Write the standard equation of a circle having center (9, 1) and a point on circle at (-2, -5).
Answers
Answer:
\((x-9)^2+(y-1)^2=(\sqrt{157} )^2.\)
Step-by-step explanation:
1. the rule is:
(x-x₀)²+(y-y₀)²=r², where (x₀;y₀) - the centre of the given circle, r - its radius.
2. using the given point (9;1) and the centre (-2;-5) it is possible to calculate 'r²':
\(r^2=(9+2)^2+(1+5)^2=157=\sqrt{157^2} .\)
3. finally,
\((x-9)^2+(y-1)^2=\sqrt{157^2} .\)
Related Questions
Question 7 of 10
Describe the nature of the roots for this equation. x²+3x-7=0
A. One real, double root
B. Two real, irrational roots
C. Two real, rational roots
D. Two complex roots
Answers
Answer:
B
Step-by-step explanation:
Given a quadratic equation in standard form
ax² + bx + c = 0 ( a ≠ 0 )
Then the discriminant is
Δ = b² - 4ac
• If b² - 4ac > 0 then 2 real irrational roots
• If b² - 4ac > 0 and a perfect square then 2 real rational roots
• If b² - 4ac = 0 then 1 real double root
• If b² - 4ac < 0 then 2 complex roots
Given
x² + 3x - 7 = 0 ← in standard form
with a = 1, b = 3, c = - 7 , then
b² - 4ac
= 3² - (4 × 1 × - 7) = 9 + 28 = 37
Since b² - 4ac > 0 then 2 real irrational roots
Question 5 Let x be the first factor in an expression in scientific notation. Which describes this facto Ol
Answers
The correct answer is
\(\text{ 1 }\leq\text{ x < 10}\)look at pic 10 pts will mark brainilest
C: ( 9 x 18) + (6 x 2)
D: (20 x 6) + (18 x 3)
E: (20 x 9) - (3 x 2)
Answers
Answer:
Step-by-step explanation:
C and E
There is a mistake in this problem find the mistake
Answers
Answer:
The mistake is the problem itself. It should be
5x=100
x=100÷5
x=20
Step-by-step explanation:
The mistake is the problem itself. It should be
5x=100
x=100÷5
x=20
Susan works as a hostess where she makes $8.75 per hour. She also babysits and earns $10 per hour. Last week she made $165. If she worked six hours more as a hostess then she did babysitting, how many hours did she babysat last week?
Answers
Answer:
she babby sat atleast 4 hours last week
Find the value of x for which the lines rand s are parallel.
Answers
Answer:
x = 12
Step-by-step explanation:
<1 and the 142-deg angle are vertical, so m<1 = 142 deg
The angle measuring 3x + 2 and <1 are same-side interior angles. If the lines are parallel, then those two angles are supplementary.
3x + 2 + 142 = 180
3x + 144 = 180
3x = 36
x = 12
(SAT Prep) Find the value of x.
Answers
Answer: 36˚
Step-by-step explanation:
180 - 3x = 2x
180 = 5x
.: x = 36˚
Each side of a square classroom is 6 yards long. The school wants to replace the carpet in the classroom with new carpet that costs $53.00 per square yard. How much will the new carpet cost?
Answers
The new carpet will cοst $1,908.00.
What is an area?
The size οf a regiοn οn a surface is measured by its area. While surface area refers tο the area οf an οpen surface οr the bοundary οf a three-dimensiοnal οbject, the area οf a plane regiοn οr plane area refers tο the area οf a shape οr planar lamina.
Area can be interpreted as the quantity οf material with a particular thickness required tο create a mοdel οf the shape οr as the quantity οf paint required tο cοmpletely cοver a surface in a single cοat. It is the twο-dimensiοnal equivalent οf the vοlume οf a sοlid οr the length οf a curve (a οne-dimensiοnal cοncept) (a three-dimensiοnal cοncept).
The area οf the classrοοm is the square οf the length οf its side, which is:
6 yards × 6 yards = 36 square yardsTο find the cοst οf the new carpet, we need tο multiply the area οf the classrοοm by the cοst per square yard:
36 square yards × $53.00/square yard = $1,908.00
Therefοre, the new carpet will cοst $1,908.00.
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6 Explain in words how to simplify: (153 to the 2nd power times 7
Answers
Step-by-step explanation:
153^2×7
163863
plss mark me brainliest
Please help me.
Find the distance between the points A and B shown on the
coordinate plane.
A
A. 13 units
B. 11.5 units
C. 12.1 units
D. 11.2 units
Answers
Answer:
d = 12.1 units
Step-by-step explanation:
Given
A(-6, 6)B(5, 1)\(\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\)
\(d=\sqrt{\left(5-\left(-6\right)\right)^2+\left(1-6\right)^2}\)
\(=\sqrt{\left(5+6\right)^2+\left(1-6\right)^2}\)
\(=\sqrt{11^2+5^2}\)
\(=\sqrt{146}\)
d = 12.1 units
Two friends are playing with water balloons. They each start at the bucket of balloons and walk in opposite directions before tossing their balloons at each other. Joy walked 14 steps
forward, and Shaunte walked 5 steps backwards. Which expression correctly represents the distance between the friends?
O 14+1-51 19 steps
O 14+5=19 steps
O-141 +1-51 = 19 steps
O-141+5=19 steps
Answers
Answer:
B
Step-by-step explanation:
because is joy walked 14 steps and her friend walks 5 steps the answer is 19 steps 14+5=19
What is the northerly Component of a wind blowing at 15ms from the South East?
Answers
The northerly component of the wind blowing at 15 m/s from the South East is approximately 10.605 m/s.
To determine the northerly component of a wind blowing from the South East, we need to consider the direction from which the wind is coming and its magnitude.
A wind blowing from the South East means it is coming from the South East direction towards the opposite direction, which is the North West. Since the wind is coming from the South East, we can say it has a southeasterly direction.
To find the northerly component, we need to break down the wind vector into its north and east components. The northerly component represents the part of the wind that is directed towards the north.
If we assume that the wind is blowing at an angle of 45 degrees with respect to the North, we can use trigonometry to find the components. Since the wind is blowing at 15 m/s, we can consider it as the hypotenuse of a right triangle.
The northerly component can be found using the sine of the angle:
Northerly Component = Wind Speed * sin(Angle)
Northerly Component = 15 m/s * sin(45°)
Using the value of sin(45°) (which is √2 / 2 ≈ 0.707), we can calculate the northerly component:
Northerly Component ≈ 15 m/s * 0.707
Northerly Component ≈ 10.605 m/s
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plssss helpppppp!!!!
Answers
Answer:
2.
a) log base 10 of 100
b) The expression means that 10 to the 2nd power equals 100.
c) 2
3.
4. It would make sense that the value is between 1 and 2 because 10 to the 1st power is 10, and 10 to the 2nd power is 100. 50 is between 10 and 100 so the value would have to be between 1 and 2. This works because logs are the inverse function to exponentiation.
a) 2.6021
b) 3 and the value is exact because the base 10 in the log expression is technically the exponent when you convert it to exponent form. This works because logs are the inverse function to exponentiation. So 10 to the 3rd power would give you exactly 1000.
The diagram shows a right-angled triangle.
24 cm
18 cm
_Not to scale
Calculate the value oft. Give your answer correct to 1 decimal place.
Answers
Answer:
can i have a photo, please?
Step-by-step explanation:
WILL GIVE BRAINLEST 658 minus what equals 98?
Answers
Answer:
-560 is the answer
Step-by-step explanation:
658 - (-560 )= 98
Answer:
Hello!!! erz here ^^
Step-by-step explanation:
658 - 560 = 98
Hope this helps!! :D
simplify (8x2y3)/(2x4y)
Answers
Answer:
1) 8x/2x = 4
2) 2y/4y = 1/2
3) (4 x 1/2 x 3) = 6
4) /2
solutions= 6/2=3
Find the quotient 820,00^3
Answers
Answer:
Correct me if I'm wrong......
Portfolio Option 1: Sports Graph
This portfolio problem will have you write. You will turn in a “mathematical paper” of about 1 page of writing. You can use this handout to write rough draft ideas first.
Brainstorm: Which of the above sports do you think the graph could represent? Why?
Brainstorm: What vocabulary and properties of graphs and functions do you see represented in the graph? How did any of those affect your choice for the sport?
Use your brainstorms above to write a 1 page paper that talks about this graph, what sport you believe it could represent, and what properties of functions and graphs support your answer. You can add diagrams as well.
Answers
Answer:The graph represent skydiving, Because when you jump out of the plane you have a bunch of speed and when you pull your parachute the speed will drop exceedingly.
Step-by-step explanation:
(URGENT)An engineer has a 40:1 scale drawing of a bridge. The dimensions of the scaled bridge deck are 24 inches by four and four fifths inches. What is the area of the actual bridge deck in square feet?
460 square feet
640 square feet
960 square feet
1,280 square feet
Answers
The area οf the actual bridge deck in square feet is 1,280 square feet.
What is Area?Area refers tο the measurement οf the size οf a twο-dimensiοnal surface, usually measured in square units such as square inches, square feet, οr square meters. It represents the amοunt οf space that is inside the bοundary οf a flat οbject οr shape.
The scale οf the drawing is 40:1, which means that the dimensiοns οf the scaled bridge deck are 40 times smaller than the actual bridge deck. Tο find the area οf the actual bridge deck in square feet, we need tο cοnvert the dimensiοns οf the scaled bridge deck frοm inches tο feet and then multiply by the square οf the scale factοr (40² = 1600).
The dimensiοns οf the scaled bridge deck in feet are:
24 inches = 2 feet
4 and 4/5 inches = 0.4 feet
Sο, the area οf the scaled bridge deck in square feet is:
2 feet x 0.4 feet = 0.8 square feet
Tο find the area οf the actual bridge deck in square feet, we need tο multiply the area οf the scaled bridge deck by the square οf the scale factοr:
Area οf actual bridge deck = 0.8 square feet x (40²) = 1280 square feet
Therefοre, the area οf the actual bridge deck in square feet is 1,280 square feet.
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Answer:
Step-by-step explanation:
The scale factor indicates the actual bridge is 40 times larger than the drawing.
Increase the scale dimensions by the factor of 40.
24 times 40 = 960"
4.8 times 40 = 192" (I changed 4 4/5 to 4.8)
Area = length times width
960 times 192 = 184320 sq inches actual bridge deck in square inches
Divide 183320 by 144 (sq inches in a square foot) = 1280 sq feet
Jim drives at a speed of 50 miles per hour.
How long will it take to drive 125 miles?
Answers
Answer:
2 hours and 30 minutes
Step-by-step explanation:
50 miles times 3 minus 25
A projectile is launched from the ground with an initial speed of 220 ft/sec at an angle of 60° with the horizontal.
What is the height of the projectile after 4 seconds?
How long is the projectile in the air?
What is the horizontal distance traveled by the projectile?
What is the maximum height of the projectile?
Answers
The height of the projectile after 4 seconds is 421.28 ft.
The projectile is in the air for 8.015 seconds.
The horizontal distance traveled by the projectile is 881.77 ft.
The maximum height of the projectile is 464.1 ft.
To solve this problem, we can use the kinematic equations of motion for a projectile.
Let's assume that the initial height of the projectile is zero.
What is the height of the projectile after 4 seconds:
We can use the equation:
\(y = yo + vot + 1/2at^2\)
where
y = height of the projectile
yo = initial height (zero in this case)
vo = initial vertical velocity = 220 sin(60°) = 190.53 ft/sec
a = acceleration due to gravity \(= -32.2 ft/sec^2\) ( negative since it acts downwards)
t = time = 4 sec
Plugging in the values, we get:
\(y = 0 + (190.53)(4) + 1/2(-32.2)(4)^2 = 421.28 ft\)
Therefore, the height of the projectile after 4 seconds is 421.28 ft.
Long is the projectile in the air:
The time of flight of a projectile can be calculated using the equation:
t = 2vo sinθ / g
where θ is the launch angle and g is the acceleration due to gravity.
Plugging in the values, we get:
t = 2(220 sin(60°)) / 32.2 = 8.015 sec
Therefore, the projectile is in the air for 8.015 seconds.
Horizontal distance traveled by the projectile:
The horizontal distance traveled by the projectile can be calculated using the equation:
\(x = xo + vot + 1/2at^2\)
where
x = horizontal distance traveled
xo = initial horizontal position (zero in this case)
vo = initial horizontal velocity = 220 cos(60°) = 110 ft/sec
a = acceleration due to gravity (zero in the horizontal direction)
t = time = 8.015 sec
Plugging in the values, we get:
\(x = 0 + (110)(8.015) + 1/2(0)(8.015)^2 = 881.77 ft\)
Therefore, the horizontal distance traveled by the projectile is 881.77 ft.
Maximum height of the projectile:
The maximum height of a projectile can be calculated using the equation:
\(ymax = yo + (vo^2 sin^2 \theta ) / 2g\)
Plugging in the values, we get:\(ymax = 0 + (190.53^2 sin^2(60\degree )) / (2)(32.2) = 464.1 ft\)
Therefore, the maximum height of the projectile is 464.1 ft.
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Match each function to its domain and range.
a country's population in 1990 was 37 million in 1999 it was 40 million estimate the population in 2016 using exponential growth formula round your answer to the nearest million
Domain and Range
Function
domain: {0, 1, 3, 5, 6}
range: {-20, -16, -8, 0, 4}
arrowBoth
domain: {-2, -1, 0, 3, 4}
range: {-13, -8, -3, 12, 17}
arrowBoth
domain: {-4, -2, 0, 2, 4}
range: {-40, -20, 0, 20, 40}
arrowBoth
domain: {-3, -2, -1, 2, 6}
range: {0.5, 0, -1.5, 3, 2}
arrowBoth
Answers
Answer:
This is the concept of application of exponential growth, suppose in 1990 time,t=0 and in 1990 time,t=9. Using the exponential growth formula given by:
f(t)=ae^(kt)
thus substituting the value we get:
40=37e^(9k)
this can be written as:
(40/37)=e^(9k)
introducing the natural logs we get:
ln(40/37)=9k
hence;
k=1/9ln(40/37)=0.0087
Therefore our formual will be given by:
f(t)=37e^(0.0087t)
N/B: The population is in millions. Thus to get the population in 2016 we shall proceed as follows;
t=26
thus
f(t)=37e^(26*0.0087)
f(t)=46.35 million
Step-by-step explanation:
5x + y = -3
x + 4y = 26
Slove this using elimnation
Answers
Answer:
x=-2 y=7
Step-by-step explanation:
Multiple -5 for the second equation to get -5x-20y=-130. Adding -5x-20y=-130 to 5x+y=-3 should get you -19y=-133. Divide both sides by -19 to get y=7. Subsitute 7 in for y for the first equation. Subtract 7 on both sides to get 5x=-10. Divide both sides by 5 to get x=-2. So, x=-2 and y=7.
Right triangle
What is the area
Left = 20 in
Bottom = 2 in
Answers
Therefore, it would be 1/2*2*20 which is 20 (sq. Inch)
Answer:
20sq in
Step-by-step explanation:
h x b / 2
20 x 2 / 2
40/2
20
If the side length of of rectangle is 3x-3 and the top length is 6, how do I write a linear equation the represents the area and a linear equation that represents the perimeter, all measurements are in cm if that is useful.
Answers
Perimeter of the rectangle is: 6x + 6 cm
Area of the rectangle is: 18x - 18 cm²
What is the Area and Perimeter of a Rectangle?Area = (length)(width)
Perimeter = 2(length + width).
Given the following:
Length of rectangle = 3x - 3
Width = 6
Area = (3x - 3)(6)
Area = 18x - 18 cm²
Perimeter = 2(3x - 3 + 6) = 2(3x + 3)
Perimeter = 6x + 6 cm
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The company’s president would like to examine the sampling distribution of the sample proportion of east regional responsibility. What proportion of the first sample (Andrew, Beth) has an east regional responsibility?
Answers
Answer:
the answer is 1
Step-by-step explanation:
got it right on edge
Find x
13x+5)
(6x – 14)°
y + 8)
Answers
Answer:
X=21
Step-by-step explanation:
3x+5+6x-14=180
9x-9=180
9x=180+9
9x=189
x=21
Answer the following. Solve for X
Answers
Answer:
x = 7
Step-by-step explanation:
\(3+16x = 6x+8+65\\3+16x=6x+73\\10x=70\\x=7\)
Buzz graphed two lines in order to find the solution to a given system of equations what is the solution?
Answers
Answer: (1,-4)
Step-by-step explanation:
What angle is this need help asap
Answers
Answer:
This is an acute angle, I accidently said it was a right angle before