The Triangle Inequality Theorem holds for these values, and only one triangle is possible with these side lengths. Lucas' claim is false.
What is Triangle Inequality Theorem ?According to the Triangle Inequality Theorem, any two triangle sides' sums must be greater than the length of the third side. In other words, the following three inequalities must hold for any three positive numbers, a, b, and c:
a+b>c
a+c>b
b+c>a
In this case, a=9, b=13, and c=15. Let's check if the Triangle Inequality Theorem holds for these values:
9+13>15 (true)
9+15>13 (true)
13+15>9 (true)
Therefore, the Triangle Inequality Theorem holds for these values, and only one triangle is possible with these side lengths.
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Find the volume of the cylinder. Round your answer to the nearest hundredth, if necessary.
Answer:
The volume is 423.33 cubic millimeters.
Step-by-step explanation:
The formula for volume of a cylinder is given by:
V = πr^2h, where
V is the volume in cubic units,r is the radius of the circle,and h is the height (distance between the two circles in a cylinder).Step 1: Find radius, r, of the cylinder:
The diagram shows us the diameter, d, of the circle is 7 mm. Since the diameter is twice the radius, r, we can find r by dividing the diameter by 2:
r = d / 2
r = 7 / 2
r = 3.5 mm
Thus, the radius of the cylinder is 3.5 mm.
Step 2: Plug in values and round to the nearest hundredth to find the volume, V, of the cylinder:
Now we can plug in 3.5 for r and 11 for h to find V, the volume of the cylinder. We can round at the end.
V = π(3.5)^2(11)
V = π(12.25)(11)
V = 134.75π
V = 423.3296101
V = 423.33 mm^2
Thus, the volume of the cylinder is 423.33 cubic millimeters.
Anna wants to determine the height of a right rectangular prism. The prism has a volume of 380 cm³ and a base whose area is 50 cm². She lets h represent the height of the prism.
What equation can she write to solve the problem?
The height of the right rectangular prism is 7.6 cm.
To determine the height of the right rectangular prism, we can use the formula for the volume of a prism:
Volume = Base Area * Height
Given that the volume is 380 cm³ and the base area is 50 cm², we can write the equation as:
380 = 50 * h
Now, let's solve for h by dividing both sides of the equation by 50:
h = 380 / 50
Simplifying the expression:
h = 7.6 cm
Therefore, the height of the right rectangular prism is 7.6 cm.
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Which is the radian measure for 30° and its associated coordinate point on the unit circle?
7 pie/6
Pie over 6
Answer:
57
Step-by-step explanation:
this is the boybfiend
What value of x would make 5 Superscript x Baseline equals 625 true? Enter the answer in the box
The value of x that makes [tex]5^x = 625[/tex] true is x = 4.
To determine the value of x in the equation [tex]5^x = 625[/tex], we need to find the exponent that results in 625 when applied to the base 5.
Since 625 can be expressed as 5 raised to the power of 4 ([tex]5^4 = 625[/tex]), the value of x that satisfies the equation is 4.
When we substitute x = 4 into the equation, we get [tex]5^4 = 625[/tex], which is true.
Therefore, x = 4 is the solution to the equation, indicating that 5 raised to the power of 4 equals 625.
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find the surface area
The Surface Area of Cone is 706.5 cm².
We have dimension of Cone
height = 12 cm
Radius = 9 cm
Now, l = √9² + 12² = √81 + 144 = 25 cm
So, the Surface Area of Cone
= πrl
= 3.14 x 9 x 25
= 706.5 cm²
Thus, the Surface Area of Cone is 706.5 cm².
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Solve for x and graph the solution on the number line below.
V
V
VI
11 2x-5 or 2x-5 > 15
IV.
Inequality Notation:
Number Line:
or
-12 -10 -8 -6
-4
-2
O
2
4
6
8
10 12
x ≤ 8 or x > 10 is the solution of the inequality 11 ≥ 2x - 5 or 2x - 5 > 15.
To solve the compound inequality 11 ≥ 2x - 5 or 2x - 5 > 15, we will solve each inequality separately and then combine the solutions.
Solve the first inequality: 11 ≥ 2x - 5
Add 5 to both sides to isolate 2x:
11 + 5 ≥ 2x
16 ≥ 2x
Divide both sides by 2:
8 ≥ x
So the solution to the first inequality is x ≤ 8.
Solve the second inequality: 2x - 5 > 15
Add 5 to both sides to isolate 2x:
2x > 15 + 5
2x > 20
Divide both sides by 2:
x > 10
So the solution to the second inequality is x > 10.
Combining the solutions, we have x ≤ 8 or x > 10.
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a rocket is launched in the air. Its height in feet is given by h=-16t^2+128t where t represents the time in seconds after launch. What is the appropriate domain for this solution?
