The hypotenuse of a 45°-45°-90° triangle measures 128 cm.What is the length of one leg of the triangle?
Answers
Answer:
Since, a 45°-45°-90° triangle is a special type of isosceles right triangle, where the two legs are congruent to one another and the non-right angles are both equal to 45 degrees.
In 45°−45°−90° triangle
Sides are in the proportion [tex]1:1:\sqrt{2}[/tex]
then,
the measures of the sides are [tex]x , x ,\sqrt{2}x[/tex]
The length of hypotenuse= [tex]\sqrt{2}[/tex] times the length of the leg. ....[1]
Given: length of hypotenuse = 128 cm.
then,
from [1] we have;
128 = [tex]\sqrt{2}\cdot x[/tex]
or
[tex]x=\frac{128}{\sqrt{2}}[/tex] = [tex]\frac{128}{\sqrt{2} } \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{128\sqrt{2}}{\sqrt{2}\cdot \sqrt{2}}[/tex]
Simplify:
[tex]x =\frac{128 \cdot \sqrt{2}}{2} =64\sqrt{2}[/tex] cm.
Therefore, the length of one leg of the triangle is; [tex]64\sqrt{2}[/tex] cm.
Related Questions
On Saturday, a local hamburger shop sold a combined total of 464 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Saturday?
Answers
The number of hamburgers will be 348.
What is an expression?
Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that On Saturday, a local hamburger shop sold a combined total of 464 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold.
The number of hamburgers will be calculated as below:-
Cheeseburgers= x
Hamburgers= 3x
3x+x=464
4x=464
x=116
Substitute the value of x in expression.
Hamburgers= 3x
Hamburgers= 3 x 116 = 348
Therefore, the number of hamburgers will be 348.
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The local hamburger shop sold 116 hamburgers on Saturday. We determined this by setting up an equation where the number of hamburgers (H) plus three times the hamburgers (3H) equaled the total sales of 464 burgers, and then solving for H.
Explanation:The question asks us to solve a basic algebra problem involving hamburgers and cheeseburgers. Let's define the number of hamburgers sold as H. Since the number of cheeseburgers sold was three times the number of hamburgers sold, we can represent the number of cheeseburgers as 3H. The total number of burgers sold was 464. Now, we can write down the equation:
H + 3H = 464
This simplifies to:
4H = 464
Now, we divide both sides by 4 to find the value of H:
H = 464 / 4
H = 116
So, the local hamburger shop sold 116 hamburgers on Saturday.
Sarah's age is five less than twice her sister's age. Sarah is fifteen years old.
Which equation could you use to solve for the age of Sarah's sister?
2x - 5 = 15
2(15) - 5 = x
15 = 5 - 2x
15 - 5 = 2x
Answers
=>sister .....x
Sarah.
twice x=2x. then less than 5
=> (2x-5 )
if Sarah = 15 years
by substation, 2x-5=15
Which transformations map the strip pattern onto itself
Answers
Below are the choices that can be found elsewhere:
a horizontal translation and a 180° rotation
a horizontal translation and a reflection across a vertical line
a horizontal translation and a glide reflection
a horizontal translation only
The answer is the first one .
Answer: a horizontal translation and a 180 rotation
Step-by-step explanation:
in the fraction 3/5 which statement best describes the denominator
Answers
write 158/4 as a mixed number in simplest terms. Thank you.
Answers
So, your final answer is 39 1/2
Hope this helps!
Final answer:
The mixed number of 158/4 simplified is 39 1/2. A proportion comparing the ratios 1/48 and w/16 is solved by cross-multiplication resulting in w = 1/3 as the solution.
Explanation:
To write 158/4 as a mixed number in simplest terms, we first divide 158 by 4. When we do this division, 4 goes into 158, 39 times completely, since 4 * 39 = 156, and we get a remainder of 2. Therefore, the mixed number form of 158/4 is 39 2/4. To simplify this fraction further, we divide the numerator and the denominator by their greatest common divisor, which in this case is 2. Simplifying 2/4 by dividing both the numerator and denominator by 2, we get 1/2. Hence, the mixed number in its simplest terms is 39 1/2.
