Determine whether following set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer.
10,16,18
The following set of numbers, 10, 16, and 18, can be the measures of the sides of an acute triangle.
To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.
let a = 10, b = 16, and c = 18
a + b > c 10 + 16 > 18 26 > 18 True
a + c > b 10 + 18 > 21 28 > 16 True
b + c > a 16 + 18 > 21 34 > 10 True
To know what type of triangle based on the length of its side:
1. Take the sum of the squares of the two smaller sides.
10^2 + 16^2 = 356
2. Compare it to the square of the largest side.
18^2 = 324
324 < 356
If the sum of the squares of the 2 is larger than the square of the 3rd, it is an acute triangle.
if they are equal, it is a right triangle
if they are smaller, then it is an obtuse triangle.
Hence, 10, 16, and 18 can be the measure of the sides of an acute triangle.
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Determine whether following set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer.
20,21,31
The following set of numbers, 20, 21 and 31, can be the measures of the sides of an obtuse triangle.
A triangle is a polygon with three sides and three vertices.
To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.
let a = 20, b = 21, and c = 31
a + b > c 20 + 21 > 31 41 > 31 True
a + c > b 20 + 31 > 21 51 > 21 True
b + c > a 21 + 31 > 21 52 > 20 True
To know what type of triangle based on the length of its side:
1. Take the sum of the squares of the two smaller sides.
20^2 + 21^2 = 841
2. Compare it to the square of the largest side.
31^2 = 961
961 > 841
If the sum of the squares of the 2 is larger than the square of the 3rd, it is an acute triangle.
if they are equal, it is a right triangle
if they are smaller, then it is an obtuse triangle.
Hence, 20, 21 and 31 can be the measure of the sides of an obtuse triangle.
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Given the rule what is the new coordinate? Show all of your work.
Rule: (x, y) → (x − 7.5, y + 6.8)
-
Original coordinate: (5, 3)
Using translation concepts, the new coordinates of the point are given as follows:
(-2.5, 9.8).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x). Examples are shift left, shift right, shift down, shift up, vertical stretching, horizontal stretching, vertical compression, horizontal compression, reflection over the x-axis, reflection over the y-axis, and rotations by a determined amount(in degrees). All these translations have predetermined rules that we apply to the figures.
For this problem, the translation rule for each point is given as follows:
(x, y) → (x - 7.5, y + 6.8)
This translation rule means that the figure is shifted:
7.5 units left, because x -> x - 7.5.6.8 units up, because y -> y + 6.8.The original coordinate is given by:
(5,3), meaning that x = 5 and y = 3.
Applying the rule to the original coordinates, we have tat:
5 - 7.5 = -2.5.3 + 6.8 = 9.8.Hence the new coordinates, after the rule is applied to the original coordinates, are given as follows:
(-2.5, 9.8).
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Solve each system by elimination or substitution.
2 = 4y - 3x , 5x = 2y - 3
Using elimination method, the solution of the given system of equations is (-4/7, 1/14)
A system of equation can be solved using:
graphical methodsubstitution methodelimination methodThe given system of equations:
2 = 4y - 3x ............ (1)
5x = 2y - 3 .............. (2)
Re-arrange the equations so that all variables are on the left sides:
2 = 4y - 3x
⇔ -3x + 4y = 2 ....... (3)
5x = 2y - 3
⇔ 5x - 2y = -3 ....... (4)
Choose one variable to eliminate. Let us choose y. Multiply equation (4) by 2, we get:
10x - 4y = -6 ....... (5)
Add equation (3) and (5)
-3x + 4y = 2
10x - 4y = -6 +
7x = -4
x = -4/7
Substitute back x = -4/7 into equation (3):
-3x + 4y = 2
-3.(-4/7) + 4y = 2
12/7 + 4y = 14/7
4y = 2/7
y = 2/28 = 1/14
Hence, the solution is (-4/7, 1/14)
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The average of the five numbers in a list is 54. the average of the first two numbers is 48. what is the average of the last three numbers?
The average of the last three numbers is 58 if the average of the five numbers in a list is 54. the average of the first two numbers is 48.