The quadratic function has the following domain: 0 ≤ t ≤ 8.
How to find the domain of a quadratic equation
Herein we find a quadratic equation that models the height of the rocket in time. The domain is the set of all values of t such that all values of h exist.
Mathematically speaking, the domain of quadratic equations is the set of all real numbers, but physically speaking, this domain is formed by the set of all non-negative numbers such that h ≥ 0. The domain is found by algebra properties:
h = - 16 · t² + 128 · t
h = - 16 · t · (t - 8)
Then, the domain of the quadratic function is: 0 ≤ t ≤ 8.
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which of the following angle pairs represent consultative interior angles please help
The correct option is b, the pair of consecutive interior angles is 1 and 7.
Which of the following angle pairs represent consultative interior angles?
First, we can see that the interior angles are the angles that are "interior" to the intersections.
These are 1, 4, 6, and 7.
Because the two lines are parallel, the consecutive interior angles are angles that would be adjacent (add up to 180°) but that are in different intersections.
Then the consecutive interior angles are:
3 and 6
1 and 7
The correct option is b.
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(09.03 MC)
The daily temperature in the month of February in a certain country varies from a low of 28°F to a high of 50°F. The temperature reaches the
freezing point of 32°F when time (t) is 0 and completes a full cycle in 8 hours. What is the amplitude, period, and midline of a function that
would model this periodic phenomenon?
O a
Ob
Oc
Od
Amplitude 11°F; period - 8 hours; midline: y = 39
Amplitude 11°F; period=4 hours; midline: y = 11
Amplitude = 22°F; period - 8 hours; midline: y = 39
Amplitude = 22°F; period - 4 hours; midline: y = 11
Answer:
The correct answer is:
Amplitude = 11°F; period = 8 hours; midline: y = 39
Step-by-step explanation:
Answer: A
Step-by-step explanation: Amplitude 11°F; period - 8 hours; midline: y = 39
Will someone please answer this and show me how you got it
(a) Using Excel, the calculations are shown below:
Mean = 608.67
Median = 610.00
Mode = 610.00
Standard Deviation = 96.89
(b) The measure of central tendency would be appropriate are the median and the mode.
How do we calculate?The median is fitting because it is a representation of the middle value in the data set and is not affected by extreme values.
We can see that our median rent is $610.00 and an appropriate representation of the typical rent paid by the students.
The mode is $610.00 and also an indication that this rent amount is the most common among the students.
In conclusion, a measure of the variability or dispersion in the data set is provided by the standard deviation, which is determined to be 96.89. It demonstrates how widely the rents vary from the mean.
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find the surface area
The surface area of the triangular prism is 193.05 cm².
We have,
The figure is a triangular prism.
Now,
There are 4 triangular surfaces.
Each surface area is the same except the base surface.
So,
3 surface area.
= 3 x (1/2 x 9 x 11.3)
= 3 x 50.85
= 152.55 cm²
And,
Base surface area.
= 1/2 x 9 x 9
= 40.5 cm²
Now,
The surface area of the triangular prism.
= 152.55 + 40.5
= 193.05 cm²
Thus,
The surface area of the triangular prism is 193.05 cm².
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Jonah's swimming pool is 21 meters by 20 meters. He swam from one corner of the pool to the opposite corner. How far did Jonah swim?
Jonah swam a distance of 29 meters from one corner of the pool to the opposite corner.
To determine how far Jonah swam from one corner of the pool to the opposite corner, we can use the Pythagorean theorem. According to the theorem, 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.
In this case, the two sides of the right-angled triangle are the length and width of the swimming pool, which are 21 meters and 20 meters respectively. The distance Jonah swam represents the hypotenuse of the triangle.
Using the Pythagorean theorem:
[tex]Hypotenuse^2 = Length^2 + Width^2[/tex]
[tex]Hypotenuse^2[/tex] =[tex]21^2 + 20^2[/tex]
[tex]Hypotenuse^2[/tex]= 441 + 400
[tex]Hypotenuse^2[/tex]= 841
Taking the square root of both sides, we find:
Hypotenuse =[tex]\sqrt{841[/tex]
Hypotenuse = 29
Jonah swam a distance of 29 meters from one corner of the pool to the opposite corner.
According to the Pythagorean theorem, 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 two sides of the right-angled triangle are the length and width of the swimming pool, which are 21 meters and 20 meters respectively. The distance Jonah swam represents the hypotenuse of the triangle.
Using the Pythagorean theorem:
[tex]Hypotenuse^2 = Length^2 + Width^2\\Hypotenuse^2 = 21^2 + 20^2\\Hypotenuse^2 = 441 + 400\\Hypotenuse^2 = 841[/tex]
Taking the square root of both sides, we find:
Hypotenuse = [tex]\sqrt841[/tex]
Hypotenuse = 29
Jonah swam a distance of 29 meters from one corner of the pool to the opposite corner.
