Given:
In △ABC is a right angle triangle.
AC is 6 units longer than side BC.
[tex]Hypotenuse=2\sqrt{17}[/tex]
To find:
The length of AC.
Solution:
Let the length of BC be x.
So, Length of AC = x+6
According to the Pythagoras theorem, in a right angle triangle
[tex]Hypotenuse^2=Base^2+Perpendicualar^2[/tex]
△ABC is a right angle triangle and AC is hypotenuse, so
[tex](2\sqrt{17})^2=(x)^2+(x+6)^2[/tex]
[tex]68=x^2+x^2+12x+36[/tex] [tex][\because (a+b)^2=a^2+2ab+b^2][/tex]
Subtract 68 from both sides.
[tex]0=2x^2+12x+36-68[/tex]
[tex]0=2x^2+12x-32[/tex]
[tex]0=2(x^2+6x-16)[/tex]
Divide both sides by 2.
[tex]x^2+6x-16=0[/tex]
Splitting the middle term, we get
[tex]x^2+8x-2x-16=0[/tex]
[tex]x(x+8)-2(x+8)=0[/tex]
[tex](x+8)(x-2)=0[/tex]
[tex]x=-8,2[/tex]
Side cannot be negative, so x=2 only.
Now,
[tex]AC=x+6[/tex]
[tex]AC=2+6[/tex]
[tex]AC=8[/tex]
Therefore, the length of AC is 8 units.
what is the correct standard form for 30+2+0.1+0.005
Answer:
32.105
Step-by-step explanation:
30
2
+ 0.1
0.005
32.105 so answer is 32.105
Forty-seven thousand people ride the city bus every day. On
average, about how many people ride the bus each hour?
Can someone Help me ASAP plss!!
In the figure shown, What is the value of x? a. 57° b. 123° c. 33° d. 147°
a plane takes off from an airport and travels at a steady speed of 350 miles per hour. which of these graphs best represents the distance the plane is from the airport, y, after traveling for x hours?
Answer:
what do the graphs look like, it would have a slope of 350
Step-by-step explanation:
16x^2+25 factor completely
Answer:
You can't factor further
Hope this helps!
Store A sells 3 candy bars for $3.45.
Store B charges $5.45 for 5 candy bars.
Store C sells 7 candy bars for $7.56.
Which store offers the best value?
Answer:
store C
Step-by-step explanation:
if you divide 7.56 by 7 it'll be $1.08 per candy bar.
Will mark as brainless if you answer correctly
Answer:
ans=10
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
10(4-7) / -(4 - 1)
10(-3) / -(3)
-30 / -3 =
10
18. Which product is greater. (-4)-(-6) or
(-7).(-8)? Explain.
Answer:
So when u do (-4)-(-6) it equals 2.
But when u do (-7)*(-8) it equals 56
Therefore saying that (-7)*(-8)=56 is the greatest product.
Step-by-step explanation:
-413.4=-15.9n please help
Answer:
[tex]\boxed {n = 26}[/tex]
Step-by-step explanation:
Solve for [tex]n[/tex]:
[tex]-413.4 = -15.9n[/tex]
-Switch sides:
[tex]-15.9n = -413.4[/tex]
-Divide both sides by [tex]15.9[/tex] and expand by multiplying both numerator and denominator by [tex]10[/tex]:
[tex]\frac{-15.9n}{-15.9} = \frac{-413.4}{-15.9}[/tex]
[tex]n = \frac{-4134}{-159}[/tex]
-Divide [tex]-4134[/tex] and [tex]-159[/tex]:
[tex]n = \frac{-4134}{-159}[/tex]
[tex]\boxed {n = 26}[/tex]
Therefore, the value of [tex]n[/tex] is [tex]26[/tex].
Find all whole numbers m such that m and 5m+1 are prime numbers.
Answer:
2 only
Step-by-step explanation:
Only even PRIME number is 2.
Why do we need EVEN PRIME numbers?
Say we do 11*5 we get 55 but when we add one we get 56
Meaning: An odd number multiplied by an odd number plus an odd number equals EVEN number which isn't PRIME. 2 being the ONLY even prime is therefore the only number we can choose.
What is 20 divided by 740 with remainder
Answer:
37 R0
Step-by-step explanation:
740/20=37, so there is no remainder.
I hope this helps you! Have a great day c:
Dividing 20 by 740 gives us remainder 20 and quotient 0.
To find the result of 20 divided by 740 with a remainder,
Perform the division and take note of the quotient and remainder.
20 ÷ 740 = 0 with a remainder of 20.
Division is a mathematical operation that involves splitting a number (the dividend) into equal parts,
with a divisor indicating how many parts we want to split it into.
The quotient is the number of equal parts, and the remainder is what's left after have split the dividend into as many equal parts as possible.
20 divided by 740, we are trying to find out how many times 740 can fit into 20.
Since 740 is much larger than 20, it cannot fit even once.
So, the quotient is 0, indicating that 0 whole units of 740 can fit into 20.
However, there is a remainder of 20.
The remainder represents the portion of 20 that cannot be evenly divided by 740.
It is what remains after we have divided the dividend by the divisor as many times as possible.
Therefore, 20 divided by 740 is 0 with a remainder of 20.
learn more about remainder here
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PLZZZZZZZZZZZZZZZZZZZZZZ HELP!
-3x+4=-2 show your work!!!
Answer:
x=2
Step-by-step explanation:
rationalise the denominator 1/√20
Answer:
1/10
Step-by-step explanation:
uf no me dij hi g go be h in go i
Step-by-step explanation:
Given:1/√20
The denominator = 20
We know that
The rationalising factor of √a is √a. To rationalise the denominator of 1/√20, we multiply this by √20/√20.
1/√20
→ (1/√20) * (√20/√20)
→ [1(√20)]/[(√20)(√20)]
→ (√20)/√(20×20)
→ √20/20 Ans.
David has available 40 yards of fencing and wishes to enclose a rectangular area.
Answer:
5 units will be your width and 15 will be your length so it would look like side#1=5 side #2=15 side number3 is 5 and side number 4 is 15 assuming that side 1 and 3 are parallel.
Step-by-step explanation:
yes
You have 1 pounds of egg whites
You need 8 oz to make one serving of meringue
How many servings can you make?
Answer:
2 servings
Step-by-step explanation:
1 pound is 16 ounces
3z2 - 2z + 8
-
(10z2 +7z - 12)
Answer: 7z²-9z+20
Step-by-step explanation:
PEMDAS - Please Excuse My Dear Aunt Sally - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
An item that cost $220 has been marked up by 15% since last year. However, a person can buy the item for a 25%
employee discount. How much will the employee pay?
Answer:189.75
Step-by-step explanation: 220 * 0.15 = 33
220 + 33 = 253
253 * 0.25 = 63.25
253 - 63.25 = 189.75
i need help pls i cant understand my math hw
Answer:
Ok
Step-by-step explanation:
So what are we magically supposed to know what the equation is
Answer:
uh
Step-by-step explanation:
for us to help please write the question you are stuck on
as for $65 each and included a 60% mark
+
Answer:
revenue: $104 profit: $39
Step-by-step explanation:
when a pendulum swings, at which point is potential energy highest?
At Mr. McNeely's farm, there were 75 sheep and 60 cows. What is the ratio of the number of cows to the number of sheep at Mr. McNeely's farm?
Answer:
4:5
Step-by-step explanation:
The ratio will be 60 : 75
When simplified becomes 4:5
An electric company charges each of its customers a monthly fee of $19 to maintain the account and nine cents per kilowatt hour what is an equation that relates the monthly cost c in dollars of power consumed P in kilowatt hours 
Answer:
c = 19 + 0.09P
Step-by-step explanation:
The total cost is the $19 monthly fee plus the amount per hour.
c = 19 + 0.09P
Simplify.
7√10+2√10-√10
7√10+2√10-√10
Every square root has the same radicand, which is 10. So, simply combine terms.
7 + 2 - 1 = 9 - 1 = 8
Answer: 8√10
A car covered a certain distance at a speed of 24 mph. While returning, the car covered the same distance at a speed of 16 mph. What was the average speed of the car for the entire journey? \
Answer:
19.2 mph
Step-by-step explanation:
just trust me
Use these methods to normalize the following group of data:
200, 300, 400, 600, 1000
a) min-max normalization by setting min = 0 and max = 1
b) z-score normalization
c) normalization by decimal scaling
Step-by-step explanation:
b is the answer , z-score normalization
Normalization is applied to data values in other to ensure that the data scales well, such that data values conforms to a certain range. The output of the various normalization techniques are given below ;
Given the data:
200, 300, 400, 600, 10001.)
Min - Max normalization :
[tex]\frac{value - min}{max - min} [/tex] Min = minimum = 200Max = maximum = 1000Value = 200 :
[tex]\frac{200 - 200}{1000 - 200} = 0[/tex]
Value = 300 :
[tex]\frac{300 - 200}{1000 - 200} = 0.125[/tex]
Value = 400 :
[tex]\frac{400 - 200}{1000 - 200} = 0.25[/tex]
Value = 600 :
[tex]\frac{600 - 200}{1000 - 200} = 0.5[/tex]
Value = 1000 :
[tex]\frac{1000 - 200}{1000 - 200} = 1[/tex]
Normalized values = (0, 0.125, 0.25, 0.5, 1)
2.)
Zscore normalization :
[tex]\frac{value - μ}{σ} [/tex]Using a calculator :
Mean, μ = 500Standard deviation = 316.227Value = 200 :
[tex]\frac{200 - 500}{316.227} = -0.949[/tex]
Value = 300 :
[tex]\frac{300 - 500}{316.227} = -0.632[/tex]
Value = 400 :
[tex]\frac{400 - 500}{316.227} = -0.316[/tex]
Value = 600 :
[tex]\frac{600 - 500}{316.227} = 0.316[/tex]
Value = 1000 :
[tex]\frac{1000 - 500}{316.227} = 1.581[/tex]
Normalized values = (-0.949, -0.632, -0.316, 0.316, 1.581)
3.)
Decimal Scaling :
Maximum value = 1000Hence, we can divide our values by 10000200 / 10000 = 0.02
300/1000 = 0.03
400/1000 = 0.04
600/1000 = 0.06
1000/1000 = 0.1
Hence, the Normalized values (0.02, 0.03, 0.04, 0.06, 0.1)
Learn more : https://brainly.com/question/19132215
A builder is designing a rectangular patio that has a length of 12 units. Find the total number of square units the patio will cover if the width is 4
Answer:
48 square units
Step-by-step explanation:
Use the area formula, A = lw, where l is the length and w is the width
Plug in the length and width:
A = lw
A = (12)(4)
A = 48
So, the patio will cover 48 units²
determine the slope of the line that passes through each pair of points (3,8) and (1,5)
Answer:
3/2
Step-by-step explanation:
Simplify the fraction 36/8
Answer:
4 4/8
Step-by-step explanation:
36 can go into 8, 4 times. With 4 left over so the answer is 4 4/8.
Answer:
[tex]4\frac{1}{2}[/tex]
Step-by-step explanation:
The ratio of boys to girls is 1:1.
If there are 250 boys, how many
girls are there?