Answer:
(a) Circle Q is 9.4 units to the center of circle P
(b) Circle Q has a smaller radius
Step-by-step explanation:
Given
[tex]P:(x - 1)^2 + (y + 6)^2 = 9[/tex]
[tex]Q:(x + 4)^2 + (y + 14)^2 = 4[/tex]
Solving (a): The distance between both
The equation of a circle is:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
Where
[tex]Center: (h,k)[/tex]
[tex]Radius:r[/tex]
P and Q can be rewritten as:
[tex]P:(x - 1)^2 + (y + 6)^2 = 3^2[/tex]
[tex]Q:(x + 4)^2 + (y + 14)^2 = 2^2[/tex]
So, for P:
[tex]Center = (1,-6)[/tex]
[tex]r = 3[/tex]
For Q:
[tex]Center = (-4,-14)[/tex]
[tex]r = 2[/tex]
The distance between them is:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2[/tex]
Where:
[tex]Center = (1,-6)[/tex] --- [tex](x_1,y_1)[/tex]
[tex]Center = (-4,-14)[/tex] --- [tex](x_2,y_2)[/tex]
So:
[tex]d = \sqrt{(1 - -4)^2 + (-6 - -14)^2[/tex]
[tex]d = \sqrt{(5)^2 + (8)^2[/tex]
[tex]d = \sqrt{25 + 64[/tex]
[tex]d = \sqrt{89[/tex]
[tex]d = 9.4[/tex]
Solving (b): The radius;
In (a), we have:
[tex]r = 3[/tex] --- circle P
[tex]r = 2[/tex] --- circle Q
By comparison
[tex]2 < 3[/tex]
Hence, circle Q has a smaller radius
Log5(36)-Log5(9)
-
-
-
Condense following logarithms.
Given:
The expression is:
[tex]\log_5(36)-\log_5(9)[/tex]
To find:
The simplified form of the given expression.
Solution:
We have,
[tex]\log_5(36)-\log_5(9)[/tex]
It can be written as:
[tex]\log_5(36)-\log_5(9)=\log_5\dfrac{36}{9}[/tex] [tex][\because \log_m\dfrac{a}{b}=\log_ma-\log_m b][/tex]
[tex]\log_5(36)-\log_5(9)=\log_54[/tex]
Therefore, the simplified form of the given expression is [tex]\log_54[/tex].
whats the correct equation to solve for x
Answer:
12x - 29 + 4x + 1 = 180
Step-by-step explanation:
(12x - 29) and (4x + 1) are same- side interior angles and sum to 180° , then
12x - 29 + 4x + 1 = 180 ← is the equation to solve for x
16x - 28 = 180 ( add 28 to both sides )
16x = 208 ( divide both sides by 16 )
x = 13
On Sunday, the wind chill temperature reached −36 °F. On Monday, the wind chill temperature only reached 1 4 of Sunday's wind chill temperature. What was the lowest wind chill temperature on Monday? A −144 °F B −36 1 4 °F C −9 °F D −40 °F
Answer:
(A) -9 °F
Step-by-step explanation:
On Sunday, the wind chill temperature reached - 36 °F. On Monday, the wind chill
temperature only reached¼ of Sunday's wind chill temperature. What was the
lowest wind chill temperature on Monday? (A) -9 °F (B) -36¼°F (C) -40 °F (D) -144 °F
Sunday temperature = - 36 °F
Monday temperature = ¼ of Sunday's wind chill temperature
Monday = 1/4 of - 36 °F
= 1/4 * -36 °F
= (1 * -36)/4 °F
= -36/4 °F
= -9 °F
Monday temperature = -9 °F
The correct answer is (A) -9 °F
help me plzz plzzz plzzzz
Answer:
60 degree
Step-by-step explanation:
a hexagon has a total sum of angles equal to 720
720/6 = 120
180-120 = 60
-4(7.5x-8)=-5(6.3x+8)
Answer:
x = -48
Step-by-step explanation:
-4(7.5x - 8) = -5(6.3x + 8)
-30x + 32 = -31.5x - 40
-30x + 31.5x = -40 - 32
1.5x = -72
x = -72/(1.5)
x = -48
What is the volume of a hexagon of 6.2 cm 9 cm and 5cm ?
If a position on the ocean floor is 12 kilometers below the sea level, which value describes the elevation of the ocean floor
Answer:
- 12
Step-by-step explanation:
The sea level serves as a reference point and may be used to describe objacetsvir positions above or below it. Therefore, the sea level is regarded as a zero point or level. Hence, objects below are describes to be at a negative distance while those above are assigned the positive sign. Hence, for a position which is 12 km below sea level, then the object is said to be at a distance of - 12 km (below sea level takes the negative sign.)
What is the solution to the system of equations below?