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Find the area of a trapezoid with bases of 16 feet and 10 feet and a height of 3 feet. 39 ft2 78 ft2 240 ft2 480 ft2
Answer: 39 ft2
Step-by-step explanation:
The area of the trapezoid is 39 square feet.
To find the area of a trapezoid, you can use the formula:
Area = (1/2) × (base1 + base2) × height
Given that the bases of the trapezoid are 16 feet and 10 feet, and the height is 3 feet, we can substitute these values into the formula:
Area = (1/2) × (16 + 10) × 3
Area = (1/2) × 26 × 3
Area = (1/2) × 78
Area = 39 ft^2
Therefore, the area of the trapezoid is 39 square feet.
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Test a claim on three locations ?
The slope constraint for the zip line is 6 to 8 feet of vertical change for every 100 feet of horizontal change.
How to explain the informationSo, if the vertical change is 7 feet, the horizontal change must be between 7/6 and 7/8 of a hundred feet, or between 11.67 and 12.5 feet.
For Zip line A, the horizontal distance is 120 feet. So, the vertical change of 7 feet is within the slope constraint.
For Zip line B, the horizontal distance is 140 feet. So, the vertical change of 7 feet is within the slope constraint.
For Zip line C, the horizontal distance is 150 feet. So, the vertical change of 7 feet is within the slope constraint.
Therefore, LaTisha's claim is correct. The vertical change of 7 feet will satisfy the slope constraint for all three locations.
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round 52754.1683 the nearest.ten
Answer:
52750
Step-by-step explanation:
Step 1: Identify the digit in the tens place:
The digit in the tens place is always 2 spaces to the left of the decimal.Thus, the digit in the tens place is 5 (the one sandwiched between 7 and 4).Step 2: Examine the digit to the right of the tens place:
In this case, the digit to the right of the tens place is 4.Step 3: Determine the rounding:
When the digit to the right of the tens place is 5 or greater (5, 6, 7, 8, or 9), you round up the tens place digit by adding 1 to the digit in the tens place.Also, we remove the decimal point and everything to the left of it, using a whole number only.When the digit to the right of the tens place is less than 5 (4, 3, 2, 1, or 0), you keep the tens place digit as it is and the number to right of tens place digit it replaced by 0.We still remove the decimal point and everything to the left of it, using a whole number only.Since the digit to the right of the tens place is 4 (which is less than 5), we keep the tens place digit as is.
Original number: 52754.1683
Rounding to the nearest ten: 52750
Thus, rounding 52754.1683 to the nearest ten gives us 52750.
How mant times does 9 go into 18
Answer:
2 times, with a remainder of 0.
Step-by-step explanation:
If you had 2 friends and you had to divide 18 between both you would get 9. each with no left over
What is the sum of the exterior angles in a regular 20-gon?
The sum of the exterior angles in a regular 20-gon is given as follows:
360º.
How to obtain the sum of the exterior angles?An exterior angle of a polygon is defined as the angle between a side and its adjacent extended side.
The sum of exterior angles formula states the sum of all exterior angles in any polygon is 360°, no matter the number of sides.
For this problem, we have a 20-gon, that is a polygon of 20 sides, however, as the formula states, the sum of the exterior angles in a regular 20-gon is given as follows:
360º.
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What is the equation of a circle, if the end points of its
longest chord are (4, -3) and (-2,5)?
Answer:
The answer is D, the last one.
Find the value of x in the equation, 3^2x-1 = 81
Step-by-step explanation:
3^(2x-1) = 81 LOG both sides I had to assume there were parens.
(2x-1) LOG 3 = LOG 81
2x-1 = LOG(81) / (LOG 3) = 4
2x = 5
x = 2.5
thomas has a cube with the numbers 3,4,5,7,8 and 9 written on its faces. he rolls the cube twice and records the outcome. What is the probability that both numbers are greater than 5.
a) 1/9 b)1/4 c)1/5 d)1/16
Answer:
None of the options provided (a, b, c, d) matches the correct probability. The correct probability is 1/18.
Step-by-step explanation:
What is the area of the rectangle above?
OA. 96 square units
OB. 20 square units
OC. 104 square units
OD. 40 square units
The area of the rectangle with a length of 12 units and a width of 8 units is 96 sqaure units.
How to determine the area of a rectangle?A rectangle is a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.
The area of a rectangle is expressed as;
Area = length × breadth
From the image:
Length of the rectangle = 12 units
Breadth of the rectangle = 8 units
Area of the rectangle = ?
Plug the given values into the above formula and solve for the area:
Area = length × breadth
Area = 12 units × 8 units
Area = 96 sqaure units
Therefore, the measure of the area is 96 sqaure units.
