A triangle has a base of x^1/3 m and a height of x^1/2 m. If the area of the triangle is 16 m^2, what are the base and height of the triangle?
The base is....and the height is......
Answers
Can rewrite it as
A= b * h * 1/2
16 = (x^(1/3)) * ( x^(1/2)) * (1/2))
Multiply by 2 to simplify
32 = x^(1/3) * x^(1/2)
32=x ^(5/6)
X=64
Base = 4
Height = 8
Please look below at how you multiply variables that have fractions as exponents (you need to add the exponents, common denominator and all that)
The base of the triangle is 4 m and the height of the triangle is 8 m.
What is the area of the triangle?The are of the triangle is A = 1/2 × b × h
where 'b' is the base and 'h' is the height
For given example,
A triangle has a base of x^1/3 m and a height of x^1/2 m.
Also, the area of the triangle is 16 m^2
⇒ [tex]b = x^{\frac{1}{3}} ~m,h=x^{\frac{1}{2} }~m, A=16~m^{2}[/tex]
Using the formula for area of the triangle,
[tex]\Rightarrow A=\frac{1}{2}\times b\times h\\\\\Rightarrow 16=\frac{1}{2}\times x^{\frac{1}{3} }\times x^{\frac{1}{2} }\\\\\Rightarrow 16\times 2=x^{\frac{1}{3} + \frac{1}{2} }\\\\\Rightarrow 32=x^{\frac{5}{6} }\\\\\Rightarrow 32^6=(x^{\frac{5}{6} })^6\\\\\Rightarrow 32^6=x^5\\\\\Rightarrow x=32^{\frac{6}{5}}\\\\\Rightarrow x=64[/tex]
So, the base of the triangle would be,
[tex]\Rightarrow b=x^{\frac{1}{3} }\\\\\Rightarrow b=64^{\frac{1}{3} }\\\\\Rightarrow \bold{b=4}[/tex]
and the height of the triangle would be,
[tex]\Rightarrow h=x^{\frac{1}{2}}\\\\\Rightarrow h=64^{\frac{1}{2} }\\\\\Rightarrow \bold{h=8}[/tex]
Therefore, the base of the triangle is 4 m and the height of the triangle is 8 m.
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Related Questions
Li bought his dog Spot a huge bone that is 15 inches long. Spot chews 4 inches off the bone every day. What is the new length of the bone after 3 days?
Answers
Answer:
3 inches
Step-by-step explanation:
If the dog chews off 4 inches every day, you first have to multiply the inches by the number of days, which in this case is 3 x 4, which equals 12. In 3 days, he chewed off 12 of the original 15 inches, leaving only 3 inches left.
246.8 is what percent of 128? Round to the nearest thousandth.
Answers
Answer:
60%
Step-by-step explanation:
Answer:
Most 193%
Step-by-step explanation:
246.8/128= 1.928
Which of the equations are true identities? \begin{aligned} \text{A. }&(y+6)(y-7)+42=y^2-y \\\\ \text{B. }&(x+3)(x-8)=x^2-5x \end{aligned} A. B. (y+6)(y−7)+42=y 2 −y (x+3)(x−8)=x 2 −5x
Answers
Answer:
Only A, the first equation is true.
Step-by-step explanation:
A. (y + 6)(y – 7) + 42 = y² + 6y –7y – 42 + 42 = y² – y. This means A is true
B. (x + 3)(X – 8) = x² + 3x – 8x – 24 = x² – 5x – 24. This means B is false.
how long is the cable
Answers
Answer:
anywhere from 169 to 220 metres,
Step-by-step explanation:
The amount and the concentration of a salt solution is given. How much salt would you get if you evaporated all water from this solution? 375g of a 12% solution
Answers
Answer:
45 grams
Step-by-step explanation:
12% of 375 is 45
Which object is moving faster?
Answers
Since it is covering more distance in a shorter timeframe than object b, it is faster
Answer:
Object A
Step-by-step explanation:
Usually for these kinds of questions you would look at the steepness of the slope, the steeper it is, the quicker/faster it is.
HELP ME PLEASE 100 POINTS TO ANSWER THESE
Answers
Answer:
i did this before 1 24 2 105 3 135 4 36
Step-by-step explanation:
Answer:
1: 35/7= 5 and 5*2= 10 pencils
2: 30/5= 6 and 6*6= 36 oz of yellow paint
3: 60/4= 15 and 15*9= 135 cups of grapefruit juice
4: 63/3= 21 and 21*5= 105 grams of food
plz help i have to submit in 20 minutes !!!
