Answer:
Step-by-step explanation:
Find the centre first by reoriganisation it into the form (x - cx)^2 + (y -cy)^2 = r^2
x^2 + y^2 + 6x -6y +5 = 0
(x + 3)^2 - 9 + (y - 3)^2 - 9 + 5 = 0
(x + 3)^2 + (y - 3)^2 = 13
The radius does not matter the centre is ( -3, +3)
The diameter must pass through the center so substituting into the equation for the line
2x-y+a = 0
-6 -3 + a = 0 so a = 9
The value of 'a' is 0 and this can be determined by using the standard form of the equation of a circle.
Given :
Equation of a Circle -- [tex]x^2-2x+y^2-4y-4=0[/tex]
Equation of a Line -- 2x - y + a = 0
The following steps can be used in order to determine the value of 'a':
Step 1 - First make the equation of a circle in standard form.
[tex]x^2-2x+y^2-4y-4=0[/tex]
[tex](x-1)^2-1+(y-2)^2-4-4=0[/tex]
[tex](x-1)^2+(y-2)^2 = 3^2[/tex]
Step 2 - From the above step, it can be concluded that the center of the circle is (1,2).
Step 3 - If (1,2) is the center of the circle then it also satisfies the equation of diameter (2x - y + a = 0).
2x - y + a = 0
2(1) - 2 + a = 0
a = 0
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If a^2+b^2= 4 and ab = 5, what is the value of
(a+b)^2?
A. 10
B. 12
C. 14
D. 16
Answer:
14
Step-by-step explanation:
(a+b)^2
(a+b)(a+b)
FOIL
a^2 + ab+ab + b^2
Combine like terms
a^2 +2ab + b^2
Rearranging
a^2+b^2 +2ab
We know a^2+b^2 = 4 and ab= 5
4 + 2(5)
4+10
14
Answer:
C. 14.
Step-by-step explanation:
We use the identity:-
a^2 + b^2 = (a + b)^2 - 2ab
So 4 = (a + b)^2 - 2(5)
(a + b)^2 = 4 + 2(5)
= 14.
Suppose X has an exponential distribution with mean equal to 16. Determine the following:
(a) P(x >10) (Round your answer to 3 decimal places.)
(b) P( >20) (Round your answer to 3 decimal places.)
(c) P(x < 30) (Round your answer to 3 decimal places.)
(d) Find the value of x such that P(X 〈 x) = 0.95. (Round your answer to 2 decimal places.)
constant of proportionality
Answer:
4.2
Step-by-step explanation:
Constant of proportionality = y/x = 8.4 / 2 = 4.2
3. The product of three numbers geometric progression is l, their sum is -7÷3 . Find the numbers
Answer:
below
Step-by-step explanation:
hope it is well understood
Water is flowing into a tank at a rate of 20 cm3/min. At the start, there is 250 cm3 of water in the tank.
(i) How much water will be in the tank after 30 minutes?
(ii) Find the time when there is 1210 cm3 of water in the tank.
Answer:
i) 410 cm³
ii) 48 min
Step-by-step explanation:
we start with 250 cm³.
and then we fill in 20 cm³ per minute.
i)
after 30 minutes we have
250 + 8×20 = 250 + 160 = 410 cm³
ii)
how long (how many minutes) does it take to reach 1210 cm³ in the tank ?
well, first we subtract the start amount (250).
and then we see how often 20 cm³ will "fit" into the remainder. and then we know how many minutes the water has to run.
1210 - 250 = 960 cm³
so, the incoming water needs to reach 960 cm³ to have a total of 1210 cm³.
and
960 cm³ / (20 cm³ / min) = 960 cm³ min / 20 cm³ =
= 960 min / 20 = 48 min
Translate and solve: five less than z is 4
z -5 =4
neutralize the left -5 by adding 5 on both sides
z -5 (+5) = 4 (+5)
z = 9
Dog food is sold in a 12 ½ pound bag. My dog, Max, eats a ¾ pound serving every day. How many servings of dog food are in the bag?
the pound bag has 25/2 of dog food, or 50/4
if the dog eats 3/4, and the pound has 50/4
[tex]\frac{50}{4} . \frac{4}{3} = \frac{50}{3}[/tex]
if you divide 50 by 3, you'll find 16,66666...
since you need full days, the answer is 16 days
hope it helps :)
Write the sum using summation notation, assuming the suggested pattern continues.
2, -10, 50, -250, +…
Is this sequence arithmetic or geometric? How do you know?
Answer:
Step-by-step explanation:
It's geometric. The nth term differs by -5 when compared to the n+1 term.
Sum 0 to n a(-5)^n-1 where a = 2
I think this is what you want, but there is also a formula. See below.