2 x + y = 7 3 x + 2 y = 16
Answer:
2x+y=7; 3x+2y=16
X = -2
Y = 11
Identify the equation of the circle X that passes through (-3, -5) and has center (4, -7).
( x - 4 )^2 + ( y + 7 )^2 = 53
...................................................
what's the value of x and y?
Answer:
x = 45 and y = 90
Step-by-step explanation:
Let the third angle be z
z = 180 - 135 (Linear Pair)
z = 45
Since its an iscosceles triangle,
<z = <x (angles opposite to equal sides have equal angles)
<x = 45 degree
<z + <x + <y = 180
45 + 45+ <y = 180
90 + <y = 180
<y = 180 - 90
<y = 90
Therefore x = 45 and y = 90
Hope u understood please mark as brainliest
Thank You
Answer:
x= 45°
y= 90°
Step-by-step explanation:
x= angles on a straight line add up to 180°. 180°-135° = x.
y= x+y=135° & x =45°
135°- 45° = y
5ft and 12ft What is the length of the hypotenuse? feet
Answer:
The answer is 13 feet.
Step-by-step explanation:
Assuming that the lengths 5ft and 12ft are the legs of the triangle, use the Pythagorean Theorem to find the unknown length of the hypotenuse:
a^2 + b^2 = c^2
Now, simply plug in the values of the triangle legs:
5^2 + 12^2 = c^2
25 + 144 = c^2
169 = c^2
c = 13
Answer:
13 ft
Step-by-step explanation:
The formula to find the length of the hypotenuse is:
[tex]a^2+b^2=c^2[/tex]
---------------------------------------------------------------------------------------------------------------
So:
25 + 144 = 13
Have a good day :)
Tara bought one share of Apple stock in 2018 for $43.75. Then, three years later, she sold it for $136.76. How much money did she gain/lose with this stock? What was her return on investment?
Answer:
Gain= $93.01
ROI= 212.59%
Step-by-step explanation:
Given data
Cost of apple share in 2018 = $43.75
Sale price of apple share= $136.76
1. Her gain is
Gain= Sales price- Cost price
Gain = 136.76-43.75
Gain= $93.01
2. ROI is
ROI= Gain/cost*100
ROI= 93.01/43.75*100
ROI=2.1259*100
ROI= 212.59%
Photos-To-Go printed 2,102 copies of a brochure for a travel agency. The brochure included 5 photos of popular vacation destinations. How many times will all 5 photos appear in all of the printed brochures? How do you know your answer is reasonable?
Answer:
All 5 photos will appear once in all the printed brochures
Step-by-step explanation:
Given
[tex]Copies = 2102[/tex]
[tex]Photos =5[/tex]
Required
The number of times the photo will appear
The interpretation of the question is to determine the number of times the 5 photos will appear in each copy.
From the question, we understand that the photos will appear once in a copy.
By extension, the 5 photos will appear once in other copies.
what is eight less than a number as an algebraic expression
Answer: n-8
Step-by-step explanation: n represents the unknown number. You need to subtract 8 from the number since "less than" is another phrase to describe subtraction.
I hope this helps, have a nice day.
Find an explicit rule for the nth term of the sequence.
-2, -8, -32, -128
Answer:
[tex]a_{n}[/tex] = - 2 [tex](4)^{n-1}[/tex]
Step-by-step explanation:
There is a common ratio between consecutive terms , that is
r = - 8 ÷ - 2 = - 32 ÷ - 8 = - 128 ÷ - 32 = 4
This indicates the sequence is geometric with nth term
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = - 2 and r = 4 , then explicit formula is
[tex]a_{n}[/tex] = - 2 [tex](4)^{n-1}[/tex]
What is the first step you will use to solve this equation:
4x +2 = 7x - 13
A.Subtract 13 from both sides
B.Add 7x to both sides
C.Add 2 to both sides
D.Subtract 4x from both sides
Answer:
E.? subtract 2 on both sides
Step-by-step explanation:
the wording (to me) is mixed up for a and c
sry if its not correct
hey what's the answer
thanks.
Step-by-step explanation:
if b+c=0
b=-c
x^b=x^-c
so
1/[2(x^b)+1]
There is a positive correlation between number of TVs owned by a person, x, and the average life expectancy, y. What conclusion is TRUE?
Answer:
c
Step-by-step explanation:
i think this is right
hey! please help i’ll give brainliest
Answer:
I think A is the answer
hope this helps
have a good day :)
Step-by-step explanation:
complete the remainder of the rule table for the given function rule:
y = -2x - 7
x: -6, -3, 0, 3, 6
y: 5, _, _, _, _
Answer:
x=-6
y=-2(-6)-7
y=5
x=-3
y=-2(-3)-7
y=6-7=-1
y=-1
x=0
y=-2(0)-7
y=-7
x=3
y=-2(3)-7
y=-6-7=-13
x=6
y=-2(6)-7
y=-12-7
y=-19
A functional rule is the relationship between an input or domain and an output or scope.
