Answer:
Center (h, k) = 2 and -3
Radius = 4
Step-by-step explanation:
Given the mathematical expression;
(x - 2)² + (y + 3)² = 16 ......equation 1.
The general equation for a circle is given by the formula;
x² + y² + 2hx + 2ky + c = 0 ......equation 2.
Where the center is C(-h, -k)
Similarly, the standard form of the equation of a circle is;
(x - h)² + (y - k)² = r² ......equation 3.
Where;
h and k represents the coordinates of the centre.r represents the radius of the circle.Comparing equation 1 and equation 3, we have;
The center of the circle, C(h, k) are 2 and -3
Radius = √16 = 4
Rectangle PQRS is rotated 90° clockwise about the origin.
On a coordinate plane, rectangle P Q R S has points (negative 3, negative 1), (negative 1, negative 1), (negative 1, negative 4), (negative 3, negative 4).
What are the coordinates of R’?
R’(4,–1)
R’(–4,1)
R’(1,4)
R’(–1,–4)
Answer:
R' (-4 , 1)
Step-by-step explanation:
Rotation of 90°
(Clockwise)
(x, y) ----> (y, -x) (take opposite of x, then switch the x and y)
Rotation of 90°
(CounterClockwise)
(x, y)------>(-y, x)
Rotation of 180°
(Both Clockwise and Counterclockwise)
(x, y) ----->(-x, -y)
Rotation of 270°
(Clockwise)
(x, y) ----->(-y, x)
Rotation of 270°
(CounterClockwise)
(x, y)------>(y, -x)
Answer:
The answer is: R'(-4,1).
Step-by-step explanation:
If the 90 degree angle is clockwise, the new figure will be in quadrant 2 (or in the section directly above the pre-image). Therefore, (x,y) maps to (y,-x), which will give us (-4,1).
If a = 5, b = 4, and c = 7, find the value for 3(b + a) = c.
10
15
34
20
Answer:
20
Step-by-step explanation:
3 (b + a) = c
3 (4 + 5) = 7
12 + 15 = 7
27 = 7
27 - 7
20
[tex]\huge\boxed{ \sf{Answer}} [/tex]
Given,
[tex]a = 5 \\ b = 4 \\ c = 7[/tex]
And the equation we need to solve is,
[tex]3(b + a) = c[/tex]
To find the answer, you need to substitute the values of a, b & c in the equation.
[tex]3(b + a) = c \\ 3b + 3a = c \\ ( 3 \times 4) +( 3 \times 5) = 7 \\ 12 + 15 = 7 \\ 12 + 15 - 7 = 0 \\ = 27 - 7 \\ = 20[/tex]
↦ The answer is 20.
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
Question 8: Find the equation of the straight line that:
(a) has a gradient of 4 and passes through the point (1, 10)
Answer:
[tex]y=4x+6[/tex]
Step-by-step explanation:
Hi there!
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope (also called the gradient) and b is the y-intercept (the value of y when x is 0)
1) Plug the gradient into the equation (b)
[tex]y=mx+b[/tex]
We're given that the gradient of the line is 4. Plug this into [tex]y=mx+b[/tex] as m:
[tex]y=4x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=4x+b[/tex]
Plug in the given point (1,10) as (x,y) and solve for b
[tex]10=4(1)+b\\10=4+b[/tex]
Subtract 4 from both sides to isolate b
[tex]10-4=4+b-4\\6=b[/tex]
Therefore, the y-intercept of the line is 6. Plug this back into [tex]y=4x+b[/tex] as b:
[tex]y=4x+6[/tex]
I hope this helps!
