The points 2, -1+i√3, and -1-i√3 form an equilateral triangle on the Argand plane.
To prove that the points 2, -1+i√3, and -1-i√3 form an equilateral triangle on the Argand plane, we need to show that the distances between these points are equal.
Let's calculate the distances between the points using the distance formula:
Distance between 2 and -1+i√3:
d₁ = |2 - (-1+i√3)|
= |3 - i√3|
= √(3² + (√3)²)
= √(9 + 3)
= √12
= 2√3
Distance between -1+i√3 and -1-i√3:
d₂ = |-1+i√3 - (-1-i√3)|
= |-1+i√3 + 1+i√3|
= |2i√3|
= 2√3
Distance between -1-i√3 and 2:
d₃ = |-1-i√3 - 2|
= |-3 - i√3|
= √((-3)² + (√3)²)
= √(9 + 3)
= √12
= 2√3
We have shown that the distances between the three pairs of points are all equal to 2√3.
Therefore, the points 2, -1+i√3, and -1-i√3 form an equilateral triangle on the Argand plane.
To find the length of a side of this equilateral triangle, we can take any of the distances calculated above. In this case, each side of the triangle has a length of 2√3.
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This sample of jelly beans has been selected from a bag containing 500 jelly beans. Based on this sample, how many blue jelly beans would you expect to find in the bag?
Blue: 3
Yellow: 1
Purple: 2
Pink: 1
Green: 2
Red: 1
Answer:
Step-by-step explanation:
[tex]P(blue)=\frac{3}{10} \\[/tex]
For sample of 500 jellybeans:
[tex]E(blue)=\frac{3}{10}\times500=150[/tex]
Solution: 150 blue jellybeans.
.............................................................
Step-by-step explanation:
for the first one the sales on table is going downn while the days are increasing
for the second one the arrow going up signifies that the sales are going up according to days
Review the points versus no points chart to answer the question:
Loan Terms Example 1 (No Points) Example 2 (One Point)
Loan Principal (after down payment) $292,670.00 $292,670.00
APR: fixed 4.1% 3.85%
Discount Points No points 1 point = $2,927.00
Total Interest over 30-Year Term $216,370.00 $201,250.00
Calculate the percent increase of total interest paid between purchasing one point and purchasing no points. Round the final answer to the nearest tenth.
6.0%
6.9%
8.9%
9.2%
The percent increase of total interest paid between purchasing one point and purchasing no points is approximately [tex]6.9[/tex]%.
To calculate the percent increase of total interest paid between purchasing one point and purchasing no points, we need to find the difference in total interest and then calculate the percentage increase.
For Example 1 (No Points), the total interest paid is $[tex]216,370.00[/tex].
For Example 2 (One Point), the total interest paid is $[tex]201,250.00[/tex].
The difference in total interest is $[tex]216,370.00[/tex] - $[tex]201,250.00[/tex] = $[tex]15,120.00[/tex].
To calculate the percentage increase, we divide the difference by the total interest of Example 1 and multiply by [tex]100[/tex]:
[tex]\[\frac{15,120.00}{216,370.00} \times 100 \approx 6.9\%\][/tex]
Therefore, it can be said that the percent increase of total interest paid between purchasing one point and purchasing no points is approximately [tex]6.9[/tex]% (rounded to the nearest tenth).
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Concept Check
Complete the problem. (From Example 1)
1. Liz Reynolds deposited $2,000 into a savings account that pays 8% compounded quarterly, Complete the
table to compute the amount in the account after 1 year.
Original Principal
Interest for First Quarter
Amount at End of First Quarter
Interest for Second Quarter
Amount at End of Second Quarter
Interest for Third Quarter
Amount at End of Third Quarter
Interest for Fourth Quarter
Amount at End of Fourth Quarter
$2,000.00 x 8%*%=
$2,000.00+ $40,00-
$2,040.00 x 8% x = b.
e.
$40.00
h.
F
4
m
a.
+C.
d.
+1.
W
98 +1.
$2,000,00
$40.00
Liz table that shows her compounded interest should be completed the following way;
Original Principal $2,000
Interest for First Quarter $2,000.00 x 8% ×1/4 = $40 = + $ 40
Amount/End of First Quarter $2,000.00+ $40.00 = $2040 = + $ 2040
Interest for Second Quarter $ 2040 × 8% ×1/4 = $ 40.8 = + $ $ 40.8
Amount/End of Second Quarter 2040 + 40.8 = $ 2080.8 = + $ 2080.8
Interest for Third Quarter 2080.8 × 8% ×1/4 = $ 41.616 = + $ 41.616
Amount/End Third Quarter 2080.8+41.616 = $2122.416 = + $ 2122.416
Interest/Fourth Quarter 2122.416 × 8% ×1/4 = $ 42.4483 = + 42.4483
Amount/ End of Fourth Quarter $2122.416 + $42.4483 = 2164.8643
What is meant by quarterly compound interest?Quarterly compound interest is a type of interest that is calculated and paid out four times in a year. This means that the interest earned in one quarter is added to the principal amount, and then interest is calculated on the new, larger principal amount in the next quarter.
Quarterly compound interest is more profitable than annual compound interest in many cases, however, it depends on the percentage increase.
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Your lab regularly runs tests on mice, resulting in several bags of leftover mouse food sitting
in your storage closet. Your manager is setting a budget for next year and needs to know
if the lab can get by using just the leftovers or if you will need to purchase more mouse
food. Fortunately, you've been tracking the lab's food stores in your logs. Will the lab's
reserve of mouse food hold up for the entirety of next year? If not, when will the lab need
more food? Assume that next year is not a leap year.
Day
12/13
12/14
12/15
12/16
12/17
12/20
12/21
Food Reserves
112.6 kg
112.4 kg
111.2 kg
110.7 kg
110.4 kg
109.4kg
109.1kg
Your lab regularly runs tests on mice, resulting in several bags of leftover mouse food sitting in your storage closet, the lab will need more food around day 116 of the year.
To determine if the lab's reserve of mouse meals will hold up for the entirety of subsequent year, we need to research the fee at which the food reserves are reducing.
Let's calculate the common day by day decrease in meals reserves:
Average daily decrease = (Initial food reserves - Final food reserves) / (Number of days)
Initial food reserves = 112.6 kg
Final food reserves = 109.1 kg
Number of days = 8 (from December 13 to December 21)
Average daily decrease = (112.6 kg - 109.1 kg) / 8 ≈ 0.4375 kg/day
Number of days until food reserves reach zero = Final food reserves / Average daily decrease
Number of days until food reserves reach zero = 109.1 kg / 0.4375 kg/day ≈ 249.14 days
Thus, the lab will need more food approximately 365 - 249.14 = 115.86 days into the year. Round it up to the nearest whole number, and the lab will need more food around day 116 of the year.
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Target Business is interested in buying a piece of equipment for $150,000.
The average useful life
of the equipment is 5 years, with projected annual cash flow of $22,000
Calculate the net present value of the equipment at 8%. no salvage value.
The net present value of the equipment is, $7,564.56.
Now, Based on the information , the net present value (NPV) of the equipment can be calculated using the formula:
NPV = (-Initial Investment) + (CF1 / (1+r)) + (CF2 / (1+r)) + ... + (CFn / (1+r)^n)
Where:
Initial Investment = $150,000
CF₁ - CFn = $22,000
r = 8%
Plugging in these values, we get:
NPV = (-$150,000) + ($22,000 / (1+0.08)) + ($22,000 / (1+0.08)) + ($22,000 / (1+0.08)) + ($22,000 / (1+0.08)) + ($22,000 / (1+0.08))
Simplifying the equation, we get:
NPV = -$150,000 + $20,370.37 + $18,828.67 + $17,405.10 + $16,088.71 + $14,871.71
Therefore, the net present value of the equipment is $7,564.56.