To set up a proportion using the given ratios, we start with the ratio 1/48 and set it equal to w/16, which can be represented as:
1/48 = w/16
When solving for w, we cross-multiply to get:
1 * 16 = 48 * w
Which simplifies to:
16 = 48w
Finally, to find the value of w, we divide both sides of the equation by 48, which gives us w = 16/48. Simplifying by dividing both numerator and denominator by the greatest common divisor, 16, we get:
w = 1/3
Fill in the missing numbers to complete the factorization. Some of the numbers could be negative. Type the numbers in increasing order.
x 3 + 2x 2 - x - 2 = (x +
Answers
Answer:
[tex]x^3+2x^2-x-2=(x+1)(x-1)(x+2)[/tex]
Step-by-step explanation:
We have given equation : [tex]x^3+2x^2-x-2=(x+[/tex]
To find : the missing numbers
We have given that missing numbers complete the factorization
so, we find the factors of the given equation
[tex]x^3+2x^2-x-2=0[/tex]
with the help of graph(attached) we find the roots of the equation or you can also take help of hit n trial method.
Roots of the equation are = 1,-1,-2
therefore the factors are (x+1)(x-1)(x+2)
and the missing terms are the factors of the equation = (x+1)(x-1)(x+2)
Answer:
[tex](x-1)>(x+1)>(x+2)[/tex]
Step-by-step explanation:
The given equation is:
[tex]x^3+2x^2-x-2[/tex]
Factorizing the above equation, we get
[tex](x+1)(x^2+x-2)[/tex]
[tex](x+1)(x^2+2x-x-2)[/tex]
[tex](x+1)(x(x+2)-1(x+2))[/tex]
[tex](x+1)(x-1)(x+2)[/tex]
which is the required factorized form of the given equation.
Now, the numbers in increasing order are:
[tex](x-1)>(x+1)>(x+2)[/tex]
Marietta drives her tow truck 312 miles in 8 hours. What is her average speed in miles per hour? Be sure to include the equation for speed in your answer.
Answers
We have, distance = 312 miles &
Time = 8 hours,
Substitute their values into the expression,
Savg = 312 / 8 = 39 miles/hour
So, the final average speed is 39 miles / hour
Hope this helps!
The average speed in miles per hour is 39mi/hr
How to calculate Speed of a bodySpeed is the ratio of distance with respect to time. The formula for calculating speed is expressed as:
Speed = Distance/Time
Given the following
Distance = 312 miles
Time = 8 hours
Substitute
Speed = 312/8
Speed = 39mi/hr
Hence the average speed in miles per hour is 39mi/hr
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The gross weight of a package and its contents is 11 pounds 5 ounces . If the packaging weighs 1 pound 15 ounces , what's the net weight of the contents
Answers
Samuel drove 28 miles in 32 minutes. Beverly drove 42 miles in 48 minutes.
Are the ratios of miles to minutes for Samuel and Beverly proportional?
Answers
Apply to Beverly. 48 divided by 48 to give 1 minute. 42 divided by 48 is 0.875 miles in a minute.
The answer is yes, they are proportional.
Answer:
Yes. Ratios of miles to minutes for Samuel and Beverly are proportional
Step-by-step explanation:
Samuel's speed can be calculated as following:
[tex]28/32=0,875[/tex]
0,875 miles per minute.
On the other hand Beverly's speed can be calculated as following:
[tex]42/48=0,875[/tex]
0,875 miles per minute
If we convert the speed to mile per hour:
[tex]0,875*60=52,5[/tex]
It can be easily seen that both Samuel and Beverly drove at the same speed at 52,5 miles per hour.
What is the exact value for the expression the square root of 56. − the square root of 14. + the square root of 126.? Simplify if possible.
the square root of 14.
4 the square root of 14.
2 the square root of 42.
8 the square root of 42.
...?
Answers
The right answer will be B.
Answer:
B- [tex]\sqrt(56)-\sqrt(14)+\sqrt(126)=14.966[/tex]
Step-by-step explanation:
Given equation : square root of 56 − the square root of 14 + the square root of 126 or [tex]\sqrt(56)-\sqrt(14)+\sqrt(126)[/tex]
Solution of the equation :
[tex]\sqrt(56)-\sqrt(14)+\sqrt(126)[/tex]
= [tex]2\sqrt(14)-\sqrt(14)+3\sqrt(14)[/tex]
= [tex]\sqrt(14)(2-1+3)[/tex]
= [tex]4\sqrt(14)[/tex]
=14.966
Now,
square root of 14 =√14 =3.7414 the square root of 14 = 4√14 = 14.9662 the square root of 42= 2√42 = 12.9618 the square root of 42 = 8√42= 51.845Therefore, Option B is correct
name the property used in each equation. then find the value of n.
2.) 1·n=8
3.) 28·n=0
4.) 0+n=22
5.) 1/4·n=1
Answers
3. n = 0 (Zero Property)
4. n = 22 (Additive Identity Property)
5. n = 4 (Fractal property)
A piece of cloth is folded into a square with a side length measuring x inches. When it is unfolded, it has an area of x2 + 27x + 162 square inches.