answer = y = 4x + 6
y = mx + b
gradient = slope = m = 4
(1,10) = (x,y)
plug in the values
10 = 4 (1) + b
10 = 4 + b
b = 6
y = 4x + 6
Find the values of x and y from the following equal ordered pairs. a) (x,-2) = (4,y) b) (3x, 4) = (6, 2y) c) (2x-1, y + 2) = (-1,2) d) (2x + 4, y + 5) = (3x + 3,6) e) (x + y,y + 3) = (6, 2y) f) (x + y, x - y) - (8,0)
Answer:
a)
x=4, y=-2
b)
x=2, y=2
c)
x=0, y=0
d)
x=1, y=1
e)
x=3, y=3
f)
x=4, y=4
Step-by-step explanation:
a) (x,-2) = (4,y)
x=4
y=-2
b) (3x, 4) = (6, 2y)
3x=6 => x=2
2y=4 => y=2
c) (2x-1, y + 2) = (-1,2)
2x-1 =-1 => x=0
y+2 = 2 => y=0
d) (2x + 4, y + 5) = (3x + 3,6)
2x+4 = 3x+3 => x=1
y+5 = 6 => y=1
e) (x + y,y + 3) = (6, 2y)
x+y = 6 => x+3 = 6 => x=3
y+3 = 2y => y=3
f) (x + y, x - y) - (8,0)
x+y = 8 => 2x=8 => x=4
x-y = 0 => x=y => y=4
find the volume of the cylinder in terms of pi and to the nearest tenth
Answer:
100π
Step-by-step explanation:
Before we even begin solving for the volume we should note that the question says to find the volume of the cylinder " in terms of pi". this means that if pi is present we do not apply it to our final answer and we just leave our answer as __pi
Having that being cleared let's find the volume
volume of a cylinder = πr²h
where r = radius and h = height
looking at the figure the cylinder has a known radius of 5in and a given height of 4in
so r = 5 and h = 4
that being said we want to plug in these given variables into the volume of a cylinder formula
V = πr²h
r = 5 and h = 4
V = π5²4
5²=25
25(4)=100
V = 100π
once again we must leave our answer in terms of pi so the final answer would be 100π
According to the rational root theorem which of the following are possible roots for the function below x^4-29x^2+100
Hello,
The rational roots may be all divisors of 100
+1,-1,+2,-2,+4,-4,+5,-5,+10,-10,+20,-20,+25,-25,+50,-50,+100,-100
f(x)=x^4-29x^2+100
f(5)=5^4-29*5^2+100=0 : 5 is a root
f(-5)=(-5)^4-29*(-5)²+100=0 : -5 is a root
f(2)=2^4-29*2²+100=0 : 2 is a root
f(-2)=(-2^)^4-26*(-2)²+100= 0 : -2 is the last root.
someone help me for this algebra task please
Answer:
The answer is
[tex]4+ x[/tex]
Using the definition of linear equation,
[tex]y = 4 + x[/tex]
Is the answer.
Create an exponential function, and then create a second exponential function that shifts your original function down 7 units
Answer:
A general exponential function is written as:
f(x) = A*e^(k*x)
Where A and k are real numbers.
Because we want to "create" a exponential function, we must assign numbers to A and k, let's assign:
A = 1
k = 1
then our function is just:
f(x) = e^(x)
Now we want to shift down 7 units.
So let's describe a general vertical shift.
For a general function f(x), a vertical shift is written as:
g(x) = f(x) + N
if N is positive, the shift is upwards
if N is negative, the shift is downwards.
Here we want to have a shift down of 7 units, then we would write:
g(x) = f(x) - 7
Replacing by the actual function f(x) we get:
g(x) = e^x - 7
Below you can see the graphs of both functions:
Where the orange one is f(x) and the purple one is g(x).
Which statement about y= 7x2 + 23x + 6 is true?
Answer:
Please include the statements too
If P(A) = 2/3, P(B) = 4/5 and P(AnB) = 3/5, what is P(AuB)?
Answer:
13/15
Step-by-step explanation:
P(A∪B) = P(A) + P(B) – P(A∩B)
= 2/3 + 4/5 - 3/5
Getting a common denominator
2/3 *5/5 + 4/5*3/3 - 3/5 *3/3
10/15 + 12/15 - 9/15
13/15
Answer:
[tex] \frac{13}{15} [/tex]
Step-by-step explanation:
We know that,
P(AUB) = P(A) + P(B) - P(A n B)
So,
[tex]P(AUB) = P(A) + P(B) - P(A n B) \\ = \frac{2}{3} + \frac{4}{5} - \frac{3}{5} \\ = \frac{10 + 12 - 9}{15} \\ = \frac{22 - 9}{15} \\ = \frac{13}{15} [/tex]
hope this helps you.
Have a nice day!
Currently they sell a tub of popcorn for $10. SHOW or EXPLAIN what the cost of the cone of popcorn should be. Door context: The tub has a volume of 540.473 and costs $10. The cone has a volume of 140.035. I need the cost of the cone and preferibly be taught how to do this.
Answer:
The cost of cone of popcorn is $ 2.59.
Step-by-step explanation:
The tub has a volume of 540.473 and costs $10. The cone has a volume of 140.035.
The cost of per unit volume is
$10/540.473
The cost of cone of popcorn is
[tex]\frac{10}{540.473}\times 140.035\\\\2.59[/tex]
Bạn đang kiểm toán khoản mục nợ phải trả của Công ty Hoàn Vũ cho niên độ kết thúc ngày 31/12/200x. Trên bảng cân đối kế toán, có 1 khoản nợ phải trả như sau: - Tiền lương lũy kế phải trả công nhân viên 21.270.000đ - Phải trả cho nhà cung cấp về số hàng mua đã nhận nhưng chưa nhận được hóa đơn vào ngày 30/06/200x: 40.000.000đ yêu cầu: Cho biết các thử nghiệm chi tiết mà bạn cần thực hiện nhằm xác định tính trung thực và hợp lý của các khoản trên.
