The standard form equation of the circle with endpoints (-10, -8) and (-6, -2) is (x + 8)^2 + (y + 5)^2 = 13.
Explanation:To find the standard form equation of a circle, we need to find the center and the radius. Since the endpoints of the diameter are given, we can find the center by finding the midpoint of the diameter. The x-coordinate of the center is the average of the x-coordinates of the endpoints, and the y-coordinate of the center is the average of the y-coordinates of the endpoints. The radius is half the length of the diameter. Once we have the center and radius, we can plug them into the standard form equation of a circle, which is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.
Step 1: Find the midpoint of the diameter using the formula:
(x, y) = ((x1 + x2) / 2, (y1 + y2) / 2)
(x, y) = ((-10 + -6) / 2, (-8 + -2) / 2) = (-16 / 2, -10 / 2) = (-8, -5)
Step 2: Find the radius by halving the length of the diameter:
Length of the diameter = √((x2 - x1)^2 + (y2 - y1)^2) = √((-6 - -10)^2 + (-2 - -8)^2) = √(16 + 36) = √(52)
Radius = √(52) / 2 = √(13)
Step 3: Plug the center and radius into the standard form equation of a circle:
(x + 8)^2 + (y + 5)^2 = 13
Eleven is 20% of _______?
Answer: the answer is 55, eleven is 20% of 55
Write each statement as a proportion using colons. 4 is to 20 as 2 is to 10.
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Can someone help please........ thanks
Nate tells his mom that he took a test with 60 questions and scored 85%. How many questions did he answer correctly? Show how you know.
Koji is installing a rectangular window in a office building, the window is
8
2
3
feet wide and
5
3
4
feet high. The formula for the area of a rectangle is
A=bh
.What is the area of the window?Enter your answer as a mixed number in simplest form in the box. URGENT WORTH 58 POINTS AND WILL GIVE BRAINLIEST!!
Given a right prism where p is the perimeter of the base, h is the height, BA is the area of the bases, and LA is the lateral area, what is the surface area?
Check all that apply.Mulitple answers not just one answer!
A. SA=16-LA
B. SA=BA+LA
C. SA=1/2 16+LA
D. SA=BA+ph
E. SA=p+LA
Answer:
SA= BA+ph
SA= BA+LA
Step-by-step explanation:
Just did this question on APEX.
Alicia is making a triangular sign for the school play. The area of the sign is 558 in. The base of the triangle is 36in. What is the height of the triangle?
Answer:31 in
Step-by-step explanation:558 ×1/2 ×36 × h = 31 in
In the figure, a∥e , m∥n , and m∠2 = 117°.
What is m∠5 ?
63°
90°
117°
180°
63 is the answer
what the person said
Help I’m really stuck and need help fastttttttt!!!!!!!?
Jessica is saving for college. She makes a $75 deposit each week into her savings account. She also decided to use some of the money from the savings account to buy a new music player for $225. The inequality 75x−225≥975 can be used to find x, the number of weeks it will take Jessica to have at least $975 in the account for college. Which graph shows the solution of this inequality?
how to find the surface area of the cube
how to solve Questions 1&2?
Write the explicit formula that represents the geometric sequence -2, 8, -32, 128
The Geometric Sequence Formula:
[tex]a_n=a_1r^{n-1}[/tex]
We have:
[tex]a_1=-2,\ a_2=8,\ a_3=-32,\ a_4=128,\ ...[/tex]
[tex]d=\dfrac{a_{n+1}}{a_n}\to d=\dfrac{8}{-2}=-4[/tex]
Substitute:
[tex]a_n=-22\cdot(-4)^{n-1}=-22\cdot(-4)^n\cdot(-4)^{-1}=-22\cdot(-4)^n\cdot\left(-\dfrac{1}{4}\right)=5.5(-4)^n[/tex]
Answer:
Step-by-step explanation:
so the answer would be?????
Two consecutive odd numbers are such that seven times the smaller, subtracted from nine times the bigger, gives 144. Find the numbers.
The smaller odd number is 63, and the next consecutive odd number is 65.
To find the consecutive odd numbers, an algebraic equation is set up and solved, yielding the smaller odd number as 63 and the next consecutive odd number as 65.
To find two consecutive odd numbers meeting the stipulated condition, we will set up an algebraic equation. Let the smaller odd number be represented by n, then the next consecutive odd number is n + 2. The given condition is that seven times the smaller odd number subtracted from nine times the bigger odd number equals 144. This can be expressed as the equation 9(n + 2) - 7n = 144.
Solving the equation:
Expand the equation: 9n + 18 - 7n = 144Combine like terms: 2n + 18 = 144Subtract 18 from both sides: 2n = 126Divide both sides by 2: n = 63Therefore, the smaller odd number is 63, and the next consecutive odd number is 65.
4/9. 11/13. 6/5. 14/21 in simplest form
vince begin practicing up on a piano at 5:15 p.m. he stopped playing at 5:35 p.m. how many degrees did the minute hand turn during vince's
practice time explain how you found your answer.
The Wilkes family sold both of their cars. They sold one car for $7,700 and the other for $9,050. Estimate the difference in the selling price of the two cars by rounding to the nearest thousand and then subtracting.
How many 1/8s are in 3?
There are 24 number of 1/8s are in 3.
What is Division?A division is a process of splitting a specific amount into equal parts.
We need to find how many 1/8 's are in 3.
To find this we just need to divide three by 1/8.
3/1/8
Three is divided by one by eight.
The whole number is divided by the fraction.
The fractions has numerator and denominator.
When whole number is divide by the fraction the result we get by multiplying the whole number by denominator of the fraction.
3×8/1
24
Hence, there are 24 number of 1/8s are in 3.
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Help please I’m stuck on this problem
find the area of the trapezoid with a base of 19 inches, height 12.6 inches and base 29.2 inches
Malik drinks 1/2 liter of water and 1/3 liter of juice. Did Malik drink more water or juice?
Read the following statement: Line segment AB is congruent to line segment QR. Which of the following is an equivalent statement?
AB overbar is similar to QR overbar
AB overbar equals QR overbar
AB overbar is an element of QR overbar
AB overbar is congruent to QR overbar
Answer: [tex]\overline{AB}[/tex] is congruent to [tex]\overline{QR}[/tex].
OR
AB overbar is congruent to QR overbar.
Step-by-step explanation:
The given phrase : Line segment AB is congruent to line segment QR.
We know that to represent a line segment MN we write it in the below notation:-
[tex]\overline{MN}[/tex] (By putting a bar on the name)
Similarly , Line segment AB can be written as [tex]\overline{AB}[/tex] and Line segment QR can be written as [tex]\overline{QR}[/tex]
Therefore , we write the given phrase as : [tex]\overline{AB}[/tex] is congruent to [tex]\overline{QR}[/tex].
Evaluate the expression when a=−15 and b=−5.
b2
------------ =
a + 5
Help
The value of the given mathematical expression b^2 divided by a+5 when a=-15 and b=-5 is -2.5.
Explanation:In the given expression, we're asked to evaluate b2 divided by (a + 5), where a = -15 and b = -5. First we substitute the values of a and b into the expression.
So, b2 becomes (-5)2 = 25 and a + 5 becomes -15 + 5 = -10.
Now, substituting these results back into the original expression, we get 25 divided by -10, which equals -2.5.
Therefore, the value of the given expression when a=-15 and b=-5, is -2.5.
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A cylinder has a surface area of 1850 square meters and a radius of 9 meters. Estimate the volume of the cylinder to the nearest whole number.
the equation of a circle is x - y + 1 = 0 . if one end of the diameter is ( 3, p) and other end is ( a, 2 ) , find the equation of the circle.
The equation of the circle in standard form is represented by the expression x² + y² = 2.