Which could be the dimensions of the rectangular piece of cloth when it is unfolded? Remember, the area of a rectangle can be determined using the formula A = lw.
Answers
we need to factor the expression
[tex] x^{2} + 27x + 162 [/tex]
Equate to zero the expression
[tex] x^{2} + 27x + 162=0 [/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex] x^{2} + 27x =-162 [/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex] x^{2} + 27x +182.25=-162+182.25 [/tex]
[tex] x^{2} + 27x +182.25=20.25 [/tex]
Rewrite as perfect squares
[tex] (x+13.5)^{2}=20.25 [/tex]
[tex] (x+13.5)=(+/-)4.5 [/tex]
[tex] x1=-13.5+4.5= -9 [/tex]
[tex] x2=-13.5-4.5= -18 [/tex]
Hence
[tex] x^{2} + 27x + 162 =(x+9)*(x+18) [/tex]
Remember that the area of the rectangle is equal to
[tex] A=L*W [/tex]
therefore
the answer is
the dimensions of the rectangular piece of cloth could be
[tex] L=(x+18)\ inches\\ W=(x+9)\ inches [/tex]
Jolie uses 2 tomatoes every day to prepare her salad. If n equals the number of tomatoes Jolie had before she made her salad and c equals the number of tomatoes left after the salad is made, which equation represents the number of tomatoes Jolie has after she made her salad?
n = 2 − c
c = n − 2
c = 2 − n
n = c − 2
please just give me the answer.
Answers
n - the number of tomatoes before the salad is made
c - the number of tomatoes after the salad is made
Jolie uses 2 tomatoes (n - 2) every day to prepare her salad and then c tomatoes remained: n - 2 = c
Or:
c = n - 2
Answer:
d the answer is d
Find the domain and range of the relation and determine whether it is a function.
Domain: positive integers; range: positive integers; no, it is not a function.
Domain: x > 3; range: y > 0; yes, it is a function.
Domain: all real numbers; range: all real numbers; yes, it is a function.
Domain: x ³ 0; range: y > 3; no, it is not a function.
Answers
Answer:
y>0
Step-by-step explanation:
Eleven less than a number is more than seventeen in number form
Answers
add 11 to both sides
11-11+n>17+11
0+n>28
n>28
A certain small factory employs 98 workers of these 10 recieve a wage of 150 dollars per day and the rest recieve 85.50 dollars a day to the management a week is equal to 6 working days how much does the factory pay out for each week
Answers
88 × $85.50 = $7524
1500 + 7524 = $9024 a day.
9024 × 6 = $54,144 (the answer)
Hope this helps!
Answer:
The factor payout for each week is $54144. Below is the explanation
Step-by-step explanation:
Given:
There are 98 employs
10 of them receive $150 per day
88 of them receive $85.50 per day.
There are 6 working days in a week.
To find:
Let's find the wage per week by multiplying the wage per day by the number of people and the number of days in a week.
10 of them receive $150 per day.
So, they will receive $150*10*6
Which is simplified as $9000.
88 of them receive $85.50 per day
So, they will receive $85.50*88*6
Which is simplified to $45144.
So, the sum of wages for both would be $9000+$45144.
Add them together, which gives $54144.
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Which term describes a rate in which the second quantity is 1?
unit rate
percent
proportion
ratio
Answers
graph the fraction 1/2 on the number line.
the number of equally sized spaces needed between 0 and 1 is ?
Answers
which ratio is proportional to 10/24
A 20/36
B 5/8
C 35/84
D 5/6
Answers
Answer:
C 35/84
Step-by-step explanation:
The given ratio is less than 1/2. Only one answer choice is less than 1/2: 35/84.
__
The given ratio reduces to 5/12. The reduced ratios of the answer choices are ...
A 5/9
B 5/8
C 5/12 . . . . your answer
D 5/6
The Smiths plan to recarpet their family room, which measures 15 ft. by 20 ft. How many square yards of carpet are needed?
Answers
Area = width x length
w= 15 x 1/3 = 5
l = 20 x 1/3 = 6 2/3
Area = 5 x 6 2/3
33 1/3 square yards
Answer: [tex]33\frac{1}{3}[/tex] square yards of carpet is needed.
Step-by-step explanation:
Given: The dimensions for the carpet is 15 ft. by 20 ft.
We know that area ( in square units ) of a rectangle is given by :-
[tex]Area=length\times width[/tex]
Therefore, area of the required carpet is given by :-
[tex]Area=20\times15=300\text{ square feet}[/tex]
We know that 1 feet =1/3 yard
Now,
[tex]300\text{ square feet}=300\times\frac{1}{3}\times\frac{1}{3}\\=\frac{100}{3} \text{square yards}=33\frac{1}{3}\text{ square yards}[/tex]
Hence, [tex]33\frac{1}{3}[/tex] square yards of carpet is needed.
The function p(t) represents the value of a new car t years after it was manufactured.
p(t)=24,525(0.94)^t
What does the value 0.94 represent in this situation?
The value of the car increases by 94% each year.
The value of the car decreases by 94% each year.
The value of the car is 0.94 times the value of the car the previous year.
The initial value of the car is 0.94.
Answers
Answer:
The value of the car is 0.94 times the value of the car the previous year.
one horsepower is equal to how many foot pounds of work per second
Answers
hp= 550.00 foot pounds per second ft-lb/sec
Find the area of an equilateral triangle with a radius 6 square root of 3. Leave your answer in simplest radical form
Answers
Final answer:
The area of the equilateral triangle with a radius of 6√3 is 27√3 square units.
Explanation:
An equilateral triangle has all three sides equal in length and all three angles equal to 60 degrees. In this case, the radius of the circumscribed circle is given as 6√3. This radius is equal to the length of the side of the equilateral triangle.
To find the area of an equilateral triangle, we can use the formula A = (sqrt(3)/4) * s^2, where s is the length of the side of the triangle.
Substituting the given value of the radius into the formula, we have:
A = (sqrt(3)/4) * (6√3)^2 = (sqrt(3)/4) * 108 = 27sqrt(3).
Therefore, the area of the equilateral triangle is 27sqrt(3) square units.
Of the students in ms. dancer's class, 6 walk to school. this represents 30% of her students. how many students are in ms. dancer's class?
Answers
x is the number of students in the class in total
[tex]30x=600[/tex]
[tex]x=20[/tex]
The equation √7-x=x 5 has two possible solution.
Answers
Answer:
What is the extraneous solution of the equation? Answer: x= -9
What is the true solution of the equation? Answer: x= -2
This is the correct answer.
Hoped this helped!
What segment is an altitude of triangle ABC?
segment AC
segment BC
segment BD
segment CD
...?
Answers
Line segment BD is the altitude of triangle ABC.
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
A ball is kicked upward with an initial velocity of 56 feet per second. The ball's height h (in feet) can be expressed as a function of time t (in seconds) by the equation h = -16t2 + 56t. How much time does the ball take to return to the ground?
A) 1.75 seconds
B) 2.50 seconds
C) 2.75 seconds
D) 3.50 seconds
Answers
Answer:
D) 3.50 seconds
Step-by-step explanation:
You are interested in the positive value of t such that h=0. Substituting 0 for h, we get ...
0 = -16t^2 +56t
0 = -16t(t -3.5) . . . . . factored form
The product is zero when the factors are zero. Here, the factor of interest is ...
0 = t-3.5
3.5 = t . . . . . add 3.5 to both sides
The ball takes 3.5 seconds to return to the ground.
Final answer:
The ball takes D. 3.5 seconds to return to the ground.
Explanation:
To find the time it takes for the ball to return to the ground, we need to set the height function h equal to 0 and solve for t.
So, we have the equation -16t^2 + 56t = 0.
Factoring out t, we get t(-16t + 56) = 0.
Setting each factor equal to 0, we find that t = 0 or t = 3.5.
Since time cannot be negative, we disregard the t = 0 solution.
Therefore, the ball takes 3.5 seconds to return to the ground.
what is 32 percent of 60
Answers
What are the coordinates of the vertex for f(x) = 2x^2 + 4x + 9?
(−2, 4)
(−1, 7)
(1, 15)
(2, 9)
Answers
a = 2
b = 4
c = 9
Plug these into h = -b/(2a) to get
h = -b/(2a)
h = -4/(2*2)
h = -1
Then plug this into the function to get
f(x) = 2x^2 + 4x + 9
f(-1) = 2(-1)^2 + 4(-1) + 9
f(-1) = 2(1) + 4(-1) + 9
f(-1) = 2-4+9
f(-1) = -2+9
f(-1) = 7
So the vertex is at (-1,7)
Hillary wants to go on the latin club trip to italy it cost 2730 for the trip the trip is 30 weeks away and she wants to make equal weekly payments how much money altogether does hillary need to pay at the end of week eight
Answers
at the end of 8 weeks she will need $ 728.00 all together