Answer:
The centre is at (-12, 9) and the radius = 5 units.
Step-by-step explanation:
x^2 + y^2 + 24x - 18y + 200 = 0
x^2 + 24x + y^2 - 18y = -200
Completing the square on the x and y terms:
(x + 12)^2 - 144 + (y - 9)^2 - 81 = -200
(x + 12)^2 + (y - 9)^2 = -200 + 144 + 81
(x + 12)^2 + (y - 9)^2 = 25
So the centre is at (-12, 9) and the radius = the square root of 25 = 5.
Answer:
centre = (- 12, 9), radius = 5
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given
x² + y² + 24x - 18y + 200 = 0
Collect the terms in x/ y together and subtract 200 from both sides
x² + 24x + y² - 18y = - 200
Using the method of completing the square
add ( half the coefficient of the x/ y term )² to both sides
x² + 2(12)x + 144 + y² + 2(- 9)y + 81 = - 200 + 144 + 81
(x + 12)² + (y - 9)² = 25 ← in standard form
with centre (- 12, 9) and r = [tex]\sqrt{25}[/tex] = 5
A shipping crate is packed with unit cubes. The length of the crate is 4 units, the width is 2 units and the height is 4 units. Find the volume If the shipping crate
Answer:
32 unit³
Step-by-step explanation:
Length of the crate has been given as 4 units
width of the crate = 2 units
Height of the crate = 4 units
Since the crate has been packed packed with the unit cubes.
Therefore, shape of the crate will be in the form of a rectangular prism.
Volume of the prism = Length × width × height
crate = 4 × 2 × 4
= 32 unit³
Volume of the shipping crate is 32 unit³.
Answer:
32 Units
Step-by-step explanation:
If u do 4x2x4=32 that is your answer all you got to do is x Lxwxh and U will find the volume
What is the area of a pyramid?
Answer:
Area of a pyramid = (1/3) x (base area) x (height)
I Need Help With This One, .......again
Answer:
1249.37
Step-by-step explanation:
7850 = 2 pi r
r = 7850/(2pi) = 1249.37
ANSWER
The radius is approximately 1249 units.
EXPLANATION
The relation between the radius of a circle and its circumference is expressed in the formula:
[tex]C = 2\pi \: r[/tex]
The circumference is given as 7,850 .
This implies that
[tex]7850 = 2\pi \: r[/tex]
[tex]r = \frac{7850}{2 \: \pi} [/tex]
[tex]r = 1249.4[/tex]
to the nearest tenth.
What is the solution of 4x 2 36?
Answer:
x= 8.5 or 9, or deciding if u adding or subtracting the problem, x= 9.5 or 10
Step-by-step explanation:
If you're meaning 4x+2=36 or 4x-2=36
-2 -2 +2 +2
4x=34 4x=38
4 4 4 4
x= 8.5 or 9 x= 9.5 or 10
Hope i have helped you! :)
given that ABCDEF = PQRSTU , solve for z
the answer is z=7 (as 3z-4=17)
Answer:
A. 5
Step-by-step explanation:
Which ordered pair is the best estimate for the solution of
the system of equations?
y= -2.5x + 6.5
y=x+1
A (1.5,2.5)
B (1.25,2.5)
C (1.75,2.25)
D (1.25,1.75)
Answer:
(1.5, 2.5) is the best approximate solution.
Step-by-step explanation:
According to the graph, at the point of intersection of these two lines, x is closest to 1.5 and y is simultaneously closest to 2.5.
(1.5, 2.5) is the best approximate solution.
Answer:
Step-by-step explanation:
1.5 AND 2.5
A triangular pyramid with a volume of 270 cubic centimeters, a base edge of 15 centimeters, and the height of the base as 4 centimeters has a height of____ centimeters.
Answer:
The height of the triangular pyramid is [tex]27\ cm[/tex]
Step-by-step explanation:
we know that
The volume of a triangular pyramid is equal to
[tex]V=\frac{1}{3}BH[/tex]
where
B is the area of the triangular base
H is the height of the pyramid
Find the area of the base B
[tex]B=\frac{1}{2}(15)(4)=30\ cm^{2}[/tex]
we have
[tex]V=270\ cm^{3}[/tex]
substitute and solve for H
[tex]270=\frac{1}{3}(30)H[/tex]
[tex]270=10H[/tex]
[tex]H=270/10=27\ cm[/tex]
Which is the same distance from zero on the number line as 25? 1.) 50 2.) 0 3.) −25 4.) −50
Answer:
-25
Step-by-step explanation:
-25 is the same distance away from zero as is 25.