What is average?It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.
It is given that:
The average of the five numbers in a list is 54. and the average of the first two numbers is 48.
54 = sum of the five numbers/5
54x5 = sum of the five numbers
270 = sum of the five numbers
48 = sum of the two numbers/2
48x2 = sum of the two numbers
96 = sum of the two numbers
Sum of three numbers = 270 - 96
Sum of three numbers = 174
The average of the last three numbers = 174/3 = 58
Thus, the average of the last three numbers is 58 if the average of the five numbers in a list is 54. the average of the first two numbers is 48.
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If you throw a dart, what is the probability of
hitting the area of the shaded region?
Use 3.14 for T. Round answers to nearest Hundredth(two decimal places).
The probability of hitting the area of the shaded region is 0.21 (in the form of two decimal places) when you throw a dar.
What is probability?The probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
We have been given that the radius of the circle = 2cm
So one side of square = 2+2 = 4cm
Area of circle = πr² = (3.14) ×(2)²= (3.14)×4 = 12.57cm²
Area of square = (a)² = (4)² =16cm²
Then the area of the shaded region = 16−12.57 = 3.43cm²
So the probability of hits in the shaded region = 3.43/16 = 0.2144
Round to the nearest Hundredth (two decimal places).
The probability of hits in the shaded region = 0.21
Hence, the probability of hitting the area of the shaded region is 0.21 (in the form of two decimal places) when you throw a dar.
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How do you show your work to 6x-4=-24
Answer:
x = - 10/3
Step-by-step explanation:
1. Add 4 to both sides
6x = -20
2. Simplify
x = - 10/3
Find the diameter and radius of a circle with the given circumference. Round to the nearest hundredth. (Lesson 10-1) C=78 ft
The diameter and radius of circle is 24.84 feet and 12.42 feet.
We are given the circumference of circle. So, using the formula of circumference, we will find the diameter. As we know, the radius of circle is half of its diameter.
Performing calculation now -
Circumference = π×d, where d stands for diameter of circle.
Taking the value of π as 3.14.
Keep the values in formula to find the diameter of circle
Diameter = 78÷3.14
Performing division
Diameter = 24.840
Rounding to nearest hundredth -
Diameter = 24.84 feet
Now, calculating radius by the formula -
Radius = diameter÷2
Radius = 24.84÷2
Performing division to find the radius of circle
Radius = 12.42 feet
Hence, the diameter and radius of circle is 24.84 feet and 12.42 feet.
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The local gym holds three 45-minute workout sessions and two 30-minute sessions each week. Judy attended all of the sessions this week but left 5 minutes early during the 30-minute sessions and 10 minutes early during the 45-minute sessions. How many total minutes did Judy work out for the week?
The local gym holds three 45-minute workout sessions and two 30-minute sessions each week. Then the, total number of minutes Judy worked out for the week was 155 minutes.
We are to determine the total number of minutes Judy worked out for the week.
The gym holds three 45-minute workout sessions and two 30-minute sessions each week
So,
We can write,
The total number of minutes the gym holds workout sessions is
3 × 45 + 2 × 30
= 135 + 60
= 195 minutes
Also, from the information,
Judy left 5 minutes early during the 30-minute sessions and 10 minutes early during the 45-minute sessions.
The total number of minutes Judy didn't attend is
= 3 × 10 + 2 × 5
= 30 + 10
= 40 minutes
Then,
The total number of minutes Judy worked out for the week was,
= 195 minutes - 40 minutes
= 155 minutes
Therefore,
The total number of minutes Judy worked out for the week was 155 minutes.
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A building in a city has a rectangular base. The length of the base measures 75 ft less than twice the width. The perimeter of this base is 840 ft. What are the dimensions of the base?
The dimensions of the base are 180 feet in length and 165 feet in width.
