Since this is a right triangle, we know we have to use the Pythagorean Theorem: A² + B² = C² , where A and B = the legs of the triangle (which are shorter than the hypotenuse) and C = the hypotenuse.
In this isosceles triangle, A = B (because the legs are the same size) and C is 10cm longer than A and B.
Thus we get the following,
A = x
B = x
C = x + 10
We simply plug in these variables into the equation and solve for x:
x² + x² = (x+10)²
2x² = x² + 20x + 100
x² - 20x - 100 = 0
We solve for x by completing the square:
(x² - 20x + 100) - 100 = 100
(x-10)² -100 = 100
(x-10)² = 200
x - 10 = √(200)
x - 10 = 10 √2
x = 10 + 10√2 = 24
Finally,
A ≈ 24 (or 10 + 10√2)
B ≈ 24 (or 10 + 10√2)
C ≈ 24 + 10 ≈ 34 (or 10 + 10√2 + 10 = 20 + 10√2)
Rewrite as equivalent rational expressions with denominator (c- 9) (c+9)(c + 6):
Answer:
Step-by-step explanation:
as (c + 9)(c - 9) = c² - 81
and (c - 9)(c + 6) = c² - 3c - 54
8(c + 6) = 8c + 48
(c² - 81)(c + 6) (c - 9)(c + 9)(c + 6)
10c(c + 9) = 10c² + 90c
(c² - 3c - 54)(c + 9) (c - 9)(c + 9)(c + 6)
The equivalent rational expressions with denominator (c- 9) (c+9)(c + 6) are;
1. 8 / (c² - 81) = 8 / (c + 9) (c - 9)
2. 10c / (c² - 3c - 54) = 10c / (c + 6) (c - 9)
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expressions are,
1. 8 / (c² - 81)
2. 10c / (c² - 3c - 54)
Now,
Solve the expressions for the denominator (c- 9) (c+9)(c + 6) as;
1. 8 / (c² - 81) = 8 / (c² - 9²)
= 8 / (c + 9) (c - 9)
Thus, 8 / (c² - 81) = 8 / (c + 9) (c - 9)
2. 10c / (c² - 3c - 54) = 10c / (c² - (9- 6)c - 54)
= 10c / (c² - 9c + 6c - 54)
= 10c / [c(c-9) + 6(c - 9)]
= 10c / (c + 6) (c - 9)
Thus, 10c / (c² - 3c - 54) = 10c / (c + 6) (c - 9)
Therefore, The equivalent rational expressions with denominator (c- 9) (c+9)(c + 6) are;
1. 8 / (c² - 81) = 8 / (c + 9) (c - 9)
2. 10c / (c² - 3c - 54) = 10c / (c + 6) (c - 9)
Learn more about the mathematical expression visit:
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-5/8 - (-4/3)
Pls help
Answer:
Step 1 of 2: Subtract.
Subtract
(
negative 5 over 8
−
5
8
) − (
negative 4 over 3
−
4
3
) =
17 over 24
17
24
Step 1 of 2: Subtract, sub-step a: Subtract a negative.
Subtract a negative
negative 5 over 8
−
5
8
− (
negative 4 over 3
−
4
3
) =
negative 5 over 8
−
5
8
+
4 over 3
4
3
Subtracting a negative is the same as adding a positive.
Step 1 of 2: Subtract, sub-step b: Find common denominator.
Find common denominator
negative 5 over 8
−
5
8
+
4 over 3
4
3
= −
( 5 × 3 ) over ( 8 × 3 )
5 × 3
8 × 3
+
( 4 × 8 ) over ( 3 × 8 )
4 × 8
3 × 8
=
negative 15 over 24
−
15
24
+
32 over 24
32
24
24 is the least common multiple of denominators 8 and 3. Use it to convert to equivalent fractions with this common denominator.
Step 1 of 2: Subtract, sub-step c: Add.
Add
negative 15 over 24
−
15
24
+
32 over 24
32
24
=
(
negative 15
−15 + 32 ) over 24
negative 15
−15 + 32
24
=
17 over 24
17
24
Answer:
The answer would be 17/24
Step-by-step explanation:
1. Common denominator is going to be 24. 3(-5/8) - 8(-4/3)
2. Next multiply. -15/24 + 32/24
3. After addition you get 17/24 or 0.7
what are the relationships between inscribed, central, and circumscribed angles of a circle?
Answer:
Topics include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. Common Core: HSG-C.A.2
Step-by-step explanation:
PA BRAINLIEST
Consider the figures below. Which of the following statements are true, given <S is congruent to <J and <N is congruent to <E? Select all that apply.