Sum = a (r^n - 1)/(r - 1)
 In one of the examples he is working on, he knows that the two coordinates (0,6) and
(8, 10) are on the function that he is deriving. Using the information from these two
coordinates, determine the slope and y-intercept of the function Mike is looking for, and
then write out the correct function.
9514 1404 393
Answer:
y = 1/2x + 6
Step-by-step explanation:
The slope m is given by the formula ...
m = (y2 -y1)/(x2 -x1)
m = (10 -6)/(8 -0) = 4/8 = 1/2
The y-intercept is given by the formula ...
b = y -mx
b = 6 -(1/2)(0) = 6
Then the slope-intercept equation is ...
y = mx +b
y = 1/2x +6
What effect will replacing x with (x−4) have on the graph of the equation y=(x−3)2 y = ( x − 3 ) 2 ?
Answer:
y"= 2 wich is positive
Step-by-step explanation:
Step-by-step explanation:
Our equation is: y=(x-3)²
x should be replaced by x-4
y=(x-3)²
y=[(x-4)-3]²
y=(x-4-3)²
y=(x-7)²
The graph is still a parabola but with a different vertex
The vertex here is :
y= (x-7)²
y= x²-14x-49
y'= 2x-14
solve y'=0
2x-14=0
2x=14
x=7
You can easily find it without derivating by dividing -14 by -2
since: x²-14x-49
a=1 b= -14 c=-49
-b/2a = 14/2 = 7
the image of 7 is:
y=(7-7)² = 0
so the coordinates of the new vertex are (7,0) and it's a maximum
since y">0
y'= 2x-14
y"= 2 wich is positive
A plumber can do a job in 4 hours. When he and his 2 helpers do the job, they can finish it in 2 hours. If both helpers work at the same rate, how many hours would each helper take to do the job alone?
I need help on this math problem
Answer:
for the first one, simply add g(x) and h(x) :
x+3 + 4x+1 = 5x + 4
the second one, you would multiply them :
(x+3)(4x+1) = 4x^2 + 13x + 3
the last one, you would subtract :
(x+3)-(4x+1) = -3x + 2
and then substitute 2 for 'x' :
-3*2 + 2 = -6 + 2 = -4
Answer:
1. 5x+4
2. [tex]4x^2+13x+3[/tex]
3. -4
Step-by-step explanation:
1. (x+3)+(4x+1)
Take off the parentheses and Add.
5x+4
2. (x+3)(4x+1)
Use the FOIL method to multiply.
[tex]4x^2+x+12x+3[/tex]
[tex]4x^2+13x+3[/tex]
3. First, set up the equation as (g-h)(x)
(x+3)-(4x+1)
x+3-4x-1
Solve.
-3x+2
Substitute in 2 for x.
-3(2)+2
-6+2
-4
salifye pizza charges a base pizza of $12.77 for large plus 7.44 additional topping.
a) Find a function that models the price of a pizza with toppings.
Find the inverse of the function. What does−1 represent?
If a pizza costs $20.20, how many toppings does it have?
Answer:
Sharjah Call Girls +971529238486 | Call Girls In Sharjah
Step-by-step explanation:
Sharjah Call Girls and our group are very a good deal satisfied to participate withinside the boom of the leisure field. Lots of customers are touring Sharjah now no longer handiest for playing the splendor of the town however additionally to the sensual entertainments our profiles.
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9514 1404 393
Answer:
C
Step-by-step explanation:
The graph shows two vertical asymptotes, so the relevant function will be zero in the denominator for two different x-values. The only possibility is ...
[tex]F(x)=\dfrac{1}{(x-1)(x+1)}[/tex]
95% confident that the true mean difference in mean crying time after being given a vitamin K shot between infants using conventional methods and infants held by their mothers is between ____________and ___________________. In other words, the mean crying time of infants given vitamin K shot using conventional methods is anywhere from ______________ less than to _______________more than the mean crying time of infants given vitamin K shot using new methods.
Solution :
Two sample T-test and CI : Conventional methods, New methods
Two sample T for conventional method Vs new method
N Mean StDev Se Mean
Conventional mean 30 35.3 20.8 3.8
New methods 30 35.1 22.3 4.1
Difference = μ (conventional method) - μ (new method)
Estimate for difference : 0.17
95% CI for difference : (-10.976, 11.309)
T-Test of difference = 0(vs <): T-value = 0.03 P-value =0.5119 DF = 57
95% confident that the true mean difference in mean crying time after being given a vitamin K shot between infants using conventional methods and infants held by their mothers is between -10.976 and 11.309. In other words, the mean crying time of infants given vitamin K shot using conventional methods is anywhere from -10.976 less than to 11.309 more than the mean crying time of infants given vitamin K shot using new methods.