Option A) 96 sqaure units is the correct answer.
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Find the area please answer asap need help
Answer:
5.85
Step-by-step explanation:
PLEASE SOLVE THIS FAST!!!!
A surveyor wants to determine the width of a river. She surveys the area and finds the following measures below.
She uses a pair of similar triangles, to help her find the answer.
A surveyor wants to determine the width of a river is 43.34 m.
From given figure, angle ACB = angle ECD (Vertically opposite angles are equal)
Angle BAC = Angle EDC = 90
So, triangle ABC and triangle ECD are similar.
AB/DE = AC/CD
AB/18.6 = 79.6/34.2
AB/18.6 = 2.33
AB = 2.33×18.6
AB = 43.34 m
Therefore, a surveyor wants to determine the width of a river is 43.34 m.
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PLS HELP WILL GIVE BRAINLIEST IF CORRECT (NO LINKS)
Find the measure of arc BC.
Answer: A 129
Step-by-step explanation:
Because the 2 chords are the same (lines in the circle), the 2 arcs are the same create an equation that makes them equal
3x+24 = 4x -11 >bring x to one side by subtracting both sides by 3x
24 = x -11 > add both sides by 11
35 = x
Now that we have solved for x you need to plug that back into the equation for BC
BC= 4x-11
BC = 4(35) - 11
BC = 140 - 11
BC = 129 >A
In a math class with 19students , a test was given the same day that an assignment was due.There we’re 10 students who passed the test and 14stdents who completed the assignments
In a math class with 19 students, on a day when a test and an assignment were given, there were 10 students who passed the test and 14 students who completed the assignment.
In a math class with 19 students, a test and an assignment were given on the same day.
Out of the 19 students, 10 of them passed the test and 14 students completed the assignment.
This information allows us to analyze the performance and completion rate of the students in the class.
Firstly, we can determine that there are at least 10 students who demonstrated a satisfactory level of understanding and knowledge in the subject matter, as they successfully passed the test.
This indicates that approximately 52.63% (10 out of 19) of the students achieved a passing grade on the test.
Furthermore, we know that 14 students completed the assignment.
This implies that these students fulfilled the requirements and submitted the necessary work within the given timeframe.
Consequently, we can deduce that approximately 73.68% (14 out of 19) of the students in the class completed the assignment.
It's worth noting that there may be overlap between the students who passed the test and those who completed the assignment, as well as students who did both.
However, without additional information, we cannot determine the exact number of students who passed the test, completed the assignment, or did both.
This data provides insight into the performance and diligence of the students in the math class, indicating the proportions of students who met the criteria for passing the test and completing the assignment.
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Which statement is true? 3x-4y=4 or 3x-4y=8
Answer:3x-4y=8
Step-by-step explanation:
80% of the sixth graders have lunch during fourth period if 120 sixth graders had lunch fourth periods how many total six graders are there?
Answer: there is a total of 150 sixth graders
explanation :
0.8x = 120
120 / 0.8 = 150
6th graders at lunch = 150
Select all of the words for which the probability of selecting the letter A at random is 13
Responses
CAB
CAB
ANT
ANT
BANK
BANK
ALPINE
ALPINE
ABOARD
ABOARD
ABRASIONS
ABRASIONS
BASEBOARDS
The words for which the probability of selecting the letter A at random is 1/3 are:
a) CAB
b) ANT
c) ABOARD
Given data ,
Let the probability of selecting the letter A at random be P ( A ) = 1/3
Now , the number of letters in the words CAB are = 3
The number of A's in the word CAB = 1
So , the probability is P ( A ) = 1/3
Now , Now , the number of letters in the words ANT are = 3
The number of A's in the word ANT = 1
So , the probability is P ( A ) = 1/3
And , Now , the number of letters in the words ABROAD are = 6
The number of A's in the word ABROAD = 2
So , the probability is P ( A ) = 2/6 = 1/3
Hence , the probability is solved
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The graph shows the number of weeks of practice (x) and the number of
shots missed in a free-throw drill (y). The equation of the trend line that best
fits the data is y = - + 6. Predict the number of missed shots after 10
weeks of practice.
A. 1
B. 2
C. 3
D. 4
The number of missed shots after 10 weeks of practice is 1
Predicting the number of missed shots after 10 weeks of practice.From the question, we have the following parameters that can be used in our computation:
The line of best fit
Also, we have the equation to be
y = -1/2x + 6
At the 10th weeks, we have
x = 10
Substitute the known values in the above equation, so, we have the following representation
y = -1/2 * 10 + 6
Evaluate
y = 1
Hence, the number of missed shots after 10 weeks of practice is 1
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find the surface area
400Answer:
Step-by-step explanation: