What is the center of a circle whose equation is x2 y2 4x â€" 8y 11 = 0? (â€"2, 4) (â€"4, 8) (2, â€"4) (4, â€"8)
Given the equation x² + y² + 4x - 8y + 11 = 0, the center of the circle is (-2, 4).
The standard form of the equation of circle is given by
(x - h)² + (y - k)² = r²
where (h , k) is the location of the center and r is the radius of the circle.
On the other hand, the general form of the equation of circle is given by
x² + y² + Dx + Ey + F = 0
where D = -2h, E = -2k, and F = h² + k² - r².
If the equation of the circle in general form is x² + y² + 4x - 8y + 11 = 0, then the coefficients are:
D = 4
E = -8
F = 11
If D = -2h and D = 4, then
4 = -2h
h = -2
If E = -2k and E = -8, then
-8 = -2k
k = 4
Hence, the center of the circle is (h, k) = (-2, 4).
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Convert 37/2 to a mixed fraction
How to solve completing the square with the formula a (X+h)2 + k
The solutions of the given quadratic equation are
[tex]x = 3 \ or \ x = -\frac{1}{4}[/tex]
What is quadratic equation?
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A two degree equation is known as Quadratic equation.
The given quadratic equation is
[tex]4x^2 - 11x - 3[/tex]
Now,
[tex]4x^2 - 11x - 3 = 0\\\\(2x)^2 - 2 \times 2x \times \frac{11}{4} + (\frac{11}{4})^2 - (\frac{11}{4})^2 -3 = 0\\\\(2x - \frac{11}{4})^2 = \frac{121}{16} + 3\\\\(2x - \frac{11}{4})^2 = \frac{121+48}{16}\\\\(2x - \frac{11}{4})^2 = \frac{169}{16}\\\\2x - \frac{11}{4} = \sqrt{\frac{169}{16}}\\\\2x - \frac{11}{4} = \pm\frac{13}{4}\\\\2x - \frac{11}{4} = \frac{13}{4} \ or \ 2x - \frac{11}{4} = -\frac{13}{4}\\\\2x = \frac{13}{4} + \frac{11}{4} \ or \ 2x = \frac{11}{4} - \frac{13}{4}\\\\[/tex]
[tex]2x = 6 \ or \ 2x = -\frac{1}{2}\\x = 3 \ or \ x = -\frac{1}{4}[/tex]
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the fast-food smoothie contains only a small amount of fruit. it has 76 g of sugar. if there are 4 g of sugar in a teaspoon of sugar, how many teaspoons of sugar are in this fast-food smoothie?
The total amount of sugar which contains in 4 grams of sugar = 304 grams.
Amount of sugar fast food smoothie has = 76 gram
amount of sugar a teaspoon of sugar contains = 4 gram
Thus the total amount of sugar which contains in 4 grams of sugar = 4 × 76
this implies the total amount of sugar which contains in 4 grams of sugar = 304 grams
In this question we used the unitary method where we multiplied a quantity with a known quantity to find the value of an unknown quantity.
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1. Which can be used to prove dit? (1 point)
d
O Transitive Property of Parallel Lines
O Transitive Property of Congruence
O Perpendicular Transversal Theorem
O converse of the Corresponding Angles Postulate
Make x the subject of y = 3x-2
You may use the flowchart to help you if you wish.
x 3
- 2
Answer:
x=y/3 + 2/3
Step-by-step explanation:
Is this what you wanted?
at a certain clothing store, the clothes are displayed on racks. the clothes on each rack have similar prices, but the prices among the racks are very different. to estimate the typical price of a single piece of clothing, a consumer will randomly select four pieces of clothing from each rack. what type of sample is the consumer selecting? responses a census a census a cluster sample a cluster sample a simple random sample a simple random sample
The clothing in the store is separated into strata, each of which is a rack of items with comparable prices. An illustration of the use of a stratified random sample is the mean price calculated using the randomly chosen articles of clothing from the strata.
Describe a random sample.In the random sampling method of sampling, each sample has an equal chance of being chosen. In order to fairly represent the entire population, a sample is chosen at random. From a pool of 250 employees, 25 names could be chosen at random to represent a simple random sample. The sample in this case is random, and the population in this case is the employees since each has an equal chance of being chosen.