Answers
Answer:
Step-by-step explanation:
1. a). Hypotenuse² = (Leg 1)² + (Leg 2)²
h² = 10² + 24²
h = √676
h = 26
(b). Hypotenuse² = (Leg 1)² + (Leg 2)²
(25)² = (15)² + (leg 2)²
Leg 2 = √(625 - 225)
= √400
= 20
(c). Hypotenuse² = (Leg 1)² + (Leg 2)²
h² = 4² + 6²
h = √(16 + 36)
h = √52
h = 2√13
(d). Hypotenuse² = (Leg 1)² + (Leg 2)²
(14)² = (Leg 1)² + 7²
Leg 1 = √(196 - 49)
= √147
= 7√3
2). Hypotenuse² = (Leg 1)² + (Leg 2)²
Leg 1 = leg 2 = 7 units [Since, triangle is an isosceles triangle]
h² = 7² + 7²
h = √98
h = 7√2
Option (1) is the correct option.
3). Hypotenuse² = (Leg 1)² + (Leg 2)²
(26)² = (Leg 1)² + (10)²
Leg 1 = √(676 - 100) = 24
Area of a right triangle = [tex]\frac{1}{2}(\text{Leg 1})(\text{Leg 2})[/tex]
= [tex]\frac{1}{2}(24)(10)[/tex]
= 120 square units
Option (3) is the correct option.
The coach recorded how fast her runners ran 1 mile. Eric ran a mile in 10.84 minutes, Kay ran a mile in 12.79 minutes, and Rosie ran a mile in 9.58 minutes. How many more minutes did Eric run than Rosie?
Answers
Answer:
1.26 minutes
Step-by-step explanation:
The runners all ran the same distance of 1 mile.
Eric's time to run 1 mile = 10.84 minutes
Kay's time to run 1 mile = 12.79 minutes
Rosie's time to run 1 mile = 9.58 minutes
This implies that Rosie is the fastest runner among the three.
The difference between Eric and Rosie's time = Eric's time - Rosie's time
= 10.84 - 9.58
= 1.26
The difference between Eric and Rosie's time shows the minutes Eric ran more than Rosie. Therefore, Eric ran 1.26 minutes more than Rosie.
− 7 / 12 + 3 / 8 thanks
Answers
Answer:
-5/24
Step-by-step explanation:
Simplify the denominators
-14/24 + 9/24
Add them but keep the denominator
-5/24
Answer:
-840
Step-by-step explanation:
12+3=15
-7*15=-105
-105*8=-840
In isosceles triangle QRS, RT is the angle bisector of ∠QRS. Mikah begins the proof by stating ∠1≅∠2. What is a valid reason for this statement? Please HELP ME!
A. Definition of Angle Bisector
B. Reflexive Property of Congruence
C. Symmetric Property of Congruence
D. Corresponding angles are congruent.
Answers
Answer:
its a
Step-by-step explanation:
Segment RT bisects ∠QRS in ΔQRS and therefore, the angles ∠1 and ∠2
formed are equal.
The valid reason for the statement ∠1 ≅ ∠2 is; A. Definition of Angle Bisector.
Reasons:
The information on the triangle ΔQRS are;
The angle bisector of ∠QRS = RT
Therefore;
∠QRT = ∠1, ∠SRT = ∠2 Given in the diagram
∠QRS = ∠QRT + ∠SRT by angle addition property
∠QRT ≅ ∠SRT by definition of angle bisector
∠1 ≅ ∠2 by definition of ∠QRT and ∠SRT
By substituting ∠QRT with ∠1 and ∠SRT with ∠2, we have;
∠1 ≅ ∠2 by definition of angle bisector
The valid reason for the statement is therefore; A. Definition of angle
bisector.
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What is the equation in point-slope form of the line that passes through the point (4,8) and has a slope of 14?
A. Y+8=1/4(x-4)
B. Y-4=1/4(x+8)
C. Y-8=1/4(x+4)
D. Y+4=1/4(x-8)
Answers
Answer:
The answer is A
Step-by-step explanation:
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Answer:
A= because it has two longer sides and two shorter sides
Step-by-step explanation:
Help me and I’ll give brainliest to u
Answers
Answer:
17
Step-by-step explanation:
5 + 6 - 5 + 4 +7 - 3 + 6 - 3 = 5 + 6 + 4 + 7 + 6 - 5 - 3 - 3
= 28 - 11
= 17
Answer 17
Step-by-step explanation:
5+6=11-5=6+4=10+7=17-3=14+6=20-3=17
9. To make lemonade you need 30 ounces of water and
18 ounces of sugar. Which graph has a slope that best
represents the ratio of water to sugar in this lemonade?
A.
noong
B.
Sugar once)
c.
Sugar ounces)
Answers
Answer:
A
Step-by-step explanation:
Hopefully this helps
The students at Plymouth South and the students at Plymouth North both planned trips to Six Flags. The students at South rented and filled 2 vans and 11 buses with 674 students. North rented and filled 6 vans and 14 buses with 882 students. Each van and each bus carried the same number of students. Find the number of students each van and In each bus. (Write your answer as an
Answers
Answer:
Number of vans = 7 students
Number of buses = 60 students
Step-by-step explanation:
Let
Number of vans = x
Number of buses = y
2x + 11y = 674 (1)
6x + 14y = 882 (2)
Multiply (1) by 3
6x + 33y = 2,022 (3)
6x + 14y = 882 (2)
Subtract (2) from (3)
33y - 14y = 2,022 - 882
19y = 1,140
y = 1,140 / 19
= 60
y = 60 students
Substitute y = 60 into
2x + 11y = 674 (1)
2x + 11(60) = 674
2x + 660 = 674
2x = 674 - 660
2x = 14
x = 14/2
= 7
x = 7 students
Candice skipped 12 m in 3 seconds. What was her speed in m/s?
A. 4 m/s
B. 3 m/s
C. 12 m/s
Answers
Answer:
her speed is answer in m/s A 4 m/a
If a car travels 400 m over 80 seconds, how fast is the car traveling?
Answers
300 meters per minute: 3600 meters per hour
YW BRAINLIEST PLEASE
Which letter is the other base angle? In the same triangle which angle is the vertex angle
Answers
Answer:
e and b
Step-by-step explanation:
The base angles are the angles below the congruent sides
Then e is the other base angle.
The vertex is the third angle in the triangle, that is b
For large parties at a seafood restaurant, a tip of 18% is automatically included on the bill. Jerome’s family went out for his grandmother’s 75th birthday. Their bill came to $268.21 before tip. Calculate the amount of tip that will be charged and the total amount after tip. Round to the nearest cent if necessary .
Answers
Answer:
tip=48.28
total cost =316.49
Step-by-step explanation:
tip = 48.28
Total + tip= 316.49
F(x)=2x+4 and g(3)=x^2+3
Answers
F(x) would be that x is -2
PLEASE HURRY ON A TEST!!
Given similar figures, find the length of the missing side.
Answers
Answer:
It would be A.10
Step-by-step explanation:
20/5 = 4
9/2.25= 4
40/10 = 4
Answer: i think 20
Step-by-step explanation:
Practice Problems Unit 3 Lesson 12
There are 70 students in the school band. 40% of them are sixth graders, 20% are seventh graders, and the rest are eighth graders.
How many band members are sixth graders?
Answers
Answer:
28 band members
Step-by-step explanation:
Since 40% of the band members are sixth graders, we need to take 40% of 70 total students.
40% of 70 = 0.40*70 = 28
So 28 band members are in sixth grade
4. Emilio asks his classmates what month they were born. He finds that 15
out of 125 classmates were born in July. If there are 1,280 students in
Emilio's school, how many students can he expect to have birthdays in July
based on the experimental probability?
Ok
Answers
Answer:153
Step-by-step explanation:
From the question, we are informed that Emilio asks his classmates what month they were born and that he finds that 15 out of 125 classmates were born in July. This gives us a fraction of 15/125 = 3/25.
If there are 1,280 students in Emilio's school, the number of students that he can expect to have birthdays in July would be:
= 3/25 × 1280
= 153.6
There will be 153 students expected
Cecilia's mom ordered pizza for dinner. The pizza has two slices of pepperoni, two slices of mushroom, and two slices of anchovy. Cecilia asks her brother to bring her two slices. List all the possible combinations where the first choice is pepperoni.
Answers
Answer:
If the first slice is pepperoni, then we have left:
1 slice of pepperoni.
2 slices of mushrooms.
2 slices of anchovy.
Then the possible combinations are:
Pepperoni and pepperoni (in only one combination)
Pepperoni and mushrooms (in two combinations, because there are two slices left)
Pepperoni and anchovy (Again in two combinations, because there are two slices left)
These are the 3 possible combinations, 5 in total.
Simplify the expression: – 9+ – 10h+4h+8
Answers
Answer:
-6h - 1
Step-by-step explanation:
-9 + (-10h) + 4h + 8
-9 + (-6h) + 8
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Answers
Answer:
Step-by-step explanation:
find all of tehe factors to both numbers
15x = 5 3 x
35 = 5 7
pull 5 out of both of them and put the remaining factors in parentheses
5(3x + 7)
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Answers
y =− 11/2≈−0.181818182 is that what your looking for
Sara says, "If you subtract 17 from my number and multiply the difference by - 6, the result is
- 36." What is Sara's number?
Sara's number is
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Find the solution of the system of equations.
2x + 5y = –11
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Submit Answer
Answers
Answer:
x=-6
Step-by-step explanation: