Answer:
Center of circle: (1, -2)
Radius: √6
Step-by-step explanation:
First, we need to isolate the constant:
[tex]4x^2 + 4y^2 - 8x + 16y = 4[/tex]
Then, we can divide the whole equation by 4:
[tex]x^2+y^2-2x+4y=1[/tex]
Then, we can complete the square(reminder: (a+b)^2 = a^2 + 2ab + b^2)
[tex](x^2-2x)+(y^2+4y)=1\\(x^2-2x+1)+(y^2+4y)=1+1\\(x^2-2x+1)+(y^2+4y+4)=1+1+4\\(x-1)^2+(y+2)^2=6[/tex]
Now that we got the standard equation of the circle, we can find the center and radius by using the equation [tex](x-h)^2+(y-k)^2=r^2[/tex], where (h, k) is the coordinate of the center, and r is the radius.
Therefore, the center of the circle is (1, -2), and the radius of the circle is √6.
The center of the circle is (1,-2) and the radius is [tex]\sqrt{6}[/tex].
Important information:
The given equation of a circle is [tex]4x^2+4y^2-8x+16y-4=0[/tex].Circle:The standard equation of the circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex] ...(i)
Where, [tex](h,k)[/tex] is center and [tex]r[/tex] is the radius.
The given equation can be written as:
[tex]4(x^2+y^2-2x+4y-1)=0[/tex]
[tex](x^2-2x)+(y^2+4y)=1[/tex]
Add square of half of coefficients of [tex]x[/tex] and [tex]y[/tex].
[tex]\left(x^2-2x+1^2\right)+(y^2+4y+2^2)=1+1^2+2^2[/tex]
[tex](x-1)^2+(y+2)^2=1+1+4[/tex]
[tex](x-1)^2+(y+2)^2=6[/tex]
[tex](x-1)^2+(y+2)^2=(\sqrt{6})^2[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]h=1[/tex]
[tex]k=-2[/tex]
[tex]r=\sqrt{6}[/tex]
Therefore, the center of the circle is (1,-2) and the radius is [tex]\sqrt{6}[/tex].
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Which of these functions has a y-intercept of (0, 7)? Select all that apply
Answer:
(0,7)
Step-by-step explanation:
there is no problem work shown.
"Calculate the mean of the following data set of values:
33; 42; 49; 49; 53; 55; 55; 61; 63; 67: 68; 68; 69; 69; 72;
73; 74; 78 80; 83; 88; 88; 88; 90; 92; 94; 94; 94; 94;
96;100
To calculate the mean of a data set, we need to sum up all the values and then divide by the total number of values.
Sum of the data set = 33 + 42 + 49 + 49 + 53 + 55 + 55 + 61 + 63 + 67 + 68 + 68 + 69 + 69 + 72 + 73 + 74 + 78 + 80 + 83 + 88 + 88 + 88 + 90 + 92 + 94 + 94 + 94 + 94 + 96 + 100
Count of values = 31
Mean = (Sum of the data set) / (Count of values)
Now we can substitute the values and calculate:
Mean = (33 + 42 + 49 + 49 + 53 + 55 + 55 + 61 + 63 + 67 + 68 + 68 + 69 + 69 + 72 + 73 + 74 + 78 + 80 + 83 + 88 + 88 + 88 + 90 + 92 + 94 + 94 + 94 + 94 + 96 + 100) / 31
After evaluating this expression, we find that the mean of the given data set is approximately 71.29 (rounded to two decimal places).
Therefore, the mean of the data set is 71.29.
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Distance between Ben and the Dolphin
Answer:
43
Step-by-step explanation:
The distance between ben and the dolphin is 43 hope this helped
6: John has a coupon for 20% off any item in a store. What would the final cost be for an item that originally cost $15 if he uses his coupon?
Answer:
12$!❤️
Step-by-step explanation:
The number of bacteria growing in an incubation culture increases with time according to B() 9800 (3)x, where x is time in days. After how many days will the number of bacteria in the culture be 7,144,200?
After approximately 2.4744 days, the number of bacteria in the culture will reach 7,144,200.
To find the number of days (x) after which the number of bacteria in the culture reaches 7,144,200, we need to solve the equation B(x) = 7,144,200.
The given equation for the growth of bacteria is B(x) = 9800(3)^x.
Setting B(x) equal to 7,144,200, we have:
9800(3)^x = 7,144,200
To solve for x, we can take the logarithm of both sides using base 3 logarithm:
log₃(9800(3)^x) = log₃(7,144,200)
Using logarithmic properties, we can simplify the equation:
log₃(9800) + log₃(3)^x = log₃(7,144,200)
Since log₃(3)^x is equivalent to x (since log₃(3) = 1), we can rewrite the equation as:
log₃(9800) + x = log₃(7,144,200)
Now, we can solve for x by isolating it:
x = log₃(7,144,200) - log₃(9800)
Using a calculator, we can compute the values:
x ≈ 5.2456 - 2.7712
x ≈ 2.4744
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If the point (x,y) is equidistant from the points (-3,2) and (-5,-4),
prove that x+3y+7=0.