Let the width of the base be "x".The length of the base is 75 less than twice the width.The length of the base is 2x-75.The perimeter of the base is given to be 840 feet.The perimeter of a rectangular base is twice the sum of its length and its width.The perimeter of a rectangular base is 2[tex]\times[/tex][(2x-75) + x].840 = 2[tex]\times[/tex](3x-75)420 = 3x-753x = 495x = 165Thus, the width is 165 feet.The length is equal to 2(165-75) = 2[tex]\times[/tex]90 = 180 feet.The whole length of any closed shape's boundary is known as its perimeter. Let's use an illustration to try to comprehend this. You may have a sizable square-shaped farm, for instance. You now decide to fence your farm in order to protect it from stray animals. Finding the entire length of the farm's boundary is as simple as multiplying the length of one side of the farm by 4. There are a lot of situations like this when we can be applying the perimeter-finding notion without even realizing it.
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Classify the relationship between the pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
∠2 and ∠8
The relationship between the ∠2 and ∠8 is that both are alternate exterior angles
Given,
The angles =∠2 and ∠8
Here,
∠2 and ∠8 are both lies on opposite sides of the transversal and they are nonadjacent exterior angles.
So, ∠2 and ∠8 are alternate exterior angles
Hence, the relationship between the ∠2 and ∠8 is, both are alternate exterior angles
The complete question is :
Classify the relationship between the pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
∠2 and ∠8
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How do I Evaluate this expression
|-3d-6|+|-5-d²| for d = -3
After evaluating the expression | - 3 d - 6 | + | - 5 - d² | for d = - 3, we get that the result is 17.
We are given the expression:
| - 3 d - 6 | + | - 5 - d² |
We need to evaluate the expression for d = - 3
Put the value of d as - 3 in the expression, we get that:
| - 3 ( - 3 ) - 6 | + | - 5 - ( - 3 )² |
Solving the expression further, we get that:
| 9 - 6 | + | - 5 - 9 |
| 3 | + | - 14 |
= 3 + 14
= 17
Therefore, after evaluating the expression | - 3 d - 6 | + | - 5 - d² | for d = - 3, we get that the result is 17.
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When using PEMDAS to evaluate a numerical expression, we move from
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
Multiplication and Division - whatever comes first from left to right (i.e. 6*7*2, do 6*7 first)
Addition and Subtraction - same thing as multiplication and division, whatever comes first
How do you find significant figures? Explain in detail with examples.
Find the distance between each pair of points.
R(8,0), S(-9,6)
The distance between the points R and S is 18.03 units.
We know that for points P(x1, y1) and Q(x2, y2) the distance between points is given as:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
In this question, we have been given two points R(8,0), S(-9,6)
We need to find the the distance between the points R(8,0) and S(-9,6)
Let R(8,0) = (x1, y1) and S(-9,6) = (x2, y2)
Using distance formula the distance between the points R and S is:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\d=\sqrt{(-9-8)^2+(6-0)^2} \\\\d=\sqrt{(-17)^2+6^2}\\\\ d=\sqrt{289+36}\\\\ d=\sqrt{325}\\\\d=18.03~~units[/tex]
Therefore, the distance between the points R and S is 18.03 units.
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Which statement is always true?
O If two variables have a negative correlation, then the variables do not have a cause-and-effect
relationship.
O If two variables do not have a cause-and-effect relationship, then the variables have no
correlation.
O If two variables have a cause-and-effect relationship, then the variables will have a correlation.
O If two variables have a positive correlation, then the variables have a cause-and-effect
relationship.
Answer:
If two variables have a cause-and-effect relationship, then the variables will have a correlation.
Step-by-step explanation:
Nagi has 8 red marbles
and 12 yellow marbles.
His mom doubled his red
and yellow marbles for
his birthday. Use the
distributive property to
show how many marbles
Nagi has now.
Answer:
16red 24yellow in total 40
Step-by-step explanation:
8 x 2 =16
12 x 2 = 24
A car is traveling at 34miles/hour down a road. A rabbit appears 0.040km away on the road. If the car takes 2.5seconds to stop, will the car hit the rabbit or stop before?
What is the distance between the rabbit and where the car stops?
