The equation 5x^2 + 5y^2 + 10x - y = 0 represents a circle. By completing the square, the equation is rewritten in the standard form as (x + 1)^2 + (y - 1/10)^2 = 101/100. The circle's center is at (-1, 1/10) with a radius of approximately 1.005.
Explanation:To show that the equation 5x^2 + 5y^2 + 10x - y = 0 represents a circle and to rewrite it in standard form, we can complete the square for both x and y terms. First, factor out the coefficients of the squared terms:
5(x^2 + 2x) + 5(y^2 - 1/5y) = 0Divide both sides by 5 to simplify the equation:
(x^2 + 2x) + (y^2 - 1/5y) = 0Now, complete the square by adding and subtracting the necessary constants inside each parenthesis:
(x^2 + 2x + 1) - 1 + (y^2 - 1/5y + 1/100) - 1/100 = 0By completing the square, the equation becomes:
(x + 1)^2 + (y - 1/10)^2 = 1 + 1/100This can be further simplified to:
(x + 1)^2 + (y - 1/10)^2 = 101/100The standard form of the equation for a circle is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius of the circle. Therefore, our circle's center is at (-1, 1/10) and its radius is the square root of 101/100, which simplifies to 10.05/10 or approximately 1.005.
12+5x-8=12x-10
Help me solve it step by step
The solution to 2x - 5 = 27 is also a solution of which of the following equations?
3 + 5x = 58
3x - 2 = 31
2x + 3 = 35
27 - 2x = 5
Which description best describes the graph?
Linear increasing
Linear decreasing
Nonlinear increasing
Nonlinear decreasing
Answer:
linear increasing
Step-by-step explanation:
a^2b(3a^2 + 4ab^2) ...?
Julia ran 7000 meters, while carol ran 4 kilometers. who ran farther?
The decimal of 2 quarters, 1 dime, and 4 pennies
sin(θ) cos(3θ) + cos(θ) sin(3θ) = 0
Millions for defense, but not one cent for trubute" was in reference to what?
Answer:
The Americans would pay millions of dollars to defend their country, but not 1 cent towards the bribe in response to the XYZ affair. Hope this helps! :)
Step-by-step explanation:
I'm smart
Kyra observed that 85% of the students at a library liked reading mystery stories. If 30 students at the library did not like reading mystery stories, the number of students at the library who liked mystery stories was _____. (only put numeric values, no other symbols)
Solve 8m^2+20m=12 for m by factoring.
The solutions of the quadratic equation [tex]8m^2 + 20m = 12[/tex] by factoring method are [tex]m = \dfrac{1}{2}[/tex] and [tex]m = - 3[/tex]
Using the formula of the quadratic equation which states that,
The roots of the standard form of a quadratic equation [tex]ax^2 + bx + c = 0[/tex] are calculated as,
[tex]x = \dfrac{- b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]
Given that,
A quadratic equation,
[tex]8m^2 + 20m = 12[/tex]
Now, simplify the equation,
[tex]8m^2 + 20m = 12[/tex]
Subtract 12 on both sides,
[tex]8m^2 + 20m - 12 = 0[/tex]
Take 4 as a common term,
[tex]4 (2m^2 + 5m - 3) = 0[/tex]
Since, [tex]4 \neq 0[/tex]
[tex]2m^2 + 5m - 3 = 0[/tex]
Apply the factoring method in the above equation,
[tex]2m^2 + 5m - 3 = 0[/tex]
[tex]2m^2 + (6 - 1)m - 3 = 0[/tex]
[tex]2m^2 + 6m - m - 3 = 0[/tex]
[tex]2m (m + 3) - 1(m + 3) = 0[/tex]
[tex](2m - 1) (m + 3) = 0[/tex]
This gives two solutions,
[tex]2m - 1 = 0\\2m = 1\\m = \dfrac{1}{2}[/tex]
[tex]m + 3 = 0\\m = - 3[/tex]
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What is 1.3 repeating as a fraction?
How many factors are in (3 3)(2*y 4*y) (2-2)(2 2)?
Jerome walked 2/3 mile in the morning and 11/12 mile in the evning. How many miles did he walk in all?
A.)19/24
B.)7/12
C.)1 and 7/12
D.)1 and 1/3
Compute the area of the triangle.
h = 8 cm
b = 14 cm
a = a0 cm2
Answer:
The area of the triangle is, [tex]56 cm^2[/tex]
Step-by-step explanation:
Area of the triangle(a) is given by:
[tex]a = \frac{1}{2} \cdot bh[/tex] ....[1]
where,
b is the base and h is the height of the triangle.
As per the statement:
Given:
h = 8 cm
b = 14 cm
Substitute in [1] we have;
[tex]a = \frac{1}{2} \cdot 8 \cdot 14 = 4 \cdot 14[/tex]
⇒[tex]a = 56 cm^2[/tex]
Therefore, the area of the triangle is, [tex]56 cm^2[/tex]
Megan is trying to remember her password for her computer. All she can remember is that it is 2 letters followed by 3 digits.
How many possible combinations are there for Megan's password?
A. 1,560
B. 1,676
C. 468,000
D. 492,804
E. 676,000
The number of permutations possible is 468000.
What is permutation?A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.
The first two places are occupied by letters.
The last 3 places are occupied by numbers.
The permutation for the first 2 places is: [tex]26P_2[/tex]
The permutation for the last 3 places is: [tex]10P_3[/tex]
The total permutation is:
[tex]26P_2 \times 10P_3\\\\=468000[/tex]
Hence the correct option is option C.
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How do you do long divison with 2 digits?
A grocery store sells a 7 oz bag of raisins for $1.10 and a 9 oz bag of raisins for $1.46. which size bag has the lower price per ounce?
Whats the perimeter of a square with a side measurement of 6 in?
what 18/25 as a percent and decimal
In order to write [tex]\frac{18}{25}[/tex] as a decimal, we need to find a fraction equivalent to[tex]\frac{18}{25}[/tex] with a 100 in the denominator. Notice that if we multiply the numerator and the denominator of [tex]\frac{18}{25}[/tex] by 4, we get the equivalent fraction [tex]\frac{72}{100}[/tex] which we can now write as a decimal. Remember that the hundredths place is 2 places to the right of the decimal point. Therefore, we can write [tex]\frac{72}{100}[/tex] as 0.72.
To write a fraction to a percent, first remember that a percent is a ratio of a number to 100 so to write [tex]\frac{18}{25}[/tex] as a percent, we need to find a fraction equivalent to [tex]\frac{18}{25}[/tex] that has a 100 in the denominator. We can . do this by setting up a proportion.
[tex]\frac{18}{25}[/tex] ≈ [tex]\frac{n}{100}[/tex]
Now, we can use cross products to find the missing value.
25n = 1800
÷ 25 ÷25
n = 72%
Therefore, [tex]\frac{18}{25}[/tex] is equal to 72%.
Find an equation of the tangent line to the curve
xey + yex = 5
The equation of the tangent line to the curve is derived by first finding the slope of the tangent line at a certain point using implicit differentiation. After finding the slope, we then use the point-slope form of a linear equation to get the equation of the tangent line.
Explanation:To find an equation of the tangent line to the curve given by the equation xey + yex = 5, it's necessary to find the derivative of the function, which gives us the slope of the tangent line at any point. Implicit differentiation is the key here, since y is not explicitly solved in terms of x.
Differentiating the given equation implicitly with respect to x, we get: exy + yex +ex + yex = 0. From this, we can express dy/dx (the derivative of y with respect to x, i.e., the slope of the tangent line) in terms of x and y.
Next, simply plug in the given coordinates of the point at which we are finding the tangent into this dy/dx equation. This gives the slope of the tangent line at the specific point.
To finally find the equation of the tangent line, use the point-slope form of a linear equation y - y1 = m(x - x1), where m is the slope we found, and (x1, y1) are the coordinates of the point. Substitute these values in, and that gives the equation of the tangent line to the curve at the point.
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In which figure is DE\\BC ? figure 1 figure 2 figure 3 figure 4
In Figure 4, in the triangle ΔABC, DE is parallel to BC, i.e., DE||BC.
A triangle is one of the most basic geometric figures, having 3 sides, 3 angles, and 3 vertices.
By the theorem of the triangle, if a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side. Let's check the theorem holds for which triangle in the given figures.
Figure 1:
[tex]\frac{AD}{BD} = \frac{6}{15} =\frac{2}{5}[/tex]
[tex]\frac{AE}{CE} = \frac{6.6}{17.5} =\frac{66}{175}[/tex]
Since, [tex]\frac{AD}{BD}\neq \frac{AE}{CE}[/tex],
Here, in triangle ABC, DE is not parallel to BC.
Figure 2:
[tex]\frac{AD}{BD} = \frac{5}{12}[/tex]
[tex]\frac{AE}{CE} = \frac{6}{15} =\frac{2}{5}[/tex]
Since, [tex]\frac{AD}{BD}\neq \frac{AE}{CE}[/tex],
Here, in triangle ABC, DE is not parallel to BC.
Figure 3:
[tex]\frac{AD}{BD} = \frac{4}{12} =\frac{1}{3}[/tex]
[tex]\frac{AE}{CE} = \frac{5}{16}[/tex]
Since, [tex]\frac{AD}{BD}\neq \frac{AE}{CE}[/tex],
Here, in triangle ABC, DE is not parallel to BC.
Figure 4 :
[tex]\frac{AD}{BD} = \frac{5.5}{15}[/tex]
[tex]= \frac{55}{150}\\ = \frac{11}{30}[/tex]
[tex]\frac{AE}{CE} = \frac{6.6}{18}[/tex]
[tex]=\frac{66}{180}\\ =\frac{11}{30}[/tex]
Since, [tex]\frac{AD}{BD} = \frac{AE}{CE}[/tex],
Therefore, in triangle ABC, DE is parallel to BC, i.e., DE||BC.
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Eddie goes jogging every other day, lifts weights every third day, and swims every fourth day. If Eddie begins all three activities on Monday , how many days will it be before he does all three activities on the same day again?
(BTW YOU'RE SUPPOSED TO USE LCM)
By applying the concept of Least Common Multiple (LCM), which is 12 in this case, we realize that Eddie will perform all three activities on the same day again after 12 days and that the day will be a Friday.
Explanation:If Eddie goes jogging every other day (2 days), lifts weights every third day (3 days), and swims every fourth day (4 days), then we must find the LCM of 2, 3, and 4 to find out when will he do all three activities on the same day again.
The LCM of 2, 3, and 4 is 12. Therefore, Eddie will perform all three activities on the same day after 12 days. If he begins on Monday, he will surprisingly end up on a Friday, as the 12th day falls on a Friday. This is because, typically, 7 days from Monday is another Monday. Therefore, five additional days (to total 12) will fall on a Friday.
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Two-thirds of a number is negative six. Find the number.
-9
-8
-4 ...?
The answer would be negative 9 (-9)
three kids named ricky, bobby, and terry have a total of 68 tech decks. Ricky has 8 more than bobby. terry has triple the number bobby has how many tech decks does each kid have?
Final answer:
Bobby has 12 tech decks, Ricky has 20 tech decks, and Terry has 36 tech decks.
Explanation:
Let's represent the number of tech decks each child has using variables.
Let's say Bobby has x tech decks. Since Ricky has 8 more tech decks than Bobby, Ricky has x + 8 tech decks. Terry has triple the number of tech decks that Bobby has, so Terry has 3x tech decks.
Now, we can set up an equation to represent the total number of tech decks:
x + x + 8 + 3x = 68
5x + 8 = 68
5x = 60
x = 12
So, Bobby has 12 tech decks, Ricky has 12 + 8 = 20 tech decks, and Terry has 3 * 12 = 36 tech decks.
A regular octagon rotates 360° about its center. How many times does the image of the octagon coincide with the preimage during the rotation?
The slope of the line below is –4. Use the coordinates of the labeled point to find a point-slope equation of the line.
A. y – 9 = 4(x + 4)
B. y + 9 = –4(x – 4)
C. y – 9 = –4(x + 4)
D. y + 9 = 4(x – 4)
Answer: y+9=-4(x-4)
Step-by-step explanation:
A P E X
Gfc to reduce fractions 28/14
Which expression represents the composition g(f(x)) for the functions below?
f(x) = –3x2
g(x) = 3x
Answer:
[tex]g(f(x))=-9x^2[/tex]
Step-by-step explanation:
[tex]f(x) = -3x^2[/tex]
[tex]g(x) = 3x[/tex]
WE need to find composition of function g(f(x))
To find g(f(x)) we replace f(x) in g(x)
[tex]g(f(x))= g(-3x^2)[/tex]
Now we replace -3x^2 inside g(x)
[tex]g(-3x^2)=3(-3x^2)= -9x^2[/tex]
[tex]g(f(x))=-9x^2[/tex]
I have 28 toys that are solar 2/7 of them are Disney characters how many solar toys are Disney characters
Final answer:
To find out how many solar toys are Disney characters, multiply the total number of toys by the fraction of toys that are Disney characters.
Explanation:
To find out how many solar toys are Disney characters, we need to multiply the total number of toys by the fraction of toys that are Disney characters. In this case, 2/7 of the toys are Disney characters. So, we can calculate:
Number of solar Disney toys = Total number of solar toys × Fraction of Disney toys
Number of solar Disney toys = 28 × 2/7 = 8
Therefore, there are 8 solar toys that are Disney characters.
You are making small pizzas. you have 12 cups of flour. each pizza crust requires 3/4 cup of flour. how many pizza crusts can you make?