How to analyze a geometric locus
Geometric loci are point sets that represents a figure. A circle is a case of geometric locus. In this question we must determine the coordinates of the two points contained in the circumference and derive a circle equation in standard form.
Now we proceed to solve the following system of linear equations:
p = 4 (1)
a = 1 (2)
Then, the ends of the diameter are (3, 4) and (1, 2) and the radius of the circle is found by the following Pythagorean expression:
[tex]r = \frac{1}{2}\cdot \sqrt{(1-3)^{2}+(2-4)^{2}}[/tex]
r = √2
Lastly, the equation of the circle in standard form is represented by the expression x² + y² = 2. [tex]\blacksquare[/tex]
RemarkThe statement is incomplete. Complete statement is shown below:
The equation of the diameter of a circle is x - y + 1 = 0. If one end of the diameter is (3, p) and other end is (a, 2). Find the equation of the circle.
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A survey finds that 40% of students ride in a car to school. Eri would like to estimate the probability that if 3 students were randomly selected, only 1 rides in a car. To simulate this probability, she lets the numbers 0, 1, 2, and 3 represent a student who rides in a car to school and then 4, 5, 6, 7, 8, and 9 represent a student who does not ride in a car to school. She then has a computer randomly select 3 numbers. She repeats this process for 20 trials. The results of these trials are shown in the table. 468 380 120 220 553 945 935 607 473 490 074 981 692 518 408 954 943 389 594 569 Based on this simulation, what is the estimated probability that only 1 of 3 randomly selected students rides in a car to school? Enter your answer, as a decimal, in the box.
The estimated probability that only 1 of 3 randomly selected students rides in a car to school is 0.4 or 40%.
Explanation:The estimated probability that only 1 of 3 randomly selected students rides in a car to school can be calculated by dividing the number of trials where only 1 student rides in a car by the total number of trials. In this case, there were 8 trials where only 1 student rides in a car out of a total of 20 trials.
Therefore, the estimated probability is:
8 / 20 = 0.4
So, the estimated probability is 0.4 or 40%.
Of each side of a equilateral triangle has a measure of 14 units what is the measure of the altitude (1 point)
Please help!
A square hot tub will be placed in the center of an enclosed area near the pool. Each side of the hot tub measures 6 feet. It will be surrounded by x feet of deck on each side. The enclosed space is also square and has an area of 169 square feet. Find the width o the deck space around the hot tub, x.
Part 1
Write an equation for the area of the enclosed space in the form y=(side length)^2. Hint: Don't forget to add x to each side of the hot tub.
Part 2
Substitute the area of the enclosed space for y in your equation.
Part 3 Solve your equation from part 2 for x.
Part 4
What is the width of the deck around the hot tub.
Describe how to draw the geometric mean in a right triangle
To draw the geometric mean in a right triangle, first draw a perpendicular from the right angle to the hypotenuse, creating two smaller triangles. Then use the properties of similar triangles or the Pythagorean theorem to find the geometric mean, which is the length of the perpendicular you drew.
Explanation:To draw the geometric mean in a right triangle, you can use the following step-by-step method:
Identify the right triangle within which you want to find the geometric mean. Assume this triangle has sides of lengths a and b, with c being the hypotenuse.Drop a perpendicular from the right angle to the hypotenuse, subdividing the original triangle into two smaller right triangles. This line segment will be the geometric mean, which we can label as x.Apply the properties of similar triangles or the Pythagorean theorem. The two smaller triangles will be similar to the original right triangle and to each other.The geometric mean x relates to the segments of the hypotenuse (which can be labeled d and e, where d + e = c), through the relationships x² = ad and x² = be.Since x is the geometric mean between a and b, the equations can also be written as x = √(ad) and x = √(be).Finally, measure the length of the perpendicular line you have drawn with a ruler to get the magnitude of the geometric mean x, or calculate it using the relationships stated.The Pythagorean theorem, a² + b² = c², can also be helpful in finding the lengths of the segments on the hypotenuse if they are not given.