Complete question is;
Given a circle with (4. -3) and (2, 1) as the endpoints of the diameter. Write the equation of the circle.
Answer:
x² + y² - 6x + 2y + 5 = 0
Step-by-step explanation:
The end points of the diameter are;
(4. -3) and (2, 1).
Thus, the centre coordinates will be the midpoint of the diameter endpoints.
Thus;
Centre coordinates = ((4 + 2)/2), ((-3 + 1)/2) = (3, -1)
Diameter;
d = √(1 - (-3))² + (2 - 4)²)
d = √20
d = 2√5
Radius = ½ × diameter
Thus;
r = ½ × 2√5
r = √5
Equation of a circle is;
(x - a)² + (y - b)² = r²
Where;
(a, b) are coordinates of the centre of the circle
r is radius.
Thus;
(x - 3)² + (y - (-1))² = (√5)²
x² - 6x + 9 + y² + 2y + 1 = 5
x² + y² - 6x + 2y + 10 = 5
x² + y² - 6x + 2y + 10 - 5 = 0
x² + y² - 6x + 2y + 5 = 0
Instructions: Find the measure of the indicated angle to the nearest
degree.
19
?
8
=
Answer:
? ≈ 65°
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos? = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{8}{19}[/tex] , then
? = [tex]cos^{-1}[/tex] ([tex]\frac{8}{19}[/tex] ) ≈ 65° ( to the nearest degree )
Can anyone help me with this answer?
Answer: B. 1.5 × 10⁻¹⁸
Step-by-step explanation:
Concept:
When multiplying exponents, add the exponents together.
When dividing exponents, subtract the exponents.
When converting scientific notation to an integer:
If the exponent is negative, move the decimal to the left with the same amount of units as the exponents. For example: If converting 5 × 10⁻³, since the exponent is -3, we move the decimal to the left 3 unitsIf the exponent is positive, move the decimal to the right with the same amount of units as the exponentsFor example: If converting 2 × 10⁴, since the exponent is 4, we move the decimal to the right 4 unitsWhen converting an integer to scientific notation:
If the number is ≥1, then count the moves of decimal point until the integer is 0<integer<10. The number of moves will be the exponent that is positive.For example: If converting 300, since there are two moves until it is left with 0<3<10. Thus, the scientific notation will be 3 × 10²If the number is <1, then count the moves of decimal point until the integer is 0<integer<10. The number of moves will be the exponent that is negative.For example: If converting 0.004, since there are three moves until it is left with 0<4<10. Thus, the scientific notation will be 4 × 10⁻³Given:
Mass of one water molecule = 3.0 × 10⁻²³
Total number of molecules (required by the question) = 50,000
Solve:
Formula
Total mass = Mass of one water molecule × Total number of molecules
Substitute the values into the formula
Total mass = 3.0 × 10⁻²³ × 50,000
Convert 50,000 into scientific notation
Total mass = 3.0 × 10⁻²³ × 5 × 10⁴
Multiply numbers together/ Multiply exponents together
Total mass = 15 × 10⁻¹⁹ = 1.5 × 10⁻¹⁸
Hope this helps!! :)
Please let me know if you have any questions
A school wants to buy a chalkboard that measures 1 meter by 2 meters. The chalkboard costs $27.00 per square meter. How much will the chalkboard cost?
Answer:
The chalkboard costs $54.00
Step-by-step explanation:
A chalkboard is in a shape of a rectangle. The chalkboard mentioned measures 1 meter by 2 meters.
The area of a rectangle is given by the formula:
A = lw
Use formula:
A = (2)(1) = 2 m^2
The chalkboard costs $27.00 per square meter so:
2 x 27 = 54
The chalkboard costs $54.00
the ratio of Ages of Minu and her brother Sudhir is 3:4 the difference between their ages is 5 years then find their present ages
Let the ages be 3x and 4x
ATQ
[tex]\\ \Large\sf\longmapsto 4x-3x=5[/tex]
[tex]\\ \Large\sf\longmapsto x=5[/tex]
Now
[tex]\\ \Large\sf\longmapsto Age\:of\:Minu=3x=3(5)=15years[/tex]
[tex]\\ \Large\sf\longmapsto Age\:of\:Sudhir=4x=4(5)=20years[/tex]
Their present ages are 15 and 20 years.
Let the age of Minu be represented by x
Since the difference between their ages is 5 years, then the age of her brother will be x + 5.
Based on the information given in the question, the equation to use in solving the question will be:
x/(x + 5) = 3/4
Cross multiply
(4 × x) = 3(x + 5)
4x = 3x + 15
Collect like terms
4x - 3x = 15
x = 15
Minu's age is 15 years
Therefore, her brother's age will be:
= x + 5
= 15 + 5
= 20 years
In conclusion, their present ages are 15 and 20 years.
Read more on:
https://brainly.com/question/17671517
To wash a window that is 4 meters off the ground, Rafi leans a 5-meter ladder against the side of the building. To reach the window, how far away from the building should Rafi place the base of the ladder?
Answer:
Base of the ladder is 3 meters away from the building.
Step-by-step explanation:
Let's use Pythagoras theorem to solve.
Pythagoras theorem says,
[tex]a^{2} +b^{2} =c^{2}[/tex]
Here let horizontal distance is "a''
Vertical distance of window is 4 m
So, b=4
The Rafi leans 5 m ladder against the wall. So, c=5.
[tex]a^{2} +4^{2} =5^{2}[/tex]
Simplify it
[tex]a^{2} +16=25[/tex]
Subtract both sides 16
[tex]a^{2} =9[/tex]
Take square root on both sides
a=±3
So, base of the ladder is 3 meters away from the building.
Find the value of x.
Answer:
A - 55 degrees
Step-by-step explanation:
secant-tangent angle: 1/2(larger-smaller)
1/2(180-70)
1/2(110)
55 degrees
cho tam giác ABC vuông tại A < góc B=a chứng minh: a) 1+[tex]tan^{2}[/tex]a=[tex]\frac{1}{sin^{2}a }[/tex]
làm giúp mình với
[tex]\\ \sf\longmapsto 1+tan^2A[/tex]
[tex]\boxed{\sf tanA=\dfrac{sinA}{cosA}}[/tex]
[tex]\\ \sf\longmapsto 1+\dfrac{sin^2A}{cos^2A}[/tex]
[tex]\\ \sf\longmapsto \dfrac{cos^2A+sin^2A}{cos^2A}[/tex]
[tex]\boxed{\sf cos^2A+sin^2A=1}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{cos^2A}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{1-sin^2A}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{1}-\dfrac{1}{sin^2A}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{sin^2A}[/tex]
Hence verified
find the lcm of 10a²b,15ab²c and 20bc²
Answer:
jsjuuusjus??dujj??uu?jw?wuw?jjdj
Step-by-step explanation:
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q
iwsj
l
Please help !!!!!!!!!!!
Answer:
98°+62°+6x = 180
160+6x = 180
6x = 180 - 160
6x = 20
x= 20/6
x= 3.33
therefor your answer is 3.33
what is a possible solution to the inequality?
1/4a +1 > 9
Answer:
a > 32 is one possible solution to the inequality 1/4a +1 > 9.
Step-by-step explanation:
A small bird can flap its wings 120 times in 30 s. What is the rate of change of wing flaps?
Answer:
4 Flaps per second
Step-by-step explanation:
M = 120/30
Answer:
4 times per second
Step-by-step explanation:
120 ÷ 30 = 4
30 ÷ 30 = 1
4 flaps per 1 second
so basically 4
if line y bisects line AC, AB = 4 - 5x, and BC = 2x+25, find AC
Answer:
4-5x = 2x+25
-5x+4 = 2x+25
-7x = 21
x = -3
4 - 5(-3)
4 + 15
19
AC = 2 x 19
AC = 38
Let me know if this helps!
Find the missing value in each figure below. What does “y” equal?
Answer:
Step-by-step explanation:
The perpendicular is equal to 6. That's because the left triangle's missing angle is 180 - 45 -90 = 45
The angle in the right triangle is given as 52.
The cos(52) = adjacent side (which we just found to be 6) / y
Multiply both sides by y
y cos(52) = 6
cos(52) = 0.6157
Divide by sides by cos(52)
y = 6 / cos(52)
y = 6 / 0.6157
y = 9.76
help me with the picture please
=====================================================
Explanation:
Refer to the diagram below. I've drawn diagonal that slopes upward. This diagonal cuts the quadrilateral into two triangles: One is equilateral and the other is isosceles.
The equilateral triangle marked in blue has all three angles 60 degrees each.
