Answer: 50.24 mm
Step-by-step explanation:
Circumference= 2πr
C = 2 x 3.14 x 8mm
C = 50.24 mm
Answer:
Step-by-step explanation:
d=16mm
therefore r=8mm
therefore circumference = 2pi r = 2* 3.14*8
=50.42cm
hope it helps
Convert -(3)^1/2 - i to polar form
Answer:
2(cos30°+isin30°)
Step-by-step explanation:
Complex value z is written in a rectangular form as z = x+iy where (x, y) is the rectangular coordinates.
On converting the rectangluar to polar form of the complex number;
x = rcosθ and y = rsinθ
Substituting in the rectangular form of the comlex number above;
z = rcosθ + irsinθ
z = r(cosθ+isinθ)
r is the modulus of the complex number and θ is the argument
r =√x²+y² and θ = tan⁻¹y/x
Given the complex number in rectangular form z = -(3)^1/2 - i
z = -√3 - i
x = -√3 and y = -1
r = √(-√3)²+(-1)²
r = √3+1
r = √4
r = 2
θ = tan⁻¹ (-1/-√3)
θ = tan⁻¹ (1/√3)
θ = 30°
Hence the complex number in polar form will be z = 2(cos30°+isin30°)
The slope-intercept form of the equation of a line that passes through point (-3, 8) is y = -2/3x + 6. What is the poin
slope form of the equation for this line?
Answer:
Step-by-step explanation:
y - 8 = -2/3(x + 3)
the solution is the 4th option
If the area of the trapezoid below is 75 square units, what is the value of x? AB=17 DC=8
A. 1.5
B. 12
C. 6
D. 3
Diagram related to the question can be found in the attached picture below :
Answer: 6 units
Step-by-step explanation:
From the diagram attached to the question:
Length AB = 17
Length DC = 8
height (h) = x
Area of trapezium = 75sq units
The Area (A) of a trapezium is given by:
(1/2) × (a + b) × h
Where ;
a and b are the upper and base lengths of the trapezium
h = height of trapezium
A = (1/2) × (a + b) × h
75 = (1/2) * (17 + 8) * x
75 = 0.5*25*x
75 = 12.5x
x = 75 / 12.5
x = 6 units
Solve 0 = 4x2+12x+9.
Select the equation that shows the correct
substitution of a, b, and c in the quadratic formula.
121 122 - 4(4309)
2(4)
X=
-12 + 122 +4(4)(9)
2(4)
o
-121 122 – 4(4)(9)
2(4)
Answer:
The correct substitution of a, b, and c in the quadratic formula is given by
[tex]$ x=\frac{-12\pm\sqrt{(12)^2-4(4)(9)}}{2(4)} $[/tex]
[tex]x = - \frac{ 3}{2} \: and \: x = -\frac{ 3}{2} \\\\[/tex]
The solutions of the given quadratic equation are real and equal.
Step-by-step explanation:
The given quadratic equation is
[tex]4x^2+12x+9 = 0[/tex]
The coefficients a, b and c are as follow:
[tex]a = 4 \\\\b = 12\\\\c = 9[/tex]
The quadratic formula is given by
[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]
The correct substitution of a, b, and c in the quadratic formula is given by
[tex]$ x=\frac{-12\pm\sqrt{(12)^2-4(4)(9)}}{2(4)} $[/tex]
Bonus:
The solution of this quadratic equation is given by
[tex]x=\frac{-12\pm\sqrt{(144 - 144)}}{8} \\\\x=\frac{-12\pm\sqrt{0}}{8} \\\\x=\frac{-12\pm 0}{8} \\\\x=\frac{-12 + 0}{8} \: and \: x=\frac{-12 - 0}{8}\\\\x= -\frac{ 3}{2} \: and \: x = -\frac{ 3}{2} \\\\[/tex]
Therefore, the solutions of the given quadratic equation are real and equal.
The number 35 has the property that when its digits are both increased by 2, and
then multiplied, the result is 5 x 7 = 35, equal to the original number.
Find the sum of all two-digit numbers such that when you increase both digits by 2,
and then multiply these numbers, the product is equal to the original number.
Answer: The sum is 127
Step-by-step explanation:
A 2-digit number N = ab can be written as (where a and b are single-digit numbers)
a*10 + b.
Now, we want that:
(a + 2)*(b + 2) = a*10 + b.
So we must find all the solutions to that equation such that a can not be zero (if a = 0, then the number is not a 2-digit number)
We have:
(a + 2)*(b + 2) = a*b + 2*a + 2*b + 4 = a*10 + b
a*b + 2*b - b + 4 = a*10 - a*2
a*b + 4 + b = a*8
a*b + 4 + b - a*8 = 0.
Now we can give one of the variables different values, and see if the equation has solutions:
>a = 1:
1*b + 4 + b - 8 = 0
2*b - 4 = 0
b = 4/2 = 2
Then the number 12 has the property.
> if a = 2:
2*b + 4 + b -16 = 0
3b -12 = 0
b = 12/3 = 4
The number 24 has the property.
>a = 3 is already known, here the solution is 35.
>a = 4.
4*b + 4 + b - 8*4 = 0
5*b + 4 - 32 = 0
5*b = 28
b = 28/5
this is not an integer, so here we do not have a solution.
>if a = 5.
5*b + 4 + b - 8*5 = 0
6b + 4 - 40 = 0
6b - 36 = 0
b = 36/6 = 6
So the number 56 also has the property.
>if a = 6
6*b + 4 + b - 8*6 = 0
7b + 4 - 48 = 0
7b - 44 = 0
b = 44/7 this is not an integer, so here we do not have any solution.
>if a = 7
7*b + 4 + b -8*7 = 0
8b -52 = 0
b = 52/8 = 6.5 this is not an integer, so we here do not have a solution.
>if a = 8
8*b + 4 + b -8*8 = 0
9*b + 4 - 64 = 0
9*b = 60
b = 60/9 this is not an integer, so we here do not have any solution:
>if a = 9
9*b + 4 + b - 8*9 = 0
10b + 4 - 72 = 0
10b -68 = 0
b = 68/10 again, this is not an integer.
So the numbers with the property are:
12, 24, 35 and 56
And the sum is:
12 + 24 + 35 + 56 = 127
Trignometry Question Please help
Answer:
19.45°
Step-by-step explanation:
Suppose the post is 1 unit high. Then the distance from the post to another corner of the rectangle will satisfy the relation ...
distance/1 = tan(90° -angle of elevation)
So, for the near corner, the distance from the post is ...
distance = tan(90° -36°) = tan(54°) = 1.37638 . . . post lengths
For the other given corner, the distance from the post is ...
distance = tan(90° -22°) = tan(68°) = 2.47509 . . . post lengths
The Pythagorean theorem can be used to find the distance from the post to the diagonally opposite corner:
distance^2 = 1.37638^2 +2.47509^2 = 8.02048
distance = √8.02048 ≈ 2.83205
The relation of this to the angle of elevation is ...
tan(angle of elevation) = 1/2.83205
angle of elevation = arctan(1/2.83205) ≈ 19.45°
_____
In the attached diagram, we have used segments BP and CP as surrogates for the post, so we could determine distances PD and PE that are the sides of the rectangular courtyard. Then the courtyard diagonal is PF. Using PA as a surrogate for the post, we found the angle of elevation from F to A (the top of the post) to be 19.45°, as computed above.
What will be the perimeter and the area of the rectangle below if it is enlarged using a scale factor of 3.5?
Perimeter = 98 cm, area = 588 cm2
Perimeter = 42 cm, area = 109.25 cm2
Perimeter = 42 cm, area = 588 cm2
Perimeter = 98 cm, area = 109.25 cm2
Answer:
first option
Step-by-step explanation:
After it's enlarged, the new dimensions will be 6 * 3.5 = 21 and 8 * 3.5 = 28, therefore, the new perimeter will be 2(21 + 28) = 2 * 49 = 98 and the area will be 21 * 28 = 588.
PLEASE help me with this! I can't fail this...
Answer:
The fourthStep-by-step explanation:
The orthocenter of a triangle is the point of intersection of the lines containing its heights.
You find line like that leading line perpendicular to the side of the triangle and crossing the opposite vertex.
Point A is opposite to side BC so line perpendicular to BC that intersects point A is one of the lines needed to find orthocenter.
Suppose the average length of a fish caught in Lake Springfield is 10.6 in with standard deviation 4.1 in. Assuming lengths of fish caught in Lake Springfield are normally distributed, find the probability that a fish caught there will be longer than 18 in.
