The triangle with sides 54 m , 78 m and 90 m is not a right angle triangle
What is a Triangle?
A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Given data ,
Let the triangle be represented as ΔABC
Now , the value of the sides of the triangle is
AB = 54 m
BC = 78 m
AC = 90 m
Now , for the triangle to be right angle triangle , it should satisfy the Pythagoras Theorem
So , For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Substitute the values in the equation , we get
AC² = AB² + BC²
90² = 54² + 78²
8100 = 2916 + 6084
8100 ≠ 9000
Therefore , the triangle ΔABC is not a right angle triangle
Hence ,
The triangle with sides 54 m , 78 m and 90 m is not a right angle triangle
To learn more about triangles click :
https://brainly.com/question/16739377
#SPJ1
What is the equation of the line that passes through the point (6, 5) and has a
slope of
-1/3
Answer:
y= -1/3x+7
i graphed it so it should be right
What are the roots of the quadratic equation 2x² √ 5x 2 0 Using the quadratic formula?
The roots of the quadratic equation 2x² + 5x - 2 = 0 are -2.7 and 1.3.
The quadratic equation is 2x² + 5x - 2 = 0.
We can solve this equation using the Quadratic Formula:
x = [-b ± Â√(b² - 4ac)] / 2a
Where a = 2, b = 5, and c = -2.
Substituting these values into the formula, we get:
x = [-5 ± Â√(5² - 4(2)(-2))] / 2(2)
x = [-5 ± Â√41] / 4
x = [-5 ± Â√41] / 4
x = [-5 ± 6.4] / 4
x = -2.7 or 1.3
Therefore, the roots of the quadratic equation 2x² + 5x - 2 = 0 are -2.7 and 1.3.
Learn more about quadratic equation here :
https://brainly.com/question/17177510
#SPJ4
What is the formula for the variance of a probability distribution?
The general formula for the variance varies according to the distribution, For the discrete and continuous probability distribution, The expected values formula varies. The variance is given by [tex]E(X^{2})-(E(X))^{2}[/tex] .
What do you mean by probability distribution?A probability distribution is a mathematical function used in probability theory and statistics that estimates the likelihood that various possible outcomes of an experiment will occur. In terms of its sample space and event probability, it is a mathematical description of a random phenomena.
What is standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
If distribution is discrete , E(X) = x*P(x).
If distribution is continuous , E(x) = x *f(x).
Variance = [tex]E(X^{2})-(E(X))^{2}[/tex]
To learn more about probability variance visit:
https://brainly.com/question/13708253
#SPJ4
What is the median of 13 16 12 14 19 12 14 13 14?
There are nine numbers in this set, so the median is the fifth number. The fifth number in this set is 14, so the median is 14.
The median of a set of numbers is the value that is exactly in the middle of the set when it is ordered from least to greatest. In this case, the set of numbers is 13, 16, 12, 14, 19, 12, 14, 13, 14. When we order this set from least to greatest, we get 12, 12, 13, 13, 14, 14, 14, 16, 19. There are nine numbers in this set, so the median is the fifth number. The fifth number in this set is 14, so the median is 14.
To find the median, we first need to arrange the numbers in order from least to greatest. If there is an odd number of numbers in the set, the median is the middle number. If there is an even number of numbers in the set, the median is the average of the two middle numbers. In this case, there are nine numbers in the set, so the median is the middle number.
To learn more about median, visit:
brainly.com/question/28060453
#SPJ4
14.
In the figure (not drawn to scale), MO bisects LMN, mZNMO = (6x +19), and m/LMO = (9x -
14). Solve for x and find ZLMN.
A. x= 11, m ZLMN = 198°
B. x= 11, m ZLMN = 170°
C. x=8, m
D. x=8, m
The value of ZLMN is 58.
What is bisects?
Bisection in geometry is the division of an object into two equal or congruent halves, typically by a line, which is subsequently referred to as a bisector. The segment bisector and the angle bisector are the two forms of bisectors that are most frequently used.
LMO+NMO = LMN,
x+34 + NMO = 6x-28
But, MO bisects LMN, so LMO=NMO
x+34 + x+34 = 6x-28
2x+68 = 6x-28
4x = 96
x = 24
That would makem it
24 + 34 =58 T NMO = 6(24)-28
58 + nmo = 144 - 28 = 119
116- 58 = 58
To learn more about bisects visit.
https://brainly.com/question/17445304
#SPJ1
to use a normal distribution to approximate binomial probabilities, why do we require that both np and n(1 - p) be at least 10?