Answer:
The rabbit will get hit because the car takes too long to break
Step-by-step explanation:
2/106 = x/901 what is x?
x=567
Step-by-step explanation:
2
If x²- y² = 20 and x+y = 10, then find x
Answer:
x = 6
Step-by-step explanation:
x² - y² is a difference of squares and factors as (x + y)(x - y)
given
x² - y² = 20 , then
(x + y)(x - y) = 20 ← substitute x + y = 10
10(x - y) = 20 ( divide both sides by 10 )
x - y = 2 → (1)
x + y = 10 → (2)
add (1) and (2) term by term to eliminate y
2x + 0 = 12
2x = 12 ( divide both sides by 2 )
x = 6
A rectangular mural measures 234 inches by 245 inches. rhianon creates a new mural that is 33 inches longer. what is the perimeter of rhianon's new mural?
The new mural created by Rhianon, which is 33 inches longer, has a perimeter of 1024 inches.
Perimeter refers to the total distance around a two-dimensional figure. The perimeter of a rectangle is the sum of all its 4 sides and is given by the formula
P = 2l + 2w
where l = length
w = width
If a rectangular mural measures 234 inches by 245 inches, length is usually longer than the width, and Rhianon creates a new mural that is 33 inches longer, then the length of Rhianon's mural is:
l = 245 inches + 33 inches
l = 278 inches
If the new mural is the same as the width of the rectangular mural and its length is 278 inches, then the perimeter can be solved using the formula for the perimeter of a rectangle.
P = 2l + 2w
P = 2(278 inches) + 2(234 inches)
P = 556 inches + 468 inches
P = 1024 inches
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can someone please help me
Answer:
KN = 45, NM= 31, m<K = 61° m<L = 119°, m<M = 61°
Step-by-step explanation:
Given: KL = 31 LM = 45 N = 119°
This is a parallelogram so sides will equal.
KL = NM (31) LM = KN (45)
The inside of a parallelogram equals 360°. Opposite angles are congruent.
L = N (119°) So, 119 + 119 = 238
360 - 238 = 122
122 ÷ 2 = 61°
So, K = 61° M = 61° L = 119°
WILL GIVE U EXTRA POINTS :d
Two angles are Complementary. If the measure of one of the angles is 58.0 degrees, what is the measure of the other angle? Answer to the first decimal place, IE 79.5.
Answer: x = 32.0°
Step-by-step explanation:
When the sum of two angles is equal to 90 degrees, they are called complementary angles.
x + 58° = 90°
x = 90° - 58°
x = 32.0°
Jason is adding a climbing wall to his little brother's swing-set. If he starts building 5 feet out from the existing structure, and wants it to have a 60°C angle, how long should the wall be?
If Jason starts building 5 feet out from the existing structure, and wants it to have a 60° angle, then the wall should be 10 feet long.
For given question,
Jason starts building 5 feet out from the existing structure, and wants it to have a 60°C angle.
The ground and the side of the play structure make a 90° angle.
So, the given triangle would be a - 30°- 60° - 90° - triangle.
The short side is 5 feet. The climbing wall will be the hypotenuse.
The angle opposite to the short side is 5 feet.
Now we need to find the hypotenuse.
Consider the sine of angle 30°
sin(30°) = 5/hypotenuse
1/2 = 5/hypotenuse
hypotenuse = 5 × 2
hypotenuse = 10
Therefore, if Jason starts building 5 feet out from the existing structure, and wants it to have a 60° angle, then the wall should be 10 feet long.
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For some time, Johannes Kepler thought that the Platonic solids were related to the orbits of the planets. He made models of each of the Platonic solids. He made a frame of each of the platonic solids by fashioning together wooden edges. How many wooden edges did Kepler have to make for the cube?
Kepler had 9 wooden edges to make for the cube.
As it is given in the data that the platonic solids are related to the orbits of the planets, and he made models of each of the Platonic solids. Kepler made a frame of each of the platonic solids by fashioning together wooden edges. At that time six planets were discovered and out of the six, two platonic solids were considered as cube. A cube is a three dimentional structure which has 8 corners and 12 edges.
So the number of edges = 4 x 2 + 1
= 9
Kepler has 9 wooden edges to make for the cube, to make a frame of each of the platonic solids by fashioning together wooden edges.
