The equation of the circle centered at (1, 3) with a radius of 4 units is:
(x - 1)^2 + (y - 3)^2 = 16
How to write the equation of a circle?For a circle with the center on the point (a, b) and radius R, the equation is:
(x- a)^2 + (y - b)^2 = R^2
In this case, the center is (1, 3) and the radius is R = 4, so the equation will be, so we just replace these in the general equation that we have above.
(x - 1)^2 + (y - 3)^2 = 4^2
(x - 1)^2 + (y - 3)^2 = 16
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Exercise #5: Quadrilateral EFGH has vertices at E(-6,2), F(3,8), G(7,2), and H(-2,-4).
Calculate the slopes of all four sides of EFGH. Use these slopes to prove that EFGH is a rectangle.
Answer:
The slope of both EF and GH are 2/3
The slope of both FG and EH are -3/2
You can see that these slopes are perpendicular, forming a rectangle
Step-by-step explanation:
To find slope use the slope formula: y1 - y2 / x1 - x2
so first:
8 - 2 / 3 - (-6) = 2/3
(-4) - 2 / (-2) - 7 = 2/3
Then:
8 - 2 / 3 - 7 = -3/2
2 - (-4) / (-6) - (-2) = -3/2
100 POINTS! ! !
Exploiting will be reported.
Chase deposits $6,604.80 into a savings account that pays a simple annual interest rate of 3.22%. How much interest will he earn after 4 years?
SHOW WORK and will give brainlist.
Answer:
$850.69824
Step-by-step explanation:
simple interest formula : (principal * rate of interest * time)/100(6,604.80 * 3.22 * 4)/100$850.69824Answer:
$850.70 (nearest cent)
Step-by-step explanation:
Simple interest formula: A = P(1 + rt)
where:
A = final amountP = principal (initial balance)r = annual interest rate (in decimal form)t = time (in years)Given:
P = $6,604.80r = 3.22% = 0.0322t = 4 yearsSubstituting given values into the formula, and solving to find A:
⇒ A = 6604.8(1 + 0.0322 · 4)
= 6604.8(1.1288)
= $7455.50 (nearest cent)
Therefore, to find the amount of interest earned, subtract the principal from the final amount:
⇒ I = A - P
= 7455.50 - 6604.80
= $850.70 (nearest cent)
Solve the equation, 3x – 6 = 12, for x. Which of the following properties did you apply? Question 2 options: A) Addition property of equality and multiplication property of equality B) Addition property of equality and division property of equality C) Distributive property, subtraction property of equality, and multiplication property of equality D) Distributive property, addition property of equality, and division property of equality
If 18% of a number is 24, find 3% of that number. You must show your work in the work space.
Answer:
hello
18 % = 24
3 % = ( 3 x 24 ) / 18 = 4
Step-by-step explanation:
Reflections on a Coordinate Plane
Answer:
The reflection coordinates of JKL would be:
J (3,7)
K (2,3)
L (-1,5)
The reflection coordinates of MNP would be:
M (8,-6)
N (2,-4)
P (8,-4)
Step-by-step explanation:
Select the correct answer.
Function m is the result of a transformation on the parent tangent function.
Answer:
C
Step-by-step explanation:
General equation of a tangent function is: y=atanb(theta-c)+d
Based on the graph, it moved pi/2 to the right.
So, the answer is C.
The result of a transformation on the parent tangent function is g(x) = tan( x - (π / 3 ). The correct option is C.
What is a parent function?A parent function in mathematics is the simplest function in a family of functions that keeps the definition of the entire family.
The general equation of a tangent function is represented as below:-
y=atanb(Ф-c)+d
Based on the graph, it moved π/2 to the right. Therefore, the result of a transformation on the parent tangent function is g(x) = tan( x - (π / 3 ). The correct option is C.
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Find the average of this set of numbers.28, 26, 21, 13
A) 22
B) 20
C) 19
D) none of the above
Answer:
A
Step-by-step explanation:
26 + 28 = 54
54 + 21 = 75
75 + 13 = 88
88 / 4 = 22
Answer is A
Answer: 22
Step-by-step explanation: Add all of the numbers in the data set: 28+26+21+13= 88
Then divide 88 by 4: 22
=
If f(x) is an exponential function where f(-2) = 25 and f(7) = 85, then find the
value of f(14), to the nearest hundredth.
=
Exponential from two points
The exponential function f(x) can represent growth or decay
The value of f(14) is 226.07
How to determine the value of f(14)?The given parameters are:
f(-2) = 25 and f(7) = 85
An exponential function is represented as:
f(x) = ab^x
So, we have:
ab^-2 = 25
Also, we have:
ab^7 = 85
Divide both equations.
This gives
b^9 = 3.4
Take the 9th root of both sides
b = 1.15
Recall that:
ab^7 = 85
This gives
a* 1.15^7 = 85
Solve for a
a = 31.95
So, the exponential function is:
f(x) = 31.95 * 1.15^x
Substitute 14 for x
f(14) = 31.95 * 1.15^14
f(14) = 226.07
Hence, the value of f(14) is 226.07
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I really need help... can someone pls help me
Volume = length x width x height
Volume of large box = 4 x 3 x 5 = 60 cubic feet.
the volume of the smaller boxes is greater than the volume of the larger box so he cannot fit them all.
Two students each write a function, C(n), that they think can be used to find the number of circles needed to make the nth figure in the pattern shown.
Use the drop-down menus to explain why each function does or does not represent the number of circles needed to make the nth figure in the pattern.
The function that can be find used to find the number of circles needed to make the nth figure in the sequence is (C + 1) + 4.
How to calculate the sequence?The sequence can be illustrated through the function (C + 1) + 4 where C is the previous number. For the third picture, the number of circles will be:
= (C + 1) + 4
= 5 + 4
= 9
The fourth term will be:
= 9 + 4
= 13
Therefore, each figure uses 4 circles more than the previous one.
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Answer:
Step-by-step explanation: This function can be used to find the number of circles needed to make the nth figure in the pattern.
Each figure uses 4 more circle(s) than the previous figure because an additional circle is added to the top, bottom, left, and right sides.
the other half i got incorrect.
prove that it is congruent
Answer:
The dashes on the side lengths mean that they are equal in length
⇒ PQ = RP
The triangles share one side PS
The figure also states that m∠QPS = m∠RPS
Therefore, the triangles are SAS congruent since they have two pairs of congruent sides and a congruent included angle.
write an equation for the graph below in the terms of x
An airplane flies with a constant speed
of 840 km/h. How far can it travel in
1 hour?
Answer:
840 km
Step-by-step explanation:
The speed expression ...
840 kilometers per hour
means the plane files 840 kilometers in each hour.
In 1 hour, it will travel 840 km.
Find the missing number if the average is 8.8 and _____
A) 4
B) 8
C) 12
D) none of the above
Answer:
none of the above
Step-by-step explanation:
Let us call x the smallest integer. Because the next two numbers are consecutive even integers, we can call represent them as x + 2 and x + 4. We are told the sum of x, x+2, and x+4 is equal to 72.
x + (x + 2) + (x + 4) = 72
3x + 6 = 72
3x = 66
x = 22.
This means that the integers are 22, 24, and 26. The question asks us for the product of these numbers, which is 22(24)(26) = 13728.
The answer is 13728.
y=1/2x+2 y=1/3x+2 solve for graphing
Answer:
I plotted it out on the graph and here it is:
A company promises to release a new smartphone model every month. Each model's battery life will be 5% longer than the previous model's. If the current model's battery life is 663.0 minutes, what will the latest model's battery life be 7 months from now?
Answer:
895.05
Step-by-step explanation:
5% of 663 is 33.15, so times 33.15 by the 7 months and the answer to that is 232.05 then add that to the current battier life.
The answer is 895.05
What is the result when you combine only the constants in the following expression?
3a-6b+3-7a+ 10
Can somebody please help me
Answer: C
Step-by-step explanation:
This is just a straight definition - for a normal distribution, the percent within 2 standard deviations of the mean is about 95.44%.
Find the domain and range of the function shown.
Please help I’ll mark brainliest thank you.
Answer:
A
Step-by-step explanation:
Remember domain is input and range is output.
Input: All real numbers
Output: [0, infinity)
A
The polynomial below is a perfect square trinomial of the form A^2 - 2AB + B^2
9x^2 - 12x + 4
A. True
B. False
Answer:
True
Step-by-step explanation:
[tex]9x^2-12x +4 \\\\=(3x)^2 - 2\cdot 3x \cdot 2+2^2\\\\=(3x-2)^2[/tex]
If tanθ= 2 find cotθ using identities. This is in quad. 1.