<A is congruent to <O
Triangle SAN~TriangleJOE
Triangle SAN is congruent to Triangle JOE
SN is congruent to JE
The perimeter of Triangle JOE is half the perimeter of Triangle SAN
There exists a sequence of rigid motion that maps Triangle JOE onto Triangle SAN
There exists a sequence of rigid and non-rigid motions that maps Triangle SAN onto Triangle JOE
Answer:
<A is congruent to <O
Triangle SAN~TriangleJoe
There exists a sequence of rigid motion that maps Triangle JOE onto Triangle SAN
Step-by-step explanation:
So sorry if i am wrong!! I hope this can help!
Answer:
A
B
G
Angle A is congruent to angle O
Triangle SAN ~ Triangle JOE
There exists a sequence of rigid and non-rigid motions that maps triangle SAN onto triangle JOE
Step-by-step explanation:
Just got the question wrong, this was the correct answer
please answer fully///////////////
Answer:
14
Step-by-step explanation:
(4+(16-1)/5)*2
(4+15/5)*2
(4+3)*2
7*2
14
pleaseeeeeeeeeeeeeeeeeeee help
Answer:
x|x∈R(all real numbers)
y|y∈R(all real number)
Yes its is
Hope This Helps!!!
what has a fraction in numerator, denominator or both???
4. Sale of Mathematics and English books in the year 2005, 2006, 2007 and 2008 are given below : Years Mathematics English 2005 200 100 2006 300 250 2007 400 200 2008 500 500 Question 1. In which year is the difference in the sale minimum? (a) 2008 (b) 2007 (c) 2006 (d) 2005 Question 2.
Step-by-step explanation:
2008because there is no difference between the number of sold notebooks
a lamp post cast a Shadow 15 feet long while a 6 foot man standing nearby cast a shadow 5 ft long. what proportion can be used to determine the hight of the lamp post
Answer:
6/5=x/15
Step-by-step explanation:
6/5=x/15,where x is hight of the lamp post
x=18
Find the missing measurements
Answer:
O = 16.7 degrees
A = 73.3 degrees
Step-by-step explanation:
used a triangle calculator
Please take a look at the picture
Answer:
A) -3/-11
Step-by-step explanation:
-3/-11-3/11
-3/-11
Reduce the fraction with -1.
3/11
Hope this help :)
Relatively Simple Math, pls lend a hand. 50 points and Brainliest
Answer:
B. 192 miles in 3 hoursStep-by-step explanation:
Mr. Anderson's rate is:
480 / 7.5 = 64 mphGiven options, find rates and compare with the above number:
A. 120/2 = 60 mph, NoB. 192/3 = 64 mph, YesC. 100/1.5 = 66.66 mph, NoD. 240/3.25 = 73.85 mph, Noplease answer fully/////////////
Answer:
Step-by-step explanation:
Tear this apart piece by piece
15 - 8 = 7
7 * 3 = 21
11 + 21 = 32
Now so far this much is correct. The problem is the next sign. Is it add or is it divide. The only way to resolve it is to do it both ways.
Add 4
32 + 4 = 36
Divide 4
32 / 4 = 8 1/4 = 8
Answer:
8Step-by-step explanation:
Use PEMDAS:
P Parentheses first
E Exponents (ie Powers and Square Roots, etc.)
MD Multiplication and Division (left-to-right)
AS Addition and Subtraction (left-to-right)
[tex]\ [11+(15-8)\cdot3]:4=(11+7\cdot3):4=(11+21):4=32:4=8[/tex]
Help my first time learning this it’s an easy problem
Answer:
I don't know but I I would just say C maybe?
Answer:
I say do B
Step-by-step explanation:
B and C look approximately the same but B look smaller
If I’m wrong I’m srry :<
Find the equation of a line that passes through the point (2,5) and has a gradient of 2. Leave your answer in the form y = m x + c
Answer:
y=2x+1
Step-by-step explanation:
y-5/x-2=2
2x-4=y-5
y=2x+1
Grace and Jackie are both accountants. They each charge their customers an hourly fee for their service, as described below. Grace charges $540 for 18 hours of service. Jackie charges $40 per hour. Who charges more per hour?
Answer:
Jackie
Step-by-step explanation:
Since Grace charges 30 an hour (540 divided by 18 is 30) and Jackie charges 40 and hour, so Jackie would charge more.
Tara's pool is 50 yards in length and 20 feet in width. How many square feet is the pool? How many square yards in the pool? Show your work.
Plz help I need help
x + 23 = -22
x = ?
x = -22 - 23
x = - ( 22 + 23 )
x = -45
x = -45 ✔️
Answer:
x - 23 = -22
x= -45
Step-by-step explanation:
x - 23 = -22
x = -22 - 23
x = -(22+23)
x = -45
Which of the following is the graph of f(x) = |x|?
Graph 1
Graph 2
Graph 3
Graph 4
Answer:
i think its the second graph
Step-by-step explanation:
2.
Use the quadratic model y = -4x^2 + 8x + 8 to predict y if x equals 100.
A. 39,208
B. –40,792
C. –39,192
D. 40,808
Answer: I can't find the answer :(
Step-by-step explanation: :(
Answer:
-4*100^2 + 8 *100 + 8
-4 * 100^2 + 800 + 8
-4 * 10000 + 808
-40000 + 808
= -39192
-39192 is the answer
Step-by-step explanation:
Someone pls help me with these worksheets >.<
(Please answer properly, if u don't know, just ignore so someone who knows can answer)
Answer:
gsdddddddddddddddddddddddddddd
Step-by-step explanation:
Which is the better deal? $39.55 for 7 pairs of jeans OR $22.48 for 4 pairs of jeans
Answer:
I will say %39.56 for 7 pairs because you'll have 7 pair of jeans so you don't have to buy more if some of your jeans rips or something happens so yeah.
Answer:
$39.55 for 7 pairs of jeans
Step-by-step explanation:
The LCM of 7 and 4 is 28, so I decided to use that as an example.
4×7=28
22.48×8=179.84
So if you wanted 28 jeans, you'd be paying $179.84
- - - - -
Now the first deal.
7×4=28
39.55×4=158.2
For 28 jeans, you'd be paying $158.20
For 28 jeans, the first choice offers a better deal than the other.
Mind you, I know the word problem isnt about 28 jeans. But since 28 was the LCM of 4 and 7, I decided to use it as an example
An airline finds that if it prices a cross-country ticket at $300, it will sell 400 tickets per day. It estimates that each $10 price reduction will result in 50 more tickets sold per day. Find the ticket price (and the number of tickets sold) that will maximize the airline's revenue.
Answer:
price = $190
quantity = 950 tickets
Step-by-step explanation:
revenue = price * quantity
n = number of $10 price reductions
price = 300 - 10n
quantity = 400 + 50n
r = (300 - 10n)(400 + 50n)
recognize these as the factors of a quadratic that opens down
the vertex will therefor be the maximum revenue
the roots are:
300 - 10n = 0
300 = 10n
n = 30
400 + 50n = 0
50n = -400
n = -8
vertex is at mid point of the roots
n = (-8 + 30)/2
n = 11
price = 300 - 10n
price = 300 - 10(11)
price = 190
quantity = 400 + 50n
quantity = 400 + 50(11)
quantity = 950
Which expression is equivalent to 4 (5X + 3y)
Answer:
20x + 12y
Step-by-step explanation:
=> 4(5x + 3y)
=> 20x + 12y
Since we can't simplify this further, 20x + 12y is out answer.
Hoped this helped.
According to this diagram, what is sin 23°?
67°
13
5
Сл
23°
90°
12
O A.
13
5
12
O B.
B. 13
12
13
O c.
c.13
O D.
D.
5
13
O E.
13
12
5
OF.
Using relations in a right triangle, it is found that the sine of 23 degrees is given by:
D. 5/13.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.Looking at the graph, the side opposite to the angle of 23º is of 5, while the hypotenuse is of 13, hence the sine is given by:
sin(23º) = 5/13.
Which means that option D is correct.
More can be learned about relations in a right triangle at https://brainly.com/question/26396675
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Complete the equation of the line whose y-intercept is (0,-1) and slope of 4
y=(answer)
x2 +
x + 36
Help me lol
Answer:
x²+12x+36 =0
Step-by-step explanation:
Hii, so I'm assuming your equation is equal to 0-->
x²+_x+36 =0
this could go many ways..
x²+12x+36 =0
which factor to (x+6)(x+6)
x²+15x+36 =0
which factor to (x+12)(x+3)
x²+13x+36 =0
which factor to (x+9)(x+4)
If I had to choose a answer.. I would go with the 1st option x²+12x+36 =0
Hope this helps, if there was more to this question, leave a comment and I can come back and help you ;)
Answer:
Step-by-step explanation:
What is 55% of 20?!?!?!
Answer:
11
Step-by-step explanation:
Since, finding the fraction of a number is same as multiplying the fraction with the number, we have
use the method:
is/of and %/100
plug in 55 for the percent, and 20 for 'of'
should be: x/20 and 55/100
cross multiply to get 11.
1%of 20 is 0.2 0.2x5=1 5% of 20 is 1
10% of 20 is 2 2x5=10 50% of 20 is 10
1+10=11
That is just how i do it to make it easier for others, and sometimes for me.
The cost of a trailer decreases in value by 25% What is the cost of the trailer if it was initially bought for $125 b $250 C. $375 d. $750 e x dollars
Answer:
the answer isn't there, but the answer is $93.75
Step-by-step explanation:
help me out guys I don't get this ?!
Answer:
B: (-2,-3)
Step-by-step explanation:
The problem basically wants you to find the vertex because that is the turning point of an absolute value graph where the slope goes from negative to positive immediately. B is the best choice because the vertex is translated 2 to the left and 3 down.