A(,-2,4)=b= -2
B,(5,2)= b=17
find an equation of the circle whose diameter has endpoints (-2,-5) and (6,-1)
The equation of the circle in standard form with a center at (2, -3) and a radius [tex]\(4\sqrt{5}\)[/tex] is [tex]\( (x - 2)^2 + (y + 3)^2 = 80 \)[/tex].
To find the equation of the circle with the diameter endpoints given,
The midpoint of a segment with endpoints (x1, y1) and (x2, y2) is given by the formula:
Midpoint [tex]\((M_x, M_y)[/tex] = [tex]\left(\frac{x1 + x2}{2}, \frac{y1 + y2}{2}\right)\)[/tex]
For the endpoints A (-2,-5) and B (6,-1), we calculate:
[tex]\(M_x = \frac{-2 + 6}{2} = \frac{4}{2} = 2\)[/tex]
[tex]\(M_y = \frac{-5 + (-1)}{2} = \frac{-6}{2} = -3\)[/tex]
So, the midpoint, which is the center of the circle, is C (2, -3).
The radius is half the length of the diameter, and the length of the diameter is the distance between the endpoints A and B using the distance formula:
Distance d = [tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2} \)[/tex]
r = [tex]\frac{d}{2} = \frac{\sqrt{(6 - (-2))^2 + (-1 - (-5))^2}}{2} \)[/tex]
Calculating the expressions:
r = [tex]\frac{\sqrt{(6 + 2)^2 + (-1 + 5)^2}}{2} \)[/tex]
= [tex]\frac{\sqrt{8^2 + 4^2}}{2} \)[/tex]
= [tex]\frac{\sqrt{64 + 16}}{2} \)[/tex]
= [tex]\frac{\sqrt{80}}{2} \)[/tex]
= [tex]\frac{8\sqrt{5}}{2} \)[/tex]
r = [tex]4\sqrt{5} \)[/tex]
The equation of a circle with center (h, k) and radius r can be represented as:
[tex]\( (x - h)^2 + (y - k)^2 = r^2 \)[/tex]
Plugging our midpoint as the center and our radius into the equation:
[tex]\( (x - 2)^2 + (y + 3)^2 = (4\sqrt{5})^2 \)[/tex]
Simplifying,
[tex]\( (x - 2)^2 + (y + 3)^2 = 16 \cdot 5 \)[/tex]
[tex]\( (x - 2)^2 + (y + 3)^2 = 80 \)[/tex]
Thus, the required equation is [tex]\( (x - 2)^2 + (y + 3)^2 = 80[/tex].
help me with this problem
- 9 ≤ x ≤ 7
the domain is the values of x on the x- axis that define y = f(x)
y is defined for all values of x in the stated domain
SHOW WORK
1) copper has density of 8.92 g/cm^3. How many milliliters of water would be displaced if 46kg of copper granules were poured into a barrel filled with water?
2) If the density of water is 1.00 g/mL, will the substances above float or sink in the water??
Answer:
1) Volume of water displaced = 5.16 L
2) Copper sinks in water.
Explanation:
1) Density of copper = 8.92[tex]g/cm^3[/tex]
Mass of copper = 46 kg = 46000 g
We know that, Density = Mass / volume
So, Volume = Mass/ density
Volume of copper = 46000/8.92 = 5156.95 [tex]cm^3[/tex]
Since the density of copper 8.92[tex]g/cm^3[/tex] is greater than density of water 1[tex]g/cm^3[/tex], the copper immerses in water. Since it immerses it will displace a volume of water which is equal to the volume of copper.
So volume of water displaced = volume of copper = 5156.95 [tex]cm^3[/tex] =5.16 L of water
2) Since the density of copper 8.92[tex]g/cm^3[/tex] is greater than density of water 1[tex]g/cm^3[/tex], the copper immerses in water. So copper sink in water.
Rameen’s heating bill is $5.42 per month plus $1.08 per therm. How many therms can Rameen use if he wants his heating bill to be a maximum of $87.50? Write the solution in interval notation.
Write and solve an inequality:
Total(t) = $5.42 + ($1.08/therm)(t) ≤ $87.50.
First, subtract $5.42 from $87.50: then ($1.08/therm)(t) ≤ $82.08
Next, divide both sides by $1.08 per therm:
t ≤ ($82.08) / ($1.08/therm) = 76 therms (maximum). Thus, Rameen's usage could be [0,76] (therms).
Answer:
[0,76]
Step-by-step explanation:
Step 1. Read the problem.
Step 2. Identify what you are looking for.
the number of therms Rameen can buy
Step 3. Name what you are looking for. Choose a variable to represent that quantity.
Let t= the number of therms.
Step 4. Translate. Write a sentence that gives the information to find it. Translate into an inequality.
$5.42 plus $1.08 times the number of therms is less than or equal to $87.50.
5.42+1.08t≤87.50
Step 5. Solve the inequality.
1.08tt≤82.08≤76
Step 6. Check the answer in the problem and make sure it makes sense.
Yes, 5.42+1.08(76)=87.50.
Step 7. Answer the question with a complete sentence.
Rameen can buy no more than 76 therms if he wants his heating bill to be a maximum of $87.50.
Since it is not possible to buy a negative number of therms, the lest number of therms Rameen can buy is 0.
In interval notation, the amount of therms Rameen can buy is [0,76].
What percentage increase is this?
400 to 500
9514 1404 393
Answer:
25% increase
Step-by-step explanation:
A percentage change is calculated using the formula ...
percent change = ((new value) - (old value))/(old value) × 100%
= (500 -400)/400 × 100%
= 100/400 × 100%
= 25%
A positive percentage change indicates an increase.
The change from 400 to 500 is a 25% increase.
Mrs. Riley is teaching her class to sew pillows. Each pillow requires yards of fabric. The fabric she purchased cost $2.40 per yard.
How many pillows will her class be able to make if she purchased $405 of fabric?
A.
75 pillows
B.
78 pillows
C.
85 pillows
D.
98 pillows
Mrs. Riley can make 168 pillows because she bought 168.75 yards of fabric and each pillow requires 1 yard of fabric.
Explanation:First, we need to determine how many yards of fabric Mrs. Riley purchased. We do this by dividing the total cost of the fabric ($405) by the cost per yard ($2.40). So, 405 ÷ 2.4 = 168.75 yards. Each pillow requires 1 yard of fabric, therefore she can sew 168 pillows with no leftover fabric.
Here is the calculation in more detail:
Divide the total money Mrs. Riley spent on fabric by the cost of fabric per yard. That is, 405 ÷ 2.4 = 168.75.Since each pillow requires 1 yard of fabric, the number of pillows that can be made is the same as the number of yards of fabric purchased. Therefore, Mrs. Riley can make 168 pillows (rounding down to the nearest whole pillow).Learn more about Math Calculation here:https://brainly.com/question/31573607
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The longest side of an acute triangle measures 30inches. The two remaining sides are congruent, but their length is unknown. What is the smallest possible perimeter of the triangle, rounded out the nearest hundredth
The two short sides must be longer than those required in an isosceles right triangle. The ratio of side length to hypotenuse length in a 45°-45°-90° triangle is 1 : √2. So, such a triangle requires side lengths of 30/√2 ≈ 21.213 inches. Its perimeter will be about
... (30 +21.213 +21.213) in = 72.426 in
Since the perimeter needs to be slightly longer than that for the triangle to be acute, the smallest possible perimeter is ...
... 72.43 in
You are asked to choose your favourite season of the year, and then your second favourite season. Draw a tree diagram to display the number of different possible outcomes.
800 is 10 times more
8000 because u add an extra 0 if u multiple with a number with a zero or no
3(4x-2)=12 how many solutions
ONE solution was found, 1.5
What is the value of –2x2 + 4y if x = –2 and y = 3?
You would first substitute x and y into the equation so: -2(-2)^2+4(3)
Then you solve:
-2(-2)^2+4(3)
8+12
so your answer will be 20
Use the identity a^3+b^3=(a+b)^3−3ab(a+b) to determine the sum of the cubes of two numbers if the sum of the two numbers is 4 and the product of the two numbers is 1.
Your identity says ...
... sum of cubes = (sum)³ -3(product)(sum)
... = 4³ -3·1·4
... = 64 -12 = 52
_____
The two numbers are 2±√3, and the sum of their cubes is indeed 52.
Divide. (5 1/4)÷(−2 1/2) Enter your answer as a mixed number, in simplified form, in the box.
Answer:
2 1/10
Step-by-step explanation:
(5 1/4)/(2 1/2)
Change mixed fraction to improper fractions
(21/4)/(2 1/2)
(21/4)/(5/2) =21/10
=2 1/10
Answer:
2 1/10
Step-by-step explanation:
You fill a large water tank with 3.4 x 10^3 gallons of water. About 6.1% of the water is not fresh water. How many gallons of fresh water are in a tank? Show work.
Answer:
Total gallons of fresh water in the tank [tex]3.1926*10^3[/tex] gallons.
Step-by-step explanation:
Percentage of fresh water = [tex]100%-6.1%[/tex]
=93.9%
Total number of gallons of water in tank = [tex]3.4*10^3[/tex] (given in the question)
Therefore,
Total gallons of fresh water in the tank = [tex]3.4*10^3*93.9/100[/tex]
=[tex]3.1926*10^3[/tex] gallons.
144 divide by 12 - 18 + 3?
if im not mastaken the answer is -48
Please help!!
Christa buys 14 flowerpots. Some are small and cost $2.40 each. The rest are large and cost $5.60 each. She spends a total of $49.60. Which equation models this situation? Let s represent the number of small flowerpots she buys.
A. 5.6s + 2.4(s + 14) = 49.6
B. (2.4 + 9.6)(14 – s) = 49.6
C. 2.4s + 5.6(14 – s) = 49.6
D. 5.6s + 2.8(14) = 49.6
The price of the small pots is $2.40 so you would have 2.4s ( multiply the number of small pots by the price)
She bought a total of 14 pots, so the number of large pots would be 14 - s ( subtract the number of small pots from the total )
Now you have:
L = 14-s
2.4s + 5.6(14-s) = 49.6
The answer is C.
There are 4,200 adults in Lakeview. Three-eighths of the adults in Lakeview do not have children. How many adults in Lakeview have children? Need to show work of how I reached the answer
Assuming the adults that have children and the ones that don't together make up the entire population of adults, then the number that have children will be ...
... 4200 - (3/8)×4200
... = 4200×(1 -3/8) = 4200×5/8 = 2625
2625 adults in Lakeview have children
. The dimensions of a large broken window are 122⁄3 feet wide and 81⁄3 feet tall. How many square feet of glass are required to replace the window?
Answer:
[tex]1098[/tex] square feet of glass is needed to replace the window.
Step-by-step explanation:
Square feet is the unit of measure of Area. How many square feet of glass are required to replace the window can be found by calculating the area of the window.
Area of the window = Width * Length
=[tex]\frac{122}{3}*\frac{81}{3}[/tex]
=[tex]\frac{122*81}{3*3}[/tex]
=[tex]\frac{9882}{9}[/tex]
=[tex]1098[/tex] square feet.
∴ we need [tex]1098[/tex] square feet of glass.
1098 ft²
Area = width × height
= [tex]\frac{122}{3}[/tex] × [tex]\frac{81}{3}[/tex]
= [tex]\frac{122(81)}{3(3)}[/tex] = [tex]\frac{9882}{9}[/tex]= 1098 ft²
Which two points are on the graph of y = -x + 3?
a. (-1, -2), (1, 4)
b. (1, 2), (0, -3)
c. (0, 3), (4, -1)
d. (4, -1), (1, 3)
FYI: There is only one answer to this question
c. (0, 3), (4, -1)
for (0,3): 3 = -0 + 3 good
for (4,-1): -1 = -4 + 3 good
(c)
Substitute the x-coordinate from each point into the equation and if equal to the corresponding y- coordinate then the point lies on the line
(a)
x = - 1 : y = 1 + 3 = 4 ≠ - 2
x = 1 : y = - 1 + 3 = 2 ≠ 4
(b)
x = 1 : y = 2 = 2
x = 0 : y = 0 + 3 = 3 ≠ - 3
(c)
x = 0 : y = 3 = 3 ← correct
x = 4 : y = - 4 + 3 = - 1 = - 1 ← correct
the pair of points is (c)
Balls numbered from 1 to 38 are placed in a contianer and stirred. If one is drawn at random what is the probability that the number is a prime number?
The primes in the range 1–38 are ...
... 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37
There are 12 of them, so the probability of drawing a prime is
... 12/38 = 6/19
Answer:
[tex]\text{Probability}=\frac{6}{19}[/tex]
Step-by-step explanation:
Given : Balls numbered from 1 to 38 are placed in a container and stirred. If one is drawn at random.
To find : The probability that the number is a prime number
Solution :
Probability is defined by,
[tex]\text{Probability}=\frac{\text{Favorable outcome}}{\text{Total number of outcome}}[/tex]
Favorable outcomes - To get the number is prime number from 1 to 38
Prime numbers are those which were not divisble by any number except 1 and itself.
From 1 to 38 - 2,3,5,7,11,13,17,19,23,29,31,37
Favorable outcome = 12
Total number of outcome is 1 to 38 = 38
[tex]\text{Probability}=\frac{\text{Favorable outcome}}{\text{Total number of outcome}}[/tex]
[tex]\text{Probability}=\frac{12}{38}[/tex]
[tex]\text{Probability}=\frac{6}{19}[/tex]
How can you write 0.326 in two other forms
Which of the following is the equation of a line that passes through the point (3,2) and is parallel to the y-axis? A. x = 2 B. y = 3 C. x = 3 D. y = 2
Answer:
Option C is right answer
Step-by-step explanation:
We have in coordinate geometry a straight line in slope intercept form as
y = mx+c
where m is the slope and c is the y intercept
There are special lines when m=0 and m = infinity.
When a line is parallel to y axis, it has slope = tan90 = infinity.
Hence line will have equation of the form x = a for some a.
Since the line passes through (3,2) we can find a using this.
Substitute x value to get 3 = x
Hence equation of the line is x =3
Answer:
X=3
Step-by-step explanation:
Daniel is currently 26 years older than his son. In 6 years he will be 3 times older than his son. How old are both of them?
daniel will be 32 and his son will be 8
To find the number of boys, you can set up an equation using the given information. Solve the equation to find the number of boys.
Explanation:To solve this problem, let's define a variable for the number of boys. Let x represent the number of boys.
According to the problem, we know that the amount of boys is 3 times the number of boys, minus 2. So the expression for the number of boys is 3x - 2.
We also know that the total number of people is 26. Therefore, we can set up an equation: 3x - 2 + x = 26.
By combining like terms and solving the equation, we can find the number of boys. The solution is x = 7. Therefore, there are 7 boys.
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Q # 4 if anybody can help me
Solution:
Given equation of line [tex]-4x+2y=24[/tex]
To find the x-intercept of the equation, substitute [tex]y=0[/tex] in the equation,
[tex]\Rightarrow -4x+2(0)=24\\\Rightarrow -4x=24\\\Rightarrow x=-\frac{24}{4} =-6[/tex]
Hence, x-intercept of the equation is [tex](-6,0)[/tex].
To find the y-intercept of the equation, substitute [tex]x=0[/tex] in the equation,
[tex]\Rightarrow -4(0)+2y=24\\\Rightarrow 2y=24\\\Rightarrow y=\frac{24}{2} =12[/tex]
Hence, y-intercept of the equation is [tex](0,12)[/tex].
Travis had a rectangular garden that measured 10feet by 12 feet. He planted pumpkins in his garden. Each pumpkin olant took up 2 feet by two feet. How many pumpkin plants did Travis fit in the garden
30
dividing the length and width by 2
10 ÷ 2 = 5 and 12 ÷ 2 = 6
he can plant 5 × 6 = 30 pumpkin plants
rearrange 2y=x into y=mx+b
You want to get y by itself
y=1/2 x
y=mx+b
m=1/2 b=0
y = [tex]\frac{1}{2}[/tex] x + 0
given 2y = x ( divide both sides by 2 )
y = [tex]\frac{1}{2}[/tex] x + 0
Find the quotient 4/15÷1/6
Answer:
1 3/5
Step-by-step explanation:
4/15÷1/6
Copy dot flip
4/15 * 6/1
24/15
Divide the top and bottom by 3
8/5
Change the improper fraction to a mixed number
5 goes into 8 1 time with 3 left over
1 3/5
Simplify. 8√-76 Enter your answer, in simplest radical form, in the box.
Answer:
6i\sqrt{19}
Step-by-step explanation:
Given: △PTC
m∠T=120°, m∠C=30°
PT=4
Find: PC.
Givens
m<T = 120
m<C = 30
PC = 4
Find PC
Solution
4/sin(30) = PC / sin(120) Note: this is the sine law.
Multiply both sides by sin(120)
[tex]\dfrac{4*sin(120)}{sin(30)} = \text{PC}[/tex]
4*0.866/0.5 = PC
Answer
PC= 6.928
steve has quiz scores of 60,64,75,71. If all the quizzes count the same, what is the lowest grade he can make on the next quiz to have an average score of 70? how do i solve this problem
Answer:
The last quiz score must be at least an 80 to get the average to be a 70.
Step-by-step explanation:
In order to find this, you need to take the average of the 4 test scores along with the unknown test score (x). So, to find an average, we add all the numbers together and divide by the amount of tests taken. We can then set this equal to 70 since that is the minimum average.
(60 + 64 + 75 + 71 + x)/5 = 70 ------> Multiply both sides by 5
(60 + 64 + 75 + 71 + x) = 350 -----> Combine like terms
270 + x = 350 -----> Subtract 270 from both sides
x = 80