Answer: 1/2
Step-by-step explanation:
Can someone please help me
Find the value of y and z
[tex]\qquad\qquad\huge\underline{{\sf Answer}} \huge♨[/tex]
In the given figure, NQ acts as a diameter and since diameter subtends 90° at the arc of the circle, so we can conclude that ~
[tex]\qquad \sf \dashrightarrow \:3y = 90 \degree[/tex]
[tex]\qquad \sf \dashrightarrow \:y = 90 \degree \div 3[/tex]
[tex]\qquad \sf \dashrightarrow \:y = 30 \degree [/tex]
Now, Let's use Angle sum property of Triangle to solve for z :
[tex]\qquad \sf \dashrightarrow \:4z + 3y + 50 \degree = 180 \degree[/tex]
[tex]\qquad \sf \dashrightarrow \:4z +90 \degree + 50 \degree = 180 \degree[/tex]
[tex]\qquad \sf \dashrightarrow \:4z = 180 \degree - (50 \degree + 90\degree)[/tex]
[tex]\qquad \sf \dashrightarrow \:4z = 180 \degree - (140\degree)[/tex]
[tex]\qquad \sf \dashrightarrow \:4z = 40 \degree[/tex]
[tex]\qquad \sf \dashrightarrow \:z = 40 \degree \div 4[/tex]
[tex]\qquad \sf \dashrightarrow \:z = 10 \degree [/tex]
I hope you understood the procedure, you can ask me in comments if you have any doubts.
Help me pls
Question 4 Part B (2 points): In part A you factored f(x) = 9m2 + 3m - 2. What are the x intercepts of this function? SELECT ALL THAT APPLY.
A.
m = -1/3
B.
m = 1/3
C.
m = -2/3
D.
m = 2/3
E.
m = 3
F.
m = -3
G.
m = 6
H.
m = -6
We need zeros
[tex]\\ \rm\Rrightarrow 9m^2+3m-2=0[/tex]
[tex]\\ \rm\Rrightarrow 9m^2-3m+6m-2=0[/tex]
[tex]\\ \rm\Rrightarrow 3m(3m-1)-2(3m-1)=0[/tex]
[tex]\\ \rm\Rrightarrow (3m-2)(3m-1)=0[/tex]
m=2/3mm=1/3Work out the length of X.
25 cm
х
24 cm
The diagram is not drawn accurately.
0
cm
Answer:
By Pythagoras theorem
H^2=P^2+B^2
25^2=x^2+24^2
625=x^2 + 576
625-576=x^2
49=x^2
x^2=49
x=√49
x=7cm
Hope this helps uhh
If we randomly select 2 students at a time and record their drinking habits, what is the probability that both students drink
Answer:
1 liter
Step-by-step explanation:
x2by 100%8hdofux27675 868*uhf
How many more quarters does
Tommy need before he has $3.00
in quarters?
Helppppp!!! 50 pts!
Translate the sentence into an equation.
Three times the sum of a number and 5 is 7.
Use the variable C for the unknown number.
Answer:
3(C + 5) = 7
Step-by-step explanation:
Let C = unknown number
The sum of a number and 5:
C + 5
Three times the sum of a number and 5:
3(C + 5)
Three times the sum of a number and 5 is 7:
3(C + 5) = 7
To solve
Use the distributive law: a(b + c) = ab + ac
⇒ 3C + 15 = 7
Subtract 15 from both sides:
⇒ 3C = -8
Divide both sides by 3:
⇒ C = -8/3
So
The expression is
3(c+5)=7On solving
3c+15=73c=-8c=-8/3Find the 10th term, 18, 72,288,...
Step-by-step explanation:
a = 18
n = 10 th term
difference (d) = 72-10 = 62
an ( n th term ) = a + (n-1)d
a10 ( 10 th term = 18 + (10-1)62
= 18 + 9×62
= 18 + 558
10 the term = 576
to get to a library you must travel 1/2 mi down one street, 3/5 mi down another street and 1 1/10 mi down a third street. How many miles did you travel total to get to the library?
Answer:
11/5mi or 2.2mi
Step-by-step explanation:
1/2 +3/5 +11/10 =11/5mi
Hey there!
0.5 + 0.6 + 1.1 = 2.2
Total miles = 2.2mi