Answer: [tex]28\sqrt 3[/tex]
Step-by-step explanation:
8 x 14 x 21 = 2352, so:
√8⋅√14⋅√21 = √2352
√2352 in simplest form is 28√3
I hope this helps!
Select all the conditions for which it is possible to construct a triangle. (7.G.1.2) Group of answer choices a. A triangle with angle measures 60°, 80°, and 80° b. A triangle with side lengths 4 cm, 5 cm, and 6 cm c. A triangle with side lengths 4 cm, 5 cm, and 15 cm d. A triangle with side lengths 4 cm, 5 cm, and a 50° angle across from the 4 cm side e. A triangle with angle measures 30° and 60°, and an included 3 cm side length f. A triangle with angle measures 60°, 20°, and 100°
Answer:
b, d, e, f
Step-by-step explanation:
Here are the applicable restrictions:
The sum of angles in a triangle is 180°, no more, no less. The sum of the lengths of the two shortest sides exceeds the longest side.When two sides and the angle opposite the shortest is given, the sine of the given angle must be at most the ratio of the shortest to longest sides.a. A triangle with angle measures 60°, 80°, and 80° (angle sum ≠ 180°, not OK)
b. A triangle with side lengths 4 cm, 5 cm, and 6 cm (4+5 > 6, OK)
c. A triangle with side lengths 4 cm, 5 cm, and 15 cm (4+5 < 15, not OK)
d. A triangle with side lengths 4 cm, 5 cm, and a 50° angle across from the 4 cm side (sin(50°) ≈ 0.766 < 4/5, OK)
e. A triangle with angle measures 30° and 60°, and an included 3 cm side length (OK)
f. A triangle with angle measures 60°, 20°, and 100° (angle sum = 180°, OK)
_____
Additional comment
In choice "e", two angles and the side between them are specified. As long as the sum of the two angles is less than 180°, a triangle can be formed. The length of the side is immaterial with respect to whether a triangle can be made.
__
The congruence postulates for triangles are ...
SSS, SAS, ASA, AAS, and HL
These essentially tell you the side and angle specifications necessary to define a singular triangle. As we discussed above, the triangle inequality puts limits on the side lengths specified in SSS. The angle sum theorem puts limits on the angles when only two are specified (ASA, AAS).
In terms of sides and angles, the HL postulate is equivalent to an SSA theorem, where the angle is 90°. In that case, the angle is opposite the longest side (H). In general, SSA will specify a singular triangle when the angle is opposite the longest specified side, regardless of that angle's measure. However, when the angle is opposite the shortest specified side, the above-described ratio restriction holds. If the sine of the angle is less than the ratio of sides, then two possible triangles are specified.
2. Solve the problem and find the answer
Answer:
x ≈ 19.3
Step-by-step explanation:
The marked sides are adjacent to, and opposite of the given angle. The relevant trig relation is ...
Tan = Opposite/Adjacent
tan(65°) = x/9
x = 9·tan(65°)
x ≈ 19.3
What is the value of d to the nearest hundredth?
E
da
7.2
D
42°
d
F
Answer: 6.48
Step-by-step explanation: hope it helps
In right angle ΔDEF, Value of d = 6.48 .
What is trigonometric ratio?In trigonometry, there are six trigonometric ratios, namely, sine, cosine, tangent, secant, cosecant, and cotangent. These ratios are written as sin, cos, tan, sec, cosec, and cot in short.
sin θ = Perpendicular/Hypotenuse
cos θ = Base/Hypotenuse
tan θ = Perpendicular/Base
sec θ = Hypotenuse/Base
cosec θ = Hypotenuse/Perpendicular
cot θ = Base/Perpendicular
Given, In figure
ΔDEF is right angle triangle
DE = 7.2
∠D = 42°
∠E = 90°
EF = d =?
tan D = EF/DE
tan 42° = d/7.2
0.900 = d/ 7.2
d = 6.48
Hence, 6.48 is the value of d in right angle ΔDEF.
Learn more about trigonometry ratio:
https://brainly.com/question/29079511
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Stephanie borrowed $35,000 on August 6 with interest due on December 14. If the interest rate is 6%, find the interest on the loan using exact interest and ordinary interest. What is the difference between the 2 interest amounts?
Step-by-step explanation:
This is the answer to the question you have given. Understand this and write it in your notebook.
I prepaid 70% of the total cost of $127.50 last week . The total you still owe is______?
Answer:
38.25
Step-by-step explanation:
Note:
Paid 70%
Total 127.50
Solution:
127.50 · 70% = 89.25
127.50 - 89.25 = 38.25
Hence, The total you still owe is $38.25
Jack designed a bridge that will be 0.2 miles long and 0.6 of the bridge has been built. How long is the section of the bridge that is finished?
Answer:
0.12miles
Step-by-step explanation:
0.6 of 0.2 miles is 0.12miles which is complete
What is the volume of the prism if each cube is 1 cm to the third power?
Answer:
42 cm^3
Step-by-step explanation:
volume of a rectangular prism = L x W x H
the dimensions are7x3x2 so you multiply those numbers and get the volume which is 42
A pizza with 16 slices is served for lunch. After lunch, 3 slices are left. How many slices were eaten at lunch?
A bag with 8 marbles has 8 yellow marbles. A marble is chosen from the bag at random. What is the probability that it is yellow?
Write your answer as a fraction in simplest form.
Answer:
8/8 or just 1 whole will be yellow
What is the area of this quadrilateral?
3 ft
4 ft
3 fty
Answer:
D
Step-by-step explanation:
12 square feet
Solve four sixths plus one third
six sixths or 1
seven sixths
five thirds
twelve sixths or 2
Answer:
Solve four sixths plus one third
The answer is 1
someone please help i am very confused.
Answer:
Rectangle A's length = 22 ft., Rectangle B's length = 44 ft.
Step-by-step explanation:
Since we know that the length of Rectangle B is twice the length of Rectangle A, we know that 2*(3x + 7) = Rectangle B's length.
We must set this equation to the dimensions already given for Rectangle B, which gives us 2(3x + 7) = 2 (5x - 3).
Using the distributive property gives us 6x + 14 = 10x - 6 and solving for x gives us x = 5.
We must plug five into the original dimensions to find that the lengths of Rectangles A and B are 22 feet and 44 feet respectively.
How is this excerpt important to the poem as a whole?
It introduces the problem the speaker has playing his baseball position.
It shows why the speaker does not like playing baseball.
It shows how the speaker’s feelings about himself begin to change.
It develops the idea that the speaker feels like an outsider with the other boys.
Answer:D
i believe thts correct
-16t^2+8t+120
Factor out the GCF and write in parentheses what is left over
Answer:
8(-2t^2 + t + 15)
Step-by-step explanation:
8 will go into each term so it becomes
8(-2t^2 + t + 15)
1.
Slope = (7,-1) and 12,-2)
Answer: -1/5
Step-by-step explanation:
the equation to solve slope with two points is the y coordinate in the second point minus the y coordinate in the first point over the x coordinate in the second point minus the x coordinate in the first point so this one would be
(-2 - -1)/(12-7)
On the top you subtract a negative it becomes a positive and you get -1/5
There are no solutions to the system of inequalities shown below.
y< x + 3
y>-2x-1
O A. True
B. False
False it does have a solution or solutions
evaluate each function for the given value
Answer:
3) 5
5) 1
Step-by-step explanation:
substitute the value of 9 for each 'x' in the expression
3) h(9) = 2/3(9) - 1
= 18/3 - 1
= 6-1 or 5
substitute the value of 5 for each 'x' in the expression
5) f(5) = -5² + 6(5) - 4
= -25 + 30 - 4
= 5-4 or 1
Would someone be able to help me with problem number two plz
PLEASE HELLPO I NEED SOMEONE PLS
Answer (if it is possible check the answer in other sources):
1: y=7x+5.553;
2: y=7x+7.99.
Step-by-step explanation:
all the details can be found in the attachment (the answer is marked with colour).
1) to determine f'(x);
2) to calculate the values x₀ within the given interval;
3) to calculate the values f(x₀);
4) to calculate the values of interception 'i';
5) to write the required equations using 's' and 'i'.
The difference between 7/10 and 3 2/5
Answer:
2 7/10
Step-by-step explanation:
To find difference we subtract.
3 2/5 - 7/10 = 2 7/10
The answer is 2 7/10. Please mark brainliest if possible.
christian reads 1/4 of a book every 2/3 weeks how many books does Christain read per week
Answer:
3/8 of a book per week
Step-by-step explanation:
Which is the correct solution for the expansion 3+5^2?
Answer:
3+5^2 = 28
Step-by-step explanation:
The answer to the expansion of the expression, 3+5^2 is 28
How to expand an expansionAn expansion of an expression is the evaluation of the expression to its simplest form
Given:
3+5^2
= 3 + 5²
= 3 + (5 × 5)
= 3 + 25
= 28
Therefore, answer to the expansion of the expression, 3+5^2 is 28
Learn more about expansion:
https://brainly.com/question/13602562
Which fossil would you be most likely to find in a coal mine?
Nick has two pet rabbits. His Flemish giant rabbit weighs 5 times as much as his Holland lop rabbit. If Nick's Flemish giant rabbit weighs 12 more pounds than his Holland lop rabbit, how much does his Flemish giant rabbit weigh?
Answer:
15 poundsStep-by-step explanation:
so we know that his Holland lop rabbit weighs1/5 of his Flemish giant rabbit.
so 4/5 is 12
divide by 4 to get 1/5
=3
x by 5 to get 5/5 (1)
15
Answer: 15 pounds
Step-by-step explanation: how am i supposed to know
Over the next 13 months you have read at least 39 books you have to read x books per month. The inequality 13x >39 represents this situation. Solve the inequality to find the number of books you have to read per month
Answer:
x>3 (x is greater than three)
Step-by-step explanation:
Simply divide 39/13 to get x>3
What is the surface area of a cube with a edge of 5
Answer:
Step-by-step explanation:
A cube is made up of 6 squares
One square has 4 edges of equal length
The area of one face is Area = s^2
Therefore the surface area is 6 * s^2
The area of this cube is 6 * 5 * 5 = 150 units.
Need help fast please!
no links please!
For Plato
Answer:
B. (g . f)(x) = 5x log(5x) + 4log(5x)Step-by-step explanation:
[tex]\sf (g*f)(x)[/tex]
[tex]\sf f(x)=log(5x)[/tex]
[tex]\sf g(x)=5x+4[/tex]
[tex]\sf (g*f)(x)[/tex]
[tex]\sf =g(x).\:f(x)[/tex]
[tex]\sf =(5x+4)(log5x)[/tex]
[tex]\sf =5x\:log(5x)+4\:log(5x)[/tex]
there are 102 teachers in a school of 3300 students find the ratio of the number of teachers to the number of students
Answer:
17:550
Step-by-step explanation:
Ratio of the no. of teachers to the no. of students = 102 / 3300 = 17/550 = 17:550
Answer:
1 teacher to 32.4 students
Step-by-step explanation:
3300/102 = 32.4
Answer 1 teacher to 32.4 students
Jordan poured 20 L of water into an empty fish tank if 5/6 of the fish tank was filled find the capacity of the tank
Answer:
the capacity of the tank would be 24 L
Step-by-step explanation:
24 ÷ 6 = 4
4 x 5 = 20
Margaret owes $7,000 to the bank. The debt grows with simple interest at a rate of 4% per year. How much will Margaret owe after 5 years?
Answer:
I=p×r×t
7000×4÷ 100×5
7000×0.04 ×5
I =1400