Answer:
Never going to give you up.
Step-by-step explanation:
We're no strangers to love
You know the rules and so do I
A full commitment's what I'm thinking of
You wouldn't get this from any other guy
I just wanna tell you how I'm feeling
Gotta make you understand
Never gonna give you up
Never gonna let you down
Never gonna run around and desert you
Never gonna make you cry
Never gonna say goodbye
Never gonna tell a lie and hurt you
We've known each other for so long
Your heart's been aching but you're too shy to say it
Inside we both know what's been going on
We know the game and we're gonna play it
And if you ask me how I'm feeling
Don't tell me you're too blind to see
Never gonna give you up
Never gonna let you down
Never gonna run around and desert you
Never gonna make you cry
Never gonna say goodbye
graphical representation of the function x = f( y) shows that the zeroes will come on
Answers
The zeros of a function represent the x-intercept(s) when the function is graphed. The zeros of a function represent the root(s) of a function.
the width of a newspaper is 13 3/4 inches. The left margin is 7/16 inch and the right margin is 1/2 inch. what is the width of the written page inside the margin?
Answer:
biggafigure a
mnn
Step-by-step explanation:
the diagram on the right shows a circle.given that the length of arcs RS=2QR , angle QPR=35° and anglePSQ=45°,determine the value of
(a) angle SPR
(b) angle SRP
9514 1404 393
Answer:
(a) ∠SPR = 70°
(b) ∠SRP = 30°
Step-by-step explanation:
The applicable relationships are ...
the measure of an arc is twice the measure of the inscribed angle it subtendsthe sum of measures of the arcs of a circle is 360°the sum of measures of the angles of a triangle is 180°__
QR is subtended by 35° inscribed angle QPR, so is 2×35° = 70°.
PQ is subtended by 45° inscribed angle PSQ, so is 2×45° = 90°.
RS is 2×QR, so is 2×70° = 140°.
(a) Inscribed angle SPR is half the measure of arc RS, so is 140°/2 = 70°.
__
(b) Arc SP is the remaining arc in the circle, so is ...
arc SP = 360° -arc PQ -arc QR -arc RS = 360° -90° -70° -140° = 60°.
Inscribed angle SRP is half the measure of arc SP, so is 60°/2 = 30°
Find the measure of the indicated angle
Answer:
X = 88 degrees
Step-by-step explanation:
Because its an isosceles triangle the two top angles are 46.
46 + 46 = 98
then you take the degree of the triangle 180 and subtract 98 from it to get 88 degrees
A man is twice as old as his son. Five years ago, the ratio of their ages was 9:4. Find the son's present age
Answer:
Son's age is 25.
Step-by-step explanation:
Let the Father's age be 2x.
Let the son's age be x.
Five years ago:
Man's age will be = 2x - 5
Son's age will be = x - 5
If the ratio of their ages five years ago was 9:4, then:
2x - 5/x-5 = 9/4
⇒ 4(2x - 5) = 9(x - 5)
⇒ 8x - 20 = 9x - 45
⇒ -20 + 45 = 9x - 8x
⇒ 25 = x
∴ x = 25
Hence, the son's age = 25 years
If x = 25, the father's age (2x) will be 2 × 25 = 50 years
Which function has a vertex at (2, 6)?
O f(x) = 2|x – 2| – 6
O f(x) = 2|x – 2| + 6
Of(x) = 2|x + 2| + 6
Of(x) = 2|x + 2| - 6
Answer:
B
Step-by-step explanation:
Trust me bro. It’s “B.”
Does anyone know this
The total width is shown as 12 ft. The width of the small square is 2 ft so the width of the larger square is 12-2 = 10 ft.
Area of each square: 10 x 10 = 100
2 x 2 = 4
Total area = 109 + 4 = 104 square ft.
add the quotient of d and b and the difference of c and a
Answer:
d/b + c - a
Step-by-step explanation:
if there is nothing missing from the problem statement, then this is the only possible answer.
Do you agree? Explain why or why not.
Answer:
if x = 4
[tex]\sqrt{8 + 1} + 3 = 0[/tex]
[tex]\sqrt{9} + 3 = 0[/tex]
3 + 3 = 0
6 = 0
wrong.
प्रश्नावली- 13.2 1. एक तम्बू के नीचे का भाग लम्बवृत्तीय बेलनाकार तथा ऊपरी भाग शंक्वाकार है। यदि तम्बू के आधार का व्यास 14 मील बेलनाकार भाग की ऊँचाई 5 मीटर तथा तम्बू की सम्पूर्ण ऊँचाई 14 मोटर है तो तम्बू का आयतन ज्ञात कोजिए। P.01 :
I can't understand the meaning of question
The length of a rectangle is 3
more than 5 times its width.
