No triangles can be constructed from line segments of 4 cm, 5 cm, and 9 cm in length, because the Triangle Inequality Theorem requires the sum of any two sides to be greater than the third side, which is not the case here.
The lengths of three line segments are 4 centimeters, 5 centimeters, and 9 centimeters. To determine how many triangles can be constructed with these segments as sides, we need to apply the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, the sum of the two shortest sides, 4 cm and 5 cm, is 9 cm, which is equal to the length of the longest side. Because one condition for the Triangle Inequality Theorem is not strictly being met (the sum must be greater, not equal), we can conclude that no triangles can be constructed using these three segments as sides.
When constructing triangles from three measures of angles or sides, it's important to realize that these conditions determine whether you can create a unique triangle, more than one triangle, or no triangle at all.
43 coins, no nickels, $4.51 equal amount amount of pennies and dimes, how many of each coin
You scored the following grades on your first three math tests: 71, 78, 81. You only have one test remaining. What is the highest possible test average you can get?
Estimate the probability that if the company books 225 persons. not enough seats will be available. 1-.81^225
The Frostburg-Truth bus travels on a straight road from Frostburg Mall to Sojourner Truth Park. The mall is 3 miles west and 4 miles south of the City Center. The park is 3 miles east and 5 miles north of the Center. How far is it from the mall to the park to the nearest tenth of a mile/12482564/8273204d?utm_source=registration
Please please help me with this
Two positive numbers have a difference of four and a product of 96 what are the numbers
Answer:
The two positive numbers are 12 and 8.
Explanation:
The first phrase in the sentence tells us the difference between numbers equals 4, which can be represented a - b = 4
The second phrase tells us when multiplied together, it equals 96, which can be represented by the ab = 96, or a(b) = 96
So, first step is to list the factors of 96. I prefer to list them as pairs:
1, 96; 2, 48; 3, 32; 4, 24; 6, 16; and 8, 12
Now we plug each these pairs into the first equation to see if they satisfy the equation.
96 - 1 = 95 24 - 4 = 20
95 > 4 20 > 4
48 - 2 = 46 16 - 6 = 10
46 > 4 10 > 4
32 - 3 = 29 12 - 8 = 4
29 > 4 4 = 4
Because a = 12 and b = 8 satisfies both equations that represent the given sentence, the two positive numbers are 12 and 8.
Q # 15 find the volume of the sphere
John plays a game in which he throws a baseball java questions
Use a calculator to find the mean and standard deviation of the data. Round to the nearest tenth. 6, 7, 19, 7, 18, 7
Answer:
The mean is 10.7 and the standard deviation is 5.6.
Step-by-step explanation:
To find the mean, add together all of the data and divide by the number of data points:
(6+7+19+7+18+7)/6 = 64/6 = 10.7
To find the standard deviation, subtract each data point from the mean, square them and find the sum:
(6-10.7)²+(7-10.7)²+(19-10.7)²+(7-10.7)²+(18-10.7)²+(7-10.7)²
=(-4.7)²+(-3.7)²+(8.3)²+(-3.7)²+(7.3)²+(-3.7)²
=22.09+13.69+68.89+13.69+53.29+13.69 = 185.34
Next divide this by 6, the number of data points:
185.34/6 = 30.89
Lastly, take the square root:
√30.89 = 5.6
A bag of marbles contains 12 red marbles 8 blue marbles and 5 green marbles. If three marbles are pulled out find each of the probabilities. Find the probability of pulling three green marbles out with replacement
[tex] |\Omega|=25\cdot24\cdot23=13800\\
|A|=5\cdot4\cdot3=60\\\\
P(A)=\dfrac{60}{13800}=\dfrac{1}{230}\approx0.4\% [/tex]
The probability of an event is calculated as = [tex] \frac{Favorable outcomes}{Total number of outcomes} [/tex]
Here, the total number of outcomes = 12 red marbles + 8 blue marbles + 5 green marbles
So, total marbles = 25 marbles
Number of favorable or green marbles = 5 marbles
Probability of three green marbles if drawn with replacement = [tex] \frac{Number of favorable or green marbles}{Total number of marbles} [/tex] ×[tex] \frac{Number of favorable or green marbles}{Total number of marbles} [/tex] × [tex] \frac{Number of favorable or green marbles}{Total number of marbles} [/tex]
Probability of three green marbles if drawn with replacement = [tex] \frac{5}{25} [/tex] × [tex] \frac{5}{25} [/tex] × [tex] \frac{5}{25} [/tex]
Probability of three green marbles if drawn with replacement = [tex] \frac{1}{125} [/tex]
If y varies inversely as the square of x, and y=7/4/ when x=1, find y when x=3
triangle abc and triangle bcd have vertices A(-6, -7), B(-6, 4), C(2, -7), D(8, 4) what is the area in square units of trapezoid ABCD which is formed by the two triangles?