Step-by-step explanation:
i hope u can understand that
Consider the triangle below.
Need help ASAP.....
Answer: See below
Step-by-step explanation:
For part a, we are given that the triangle is an isosceles triangle. That means the two sides that are marked are equal to each other. We set DE and EF equal to each other to find x.
5x-3=3x+7 [subtract both sides by 3x]
2x-3=7 [add both sides by 3]
2x=10 [divide both sides by 2]
x=5
We now know the value of x is 5.
For part b, all we have to do is plug in x=5 to find the length of each leg.
5(5)-3 [multiply]
25-3 [subtract]
DE=22 in
3(5)+7 [multiply]
15+7 [add]
EF=22 in
Now, we have the length of each leg. DE=22 in, EF=22 in
For part c, we do the same as above and plug in x=5 to find the length of the base.
6(5)-3 [multiply]
30-3 [subtract]
DF=27 in
Now, we have the length of the base. DF=27 in
find f(7) if f(x)=6x-1
Answer:
f(7) = 41
Step-by-step explanation:
6(7)-1
42-1
= 41
PLZ HELPPPPPPPP
Two sides of a four-sided figure have negative slopes. Which are the endpoints of the sides of this figure?
1. (–4, –4), (–4, –1), (–1, –4), (–1, –1)
2. (–2, –4), (–1, –1), (1, –1), (2, –4)
3. (1, 1), (2, 4), (5, 4), (4, 1)
4. (1, 4), (2, 1), (5, 1), (4, 4)
Answer:
Think
Step-by-step explanation:
Think its 2.
Select all of the following that would be an acceptable set builder notation for the set {7, 8, 9, 10, 11, 12, 13, 14}.
Group of answer choices
{x | 6 < x < 15}
{x | x is a natural number with 6 < x < 15}
{x | x is a natural number with 7 < x < 14}
{x | 7 < x < 14}
{x | x is a natural number with 6 < x < 15}
===========================================================
Explanation:
The given set is in roster notation. Think of a baseball or football team (or any sports team) how their roster lists out all of the players. In this case, each number is like a player.
The idea here is to simplify the set so we don't have to write out every single item. Instead we have a rule to make things a bit simpler.
In this case, the set {7, 8, 9, 10, 11, 12, 13, 14} describes all natural numbers from 7 to 14
This means we can say {x | x is a natural number with 6 < x < 15}
Note how the endpoints x = 6 and x = 15 are not included. This is because there isn't a "or equal to" as part of the inequality sign. Sure enough 6 and 15 are not part of the original set.
An equivalent set would be [tex]\{ x | \text{ x is a natural number with } \ 7 \le x \le 14\}[/tex] and here we have "or equal to" involved. For this example, the endpoints x = 7 and x = 14 are included.
--------------
Something like choice A and choice D are not complete answers because we don't know if x is a whole number, natural number, rational number, real number, etc. If x was say a real number, then x = 10.75 would be involved with choice A. But 10.75 is not part of the original set.
how many are 15 x 15 ?
Answer:
225
Step-by-step explanation:
Answer:
15 times 15= 225
Step-by-step explanation:
Hope this helps!!!!!!!
simplify the expression
-7(3e-2f+4)+6e-2
Answer: here it is 14f-30-15e
What is the slope-intercept form of the equation of the line that passes through the po
to the graph of 2x + 3y = -5?
1
O y=-{X-8
O y=-3x+1
O y= {x+1
O y= {x+10
Answer: m = -⅔
The slope of 2x + 3y = -5 is -⅔
Plz mark brainleist:)
Step-by-step explanation:
m=-2/3 this is the answer from this question
I need help with this!!
Answer:
B.
Step-by-step explanation:
Area of the shaded region = Total Area- Area of the unshaded region
= [(3x + 2) x (x+1)] - [(x-1) x 4]
= (3x^{2} + 5x + 2) - (4x-4)
= 3x^{2} +5x +2 -4x + 4
=3x^{2} + x + 6
C4 Let B = {₁,...,V) be a set of vectors in R". Prove that if v₁ = Ổ for some i, then B is linearly dependent.
In this question, we are given a set of vectors B in [tex]R_{n}[/tex] and we need to prove that if there exists a vector v_i in B such that v_i is the zero vector, then the set B is linearly dependent.
