The key is to check whether the given side measures satisfy the triangle inequality theorem or not, if yes then we can create a unique triangle, if no then no triangle can be created, and if the given measures are the perimeter of a triangle, we can create many triangles.
When will you be able to create a unique triangle, no triangle, and/or many triangles?When given three side measures of a triangle, the following scenarios can occur:
Unique triangle: If the three side measures given are the lengths of the three sides of a triangle and they satisfy the triangle inequality theorem, then we can create a unique triangle. The triangle inequality 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.
No triangle: If the three side measures given do not satisfy the triangle inequality theorem, then it is not possible to create a triangle with those side lengths.
Many triangles: If the three side measures given are the perimeter of a triangle, and we are allowed to vary the lengths of the three sides of the triangle within a certain range, then we can create infinitely many triangles.
Example: A triangle with perimeter 12cm, we can create a unique triangle with sides 3,4,5, or we can create many triangle with sides (2,5,5), (4,4,4),(3,4,5) and so on.
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What is tan formula?.
The tangent formula is thus written as follows:
tan θ = (opposite side) / (adjacent side)
where "opposite side" refers to the side that is across from angle x and "adjacent side" refers to the side that is right next to it.
The tangent (tan) function is discussed in the tangent formulas. Let's assume a right-angled triangle where x is the acute angle.
The tangent formulas are trigonometric formulas that describe the tangent function. One of the six trigonometric functions, the tangent function, also known as "tan," is the ratio of the opposite side to the adjacent side.
Numerous trigonometric identities and formulas can be used to obtain numerous tangent function-related formulas.
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How do you draw a triangle XYZ?.
A ruler and a pencil may be used to quickly create the triangle XYZ.
The length of the sides and the angle of the triangle XYZ are the fundamental concepts needed to start.
The steps to design a triangle whose three sides are known are as follows:
1. Mark point A, which will serve as one of the triangle's vertices.
2. Set the required length AB for the compass breadth.
3. Cut an arc by setting the compass's width to the required length of the side AC.
4. Cut an arc by setting the compass's width to the appropriate length of side BC.
You may thus obtain the needed triangle.
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50 points!!!
7. Write and solve an inequality for the value of x.
The value of x must be between -18 and -6. The solution has been obtained using Triangle inequality theorem.
What is Triangle inequality theorem?
The triangle inequality theorem explains how a triangle's three sides interact with one another. This theorem states that the sum of the lengths of any triangle's two sides is always greater than the length of the triangle's third side. In other words, the shortest distance between any two different points is always a straight line, according to this theorem.
We are given three sides of a triangle as 8, 6 and x+20
Using Triangle inequality theorem,
⇒8+6 > x+20
⇒14 > x+20
⇒-6 > x
Also,
⇒x+20+6 > 8
⇒x+26 > 8
⇒x > -18
Also,
⇒x+20+8 > 6
⇒x+28 > 6
⇒x > -22
From the above explanation it can be concluded that x is less than -6 but greater than -22 and -18.
This means that x must lie between -18 and -6.
Hence, the value of x must be between -18 and -6.
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What is the value of the expression mnp+(−n) if m = 5, n = 8, and p = –2?
Answer:
The answer is -88.
Step-by-step explanation:
We can substitute the given values into the expression to find its value:
mnp + (-n)
= (5)(8)(-2) + (-8)
= -80 + (-8)
= -88
So, the value of the expression mnp + (-n) if m = 5, n = 8, and p = -2 is -88.
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Have a nice day.
The radian measure of an angle θ is the length of the?
a) opposite side
b) diameter
c) hypotenuse
d) arc
The radian measure of an angle theta is the length of the arc that subtended angle 2Pi
We can measure angle in two form degrees or Radian.
What is the meaning of radian?
Radian can be described as a measure of angle subtended by a circular arc. It can be defined as the ratio of the arc length subtending angle to the radius of circle.
One radian is the measure of angle subtended by by an arc that is equal to the radius of circle.
Therefore,the radians measure an angle theta the length of arc.
Θ =s/r ,
where, theta is the angle subtended, s is the arc length and r is the radius of circle.
We know that the 2π radians = 360 degrees.
That subtends the angle in a circle of radius 2Pi
Therefore ,The radian measure of an angle theta is the length of the arc that subtended angle 2 Pi
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In 1997, a city had a population of 220,000 people. Each year ince, the population ha grown by 6. 2%. Let t be the number of year ince 1997. Let y be the city’ population. Write an exponential function howing the relationhip between y and t
An exponential function is a mathematical function that models a relationship between a variable (in this case, t) and a constant multiplied by the power of another variable (in this case, y). The general form of an exponential function is y = ab^t, where
a is the initial valueb is the growth factor (also called the base)t is the independent variable (in this case, the number of years since 1997).In this specific scenario, we are told that in 1997, the population of a city was 220,000 people and that each year since then, the population has grown by 6.2%. We can use this information to find the values of a and b in the exponential function.
The initial value, a, is simply the population of the city in 1997, which is given as 220,000.
To find the value of b, we need to determine how much the population increases each year as a proportion of the current population. We are told that the population grows by 6.2% each year. This means that if the population is currently P, the population will be (1 + 0.062)P the next year. We can write this as P(1.062) as the growth factor b.
So, combining the values of a and b, we have:
y = 220,000 * (1.062)^t
This equation tells us that the population of the city, y, is equal to the initial population of 220,000 multiplied by the growth factor of 1.062 raised to the power of t, where t is the number of years since 1997. This equation expresses the relationship between population and time.
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Moira can olve 15 math problem in 20 minute. How long will it take her to olve 21 math problem?
So it will take 945 sec to solve 21 math problem.
As per the data given in the above question are as bellow,
The details provided are as bellow,
Moria solve 15 math question in 20 minutes,
We have to determine how long will it take her to solve 21 math problem?
First taking how much time its take to solve one question ,
So, Total number of question divide the total time we get,
Substitute the value in above equation we get,
=15* 60 =900 Sec
=900/20
=45 sec
So the time taken to solve 21 question will be,
=45*21
=945 sec
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Rachel plays a game where she can randomly select 1 of 3 cards. If she selects Card A, she will win $10. If she selects Card B, she will win $15. If she selects Card C, she will win $50. What is the expected value of winning?
Therefore , the solution of the given problem of probability comes out to be the probability is 1/3 = 0.33 so the least value is winning $10.
What specifically does the probability method entail?Calculating the likelihood that a statement is true or that an event will take place is the focus of probability theory, a branch of mathematics. Probabilities can be expressed using the numbers 0 , 1, fractions with just a range of 0% - 100%, or an another few characters. the proportion of occurrences among a group of equally likely options out of all conceivable outcomes.
Here,
Given :
In a game, Rachel has the option of picking any one of three cards at random. She will receive $10 if she chooses Card A.
Choosing Card B will earn her $15.
She will receive $50 if she chooses Card C.
Thus ,
expected value of winning is $10 which is the least prize that is $10 on selected card A.
As the probability is 1/3 = 0.33
Therefore , the solution of the given problem of probability comes out to be the probability is 1/3 = 0.33 so the least value is winning $10.
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Answer:
Step-by-step explanation:
$25
How do you graph y =- 2x 6?.
To determine the x-intercept, solve for x while replacing y with 0. To obtain the y-intercept, solve for y while replacing x with 0.
( 3, 0 ) are the x-intercepts.
(0, 6) are the y-intercepts.
What does Y = - 2x 6's y-intercept represent?6. Y-intercept In order to find x, set x = 0 in the equation y = 2x - 6. It is -6 for the y-intercept. By selecting "New Example" below, you may read some additional examples.
What on a graph does Y = - 6 mean?The Y-value of every point 6 units below the X-axis is actually equal to -6. As a result, the plane's points that are 6 units below the X-axis form the graph of y = -6.
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Ivan tart with 150$ and ave 5 each week uma ha 45 and ave 20 each week write linear equation to repreaent ivan and uma aving
The equation that represent Ivan having is: 150+ 5x and Uma having is: 45 + 20x
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
To solve this problem, we have to state the equation using the information of the problem:
Information about the problem:
Ivan start = 150$Ivan's weekly profit= 5$Uma start = 45$Uma's weekly profit= 20$Ivan equation = ?Uma equation= ?Writing the equation according to the information gave, we have:
y(Ivan) = 150+ 5x
y(Uma) = 45 + 20x
Where:
Amount earned = yNo. weeks passed = xThe relationship between the No. weeks passed and the amount earned is: linear and direct because when the number of weeks increases (x), the amount earned (y) will decrease.
The "y" variable is the dependent variable, because it will change according to the number of weeks passed (x).
The "x" variable is the independent variable, because it doesn't depend on any other value, just the number of weeks passed.
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what do we know about data points that are plotted below our y=x? (line of best fit)
Data points plotted below the line y=x (also known as the line of best fit) indicate that the observed value is less than the predicted value.
What exactly is a math graph?
A math graph is a visual representation of mathematical data or concepts. It typically uses Cartesian coordinates (x, y) to plot points, lines, and shapes that help to illustrate mathematical relationships. Graphs can be used to represent many types of mathematical information, including functions, equations, data sets, and geometric shapes. They are commonly used in fields such as science, engineering, economics, and statistics to analyze and understand complex information. Graphs are also an important tool for conveying mathematical ideas and results in a clear and understandable way.
This could be due to measurement errors, outliers, or other factors that are not accounted for in the model used to generate the line of best fit. It's important to note that the location of data points relative to the line of best fit can provide insight into the underlying pattern or relationship between the variables being studied, but further investigation is needed to determine the specific cause of the discrepancy.
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How do you graph an absolute value piecewise function?.
The process to graph an absolute value piecewise function is explained below .
Let us consider the Absolute value function as :
y = | x -2 | ;
this absolute function can be written in piecewise wise form as :
⇒ [tex]y =\begin{array}{cc} \{ & \begin{array}{cc} -x+2 & x < 2 \\ x-2 & x\geq 2 \end{array}\end{array}[/tex] ;
this piecewise function means that the main function divides into two pieces ,
for any input value that is less than 2 , the function"-x+2" will be used , and
for any input value greater than or equal to 2, the function "x-2" , will be used ;
for example : if x = 3 , then ⇒ y = 3 - 2 = 1 ;
and is x = 1 , then ⇒ y = -1 +2 = 1 ;
the points to be plotted are (3,1) and (1,1) .
The graph of this absolute value piecewise function is shown below .
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show your work to get brainliest
what is the value of m?
Answer:
m = 0.28
Step-by-step explanation:
you can create a proportion as follows:
[tex]\frac{2.8}{m}[/tex] = [tex]\frac{4}{5.4}[/tex]
cross-multiply to get:
4m = 2.8(5.4)
4m = 15.12
m = 15.12/4
m = 3.78
Answer:
m = 3.78
Step-by-step explanation:
Find the factor of how much bigger the second triangle is:
5.4 - 4 = 1.4
1.4/4 = 0.35
Then, multiply it by the top side
0.35 x 2.8 = 0.98
Finally, add the top number and the product
0.98 + 2.8 = 3.78
There is your answer!
A pet tore employee put only ilver fih and goldfih in an aquarium. The ratio of the number of goldfih to the total number of fih in the aquarium wa 6 to 11. Which number could be the number of ilver fih the employee put in the aquarium?
The number of silverfish employees put in the aquarium is 11.
The ratio is defined as a comparison of two quantities of the same unit to determine how much of one quantity is contained in the other. Ratios are divided into two sorts.
The first is a part-to-part ratio, and the second is a part-to-whole ratio. The part-to-part ratio expresses the relationship between two distinct entities or groupings.
Given that,
The ratio of the number of g total number of fish in the aquarium = 6: 11
Let us assume that the total number of silverfish employees put in the aquarium is x
So, The total number of fish = 6+11 = 17 out of which 11 are silverfish.
Complete question: A pet store employee put only silverfish and goldfish in an aquarium. The ratio of the number of g total number of fish in the aquarium was 6 to 11. Which number could be the number of silverfish employees put in the aquarium?
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Find the slope. Find the slope.
Answer:
Step-by-step explanation:
Hello! The slope formula is rise over run, or (y2 - y1)/(x2 - x1). You can choose either y-coordinate for y2 and y1 and either x-coordinate for x2 and x1. Since you are given two points already, use those. The first coordinate in a coordinate pair is always x, and the second coordinate is always y (x, y). (0, 0) is the origin, or the point where both lines x and y meet up. The leftmost point is 3 squares below that, and y is a vertical line. The coordinates of the leftmost point on the line is (0, -3). The rightmost point on the line is located at the coordinate pair of (1, 0). Any point located below or left of the origin is negative. A point below the origin means the y is negative, and a point left of the origin means the x coordinate is negative. You now have two coordinate pairs, which is all you need to figure out the slope of the line. Use the formula (y2 - y1)/(x2 - x1) to get your answer. Substitute the y values in for the first part. The two y values are 0 and -3. The two x values are 0 and 1. You now have (0 - (-3)/(1 - 0). 0 - (-3) = 3 because two negatives make a positive. You now have 3/1. If you have to simplify this, then the slope is 3. Another easy way is shown below:
Hope this helped you solve slopes!