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Please help my head hurts to much right now to think!!
Answer:
A) y=10x-4
Step-by-step explanation:
There are 10 full boxes which means 10x (since x is the boxes of pizza)
but there are 4 already eaten slices in one, which can be subtracted at the end, making the equation y=10x-4.
Hope this helped and feel better soon! :)
Write an equation in slope-intercept form for each line described.
passes through (6,2) , parallel to y=-2/3x+1 .
The equation in slope-intercept form is y = -2/3x + 6
Given,
Points (x, y) = (6, 2)
Parallel to y = -2/3x + 1
Now,
Recall that a parallel line to the one given has to have the same slope. The slope of the line given is "-2/3" (the coefficient that accompanies "x").
Therefore the equation of a parallel line has to be of the form:
y = -2/3x + b
2 = -2/3(6) + b
2 = -12/3 + b
2 = -4 + b
b = 6
So the equation now becomes:
y = -2/3x + 6
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What is a simpler form of the complex fraction?
b. x-2 / x + 2 / x+1 / 3 / x-1 - 1/x+1
The simpler form of the complex fraction [tex]\frac{x-2}{\frac{x+2}{\frac{x+1}{\frac{3}{\frac{x-1-1}{x+1} } } } }[/tex] is equal to
3(x-2)² / (x+2)(x+1)².
As given in the question,
Given complex fraction is [tex]\frac{x-2}{\frac{x+2}{\frac{x+1}{\frac{3}{\frac{x-1-1}{x+1} } } } }[/tex]
Simplify the given complex form :
[tex]\frac{x-2}{\frac{x+2}{\frac{x+1}{\frac{3}{\frac{x-1-1}{x+1} } } } }\\\\= \frac{x-2}{\frac{x+2}{\frac{x+1}{\frac{3}{\frac{x-2}{x+1} } } } }\\\\=\frac{x-2}{\frac{x+2}{\frac{x+1}{\frac{3}{\frac{x-2}{x+1} } } } } \\\\=\frac{x-2}{\frac{x+2}{\frac{(x+1)^{2}}{3(x-2)} } } \\\\=\frac{3(x-2)^{2}}{(x+2)(x+1)^{2}}[/tex]
Therefore, the simpler form of the complex fraction [tex]\frac{x-2}{\frac{x+2}{\frac{x+1}{\frac{3}{\frac{x-1-1}{x+1} } } } }[/tex] is equal to 3(x-2)² / (x+2)(x+1)².
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Simplify 2(b-a)+5(b-a) and justify each step in your simplification.
The Simplified value of the expression 2(b-a)+5(b-a) is 7b-7a .
Distributive property for real numbers "a", "b" and "c" is defined as
a(b-c)=a*b-a*c.
In the given question
=2(b-a)+5(b-a)
Applying Distributive Property
=2*b-2*a+5*b-5*a
=2b-2a+5b-5a
Combining the like terms together
=2b+5b-2a-5a
=7b-7a (adding the like terms )
Therefore , the Simplified value of the expression 2(b-a)+5(b-a) is 7b-7a .
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Add or subtract. Simplify where possible. State any restrictions on the variables.
3/4x - 2/x²
The simplication of the given expression is (3x - 8) /4x² and the restriction on the variable in the denominator of the given expression is x ≠ 0.
According to the given question.
We have an expression 3/4x - 2/x^2
Since, we have to simplify the above expression.
Therefore,
3/4x - 2/x²
⇒ (3x - 8) /4x²
Hence, the simplication of the given expression is (3x - 8) /4x².
Also, we have to find the restriction on variable.
As we know that, we never divide by 0, a restriction on the variable of a rational function with a linear denominator would be any value of the variable that makes the linear denominator equals to 0.
So, for the restriction on the variable.
Set the denominator equals to 0.
⇒ 4x² = 0
Solve for x
x = 0 ( because 4 ≠ 0)
The denominator is 0 when x = 0. This is the only value that makes the given expression undefined.
Therefore, the restriction on the variable in the denominator of the given expression is x ≠ 0.
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