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Triangle D has been dilated to create triangle D’. Use the image to answer the question.
Determine the scale factor used.
A. Scale factor of 1/3
B. Scale factor of 3
C. Scale factor of 1/2
D. Scale factor of 2
The scale factor that was used to create triangle D' include the following: C. Scale factor of 1/2
We have,
In Mathematics and Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
Compare the corresponding sides of triangle D and triangle D':
Side DE in triangle D corresponds to side D'E in triangle D'.
Side EF in triangle D corresponds to side E'F in triangle D'.
Side FD in triangle D corresponds to side F'D in triangle D'.
Determine the ratios of the corresponding sides:
The ratio of side D'E to DE is 2:1.
The ratio of side E'F to EF is 2:1.
The ratio of side F'D to FD is 2:1.
Scale factor = Dimension of image (new figure)/Dimension of pre-image (original figure)
By substituting the given dimensions into the formula for scale factor, we have the following;
Scale factor = Dimension of image/Dimension of pre-image
Scale factor = 8/16 = 6/12 = 10/20
Scale factor = 1/2.
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Show your work please please
Answer:
[tex]9\frac{2}{3}[/tex]
Step-by-step explanation:
[tex]\displaystyle 1\frac{1}{4}+\biggr(3\frac{2}{3}+5\frac{3}{4}\biggr)\\\\1\frac{3}{12}+3\frac{8}{12}+5\frac{9}{12}\\\\(1+3+5)+\biggr(\frac{3}{12}+\frac{8}{12}+\frac{9}{12}\biggr)\\\\9+\frac{20}{12}\\\\9+1\frac{8}{12}\\\\9+\frac{2}{3}\\\\9\frac{2}{3}[/tex]
Again, least common denominator is 3*4=12
Step-by-step explanation:
1 1/4 + ( 3 2/3 + 5 3/4)
First change them from mixed fractions to normal fractions.
= 5/4 + ( 11/3 + 23/4)
Then Find the LCM(lowest common factor) of 4 and 3 which is 12 so we'll multiply both 4 and 3 to the number so the answer would be 12. and also if we multiply the denominator we do the same to the numerator.
= 5/4 + (44/12 + 69/12)
add them.
= 5/4 + (44 + 69/12)
now find their LCM and do the same to them since 4 is a factor of 12 we'll multiply it by 3 to get 12 as a denominator to add.
= 5/4 + 113/12
= 15/4 + 113/12
= 15 + 113/12
add them.
= 128/12
Divide both numerator and the denominator by the LCM.
= 64/6
= 32/3
Answer: 32/3 or in mixed fraction: 10 2/3
A sample obtained from a population with σ = 48 has a standard error of σM = 6. How many scores are in the sample?
sin45+cos67-4554+97+64555+755577652-6622
The value of the given expression sin(45°) + cos(67°) - 4554 + 97 + 64555 + 755577652 - 6622 is approximately 755,642,129.099.
To find the value of the expression sin(45°) + cos(67°) - 4554 + 97 + 64555 + 755577652 - 6622, we can start by evaluating the trigonometric functions and then simplifying the arithmetic operations.
First, let's find the values of sin(45°) and cos(67°).
sin(45°) is equal to √2/2, approximately 0.7071, and cos(67°) is equal to 0.3919 (rounded to four decimal places).
Now, we can substitute these values into the expression:
0.7071 + 0.3919 - 4554 + 97 + 64555 + 755577652 - 6622
Next, let's perform the arithmetic operations:
0.7071 + 0.3919 = 1.099 (rounded to three decimal places)
1.099 - 4554 + 97 + 64555 + 755577652 - 6622
Simplifying further:
-4554 + 97 + 64555 = 60098
60098 + 755577652 - 6622 = 755642128
Finally, we have:
1.099 + 755642128 = 755642129.099
Note: The answer has been rounded to three decimal places for intermediate steps and provided as an approximate value due to rounding in trigonometric functions.
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please
[tex]2x {}^{2} + 2y {}^{2} - 6y - 12y = 3 [/tex]
I need help
(q15) A supply of soaps available at different prices is given by the supply curve s(x)= 180+0.3x^3/2 , where x is the product quantity. If the selling price is $250, find the producer surplus.
The producer surplus is approximately $663.772.
To find the producer surplus, we need to calculate the area between the supply curve and the selling price line.
The supply curve is given by the equation:
[tex]s(x) = 180 + 0.3x^{(3/2)[/tex]
where x is the product quantity.
Let's set the selling price to $250.
We want to find the quantity (x) at which the selling price intersects the supply curve. So, we can set:
[tex]250 = 180 + 0.3x^{(3/2)[/tex]
Now, let's solve this equation to find the value of x:
[tex]250 - 180 = 0.3x^{(3/2)[/tex]
[tex]70 = 0.3x^{(3/2)[/tex]
Divide both sides by 0.3:
[tex]x^{(3/2)} = 70 / 0.3[/tex]
[tex]x^{(3/2)} = 233.33[/tex]
Now, we can solve for x by raising both sides to the power of 2/3:
[tex]x = (233.33)^{(2/3)[/tex]
x ≈ 24.88
So, the quantity (x) at which the selling price intersects the supply curve is approximately 24.88.
To calculate the producer surplus, we need to find the area between the supply curve and the selling price line from 0 to x.
The formula for the producer surplus is:
Producer Surplus = ∫[0 to x] (s(x) - Selling Price) dx
Using the given supply curve [tex]s(x) = 180 + 0.3x^{(3/2)[/tex] and the selling price of $250, we can evaluate the integral:
Producer Surplus = ∫[0 to 24.88] ([tex]180 + 0.3x^{(3/2)[/tex]) dx
Calculating the integral we get,
= 663.772
Therefore, the producer surplus is approximately $663.772.
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Caleb has twice as many cousins as amanda. Ruby has 5 cousins, which is 11 less than caleb has. How many cousins does amanda have?
Answer:
Amanda has 8 cousins
Step-by-step explanation:
Let C be the number of cousins Caleb has, A be the number of cousins Amanda has, and R be the number of cousins Ruby has:
[tex]C=2A\\R=5\\R=C-11\\\\R=C-11\\5=C-11\\16=C\\\\C=2A\\16=2A\\8=A[/tex]
Therefore, Amanda has 8 cousins.
Answer:
Amanda has 8 cousins.
Step-by-step explanation:
Let's use algebraic variables to solve the problem.
Let's assume the number of cousins Amanda has is represented by 'A'.
Since Caleb has twice as many cousins as Amanda, the number of cousins Caleb has is '2A'.
And Ruby has 5 cousins, which is 11 less than what Caleb has, so the number of cousins Caleb has is '5 + 11 = 16'.
Equating the two expressions for the number of cousins Caleb has:
2A = 16
Now we can solve for 'A', the number of cousins Amanda has:
Divide both sides of the equation by 2:
A = 16 / 2
A = 8
Therefore, Amanda has 8 cousins.
Please help!!! 83 points
Answer:
a is -13
b is 31
c is 24
Step-by-step explanation:
The circle below is centered at the origin and has a radius of 4. What is its
equation?
OA. x^2 - y^2=16
OB.x²+ y^2=4
OC. x²+y^2=16
OD. x²- y²=4
Answer:
C) [tex]x^2+y^2=16[/tex]
Step-by-step explanation:
[tex](x-h)^2+(y-k)^2=r^2\\(x-0)^2+(y-0)^2=4^2\\x^2+y^2=16[/tex]
Therefore, C is correct
Answer:
option C:
x² + y² = 16
Step-by-step explanation:
general equation of a circle is,
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the center of the circle
r is the radius of the circle
according to the question the circle is centered at the origin so h and k will be 0
and r = 4
by substituting the values in the equation,
(x - 0)² + (y - 0)² = 4²
x² + y² = 16
Find the Value of X.