We require both to ascertain whether the findings are independent, this criterion is applied.
What is Binomial distribution?Statistics frequently employs the binomial distribution as a discrete distribution. When compared to a binomial distribution, the normal distribution is continuous. The chance for 'x' success of an investigation in 'n' trials is represented by the binomial distribution.
As per the given information in the question,
The normal distribution can be used to approximate the binomial distribution. The situation when performing a normal approximation is as follows:
np ≥ 10 and,
np(1 - p) ≥ 10
This criterion is used to determine whether the results are independent.
We are aware that when n and p are combined, the results are independent.
To know more about Binomial distribution:
https://brainly.com/question/14565246
#SPJ1
Tell weather the p=6 is a solution of p + 5 < 12 yes or no
Answer:
yes
Step-by-step explanation:
Mark’s cost does not vary directly with time spent talking because A graph titled Phone Plan Costs shows Mark's cost and Nikiya's cost and shows Time Spent Talking (hours) on the x-axis and Cost (dollar sign) on the y-axis. A straight line showing Mark's cost starts at (0, 20) and goes through (3, 40). A straight line showing Nikiya's cost starts at (0, 0) and goes through (2, 30).
The phone's cost that varies directly with time are given as follows:
Both Mark and Nikiya.
How to obtain the variation of the functions?The variation of the functions can have two classifications, given as follows:
Direct variation: When the input increases, the output also increases.Inverse variation: When the input increases, the output decreases.Mark's cost starts at (0, 20) and goes through (3, 40), meaning that when the input increases from zero to 3, the output increases from 20 to 40, hence it has a direct variation.
Nikiya's cost starts at (0, 0) and goes through (2, 30), meaning that when the input increases from zero to 2, the output increases from 0 to 30, hence it has a direct variation.
Missing Information
The problem asks for whom's function varies directly with time.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
Answer:
Based on the graph shown to the right, whose phone cost varies directly with the amount of time spent talking?
✔ Nikiya’s only
Mark’s cost does not vary directly with time spent talking because
✔ the cost of 0 hours is not 0 dollars
For Nikiya’s plan, the value of the constant of variation is
15,
which represents Nikiya’s
✔ cost per hour
Step-by-step explanation:
Hope this helps :)
PLS HELP :D here is the question attached
Answer:
y=(2/3) x+7
Step-by-step explanation:
2/3 is the slope which would be parallel
what is the value of x ?
Answer:
B - 50
Step-by-step explanation:
the exterior angle is 105, and as it's on a straight line, the interior angle is 180-105=75
75+55=130
angles in a triangle are 180
180-130=50
Answer:50 degrees
Step-by-step explanation: The 105degrees angle forms a supplementary angle with the missing degrees in the triangle
so the missing value which is not requested is 180degrees-105 degrees=75 degrees
No we have two angles inside the triangle. We can now work out the missing angle for x
We know that a triangle adds up to 180 degrees
So x=180-55-75=50 degrees as the answer
the original quantity is 10 and the new quantity is 14, what is the percent increase?
The percent increase
The original amount is 10 and the new quantity is 14 percent increase is 40%
What exactly is a percentage?An quantity or part that is contained in each hundred is known as a percentage. The symbol "%" signifies that it is a fraction with 100 as the denominator.
Here,
The increase in percentage is equal to (New quantity - Original quantity)/Original quantity 100
(14-10)/10* 100.
4/10 × 100
40%
A 40% increase from the original amount to the new quantity may be calculated as a result.
For additional information about the percentage go to the link:
brainly.com/question/14343312
#SPJ1
What is Transform () function used for?
Python's Transform function returns a self-produced data frame with transformed values after applying the function specified in its parameter. This data frame has the same length as the passed data frame.
Now, According to the question:
Python's Transform function returns a self-produced data frame with transformed values after applying the function specified in its parameter. This data frame has the same length as the passed data frame.
What does transform () do?
The transform CSS property lets you rotate, scale, skew, or translate an element. It modifies the coordinate space of the CSS visual formatting model.
The transform() function is used to call function on self producing a Series with transformed values and that has the same axis length as self. Function to use for transforming the data.
Learn more about Transform function at:
https://brainly.com/question/13810353
#SPJ4
For which situation does one quantity change at a constant rate per unit interval relative to another quantity? responses.
An employee earns $14 per hour and a trainer charges $20 for every 30 minutes of training plus a $5 tip are a constant rate per unit interval. Therefore, options A and E are the correct answers.
Given that:
an employee earns $14 per hour.
constant rate of change :
When something has a constant rate of change, one quantity changes in relation to the other. For example, for every half hour the pigeon flies, he can cover a distance of 25 miles. We can write this constant rate as a ratio. For ratios, it's always a good idea to state both units in whole terms.
A). Let the number of hours be x and the total money earned be y
So, y = 14x
B). Let the money earn by an employee each year be a and total earning in a year be b.
So, b=a+3% of a
⇒ b = a + 0.03a
⇒ b = 1.03a
C) Let the number of months be m and the total charge be t
So, t=50+30m
D) Let cost of gym equipment be p, rate of change =8% and time period = 6 months
So,
E) Let the number of hour be x.
Here, 30 minutes = 1/2 hours
Total charge = 20 + 5x/2
An employee earns $14 per hour and a trainer charges $20 for every 30 minutes of training plus a $5 tip are a constant rate per unit interval. Therefore, options A and E are the correct answers.
Learn more about the interval here:
https://brainly.com/question/29197921
#SPJ4
Full question :
For which situation does one quantity change at a constant rate per unit interval relative to another quantity? responses.
Select all that apply
A. An employee earns $14 per hour.
B. An employee earns a 3% raise each year.
C. A gym charges a $50 down payment plus $30 per month.
D. A piece of gym equipment decreases 8% in value every 6 months.
E. A trainer charges $20 for every 30 minutes of training plus a $5 tip.
Please help me !!!!!!!!!!!
Answer:
29
Step-by-step explanation:
You have 1,500 Kilometers and 32 15- kilometer races.
Step 1: Divide 1,500 by 15
step 2: Multiply the answer by 10
step 3:
1) 55% =
2) 75% =
3) 38% =
4) 90% =
5) 33% =
The average test score of RSM students in September increased by 10%. In October it increased by another 15%. By what percent did the average score on the test increase during the two months? PLS PROVIDE SHOW OF STEPS!
The percent that the average score on the test increased during the two months is 12.5%.
By what percent did the average score on the test increase during the two months?It should be noted that mean simply means the average of a set of numbers that are given. In this case, the average test score of RSM students in September increased by 10%. In October it increased by another 15%..
The average of the increase will be:
= (10% + 15%) / 2
= 25% / 2
= 12.5%
The average is 12.5%.
Learn more about mean on:
brainly.com/question/1136789
#SPJ1
What is the solution to the system of equations y equals 4x 10 y equals two?
The solution of the given system of equation is (3, 2).
In the given question we have to find the solution to the system of equations:
y = 4x − 10 and y = 2
We can solve the system of equation using the substitution method.
In substitution method we have to put the the value of one variable from one equation to the other equation.
We have to equations:
y = 4x − 10........................(1)
y = 2...................................(2)
Now putting the value of y from the equation 2 in equation 1
2 = 4x − 10
Add 10 on both side, we get
4x = 12
Divide by 4 on both side, we get
x = 3
Now putting the value of x in equation 1
y = 4(3) − 10
y = 12 − 10
y = 2
Hence, the solution of the given system of equation is (3, 2).
To learn more about substitution method link is here
brainly.com/question/14619835
#SPJ4
The right question is:
What is the solution to the system of equations y = 4x − 10 and y = 2?
What is the probability that the first roll is an even number and the second roll is a number greater than 4? one-sixth one-third two-thirds five-sixths.
Answer:
2
Step-by-step explanation:
By solving simultaneous equations, work out
the coordinates of the point where the two
lines below intersect.
2x+y=8 y
0
y=3x-2
X
The solution of the linear equations 2x + y = 8 and y = 3x - 2 will be (2, 4).
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The equations are given below.
2x + y = 8 ...1
y = 3x - 2 ...2
From equations 1 and 2, then the value of the variable 'x' is calculated as,
2x + 3x - 2 = 8
5x = 10
x = 2
Then the value of the variable 'y' will be calculated as,
y = 3(2) - 2
y = 6 - 2
y = 4
The solution of the linear equations 2x + y = 8 and y = 3x - 2 will be (2, 4).
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ1
In the past month Kaylynn rented one video game in for DVDs. The rental price for the video game was $3.30. The rental price for each DVD was $4.30. What is the total amount that Kaitlyn spent on video game and DVD rentals in the past month.
If in the past month Kaylynn rented one video game in for DVDs. the total amount that Kaitlyn spent on video game and DVD rentals in the past month. is : $7.60.
How to find the total amount?We would have to make use of this formula to find the total amount that Kaitlyn spent on video game and DVD rentals in the past month.
Total amount = (Number of video game × Video game rental price ) + Rental price for DVD
Let plug in the formula
Total amount = (1 × $3.30) + $4.30
Total amount = $3.30 + $4.30
Total amount = $7.60
Therefore we can conclude that the total amount is $7.60.
Learn more about total amount here:https://brainly.com/question/15270500
#SPJ1
What is the median of 1 2 3 4 5 6 7?
Answer:
4
Step-by-step explanation:
since there are 7 numbers, divide it by 2. Then you will get 3 remainder 1. Now, count 3 numbers from the first number and the very next number will be your median.
All of the y values or outputs are called what?
Answer:
range
Step-by-step explanation:
the x values or inputs are called the domain
the y values or outputs are called the range
Find the Slope of (7,-6) and (2,-3)
Answer:
m = -3/5
Step-by-step explanation:
The slope is rise/run or (y2 - y1) / (x2 - x1)
We see the y increase by 3 and the x decrease by 5, so the slope is
-3/5
So, m = -3/5
__________________________________________________________
Hello! In this question, we are going to find the slope of the line with the coordinates given to us in the question.
__________________________________________________________
Explanation:
In the question, we were given the points:
(7,-6)(2,-3)In order to find the slope of the line, we will use the slope formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
We will plug our coordinates into the equation and solve.
__________________________________________________________
Solve:
Plug in the coordinates into the equation and solve.
[tex]m=\frac{-3-(-6)}{2-7} \\\\m=\frac{-3+6}{2-7} \\\\m=\frac{3}{2-7} \\\\m=\frac{3}{-5}\\\\\boxed{m=-\frac{3}{5}}[/tex]
Therefore, our slope for the given coordinates would be [tex]-\frac{3}{5}[/tex]
__________________________________________________________
Answer:
[tex]\boxed{m=-\frac{3}{5}}[/tex]
__________________________________________________________
Additional info:
Learn more about the slope formula below:
https://brainly.com/question/27747743
__________________________________________________________
You are making a coffee
table with a glass top surrounded by a cherry border.
The glass is 3 feet by 3 feet. You want the cherry border
to be a uniform width. You have 7 square feet of cherry
to make the border. What should the width of the border be?
Answer:
6 inches
Step-by-step explanation:
You want to know the uniform width of border around a 3 ft square coffee table that would have an area of 7 square feet.
Border areaThe area of the border is x feet wide by 3 feet long along each of the 4 sides, together with 4 corner squares that are x ft square.
A = 7 = 4(3x +x²)
Completing the square, we have ...
x² +3x +9/4 = 7/4 +9/4 . . . . . . divide by 4, add (3/2)² to both sides
(x +3/2)² = 4 . . . . . . . . . . . . simplify
x +3/2 = √4 = 2 . . . . . . square root
x = 1/2 . . . . . . . . . foot
The width of the border should be 6 inches.
What are all the rational roots of the polynomial f x )= 20x 4 x 3 8x 2 x 12?
The rational roots of the given polynomial are +/- 1, +/- 2, +/- 3, +/- 4, +/- 6, +/- 12, +/- 1/2, +/- 1/4, +/- 1/5, +/- 1/10, and +/- 1/20.
To find the rational roots of the polynomial, we can use the Rational Root Theorem. This theorem states that if a polynomial of the form a_n*x^n + a_{n-1}x^{n-1} + ... + a_1x + a_0 has a rational root, then that root must be of the form p/q, where p is a divisor of a_0 and q is a divisor of a_n.
In this case, the polynomial is
f(x) = 20x^4 - 8x^3 - x^2 + 12x,
so a_0 = 12 and a_4 = 20. The divisors of 12 are 1, 2, 3, 4, 6, and 12. The divisors of 20 are 1, 2, 4, 5, 10, and 20. Therefore, the possible rational roots of the polynomial are
p/q = +/- 1, +/- 2, +/- 3, +/- 4, +/- 6, +/- 12, +/- 1/2, +/- 1/4, +/- 1/5, +/- 1/10, and +/- 1/20.
We can then test each of these values to see if they are actually roots of the polynomial. If a value is a root, then substituting it into the polynomial will result in a value of 0.
Therefore, the rational roots of the given polynomial are +/- 1, +/- 2, +/- 3, +/- 4, +/- 6, +/- 12, +/- 1/2, +/- 1/4, +/- 1/5, +/- 1/10, and +/- 1/20.
To learn more about rational roots,
visit; brainly.com/question/18514997
#SPJ4
This theorem states that if a polynomial of the form a_n*x^n + a_{n-1}x^{n-1} + ... + a_1x + a_0 has a rational root, then that root must be of the form p/q, where p is a divisor of a_0 and q is a divisor of a_n.
f(x) = 20x^4 - 8x^3 - x^2 + 12x,
p/q = +/- 1, +/- 2, +/- 3, +/- 4, +/- 6, +/- 12, +/- 1/2, +/- 1/4, +/- 1/5, +/- 1/10, and +/- 1/20.
Therefore, the rational roots of the given polynomial are +/- 1, +/- 2, +/- 3, +/- 4, +/- 6, +/- 12, +/- 1/2, +/- 1/4, +/- 1/5, +/- 1/10, and +/- 1/20.
If x:(x+3) = 2:3
find x
Answer: -6
Step-by-step explanation:
If x:(x+3) = 2:3, we can set up the following equation:
x / (x+3) = 2/3
Next, we can multiply both sides of the equation by 3 to get rid of the fraction on the right side:
3 * (x / (x+3)) = 3 * (2/3)
This gives us:
x / (x+3) = 2
Finally, we can multiply both sides of the equation by (x+3) to get rid of the fraction on the left side:
x = 2 * (x+3)
We can then solve for x by rearranging the terms on the right side of the equation:
x = 2x + 6
Subtracting 2x from both sides gives us:
x - 2x = 6
This simplifies to:
-x = 6
Finally, we can divide both sides of the equation by -1 to solve for x:
x = -6
Therefore, x = -6.
What is a rational function example?
The example of a rational function is f ( x) = x 2 − 1 2 x + 21. , we can represent this function in terms of ratio of p and q.
Other than than a real world example can be that , a cookie being divided among two children , the representation will be , 1 / 2.
A graph of a rational function has asymptotes which are of three types and that is what makes them different from the rest of the functions. Rational functions are the functions which can be represented in the ratio of two polynomials p and q. The solution of this equation is know as the roots of the equation.
To learn more about rational function
brainly.com/question/28193264
#SPJ4
What are the common factors of 14 28 and 42?
How do u solve 4x 2y =- 12?
To solve this equation, use the distributive property to rewrite it as 4x - 2y = 12. Then, solve the equation using either addition or subtraction.
To solve the equation 4x 2y = -12, the first step is to use the distributive property to rewrite the equation as 4x - 2y = 12. This allows us to solve the equation using either addition or subtraction. If we choose to use addition, we can add 2y to both sides of the equation to get 4x + 2y = 12. We can then subtract 2y from both sides to get 4x = 12 - 2y. Dividing both sides of the equation by 4 gives us the solution x = (12 - 2y)/4. If we choose to use subtraction, we can subtract 2y from both sides of the equation to get 4x - 2y = 12. We can then add 2y to both sides to get 4x = 12 + 2y. Dividing both sides of the equation by 4 gives us the solution x = (12 + 2y)/4. In either case, the solution is x = (12 ± 2y)/4.
Addition:
4x + 2y = 12
4x = 12 - 2y
x = (12 - 2y)/4
Subtraction:
4x - 2y = 12
4x = 12 + 2y
x = (12 + 2y)/4
Learn more about equation here
https://brainly.com/question/29657992
#SPJ4
the sides of the smallest box are 30% of the length of the sides of the largest box. the volume of the largest box is 7784 cubic inches more than the volume of the smallest box. let x represent the length of the side of the largest box. write an equation that represents the difference in the volume of the two boxes.
The length of the side of the smaller box is 6 and the length of the side of the larger box is 20. The equation for the difference in volume of the boxes is, y3 - x3 = 7784 .
Let us consider the length of side of small box be x inch & length of large box be y inch.
Length of smallest box is 30% of the length of the side of the largest box
x=30%*y
= 30 * y / 100
x = 3y / 10
Volume of the smallest box is x3.
volume of the largest box is y3.
Volume of largest box is 7784 cubic inches more than the volume of smallest box. Therefore,
y3 = x3 + 7784
= (3y/ 10 )3 + 7784
= 27y3 / 1000 + 7784
y3 - 27y3 / 1000 = 7784
973 y3 / 1000 = 7784
973 y3 = 7784 * 1000
y3 = 7784 * 1000 / 973
y3 = 8000
y = 20
Now find the smaller side.
x = 3y / 10
putting the value of y this we get,
x = 3 * 20 / 10
x= 6
To learn more about difference in volume of the rectangular box please visit:
https://brainly.com/question/21287229
#SPJ4