Answer:
44 ft
Step-by-step explanation:
Given: Julie is 6 feet tall
She stands 15 feet from the flagpole.
The edges of the square line up with the top and bottom of the flagpole.
Lets assume the height of flagpole be "h".
As given, the edges of the square line up with the top and bottom of the flagpole.
∴ Angle and base of triangle are same then ratio of corresponding sides are also equal.
Now, finding the height of flagpole by using tangent rule.
we know, [tex]tan\theta= \frac{Opposite}{adjacent}[/tex]
Remember, both the angle are equal.
∴ Ratio of opposite and adjacent leg for both right angle triangle= [tex]\frac{6}{15} : \frac{h-6}{15}[/tex]
We can put it; [tex]\frac{6}{15} = \frac{15}{h-6}[/tex]
Solving the equation now
⇒ [tex]\frac{6}{15} = \frac{15}{h-6}[/tex]
Multiplying both side by 15
⇒[tex]6 = \frac{15\times 15}{h-6}[/tex]
Multiplying both side by (h-6)
⇒ [tex]6\times (h-6) = 15\times 15[/tex]
Distributive property of multiplication
⇒ [tex]6h-36= 225[/tex]
Adding both side by 36
⇒[tex]6h= 225+36[/tex]
Dividing both side by 6
⇒[tex]h= \frac{261}{6}[/tex]
∴ [tex]h= 43.5\ feet[/tex] [tex]\approx 44 feet[/tex]
Hence, the height of flagpole is 44 feet.
Final answer:
To approximate the height of a flagpole given that Julie, who is 6 feet tall, lines up a cardboard square with the top and bottom of the flagpole while standing 15 feet away, we can use the principles of similar triangles. This results in a calculation showing that the flagpole is approximately 6 feet tall, the same as Julie's height.
Explanation:
The height of the flagpole can be approximated using similar triangles. Julie is 6 feet tall and stands 15 feet from the flagpole. Using the cardboard square, we understand that the triangle formed by Julie and her shadow is similar to the triangle formed by the flagpole and its shadow. Therefore, we can set up a proportion:
Julie's height / Julie's distance from flagpole = Flagpole's height / Flagpole's distance from cardboard.
If we assume that the cardboard square is held adjacent to Julie, the flagpole's distance from the cardboard is also 15 feet. The proportion simplifies to:
6 feet / 15 feet = Flagpole's height / 15 feet
Cross-multiplying to solve for the flagpole's height gives us:
Flagpole's height = 6 feet × (15 feet / 15 feet) = 6 feet
Therefore, the flagpole is approximately 6 feet tall.
How is selective boarding school will only admit students who plays at least 2 .5 standard deviation above the mean on a standardized test that has a mean of 100 and a standard deviation of 24. What is the minimum score that an applicant must make on the test to be accepted?
Answer:
I'd don't now
Step-by-step explanation:
ok am sorry
Where will her cut be located? Round to the nearest tenth. Genevieve is cutting a 60-inch piece of ribbon into a ratio of 2:3. Since 2 inches are frayed at one end of the ribbon, she will need to start 2 inches in. This is indicated as 2 on the number line. 25.2 in. 29.4 in. 35.1 in. 40.7 in.
Answer:
25.2 in
Step-by-step explanation:
The short piece will have a length that is 2/(2+3) = 2/5 of the entire usable length. The usable length is 60-2 = 58 inches long, so the cut will be ...
(2/5)(58 in) = 23 1/5 in
from the beginning of the usable part. Since the usable part of the ribbon starts 2 inches in, the cut will be 23 1/5 + 2 = 25 1/5 inches from the frayed end of the ribbon.
Answer:
25.2
Step-by-step explanation:
Correct on Edge 2020
Are 10(e+0.5g) and 10e+5g not equivalent or equivalent?
Are 6(p+q) and 6p+q not equivalent or equivalent?
Are 7y-15+2y and 9y-15 not equivalent or equivalent?
Are 1+(8r+9) and (2+8)+8r not equivalent or equivalent?
Are 0x11+5n and 5n not equivalent or equivalent?
Are 16s-4+s and 12s not equivalent or equivalent?
Are 11dx2 and 22d not equivalent or equivalent?
Are 8m+(9m-1) and 8m-8 not equivalent or equivalent?
Please help me...
(1) 10(e + 0.5)g
Using distributive property, a × (b + c) = a × b + a × c
10(e + 0.5)g = 10 eg + 10 × 0.5g
Therefore, 10(e + 0.5g) and 10e + 5g are not equivalent.
(2) 6(p + q)
Using distributive property,
6(p + q) = 6p + 6q
Therefore, 6(p + q) and 6p + q are not equivalent.
(3) 7y – 15 + 2y
Using commutative property, a + b = b + a
7y – 15 + 2y = 7y + 2y – 15
= 9y – 15
Therefore 7y – 15 + 2y and 9y – 15 are equivalent.
(4) 1 + (8r + 9)
Using associative property, a + (b + c) = (a + b) + c
1 + (8r + 9) = (1 + 9) + 8r
= 10 + 8r
= (2 + 8) + 8r
Therefore 1 + (8r + 9) and (2 + 8) + 8r are equivalent.
(5) 0 × 11 + 5n
Using multiplicative identity property: a × 0 = 0
0 × 11 + 5n = 0 + 5n
= 5n
Therefore, 0 × 11 + 5n and 5n are equivalent.
(6) 16s – 4 + s
Using associative property, a + (b + c) = (a + b) + c
16s – 4 + s = 16s + s – 4
= 17s – 4
Therefore, 16s – 4 + s and 12s not equivalent.
(7) 11d × 2 = 22d
Therefore, 11d × 2 and 22d are equivalent.
(8) 8m + (9m – 1)
Using associative property, a + (b + c) = (a + b) + c
8m + (9m – 1) = (8m + 9m) – 1
= 17m – 1
Therefore, 8m + (9m – 1) and 8m – 8 not equivalent.
Are the magnetic North Pole and the geographic North Pole always the same distance apart
One positive number is three larger than another positive number. If sixteen times the reciprocal of the smaller number is added to nine times the reciprocal of the larger number, the sum is one. Find the two number.
Answer: = [tex]\frac{25+\sqrt{949} }{6}[/tex] and y = \frac{25+\sqrt{949} }{6} - 3.
Step-by-step explanation:
Take x as the larger number and y as the smaller number.
x + 3 = y
[tex]\frac{16}{y}[/tex]+ [tex]\frac{9}{x}[/tex] = 1
Substitute x + 3 for y in the second equation.
[tex]\frac{16}{x+3}[/tex]+ [tex]\frac{9}{x}[/tex] = 1
Make a common denominator.
[tex]\frac{16(x) + 9(x+3)}{(x+3)(x)} =1[/tex]
Simplify and get rid of that fraction.
[tex]16x + 9x + 27 = x^{2} + 3x[/tex]
[tex]x^{2} + 3x - 25x - 27 = 0[/tex]
[tex]x^{2} -22x - 27 = 0[/tex]
By quadratic formula (and because they must be positive), x = [tex]\frac{25+\sqrt{949} }{6}[/tex] and then y = \frac{25+\sqrt{949} }{6} - 3.
To solve for the two positive numbers, we can set up an equation and solve for x.
Explanation:Let's call the smaller number x and the larger number x + 3.
From the given information, we can write the following equation:
16(1/x) + 9(1/(x + 3)) = 1
To solve this equation, we can find a common denominator and then simplify:
16(x + 3)/(x(x + 3)) + 9x/(x(x + 3)) = 1
After simplifying and solving for x, we find that the smaller number is 4 and the larger number is 7.
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when would you use a negative number to describe a real world amount? Give an example.
Answer:
Debt
Step-by-step explanation:
Let's say someone uses debit instead of credit and they don't have any money in their account. If used multiple times you could potentially end up owing the bank (be in debt) .
Negative numbers are used in real-world contexts to describe temperatures below zero, financial debts, or elevations below sea level, helping to clearly indicate quantities that are less than a referenced zero point.
You would use a negative number to describe a real-world amount when talking about temperatures below zero, debts, or elevations below sea level, among other scenarios. For example, if the temperature is 5 degrees below zero, it could be represented as -5°C. This indicates that it is 5 degrees colder than the point at which water freezes (0°C). Another example is financial: if you owe $100, you could represent your account balance as -$100, indicating a debt. Similarly, a town located 100 meters below sea level could have its elevation represented as -100 meters.
These examples show how negative numbers can effectively convey quantities less than zero in various real-world contexts, providing a clear understanding of situations where values are lacking or in deficit compared to a reference point.
The volume of a box is 39.375 inches³. What is the volume of the box if it is scaled down by a factor of 1/10?
