Answer: see proof below
Step-by-step explanation:
The standard equation of a circle is (x - h)² + (y - k)² = r² where (h. k) is the center of the circle and r is the radius. It is given that A (h, k) = (1, 3) and point B (x, y) = (-2,4) is on the circle. Substitute the center (h, k) and point B(x, y) = (-2,4) into the standard equation of a circle to get r² = 10. To prove that C(x, y) = (4, 2) is also a point on the circle, substitute the center (h, k) and the point C(x, y) = (4, 2) into the standard equation of a circle to get r² = 10. Since the radius is the same for both point B and point C and it is given that point B is on the circle, then we must conclude that point C is also on the circle.
Answer:
I am given that the center of a circle is at A(1, 3) and that point B(-2, 4) lies on the circle. Applying the distance formula to A and B, I get the following:
AB=Square Root ( (-2 - 1 )^2 + (4 - 3 )^2 ) = Square root ( 9 + 1 )
AB = Square root (10)
Since B lies on the circle, this length is the length of the radius of the circle. Applying the distance formula to A and C(4, 2), I get the following:
AC = Square Root ( ( 4 - 1 )^2 + (2 - 3 )^2 ) = Square root ( 9 + 1 )
AC = Square root (10)
Thus, the distance to C from the center A is equal to the length of the radius of the circle. Any point whose distance from the center is equal to the length of the radius lies on the circle. Therefore, point C lies on the circle.
Step-by-step explanation:
Which expressions are equivalent to 2(b+3c)2(b+3c)2, left parenthesis, b, plus, 3, c, right parenthesis ?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
3(b+2c)3(b+2c)3, left parenthesis, b, plus, 2, c, right parenthesis
(Choice B)
B
(b+3c)+(b+3c)(b+3c)+(b+3c)left parenthesis, b, plus, 3, c, right parenthesis, plus, left parenthesis, b, plus, 3, c, right parenthesis
(Choice C)
C
2(b)+2(3c)2(b)+2(3c)2,
Answer:
B. (b+3c)+(b+3c) C. 2(b)+2(3c)Step-by-step explanation:
Given this expression 2(b+3c), its equivalent expression is derived by simply opening up the bracket as shown below;
Open the parenthesis by multiplying the constant outside the bracket with all the variables in parenthesis.
= 2(b+3c)
= 2(b)+ 2(3c)
= 2b +2*3*c
= 2b +6c
It can also be written as sum of b+3c in 2 places i.e (b+3c)+(b+3c) because multiplying the function b+3c by 2 means we are to add the function by itself in two places.
Hence the equivalent expression are (b+3c)+(b+3c) and 2(b)+2(3c) or 2b+6c
what is the value of the angle ?
Answer:
47°
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles
124° is an exterior angle , thus
77 + ? = 124 ( subtract 77 from both sides )
? = 47°
What is the value of 4² - 2(3·5+1)? plz help, will mark brainliest A. 8 B. 1 C. -16 D. -21
Answer:
Hey there!
4^2-2(3(5)+1)
16-2(15+1)
16-2(16)
-16
C is correct.
Let me know if this helps :)
Answer:
[tex] \boxed{ \mathsf{ \boxed{ \purple{ \bold{{ - 16}}}}}}[/tex]Step-by-step explanation:
[tex] \mathsf{ {4}^{2} - 2(3 \times 5 + 1)}[/tex]
Evaluate the power
⇒[tex] \mathsf{16 - 2(3 \times 5 + 1)}[/tex]
Multiply the numbers
⇒[tex] \mathsf{16 - 2(15 + 1)}[/tex]
Calculate the sum
⇒[tex] \mathsf{16 - 2 \times 16}[/tex]
Multiply the numbers
⇒[tex] \mathsf{16 - 32}[/tex]
Calculate
⇒[tex] \mathsf{ - 16}[/tex]
Hope I helped!
Best regards!
Solve : 3X + 3x + 1 + 3x + 2 = 39
Step-by-step explanation:
[tex]3x + 3x + 1 + 3x + 2 = 39 \\ 9x + 3 = 39 \\ 9x = 39 - 3 \\ 9x = 36 \\ x = \frac{36}{9} \\ x = 4[/tex]
Answer:
x = 4
Step-by-step explanation:
combine all of the 3x first to get:
9x + 1 + 2 = 39
9x + 3 = 39
subtract 3 from both sides:
9x = 36
divide by 9
x = 4
If g(x) = (-2x²) - 3. Find g(0).
Answer:
-3
Step-by-step explanation:
When g(0), it means that x=0.
So, if we use 0 instead of x, the answer becomes:
-3
Answer:
-3
Step-by-step explanation:
g(0) = (-2(0)^2) -3
as anything multiplied with 0 is 0,
g(0) = 0 - 3
= - 3
If a population grows 3.5% per year, how much does it grow per decade? A. 35% B. 41.1% C. 38% D. 27.6%
Answer: 35%
Step-by-step explanation: It grows 3.5% every year. A decade is 10 years. 10 x 3.5% = 35% because you move the decimal one point to the right.
The population grows 41.1% per decade. Therefore, option B is the correct answer.
What is population growth and population decrease formula?If a constant rate of growth be R% per annum, then population after n years = P(1+R/100)ⁿ.
Given that, a population grows 3.5% per year.
Now, D(n)=P(1+R/100)ⁿ
Let P=1
So, D(1)=1(1+0.035)¹
D(1)=1.035
Similarly per 10 years with the same rate
D(10)=1(1+0.035)¹⁰
= (1.035)¹⁰
= 1.41059
= 1.411-1 (Initial population is 1)
= 0.411
= 0.411×100
= 41.1%
The population grows 41.1% per decade. Therefore, option B is the correct answer.
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Before you can make a pie chart you need to figure out how much of the circle belongs to each category. Suppose that you earned $6.00 doing odd jobs. You spent your money in this manner: Tithe$ 0.60 Missions$ 0.40 Recreation$ 1.80 Savings$ 2.40 School supplies$ 0.80 Remembering the formula, (category total) x 360°, you can figure out each part. For example: 60/600 x 360° = 36° Changing the dollars to cents saves confusion with the decimal point. Following thisformula tells us that, when we make our pie chart, 36° of the graph should belong tothe category of tithe.
Answer:
missions-24
recreation-108
savings-144
school supplies-48
tithe-36
Step-by-step explanation:
so first convert all the given costs to cents by multiplying each amount with 100 then add all of them to get the total as 600
in a pie chart we know that it's a circle and all angles within the circle must add up to 360 so to get an angle for a certain cost that will represent it in the chart you have to take that cost over the total to get the fraction of the circle it will occupy multiplied by 360 to get it in degrees or which portion of 360 will it occupy hence
60/600×360=36
Add or subtract. Write your answer in scientific notation.
4.2 x 10^6 − 1.2 x 10^5 − 2.5 x 10^5
3.3 x 10^9 + 2.6 x 10^9 + 7.7 x 10^8
8.0 x 10^4 − 3.4 x 10^4 − 1.2 x 10^3
Answer:
1. 38.3 x 10^5
2. 6.67 x 10^9
3. 4.48 x 10^4
Step-by-step explanation:
4.2 X 10 ^6 - 1.2 X 10^5 - 2.5 x 10^5
For the above question, we need to make the exponents equal
=> 42 x 10^5 - 1.2 x 10^5 - 2.5 x 10^5
SInce, all the exponents are equal, we can now add and subtract the normally.
=> (42 - 1.2 -2.5) x 10^5
=> (42 - 3.7) x 10^5
=> 38.3 x 10^5
So, the answer to the 1st question is 38.3 x 10^5
Next question:
=> 3.3 x 10^9 + 2.6 x 10^9 +7.7 x 10^8
=> we need to make the exponents equal
=> 3.3 x 10^9 + 2.6 x 10^9 + .77 x 10^9
=> All the exponents are equal, we can now add and subtract the normally.
=> (3.3 + 2.6 + .77) x 10^9
=> 6.67 x 10^9
=> So the answer to the 2nd question is 6.67 x 10^9
Next question,
=> 8 X 10^4 - 3.4 x 10^4 - 1.2 x 10^3
=> we need to make the exponents equal
=> 8 x 10^4 - 3.4 x 10^4 - .12 x 10^4
=> All the exponents are equal, we can now add and subtract the normally.
=> (8 - 3.4 - .12) x 10^4
=> 4.48 x 10^4
=> So the answer to the 3rd question is 4.48 x 10^4
The solutions to the expressions are:
[tex]4.2 \times 10^6 - 1.2 \times 10^5 - 2.5 \times 10^5[/tex]=[tex]38.3\times 10^5[/tex]
[tex]3.3 \times 10^9 + 2.6 \times 10^9 + 7.7 \times 10^8[/tex] = [tex]6.67\times 10^9[/tex]
[tex]8.0 \times 10^4 -3.4 \times 10^4 - 1.2 \times 10^3[/tex] = [tex]4.48 \times 10^4[/tex]
[tex]4.2 \times 10^6 - 1.2 \times 10^5 - 2.5 \times 10^5[/tex]
Combine like terms:
[tex]4.2 \times 10^6 - (1.2+2.5) \times 10^5[/tex]
[tex]4.2 \times 10^6 - 3.7 \times 10^5[/tex]
[tex]42 \times 10^5 - 3.7 \times 10^5[/tex]
[tex](42-3.7)\times 10^5[/tex]
[tex]38.3\times 10^5[/tex]
[tex]3.3 \times 10^9 + 2.6 \times 10^9 + 7.7 \times 10^8[/tex]
Convert all terms with same power:
[tex]3.3 \times 10^9 + 2.6 \times 10^9 + 0.77 \times 10^9[/tex]
[tex](3.3+2.6+0.77) \times 10^9[/tex]
[tex]6.67\times 10^9[/tex]
[tex]8.0 \times 10^4 -3.4 \times 10^4 - 1.2 \times 10^3[/tex]
[tex]8.0 \times 10^4 - 3.4 \times 10^4 - 0.12 \times 10^4[/tex]
[tex](8.0-3.4-0.12) \times 10^4[/tex]
[tex]4.48 \times 10^4[/tex]
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Find the surface area of the composite figure
Answer:
144 cm²
Step-by-step explanation:
This figure is formed by rectangles and triangles, so we need to find the surface area of they and add all to have the surface area of the figure:
area of the rectangles:
4×3 = 12, and there are two of these rectangles
6×3 = 18, and there are just one of that
4×6 = 24, and there are two of these
5×3 = 15, and there are two of these
Now the area of a triangle:
6×4/2 = 12, and there are two of these
12×2 + 18 + 24×2 + 15×2 + 12×2 = 144 cm²
sorry for the really bad quality!!
Answer:
B
Step-by-step explanation:
f(x) = x+5 when x>0. f(5)=10
Answer ASAP, Will give brainliest.
Answer:
[tex]\huge\boxed{10.4\ units\²}[/tex]
Step-by-step explanation:
Area of circle:
=> [tex]\pi r^2[/tex]
Where r = 2.8
=> [tex](3.14)(2.8)^2[/tex]
=> (3.14)(7.84)
=> 24.6 units²
Area of Triangle:
=> 1/2 (Base)(Height)
=> 1/2 (10)(7)
=> 5 * 7
=> 35 units²
Area of the shaded region:
=> 35 - 24.6
=> 10.4 units²
If the equation of a line is y = -2/3x + 1/3, what is the slope and y-intercept?
Step-by-step explanation:
Hey, there!!!
Let me explain you very simply,
The equation is;
y= -2/3 x +1/3
Now, we know the equation of a st.line in slope intercept form is,
y= m.x + c
now, comparing the given equation with y= m.x + c. we get,
m= -2/3
and y-intercept = 1/3.
Hope it helps...
Which set of whole numbers but not natural numbers
Answer:
C
Step-by-step explanation:
C is the set with whole numbers as it contains 0 and natural numbers
Can you please help me on add and subtract fractions level 1 9/8-11/8
Answer:
7/8
Step-by-step explanation:
1. Make 1 9/8 into an improper fraction
1 = 8/8
8/8 + 9/8 = 17/8
2. Subtract
17/8 - 11/8 = 7/8
Find tan 0 if sin 0 = 1/2
is in the second quadrant.
sin O = 1/2 = p/h
p=1, h = 2.
by pythagoras tgeorem,
b =
[tex] \sqrt{3} [/tex]
tan0= p/b
[tex]1 \div \sqrt{3} [/tex]
BC has endpoints B(5,9) and C(-4,-3). Find the coordinates of the midpoint of BC.
I need help !!
Answer:
(0.5,3)
Hope this helps..Have a good day!!
PLEASE ANSWER QUICKLY ASAP
ANSWER QUESTION A AND B
Answer:
a) [tex]a+b+c=\begin{pmatrix}-2\\-3\end{pmatrix}[/tex]
b) (i) [tex]a+2c=\begin{pmatrix}-4\\2\end{pmatrix}[/tex]
(ii) [tex]k=2[/tex]
Step-by-step explanation:
It is given that,
[tex]a=\begin{pmatrix}4\\-10\end{pmatrix},b=\begin{pmatrix}-2\\1\end{pmatrix},c=\begin{pmatrix}-4\\6\end{pmatrix}[/tex]
a)
We need to find the value of a+b+c.
[tex]a+b+c=\begin{pmatrix}4\\-10\end{pmatrix}+\begin{pmatrix}-2\\1\end{pmatrix}+\begin{pmatrix}-4\\6\end{pmatrix}[/tex]
[tex]a+b+c=\begin{pmatrix}4+(-2)+(-4)\\-10+1+6\end{pmatrix}[/tex]
[tex]a+b+c=\begin{pmatrix}-2\\-3\end{pmatrix}[/tex]
b)
(i) We need to find the value of a+2c.
[tex]a+2c=\begin{pmatrix}4\\-10\end{pmatrix}+2\begin{pmatrix}-4\\6\end{pmatrix}[/tex]
[tex]a+2c=\begin{pmatrix}4\\-10\end{pmatrix}+\begin{pmatrix}-8\\12\end{pmatrix}[/tex]
[tex]a+2c=\begin{pmatrix}4+(-8)\\-10+12\end{pmatrix}[/tex]
[tex]a+2c=\begin{pmatrix}-4\\2\end{pmatrix}[/tex]
(ii) It is given that a+2c=kb, where k is an integer. We need to find the value of k.
[tex]a+2c=k\begin{pmatrix}-2\\1\end{pmatrix}[/tex]
[tex]\begin{pmatrix}-4\\2\end{pmatrix}=\begin{pmatrix}-2k\\k\end{pmatrix}[/tex]
On comparing both sides, we get
[tex]k=2[/tex]
Write an expression for 267 multiplied by x
Answer:
267x
Step-by-step explanation:
Multiplication means times
267 * x
267x
Answer:
267x
when you multiply a number by a variable, you can combine the terms if there is no coefficient for the variable.
M1: L12a: Solving Equations Exit Ticket Determine which of the following equations have the same solution set. Must show work. 1. 3y + 8 = -10 - 3y 2. 6r+ 7 = 13 + 7r 3. 13 - 4m = 1 - m 4.-8-h=-3h 5. 38+7f=8f + 32 6. -6n + 20 = -14n - 4
determine which of the following has the same solution set must show work
Answer:
uhfcytuyyytt ryffffffffgtgghhh
Please show your work. I will give brainliest to the right answer!
Answer:
[tex]y = \frac{1}{8}(x + 4)^2 + 4[/tex]
Step-by-step explanation:
Given:
Focus of parabola: (-4, 6)
Directrix: y = 2
Required:
Equation for the parabola
SOLUTION:Using the formula, [tex] y = \frac{1}{2(b - k)}(x - a)^2 + \frac{1}{2}(b + k) [/tex] , the equation for the parabola can be derived.
Where,
a = -4
b = 6
k = 2
Plug these values into the equation formula
[tex] y = \frac{1}{2(6 - 2)}(x - (-4))^2 + \frac{1}{2}(6 + 2) [/tex]
[tex]y = \frac{1}{2(4)}(x + 4)^2 + \frac{1}{2}(8)[/tex]
[tex]y = \frac{1}{8}(x + 4)^2 + \frac{8}{2}[/tex]
[tex]y = \frac{1}{8}(x + 4)^2 + 4[/tex]
The average age of cars owned by residents of a small city is 6 years with a standard deviation of 2.2 years. A simple random sample of 400 cars is to be selected, and the sample mean age of these cars is to be computed. We know the random variable has approximately a normal distribution because of
Answer:
The random variable [tex]\bar x[/tex] has approximately a normal distribution because of the central limit theorem.
Step-by-step explanation:
According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n ≥ 30) are selected from the population with replacement, then the sampling distribution of the sample mean will be approximately normally distributed.
Then, the mean of the sample means is given by,
[tex]\mu_{\bar x}=\mu[/tex]
And the standard deviation of the sample means is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
Let the random variable X be defined as the age of cars owned by residents of a small city.
It is provided that:
μ = 6 years
σ = 2.2 years
n = 400
As the sample selected is too large, i.e. n = 400 > 30, according to the central limit theorem the sampling distribution of the sample mean ([tex]\bar x[/tex]) will be approximately normally distributed.
Find all solutions to the equation
in the interval [0, 21). Enter the
solutions in increasing order.
Answer:
0,1,2,3,4,5,6.......19,20
Step-by-step explanation:
in this interval 0 is included and 21 is not included. So starting from 0 up to 20, all are the solutions
i need help this is the question.
A manufacturer determines that the cost of making a computer component is $.3.191919 Write the repeating decimal cost as a fraction and as a mixed number.
Let x = 3.191919…. Then 100x = 319.191919…, and we have
100x - x = 319.191919… - 3.191919…
99x = 316
x = 316/99
Next, we have
316 = 297 + 19 = 3 × 99 + 19
so
316/99 = (3 × 99 + 19)/99 = 3 + 19/99
\large 6\cdot\frac{6+2^2}{6+2-6}
Answer:
30Step-by-step explanation:
Given the expression [tex]\large 6\cdot\frac{6+2^2}{6+2-6}[/tex], on simplification we have;
[tex]= \large 6\cdot\frac{6+2^2}{6+2-6}\\\\= \large 6\cdot\frac{6+4}{8-6}\\\\= \large 6\cdot\frac{10}{2}\\\\= 6* 5\\\\= 30[/tex]
Hence the equivalent value of the expression is 30
Please answer this question now
Answer:
48°
Step-by-step explanation:
arc BC = 136(2) -145 = 127
arc DC = 83(2) - 127 = 39
arc AD = 360 - 145- 127 - 39 = 48
Answer:
49 degrees
Step-by-step explanation:
Measure of arc ABC = 116*2 = 232 degrees.
Measure of arc BC = 232-145 = 87 degrees.
Measure of arc BCD = 83*2 = 166 degrees.
Measure of arc DC = 166-87 = 79 degrees.
Measure of arc AD = 360 - (145+87+79) = 360 - 311 = 49 degrees
ASAP how many solutions are there for the system of equations shown on the graph?
Answer: Infinitely many solutions
Step-by-step explanation:
The lines is on top of each other so this makes it many solution.
It can't be NO solution because the lines are not parallel to each, which means they will not intersect.
It can't be one solution because the lines doesn't intersect.
It can't be two solutions because the lines never intersect and they never intersect twice either.
ABCD is a quadrilateral, P Q R and S divide AB, CB, CD and AD in ratio 1:3 respectively. Prove that a//m. (Please hurry up, I will mark you as Brainliest)
Two lines are parallel if they are equidistant from one another. The following proves [tex]a || m[/tex]
[tex]Ratio = 1:3[/tex] means that:
[tex]BP=3PA[/tex]
[tex]BQ=3QC[/tex]
To prove that [tex]a || m[/tex] is to prove that side length SR and side length PQ are parallel because:
[tex]SR = a\\ PQ = m[/tex] --------- See attachment for quadrilateral
Considering [tex]\triangle ABC[/tex], we have: [tex]BP=3PA[/tex]
Divide both sides by PA
[tex]\frac{BP}{PA} = \frac{3PA}{PA}[/tex]
[tex]\frac{BP}{PA} = 3[/tex]
Similarly: [tex]BQ=3QC[/tex]
Divide both sides by QC
[tex]\frac{BQ}{QC} = \frac{3BQ}{QC}[/tex]
[tex]\frac{BQ}{QC} = 3[/tex]
So, we have:
[tex]\frac{BP}{PA} = \frac{BQ}{QC} = 3[/tex]
Express as ratios
[tex]BP:PA = BQ:QC = 3[/tex]
[tex]BP:PA \to[/tex] means point P divided side length BA into 3:1
[tex]BQ:QC \to[/tex] means point Q divided side length BC into 3:1
Thales Theorem states that: A line that divides any two sides of a triangle in the same ratio is parallel to the third side.
The third side of [tex]\triangle ABC[/tex] is [tex]AC[/tex].
This means that: [tex]PQ[/tex] is parallel to [tex]AC[/tex]
Since [tex]AC[/tex] is parallel to [tex]SR[/tex], then [tex]PQ[/tex] is parallel to [tex]SR[/tex]
i.e. [tex]SR || PQ[/tex]
Recall that:
[tex]SR = a\\ PQ = m[/tex]
Hence:
[tex]a || m[/tex] has been proved.
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2. Give an example of a rational number that is not a whole number.
This are a few of Rational numbers are not whole numbers: 8,−3,32,7−5.
Step-by-step explanation: Hope this helps
Convert 1 3/4 into a improper fraction.
Answer:
the answer must be 7/4 because
Step-by-step explanation:
1 3/4 4×1+3=7
Each lap around a park is 1 1⁄5 miles. Kellyn plans to jog at least 7 1⁄2 miles at the park without doing partial laps. How many laps must Kellyn jog to meet her goal?
Answer:
25/4 laps or (6.25 laps)
Step-by-step explanation:
1 lap = 1 1/5 miles
kellyn plans to jog 7 1/2 miles
1 lap
number of laps = 7 1/2 miles x -------------- = 25/4 laps or (6.25 laps)
1 1/5 miles