Hey there, everyone!
I just wanted to shout out to all of those whom have helped me through my tortuous math homework and say thank you very much. XD
I manage to pass my very first year of high school without physically going to school.
It was a lot of twist and turns, I must say. But at least I managed to pass through!
Man, I'm gonna miss 2021 because now I'll have to ACTUALLY go to school. But when that day comes, I do hope you guys will continue helping me on!
In the mean time, stay safe everyone and thanks a lot!
But hold up! I got one more question!
I really want to delete my account so badly but I can't because I forgot my password and I'm using my school email unfortunately. Anyone got a solution to my issue? :(
Answer:
I don't know the answer please tell me
PLEASE HELP!
Suppose you want to purchase a house. Your take-home pay is $2920 per month, and you wish to stay within the recommended guidelines for mortgage amounts by only spending 14 of your take-home pay on a house payment. You have $15,900 saved for a down payment and you can get an APR from your bank of 4.05%, compounded monthly. What is the total cost of a house you could afford with a 15-year mortgage? Round your answer to the nearest cent, if necessary.
Answer:
Had a problem in school like this, all you gotta dois ta
Which graph represents the equation x2 = 8y? On a coordinate plane, a parabola opens up. It has a vertex at (0, 0), a focus at (0, 8), and a directrix at y = negative 8. On a coordinate plane, a parabola opens up. It has a vertex at (0, 0), a focus at (0, 2), and a directrix at y = negative 2. On a coordinate plane, a parabola opens to the right. It has a vertex at (0, 0), a focus at (2, 0), and a directrix at x = negative 2. On a coordinate plane, a parabola opens to the right. It has a vertex at (0, 0), a focus at (8, 0), and a directrix at x = negative 8.
Answer:
The parabola x²=8y has,
vertex: (0,0)
focus: (0,2)
directrix: y=-2
so that option is the answer,
btw, the parabola opens up to the top and axis of symmetry is x=0
Answer:
It's A!
Step-by-step explanation:
Got it correct on my test! :)
I really need the help please and thank you
Answer:
B. [tex]f^{-1}(x)=\frac{x-4}{5}[/tex]
Step-by-step explanation:
To find the inverse of a function/equation:
Replace f(x) with y: y=5x+4 Switch x and y: x=5y+4 Solve for y: x-4=5y -> [tex]y=\frac{x-4}{5}[/tex]Write in standard inverse notation: [tex]f^{-1}(x)=\frac{x-4}{5}[/tex]I hope this helps!!
gl!
Choose the correct correspondence
Answer:
The Answer is K.
Step-by-step explanation:
K is the answer because it is the only other point on the line DK
Find the equation of the linear function represented by the table below in slope-intercept form.
Answer:
y=-4x-5
Step-by-step explanation:
The slope of the line is - 4, the equation of line is y=-4x-5
Find the area of the shaded regions.
Answer:
around 22, or 21.98
Step-by-step explanation:
[tex]s1 = {r}^{2} \times \pi = 9 \times 3.14 = 28.26[/tex]
[tex]s2 = 1 \times 3.14 = 3.14[/tex]
[tex]s3 = 28.26 - (3.14 \times 2) = 28.26 - 6.28 = 21.98[/tex]
What is the slope of a relation with ordered pairs of (-5, 3) and (4.1).
9/2
2/9
-9/2
-2/9
2
-2
1000 randomly selected Americans were asked if they believed the minimum
wage should be raised. 600 said "yes." What is the 99% confidence interval
for the proportion of Americans who believe that the minimum wage should
be raised?
Answer:i dont now
Step-by-step explanation:
I need the help ASAP please
Answer:
Option B
Answered by GAUTHMATH
The one-to-one functions g and h are defined as follows.
Answer:
Step-by-step explanation:
The one-to-one functions g and h are defined as follows.
g={(-7,-6), (-5,4), (4,-7)(7,6)}
h(x)= 3x-14
Find the following.
g-1(4)=
"g-1(4)" just says "Find the pair of coordinates that has 4 for its
y-coordinate, and the answer is its x-coordinate". So we look through those
and find (-5,4) is the only one of those up there that has a 4 for it's y-
coordinate, and so its x-coordinate is -5 and we write:
g-1(4)=-5
The Required value for the function are:
1. g⁻¹(-3) = -1.
2. h⁻¹(x) = (x - 2) / 7.
3. (h o h⁻¹)(0) = -16/49.
1. g⁻¹(-3):
Looking at the pairs in g, we can see that (-1, -3) is the pair where the output is -3.
