Question
If a 45°-45°-90° triangle has a hypotenuse length of 72, what is the length of each leg of the triangle?
Select the correct answer.
O 7V2
O 7
O V2
O 2
Answers
Answer: B
Step-by-step explanation:
We are given that a 45-45-90 triangle has a hypotenuse of [tex]7\sqrt{2}[/tex].
In a 45-45-90 triangle, the legs are congruent. Therefore we can use the Pythagorean Theorem to solve.
[tex]a^2+a^2=(7\sqrt{2})^{2}[/tex] [combine like terms]
[tex]2a^2=(7\sqrt{2})^2[/tex] [square root both sides]
[tex]a\sqrt{2} =7\sqrt{2}[/tex] [divide both sides by root 2]
[tex]a=7[/tex]
Now, we know that a leg is length 7, which is B.
Related Questions
A researcher asked 36 tourists which Caribbean island was their favourite The results showed that 9 tourists said Tobago. The researcher wants to draw a pie chart to show this information What should the angle for the Tobago segment measure?
A. 9 degree
B. 14 degree
C.25 degree
D. 90 degree
Answers
Explanation= the fraction would be 9/36 people think Tobago if that fraction were to made out of 360 degrees like in a circle it would be 90:360
.
Tom wants to borrow $16,578 for a car. The bank is going to charge him 12% interest annually, compounded monthly. If his car payment is $345.00 a month. How much will he owe at the end of 4 months? (Take this one month at a time. Determine the interest for the month; add it to the principal. Then subtract the payment, and that is your new principal for the next month.)
Answers
Answer:
Step-by-step explanation:
Principal, P = $16,578
Interest rate, r = 12% = 0.12
Monthly interest rate = annual interest rate / 12
= 12%/12
= 1%
= 0.01
Time, t = 1 year
Number of period, n = 12
Car payment per month = $345.00
Month 1:
A = P(1 + r/n)^nt
A = 16,578(1 + 0.01/12)^(12)(1)
A = 16,578(1 + 0.000833333)^(12)
= 16578(1.000833333)^12
= 16578(1.0100459608871)
A = $16,744.54
Principal after month 1 repayment = $16,744.54 - $345
= $16,399.54
Month 2:
A = P(1 + r/n)^nt
= $16,399.54(1 + 0.01/12)^(12)(1)
= 16,399.54(1 + 0.000833333)^(12)
= 16,399.54(1.000833333)^12
= 16399.54(1.0100459608871)
= 16,564.289137406431934
= $16,564.29
Principal after month 2 repayment = $16,564.29 - $345
= $16,219.29
Month 3:
A = P(1 + r/n)^nt
= $16,219.29(1 + 0.01/12)^(12)(1)
= 16,219.29(1 + 0.000833333)^(12)
= 16,219.29(1.000833333)^12
= 16219.29(1.0100459608871)
= 16382.228352956532159
= $16,382.23
Principal after month 3 repayment = $16,382.23 - $345
= $16,037.23
Month 4:
A = P(1 + r/n)^nt
= $16,037.23(1 + 0.01/12)^(12)(1)
= 16,037.23(1 + 0.000833333)^(12)
= 16,037.23(1.000833333)^12
= 16037.23(1.0100459608871)
= 16198.339385317426733
= $16,198.34
Principal after month 4 repayment = $16,198.34 - $345
= $15,853.34
Bella has joined a new gym in town. The cost of membership is $25 per month. The after-hours policy at the gym allows her to work out late at night for an extra fee of $4 per visit. If Bella's first monthly bill totaled $53, which equation can be used to determine how many times Bella worked out after hours?
Answers
Answer:
So, we get
$25+4n = $53 is the required equation.
Therefore, $25+4n = $53 equation can be used to determine how many times Bella worked out after hours.
Step-by-step explanation:
The total monthly bill of the gym = $53
The cost of membership of a month = $25
Let 'n' be extra the number of hours Bella worked on.
The cost for working on extra hours = $4
So, we have to determine the equation, Bella worked out after hours.
