Answer:
y = 3x-2
Step-by-step explanation:
Circle P is described by the equation (x−1)2+(y+6)2=9 and circle Q is described by the equation (x+4)2+(y+14)2=4. Select from the drop-down menus to correctly complete the statements. Circle Q is Choose... units to the Choose... of circle P and Choose... units Choose..Circle P is described by the equation (x−1)2+(y+6)2=9 and circle Q is described by the equation (x+4)2+(y+14)2=4. Select from the drop-down menus to correctly complete the statements. Circle Q is Choose... units to the Choose... of circle P and Choose... units Choose... it. Circle Q has Choose... circle P.. it. Circle Q has Choose... circle P.
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
2. One important factor in inventory control is the variance of the daily demand for a product. Management believes that demand is normally distributed with the variance equal to 250. In an experiment to test this belief about , the daily demand was recorded for 25 days. The data has been summarized as follows: xbar = 50.6 and s2 = 500 Do the data provide sufficient evidence to show that management's belief about the variance is untrue? (Use alpa=0.01 ).
Answer:
we reject H0 and conclude that management's belief about variance is untrue.
Step-by-step explanation:
H0 : σ² = 250
H1 : σ² ≠ 250
Sample size, n = 25
xbar = 50.6 ; s² = 500
α = 0.01 ;
The test statistic :
χ² = [(n - 1)s²] ÷ σ²
χ² = [(25 - 1)* 500] ÷ 250
χ² = (24 * 500) / 250
χ² = 12000 / 250
χ² = 48
The critical value:
df = n-1 ; 25 - 1 = 24
χ²(0.01/2 ; 24) = 45.559
Decison :
Reject H0 : if |χ² statistic| > critical value
Since 48 > 45.559
Hemce, we reject H0 and conclude that management's belief about variance is untrue.
Use the function r(x)=2x+1
if r(b)=19 what is the value of b?
Let's think of this like a point. We know the y-value, but not the x-value. Therefore, in order to find b, we should plug in our known y-value, 19, for r(x).
19 = 2b + 1 || We can leave it as x in our equation or change it to b. Either way you will get the same answer. I changed it to b in this case just to follow through with what the question is asking.
18 = 2b
b = 9
Hope this helps!! :)
Answer:
9
Step-by-step explanation:
They are asking what value of x can you input into 2x+1 so that the outpot is 19.
In other words, you need to solve 2x+1=19.
Subtracting 1 on both sides gives: 2x=18.
Dividing 2 on both sides gives: x=9.
So r(9)=19 since 2(9)+1 is 19.
Four students are painting a wall mural for their school.Each student paints 5/7 square yard of wall space.What is the total area of the wall mural that is being painted(ASAP PLEASE)
what is the volume of a cube if the length, width, and height are 1ft?
a)6 cubic feet
b)3 cubic feet
c)4 cubic feet
d) 1 cubic foot
Answer:
The answer is D. 1 cubic foot.
Step-by-step explanation:
To solve for the volume of a cube, use the formula V= [tex]a^{3}[/tex]. This is the formula because the volume of a cube formula equals length times width times height. Since the length, width, and height are all the same values, the simplest volume of a cube formula is [tex]a^{3}[/tex].
Next, plug in the information from the question into the formula, which will look like V= [tex]1^{3}[/tex]. Then, solve the equation, and the final answer will be 1 cubic foot.
The length of a trip varies directly as the amount of gasoline used. Yael's car used 16 L for the first 145 km of his trip from Toronto to Montreal. a) How much gasoline, rounded to the nearest litre, should he expect to use in the remaining 400 km of his trip? b) Can he complete the trip with a budget of $70, if gasoline costs $1.13/L?
Answer:
44
yes. the total cost is 68 which is less than 70
Step-by-step explanation:
There is positive proportionality is two variables are positively related to each other.
The equation for direct proportionality =
y = bx
where y = dependent variable
b = constant
x = independent variable
amount of gasoline = b x length of the trip
16 = b x 145
b = 16/145 = 0.110345
a. 400 x 0.110345 = 44
total litres used for the trip = 44 + 16 = 60
total cost of the trip = 60 x 1.13 = 67.8
total amount spent on gasoline is 67.8. this is less than the budget
pls help
In Miss McGee's homeroom, there are 5 blonds, 9 brunettes, 2 redheads, and 2 students with black hair. If Miss McGee chose a student at random, what is the probability that the student would be a red head
Answer:
2/18 or if needed simplified 1/9. count all the people you get 18 the red head is 2.
Answer:
2 out of 18
Step-by-step explanation:
5+2+2+9= 18 redheads = 2
F(x)=3x^2+2 the quadratic function g(x) is the function f(x) stretched vertically by a factor of 4. Enter the equation of g(x) in the box
Answer:
g(x) = 12*x^2 + 8
Step-by-step explanation:
For a function f(x), a vertical stretch of scale factor k is defined as:
g(x) = k*f(x)
In this case, we know that f(x) = 3*x^2 + 2
And the function g(x) is the function f(x) vertically stretched by a factor of 4, then we have k = 4
and:
g(x) = 4*f(x)
Replacing by the actual function, we get
g(x) = 4*(3*x^2 + 2)
g(x) = 4*3*x^2 + 4*2
g(x) = 12*x^2 + 8
HURRYYYY PLEASE!!! Does the graph of this equation open up or down?
f(x) = 22
- 5
O up
O down
Answer: Down
Step-by-step explanation:
down nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn
NEED HELP with my question
Answer:
Should be around 3.60555
Step-by-step explanation:
Round it to whichever place it needs to be rounded
Expand and combine like terms.
(6y^2+ 5y^4)^2
Answer:
36y⁴ + 60y⁶ + 25y⁸
Step-by-step explanation:
(6y² + 5y⁴)² = (6y² + 5y⁴)(6y² + 5y⁴)
we can use the FOIL method to get:
36y⁴ + 30y⁶ + 30y⁶ + 25y⁸
we can simplify the two middle terms and get:
36y⁴ + 60y⁶ + 25y⁸
Answer:
[tex]\left(6y^2+5y^4\right)^2[/tex]
[tex](6y^2+5y^4)^2=36y^4+60y^6+25y^8[/tex]
[tex]=\left(25y^8+60y^6+36y^4\right)[/tex]
[tex]=\left(36y^4+60y^6+25y^8\right)[/tex]
[tex]=36y^4+60y^6+25y^8[/tex]
---------------------------
hope it helps...
have a great day!!
please help me with this one
Step-by-step explanation:
15*8= 120
120/2= 60
60*13= 780
So its B.
Need help !! Slove for c
Please help me with this
9514 1404 393
Answer:
2/3
Step-by-step explanation:
The value of the function at x=-1 can be found by substituting that value for x and doing the arithmetic.
f(-1) = 1/3(-1)³ -(-1)
f(-1) = -1/3 +1 = 2/3
The relative maximum value is 2/3.
Solve the expression for a=12 , b=6 and c=3
Answer: 24
Step-by-step explanation: First, you fill in the values for each letter; replace any a with 12, replace any b with 6, and replace any c with 3. Then, enter the equation into the calculator like so, and it should be equal to 24.
I hope this helps. Have a nice day.
I need help on this one 2 pls !?
Answer: The answer is 60 mi^2
Step-by-step explanation:
the height in feet above the ground of an arrow after it is shot can be modeled by y=-16r^2+63r+4.Can the arrow pass over a tree that is 68 feet tall? Explain.
Answer:
yes
Step-by-step explanation:
y=-16r^2+63r+4
maximum value of y :
y'=0
-32r +63=0
r= 63/32
y = -16(63/32)²+63(63/32)+4
= -4 + 124 + 4 = 124 ft
124 > 68
the Arrow can pass over the tree
I need help! Will give Brainliest to right answer!
Answer:
(0,-7)
Step-by-step explanation:
a^2+B+c
c= y intercept.
therefore the answer is (0,-7)
Answer:
the y intersept is (0,-7)
Step-by-step explanation:
Pls help
What are the coordinates of the vertex of the parabola y = 2(x + 2)?
Enter your answer as an ordered pair, like this: (42, 53)
Answer:
vertex is (-2,0)
Step-by-step explanation:
Overnight the temperature in Chicago was -7F but by noon it had risen to 9 degrees F. What was the temperature in Chicago that afternoon?
Answer:
2 °F
Step-by-step explanation:
Overnight temperature = -7 °F
Total Noon temperature = 9 °F
What was the temperature in Chicago that afternoon?
Temperature in Chicago that afternoon = Total Noon temperature + Overnight temperature
= 9 °F + (-7 °F)
= 9 °F - 7 °F
= 2 °F
Temperature in Chicago that afternoon = 2 °F
Who would I solve this?
Marta is building a scale model of the Empire State building which has a rectangular base. The scale on the model is 1 inch = 35 feet. Her model is 4 inches in length and 1 inch in width. What is the actual area, in square feet, of the base of the building?
Answer: The actual area of the base of the building is 4900 square feet.
Step-by-step explanation:
We have given, the scale on the model: 1 inch = 35 feet
In model,
Length= 4 feet , Width = 1 inch
As per scale ,
Actual length = 4 x 35 feet
= 140 feet
Actual width = 35 feet
Area of base of the building = Length x width
= 140 x 35
= 4900 square feet
Hence, the actual area of the base of the building is 4900 square feet.
please help asap, i need to get this done
Answer:
25.5 = c
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
17^2 + 19 ^2 = c^2
289+361 = c^2
650 = c^2
Take the square root of each side
sqrt(650) = sqrt(c^2)
25.49509757=c
To the nearest tenth
25.5 = c
Answer:
C = 25.5
Step-by-step explanation:
17² + 19² = x²
289 + 361 = x
289 + 361 = 650
√650 = 25.495097567963924150141120545114
25.495097567963924150141120545114 ≅ 25.5
Exercice 6 (3 points). Résoudre le problème suivant :
On partage 9 800 euros entre 3 personnes. La première reçoit 240 euros de moins que la
seconde
et la part du troisième est égale aux trois quarts de la somme des parts des deux autres.
Calculer la part de chaque personne.
Answer:
P 2.680 S 2.920 T 4.200
Step-by-step explanation:
S = seconde
Premiere = S-240
Troisieme = 3/4( 2S -240)
S + S-240 + 3/4(2S-240) = 9800
Multiplie tout par 4 pour eliminer la fraction
4S + 4S -960 + 6S - 720 = 39200
14 S = 40.880
S = 2.920
P = 2.920-240 = 2.680
T =3/4(5.600) = 4.200
2.920 + 2.680 + 4.200 = 9.800
find the value.plzzz I will mark as the brillianest plzzzzzzzzzzzzzzzzzzzz
Answer:
n= 75
y= 75
z= 50
p= 105
other n across from p= 105
Step-by-step explanation:
n and y are the same since the triangle is isoseles.
p is supplemetary to n
z and 50 are opposites in a quadrilateral
HELP ME!! First to answer gets brainiest!!!
Answer:
11 1/5 minutes
Step-by-step explanation:
All you have to do is add up all the songs together.
3 1/2 = 3 30/60
2 57/60= 2 57/60
4 3/4 = 4 45/60
Add this all up
9 132/60
11 12/60
11 1/5
11 1/5 minutes
If this helps please mark as brainliest
As shown in the example, one corner of the solar panel has coordinates (3,6). What are thr coordinates of the other cornor of this side that is 3 meters from the edge?
Answer:
The co-ordinates of the other corner of this side which is 3 meter from the edge is (3,3)
Step-by-step explanation:
Given
One corner of the solar panel is (3,6)
The co-ordinates of the other corner of this side which is 3 meter from the edge is
X co-ordinates = 3
Y co-ordinates = 6-3 = 3
The co-ordinates of the other corner of this side which is 3 meter from the edge is (3,3)
You roll two six-sided dice. What is the probability that the sum will be even or a multiple of five? Round your answer to the nearest tenth of a percent.
Answer:
0.51
Step-by-step explanation:
A N S W E R
Q U I C K L Y
P L E A S E
Answer:
Your answer is D
Step-by-step explanation:
I literally have an Math Expert right next to me and he verified this answer!
Plz gimme a like!!
What is the probability that the next person you meet was not born in February assume no leap year
A)337/365
B)28/365
C)11/12
D)1/2
Answer:
C, 11/12.
Step-by-step explanation:
There is only one February in one year, and there are eleven other months (January, March, April, May, June, July, August, September, October, November, December) so therefore 11/12 is the correct answer.