Note that the 60 and y angles combined to form 130, so,
60+y = 130
y = 130-60
y = 70
Then focus on the isosceles triangle (angles y, w and w). These three interior angles must add to 180
y+w+w = 180
70+2w = 180
2w = 180-70
2w = 110
w = 110/2
w = 55
This adds onto its adjacent neighbor of 60 to get w+60 = 55+60 = 115 degrees which is the value of x.
Aaron's car used 2 gallons of gas to drive 32 miles. At what rate does his car use gas in miles per gallon?
Answer: 16miles per gallon
Step-by-step explanation:
If he went 32 miles with 2 gallons then divide both sides by 2 to get 16 miles with 1 gallon so he travels 16 miles per gallon
find a number such that when 3/4 of it is added to 3½the sum is the same as when 2/3 of it is subtracted from 6½. PLEASE HELP
Answer:
- 120
Step-by-step explanation:
call x is the number you want to find
(3/4 )x + 3[tex]\frac{1}{2}[/tex] = (2/3)x - 6[tex]\frac{1}{2}[/tex](3/4)x + (7/2) = (2/3)x - (13/2)(3/4)x - (2/3)x = - (13 /2) - (7/2)(1/12)x = -10x = -10 / (1/12) = -120The ratio of the measures of the acute angles of a right triangle is $8:1$. In degrees, what is the measure of the largest angle of the triangle?
Answer:
The angles in the triangle and 10, 80 and 90
Step-by-step explanation:
The two angles that are left in a right triangle add to 90 degrees
8:1 means that there total is 9
8x+1x = 9x
9x = 90
Divide by 9
9x/9 = 90/9
x = 10
8*10 = 80
1*10 = 10
The angles are 80 and 10
The angles in the triangle and 10, 80 and 90
Does anyone know the ratio? It’s the numbers below
The ratio x : x : x√2 has two parts identical to each other ( x : x) this means two of the angles also need to be identical.
Answer: 45 -45 -90
It is known that seventy percent (70%) of married couples paid for their honeymoon themselves. You randomly select 9 independent married couples and ask each if they paid for their honeymoon themselves. Let our random variable be X = the number of married couples that paid for their honeymoon themselves. What is the probability that all married coupled asked stated they paid for their honeymoon themselves? (Round your answer to four decimal places).
Answer:
0.0404 = 4.04% probability that all married coupled asked stated they paid for their honeymoon themselves.
Step-by-step explanation:
For each couple, there are only two possible outcomes. Either they paid for their honeymoon, or they did not. The probability of a couple having paid for their honeymoon is independent of any other couple, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
It is known that seventy percent (70%) of married couples paid for their honeymoon themselves.
This means that [tex]p = 0.7[/tex]
You randomly select 9 independent married couples.
This means that [tex]n = 9[/tex]
What is the probability that all married coupled asked stated they paid for their honeymoon themselves?
This is P(X = 9). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 9) = C_{9,9}.(0.7)^{9}.(0.3)^{0} = 0.0404[/tex]
0.0404 = 4.04% probability that all married coupled asked stated they paid for their honeymoon themselves.
A team of 5people to be selected from 7women & 6men. Find the number of different teams that could be selected if there must be more women than men in the team
Answer:i would say 2 differentt teams where there is more then women than men in the team
Step-by-step explanation:
well how i came to this answer is that the team is limited to only 5 people giving the only team where there is more women over men is this first team would be 4 women and 1 men , second team would be 3 women and 2 men anything lower then 3 make its where the team has more men than women so the only options would be 2 team where either they go with 4 women or 3 women and you can't go with more then 4 because then there would be no men in the team which is what the question asks for please go with 2 teams
if this helps please make me brainlist ?!
Nina is making pink candles to use as decorations on Valentine's Day. She melts red and white wax together and pours them into a heart-shaped mould. Then, she melts double the amount of red wax and double the amount of white wax together and pours them into a flower-shaped mould. Which candle is a lighter shade of pink?
Answer:
answer is neither, they are both the same shade.
Step-by-step explanation:
if she doubled the colors exactly then it wouldn't be any different. Also IXL told me I'm right :)
Answer:
Neither.
Step-by-step explanation:
Originally, she used the same amount. For the second one, she used double the same amount, but it was still the amount of red wax as of white wax. So, they both had the same amount, which means it is neither.
Can you write a formula with variables a, b and c such that we cannot make a as the subject of the formula?
Answer:
I think the one below is correct
Step-by-step explanation:
3a^2 + 2ab + c^2 = 0
find the measure of the indicated angle to the nearest degree
[tex]\boxed{\sf sin\Theta=\dfrac{P}{H}}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=\dfrac{16}{26}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=\dfrac{8}{13}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=0.5[/tex]
Convert to p/q form[tex]\\ \sf\longmapsto sin\Theta=\dfrac{5}{10}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=\dfrac{1}{2}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=sin30[/tex]
[tex]\\ \sf\longmapsto \Theta\approx30°[/tex]
Which of the following examples best represents the use of an interval scale? measuring the number of cookie boxes sold by scouts on the west coast of a town versus those sold on the east coast of the town naming the different car brands seen in a school's parking lot assessing students' ratings of their professors' performance on a five-point scale ranging from poor to excellent ranking the participants of a race based on their performance
Answer:
students' ratings of their professors' performance on a five-point scale ranging from poor to excellent
Step-by-step explanation:
There are four type of scales in mathematics. They include:
1. Nominal scale : they do not measure quantity. they are used to classify a population into two or more scales that are exhaustive and mutually exclusive. e.g. classifying a population based on gender, naming the different car brands seen in a school's parking lot
2. Ordinal scale : this scale measures ranks a population from best to worst or from least to most. e.g. ranking the participants of a race based on their performance
3. Interval scale : this scale has the property of order and equal intervals. Zero is not meaningful.
Interval scale is used when the difference between the numbers are meaningful. e.g. students' ratings of their professors' performance on a five-point scale ranging from poor to excellent Here a child who is scored 1, did very poorly and a child scored 5, performed excellently well.
4. Ratio scale : this scale has the property of order, a meaningful zero and equal intervals.
if the radius of a sphere is7 cm find its volume
Answer:
1437.33 cm square
Step-by-step explanation:
Now we will use the frmula to et the volume of a sphere
volume of sphere is
4÷3pi r cube
where r is the radius of the sphere
which linear inequatly is represented by the graph
Answer:
5
Step-by-step explanation:
Please help me: -3/4(8h + 12) = 3(n - 3)
Answer:
n = 0
Step-by-step explanation:
[tex]-\frac{3}{4}(8n+12)=3(n-3)\\\\-6n-9=3n-9\\\\-9n-9=-9\\\\-9n=0\\\\ n=0[/tex]
Answer:
n = 0
Step-by-step explanation:
-3/4(8h + 12) = 3(n - 3)
-6h - 9 = 3n - 9
-6h - 3n = -9 + 9
-9n = 0
n = 0
If [ -2 5 7 6] and |B| = -|A|, which matrix is matrix B?
|A| and |B| denote the determinants of the matrices A and B.
We have
[tex]|A| = \begin{vmatrix}-2&5\\7&6\end{vmatrix} = (-2)\times6-7\times5 = -12 - 35 = -47[/tex]
Then B is a matrix such that |B| = -|A| = +47.
The only choice satisfying this is C, since
[tex]\begin{vmatrix}12&1\\13&5\end{vmatrix} = 12\times5-13\times1 = 60 - 13 = 47[/tex]
find the missing side. Round it to the nearest tenth.
Answer:
14.3
Step-by-step explanation:
sin73 = opposite/hypotenuse = x/15
x = 15sin73 = 14.344571 = 14.3
What is the approximate value of x in the diagram below
Answer:
x = 8 cm
Step-by-step explanation:
The first step in solving this problem is to determine which trig function applies. The diagram shows that this triangle is a right triangle, that side x is opposite the 25-degree angle, and that the hypotenuse has a length of 18 cm.
The sine function of an angle Ф is defined as the ratio of the opposite side to the hypotenuse. In this case, sin Ф (or sin 25 degrees) equals x/(18 cm).
We need to determine the value of x. Adapt the above equation to this particular situation: sin 25 degrees = x/(18 cm).
To solve for x, multiply both sides of the most recent equation, above, by (18 cm). The following results: (18 cm)(sin 25 degrees) = x.
Next, use a calculator to find the value of sin 25 degrees: It is 0.4226.
Then the desired value of x is (18 cm)(0.4226), or x = 7.61 cm. This should be rounded off to x = 8 cm to reflect the level of accuracy of the given 18 cm.