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Describe the relationship as parallel intersecting or skew AB or BC
Based on the image attached, the relationship are:
a). AB and BC - Both the segments are said to be perpendicular and they are intersecting at the point B.
b). AE and BF - Both segments are said to be parallel
c). EF and ED - Both are skew
d). Plane ABC and plane ABF - Both of the planes do intersect at point AB
e). Plane AED and plane BFC - Both of the given planes are known to be parallel
How do you know if lines are parallel intersecting or skew?if the ratio equality is accurate, parallel. If the lines are not parallel or if you can solve them as a system of simultaneous equations, the lines will intersect. If two crossing lines have a zero dot product, they are perpendicular.
If the lines are not parallel or intersecting, they are said to skew. Lines that are parallel never cross.
Therefore,
if lines are in the same plane, do not intersect, and are parallelif lines only meet at one point, then they are intersecting.If lines are on two distinct planes and don't intersect, they skew.Learn more about parallel intersection from
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esearchers performed a study on the effects of a nonsteroidal anti-inflammatory drug (nsaid) given before and after arthroscopic knee surgery. a sample of 67 patients undergoing elective knee arthroscopy was randomly divided into three treatment groups. researchers compared the mean pain scores of the patients in the three treatment groups one day after surgery, and the f value obtained was 4.79. which statement is false?
The F-test is used in regression analysis to test the hypothesis that all model parameters are zero. It is also used in statistical analysis when comparing statistical models.
Statistical models that have been fitted using the same underlying factors and data set to determine the model with the best fit. That is:
H₀ : B₁ = B₂ = ............. = Bₓ =0
H₁: Bₙ ≠ 0 for at least one j.
The F-test was developed by Ronald A. Fisher (hence F-test) and is a measure of the ratio of variances. The F-statistic is defined as:
F = [tex]\frac{explained variables}{unexplained variables}[/tex]
A general rule of thumb that is often used in regression analysis is that if
F > 2.5then we can reject the null hypothesis. We would conclude that there is a least one parameter value that is nonzero.
The F-distribution is generally a skewed distribution and also related to a chi-squared distribution. The f distribution is the ratio of X1 random chi-square variable with degrees of freedom ϑ1 and X2 random chi-square variable with degrees of freedom ϑ2. (In other words each of the chi-square random variable has been divided by its degrees of freedom)
The F-distribution is generally a skewed distribution and also related to a chi-squared distribution. The f distribution is the ratio of X1 random chi-square variable with degrees of freedom ϑ1 and X2 random chi-square variable with degrees of freedom ϑ2. (In other words each of the chi-square random variable has been divided by its degrees of freedom)
F =[tex]\frac{x_{1}/v_{1} }{x_{2}/v_{2} }[/tex]
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Can someone please explain to me in simple words how to construct the circumcenter and incenter of a triangle? I've tried watching videos and reading articles but the wording is too complicated.
I'm doing the IXL skill if that helps
The circumcenter is where three perpendicular bisectors intersect and the incenter is where the three angle bisectors intersect.
What is circumcenter?The circumscribed circle or circumcircle of a polygon in geometry is a circle that passes through each of the polygon's vertices. This circle's circumcenter and circumradius are its centre and radius, respectively.
Construct angle bisectors of each angle of the triangle and their intersection point gives the incenter.
To find Circumcenter:
Construct perpendicular bisectors of all sides of the triangle and their intersection point gives the circumcenter.
Circumcenter Theorem: It states that the vertices of a triangle are equidistant from the circumcenter.
Incenter Theorem: It states that the incenter is equidistant from the sides of the triangle.
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is 8.75x linear or non-linear
Find the degree of the equation to determine if linear.
Linear
Constant Speed Quick Check
Constant Speed Quick Check
Volunteers put together 40 school-supply kits in 8 minutes. At this rate, how many could they put together in 30 minutes
Solve this problem using a unit rate. (1 point)
O 150 school-supply kits
O 10.67 school-supply kits
O 6 school-supply kits
O 9,600 school-supply kits
6 school-supply kits can be put together in 30 minutes.
What do you mean by the Unitary method?
By using the unitary technique, we may determine the value of a single unit and, using that value, get the value of the necessary number of units.
According to the questions,
By applying the unitary method,
40 school supply kits can be put together in 8 minutes.
∴1 school supply kit can be prepared in (8/40) minutes
∴30 school supply kits can be prepared in (30/5) minutes
Hence,
6 school-supply kits can be put together in 30 minutes.
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Given the following function, find the vertex, y=5x^2-8x+6
Answer:
The vertex is (0.8, 2.8)------------------------------------
GivenFunction y = 5x² - 8x + 6Find the x-coordinate of the vertexx = - b/(2a)x = - (-8)/(2*5) = 8/10 = 0.8Find the y-coordinate of the vertexy = 5(0.8²) - 8(0.8) + 6 = 2.8The function f(t)=9300(0.994)t represents the change in a quantity over t minutes. What does the constant 0.994 reveal about the rate of change of the quantity?
The function is ________exponentially at a rate of _______% every _______.
Please!!!! Help
Answer:
Step-by-step explanation:
NOSEEEEEE
in october 2012, apple introduced a much smaller version of the apple ipad, known as the ipad mini. weighing less than 11 ounces, it was 50% lighter than the standard ipad. battery tests for the mini ipad showed that battery life is uniformly distributed between 8.5 and 12 hours. what is the value of 'a'? answer to one decimal.
a) The Probability density function of given uniform distribution example is
F(x) = 1/3.5 for 8.5 < x< 12
Uniform distribution in Statistics is a type of probability distribution in which all possible outcomes have equally likely chance to occur. It is generally represented by U(x,y) where
x ---> minimum value and y---> maximum value
Probability density function is a probability function which defines the density of continuous random variable lying between specified range
values. It is denoted by f( a<X<b)
Probability density function for uniform distribution is F(x) = 1/(b-a) for a<x<b where a and b are parameters of uniform distribution.
We have following informations,
weigh of mini iPad = 11 ounces or 50% lighter than standard iPad.
Assume that the battery of iPad is uniformly distributed between 8.5 hours to 12 hours.
this implies a = 8.5 , b = 12
F(x) = 1/(12 - 8.5) = 1/3.5 for 8.5<x<12
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#Complete Qestion :
In October 2012, Apple introduced a much smaller variant of the Apple iPad, known as the iPad Mini. Weighing less than 11 ounces, it was about 50% lighter than the standard iPad. Battery tests for the mini ipad showed that battery life is uniformly distributed between 8.5 and 12 hours. what is the value of 'a'? answer to one decimal. Assume that the battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours.
a) What is the probability that the battery life for an iPad Mini will be 10 hours or less?
These points are linear.
Find the slope.
x 56 7 8 9
y| 11 | 16 | 21 | 26 | 31
Hint: First calculate the change
between each y-value.
[?]
Slope =
The slope is m = 5.
What is slope?
The change in y coordinate relative to the change in x coordinate is referred to as a line's slope in mathematics. The symbols Δy and Δx stand for the net change in the y-coordinate and the net change in the x-coordinate, respectively. where "m" denotes a line's gradient. tanθ then represents the slope of a line.
We have to find the slope of the points given.
First to find the change between each y - value.
16 - 11 = 5
21 - 16 = 5
26 - 21 = 5
31 - 26 = 5
So the change between each y - value is 5.
Now, to find the slope of the points.
Since,
Slope = m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m_1=\frac{16-11}{6-5}= \frac{5}{1} =5\\ m_2=\frac{21-16}{7-6}=\frac{5}{1} =5\\ m_3=\frac{26-21}{8-7}=\frac{5}{1}=5\\m_4=\frac{31-26}{9-8}=\frac{5}{1} =5[/tex]
Hence, the slope of the given points is 5.
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Answer:
The answer is 5
Step-by-step explanation:
Though there is also a bottom number, just put a 1 in the bottom number
a comic book costs $3.99. it is marked up 45%. what is the final price of the comic book after it is marked up?
The final price of the comic book after it is marked up is $5.79.
Since we have given that
Cost of a comic book including tax = $ 3.99
According to the question, it is given that it is marked up 45%,
=3.99 × (100+45)÷100
=3.99 × 145/100
=399 × 1.45
=5.79
Hence, the final price of the comic book after it is marked up is $5.79.
