Answers
Explanation:
1. The hypotenuse of the triangle is the larger side. Keeping this on mind, you must apply the Phytagorean Theoream, as below:ç
a²=b²+c²
"a" is the hyptenuse and "b" and "c" are the legs of the right triangle.
2. Then, you have:
a=13
b=12
c=5
3. If you apply the formula above to calculate the hypotenuse and the result is 13, then those are the lengths of sides of the right triangle. Therefore:
a²=b²+c²
a=√b²+c²
a=√(12)²+(5)²
a=√144+25
a=13
Related Questions
Someone please help
Answers
9-6 = 3
answer would be 4k^3
The sum of Emil’s and Rosa’s ages is 27 years. Nine years ago Emil was twice as old
as Rosa was then. How old is each person?
Answers
e - 9 = 2 x ( r - 9 );
So, e = 27 - r;
Then, 27 -r - 9 = 2r - 18;
18 - r = 2r - 18;
18 + 18 = 2r + r;
36 = 3r
Finally, r = 12 years (Rosa);
e = 27 - 12;
e = 15 years (Emil);
Harry's Health club costs $20 per month plus a $75 membership fee. Fiona's fitness costs $35 per month. What is the dollar amount at the break even point?
Answers
First, we need to set up an equation for each plan.
Harry's Health Club can be y = 20x + 75 because it starts at 75 and increase 20 per month.
Fiona's Fitness can be just y = 35x because it is just 35 per month.
Set the equation equal to each other and solve.
20x + 75 = 35x
75 = 15x
5 = x
A square pyramid and a cube have the same volume if the length of each side of the base of the square pyramid is 2 cm in the height of the cube is 4 cm what is the height of the pyramid
a 8cm
b 16cm
c 24cm
d 48 cm
Answers
Vol cube = s^3
since height of cube is 4, that height = s
V = (4)^3 = 64 cubic cm
now since their Vs are the same,
1/3×s^2×h = 64
they said length of side in square pyramid
was 2, then:
1/3×(2)^2×h = 64
1/3×4×h = 64
4/3 h = 64
h = 64×3/4 = 16×3 = 48 cm
D) is the correct answer
if g(x) equals 4x + 5, which statement is true? Select the correct answer.
Answers
Hey l need summ more info just email me and we can get this done
Please help me 4and 5
Answers
Find the area of the trapezoid.
A) 38.75 in2
B) 77.5 in2
C) 155 in2
D) 198 in2
Answers
To solve this add the two lengths. . .
22 + 9 = 31
Multiply the height and the total. . .
31 x 5 = 155
Divide 155 and 2 . . .
155 divided by 2 = 77.5 <------
The correct answer to your question is option B.
Hope this helps you.
Have a great day!
Answer: The answer is b) 77.5
Step-by-step explanation:
hope i helped
Joel is looking at costs for using a gym. He could pay $50 per month for unlimited use or he could pay $12 per month plus $4 per visit. How many visits would he have to make each month to make the $50 per month unlimited use option the cheapest one?
Answers
[tex]y = 4x + 12[/tex]
Joel would have to go at least 10 times per month to make the 50 dollars per month the cheapest one.
Answer:
First choice is cheaper.
Step-by-step explanation:
Joel could pay $50 per month for unlimited use or he could pay $12 per month plus $4 per visit.
Let the monthly visits be x
We can define this as :
[tex]12+4x> 50[/tex]
[tex]4x >50-12[/tex]
[tex]4x >38[/tex]
[tex]x> 9.5[/tex]
So, x can be greater than 9.5 means 10.
[tex]4(10)+12>50[/tex]
[tex]52 > 50[/tex]
Comparing both we can say that the first choice is cheaper.
Five years ago the population of Australia was 23.13 million. It has grown by 870 000. What is the population of Australia now?
Answers
The current population of Australia is 24 million.
It is given to us that the initial population was 23.13 million and the population 5 year later has grown by 870000 or 0.87 million. Thus to find the current population we simply need to add the initial population and the growth that has happened in 5 years. This gives us:
[tex]Current\ population = 23.13\ million + 0.87\ million = 24\ million[/tex]
Thus, the current population of Australia is 24 million.
What is the value of x^2 + 4 for x = 5?
Answers
PLEASE HELP QUICK
Which question can best be answered by finding the volume of a figure?
A)How much gas is needed to fill a gas tank?
B)How much wrapping paper is needed to cover a prism?
C)How much wood is needed to frame a window?
D)How much material is needed to line a garden with a sheet of weed-blocking material?
Answers
Hope this helps
~ Jordan ~
i really need help. thanks
Answers
An airplane takes 5 hours to travel a distance of 3300 miles with the wind. The return trip takes 6 hours against the wind. Find the speed of the plane in still air and the speed of the wind.
Answers
The speed against the wind is (3300 mi)/(6 h) = 550 mi/h.
The speed of the plane in still air is the average of these speeds, 605 mi/h.
The speed of the wind is the difference between the plane's speed in still air and its speed in moving air, 55 mph.
The speed of the plane in still air is 605 miles per hour and the wind speed is 55 miles per hour. This is found through solving simultaneous equations derived from the given distance, and time taken both with and against the wind.
Explanation:In this problem, the plane's speed in still air can be denoted as 'p' and the wind speed as 'w'. Given the total distance of the trip as 3300 miles, the total time with the wind as 5 hours, and the total time against the wind as 6 hours, we can create two equations: p + w = 3300/5 = 660 miles/hour (with the wind) and p - w = 3300/6 = 550 miles/hour (against the wind).
These equations can be solved simultaneously to get the values of 'p' and 'w'. By adding the two equations, we get 2p = 660 + 550 = 1210. Dividing by 2 gives p = 605 miles/hour. With the value of 'p' we can find 'w' by substituting p = 605 into either of the original equations (let's use p - w = 550): 605 - w = 550, which leads to w = 55 miles/hour.
So, the speed of the plane in still air is 605 miles per hour and the speed of the wind is 55 miles per hour.
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Which relationship between x and y in the equation shows a proportional relationship y=12x y=12/x y=2x+6 y=x/2+3
Answers
_____
y = 12/x is an inverse relationship
y = 2x+6
y = x/2 +3 are both linear relationships, but not proportional relationships.
write the rule for the pattern 1,5,9,13,17
Answers
I need to know the area of the shape base 1 (27ft) base 2(34ft) Height (12ft)
Answers
.. A = (1/2)*(b₁ +b₂)h
Use it.
.. A = (1/2)*(27 ft +34 ft)*(12 ft)
.. = (1/2)*(61 ft)*(12 ft)
.. = (30.5 ft)*(12 ft)
.. = 366 ft²
Helppp!!!! I’m not sure what this is...
Answers
.. Atrapezoid = (1/2)(b1 +b2)h
.. = (1/2)(12 in + 8 in)*(8 in)
.. = 80 in^2
The remaining faces unroll into a rectangle 8 in wide and (12 +8 +8+9) in long. The area of a rectangle is the product of its length and width.
.. Arectangle = length*width
.. = (37 in)*(8 in) = 296 in^2
The total surface area is the sum of the rectangle area and the two trapezoidal faces.
.. Atotal = Arectangle + 2*Atrapezoid
.. = 296 in^2 +2*80 in^2
.. = 456 in^2
The 1st selection is appropriate.
find the separate equations form the lins represented by 3x^2 + 10xy + 8y^2 + 14x + 22y + 15
Answers
3x^2 is factorable only as 3x and x.
15 can be 15 * 1 or 3 * 5.
As a first guess, I place 5 and 3 in that order.
The coefficients of y are unknown so far.
= (3x + Ay + 5)(x + By + 3)
= 3x^2 + 3Bxy + 9x + Axy + ABy^2 + 3Ay + 5x + 5By + 15
(3B + A)xy = 10xy
(3A + 5B)y = 22y
A + 3B = 10
3A + 5B = 22
-3A - 9B = -30
3A + 5B = 22
4B = 8
B = 2
A + 3B = 10
A + 6 = 10
A = 4
3x^2 + 10xy + 8y^2 + 14x + 22y + 15 = (3x + 4y + 5)(x + 2y + 3)
The product of (3x + 4y + 5)(x + 2y + 3) is indeed
3x^2 + 10xy + 8y^2 + 14x + 22y + 15
The lines are
3x + 4y + 5 = 0
x + 2y + 3 = 0
sorry.. I didn't know where else to send dis...(+_+)
Madeline sold $167 worth of items at a garage sale and then received her $232 paycheck. Estimate how much money she now has by rounding to the nearest ten first and then adding the rounded numbers.
Answers
Madeline has approximately $400 after rounding her garage sale earnings and paycheck to the nearest ten and adding them together.
The question involves estimating the total amount of money Madeline has after selling items at a garage sale and receiving her paycheck. To estimate the total amount, we need to round each amount to the nearest ten and then add the rounded numbers together.
First, round $167 to the nearest ten, which is $170.
Next, round $232 to the nearest ten, which is $230.
Finally, add the rounded numbers: $170 + $230 = $400.
all books in a store are being discounted by 30 percent
part a: let x represent the regular price of any book in the store.write an equation that can be used to find the sale price of any book in the store.
Jerome bought a book on sale at the store. the sale price of the book was $ 8.96.
part b: solve the equation to find the regular price of the book to the nearest cent.
Answers
The regular price of $8.96 should be 11.65.
Alison is currently three times as old as Mike. 5 years ago, Alison was eight times as old as Mike. How old is Alison now?
Answers
S = √3*73.5 /4.5=7 (Khufu’s pyramid)
The volume of Khafre’s pyramid is about 9/10 the volume of Khufu’s pyramid. If Kristina wants to make the second model pyramid so its volume is 9/10 the volume of the first model pyramid, what volume should she make the second model pyramid?
This goes with the other questions! if you need information i can get that for you!
Also, could you work it out!
Answers
3/6 should b you answer answer
Final answer:
The volume will be of 6.3 for the second model.