We will determine the equation by:
(Monthly cost of membership) + ( cost for extra hours number of hours extra worked on ) = Total monthly bill received
Find z, the total impedance, of each circuit. Express your answer in standard form
Answers
Answer:
a. 7 Ω
b. 5 Ω
c. 4.472 Ω
Step-by-step explanation:
a. Since we have two resistors in with resistances R = 4Ω and R' = 3 Ω in series, the total impedance z of the circuit is the sum of the individual resistances.
So, z = R + R' = 4 Ω + 3Ω = 7 Ω
b. Since we have a resistor of resistance R = 4Ω in series with an inductor of reactance X = 3 Ω, the total impedance is z = √(R² + X²)
z = √((4 Ω)² + (3 Ω)²)
z = √(16 Ω² + 9 Ω²)
z = √(25 Ω²)
z = 5 Ω
c. Since we have a resistor of resistance R = 4Ω in series with an inductor of reactance X = 3 Ω, and a capacitor of reactance, X' = 1 Ω the total impedance is z = √[R² + (X - X')²]
z = √((4 Ω)² + (3 Ω - 1 Ω)²)
z = √(16 Ω² + (2 Ω)²)
z = √(16 Ω² + 4 Ω²)
z = √(20 Ω²)
z = √(4 × 5) Ω
z = √4 × √5 Ω
z = 2√5 Ω
z = 4.472 Ω
If I worked 8 hours and 49 minutes but my paycheck was only 97.17$ what was my hourly wage.
Answers
Answer:
11.021$
Step-by-step explanation:
49min to hr=49/60=0.816
now total worked hrs =8hr +0.816hr=8.166hr
now 1hr wage =97.17$/total hr(8.166)=11.021$
Three fourths of the offspring of two fruit flies have short wings, while the rest have wild-type wings . In a batch of offspring from those two flies, 100 have wild-type wings. How many of the flies have short wings?
Answers
Answer:
300
Step-by-step explanation:
If three-fourths of the offspring of two fruit flies have short wings and the rest have wild-type wings, then [tex]1-\frac{3}{4}=\frac{1}{4}[/tex] of the offspring must have wild-type wings. This means that the number of offspring that have short wings must be [tex]\frac{3/4}{1/4}=\frac{3}{4}\cdot \frac{4}{1}=3[/tex] times larger than the number of offspring that have wild-type wings. Since there are 100 offspring who have wild-type wings, there must be [tex]100\cdot 3=\boxed{300}[/tex] that have short wings.
Alternative:
If three-fourths of the offspring of two fruit flies have short wings and the rest have wild-type wings, then [tex]1-\frac{3}{4}=\frac{1}{4}[/tex] of the offspring must have wild-type wings. Therefore, 100 represents one-fourth of the total number of offspring, meaning there must be [tex]100\cdot 4=400[/tex] offspring total. Thus, there are [tex]400-100=\boxed{300}[/tex] offspring with short wings.
Currently, Mike is 8 years more than twice Tom's age. In 3 years from now,
Mike's age
will be three times Tom's age. What are their current ages?
Answers
Answer:
The current age of Mike is 12 years old while that of Tom is 2 years old.
Step-by-step explanation:
Let the current age of Mike be m years old and that of Tom be t years old.
Currently
m= 2t +8
3 years from now
Tom's age= t +3
Mike's age
= m +3
= 2t +8 +3
= 2t +11
Given that in three years, Mike's age is 3 times Tom's age,
2t +11= 3(t +3)
Expand:
2t +11= 3t +9
3t -2t= 11 -9
t= 2
Current age of Mike
= 2t +8
= 2(2) +8
= 4 +8
= 12
How do u find the area of a kite using coordinates?
Answers
Answer:
What is the area of a kite equal to? The area of a kite measures the space inside the four sides. The most common way to find the area is by using the formula A = xy/2, where x and y are the lengths of the diagonals.
Which graphs show functions with direct variation? select three options.
Answers
Answer:
the daily graphs
Step-by-step explanation:
the news paper
Answer:
B C E
Step-by-step explanation:
Given JIH~ LMN. what is the value of LN?
Answers
Answer:
7 units
Step-by-step explanation:
In similar triangles, corresponding sides are same ratio.