The volume of scaled object is 0.039375 cubic inches
Solution:
Given that,
Volume of box = 39.375 cubic inches
Scaled down by a factor = [tex]\frac{1}{10}[/tex]
The volume of a scaled object will be equal to the volume of object times scale factor cubed
Therefore,
Volume of scaled object = Volume of box x scale factor cubed
[tex]Volume\ of\ scaled\ object = 39.375 \times (\frac{1}{10})^3\\\\Volume\ of\ scaled\ object = 39.375 \times \frac{1}{1000}\\\\Volume\ of\ scaled\ object = 0.039375[/tex]
Thus volume of scaled object is 0.039375 cubic inches
Which of the following equations can be a harmonic on a string that is 10 cm long? Select all that apply. (three correct answers)
A.) y=2sin(pi/5 x)
B.) y=2sin(2pi/7 x)
C.) y=2sin(pi/10 x)
D.) y=2sin(10pi x)
E.) y=2sin (5/2pi x)
Answer:
The options are: A, C and D
Step-by-step explanation:
The sine wave has a general form : y = A sin (BX)
Where A is the amplitude and B = 2π/period
So, we will check which of the options will be a harmonic on a string that is 10 cm long.
A.) y=2sin(pi/5 x)
B = π/5 ⇒ period = 2π/B = 2π ÷ π/5 = 2π * 5/π = 10
So, one cycle of y=2sin(pi/5 x) will be a harmonic on a string that is 10 cm long.
B.) y=2sin(2pi/7 x)
B = 2π/7 ⇒ period = 2π/B = 2π ÷ 2π/7 = 7
C.) y=2sin(pi/10 x)
B = π/10 ⇒ period = 2π/B = 2π ÷ π/10 = 20 = 2 * 10
So, half a cycle of y=2sin(pi/10 x) will be a harmonic on a string that is 10 cm long.
D.) y=2sin(10pi x)
B = 10π ⇒ period = 2π/B = 2π ÷ 10π = 1/5 = 10/50
So, 50 cycles of y=2sin(10pi x) will be a harmonic on a string that is 10 cm long.
E.) y=2sin (5/2pi x)
B = 5/2π ⇒ period = 2π/B = 2π ÷ (5/2π) = 4π²/5
So, options A, C and D can be a harmonic on a string that is 10 cm long.
Answer:
A. y=2sin(pi/5x)
C. y=2sin(pi/10x)
D. y=2sin(10pix)
Step-by-step explanation:
what is 6times40///////////////////////
Answer:
the answer is 240
Answer:
240
Step-by-step explanation:
i used a calculator
A play train travels around a Christmas
tree in a circle. The train track measures 6
feet in diameter. What is the distance that
the train travels?
The distance that the train travels is 18.84 feet
Solution:
Given that,
A play train travels around a Christmas tree in a circle
The train track measures 6 feet in diameter
To find: distance that the train travels
The distance the train travels is equal to the circumference of circle
The circumference of circle is given as:
[tex]C = \pi d[/tex]
Where, "d" is the diameter of circle
From given,
d = 6 feet
[tex]C = 3.14 \times 6\\\\C = 18.84[/tex]
Thus the train travels 18.84 feet
Lauryn grew p tomato plants. Padma grew 5 fewer than 3 times the number Lauryn grew. Kent grew 6 more than 4 times the number Lauryn grew. Choose an expression and a simplified expression to represent the total number of tomato plants that Lauryn, Padma, and Kent grew. Select all that apply.
A. p + (3p – 5) + (4p + 6)
B. p + (5 – 3p) + (6 + 4p)
C. p + 11
D. 8p + 1
E. 7p – 1
Answer:
the anwser is a
Step-by-step explanation:
The expression represents the total number of tomato plants is [tex]\rm p + (3p - 5) + (4p + 6)[/tex].
Given that
Lauryn grew p tomato plants.
The Padma grew 5 fewer than 3 times the number Lauryn grew.
Kent grew 6 more than 4 times the number Lauryn grew.
We have to determine
Choose an expression and a simplified expression to represent the total number of tomato plants that Lauryn, Padma, and Kent grew.
According to the question
Let the number of tomato plants be p.
Lauryn grew p tomato plants.
[tex]\rm = p[/tex]
The Padma grew 5 fewer than 3 times the number Lauryn grew.
[tex]\rm= 3p-5[/tex]
Kent grew 6 more than 4 times the number Lauryn grew.
[tex]\rm = 4p+6[/tex]
Therefore,
An expression to represent the total number of tomato plants = Lauryn + Padma + and Kent grew.
[tex]\rm p + (5 - 3p) + (6 + 4p)[/tex]
Hence, the expression represents the total number of tomato plants is [tex]\rm p + (3p - 5) + (4p + 6)[/tex].
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5f + 3s +6
use f= 6 and s = 7
What is the radius of a circle whose equation is x2 + y2 + 8x - 6y + 21 = 0?
units
Answer:r=2
Step-by-step explanation:
Answer:
A) 2
Step-by-step explanation:
I got it right on edge 2020.
Hope it helps :)
I purple you have a good year, stay safe.
Every day, Bert spends an hour commuting to and from his office, driving at an average speed of 50 mph and taking the same route each way. How far does Bert live from his office?
When speed and time are known, distance can be calculated using the formula 'distance = speed x time'. Given Bert's speed of 50 mph and travel time of 0.5 hours each way, the distance from his home to the office is calculated to be 25 miles.
Explanation:The subject of this problem is fundamentally about understanding the relationship between speed, time, and distance. In this particular case, Bert is spending a total of an hour commuting to and from office. However, this total time includes both the journey to work and the journey back home so each journey takes half an hour or 0.5 hours. Given that his average speed is 50 mph, we can calculate the distance he travels one way using the formula "Distance = Speed x Time."
So, for Bert:
Distance = 50 mph x 0.5 hours = 25 miles
Therefore, "Bert lives 25 miles from his office."
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how would I find x?
Step-by-step explanation:
In the question figure,
∠ 1 = 115 °, ∠ 2 = 115 °, ∠ 3 = 120 °, ∠ 4 = 14x °, ∠ 5 = 133 °, ∠ 6 = 167 °, ∠ 7 = 138° and ∠ 8 = 18x °
To find, the value of x = ?
We know that,
The sum of all angles of heptagon = 1080°
∴ ∠ 1 + ∠ 2 + ∠ 3 + ∠ 4 + ∠ 5 + ∠ 6 + ∠ 7 + ∠ 8 = 1080°
⇒ 115 ° + 115 ° + 120 ° + 14x ° + 133 ° + 167 ° + 138° + 18x ° = 1080°
⇒ 32x ° + 788° = 1080°
⇒ 32x ° = 1080° - 788° = 292°
⇒ x ° = 9.125°
∴ x ° = 9.125°
Which of the following options could represent a possible set of interior angles of a triangle?
60°, 150° and 150°
15°, 35°, and 40°
35°, 65°, and 80°
45°, 105°, and 120°
Answer:
35+65+80=180
Step-by-step explanation:
the total interior angle of a triangle is 180
Answer:
its the third answer
[tex]35 \: \: 65 \: \: 80[/tex]
Step-by-step explanation:
because the addition of a interior angles has to be 180.'
3. (3x + 4) - (x + 2)
I don't understand plz help
Step-by-step explanation:
Perhaps you want to simplify the given expression: Let's do it.
[tex](3x + 4) - (x + 2) \\ \\ = 3x + 4 - x - 2 \\ \\ = 3x - x + 4 - 2 \\ \\ = 2x + 2 \\ this \: is \: the \: simplest \: form \: of \: the \: \\ given \: expression.[/tex]
Answer:
2(x + 1)
Step-by-step explanation:
(3x + 4) - (x + 2)
3x + 4 - x - 2
3x - x + 4 - 2
2x + 2
2(x + 1)
Which expression is equivalent to 7/2h-3(5h-1/2)?
Answer:
-23/2h+3/2
Step-by-step explanation:
7/2h-3(5h-1/2)
7/2h-15h+3/2
7/2h-30/2h+3/2
-23/2h+3/2
Answer:
(-23h+3)/2
Step-by-step explanation:
7/2h-3(5h-1/2)=
7/2h-3*5h+3*1/2=
7/2h-15h+3/2=
7/2h-30/2h+3/2=
-23/2h+3/2 or
(-23h+3)/2
How many different ways can 5 baseball players and 4 basketball players be selected from 12 baseball players and 13 basketball players
1507 are the different ways can 5 baseball players and 4 basketball players be selected from 12 baseball players and 13 basketball players
Solution:
Given that,
5 baseball players and 4 basketball players be selected from 12 baseball players and 13 basketball players
This is a combination problem
Combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter
The formula is given as:
[tex]n C_{r}=\frac{n !}{r !(n-r) !}[/tex]
Where n represents the total number of items, and r represents the number of items being chosen at a time
Let us first calculate 5 baseball players from 12 baseball players
Here, n = 12 and r = 5
[tex]\begin{array}{l}{12 C_{5}=\frac{12 !}{5 !(12-5) !}} \\\\{12 C_{5}=\frac{12 !}{5 ! \times 7 !}}\end{array}[/tex]
For a number n, the factorial of n can be written as:
[tex]n !=n \times(n-1) \times(n-2) \times \ldots . \times 2 \times 1[/tex]
Therefore,
[tex]\begin{aligned}12 C_{5} &=\frac{12 \times 11 \times 10 \times \ldots \ldots \times 2 \times 1}{5 \times 4 \times 3 \times 2 \times 1 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1} \\\\12 C_{5} &=\frac{12 \times 11 \times 10 \times 9 \times 8}{5 \times 4 \times 3 \times 2} \\\\12 C_{5} &=792\end{aligned}[/tex]
Similarly, 4 basketball players be selected 13 basketball players
n = 13 and r = 4
Similarly we get,
[tex]\begin{aligned}&13 C_{4}=\frac{13 !}{4 !(13-4) !}\\\\&13 C_{4}=\frac{13 !}{4 ! \times 9 !}\end{aligned}[/tex]
[tex]13C_4 = 715[/tex]
Thus total number of ways are:
[tex]12C_5 + 13C_4 = 792 + 715 = 1507[/tex]
Thus there are 1507 different ways
To determine the number of ways to select 5 baseball players from 12, and 4 basketball players from 13, we use the combination formula for both and multiply the results, applying the Counting Principle.
Explanation:The question asks how many different ways can 5 baseball players and 4 basketball players be selected from 12 baseball players and 13 basketball players. This is a problem of combinatorics, specifically the use of combinations, since the order of selection does not matter.
To find the number of ways to select the baseball players, we use the combination formula C(n, k) = n! / (k! * (n-k)!), where 'n' is the total number to choose from, 'k' is the number to choose, and '!' denotes factorial. For the 5 baseball players from 12, it is C(12, 5).
For the basketball players, it's C(13, 4), as we are choosing 4 out of 13. To find the total number of ways to form the group, we multiply these two values together, because each combination of baseball players can be paired with each combination of basketball players, which is an example of the Counting Principle.
So, the calculation is C(12, 5) * C(13, 4).
Two numbers are respectively twenty percent and ten percent more than the third number. How many percent is the first number more than the second ?
Answer:
10%
Step-by-step explanation:
Let the third number is X.
then first number = (100-30)% of X
= 70% of X = 7X/10
Second number is (63X/100)
Difference = 7X/10 - 63X/100 = 7X/10
So required percentage is, difference is what percent of first number
=> (7X/100 * 10/7X * 100 )% = 10%
A square plot of land has a side length of 50 meters.
It is surrounded by a footpath that is 3 meters wide.
What is the area of the footpath?
50 m
3 m
Your answer
Answer:
636
Step-by-step explanation:
the area of the footpath=
(50m+3m+3m)^2-50^2
Eva and her children went into a restaurant and where they sell hotdogs for $5 each and tacos for $2.50 each. Eva has $30 to spend and must buy at least 7 hotdogs and tacos altogether. If Eva decided to buy 2 hotdogs, determine the maximum number of tacos that she could buy.
Answer: 8 tacos
Step-by-step explanation: 2 hotdogs are $10 as they are $5 each. Tacos are $2.50 each. $2.50 x 8 equals $20. $20 + 10 = $30. Eva can buy 8 tacos.
After buying 2 hotdogs with $10, Eva will have $20 left. With the remaining $20, she can buy a maximum of 8 tacos at $2.50 each.
Explanation:Since Eva is determined to buy 2 hotdogs at $5 each, she will spend $10 on hotdogs. She has a total of $30 to spend, meaning she will have $20 left after purchasing the hotdogs. Tacos cost $2.50 each. Therefore, with the remaining $20, Eva can afford to buy a maximum of 8 tacos (since $20 divided by $2.50 equals 8). This will also meet the condition of purchasing at least 7 hotdogs and tacos in total.
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When Sabine set off to climb Mt. Marcy, she had 18 gummi bears in her bag.
When she returned to the lodge, she had 6 gummi bears left. How many
gummi bears did she eat during her hike?
Can someone please help me with this also
Answer:
Step-by-step explanation:
each is divided into 8 sections.
So1 1/2 =1 1*4/2*4 =1 4/8 . plot in the 4 th point after 1
2 3/4
3*2/4*2 = 6/8
2 3/4 = 2 6/8. so plot in the 6th point after 2
james says that 5 fithes is greater than 9 tenthes is he correct?
Answer:
yes
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
9 tenths is 90. 5 fifths is 25.
Tickets for a school carnival cost 10$ for adult and 5 for children. last Saturday carnival sold 170 tickets worth a total of $1200 . How many adults and childeren attended the carnival
70 adults and 100 children attended the carnival.
Step-by-step explanation:
Given,
Cost of each adult ticket = $10
Cost of each child ticket = $5
Total tickets sold = 170
Total revenue generated = $1200
Let,
Number of adults = x
Number of children = y
According to given statement;
x+y=170 Eqn 1
10x+5y=1200 Eqn 2
Multiplying Eqn 1 by 10
[tex]10(x+y=170)\\10x+10y=1700\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 2 from Eqn 3
[tex](10x+10y)-(10x+5y)=1700-1200\\10x+10y-10x-5y=500\\5y=500[/tex]
Dividing both sides by 5
[tex]\frac{5y}{5}=\frac{500}{5}\\y=100[/tex]
Putting y=100 in Eqn 1
[tex]x+100=170\\x=170-100\\x=70[/tex]
70 adults and 100 children attended the carnival.
Keywords: linear equation, elimination method
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the numerator of a fraction is 12 the gcf witch stand for great common factor of the numerator and denominator is 4. what is the denominator
Answer:
16.
Step-by-step explanation:
The denominator could be 16.
The GCF of 12 and 16 is 4.
Final answer:
The denominator of the fraction with a numerator of 12 and a GCF of 4 with the denominator is 12. You divide the numerator by the GCF and then multiply the result by the GCF to get the denominator.
Explanation:
The student is asking for the denominator of a fraction when the numerator is 12 and the greatest common factor (GCF) of the numerator and the denominator is 4. To find the denominator, you would divide the numerator (12) by the GCF (4). This gives us 12 ÷ 4, which equals 3. Therefore, the denominator of the fraction must be a number that when divided by the GCF (4) will give us a quotient of 3. Since the denominator is 4 times larger than this quotient, we multiply 3 by 4 to find the denominator. Therefore, the denominator is 3 × 4, which equals 12.
W+(-4)=37 solve for w
Answer:
W=41
Step-by-step explanation:
You have to isolate the W, so you have to carry the -4 to the other side. You do the opposite, so for a -4, you have to +4 to cancel it out. Whatever you do to one side, you have to do to the other and 37+4=41
Answer:
41
Step-by-step explanation:
Expressions 5* 10 product
Answer:
50
Step-by-step explanation:
Expression 5*10 is also known as 5 x 10 which is indeed 50.
Or if 5 is to the power of 10 (5^10) the answer would be 9765625
Hope this helped!
Find the equation for the circle with center (4,-5) and passing through (5,-4)
Answer:
(x -4)^2 +(y +5)^2 = 2
Step-by-step explanation:
The equation of a circle centered at (h, k) through point (p, q) is ...
(x -h)^2 +(y -k)^2 = (p -h)^2 +(q -k)^2
Filling in your given numbers gives ...
(x -4)^2 +(y +5)^2 = (5-4)^2 +(-4+5)^2
(x -4)^2 +(y -5)^2 = 2
The equation of the circle is (x - 4)² + (y + 5)² = 2.
The center of the circle is (4, -5). The circle passes through the point (5, -4).
The general formula for the equation of a circle is: (x - h)² + (y - k)² = r² where (h, k) is the center of the circle and r is the radius.
The radius is the distance between the center (4, -5) and the point (5, -4).
Use the distance formula: Distance = √ [(x2 - x1)² + (y2 - y1)²]
Distance = √ [(5 - 4)² + (-4 - (-5))²]
Distance = √ [(1)² + (1)²]
Distance = √ [1 + 1]
Distance = √ [2]
So, the radius r = √ [2].
Substitute the center (4, -5) and radius √ [2] into the circle equation: (x - 4)² + (y + 5)² = (√ [2])² (x - 4)² + (y + 5)² = 2