Answer:
-25
Step-by-step explanation:
this is a question about absolute value. with absolute value, if the number is negative, u simply take off the negative sign. so, ur looking 4 the opposit of 25, which is -25
An entrepreneur is a _____.
new business that creates a product that raises the standard of living
person who administers career tests
person who takes a risk to create a new product or develop a better way to operate a business
person who completes tax return forms for individuals
An entrepreneur is a someone who organizes and conducts a business, and taking great financial risks.
Answer:
The correct answer would be option C, A person who takes a risk to create a new product or develop a better way to operate a business.
Step-by-step explanation:
An entrepreneur is a person who starts a new business alone. An Entrepreneur is responsible for all the profits and losses of the business. He takes risks in the hope of earning profits. He introduces new products in the market and develops better ways to operate a business. He is solely liable for all his decisions and the resulting profit or losses. Entrepreneurs are usually hard working, strong decision makers, risk takers, and highly innovative people.
Find the probability that the next 1,000 cars purchased in your city will all be the color blue.
Assuming that the probability of a car being colored blue is not equal to 0 or 1, then the most logical answer would be the smallest probability.
P= 0.001
Answer:
0.001
Step-by-step explanation:
gradpoint
calculate the slope of the line that contains the points (2,-3) and (6,-3)
Answer:
Step-by-step explanation:
y2-y1/x2-x1= -3-(-3)/6-2= 0/4
Find a quadratic equ
{-2/5 7/5}
{-2/5 7/5}={-2*7/5*5}={-14/25} or if you prefer :
Final answer:
The quadratic equation with roots -2/5 and 7/5 is 25x^2 - 25x - 14 = 0. This is derived by expressing the equation in the form a(x - α)(x - β) = 0 and substituting the given roots.
Explanation:
To find a quadratic equation with roots -2/5 and 7/5, we use the fact that if α and β are the roots of the quadratic equation ax2 + bx + c = 0, then the equation can be written as a(x - α)(x - β) = 0. For roots -2/5 and 7/5, the quadratic equation becomes:
x2 - (sum of roots)x + (product of roots) = 0
x2 - ((-2/5) + (7/5))x + ((-2/5) × (7/5)) = 0
x2 - (5/5)x - (14/25) = 0
x2 - x - 14/25 = 0
Multiplying through by 25 to clear the fraction:
25x2 - 25x - 14 = 0
This is the quadratic equation with the given roots.
What is the solution to the following system of equations?
2x + 3y = 3
-3x - 2y = 8
The answer is (-6,5)
Answer:
Your answer will be (-6,5).
Step-by-step explanation:
You multiply the first equation by 3 and the second equation by 2. You will then cancel out the x's and find your y which is 5. You plug y back into your first equation to find your x which is -6. You then have your solution set.
Solve the system of equations below.
x − y = 5
2x − 3y = 4
A (5, 0)
B (7, 2)
C (9, 4)
D (11, 6)
To solve the system of equations x − y = 5 and 2x − 3y = 4, we can use the method of substitution or elimination. By substituting the value of x from the first equation into the second equation, we can find the value of y. Then, substitute the value of y back into the first equation to find the value of x. The solution to the system of equations is (11, 6).
Explanation:To solve the system of equations x − y = 5 and 2x − 3y = 4, we can use the method of substitution or elimination. Let's use the method of substitution:
From the first equation, we can rearrange it to x = y + 5. Now substitute this value of x into the second equation:
2(y + 5) − 3y = 4
Simplify and solve for y:
2y + 10 - 3y = 4
-y + 10 = 4
-y = -6
y = 6
Now substitute this value of y back into the first equation to find x:
x − 6 = 5
x = 11
Therefore, the solution to the system of equations is (11, 6). So, the correct answer is option D.