[tex]\frac{LN}{JH}=\frac{LM}{JI}\\\\\frac{LN}{14}=\frac{5}{10}\\\\LN=\frac{5}{10}*14\\\\LN=7[/tex]
Explain how to know when to use mean, median, or mode as a measure of
central tendency. For each measure, give an example of a situation where the
center should be used.
Answers
Answer:
Step-by-step explanation:
Mean
The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.
Median
Arrange your numbers in numerical order.
Count how many numbers you have.
If you have an odd number, divide by 2 and round up to get the position of the median number.
If you have an even number, divide by 2.
Mode
To find the mode, or modal value, it is best to put the numbers in order. Then count how many of each number. A number that appears most often is the mode.
Instructions: Find the missing side. Round your answer to the nearest tenth.
53 and 10
Answers
Answer:
8
Step-by-step explanation:
10sin(53) = 7.986... = 8.0
2x^2-3x+2=x√(3x^2-2)
Answers
10 million= ___ million
Answers
Answer:
10
Step-by-step explanation:
I need answers asappppp plz
Answers
Answer:
Step-by-step explanation:
The Raptors are scheduled to play 85 games this season.
a. Create a table of values that will show some of the possible amounts Stretch might eam
throughout the first season. Number of games played is represented by n and money
earned by E.
b. Graph the information to show his earnings for the season. Use a suitable scale. Change
the money values in your table to millions of dollars before starting.
C. D) Write an equation relating Stretch's earnings to the number of games he plays.
ii) Define your variables, including units.
II) Explain what the numbers in your equation represent for Stretch.
d. How much money will Stretch make if he plays 44 games this season? Show your work.
e. Stretch's twin brother, Rory, has been offered a different contract. The following equation
defines the offer. E = 95 000n + 450 000
E represents Rory's total earnings in dollars and n represents the number of games Rory
plays. Is this a better offer than Stretch's? Give reasons for your answer by comparing the
two offers, reporting mathematical details about the comparison.
Answers
Answer:
How do you expect me to do all of that lol
Step-by-step explanation:
Lucy rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total of 10.
Answers
Answer:
10÷5 = 2, 2+2 =4, answer is 4
Where should you place the needle of your compass in the first step of an angle bisection?
Answers
Answer:
Place the compass needle on the vertex of the angle, and draw an arc across both legs of the angle.
[tex]\boxed{\text{Solve for 'x'.}}\\\\\frac{x+3}{6}=\frac{2}{3}[/tex]
Answers
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]x = 1[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Calculating the answer...}}\\\\\frac{x+3}{6}=\frac{2}{3}\\\----------\\\rightarrow (\frac{x+3}{6})6=(\frac{2}{3})6\\\\\rightarrow x + 3 = 4\\\\\rightarrow x + 3 - 3 = 4 - 3\\\\\rightarrow \boxed{x=1}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Answer:
x = 1
Step-by-step explanation:
( x + 3 ) / 6 = 2 / 3
Step 1 Cross multiply
( x + 3 ) * 3 = 3x + 9
2 * 6 = 12
We now have 3x + 9 = 12
Step 2 Subtract 9 from both sides
3x + 9 - 9 = 12 - 9
9 - 9 cancels out
12 - 9 = 3
We now have 3x = 3
Final step; divide both sides by 3
3x/3 = x
3/3 = 1
We're left with x = 1
To check our answer we can plug in 1 for x in the expression
( x + 3 ) / 6 = 2 / 3
Substitute 1 for x
1 + 3 / 6 = 2 / 3
Simplify addition
4/6 = 2/3
Simplify fraction
2/3 = 2/3 ✓
mA = (4x - 2) and mzB = (11x + 17)°. Find x if the angles are
supplementary
A.) 165
B.) 180
C.) 15
D.) 11
Answers
What is the remainder when (x^3 + 1) is divided by (x^2 – x + 1)?
O x +1
Ο x
O 2
Ο 0
Answers
Answer:
The answer is 0 .... solution is X+1 the REMAINDER IS 0
Step-by-step explanation:
The remainder when (x³ + 1) is divided by (x² - x + 1) is 0.