The given function is as follows:
x: -6, -3, 0, 3, 6
y: 5, -1, -7, -13, -19
What is meant by function rule?A functional rule is the relationship between an input or domain and an output or scope. A relation is a function only if it has a value within each domain value. Functions are written like where is the input value. The general form of the function is:
A vertical test is run graphically to determine if the relationship is a function.A formula, rule, or law that defines the relationship between one variable (the independent variable) and another (the dependent variable).Functions are ubiquitous in mathematics and essential in the natural sciences for formulating physical relationships.A formula, rule, or law that defines the relationship between one variable (the independent variable) and another (the dependent variable). Functions are ubiquitous in mathematics and essential in the natural sciences for formulating physical relationships.
Let the given function be y = -2x - 7.
Where, x = -6
substitute the values in the above equation, we get
⇒ y = -2(-6) - 7
⇒ y = 5
Let the value of x = -3
substitute the values in the above equation, we get
⇒ y = -2(-3) - 7
⇒ y = -1
Put, x = 0
substitute the values in the above equation, we get
⇒ y = -2(0) - 7
⇒ y = -7
Put, x = 3
substitute the values in the above equation, we get
⇒ y = -2(3) - 7
⇒ y = -6 - 7 = -13
Put, x = 6
substitute the values in the above equation, we get
⇒ y = -2(6) - 7
⇒ y = -19
The given function is as follows:
x: -6, -3, 0, 3, 6
y: 5, -1, -7, -13, -19
To learn more about Functions, refer to:
brainly.com/question/25638609
#SPJ2
An arc of a circle is 3πm long, and it subtends an angle of 72° at the center of the circle. Find the radius of the circle.
Answer:
7.5 m
Step-by-step explanation:
circumference = 360/72 × 3π = 15π
so the radius of the circle =
15π / 2π = 7.5 m
what is the question of 1.892 x 10^8 and 4.3 x 10^3 expressed in a scientific notation
____ x 10^—
PLS ANSWER ASAP
find the slope of the line which passes through (-2, -2) and (2, -4)
HELP ME PLS
Answer:
-1/2
Step-by-step explanation:
y2 - y1 / x2 - x1
-4 - (-2) / 2 - (-2)
-2 / 4
= -1/2
Victo scored 8, 10, 8, 9, and 10 points on his first five math quizzes. He calculated the median before and after he took the sixth quiz. The median did not change. How many points did he score on his sixth quiz? pls help!
Answer:
9
Step-by-step explanation:
the median is 9 and to keep it the same you put 9
Hope this helps!!!
express the following as indicated. (1) 5 cm (in and km)
Answer:
Convert in to cm and km to cm:
1 in = 2.54 cm ⇒ 1 cm = 1/2.54 in ⇒ 5 cm = 5/2.54 in ≈ 1.9685 in1 km = 100000 cm ⇒ 1 cm = 0.00001 km ⇒ 5 cm = 0.00005 km1cm=0.4in
5cm
5(0.4)2in(Approx)Exactly one cm is 3.39 .. in so answer will come around 1.96 which is almost 2
#2
1cm=0.00001km
5cm
0.00005kmI need help. Please someone help. .......................................................................................................
Answer:
boi its 202 -1
Step-by-step explanation:
eiroiwzjsirgjzßπkgjπøˆß
I NEED THIS ASAP
Solve for X
Answer:
x^2 = 10
x = square root symbol with 10 underneath
Or x = 3.16227 (round to appropriate place)
—————
x^3 = 316
x = cubed root symbol with 316 underneath
or x = 6.81128 (round to appropriate place)
I answered them two different ways, because sometimes your teacher wants you to leave it under the square root or cube root symbol, when it can’t be solved to an exact integer.
Round your answer to the nearest hundredth
Khan Academy
Answer:
Step-by-step explanation:
take 40 degree as reference angle
using cos rule
cos 40=adjacent/hypotenuse
0.76=5/x
0.76x=5
x=5/0.76
x=6.578
x=6.58
(50 points) Subtract. (−8.3x+4)−(3.2x−5) Enter your answer, in simplified form, in the box. (Combine and simplify the equation.)
Answer:
(−8.3x+4)−(3.2x−5)
(−8.3x+4)−3.2x+5
−8.3x+4−3.2x+5
-11.5x+9
Step-by-step explanation:
How to factorise this question
Answer:
Step-by-step explanation:
90-2(a-3)^2
=88{(a)^2-2*a*3+(3)^2]
=88[a^2-6a+9}
=88a^2-528a+792