Dakota walked the dog for 14 minutes and then completed chores for 48 minutes. If she finished the chores at 1:32 p.m. what time did she start walking the dog?
He started walking the dog at the time 12:30 p.m.
We know that Dakota completed hera chores at 1:32 p.m. and that she spent a total of 48 minutes doing them.
That means she must have started her chores at:
⇒ 1:32 p.m. - 48 minutes = 12:44 p.m.
We know that she walked the dog for 14 minutes.
We want to find out what time she started walking the dog,
so subtract 14 minutes from the time she started doing chores,
⇒ 12:44 p.m. - 14 minutes = 12:30 p.m.
Therefore,
Dakota started walking the dog at 12:30 p.m.
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help please
due today
Answer: 38.4 + 216 = 254.4
Step-by-step explanation: The volume of the block at the top is 38.4 and the volume of the block at the bottom is 216 so add them together to make 254.4
Hope it helped :D
What's the slope-intercept form of the equation of the line graphed in this figure?
A) y = –3∕5x + 1
B) y = –5∕ x – 1
C) y = 5∕3x + 1
D) y = 3∕5x + 1
Answer:
Option D
Step-by-step explanation:
Slope intercept form:(-5, -2) ; x₁ = -5 & y₁ = -2
(5 , 4) ; x₂ = 5 & y₂ = 4
Plugin the points in the below mentioned formula and find the slope.
[tex]\boxed{\bf slope =\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf = \dfrac{4-[-2]}{5-[-5]}\\\\\\=\dfrac{4+2}{5+5}\\\\=\dfrac{6}{10}\\\\=\dfrac{3}{5}[/tex]
Equation of slope-intercept form: y =mx + b
Here, m is the slope and b is the y-intercept.
[tex]\sf y = \dfrac{3}{5}x + b[/tex]
The line is passing through (5, 4). So, substitute the points in the equation and find the y-intercept.
[tex]4 =\dfrac{3}{5}*5 + b\\\\\\4=3+b\\\\[/tex]
4 - 3 = b
b = 1
Slope intercept form of the equation:
[tex]\sf y = \dfrac{3}{5}x + 1[/tex]
A factory produces bicycles and motorcycles by using two machines A and B . Machine A has at most 120 hours available and machine B has a maximum of 144 hours available. Manufacturing a bicycle requires 5 hours in machine A and 4 hours in machine B while manufacturing of a motorcycle requires 4 hours in machine A and 8 hours in machine B . if he gets profit of Rs.40 per bicycle and Rs.50 per motorcycle , how many bicycles and motorcycles should be manufactured to get maximum profit
To maximize profit, the factory should manufacture 8 bicycles and 12 motorcycles.
What is the optimal number of bicycles and motorcycles to maximize profit?Let us assume the number of bicycles as 'x'
Let us assume the number of motorcycles as 'y'.
The time constraint on machine A can be expressed as: 5x + 4y ≤ 120
The time constraint on machine B can be expressed as: 4x + 8y ≤ 144
To maximize profit, we need to maximize the objective function:
P = 40x + 50y
By graphing the constraints and finding the feasible region, we can determine the optimal solution.
Graphing the constraints:
For 5x + 4y ≤ 120:
Let's solve for y in terms of x: y ≤ (120 - 5x) / 4
For 4x + 8y ≤ 144:
Let's solve for y in terms of x: y ≤ (144 - 4x) / 8
The feasible region will be the intersection of the shaded regions:
y ≤ (120 - 5x) / 4
y ≤ (144 - 4x) / 8
Now, we will find the corner points of the feasible region:
When x = 0, y = 0
When x = 24, y = 0
When x = 8, y = 12
Substituting values into objective function P = 40x + 50y:
When x = 0, y = 0:
P = 40(0) + 50(0)
P = 0
When x = 24, y = 0:
P = 40(24) + 50(0)
P= 960
When x = 8, y = 12:
P = 40(8) + 50(12)
P = 1360.
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what is the sum 3/x+9+5/x-9
Answer:
[tex]\frac{8}{x}[/tex]
Step-by-step explanation:
what is the sum 3/x+9+5/x-9
[tex]\frac{3}{x} + 9 + \frac{5}{x} - 9 =[/tex] (add [tex]\frac{3}{x}[/tex] and [tex]\frac{5}{x}[/tex])
[tex]\frac{8}{x} + 9 - 9 =[/tex] (solve 9 - 9 = 0)
[tex]\frac{8}{x}[/tex] ( your answer)
Mano you new wom a) Divide 70,756 by 19. b) Subtract 940 from your answer to part a).
The solution of the expression is,
a) 3,724
b) 2,784
We have to given that,
a) Divide 70,756 by 19.
b) Subtract 940 from your answer to part a).
Now, We can simplify as,
a) Divide 70,756 by 19.
⇒ 70,756 ÷ 19
⇒ 3,724
And, Subtract 940 from your answer to part a). that is, 3724
⇒ 3724 - 940
⇒ 2,784
Therefore, The solution of the expression is,
a) 3,724
b) 2,784
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A broker gets 45% of the commission and an agent gets 55%. How much does an agent earn when a house is sold for $73,400.00 and the rate of commission is 5 1/2 %
When a house is sold for $73,400.00 with a commission rate of 5 1/2 %, the agent's earnings would be $2,220.35.
To calculate the agent's earnings, we need to determine the total commission earned from the sale of the house and then calculate 55% of that amount.
First, we need to calculate the total commission earned from the sale of the house. The commission rate is given as 5 1/2 %, which can be written as a decimal as 0.055.
The total commission can be found by multiplying the sale price of the house ($73,400.00) by the commission rate (0.055):
Total Commission = $73,400.00 * 0.055
= $4,037.00
Now, we need to determine the agent's earnings, which is 55% of the total commission. We can calculate this by multiplying the total commission by 55% or 0.55:
Agent's Earnings = $4,037.00 * 0.55
= $2,220.35
Therefore, when a house is sold for $73,400.00 with a commission rate of 5 1/2 %, the agent's earnings would be $2,220.35.
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Prove the following?
In both cases considered below, we have either x = m or m ∉ x. Therefore, m is an ∈-minimal element of X.
Let's consider a nonempty subset X ⊆ ℕ.
To prove that X has an ∈-minimal element, we can follow the given hint: pick an arbitrary n ∈ X and look at the intersection of X with the set {0, 1, 2, ..., n}.
Let's denote this intersection as Y = X ∩ {0, 1, 2, ..., n}.
We can observe the following:
Y is a nonempty subset of ℕ: Since X is nonempty, and we are intersecting it with a nonempty set {0, 1, 2, ..., n}, the resulting set Y = X ∩ {0, 1, 2, ..., n} will also be nonempty.
Y is a finite subset of ℕ: The set {0, 1, 2, ..., n} is finite, and the intersection of any two finite sets is also finite. Therefore, Y is a finite subset of ℕ.
Since Y is a nonempty and finite subset of ℕ, it must have a minimal element with respect to the element hood relation ∈.
Let's denote this minimal element as m, where m ∈ Y.
Now, we need to show that m is an ∈-minimal element of X, i.e., for any x ∈ X, either x = m or m ∉ x.
Consider an arbitrary element x ∈ X. We know that x ∈ Y because Y is defined as the intersection of X with {0, 1, 2, ..., n}. Since m is the minimal element of Y, we have two cases:
Case 1: If x = m, then we have x = m, satisfying the condition.
Case 2: If x ≠ m, then x ∈ Y implies that x ∉ {0, 1, 2, ..., n} \ {m}. In other words, x ∉ {0, 1, 2, ..., n} or x = m. But x ≠ m, so x ∉ {0, 1, 2, ..., n} must hold. Since x ∉ {0, 1, 2, ..., n}, we can conclude that m ∉ x.
In both cases, we have either x = m or m ∉ x. Therefore, m is an ∈-minimal element of X.
Since we picked an arbitrary n ∈ X and showed that X ∩ {0, 1, 2, ..., n} has an ∈-minimal element, we have demonstrated that every nonempty subset X ⊆ ℕ has an ∈-minimal element.
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3. Determine the total cost of the automobile after down payment and finance cost. Round your answer to the nearest penny, do not use commas in your answer.
price of car: $46,890.00, percent down: 26%, finance cost: $792.00 per month for 60 months
answer: $___
The cost of the car is $59,711.4.
Since, A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100.
Given here:
Price of the car = $46,890.00,
percent down: 26%,
finance cost: $792.00 per month for 60 months
Thus Total cost= $46,890.00×0.26+60×792
= $12191.4 + $47520
= $59,711.4
Hence, The cost of the car is $59,711.4
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Help fill this out please.
Step-by-step explanation:
Tess's expression is NOT equivalent because she forgot to include the - sign when multiplying -7 and -4.
Bernette's expression is NOT equivalent because she did 2-7 first which is not correct. Since the -7 is connected to the parenthesis, she needs to fully distribute the -7 into the parenthesis before including the 2.
Lucy's expression IS equivalent because she factored it correctly and distributed the -7 into the parenthesis.
Determine the value of x in the triangle below:
NO LINKS
Answer:
x = 12.85714286 (as a decimal)
x = [tex]\frac{90}{7}[/tex] (as a fraction)
Step-by-step explanation:
These 2 triangles are similar.
[tex]\frac{20}{x} = \frac{20 + 8}{x + 18}[/tex]
Cross-multiply both sides.20(x + 18) = x(20 + 8)
20x + 360 = 20x + 8x
20x + 360 = 28x
Take 20x away from both sides.360 = 28x
Divide both sides by 28.x = 12.85714286 or x = [tex]\frac{90}{7}[/tex]
I believe the correct anwser is 45
AB and AD are tangent to circle C. Find the length of AB, if AB = 8x and AD = x + 9. Round your answer to 2 decimal places.
Answer:
To find the length of AB, we can use the property that two tangents to a circle from the same external point are equal. This means that AB = AD. Substituting the given values, we get:
8x = x + 9
Solving for x, we get:
x = 1.5
Therefore, AB = 8x = 8(1.5) = 12.
To check our answer, we can use the Pythagorean theorem on triangle ABD, since AB is perpendicular to BD at the point of tangency. We have:
AB^2 + BD^2 = AD^2
Substituting the values, we get:
12^2 + BD^2 = (1.5 + 9)^2
Simplifying, we get:
BD^2 = 56.25
Taking the square root of both sides, we get:
BD = 7.5
Hence, the length of AB is 12 and the length of BD is 7.5.
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The circumference would ……. For example, a circle with a radius of 3 feet would have a circumference that is about 18 feet. When the radius doubles to 6 feet, the circumference is about ………. feet.
Answer:
37.7 feet
Step-by-step explanation:
The circumference of a circle can be calculated using the formula: Circumference = 2 * π * radius, where π (pi) is approximately 3.14159.
For example, if we have a circle with a radius of 3 feet, its circumference would be approximately 18.85 feet (rounded to five decimal places).
When we double the radius to 6 feet, the circumference also doubles. In this case, the circumference would be approximately 37.70 feet (rounded to five decimal places).
In summary, when the radius of a circle doubles, the circumference also doubles, maintaining a direct proportional relationship between the two measurements.
The 25 members of a basketball team are trying to raise at least $1460.00 to cover the traveling cost for a holiday tournament. If they have already raised $461.00, at least how much should each member still raise, on average, to meet the goal?
Each member should still raise, on average, at least $39.96 to meet the goal.