Answer:
Step Reason
x2 + y2 - 8x + 12y + 27 = 0 given
x2 - 8x + y2 + 12y = -27 Isolate the constant term
x2 - 8x + 16 + y2 + 12y + 36 = -27 + 16 + 36 Complete the square by adding . 16 and 36 to both sides.
(x2 - 2∙4∙x + 42) + y2 + 12y + 36 = 25 Group and rearrange terms in x.
(x - 4)2 + y2 + 12y + 36 = 25 (a - b)2 = a2 - 2ab + b2
(x - 4)2 + (y2 + 2∙6∙y + 62) = 25 Group and rearrange terms in y.
(x - 4)2 + (y + 6)2 = 25 (a + b)2 = a2 + 2ab + b2
(x - 4)2 + (y + 6)2 = 52 Take the square root to find r = 5.
Step-by-step explanation:
this is the exact answer from plato
hope this helps a little bit :))
Andrew estimated the weight of his dog to be 60 lb. The dog’s actual weight was 68 lb. What was the percent error in Andrew’s estimate? Round your answer to the nearest tenth of a percent. __________ %
the quadratic formula gives which roots for the equation 2x^2+x-6=0
The quadratic formula gives two roots for a quadratic equation. The roots of the equation 2x²+x-6=0 are 1.5 and -2.
Explanation:The quadratic formula gives the roots of a quadratic equation of the form ax²+bx+c=0. For the equation 2x²+x-6=0, the values of a, b, and c are 2, 1, and -6, respectively.
Using the quadratic formula, we can calculate the roots:
x = (-b ± √(b² - 4ac)) / (2a)
Substituting the values of a, b, and c into the formula:
x = (-1 ± √(1² - 4*2*(-6))) / (2*2)
Simplifying the expression:
x = (-1 ± √(1 + 48)) / 4
x = (-1 ± √49) / 4
x = (-1 ± 7) / 4
Therefore, the roots of the equation 2x²+x-6=0 are:
x = (-1 + 7) / 4 = 3/2 = 1.5
x = (-1 - 7) / 4 = -8/4 = -2
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The rounding rule for the correlation coefficient requires three decimal places true or false
Answer:
Round the value of r to three decimal places.
Step-by-step explanation:
The rounding rule for the correlation coefficient requires three decimal places
this statement is true.
The correlation coefficient in statistics is a parameter which measures the degree of strength of relation between two variables .
Its value lies between -1 to +1 .
The closer the correlation coefficient will be near to 1 the stronger the correlation will be.
The correlation between two variables can be positive or negative
Correlation coefficients are helpful in determining the functional relationships among the variables
So higher magnitude of correlation coefficients lead to accurate functional relation among variables.
The rounding rule for the correlation coefficient requires three decimal places
this statement is true.
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What are the values of a1 and r of the geometric series?
2 – 2 + 2 – 2 + 2
Answer: For the given geometric series, the first term is [tex]a_1=2[/tex] and the common ratio is [tex]r=-1.[/tex]
Step-by-step explanation: We are given to find the values of [tex]a_1[/tex] and [tex]r[/tex] of the following geometric series:
[tex]2-2+2-2+2-~.~.~..[/tex]
We know that
[tex]a_1[/tex] is the first term and [tex]r[/tex] is the common ratio of the given geometric series.
We can see that the first term of the given geometric series is 2.
So. we must have
[tex]a_1=2.[/tex]
Also, common ratio is found by dividing a term by its preceding term.
Therefore, the common ratio [tex]r[/tex] of the given geometric series is
[tex]r=\dfrac{-2}{2}=\dfrac{2}{-2}=~.~.~.~=-1.[/tex]
Thus, for the given geometric series, the first term is [tex]a_1=2[/tex] and the common ratio is [tex]r=-1.[/tex]
Ohm’s Law states that the electrical current, I in amperes, through a resistor is given by the formula 644-14-04-00-00_files/i0210000.jpg where V is the voltage in volts and R is the resistance in ohms. If the current is 6 amperes and the resistance is 18 ohms, what is the voltage?
Answer:
The correct answer is D., or "108 volts".
Complete the pattern ___, ___, ___, 0, 2, 4, 6
Answer:-6, -4, -2, 0, 2, 4, 6. They continue in increments of +2.
Step-by-step explanation:
A population of flies grows according to the function p(x) = 2(4)x, where x is measured in weeks. A local spider has set up shop and consumes flies according to the function s(x) = 2x + 5. What is the population of flies after two weeks with the introduced spider?
Answer:
answer is 23
Step-by-step explanation:
Which measure of variability is the most appropriate for this set of values?
13, 42, 104, 36, 28, 6, 17
Answer:
in other words that guy said E
Step-by-step explanation:
The law of cosines is a2+b2 - 2abcosC = c^2 find the value of 2abcosC .... A. 40 B. -40 C. 37 D. 20
(The sides are 2,4, and 5; A to B is 2, B to C is 4, and A to C is 5.)
Given the Law of Cosines, the value of 2abcosC after plugging in the values of a, b, and c is: [tex]\mathbf{2abcosC = 37}[/tex]
Law of Cosines is given as: [tex]a^2+b^2 - 2abcosC = c^2[/tex]
Given also are the sides of a triangle:
a = 4 (side B to C)b = 5 (side A to C)c = 2 (side A to B)Plug in the values into the Law of Cosines, [tex]a^2+b^2 - 2abcosC = c^2[/tex] to find [tex]\mathbf{2abcosC}[/tex]
Thus:[tex]4^2+5^2 - 2abcosC = 2^2\\\\16 + 25 - 2abcosC = 4\\\\41 - 2abcosC = 4[/tex]
Subtract 41 from both sides[tex]41 - 2abcosC - 41 = 4-41\\\\-2abcosC = -37[/tex]
Divide both sides by -1[tex]\mathbf{2abcosC = 37}[/tex]
Therefore, given the Law of Cosines, the value of 2abcosC after plugging in the values of a, b, and c is: [tex]\mathbf{2abcosC = 37}[/tex]
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If sin θ = 2 over 7 and tan θ > 0, what is the value of cos θ?
Which of the following is not one of the three ways to express a ratio A 3/4 B 3:4 C 3 of 4 D 3 to 4
Two standard number cubes are thrown, one after the other. What is the probability that the first cube lands showing a 1 and the second cube lands showing a number that is not 1? Round the answer to the nearest thousandth.
Answer:
B on edge
Step-by-step explanation:
A deposit of $1,295 at 7% for 180 days what is the interest earned
To find the simple interest on a deposit of $1,295 at a 7% rate for 180 days, we use the formula I = P × r × t. With 180 days being roughly 0.5 years, the interest earned is approximately $45.33.
Explanation:Calculating Simple Interest for a Deposit
To calculate the simple interest earned on a deposit, we can use the simple interest formula which is Interest (I) = Principal (P) × Rate (r) × Time (t).
In this case, a student wants to know the interest earned on a deposit of $1,295 at 7% for 180 days. Since simple interest is usually calculated on an annual basis, we need to adjust the time to reflect a portion of the year. 180 days is equivalent to ½ year (since 180/365 ≈ 0.493). Now we can plug in the values into the formula:
I = P × r × t
I = $1,295 × 0.07 × 0.5
So, the interest earned would be:
I = $1,295 × 0.07 × 0.5I = $45.325
The student will earn approximately $45.33 in interest (rounded to the nearest cent).
Write out the form of the partial fraction decomposition of the function (see example). do not determine the numerical values of the coefficients. (a) x4 + 5 / x5 + 2x3
The infinite sequence –1, –2, –3, –4, –5, ... can be generated with which explicit formula?
Answer:
An = (-1)* n
Step-by-step explanation:
An = ( -1) * n
A2 = (-1 ) * 2 = -2
A3= ( -1 ) * 3 = -3
A4= ( -1 ) * 4 = -4
A5= ( -1 ) * 5 = -5
An explicit formula also known as an exact formula is a mathematical formula used to find the nth term in a series or sequence . hence the explicit formula used to find the nth term of this sequence can be represented as
An = ( -1 ) * n where n = number of the next term
Answer:
A
Step-by-step explanation:
i got it right
If a new car is valued at $13,200 and 6 years later it is valued at $3000, then what is the average rate of change of its value during those six years?
How many minutes does it take an athlete to run a 10.0 kilometer race? assume the athlete's pace is 6.50 minutes per mile. (1 mi = 1.609 km)?
To find out how many minutes it takes an athlete to run a 10.0 kilometer race using a pace of 6.50 minutes per mile, we can set up a proportion and solve for x. The athlete takes approximately 40.33 minutes to run the race.
Explanation:To convert the athlete's pace from minutes per mile to minutes per kilometer, we will use the conversion factor 1 mile = 1.609 kilometers. Therefore, the athlete's pace is 6.50 minutes per 1.609 kilometers. To find out how many minutes it takes the athlete to run a 10.0 kilometer race, we can set up a proportion:
6.50 minutes / 1.609 kilometers = x minutes / 10.0 kilometers
Using cross multiplication, we can solve for x:
x = (6.50 minutes × 10.0 kilometers) / 1.609 kilometers
x = 40.33 minutes (rounded to two decimal places)
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Factor 2x^2-128 completely
Simplify: 4x^2+36/4x•1/5x
Answer:
Step-by-step explanation:
The given equation is:
[tex]\frac{4x^2+36}{4x}{\times}\frac{1}{5x}[/tex]
On solving the above equation, we get
=[tex]\frac{4x^2+36}{(4x)(5x)}[/tex]
=[tex]\frac{4(x^2+9)}{(4x)(5x)}[/tex]
=[tex]\frac{x^2+9}{(x)(5x)}[/tex]
=[tex]\frac{x^2+9}{(5x^2)}[/tex]
which is the required simplified form.
Thus, the simplified form of the given equation [tex]\frac{4x^2+36}{4x}{\times}\frac{1}{5x}[/tex] is [tex]\frac{x^2+9}{(5x^2)}[/tex].
Let g(x) = x - 3 and h(x) = x2 + 6. What is (h o g)(1)?
which expression is equivalent to (4h^7k^2)^4?
A: 16h^11k^6
B: 16h^28k^8
C; 256h^11k^6
D: 256h^28k^8
Answer: Option 'D' is correct.
Step-by-step explanation:
Since we have given that
[tex](4h^7k^2)^4[/tex]
We need to simplify this :
Here we go:
We will apply :
[tex](a^m)^n=a^{mn}[/tex]
[tex](4h^7k^2)^4\\\\=4^4\times (h^7)^4\times (k^2)^4\\\\=256h^{28}k^8[/tex]
Hence, option 'D' is correct.
Which are the roots of the quadratic function f(q) = q2 – 125? Check all that apply. q = 5 q = –5 q = 3 q = –3 q = 25 q = –25
Answer:
q=5 sqrt 5 and q=-5 sqrt 5
Step-by-step explanation:
got it right on edge :)
The roots of the quadratic function f(q) = q^2 − 125 are q = -5 and q = 5. Other options listed do not satisfy the function. The roots are found by factoring the equation as a difference of squares.
Explanation:The roots of the quadratic function f(q) = q2 − 125 can be found by solving the equation q2 − 125 = 0. To find the roots, we need to factor the quadratic or use the square root property since the equation is already set to zero.
We can see that this is a difference of squares equation, so it factors to (q + 5)(q - 5) = 0. Setting each factor equal to zero gives us q = -5 and q = 5.
So, the roots of the quadratic function are q = -5 and q = 5. The other options given (q = 3, q = -3, q = 25, q = -25) do not satisfy the equation f(q) = q2 − 125 = 0, hence they are not roots of this function.
Lily is standing at horizontal ground level with the base of the Sears Tower. The angle formed by the ground and the line segment from her position to the top of the building is 15.7°. The Sears Tower is 1450 feet tall. Find Lily's distance from the Sears Tower to the nearest foot.
In the figure below, segment AC is congruent to segment AB:
Triangle ABC with a segment joining vertex A to point D on side BC. Side AB is congruent to side AC
Which statement is used to prove that angle ABD is congruent to angle ACD?
the answer is A. segment AD bisects angle CAB. I just took the exam and I got it right. hope this helps!
Answer: Isosceles triangle theorem
Step-by-step explanation:
In the given picture, there a triangle whose two sides are equal AB=AC.
Therefore it is an isosceles triangle.
Now, the isosceles theorem says that the angles opposite to the equal sides of a triangle are equal.
Therefore by isosceles triangle theorem in ΔABC we have
[tex]\angle{B}=\angle{C}[/tex]
Since [tex]\angle{ACD}=\angle{C}[/tex] [Reflexive]
[tex]\angle{ABD}=\angle{B}[/tex] [Reflexive]
Therefore, [tex]\angle{ACD}=\angle{ABD}=[/tex]
The circle will be dilated by a scale factor of 6. What is the value for n if the expression nPI represents the circumference of the circles in inches?
The value of n is 12 .
What is scale factor?The scale factor is a measure for similar figures, who look the same but have different scales or measures. Suppose, two circle looks similar but they could have varying radii. The scale factor states the scale by which a figure is bigger or smaller than the original figure.
According to the question
The circle will be dilated by a scale factor of 6 .
so,
New radius of the circle R = 6r
As is it dilated by a scale factor of 6
Now ,
The circumference of the new circles = 2πR
= 2.6π
= [tex]12\pi r[/tex] -------------------- (1)
and given circumference of the new circles = nπ ---------------------(2)
when we compare both n = 12
Hence, the value of n is 12 .
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Evaluate the surface integral. ∫∫s (x2 + y2 + z2) ds s is the part of the cylinder x2 + y2 = 16 that lies between the planes z = 0 and z = 5, together with its top and bottom disks.
Evaluate the given surface integral by parameterizing the surface and computing the integral on each surface separately. Take the antiderivatives of both dimensions defining the area, from the bounds of the integral for an accurate solution.
Explanation:The problem you've presented is a surface integral in the field of calculus, specifically relating to multivariable calculus. To solve this, we need to evaluate the integral over the specified parts of the cylinder and the top and bottom disks. We start by parameterizing the surface. Given that our cylinder is x² + y² = 16 between z = 0 and z = 5, we can use cylindrical coordinates with the parameterization: r(θ, z) = <4cos(θ), 4sin(θ), z> for 0 ≤ θ ≤ 2π and 0 ≤ z ≤ 5. With this parameterization, you can derive the equation for the surface integral and solve it.
When working with surface integrals, it's essential to remember that you are totaling up the quantity across the entire surface of an object. In such a situation, we could handle this problem by separating it into three parts: the side of the cylinder, the top disk, and the bottom disk, and compute the integral on each surface separately.
The integral can be solved by taking the antiderivatives of both dimensions defining the area, with the edges of the surface in question being the bounds of the integral. You can apply this approach to all the separate parts of this question.
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Paula has 3 bananas. She wants to divide each of them into sections. How many 's are there in 3 bananas?
Answer:
B IS 21
Step-by-step explanation:
John has taken out a loan for college. He started paying off the loan with the first payment of $100. Each month he pays, he wants to pay back 1.1 times the amount he payed the month before. Explain to John how to represent his first 20 payments in sequence notation. Then explain how to find the sum of the first 20 payments using complete sentences.
whats the value of the equation
13x-2(x+4) = 8x+1 =
13x-2x-8 = 8x+1=
11x-8 = 8x+1
-8 =-3x+1=
-9 = -3x
x = -9/-3 = 3
x = 3
Determine the angular velocity, in radians per second, of 4.3 revolutions in 9 seconds. Round the answer to the nearest tenth.