)
Step-by-step explanation:
(6+(-18))/2. (-41+(-27))/2
-12/2. (-68)/2
-6. , - 34
Distance =(6--18)^2 +(-14--27)^2
23^2. +13^2
529 +169
= 698
So u will find the square root of 698
The ans u get is the distance
The answer to 48:(4+4)
Answer:
6:1
Step-by-step explanation:
48:( 4+4 )
= 48:8
= 6:1
How does the value of the 8 in 20,831 compare to the value of the 8 in 20,381?
Answer:
The eight in the first number is ten times larger than the eight in the second number.
I WILL MARK BRAINIEST PLEASE HELP ME ON THIS QUESTION
Lulu Ruby and Emma went shopping went a total of £261. Each of them had different amount of money. Lulu spent 2/3 of her money Ruby spent 1/2 of her money and Emma spent 3/4 of her money. Each of them spent the same amount of money.how much did money did they begin with?
Answer:
Lulu's money = £81
Ruby's money= £108
Emma's money= £72
Step-by-step explanation:
Let
Lulu's money = x
Ruby's money= y
Emma's money= z
x+y+z= 261
Lulu spent 2/3 of her money Ruby spent 1/2 of her money and Emma spent 3/4 of her money.
2/3x = 1/2y= 3/4z
2/3x= 1/2y
4/3x= y
2/3x= 3/4z
8/9x= z
x+y+z= 261
x+4/3x+8/9x= 261
9x+12x+8x= 2349
29x= 2349
X= 81
4/3x= y
4/3(81) =y
108= y
8/9x= z
8/9(81)= z
72= z
Answer:
Step-by-step explanation:
Each of them had different amount of money. Lulu spent 2/3 of her money Ruby spent 1/2 of her money and Emma spent 3/4 of her money.
1 answer
·
Top answer:
Answer:Lulu= £81Ruby=£108Emma=£ 72
There are five members on a student council. Two of these members will serve on a spring formal committee. How many possible spring formal committees are there
Answer:
10
Step-by-step explanation:
Given that:
There are a total of 5 members on a student council.
2 of these members will serve in Spring Formal Committee.
To find:
How many possible spring formal committees can be there ?
Solution:
If the observe this problem closely, we are actually asked nothing but the number of ways to select 2 members out of 5.
This is a simple selection problem in which we have to find the number of ways to select [tex]r[/tex] objects out of [tex]n[/tex].
The number of ways = [tex]_nC_r =\frac {n!}{r!(n-r)!}[/tex]
Here,
[tex]n = 5\\r=2[/tex]
Hence, the required number of ways are:
[tex]_5C_2 =\frac {5!}{2!(5-2)!}\\\Rightarrow \dfrac {5!}{2!3!} = \dfrac {5\times 4\times 3!}{2!3!}\\\Rightarrow \dfrac {5\times 4}{2} = \dfrac{20}{2}\\\Rightarrow \bold{10}[/tex]
So, the number of possible spring formal committees are 10.
Find the approximate side length of a square game board with an area of 131 in2.
Answer:
11.4
Step-by-step explanation:
You find the square root
Write an equation of the line that passes through the points (1,-4) and (2,-1).
An equation of the line is y=
]
PLEASE HELP!!
Answer:
y = 3x -7
Step-by-step explanation:
The 2-point form of the equation of a line is useful for this.
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (-1 -(-4))/(2 -1)(x -1) -4
y = 3(x -1) -4
y = 3x -7
What is the value of x & y?
Answer:
x=23, y=14
Step-by-step explanation:
The triangles are indeed simular