The correct option is D.
What is a polynomial?An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
We can use polynomial long division to find the remainder of (x³ + 1) divided by (x² - x + 1):
x + 1
-------------
x² - x + 1 | x³ + 0x² + 0x + 1
- (x³ - x² + x)
---------------
x² - x + 1
- (x² - x + 1)
-------------
0
Therefore, the remainder when (x³ + 1) is divided by (x² - x + 1) is 0.
To learn more about Polynomials;
brainly.com/question/11536910
#SPJ7
Help me pls‼️‼️‼️❤️❤️
Answers
Answer:
= 50%
Step-by-step explanation:
There is one point, random number = 1
There are two circles, sample space = 2
[tex]{ \tt{probability = \frac{1}{2} }} \\ { \tt{percentage = \frac{1}{2} \times 100\% }} \\ = 50\%[/tex]
Answer:
25%
Step-by-step explanation:
1. Find the area of both Circles: [tex]A = \pi r^{2}[/tex] [tex]A = \pi 2^{2}[/tex] = [tex]4\pi[/tex] [tex]A = \pi 1^{2} = \pi[/tex]
2. [tex]\frac{\pi }{4\pi }[/tex] to find the percentage
3. 0.25 = 25%
Z -7, when z=6 PLS HELP MY I AM NOT SURE IF I DID IT RIGHT I HAVE TO TURN THIS IN TOMORROW
Answers
Answer:
Z-7
6-7
-1
Step-by-step explanation:
we have to replace the value of Z and then subtract by seven.
[tex]\sf \: z = 6 \\ \\\sf z - 7 \\ \sf = (6) - 7 \\ \sf = 6 - 7 \\ = \underline{\bf - 1}[/tex]
-> Just substitute the value of z in the equation & you'll get the required solution.
The graph of a quadratic function
displays output values that approach
negative infinity. What do you know
about the leading coefficient of this
function?
A
The leading coefficient is negative.
B
The leading coefficient is positive.
Answers
Answer:
A
The leading coefficient is negative.
Step-by-step explanation:
Quadratic equation:
A quadratic equation has the following format:
[tex]y = ax^2 + bx + c[/tex]
The leading coefficient is a.
a negative:
The graph of the function is concave down, that is, it displays values that approach negative infinity.
a positive:
The graph of the function is concave up, that is, it displays values that approach up infinity.
In this question:
Displays values that approach negative infinity, so the leading coefficient is negative, and the correct answer is given by option A.
Answer:
B it's positive.. I went with negative because that's what it said, but it was wrong!
Step-by-step explanation:
find the difference between of the greatest and smallest 5 digit number
Answers
Answer:
Step-by-step explanation:
The largest 5-digit number is 99999 and the smallest 5-digit number is 10000. If it was mentioned that the largest unique 5-digit number then it would have been 98765 and the smallest 5-digit number would have been 10234.
Hope this answer helps you :)
Have a great day
Mark brainliest
first answer gets marked brainliest!!!
Answers
Answer:
A
Step-by-step explanation:
plz give brainliest
Help Please Math!!!
Find The Surface Area Of The Prism
Answers
Answer:
Surface Area=208 cm²
Step-by-step explanation:
Surface Area= 2×l×w+2×l×h+2×h×w
SA= 2×11×4+2×4×4+2×11×4=208
If Sunil earns $3672 per month, what is his annual salary?
Answers
Answer:
$44064
Step-by-step explanation:
Sunil earns $3672 every month. To find out his annual salary, we will need to multiply this monthly salary by the number of months in a year; 12.
3672 * 12 = $44064
plzzz helppp will mark brainlest stpps plzz if possible
Answers
Answer:
c.
Step-by-step explanation:
Law of sines
[tex]\frac{Sin A}{a}[/tex] = [tex]\frac{Sin B}{b}[/tex]
A and B are angles.
a and b are sides opposite corresponding angles.
Help anyone can help me do this question,I will mark brainlest.
Answers
Answer:
34 pi
Step-by-step explanation:
Use formula for circumference, 2 pi r
Find the circumference for both circles because both circles circumference are included in the shaded region
