The triangle with side lengths of 6 m, 8 m, and 9 m is possible to construct.
What is the condition to construct a triangle with given dimensions?
In a triangle, the sum of the two smaller sides must be greater than the larger side of the triangle. If this condition satisfies, then the triangle could be possible to construct.
Given,
1. A triangle with side lengths of 6 m, 8 m, and 9 m. Here, (6 + 8) > 9. Therefore, the triangle is possible to construct.
2. A triangle with side lengths of 4 m, 5 m, and 12 m. Here, (4 + 5) < 12. Therefore, the triangle is not possible to construct.
3. A triangle with side lengths of 2 m, 5 m, and 8 m. Here, (2 + 5) < 8. Therefore, the triangle is not possible to construct.
4. A triangle with side lengths of 4 m, 7 m, and 13 m. Here, (4 + 7) < 13. Therefore, the triangle is not possible to construct.
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Evaluate 5 ÷ 4/6 Give your answer as a mixed number in its simplest form.
Answer:
15/2
Step-by-step explanation:
5*6/4=30/4=15/2
Answer: 7 1/2
Step-by-step explanation:
5 ÷ 4/6 = 7.5
7.5 as a mixed number is 7 1/2
7 1/2 simplified is 7 1/2
which of the following circles lie completely within the fourth quadrant? Check all that apply.
Answer:
B and D
Step-by-step explanation
Answer:
B and D
Step-by-step explanation:
Which of the following is a Pythagorean triple?
A. (5, 12, 13)
B. (1, 1, 2)
C. (3, 4, 6)
D. (5, 8, 10)
Answer:
A
Step-by-step explanation:
Perhaps you know of the {3, 4 ,5} Pythagorean triple.
Pythagoras stated a² + b² = c²
so checking for A:
a² + b² = c²
5² + 12²
25 + 144 = 169 which is 13²
Only answer A. (5, 12, 13) is a Pythagorean triple.
The others are not.
The correct answer for Pythagorean triple are (5,12,13). The correct option is A.
A Pythagorean triple is a set three positive integers (a, b, c) that validates the Pythagorean theorem, According to which in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
The Pythagorean theorem can be written as:
[tex]a^{2} + b^{2} = c^{2}[/tex]
Check each option:
A. (5, 12, 13)
=[tex]5^{2} +12^{2} \\[/tex]
= [tex]25 + 144[/tex]
= 169
[tex]= 13^{2} \\= 169[/tex]
Since both sides are equal (169 = 169), this is a Pythagorean triple.
B. (1, 1, 2)
[tex]1^{2} +1^{2} \\= 1+1\\= 2[/tex]
[tex]= 2^{2} \\= 4[/tex]
The two sides are not equal (2 ≠ 4), so this is not a Pythagorean triple.
C. (3, 4, 6)
[tex]3^{2} +4^{2} \\= 9 + 16\\= 25[/tex]
[tex]=6^{2}[/tex]
[tex]= 36[/tex]
The two sides are not equal (25 ≠ 36), so this is not a Pythagorean triple.
D. (5, 8, 10)
[tex]= 5^{2} +8^{2}\\= 25 + 64\\= 89[/tex]
[tex]= 10^{2} \\= 100[/tex]
The two sides are not equal (89 ≠ 100), so this is not a Pythagorean triple.
The correct answer is (5,12,13). The correct option is A.
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directions for constructing the centroid of a triangle?
Step-by-step explanation:
1.Draw a triangle
2. Measure one of the sides of the triangle
3. Place a point at the midpoint of one of the sides of the triangle.
4. Draw a line segment from the midpoint to the opposite vertex. The segment you just created is called a median.
5. Repeat steps 2-4 for the remaining two sides of the triangle.
Divide: Multiple chocie PLEASE HELP
Answer:
p+q
Step-by-step explanation:
[tex]\dfrac{p^2-q^2}{p+q}\div\dfrac{p-q}{p+q}= \\\\\\\dfrac{(p-q)(p+q)}{p+q}\times \dfrac{p+q}{p-q}= \\\\\\\dfrac{(p-q)(p+q)}{p-q}= \\\\\\p+q[/tex]
Hope this helps!
Answer:
p+q
Step-by-step explanation:
We can use difference of squares to make the fractions
[tex]\frac{(p+q)(p-q)}{(p+q)} *\frac{p+q}{p-q}[/tex]
Since dividing is the same as multiplying bt the reciprocal
The (p+q) and the (p-1) cancel out so we are left with (p+q)
plsssss help due todayy!!
[tex]answer \\ = 44 \ \frac{7}{8} \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]
What is the product?
(5 r + 2)(3 r minus 4)
15 r squared + 8
15 r squared minus 8
15 r squared + 14 r minus 8
15 r squared minus 14 r minus 8
________________________________
Hey!!
Solution,
(5r+2)(3r-4)
= 5r(3r-4)+2(3r-4)
= 15r^2-20r+6r-8
= 15r^2-14r-8
So the right answer is 15 r squared minus 14 r minus 8
Hope it helps
Good luck on your assignment
_________________________________
Answer:
15 r squared minus 14 r minus 8
Step-by-step explanation:
from my understanding that what I think it is :) have an awesome day!!!!!!
Solve for w: 3(w+2) = 6 + 3w
Answer:
0
Step-by-step explanation:
you open bracket you get 3w+6=6+3w you collect like terms
you get 3w-3w=6-6
answer o=o which is 0
The space shuttle is accelerated off its launch pad to a velocity of 525 m/s in 18.0 seconds.
What is its average acceleration?
Answer:
29.17m/s²Step-by-step explanation:
Acceleration is defined as the change in velocity of a body with respect to time.
Acceleration = velocity/time
Given velocity of the space shuttle = 525m/s and time = 18.0seconds
Its average acceleration = 525/18
Its average acceleration (in m/s²) = 29.17m/s²
In what ways are sine and cosine graph similar? Be sure to include a discussion of intercepts, maxima, minima, and period.
Answer:
The sine and cosine functions are similars in:
They are periodic functions with a period of 2π.
The domain of each function is (−∞,∞) and the range is [−1,1]. Both has maxima in 1 and a minimal in -1.
Ruth contributes 18% of the total cost of her individual health care. This is $67.50
deduction from each of her biweekly paychecks. What is the total value of her individual
coverage for the year?
Total value of annual health coverage = $ 9000
Calculation of total annual health coverage
Let the total annual health care expenditure = x
Ruth pays 18% of total health care expenditure, which is $ 67.50 for two weeks (ie 15 days)
So, total paid for one month = 67.5 x 2 = 135
And, total paid for full year = 135 x 12 = 1620
As mentioned, she pays 18% of total annual health care expenditure
Hence, 18% x = 1620
18 x / 100 = 1620
x = (1620 x 100) / 18
= 9000
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Answer:
Step-by-step explanation:
Total value of annual health coverage = $ 9000
Calculation of total annual health coverage
Let the total annual health care expenditure = x
Ruth pays 18% of total health care expenditure, which is $ 67.50 for two weeks (ie 15 days)
So, total paid for one month = 67.5 x 2 = 135
And, total paid for full year = 135 x 12 = 1620
As mentioned, she pays 18% of total annual health care expenditure
Hence, 18% x = 1620
18 x / 100 = 1620
x = (1620 x 100) / 18
= 9000
What is the solution to this system of linear equations? 2x + 3y = 3 7x – 3y = 24 (2, 7) (3, –21) (3, –1) (9, 0)
2x +3y=3
7x-3y=24
solve the above equations
2x+3y=3
+7x-3y=24
9x=27
x=27/9
x=3
substitute the value of x in 2x+3y=3
2(3)+3y=3
6+3y=3
3y=3-6
3y=-3
y=-3/3
y=-1
so the solution is
{x=3,y=-1}
Answer:
C : (3, -1)
Step-by-step explanation:
Select solutions that satisfy the inequality (picture)
PLEASE HURRY I DONT KNOW THE ANSWER
Answer:
20
Step-by-step explanation:
We can use similar triangles
12/3 = x/5
x = 20
Answer:
VS = 20
Step-by-step explanation:
ST/SV = RT/QV
SV = ST×QV/RT
= 12×5/3
= 60/3
= 20
Find the area of the shaded triangle.
The area of the shaded triangle would be 12 ft.
What is a triangle?A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.
The area of the triangle is the product of half the base and the height of the triangle.
The area of the triangle = 1/2 x b x h
Area of a triangle is 1/2 x base x height.
The base of the shaded triangle is 3 ft. the height is 8 ft.
Area = 1/2 x 3 x 8
Area = 12 square feet.
so the answer is 12.
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A parking lot has four sides. One pair of opposite sides are 100 yards long. The other two sides are 60 yards long. The distance from one end of the longer side to the opposite end of the shorter side is 120 yards. Is the parking lot a rectangle? Answer the questions below to find out.
5. If the distances given form a right triangle, which number is the hypotenuse, and why?
6. Which numbers are the two sides?
Answer:
The parking lot does not form a rectangle.
Step-by-step explanation:
Given: One pair of opposite sides of parking lot are 100 yards long. The other two sides are 60 yards long.
The distance from one end of the longer side to the opposite end of the shorter side is 120 yards.
To find: If the distances given form a right triangle?
Also, to find the hypotenuse and the numbers which represent the two sides.
Solution:
In a triangle, if the square of the length of the longest side is equal to the sum of the squares of the other two sides, then the triangle is said to be a right angled triangle.
[tex](60)^2+(100)^2=3600+10000=13600\\(120)^2=14400\\\therefore (60)^2+(100)^2\neq (120)^2[/tex]
So, the triangle is not a right angled triangle.
So, none of the angles of the parking lot forming a quadrilateral is equal to [tex]90^{\circ}[/tex].
Hence, the parking lot is not a rectangle although the opposite sides are equal.
(A quadrilateral in which opposite sides are equal such each angle is [tex]90^{\circ}[/tex] is a rectangle )
The distances given do not form a right triangle.
An isosceles triangle has legs whose lengths are 10 inches and a base whose length is 12 inches. Which of
the following is the area of the triangle in square inches?
(1) 34
(2) 48
(3) 60
(4) 84
Answer:
48
Step-by-step explanation:
We have to find the height of the triangle to find its area. The altitude to the base of an isosceles triangle is also the median, meaning the altitude forms a 6-8-10 right triangle, so the length of the height is 8, and therefore the area is 0.5 * 8 * 12 = 48.
6 gallons of paint was
purchased to paint
some small rooms. If
each room needs 3/4
of a gollon, how many
room can be painted?
Answer:
1
Step-by-step explanation:
because if 1 room is a 3/4 which is almost there but not quite, and 3+3 is 6.. 3/4 + 3/4 is bigger then 6
Answer:
5 rooms can be painted
Step-by-step explanation: we can't paint six rooms because there would be no such thing a 0.2 of a room
Select two ordered pairs that satisfy the function y = –4x – 1.
Answer:
(-0.25,0) and (0,-1)
Step-by-step explanation:
I used a graphing calculator.
Put function the the calculator
then ind two points on the function and that is your answer
GUYS PLS I NEED HELP
Answer:
z = 75°
Step-by-step explanation:
You can see that CGE and FGD are vertical angles.
FGD = 15°
Now you have a 90° angle, a 15° angle, and a z° angle. They add up to 180°
105° + z° = 180°
z = 75°
Answer:
75 degrees...
Step-by-step explanation:
if you look at the diagram, the angle with 15 degrees is the same as the one opposite!
So we know that it is on a right angled corner, so all the angles here should add up to 90 degrees!
Now we do 90 degrees - 15 degrees
This gives us 75 degrees!
So x = 75 degrees!
HOPE THIS HELPS!!
Consider the following simplified algebraic expression. 10 x squared y + 6 x squared minus 7 y squared minus 6 Which could be the original expression? 8 x squared y + 7 x squared minus 5 y squared + 3 x minus 2 + 2 x squared y minus x squared minus 2 y squared + 3 x minus 4 8 x squared y + 7 x squared minus 5 y squared + 3 x minus 2 + 2 x squared y minus x squared minus 2 y squared minus 3 x minus 4 8 x squared y + 7 x squared minus 5 y squared + 3 x + 2 + 2 x squared y minus x squared minus 2 y squared minus 3 x minus 4 8 x squared y + 7 x squared minus 5 y squared + 3 x minus 2 minus 2 x squared y minus x squared minus 2 y squared minus 3 x minus 4
9514 1404 393
Answer:
(b) 8x^2y +7x^2 -5y^2 +3x -2 +2x^2y -x^2 -2y^2 -3x -4
Step-by-step explanation:
Detailed comparison of the answer choices seems to be required. The x^2y terms need to sum to 10x^2y, the 3x terms need to cancel, the constant terms need to sum to -6.
The appropriate choice on this list appears to be the second choice.
_____
Comment on the problem
In the form presented, it takes considerable time to sort the answer choices from one another and to determine what their differences are. It would be much more conducive to getting an answer if the problem were presented using the usual math symbols in a form that separates the question and the different answer possibilities.
Answer:
B
Step-by-step explanation:
i am smart
Marcus can carry a maximum of 25kg of gravel at one time
How many joumeys will he need to make to shift one and
half tonnes of gravel?
Answer: 60 journeys
Step-by-step explanation:
1 ton = 1000 kgs
1.5 tons = 1500 kgs
1500/25 = 60 journeys
Answer:
55 journeys.
Step-by-step explanation:
907185 gm = 1 ton
453592.5 gm = 1/2 ton
1360777.5 gm = 1 1/2 ton
Convert to kg (1000g= 1kg)
Then divide by 25kg
=1360.7775/25 = 54.4311
Round up decimal to 1
= 55 journeys
A falling object travels a distance given by the formula d= 3t + 3t ^2, where d is measured in feet and t is measured in seconds. How many seconds will it take for the object to travel 50 feet?
Answer:
3.61 sec
Step-by-step explanation:
Set the given d= 3t + 3t ^2 equal to 50 and solve for t:
3t^2 + 3t - 50 = 0
This is a quadratic equation with coefficients 3, 3 and -50. The discriminant is b^2 - 4ac, or 3^2 - 4(3)(-50), or 9 + 600 = 609
The roots of this quadratic are therefore:
-(3) ± √609 -3 ± 24.68 21.68
t = -------------------- = ------------------- = ----------- = 3.61 sec
2(3) 6 6
Find the infinite geometric sum of 4+2.4+1.44+...
Answer:
4+2.4=6.4+1.44=7.84
The infinite geometric sum of 4+2.4+1.44+... will be 10.
What is the common ratio?At each point in the sequence, you multiply or divide by the common ratio. Divide two sets of phrases that follow one another to find it. Whichever pair of terms is picked, as long as they appear next to one another in the sequence, is irrelevant.
It is given that, the sequence is 4+2.4+1.44+...
The sequence is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity, approaching either infinity or -infinity.
It is obtained that the common ratio is,
r=2.4/4
r=0.6
The Sum of an infinite geometric sequence is,
S = a / (1-r)
S=4 / (1-0.6)
S=10
Thus, the infinite geometric sum of 4+2.4+1.44+... will be 10.
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Which graph represents the function f(x)=3x5^x
Answer:
top right corner
Step-by-step explanation:
100 POINTS If (p−q)/2 =3 and rp−rq=12, then r= (A) −1 (B) 1 (C) 2 (D) 4 (E) It cannot be determined from the information given
Answer:
r = 2 (answer C)
Step-by-step explanation:
Given: (p - q)/2 = 3, so (p - q) = 6
Next, rp - rq = 12 can be rewritten as r(p - q) = 12, or r(6) = 12
Then r must be 2: r = 2 (answer C)
What is the height of the pyramid??
Without graphing, determine whether the equation has a graph that is symmetric with
respect to the x-axis, the y-axis, the origin, or none of these.
y=x2 +8
Choose the correct answer below.
X-axis
y-axis
origin
none of these
Answer:
girl
Step-by-step explanation:
What in the world 3000%
Quadrilateral ABCD is rotated 270° clockwise about the origin. What is the orientation of the rotated figure, and what quadrant does it lie in?
Answer:
The other person is right, I believe it is the fourth Quadrient
Step-by-step explanation: how ever there are two fourth Quadrient answers. I think it is the second fourth Quadrient one with C and B at the top. I rotated the shape and that's how it looked.
When a shape is rotated, it must be rotated through a point.
The orientation of the rotated figure is uprightThe quadrant of the rotated figure is quadrant IV.The current location of the quadrilateral is quadrant III.
A 270 degrees clockwise rotation would move the shape 3 quadrants backwards.
i.e. quadrant 2, quadrant I, and quadrant 4.
Hence, the quadrant of the rotated figure is quadrant IV.
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In the diagram below of circle o, chords AB and CD intersect at E.
If CE = 10, ED = 6, and AE = 4, what is the length of EB?
AWARDING MAX POINTS
Answer:
The length of EB is found 15
Step-by-step explanation:
As the diagram of the circle is not given in the question, I've found the diagram of the same question from internet and attached below. So that we can have a better understanding)
We can see in the diagram the chord AB and chord CD intersect each other at point E.
Each of the chord is divided into two segments.
According to the Intersecting Chords Theorem:
Products of the lengths of line segments on each chord are equal
Which means that
(AE)(EB) = (CE)(ED)
Substitute the given values;
(4)(EB) = (10)(6)
4(EB) = 60
EB = 15
Answer:
The length of EB is found 15
Step-by-step explanation:
As the diagram of the circle is not given in the question, I've found the diagram of the same question from internet and attached below. So that we can have a better understanding) We can see in the diagram the chord AB and chord CD intersect each other at point E. Each of the chord is divided into two segments. According to the Intersecting Chords Theorem: Products of the lengths of line segments on each chord are equal Which means that (AE)(EB) = (CE)(ED) Substitute the given values; (4)(EB) = (10)(6) 4(EB) = 60 EB = 15
