Answers
Answer:
a= 22.5
b= 37.5
Step-by-step explanation:
In △BCD:
Applying Pythagoras' Theorem,
a² +30²= b²
a² +900= b² -----(1)
In △ABC:
Applying Pythagoras' Theorem,
b² +50²= (40 +a)² -----(2)
Substitute (1) into (2):
a² +900 +50²= 40² +2(40)(a) +a² (expand bracket)
a² +900 +2500= 1600 +80a +a²
a² +3400= a² +80a +1600 (simplify)
a² +3400 -a² -80a -1600= 0 (bring everything to 1 side)
-80a +1800= 0
80a= 1800 (+80 on both sides)
a= 1800 ÷80
a= 22.5
Subst. a= 22.5 into (1):
22.5² +900= b²
b²= 506.25 +900
b²= 1406.25
b= √1406.25 (square root both sides)
b= 37.5 (reject negative value since b is a length)
☆(a +b)²= a² +2ab +b²
Related Questions
hey guys I need this. it's due tomorrow. and please show step by step because I am willing to give brainly
Answers
what is
2 1
_ + _ =
5 4
Answers
Answer:
3 1
– = ——
9 3
Step-by-step explanation:
I simplified it as well.
To rent a certain meeting room, a college charges a reservation fee of $34 and an additional fee of $9.30 per hour. The math club wants to spend less than $99.10 on renting the meeting room.
What are the possible amounts of time for which they could rent the meeting room?
Use t for the number of hours the meeting room is rented, and solve your inequality for t.
Answers
Answer:
9 hours.
Step-by-step explanation:
31 + 5.9*t < 84.10.
To solve it, collect the constant terms on the right side:
5.9*t < 84.10 - 31 = 53.10,
Hence, t < 53.10%2F5.9 = 9 hours.
Answer:
7 hours
Step-by-step explanation:
99.10-34=65.1
65.1 divide by 9.30=7
Hope this helps!!
Half the area of the rectangle shown is 24 inches. Write and solve an equation to find the value of 'x'
Answers
Answer:
The answer will b 4
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
A number cube is rolled 360 times and the results are recorded as follows: 52 ones, 59 twos, 67 threes, 73 fours, 42 fives, and 67 sixes. What is the experimental probability of rolling a two or a three?
Answers
Answer:
0.35
Step-by-step explanation:
Total rolled = 360 times
Two rolled = 59
Three rolled = 67
Two rolled probability = 59/360 = 0.164
Three rolled probability = 67/360 = 0.186
The experimental probability of rolling a two or a three
==> Two rolled probability + Three rolled probability
==> 0.164 + 0.186
==> 0.35
Does (3,4) satisfy the equation-5x + 2y = 23?
Answers
Answer:
[tex] - 5x + 2y = 23 \\ when \: \: x = 3 \: and \: y = 4 \\ = - 5(3) + 2(4) \\ = - 15 + 8 \\ = 7 \\ no \: it \: doesnot \\ \\ \\ if \: equation \: is \: 5x + 2y = 23 \\ = 15 + 8 \\ = 23 \\ hence \: it \: satisfies[/tex]
6. A bicycle store costs $2200 per month to operate. The store pays an average of $60
per bike. The average selling price of each bicycle is $80. How many bicycles must the
store sell each month to break even?
Answers
Simplify: 3x + 4y + 7x - 2y
Answers
Answer:
10x+2y
Step-by-step explanation:
combine like terms
Answer:
Step-by-step explanation:
3x + 4y + 7x - 2y=3x + 7x +4y - 2y
10x + 2y
Simplify 4 1/3 times 4 1/5
Answers
Answer:
Exact Form:
91 / 5
Decimal Form:
18.2
Mixed Number Form:
18 1/5
What is the solution to this function ?
Answers
Answer:
I think this is the answer
Raphael purchases a new DVD at M-Mart. He
pays 8% in tax on the cost of the DVD. If the tax
amount is $1.20, how much does Raphael
spend on the DVD, including tax?
Answers
Answer:
The amount Raphael spend on DVD including tax is $16.2
Step-by-step explanation:
Tax on DVD = 8%
Amount of tax = $1.20
We need to find the amount Raphael spend on DVD including tax.
Let the cost of DVD = x
We can write the equation: [tex]8\%\:of\:x=1.20[/tex]
Because the tax amount is 8% of actual cost and is equal to 1.20
Now solving to find x:
[tex]8\%\:of\:x=1.20\\8\%\times\:x=1.20\\\frac{8}{100}\times x=1.20 \\x=1.20 \times \frac{100}{8}\\x= 15[/tex]
So, the cost of DVD = $15
Now, The amount Raphael spend on DVD including tax = Cost of DVD + Tax
The amount Raphael spend on DVD including tax = 15 + 1.2
= 16.2
So, The amount Raphael spend on DVD including tax is $16.2
jenny has 68 1/2 pages of her left to read. How many pages will she have left after she reads 26 1/6 pages?
Answers
Answer:
42 1/3
Step-by-step explanation:
We subtract 26 1/6 from 68 1/2. We do this by finding the LCM of 6 and 2. That is 6. We multiply 1/2 by 3/3 to get 3/6. Now, we subtract. 68 - 26 is 42, and 3/6 - 1/6 is 2/6. Our answer is 42 2/6. That can be simplified to 42 1/3.
Jenny will have 42 whole 1/2 pages left after she reads 26 whole 1/6 pages if Jenny has a total of 68 whole 1/2 pages.
What is a fraction?Fraction number consists of two parts one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have:
Jenny has [tex]68\frac{1}{2}[/tex] pages.
She reads [tex]26\frac{1}{6}[/tex]
Let's suppose the remaining pages is x, then the value of x:
[tex]\rm x = 68\frac{1}{2}-26\frac{1}{6}\\\\\rm x = \frac{137}{2}-\frac{157}{6} \\\\\rm x = \frac{411-157}{6} \\\\\rm x = \frac{254}{6}[/tex]
[tex]\rm x = \frac{127}{3}[/tex] or
[tex]\rm x = 42\frac{1}{3}[/tex]
Thus, Jenny will have 42 whole 1/2 pages left after she reads 26 whole 1/6 pages if Jenny has a total of 68 whole 1/2 pages.
Learn more about the fraction here:
brainly.com/question/1301963
#SPJ2
What do I have to multiply 5/6 by to get an equivalent fraction
Answers
Answer:
you multiply 5/6 5 times to git 4
Step-by-step explanation:
4.
One-third of Olivia's age, increased by 12, is equal to twice her age, decreased by 3. How old is Olivia?
Answers
Answer:
19?
Step-by-step explanation:
maybe i got it right
Find the slope of line that passes through the points ( 0,5) and ( 2,2)
Answers
Answer:
m= -3/2
Step-by-step explanation:
2 + (-10) =
HELP ME PLEASE T^T
Answers
Answer:
The answer would be 8
Step-by-step explanation:
This equals 10-2=8
Answer:
-8
Step-by-step explanation:
If you subtract 10 from 2 you get 8 and since the negative number is greater than the positive number it would be -8
I need help with A and B
Answers
Answer:
a cube and a square-faced pyramid
Number 2 please , and if you can explain it too that would be helpful but if not it’s okay:)
Answers
Answer:
CI = 6,IA = 8
Step-by-step explanation:
I cant explain it no further
I’m not sure if you’re learning this, but there is this thing called SOHCAHTOA. The SOH stands for Sine = Opposite/Hypotenuse, CAH stands for Cosine = Adjacent/Hypotenuse, and TOA stands for Tangent = Opposite/Adjacent. Now you figure out which one of these three to use based on the values you’re given and where they are on the triangle. So we’ve been given 45 degrees for one of the angles and we want to find the lenght that is Opposite of that angle, and we’re given the side length of the hypotenuse, so you would use Sine = Opposite/Hypotenuse. How you would set that up is sin 45° = x/10rad2. You first find the value of sin 45°, which would give you about .71, so you’re equation would now be .71 = x/10rad2. You then cross multiply to find the value of X, which would give you about 10. And since this is a 45 45 90 triangle, both the legs are the same length. Hope that helps and please give brainliest if it did! :)
Twelve minutes after he starts downloading a file, Mario looks at his computer and sees this image. About how long will it take to download the entire file?
Answers
f + 12 = i
For triangles Y Z X and C D B, sides Y Z, Z X, C D, and B D are 2.5 centimeters. Sides B C and Y X are 3.8 centimeters. Angles B, C, Y, X are 36 degrees. Angles Z and D are 108 degrees.
Which of the following congruency statements is correct?
ΔYZX ≅ ΔBCD
ΔYZX ≅ ΔDCB
ΔZXY ≅ ΔDCB
ΔYXZ ≅ ΔCDB
Answers
Answer:
the answer is C
Step-by-step explanation:
edge 2021
Answer:
ΔZXY ≅ ΔDCB
Step-by-step explanation:
please someone help me
Answers
Answer:
-16
Step-by-step explanation:
-8(x+2)=24 x= -5
-8x + (-16) = 24 x= -5
-8*x = -8x
-8*2= -16
ABCD is a parallelogram with coordinates A(4, 2), B(3, −1), C(−1, −1), and D(−1, 2). To prove that ABCD is a parallelogram, you would find which of the following?
A measures of the angles
B slopes of the diagonals
C lengths of the diagonals
D slopes of the sides
Answers
The answer is A im pretty sure
If f(n)= n2. n, then f(-4) is?
Answers
Answer:
f(-4) = 16
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
f(n) = n²
f(-4) is n = -4
Step 2: Evaluate
Substitute: f(-4) = (-4)²Exponents: f(-4) = 16Plzzz someone help meeee!!!! :(
Answers
Answer:
5 feet
Step-by-step explanation:
The rose garden is trianglar and so the total of the two shorter sides need to equal more than the longest side. In this case 4+x=9. 6,7, and 8 all meet these requirments but 4+5 is 9, 9=9 which means 5 feet cannot be used
Gwen borrows $300 from her parents to buy a bike. She agrees to pay them back with 3% simple interest every month for one year. What is the total amount of money Gwen will owe her parents? *
Just enter the numerical portion of your answer - no dollar signs or change needed!
Answers
Answer:
309.12
Step-by-step explanation:
A = total amount
P = principal
r = interest rate
n = number of times interest is compounded
t = time (in years
A = P(1 + [tex]\frac{r}{n}[/tex])^nt
A = 300(1 + [tex]\frac{.03}{12}[/tex])^12 · 1
A = 300(1.0304)
A = 309.12
Answer:
408
Step-by-step explanation:
Solve the inequality and enter your solution as an inequality comparing a variable to a number x+9>13
Answers
Answer:
x>4
Step-by-step explanation:
Step 1: Subtract 9 from both sides.
x+9−9>13−9
x>4
Standard Form: 3x+4y=−16
Answers
Answer:
i know the answer
Step-by-step explanation:
my classmate is unsure about how to use side lengths to determine the type of triangle. How would i explain this to my classmate
Answers
equilateral triangles are made of all even sides with a angle of 60 degrees
isosceles triangle has two of the same sides and ond different side
scalene triangles have all different sides
brainiest please
please help. i will mark brainliest for whoever is correct.
Answers
Answer:d) g(x)=x^1/3-1.5
Step-by-step explanation:
PLEASE HELP, THIS IS A BENCHMARK. WILL GIVE BRAINLIEST!
Use the description of AABC below to solve Parts A and B.
m
Part A: Which of the following is the value of x?
A. x = 10
B. x= 5
B. x = 4
D. x = 2
Part B: Order the sides of ABC from shortest to longest. Drag and drop the displayed choices to order.