Answer:
0.035547
Step-by-step explanation:
We would be using z score formula to solve for this question
The formula for calculating a z-score is is
z = (x-μ)/σ
where x is the raw score = 18 in
μ is the population mean = 10.6 in
σ is the population standard deviation = 4.1 in
z score = 18 - 10.6/ 4.1
z score = 7.4 /4.1
z score = 1.80488
Using the normal distribution table to find the probability for the z score of 1.80488
Probability value from Z-Table:
P(z = 1.80488) = 0.96445
The probability that a fish caught there will be longer than 18 in is calculated as:
P(x>18) = 1 - P(z = 1.80488)
= 1 - 0.96445
= 0.035547
Anyone know this one ?
Answer:
y+2 = -1 ( x+4)
Step-by-step explanation:
The y intercept is 2
The slope is found by using two point
( 0,2) and ( 2,0)
m = (y2-y1)/(x2-1)
= ( 0-2)/(2-0)
= -2/2
= -1
The slope is -1 and the y intercept is 2
Using point slope form
y -y1 = m(x-x1) where m is the slope and ( x1,y1) is a point on the line
y-y1 = -1(x-x1)
It appears that we are using y1 = -2 so x = 4
y - -2 = -1( x -4)
y+2 = -1 ( x+4)
PLS HELP ME..... Question (a) and also (b)...
Step-by-step explanation:
Here,
a). As the graph is given that in 10litre of petrol 10 km can be covered .
then, in 1 liter petrol 1 km is covered.
so,
i). ans is 30 km .
ii). ans is 42km.
b). rate of petrol (r)= RM. 2.30
travelled km= 36.
used petrol = 36 litres (as per the information in graph).
now, total cost (tc)= r×used petrol
or, tc= RM. 2.30 × 36
Therefore, the total amount is RM.82.2.
Hope it helps...
|6–x|=5 plzzzzzzzzz help
Answer: x = 1, 11
Step-by-step explanation:
When answering a problem like this, normally, you first isolate the absolute value. As it is already isolated, the next thing you do is split the equation into 6–x=5 and 6–x=-5, because the contents of the absolute value could be negative or positive, and simplifying both into x = 1, and x = 11.
Hope it helps <3
An infinite geometric series converges if the common ratio is
Answer:
a proper fraction
4 ft
8 ft
3 ft
2 ft
6 ft
What is the volume of the composite figure
plz HELPPPP with this):
Answer:
Graph 4
Step-by-step explanation:
The graph of f(x) = x^3 includes point (0, 0) since f(0) = 0^3 = 0.
The exponent of x is 3. This is not a linear function.
Negative values of x cubed are negative, and positive values of x cubed are positive.
For x < 0, f(x) < 0, and for x > 0, f(x) > 0.
Answer: Graph 4.
Complete the equation: x2+10x+__=(__)^2 A. 25; x+5 B. 25; x−5 C. 10; x+10 D. 10; x−10
Answer:
Answer A) 25, and x+5
Step-by-step explanation:
You need to complete the square by adding a constant that makes the quadratic expression a perfect square of a binomial. So base your analysis on the fact that the coefficient accompanying the square term of x is one, and the fact that the middle term has coefficient 10 which is twice "5" so 5 is the likely candidate for the binomial that goes squared: (x + 5) and the square of 5 (25) is what you need to add as constant term to get the perfect square of a binomial:
[tex]x^2+10x+25=(x+5)^2[/tex]
pls answer asap i need this answer quick plus the full explanation #7
Write the equations after translating the graph of y=|2x|−1: one unit to the left
Answer:
y = | 2(x + 1) - 1
Step-by-step explanation:
Given f(x) then f(x + c) represents a horizontal translation of f(x)
• If c > 0 then shift to the left of c units
• If c < 0 then shift to the right of c units
Here the shift is 1 unit to the left , thus
y = | 2(x + 1) ] - 1
i need help quick i will mark brainilest
Answer:
x-y
Step-by-step explanation:
X is greater than y so we are subtracting the smaller number from the bigger number
That means we do not need the absolute value signs since x-y will be positive
|x-y| when x> y
x-y
Using numbers
| 5-2| 5>2
5-2
Ted and three of his friends went out to eat. They decided to split the bill evenly. Each person paid $16.88. What was the total bill?
Answer:
Total bill = $67.52
Step-by-step explanation:
Ted + 3 = 4
$16.88 × 4 = $67.52
hopefully this helped you :3
Answer:
16.88*4= 67.52 dollars
Step-by-step explanation:
Ted and 3 friends split the bill evenly, each person paid 16.88:
16.88*4= 67.52 dollars
A chemist whishes to prepare 100 liters of 45% purity of sulphuric acid .He has two kinds of acid solutions in stock ,one is 55% pure and the other is 30% pure .How many leters of each kind should be used for the mixture?
Answer:
the chemist should use 60 liters of 55% solution and 40 litres of 30% solution in order to prepare 100 liters of 45% purity of sulphuric acid.
Step-by-step explanation:
From the given information,
Let x be the litres of 55% pure solution
Let y be the litres of 30% pure solution
Also;
Given that our total volume of solution is 100 litres
x+y =100 ---- (1)
The total solution of pure by related by the sum of the individual pure concentrations to make up the concentration of final solution.
(0.55)(x)+(0.30)(y) = 0.45(100) ---- (2)
From equation (1)
Let ; y = 100 - x
Replacing the value for y = 100 - x into equation (2)
(0.55)(x)+(0.30)(100-x) = 0.45(100)
0.55x + 30 - 0.30x = 45
0.55x - 0.30x = 45 - 30
0.25x = 15
x = 15/0.25
x = 60 liters of 55% solution
From ; y = 100 - x
y = 100 - 60
y = 40 litres of 30% solution.
Therefore, the chemist should use 60 liters of 55% solution and 40 litres of 30% solution in order to prepare 100 liters of 45% purity of sulphuric acid.
The Benton Youth Soccer Team has 20 players on the team, including reserves. Of these, three are goalies. Today, the team is having a contest to see which goalie can block the most number of penalty kicks. For each penalty kick, a goalie stands in the net while the rest of the team (including other goalies) takes a shot on goal, one at a time, attempting to place the ball in the net. How many penalty kicks must be taken to ensure that everyone has gone up against each of the goalies?
Answer:
57
Step-by-step explanation:
Subtract one player from the total number, because one has to block.
19
Multiply this by the number of goalies there are.
19*3=57
There will be 57 kicks.
Please answer this question now
Answer:
16.2
Step-by-step explanation:
use Pythagorean theorem
a^2 + b^2 = c^2
15^2 + 6^
225 + 36 = 261
take the sq root of 261
plssssssss helppp 3x – 5 = 1
Answer:
x = 2
Step-by-step explanation:
Add 5 to both sides to get the 5 to the right side since we are trying to isolate the variable x:
3x – 5 + 5 = 1 + 5
Simplify: 3x=6
Divide each side by 3 to isolate and solve for x:
3x/3=6/3
Simplify: x=2
With steps , please.
[tex]\bold{\text{Answer:}\quad x=\dfrac{1}{2},\quad y=1,\quad z=\dfrac{1}{3}}[/tex]
Step-by-step explanation:
[tex]\text{Equation 1:}\quad \dfrac{x}{x+y}=\dfrac{1}{3y}\\\\\\.\qquad \qquad \qquad 3xy=x+y\\\\.\qquad \qquad \qquad 3xy-y=x\\\\.\qquad \qquad \qquad y(3x-1)=x\\\\.\qquad \qquad \qquad y=\dfrac{x}{3x-1}[/tex]
[tex]\text{Equation 2:}\quad \dfrac{y}{y+z}=\dfrac{1}{4z}\\\\\\.\qquad \qquad \qquad 4yz=y+z\\\\.\qquad \qquad \qquad 4yz-y=z\\\\.\qquad \qquad \qquad y(4z-1)=z\\\\.\qquad \qquad \qquad y=\dfrac{z}{4z-1}[/tex]
[tex]\text{Equation 3:}\quad \dfrac{z}{z+x}=\dfrac{1}{5x}\\\\\\.\qquad \qquad \qquad 5xz=z+x\\\\.\qquad \qquad \qquad 5xz-z=x\\\\.\qquad \qquad \qquad z(5x-1)=x\\\\.\qquad \qquad \qquad z=\dfrac{x}{5x-1}[/tex]
Set Equation 1 equal to Equation 2 and substitute z per Equation 3
[tex]\dfrac{x}{3x-1}=\dfrac{z}{4z-1}\\\\\\x(4z-1)=z(3x-1)\\\\4xz-x=3xz-z\\\\4x\bigg(\dfrac{x}{5x-1}\bigg)-x=3x\bigg(\dfrac{x}{5x-1}\bigg)-\dfrac{x}{5x-1}\\\\\\4x^2-x(5x-1)=3x^2-x\\\\4x^2-5x^2+x=3x^2-x\\\\0=4x^2-2x\\\\0=2x(2x-1)\\\\0=2x\qquad\qquad 0=2x-1\\\\x=0\qquad \qquad x=\dfrac{1}{2}[/tex]
Solve for y when x = 0:
[tex]\text{Equation 1:}\quad y=\dfrac{0}{3(0)-1}\quad \rightarrow \quad y=0[/tex]
Notice that x + y is in the denominator and denominator cannot equal zero so x = 0 is an invalid solution.
[tex]\text{Solve for y when}\ x=\dfrac{1}{2}:\\\\\text{Equation 1:}\quad y=\dfrac{\frac{1}{2}}{3(\frac{1}{2})-1}\quad \rightarrow \quad y=1[/tex]
[tex]\text{Solve for z when x = \dfrac{1}{2}}:\\\text{Equation 3:}\quad z=\dfrac{\frac{1}{2}}{5(\frac{1}{2})-1}\quad \rightarrow \quad z=\dfrac{1}{3}[/tex] [tex]\text{Solve for z when}\ x=\dfrac{1}{2}:\\\\\text{Equation 3:}\quad z=\dfrac{\frac{1}{2}}{5(\frac{1}{2})-1}\quad \rightarrow \quad z=\dfrac{1}{3}[/tex]
Use the grouping method to factor this polynomial x^3+2x^2+12x+24
Answer:
We can group x³ and 2x², their GCF is x² so it becomes x²(x + 2). 12x + 24 has a GCF of 12 so it becomes 12(x + 2). Since both terms have the (x + 2) factor, the answer is (x + 2)(x² + 12).
Determine if the question is statistic or not, college in Jacksonville do tennis coaches get paid more than football coaches
Answer:
Yes, because to get the answer for this question one of the things you would do is most likely look at a group of statistics average them, and see who gets paid more.
Dos conductores A y B llenan un estanqe en 20 horas .Si el conductor B fuera un desague el estanq se llenaria en 52 horas ¿En q tiempo se llenara el estanque estando solo abierto el conducto A?
Answer:
Con el conducto A abierto, el estanque se llenará en 32.5 horas.
Step-by-step explanation:
Deje que el volumen de agua presente en el estanque sea x litros
La tasa conjunta sería x / 20 litros por hora.
Para el conducto A, no sabemos la hora, llamemos a esto y así que la tasa aquí será x / y
Para el conducto B tomará 52 horas y su tasa es x / 52
Matemáticamente, cuando sumamos ambas tasas juntas, obtendremos la tasa conjunta; Así; x / y + x / 52 = x / 20
Saca x en ambos lados 1 / y+ 1/52 = 1/20
(52 + y) / 52y = 1/20
20 (52 + y) = 52y
1040 + 20y= 52y
1040 = 52y -20y
32y = 1040 y = 1040/32
y = 32.5 horas
Con el conducto A abierto, el estanque se llenará en 32.5 horas.
Jake is going to call one person from his contacts at random. He has 30 total contacts. 16 of those contacts are people he met at school.
What is P(Call a person from school)
Answer:16/30
Step-by-step explanation:
For a chemical reaction to occur, at least one-third of the solution must be an acid. If there are five liters of acid, in interval form, how much solution is present?
A. [5,8)
B. (3/5,5]
C. (5/3,5]
D. [5,15]
Answer:
Amount of solution = 15 liter
Step-by-step explanation:
Given:
One third of solution is acid
Amount of acid = 5 Liter
Find:
Amount of solution
Computation:
Amount of solution = Amount of acid (1 / One third of solution is acid)
Amount of solution = Amount of acid (3)
Amount of solution = (5)(3)
Amount of solution = 15 liter