Lance lived in Portugal and Brazil for a total of 14 months to learn Portuguese. He learned an average of 130 words per month when he lived in Portugal, and an average of 150 new words per month when he lived in Brazil. In total, he learned 1920 new words write a system of equations to represent this situation. Use x to represent Portugal, and y to represent Brazil.
I don't understand this problem can you help?
A right rectangular prism is shown. What shape best describes the cross section cut perpendicular to the base of a right rectangular prism? Parallelogram Trapezoid Rectangle Square
The shape that best describes the cross-section cut perpendicular to the base of a right rectangular prism is a rectangle.
A cross-section cut perpendicular to the base of a right rectangular prism will always result in a rectangular shape.
This is because a rectangular prism has six faces, and the base of the prism is one of those faces.
When you make a cross-section cut perpendicular to the base, you are essentially slicing through the prism parallel to one of its other faces.
Since the base is a rectangle, the cross-section will also be a rectangle.
In summary, the cross-section cut of a right rectangular prism perpendicular to its base will consistently yield a rectangular shape due to the inherent geometry of the prism.
for such more questions on perpendicular
https://brainly.com/question/1091880
#SPJ2
limit approaches infinity of 3^n / 3n+1
Which of the following points are more than 5 vertical units away from the point left-parenthesis 0 comma negative 2 right-parenthesis? Choose all that apply. (2 points) left-parenthesis 6 comma negative 2 right-parenthesis left-parenthesis negative 8 comma negative 2 right-parenthesis left-parenthesis 0 comma negative 8 right-parenthesis left-parenthesis 0 comma 4 right-parenthesis
Given point is (0, -2).
Given options are A(6, -2); B(-8, -2); C(0, -8); D(0, 4).
It says to select the options that are more than five units vertically away from the given point.
"Vertically away" means the x-coordinate would be same and y-coordinate would be shifted up or down.
Since it says to shift more than five units vertically away, so we must have :-
y > -2 + 5 or y < -2 - 5.
Therefore, y > 3 or y < -7.
Hence, option C and D are correct i.e. (0, -8) and (0, 4).
Which equation represents a hyperbola with a center at (0,0), a vertex at (0,60), and a focus at (0,-65)
Answer:
So for everybody in the future, a clarification is d)y^2/60^2 -x^2/25^2=1
Ans: [tex]\( \frac{y^2}{60^2} - \frac{x^2}{25^2} = 1 \)[/tex]
The standard form equation of a hyperbola with the center at the origin (0,0), a vertical axis, a vertex at (0, a), and a focus at (0, c) is given by:
[tex]\[\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1\][/tex]
where [tex]\(c\)[/tex] is the distance from the center to the focus, and [tex]\(b\)[/tex] is related to [tex]\(a\) and \(c\)[/tex] by the equation [tex]\(c^2 = a^2 + b^2\)[/tex].
In your case, the center is at (0,0), the vertex is at (0,60), and the focus is at (0,-65). The distance from the center to the focus is [tex]\(c = 65\)[/tex], and the distance from the center to the vertex is [tex]\(a = 60\)[/tex]. Using the relationship [tex]\(c^2 = a^2 + b^2\)[/tex], we can find b:
[tex]\[65^2 = 60^2 + b^2\][/tex]
Solving for b:
[tex]\[4225 = 3600 + b^2\][/tex]
[tex]\[b^2 = 625\][/tex]
[tex]\[b = 25\][/tex]
Now, substitute [tex]\(a\), \(b\), and \((h, k) = (0, 0)\)[/tex] into the standard form equation:
[tex]\[\frac{y^2}{60^2} - \frac{x^2}{25^2} = 1\][/tex]
So, the equation of the hyperbola is:
[tex]\[\frac{y^2}{3600} - \frac{x^2}{625} = 1\][/tex]
[tex]\( \frac{y^2}{60^2} - \frac{x^2}{25^2} = 1 \)[/tex]
If sinø= 4/7, what is cosø?
The service plan for edith's cell phone charges her $29.50 a month for 300 minutes and 10¢ a minute for each additional minute over the 300 minutes. if edith uses 400 minutes this month, how much money will she have to pay?
find the value of q in the following system so that the solution to the system is(4,2) 3x-2y=8
2x+3y=Q
Trip bought an icecream cone that is 4 inches tall with a radius of 2 inches
What is the equation of the line that passes through the points (-1,2) and (6,3) in slope intercept form
[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ &&(~ -1 &,& 2~) &&(~ 6 &,& 3~) \end{array} \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{3-2}{6-(-1)}\implies \cfrac{3-2}{6+1}\implies \cfrac{1}{7} \\\\\\ \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-2=\cfrac{1}{7}[x-(-1)]\implies y-2=\cfrac{1}{7}(x+1) \\\\\\ y-2=\cfrac{1}{7}x+\cfrac{1}{7}\implies y=\cfrac{1}{7}x+\cfrac{1}{7}+2\implies y=\cfrac{1}{7}x+\cfrac{15}{7}[/tex]
Answer:
Step 1: Choose (x1, y1). (6,3)
Step 2: x2= -1 y2=2
Step 3: 1/7
Step 4: b= 15/7
What is the equation of the line in slope-intercept form?
B) y=1/7x+15/7
Step-by-step explanation:
The bold numbers are the answers.
( I need mo pts)
stella received a package in the shape of rectangular prism. the box has a length of 21/2 feet, a width of 11/2 feet, and a height of 4 feet. stella wants to cover the box with wrapping paper. how much paper will sge need?
Answer:
Step-by-step explanation:
To get the amount of paper required to cover the box, we find the area of the box. The dimensions of the box are as follows:length=21/2 ftwidth=11/2 ftheight=4 ftArea of the box is given by the formula:SA=2lw+2lh+2hwSA=2(21/2×11/2)+2(21/2×4)+2(11/2×4)SA=2(231/4)+2(42)+2(11/2×4)SA=115.5+84+44SA=243.5 ft²Stella will need 243.5 ft²
Which number is not in scientific notation?
A: 1.10 ⋅ 103
B: 4.0 ⋅ 1016
C: 7.03 ⋅ 10−2
D: 350 ⋅ 102
the anser would be c fo it to be in scientific notation you have to have an exponet
if a plane leave the ski resort every hour. the first plane leaves at 10 and the second plane leaves at 4 how man planes leave each day
which of the following best describes the English expression the product of two and a number minus eleven
Suppose the spread of a direct contact disease in a school is modeled by the exponential function P(t) =
2,000
1 + e3 − t
where P(t) is the total number of people infected after t hours. What does 2,000 represent in equation?
A) the rate at which the disease spreads
B) the number of the people in the school
C) the expected change in number of people infected
Eliminate
D) the total number of people infected after t hours
Complete the inequality. 9% ___ 0.4
78 million in scientific notation
Answer:
[tex]78\ million=7.80\times 10^7[/tex]
Step-by-step explanation:
A number N can be written in scientific notation as :
[tex]N=p{\circ}0\times 10^q[/tex]
Where
p is the any real number
q is any integer
Here, the given number is 78 million. Firstly, we must know meaning of 1 million.
Since, [tex]1\ million=10^6[/tex]
[tex]78\ million=78.0\times 10^6[/tex]
To convert the above number in scientific notation, we can shift the decimal before 8 such that,
[tex]78\ million=7.80\times 10^7[/tex]
Hence, this is the required solution.