To prove that if v_i is the zero vector for some i, then the set B is linearly dependent, we need to show that there exist scalars c_1, c_2, ..., c_n (not all zero) such that the linear combination c_1v_1 + c_2v_2 + ... + c_nv_n equals the zero vector.
Since v_i is the zero vector, we can choose c_i = 1 and c_j = 0 for j ≠ i. Then, the linear combination becomes c_1v_1 + c_2v_2 + ... + c_nv_n = v_i, which is the zero vector.
This implies that we have found a nontrivial linear combination of the vectors in B that equals the zero vector. Therefore, B is linearly dependent.
The reason behind this is that the presence of the zero vector in a set of vectors automatically guarantees linear dependence. Any set containing the zero vector can be linearly dependent because we can always choose the scalar coefficient of the zero vector to be non-zero, resulting in a nontrivial linear combination equaling the zero vector.
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Cardi B is buying gifts for her family. She can spend no
more than $60 on all of her gifts.So far she has spent $45.95, and she has one
more gift to buy. Write an inequality that shows how much she can spend on the
final gift. (≥, ≤)
Answer:
x ≥ $14.05
Step-by-step explanation:
I subtracted 45.95 from 60 to find how much she had left, which amounts to 14.05. I used x as the amount she can spend, and the inequality is as such.
Answer: she can spend $14.05
Step-by-step explanation:
$60-$45.95=$14.05
The number of N bacteria in a culture can be modeled through the continuous growth model. If the there were 100 bacteria initially and the
value for kis 0.5, what will the population of the bacteria be in 10 hours, where is the number of hours?
Answer: A. 14,841
Step-by-step explanation:
PLEASE HELP ASAP IM STUCK HELP PLEASE
Answer:
x>-2 and x<5
-2 <x<5
Step-by-step explanation:
We have open circles at -2 and 5 and are between the two numbers so we have and AND statement. It can be written either
x>-2 and x<5
or
-2 <x<5
− 6 × 3 + |−3 ( −4 + 2^3)|
Answer:
4 – 3[4 –2(6 – 3)] ÷ 2
4 – 3[4 – 2(3)] ÷ 2
4 – 3[4 – 6] ÷ 2
4 – 3[–2] ÷ 2
4 + 6 ÷ 2
4 + 3
7
Answer:
252
Step-by-step explanation:
Segment-Part of a ____ (line,point,plane) bounded by two_____ (line,point,plane)
A company produces mopeds and bicycles. It must produce at least 10 mopeds per month. The company has the equipment to produce only 60 mopeds. It also can produce only 120 bicycles. The production of mopeds and bicycles cannot exceed 160. The profit on a moped is $134 and on a bicycle $20. How many of each should be manufactured per month to maximize profit?
(Use x = mopeds; y = bicycles)
3. State the Objective Function in the linear programming problem given:
A. P = 20x + 134y
B. P = 134x + 20y
C. P = 60x + 120y
D. P = 120x + 60y
4. Determine the vertices of the feasible region, given the constraints. (Use Desmos to help with graphing!)
Constraints (for this linear programming problem):
A. (0, 0) F. (160,0)
B. (10,120) G. (60,100)
C. (60, 0) H. (0,120)
D. (60,120) I. (40,120)
E. (10, 0) J. (10,150)
5. How many of each product should be manufactured per month to maximize profit?
A. 60 mopeds, 120 bicycles
B. 160 mopeds, 0 bicycles
C. 60 mopeds, 100 bicycles
D. 40 mopeds, 120 bicycles
PLEASE SHOW WORK.
WILL GIVE BRAINLIEST!
THE PICTURE IS FOR QUESTION 4
Answer:
3. B. P = 134x + 20y
4. J. (10, 150), I(40, 120), G(60, 100), C(60, 0) and E(10, 0)
5. C. 60 mopeds 100 bicycles
Step-by-step explanation:
3. The given information are;
The number of mopeds the company must produce per month = 10
The number of mopeds the company can produce month = 60
The number of bicycles the company can produce per month = 120
The total sum of the produced mopeds and bicycles ≤ 160
The profit on a moped = $134
The profit on a bicycle = $20
Given that the number of moped produced = x and the number of bicycles produced = y
Therefore, we have;
Profit, P = $134 × x + $20 × y
Which gives;
B. P = 134x + 20y
4) From Desmos, using the following constraints;
x + y ≤ 160
10 ≤ x ≤ 60
0 ≤ y ≤ 120 we have;
The vertices of the constraint for the feasible region are;
J. (10, 150), I(40, 120), G(60, 100), C(60, 0) and E(10, 0)
5) We note that since the profit from each moped is more than the profit from the sale of each bicycle, the maximum possible number of moped should be produced, while the rest should be used to produce bicycles
Therefore, given that from the vertices, the maximum possible number of moped = 60, the number of bicycles to be produced should be 160 - 60 = 100 bicycles
Which gives;
C. 60 mopeds 100 bicycles.
3. The objective function should be option B. P = 134x + 20y
4. The vertices of the feasible region, given the constraints should be J(10, 150), I(40, 120), G(60, 100), C(60, 0) and E(10, 0)
5. The number of each product that should be manufactured per month should be option C. 60 mopeds 100 bicycles
Objective function, vertices, and number of each product:3.
Here we assume that the number of mopeds produced = x
and the number of bicycles produced = y
So, the profit equation should be
Profit, P = $134 × x + $20 × y
That provides P = 134x + 20y
4) From Desmos, we used the following constraints;
x + y ≤ 160
10 ≤ x ≤ 60
0 ≤ y ≤ 120 we have;
So, The vertices of the constraint should be
J. (10, 150), I(40, 120), G(60, 100), C(60, 0) and E(10, 0)
5) The maximum no of mopeds should be 60
And, the no of bicycles that need to be produced is
= 160 - 60
= 100 bicycles
That provides 60 mopeds 100 bicycles.
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a carpet store has 4 commercials every hour on a local television station how many commercials will the store have in 233 hours?
Answer:
932
Step-by-step explanation:
If they have 4 every hour, and there's 233 hours, you multiply 233 by 4.
simplify the expression, answer quickly
Answer:
[tex]{7}^{3} [/tex]
Step-by-step explanation:
simplify numerator to get
[tex] {7}^{7} [/tex]
simplify denominator to get
[tex] { ({7}^{2} )}^{2} [/tex]
which simplifies to
[tex] {7}^{4} [/tex]
now that it's
[tex] \frac{ {7}^{7} }{ {7}^{4} } [/tex]
the exponents subtract to get our final answer
Answer:
Step-by-step explanation:
(16-9)^7
[(5+2)^2]^2
(16-9)^7
823543
[(5+2)^2]^2
(49)^2
2401
823543/2401 = 343
Draw your own triangle given the indicated measures and solve for the other parts using Sine Law. Write an explanation in each line of your solution. 1.
By applying the Sine Law and rearranging the equation, we can determine the missing parts of the triangle and solve for angles and sides.
We will draw a triangle based on the given measures and then use the Sine Law to solve for the other parts. The Sine Law relates the measures of angles and sides in a triangle.
Let's assume we have a triangle with sides a, b, and c, and angles A, B, and C, respectively. To solve for the other parts using the Sine Law, we need at least one side and its corresponding angle.
Suppose we are given side A and angle A. We can draw the triangle accordingly. The side opposite angle A will be labeled "a," and angle A will be opposite side a.
Next, we can use the Sine Law, which states that the ratio of a side length to the sine of its opposite angle is constant. The Sine Law can be expressed as:
a/sin(A) = b/sin(B) = c/sin(C)
With this information, we can solve for the other parts of the triangle. If we are given side A and angle A, we can use the Sine Law to find the ratios of the other sides to their corresponding angles.
By rearranging the Sine Law equation, we can solve for the unknown sides or angles. For example, to find side b, we have:
b = (a * sin(B)) / sin(A)
Similarly, we can find side c using:
c = (a * sin(C)) / sin(A)
And we can find the other angles using the inverse sine function:
B = sin^(-1)((b * sin(A)) / a)
C = sin^(-1)((c * sin(A)) / a)
By applying the Sine Law and rearranging the equation, we can determine the missing parts of the triangle and solve for angles and sides.
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Solve the equation.
-3n-4n-17=25
n=?
Answer:
n=-6
Step-by-step explanation:
-3n-4n-17=25
-7n-17=25
-7n=42
n=-6
Answer:
n = -6
Step-by-step explanation:
-3n-4n-17=25
Combine like terms
-7n -17 = 25
Add 17 to each side
-7n -17+17 = 25+17
-7n = 42
Divide each side by -7
-7n/-7 = 42/-7
n = -6
The rational number which lies between - 1/3 and 1/4
is
(a) 1
(b) - 1
(c) 0
(d) infinite numbers
Answer:
I think that's 1
Step-by-step explanation:
but not sure
C(x)=75,000+150x what is the value of x
I need help please
4. Use the number line to determine the measure of FI.
is in the picture of the questions
What is 67,795 rounded to the
nearest thousand?
Work out the following, giving your answers in their simplest form:
a) 2 1/3 divided by 1/4 b) 4/25 divided by 1 1/5
Answer:
a) 28/3 b) 4/55
Step-by-step explanation:
a) 2 1/3 x 4/1 = 7/3 x 4/1 = 28/3
b) 4/25 x 5/11 = 20/275 = 4/55
Answer:
2 1/3÷1/4=7/3÷1/4=28/3
4/25÷1 1/5=4/25÷6/5=2/15