8 points! Please help me with this problem, what is sin(theta)?
sin=√17/7
or sin=sqrt(17)/7
Answer:
[tex]\frac{\sqrt{17} }{7}[/tex]
Step-by-step explanation:
Given
cosΘ = [tex]\frac{4\sqrt{2} }{7}[/tex] = [tex]\frac{adjacent}{hypotenuse}[/tex]
Then the hypotenuse of the right triangle is 7 and the adjacent side is 4[tex]\sqrt{2}[/tex]
To find the opposite side use Pythagoras' identity
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
opp² + (4[tex]\sqrt{2}[/tex] )² = 7²
opp² + 32 = 49 ( subtract 32 from both sides )
opp² = 17 ( take the square root of both sides )
opp = [tex]\sqrt{17}[/tex]
Hence
sinΘ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{\sqrt{17} }{7}[/tex]
Information you may find on your paycheck stub may include _____.
pay period, taxable allowances, and dividends
deductions, dividends, and interest
employee benefits, date of hire, and number of dependents
employee ID, vacation time, pay period, and deductions
Answer:
Pay period, taxable allowances, and dividends
Step-by-step explanation:
Answer: Pay period, taxable allowances, and dividends
Explanation:
Paycheck stub is the type of document which include the total paid amount to the employees. It is also known as pay slip and pay stub. The pay stub is basically received by the each pay slip and period.
This pay check stub document basically show the total earnings, deductions and the net pay after the all deductions.
We can also save the paycheck stub in our records so that we can easily access it in future. In case of the employees and employer, the paycheck stub prove that the payment and the income are both consistent.
Evaluate -3x3 - 4x for x = -1. 1 7 -1
Answer:
-5
Step-by-step explanation:
-3 x 3 - 4x
x=-1
-3 x 3 - 4(-1)
-3 x 3 + 4
-9 + 4
-5
Hope This Helps! :D
Answer:
-3-4x
=-3(-1
=-3*(-1)+4
=3+4
=7
Step-by-step explanation:
that should be all you need to know
2. The 2002 Denali earthquake in Alaska had a Richter scale magnitude of 6.7. The 2003 Rat Islands earthquake in Alaska had a Richter scale magnitude of 7.8.
(SHOW WORK)
Suppose an architect has designed a building strong enough to withstand an earthquake 70 times as intense as the Denali quake and 30 times as intense as the Rat Islands quake. Find which structure is strongest. Explain your finding.
(SHOW WORK)
Answer:
the building strong enough to withstand the denali quake
Step-by-step explanation:
denali quake 6.7 x 70 = 469
the building in denali should be strong enough to withstand an earthquake of that magnitude
rat island quake 7.8 x 30 = 234
the building in the rat islands should be strong enough to withstand an earthquake of that magnitude
The price of a computer was decreased by 30% to £147. What was the price before the decrease?
A decrease by 30%, means that the price is now 70% of the original price ( 100% - 30% = 70%)
To find the original price divide the new price by the percent of the original price it is now.
147 / 0.70 = 210
The original price was £210
The price before the decrease is £210.
Given that,
The price of a computer was decreased by 30% to £147.Based on the above information, the calculation is as follows:
[tex]= 147 \div 70\%[/tex]
= £210
Therefore we can conclude that the price before the decrease is £210.
Learn more: brainly.com/question/6201432
Find dy/dx if y=sin(x+y)
Steps would be appreciated.
Answer:
[tex]\frac{dy}{dx} = \frac{cos(x+y)}{1-cos(x+y)}[/tex]
Step-by-step explanation:
We have the function [tex]y=sin(x+y)[/tex]
We need find the derivative of y with respect to x
Note that the function [tex]y = sin (x + y)[/tex] depends on the variable x and the variable y. Therefore the derivative of y with respect to x will be equal to the derivative of [tex]sin (x + y)[/tex] by the internal derivative of [tex]sin (x + y)[/tex]
[tex]\frac{dy}{dx}= cos(x+y)*\frac{d}{dx}(x+y)[/tex]
[tex]\frac{dy}{dx}= cos(x+y)*(1+\frac{dy}{dx})\\\\\frac{dy}{dx}= cos(x+y)+\frac{dy}{dx}cos(x+y)\\\\\frac{dy}{dx} -\frac{dy}{dx}cos(x+y)=cos(x+y)\\\\\frac{dy}{dx}(1-cos(x+y))=cos(x+y)\\\\\frac{dy}{dx} = \frac{cos(x+y)}{1-cos(x+y)}[/tex]
Answer:
Step-by-step explanation:
Note that y=sin(x+y) is an implicit function; y appears on both sides of the equation, which makes it difficult or impossible to solve for y.
However, our job here is to find the derivative dy/dx.
We apply the derivative operator d/dx to both sides. Here are the results:
dy
---- = cos(x + y)(dx/dx + dy/dx), or
dx Note: dx/dx = 1
dy
---- = cos(x + y)(1 + dy/dx), or = cos(x + y) + cos(x + y)(dy/dx)
dx
We move that cos(x + y)(dy/dx) term to the left side to consolidate dy/dx terms:
dy
---- - cos(x + y)(dy/dx) = cos(x + y)
dx
or:
dy
[ ---- ] [ 1 - cos(x + y) ] = cos(x + y)
dx
Finally, we divide both sides by [ 1 - cos(x + y) ], obtaining the derivative:
dy cos(x + y)
[ ---- ] -------------------------
dx 1 - cos(x + y)
WORTH 34 POINTS! PLEASE HELP ASAP!
Would you describe the association between the age of the car and its resale value as exhibiting a linear association, non-linear association, or no association? Explain your reasoning.
Answer:No assoication
Step-by-step explanation:
because they are not parellell with each other
Answer: No association.
Step-by-step explanation: They aren't parallel with each other. So, it has to be no association.
Solve the expression for x: 5x (4-2)=20
For this case we must find the value of the variable "x" of the following equation:
[tex]5x (4-2) = 20[/tex]
We solve the operation within the parenthesis:
[tex]5x (2) = 20[/tex]
We multiply the left side:
[tex]10x = 20[/tex]
We divide both sides of the equation by 10:
[tex]x = \frac {20} {10}\\x = 2[/tex]
ANswer:
[tex]x = 2[/tex]
The solution of the expression given for x is 2.
Given is an expression 5x(4-2) = 20, we need to solve for x.
To solve the expression 5x(4-2) = 20 step by step, follow these steps:
Simplify the expression inside the parentheses:
5x(4 - 2) = 20
5x(2) = 20
Multiply 5x by 2:
10x = 20
Divide both sides of the equation by 10 to isolate x:
(10x)/10 = 20/10
x = 2
Therefore, the solution for x is 2.
Learn more about expression click;
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Given: x - 8 > -3.
Choose the solution set.
1.{x | x R, x > -9}
2.{x | x R, x > -5}
3.{x | x R, x > 5}
4.{x | x R, x > 14}
Answer:
x-8>-3 {x|R, x>5 is right answer
For this case we must find the solutions of the following inequality:
[tex]x-8> -3[/tex]
Adding 8 to both sides of the inequality we have:
[tex]x> -3 + 8\\x> 5[/tex]
Thus, the solutions of the variable "x" are given by all the real numbers greater than 5.
Answer:
Option C
5 pounds of birdseed cost $10.40. What is the price per ounce ?
$0.13 per ounce. 5 pounds of birdseed cost $10.40, then the price per ounce is $0.13.
The easiest way to solve this problem is using arithmetic operations and unit conversion.
We have to calculate the price per pound. Let's divide $10.40 by 5 pounds.
10.40/5 = 2.08
The price per pound is $2.08
To calculate the price per ounce, with 1 pound = 16 ounces. Let's divide $2.08 by 16 ounces.
2.08/16 = 0.13
The price per ounce is $0.13
The overhead reach distances of adult females are normally distributed with a mean of
200 cm and a standard deviation of
8 cm.
a. Find the probability that an individual distance is greater than
210.00
210.00 cm.
b. Find the probability that the mean for
25
randomly selected distances is greater than
198.70 cm.
c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
Answer:
a)
The probability that an individual distance is greater than 210.00 cm is 0.1056
b)
The probability that the mean for 25 randomly selected distances is greater than 198.70 cm is 0.7917
c)
The normal distribution be used in part (b), even though the sample size does not exceed 30 since the parent population from which the sample has be obtained is Normal.
Step-by-step explanation:
a)
We let the random variable X denote the overhead reach distances of individual adult females. This implies that X is normally distributed with a mean of 200 cm and a standard deviation of 8 cm.