Explanation:
The student is asked to calculate the volume of the second model pyramid, Khafre's pyramid, which is 9/10 the volume of the first model, Khufu's pyramid. The student has already calculated that, for Khufu's pyramid, S = √3*73.5/4.5=7. To find the volume Kristina should make the second model, we simply multiply the volume of the first model by 9/10.
Although the question does not provide the exact volume of the first model, we will assume the value of S given is the volume of Khufu's pyramid model. Therefore, the volume of Khafre's pyramid model should be 7 * (9/10) = 6.3.
This result is based on the proportion given between the two pyramids' volumes and is a straightforward calculation of this proportion.
A recipe calls for 1/4 teaspoon of shortening for every 2/3 cup of milk. What is the unit rate of cups per teaspoon? Explain
Answers
To find the rate for a whole teaspoon, multiply 2/3 by 4 to get 8/3, or 2 2/3.
So, the rate is 2 2/3 cups of shortening per teaspoon.
Hope this helps!
A provider order has been received for a dobutamine (dobutrex®) drip at 7 mcg/kg/min. the patient's weight is 220 lbs. how many milligrams per hour should be given?
Answers
It states that a patient receives 7mcg per kg per minute, so the patient will receive 7 x 99.88=699.16 mcg per minute.
You need to convert this to a number of mcg per hour, so multiply the amount by 60 to get 41949.6 mcg per hour.
The patient's weight is first converted from lbs to kg, resulting in 100 kg. The dosage in micrograms per hour is then found to be 42000 mcg/hour. Lastly, this is converted to milligrams to give a final dosage of 42 mg/hour.
Explanation:This is a question pertaining to medical dosage calculations. First, we need to convert the patient's weight from pounds to kilograms since our dosage is based on that unit. We know that 1 kg equates to approximately 2.2 lbs. So, the patient's weight in kilograms would be 220 lbs/2.2 = 100 kg.
Now, we can use the patient's weight to find the dosage per minute: 7 mcg/kg/min * 100 kg = 700 mcg/min. But the question asks for the dosage per hour, so we must convert minutes to hours: 700 mcg/min * 60 min/hour = 42000 mcg/hour. Finally, we need convert from mcg to mg as the question asked for the amount in milligrams. Since there are 1000 mcg in 1 mg, the dosage becomes: 42000 mcg/hour / 1000 = 42 mg/hour.
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His train has been running for 2 1/2 Days straight at a constant speed of 4.8 mph. How far has he traveled?
Answers
What is the solution to the system of equations?
3x - 4y= 16
2x + 3y=5
A. (-4,1)
B. (4,-1)
C.(-4,-1)
D.(4,1)
Answers
Hope this helps!
Answer:
B: (4, –1)
Step-by-step explanation:
Must a decimal divisor and a decimal dividend have the same number of decimal places in order to have a whole number quotient? write a division equation using two decimal numbers to support your answer.
Answers
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Natalie worked during the summer for 12 weeks at an amusement park. She earned a salary and put 30% of her earnings into savings. At the end of the summer, her savings were a total of $486. How much was she paid every month (4 weeks)? Help please
Answers
162/3=54
54x10=540
$540 every 4 weeks
Find the missing length for a right triangle with hypotenuse of 18 and a leg length of 6. Round to the nearest whole number if necessary. (1 point) a) 17 b) 324 c) 19 d) 36
Answers
[tex] a^2 + 6^2 = 18^2 [/tex]
[tex] a^2 + 36 = 324 [/tex]
[tex] a^2 = 288 [/tex]
[tex] a = \sqrt{288} [/tex]
[tex] a = \sqrt{144 \times 2} [/tex]
[tex] a = 12\sqrt{2} [/tex]
[tex] a \approx 17 [/tex]
Roger served 5/8 pound of cracker wich was 2/3 of the entire box what was the weight of the crackers originally in the box
Answers
original weight of the box = 15 / 16 pounds
Explanation:
Assume that the original amount in the box is x.
We are given that:
5/8 pounds represent 2/3 of the total amount (x).
This can be translated into the following equation:
(2/3) x = 5 / 8
Now, we will solve for x as follows:
(2/3) x = 5 / 8
Multiply both sides by 24 to get rid of the denominators as follows:
(2/3) x * 24 = (5 / 8) * 24
16 x = 15
Divide both sides by 16 to isolate the x as follows:
x = 15 / 16 pounds
Hope this helps :)
The original weight of the crackers in the box is 15/16 pound.
The question asks us to determine the original weight of a box of crackers, given that 5/8 pound of crackers was served, which was 2/3 of the entire box.
We can set up the proportion by stating that 5/8 pound represents 2/3 of the whole, so let's represent the total weight of the crackers with the variable 'w'. The equation to represent this situation is (5/8) pound = (2/3) * w.
To solve for 'w', we'll multiply both sides of the equation by the reciprocal of 2/3, which is 3/2:
(5/8) * (3/2) = w
Simplifying this equation gives us the total weight:
(5 * 3) / (8 * 2) = w
15 / 16 = w
w = 15/16 pound, which is the original weight of the crackers in the box.