Find the perimeter of this
rectangle if its area is 92 m2.
[?]m
Let W = width then length = 5W + 3
Area = W(5W + 3) = 5W2 + 3W = 92
5W2 + 3W - 92 = 0 has a negative root and the positive root = 4 (by the quadratic formula)
The length = 23 and the perimeter = 2(L + W) 2 * 27 = 54
I dont know if this is right because I cant see the last part in less its like that
simplify the following radical expression -7√2 + 10 √2
Answer:
3√2
Step-by-step explanation:
* means multiply
-7√2 + 10 √2
take √2 out of the expression
√2 (-7 + 10)
√2 (3)
3√2
Someone please answer this
Answer:
(x - 1)(5x - 6)
Step-by-step explanation:
Given
5x² - 11x + 6
Consider the factors of the product of the coefficient of the x² term and the constant term (ac) which sum to give the coefficient of the x- term (b)
ac = 5 × 6 = 30 and b = - 11
The factors are - 5 and - 6
Use these factors to split the x- term
5x² - 5x - 6x + 6 ( factor the first/second and third/fourth terms )
= 5x(x - 1) - 6(x - 1) ← factor out (x - 1) from each term
= (x - 1)(5x - 6)
help me with this please
Help mee A scout troop are hiking in a forest. Starting from their base, they walk 4.2km south followed by 7.1km west. They want to walk the shortest distance back to their base. On what bearing should the scouts walk?
Answer:
They should walk on a bearing of 59.4 degrees
Step-by-step explanation:
Given
[tex]South = 4.2km[/tex]
[tex]West = 7.1km[/tex]
Required
The bearing back to the base
The given question is illustrated with the attached image.
To do this, we simply calculate the measure of angle a using:
[tex]\tan(a) = \frac{Opposite}{Adjacent}[/tex]
[tex]\tan(a) = \frac{7.1}{4,2}[/tex]
[tex]\tan(a) = 1.6905[/tex]
Take arctan of both sides
[tex]a = \tan^{-1}(1.6905)[/tex]
[tex]a = 59.4^o[/tex]
The bearing that the scout should work is N59.4W for the shortest distance
Trigonometric ratioTrigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.
Let A represent the angle that the scouts walk
tan∠A = 4.2/7.1
A = 30.6°
The bearing that the scout should work is N59.4W (90 - 30.6) for the shortest distance
Find out more on Trigonometric ratio at: https://brainly.com/question/4326804
What is the slope of the line that contains the points in the table
Answer:
C. -5
General Formulas and Concepts:
Algebra I
Coordinates (x, y)Slope Formula: [tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]Step-by-step explanation:
Step 1: Define
Find points from table
Point (-1, 6)
Point (0, 1)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points [Slope Formula]: [tex]\displaystyle m = \frac{1 - 6}{0 - -1}[/tex]Subtract: [tex]\displaystyle m = \frac{-5}{1}[/tex]Simplify: [tex]\displaystyle m = -5[/tex]PLZ I NEED ANSWER ILL GIVE BRAINLIEST
Answer:
y = -2x + 1
Step-by-step explanation:
y2 - y1 / x2 - x1
-3 - 3 / 2 - (-1)
-6 / 3
= -2
y = -2x + b
3 = -2(-1) + b
3 = 2 + b
1 = b
Maths Aryabhatta
Brainly moderators
Brainly Stars
Genius users of brainly
Solve the following pair of linear equations using substitution method :-
2x+3y + 5 = 0 ; 5x-3y+9=0
Answer:
(- 2, - [tex]\frac{1}{3}[/tex] )
Step-by-step explanation:
Given the 2 equations
2x + 3y + 5 = 0 → (1)
5x - 3y + 9 = 0 → (2)
Rearrange (1) expressing 3y in terms of x by subtracting 2x + 5 from both sides
3y = - 2x - 5
Substitute 3y = - 2x - 5 into (2)
5x - (- 2x - 5) + 9 = 0 ← distribute parenthesis on left side and simplify
5x + 2x + 5 + 9 = 0
7x + 14 = 0 ( subtract 14 from both sides )
7x = - 14 ( divide both sides by 7 )
x = - 2
Substitute x = - 2 into either of the 2 equations and solve for y
Substituting into (1)
2(- 2) + 3y + 5 = 0
- 4 + 3y + 5 = 0
1 + 3y = 0 ( subtract 1 from both sides )
3y = - 1 ( divide both sides by 3 )
y = - [tex]\frac{1}{3}[/tex]
solution is (- 2, - [tex]\frac{1}{3}[/tex] )