The probability that an individual distance is greater than 210 can be written as;
Pr(X>210)
We standardize the value to obtain the associated z-score;
[tex]P(X>210)=P(Z>\frac{210-200}{8})=P(Z>1.25)[/tex]
Using the standard normal tables, the area to the right of 1.25 is 0.1056. Therefore, the probability that an individual distance is greater than
210.00 cm is 0.1056.
b)
The first step will be to determine the sampling distribution of the sample mean given that the variable overhead reach distance is normally distributed with a mean of 200 cm and a standard deviation of 8 cm.
In this case, the sample mean will also be normally distributed with a mean of 200 cm and a standard deviation of;
[tex]\frac{sigma}{\sqrt{n} }=\frac{8}{\sqrt{25} }=1.6[/tex]
The probability that the mean for 25 randomly selected distances is greater than 198.70 cm;
Pr(sample mean >198.70)
We standardize the value to obtain the associated z-score;
[tex]=P(Z>\frac{198.70-200}{1.6})=P(Z>-0.8125)[/tex]
Using the standard normal tables, the area to the right of -0.8125 is 0.7917. Therefore, the probability that the mean for 25 randomly selected distances is greater than 198.70 cm is 0.7917.
c)
The normal distribution be used in part (b), even though the sample size does not exceed 30 since the parent population from which the sample has be obtained is Normal.
Can someone please help me with these two
Answer:
For number 14, the answer should be 100 degrees. For number 15, the answer is 80 degrees. For number 16, the answer is 120 degrees.
Step-by-step explanation:
For number 14, if a minor arc is 80 degrees, then the major arc should be 100 degrees to add to make 180 degrees. For number 15, you can see the size of the 70 degrees angle, AB. Because DE is bigger than AB, we can conclude that it is probably 80 degrees. For number 16, if XY, YZ, and ZX are all the same, and a circle always adds up to 160 degrees, then 360 divided by the three arcs is 120.
NEED HELP ASAP 100 POINTS!!!! A woman looks out a window of a building. She is 93 feet above the ground. Her line of sight makes an angle of theta with the building. The distance in feet of an object from the woman is modeled by the function d=93 secant theta. How far away are objects sighted at angles of 29degrees and 59degrees?
To find the distance of objects sighted at angles of 29 degrees and 59 degrees, use the function d = 93 sec(theta). Substituting theta values, the distances are 106.87 feet and 166.39 feet, respectively.
Explanation:To find the distance of an object sighted at angles of 29 degrees and 59 degrees, we can use the function given, d = 93 sec(theta). Substituting theta = 29 degrees, we get d = 93 sec(29) = 93*(1/cos(29)) = 93/0.8714 = 106.87 feet. Similarly, substituting theta = 59 degrees, we get d = 93 sec(59) = 93*(1/cos(59)) = 93/0.5588 = 166.39 feet.
Two and two fifths divided by one and a half
Answer:
8/5 or 1 3/5
Step-by-step explanation:
2 2/5 = 12/5
1 1/2 = 3/2
Now that we have fractions that are easier to divide, one must understand that the opposite of dividing is multiplying. So if you multiply 12/5 by the reciprocal* of 3/2, which would be 2/3, you would get your answer so...
12 3 12 2 24 8 3
— ÷ — = — × — = — = — or 1 —
5 2 5 3 15 5 5
*the reciprocal is the opposite of the fraction you have. So the denominator would become the numerator, and vise versa.
The box and whisker plot below represents students test scores of Mr. Ali’s history test.
C. Mr. Ali’s wanted more than half of the students to score 75 or greater on the test. Explain how you know that more than half of the students did NOT score greater than 75.
Answer:I know that more than half of the students did not score more than 75 because the median (the middle number) is 68.
Step-by-step explanation:
What is the volume of the following triangular prism?
A) 252 yd3
B) 126 yd3
C) 42 yd3
D) 84 yd3
Answer:
Option C. [tex]42\ yd^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the triangular prism is equal to
[tex]V=BH[/tex]
where
B is the area of the triangular base
H is the height of the prism
Convert 9 ft to yd
Remember that
1 ft=1/3 yd
9 ft=9*(1/3)=3 yd
Find the area of the base B
[tex]B=\frac{1}{2}(3)(4)=6\ yd^{2}[/tex]
we have
[tex]H=7\ yd[/tex]
substitute the values in the formula
[tex]V=BH[/tex]
[tex]V=(6)(7)=42\ yd^{3}[/tex]
Answer:
The answer is 42 yards! Sry im late. :(