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If a+4/a = 4 then find the value of a^5-1/a^5
pls answer this one as quick as possible.
Value of [tex]a^5-\frac{1}{a^5}[/tex] is 31.97.
What do you mean by algebraic expression?
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.
There are 3 main types of algebraic expressions which include:
Monomial Expression
Binomial Expression
Polynomial Expression
An algebraic expression which is having only one term is known as a monomial.
Given expression:
a + 4/a = 4
We need to simplify the above expression and will find the value of a.
[tex]a+\frac{4}{a}=4[/tex]
⇒ [tex]\frac{a^2+4}{a}=4[/tex]
⇒ [tex]a^{2}+4=4a[/tex]
⇒ [tex]a^2-4a+4=0[/tex]
⇒ [tex]a^2-2a-2a+4=0[/tex]
⇒ a(a-2) -2(a-2) = 0
⇒ (a-2)(a-2) = 0
⇒ a = 2
Now, substitute this value of a in expression , [tex]a^5-\frac{1}{a^5}[/tex]
[tex]2^5-\frac{1}{2^5}[/tex]
= 32 - 1/32
= [tex]\frac{1024-1}{32} =1023/32 = 31.97[/tex]
Therefore, value of [tex]a^5-\frac{1}{a^5}[/tex] is 31.97.
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Convert 17 weeks into days
Answer:
119days
Step-by-step explanation:
1 week= 7 days
take week as w
so 1w=7 or w=7
now 17 weeks=??
17w=??
w=7 so input in above statement:
17(7)=119days
Answer: 119 days
Step-by-step explanation:
We can set up a dimensional analysis problem to solve.
[tex]\displaystyle 17 \;\text{weeks}\;(\frac{7\;\text{days}}{1\;\text{week}} )[/tex]
The units of [tex]\frac{weeks}{weeks}[/tex] cancel out, leaving us with days. Since we are being asked to find days, this will leave us at the right point.
[tex]\displaystyle \frac{17*7}{1} =119\;\text{days}[/tex]
What is at least one social issue associated with food deserts?
Answer:
Food desert census tracts typically have fewer populations than all other census tracts, a higher percentage of unoccupied or abandoned dwellings, and residents who are less likely to have a college degree, make less money, or be employed.
a) What is the area of the shape below?
The area of the shape is 32 square yards
The given consist of one rectangle and a right triangle
The area of the figure = The area of the rectangle + The area of the right triangle
The area of the rectangle = The length × The width
The length of the rectangle = 6 yards
The width of the rectangle = 4 yards
The area of the rectangle = 6×4
= 24 square yards
The area of the triangle = (1/2)bh
The base of the triangle = 9 - 5 = 4 yards
The height = 4 yards
The area = (1/2)× 4 × 4
= 8 square yards
The area of the figure = 24 + 8
= 32 square yards
Hence, the area of the shape is 32 square yards
The complete question is:
What is the area of the shape below?
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look at picture. 100 POINTSSS
The correct number in the function f (3) will be;
⇒ f (3) = 2
What is Line segment?
Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.
Given that;
The graph is shown in figure.
Now,
Clearly, By the image of the graph;
At x = 3,
The function is defined as;
⇒ f (3) = 2
Thus, The correct number in the function f (3) will be;
⇒ f (3) = 2
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help help help helppp
The coordinate of image of P is (-6,-4)
What in math is a coordinate?
a pair of numbers that utilize the horizontal and vertical breakups from the two reference axes to define a point's location on a coordinate plane. generally expressed by the x-value and y-value pair (x,y).
P (-2,2)
Translation (x,y)=(x-4,y-6)
x= -2
y= 2
x-4= -6
y-6= -4
Hence the coordinate of image of p is (-6,-4)
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Shandra is preheating her oven before using it to bake. The initial temperature of the oven is 65° and the temperature will increase at a rate of 10° per minute after being turned on. What is the temperature of the oven 8 minutes after being turned on? What is the temperature of the oven tt minutes after being turned on?
Answer:
x=145 at 8 minutes
im not sure what tt means but please read my note at the end.
Step-by-step explanation:
if the initial temp is 65 and it increases at a rate of 10 per min the use
65+10(x)
let x be the number of minutes
65+10(8)
65 +80= 145
after 8 minutes the oven will be at 15 degrees. im not sure what tt is suppose to mean, but to find any other solution just plug it into x multiply x by 10 and add it to 65
2 3/5 times 3 1/3
NEED ASAP
Answer:
Answer is: 8 2/3 but improper is 26/3
PLEASE HELP!
6) You are playing a game with your friend that involves dice and 10 cards numbered 1-10.
a) If you were to roll the dice and pick a random card, what is the probability of rolling a 4 and picking a 4 from the numbered deck of cards?
b) If you draw 3 cards from the deck of numbered cards (without replacement) what is the probability of drawing 3 even cards?
c) If you roll a die 3 times, what is the probability of rolling 3 even numbers?
d) At one point you start rolling the die and recording your results. You suddenly realized that for the last 30 rolls of the die you have rolled an even number! What is the probability that your 31st roll is also an even number?
Answer:
1-10.
Step-by-step explanation:
at 9:30 am andrew left exeter for portsmouth, cycling at 12 mi/h. at 10:00 am stacy left portsmouth for exeter, cycling at 16 mi/h. the distance from exeter to portsmouth is 20mi.find the time they meet
Stacey meets Andrew 1.5 hours after she starts travelling at 11:30 AM and Andrew meets Stacey 2 hours after he starts travelling at 11:30 AM.
How to solve this problem?
Stacey and Andrew in the mentioned problem will meet in a time frame only when the both have travelled equal distances in respect to another.
Given, speed at which Andrew was travelling = 12 mi/h
Speed at which Stacey was travelling = 16 mi/h
Let the time taken by Stacey be = t hours
Therefore, the time taken by Andrew = (t + 0.5) hours
When Stacey overtakes Andrew, they must have covered the same distance, therefore:
16t = 12×(t + 0.5) ⇒ 16t = 12t + 6 ⇒ 4t = 6 ⇒ t = 6/4 ⇒ t = 3/2 ⇒ t = 1.5
Therefore, Stacey meets Andrew 1.5 hours after she starts travelling at 11:30 AM and Andrew meets Stacey 2 hours after he starts travelling at 11:30 AM.
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Write an inequality statement that represents "two and 5 tenths minus 2 times the quantity of the
difference of negative 3 and one half and two times a number is at least ten and three quarters".
Answer:
2.5 - 2(-3-0.5) + 2(n) > 10.75
Step-by-step explanation:
Step 1: two and 5 tenths is 2.5
Step 2: 2 times the quantity of the difference of negative three and one half is 2(-3-1/2)
Step 3: two times a number is at least ten and three quarters = 2(n) > 10.75
Combine: 2.5 - 2(-3-0.5) + 2(n) > 10.75
Given that X is directly proportional to y2. if x=4 units and y=3 units ,then find the value of y when x= 3 units
Answer:
y = 2.60 (to 3sf)
Step-by-step explanation:
Since x is directly proportional to y², then x = ky², where k is a constant.
When x = 4, y = 3,
4 = k(3)²
4 = 9k
9k = 4
∴[tex]k =\frac{4}{9}[/tex]
∴ When x = 3,
[tex]\frac{4}{9}y^{2} = 3[/tex]
∴y = 2.60 (to 3sf)
Consider the following conjecture.
There are no prime numbers between 7,608 and 7,620
How could this statement be shown to be true or false? Would it still be a conjecture if no counterexample were found? Explain
There are no prime numbers between7,608 and 7,620
A prime number is a whole number greater than 1 whose only factors are 1 and itself
The numbers between 7608 and 7620 are:
7609,7610,7611,7612,7613,7614,7615,7616,7617,7618,7619
Here we have to check these numbers are prime number or not
Prime factorization
7609=7×1087
7610=2×5×761
7611=3×43×59
7612=2×2×11×173
7613=23×331
7614=2×3×3×3×3×47
7615=5×1523
7616=2×2×2×2×2×2×7×17
7617=3×2539
7618=2×13×293
7619=19×401
Hence, proved that there are no prime numbers between7608 and 7620