Therefore, g⁻¹(-3) = -1.
2. h⁻¹(x):
To find h⁻¹(x), we need to solve the equation h(y) = x for y.
The given function h(x) = (x - 2) / 7.
So, let's substitute y for h⁻¹(x):
(x - 2) / 7 = y
x - 2 = 7y
Now, solve for y by dividing both sides by 7:
y = (x - 2) / 7
Therefore, h⁻¹(x) = (x - 2) / 7.
3. (h o h⁻¹)(0):
To find (h o h⁻¹)(0), we need to evaluate the composition of h and h⁻¹ at 0.
First, we find h⁻¹(0):
h⁻¹(0) = (0 - 2) / 7 = -2/7
Now, we substitute h⁻¹(0) into h:
h(h⁻¹(0)) = h(-2/7) = (-2/7 - 2) / 7 = (-2 - 14) / 49 = -16/49
Therefore, (h o h⁻¹)(0) = -16/49.
Learn more about Function here:
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PLEASE HELP OR IM gonna FAILLLLLLLL!!!!!!!!
Answer:
C. 1/(4^10)
Step-by-step explanation:
Let's break it down: 4^-2 = 1/(4^2)(1/(4^2))^5 = (1^5)/(4^2)^5 = 1/(4^10)A silo is built in the shape of a cylinder with a cone for a roof. If the height of the
cylinder is 5 m, the radius is 2.8 m and the slant height of the cone is 6,6 m,
determine the amount of material needed to create the rounded sides and conical
roof, Round to the nearest tenth of a cubic m.
9514 1404 393
Answer:
146.0 m²
Step-by-step explanation:
The lateral areas of the cylinder and cone are given by the formulas ...
A = πrs . . . . cone area; radius r, slant height s
A = 2πrh . . . . cylinder area; radius r, height h
__
The total area lateral area of the silo is ...
A = π(2.8 m)(6.6 m) +2π(2.8 m)(5 m) = π(2.8 m)(6.6 m +2(5 m)) = 46.48π m²
A ≈ 146.0 m² . . . area of sides and roof of silo
_____
Additional comment
The answer is requested in cubic meters. Area has units of square meters. There is nothing in this problem statement that seems to be requesting a volume, which is what would have units of cubic meters.
IF A= -35 , B = 10 , C= -5 verify that:-
a x (b+c) = a x b + a x c
Plz tell
Answer:
see below
Step-by-step explanation:
a x (b+c) = a x b + a x c
Let A= -35 , B = 10 , C= -5
-35 * ( 10 -5) = -35 *10 + -35 * -5
-35 *(5) = -350 + 175
-175 = -175
It has been claimed from previous studies that the average diameter of ball bearings from this manufacturing process is 2.30 cm. Based on the sample of 50 that you collected, is there evidence to suggest that the average diameter is greater than 2.30 cm? Perform a hypothesis test for the population mean at alpha = 0.01.
a. Define the null and alternative hypotheses in mathematical terms as well as in words.
b. Identify the level of significance.
c. Include the test statistic and the P-value.
d. Provide your conclusion and interpretation of the results. Should the null hypothesis be rejected? Why or why not?
Diameters data frame of the first sample (showing only the first five observations)
diameters
0 3.46
1 2.64
2 1.89
3 2.56
4 2.09
Diameters data frame of the second sample (showing only the first five observations)
diameters
0 3.10
1 2.04
2 2.18
3 2.60
4 2.76
test-statistic = 2.06
two tailed p-value = 0.0394
Data for all 50 samples cannot be obtained, however, the solution below uses the 10 samples below to show how the hypothesis can be tested.
Answer:
Step-by-step explanation:
Average diameter, μ = 2.30
H0 : Average diameter is equal to 2.30cm
H1 : Average diameter is greater than 2.30 cm
The hypothesis :
H0 : μ = 2.30
H1 : μ > 2.30
Using the readings from the data above :
3.46, 2.64, 1.89, 2.56, 2.09, 3.10, 2.04, 2.18, 2.60, 2.76
Sample size, n = 10
Mean, xbar = ΣX/ n = 25.32 / 10 = 2.532
Sample standard deviation, s = 0.4973 (from calculator)
The test statistic :
(xbar - μ) ÷ (s/√(n))
T = (2.532 - 2.30) ÷ (0.4973/√(10))
T = 1.475
The Pvalue :
Degree of freedom, df = n - 1 ; 10 - 1 = 9
Pvalue(1.475, 9) = 0.087
Decision region :
Reject H0 ; If Pvalue < α;
Since 0.087 > 0.01 ; we fail to reject the Null and conclude that there is no evidence to suggest that the average diameter is greater than 2.30 cm