solve 2y = -3x and y = -2x + 2 using elimations
If anybody could help explain how to solve this as well that would be great! I have a quiz on this tomorrow so any explanation on how to solve it is helpful
The solutions to the system of equations are x = 4 and y = -6
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the first equation be represented as A
Now , the value of A is
2y = -3x
Divide by 2 on both sides of the equation , we get
y = ( -3/2 )x be equation (1)
Let the second equation be represented as B
Now , the value of B is
y = -2x + 2 be equation (2)
Substituting the value of y from equation (1) in equation (2) , we get
( -3/2 )x = -2x + 2
Adding 2x on both sides of the equation , we get
2x - ( 3/2 )x = 2
( 4x - 3x ) / 2 = 2
x/2 = 2
Multiply by 2 on both sides of the equation , we get
x = 4
Substitute the value of y in equation (1) , we get
y = ( -3/2 ) 4
y = -3 ( 2 )
y = -6
Therefore , the value of x and y is 4 and -6 respectively
Hence , the equations are solved
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−3x(4x−2),2x(6x 2 +4x−3) multiply
(2x−3)(5x+6),multipy the polynomial by the box method
2x(6x2 + 4x − 3) × (2x − 3)(5x + 6)
= (2x)2(6x2 + 4x − 3)(5x + 6)
= 12x3(5x + 6) + 8x2(5x + 6) − 6x(5x + 6)
= 60x4 + 48x3 − 45x2 − 36x
Sides of a triangle are (x^2-1), (x^2+1) and 10cm. If the area of the triangle is 120cm^2, find x
If the area of the triangle is 120 cm^2, the value of x is equal to 6.
How to calculate the area of a triangle?Mathematically, the area of a triangle can be calculated by using this mathematical expression:
Area of a triangle (A) = 1/2 × b × h
Where:
b represents the base area of a triangle.h represents the height of a triangle.According to Hero's Formula area of triangle by Heron of Alexandria, if a, b, c are the side lengths of a triangle, then, the area of a triangle can be calculated by using this mathematical expression:
Area of a triangle (A) = √[s(s − a)(s − b)(s − c)]
Where:
s = (a + b + c)/2
s = (x + x + 1 + 2x - 1)/2
s = 4x/2
s = 2x
Substituting the parameters into Hero's Formula formula, we have the following;
x√10 = √[2x(2x − x)(2x − x - 1)(2x − 2x + 1)]
x√10 = x√2(x − 1)
√10 = √2(x − 1)
Taking the square of both sides, we have:
10 = 2(x - 1)
10 = 2x - 2
2x = 12
x = 12/2
x = 6.
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How to solve 2x 3y 10?.
To solve the equation 2x + 3y = 10 we need to plot the graph for the equation by calculating the intercepts for the same.
Here we see that we are given the equation
2x + 3y = 10
Since we do not have any other equation we will solve this by plotting it on a graph by the intercepts.
Intercepts of both the x and y axes are obtained by equating the other to 0.
Hence to get the x-intercept, we need to equate y to 0
Hence we get
2x = 10
or, x = 5
Hence for the y-intercept, we equate x to 0 to get
3y = 10
or, y = 10/3
By plotting these points and drawing a line through them we will get the graph for the equation.
Now to obtain a unique solution, we need to follow similar steps for the other equation and the intersecting point will give us the solution.
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Complete Question
How to solve 2x + 3y = 10?
During a food drive, one classroom collected 268268268 cans of food and another classroom collected 424424424 cans. They packed the cans in boxes with 242424 cans in each box.
Answer:
268268268 + 424424424 = 692692692
So there are 692692692 cans of food
692692692 - 242424 × x = 0
x = Amount of boxes used
x = 2857.36021186...
The rounded answer is 2857.
What is the area of this triangle in the coordinate plane?
25. 0 units²
27. 5 units²
50. 0 units²
55. 0 units²
Previous
Next
The area of this triangle in the coordinate plane with coordinates A( 4,5) , B(1,2) and C( 6,2) is equals to the 15 unit². So, option (d) is correct.
The basic formula for the area of a triangle is (1/2) × base × altitude. But we have to calculate the area of a triangle in coordinate geometry. Coordinate geometry is defined as the study of geometry using coordinate points. If coordinates of the triangle are(x₁, y₁), (x₂, y₂), and (x₃, y₃) then the area of the triangle is defined as Area = 1/2[ x₁(y₂ - y₃) + x₂( y₃ - y₁) + x₃(y₁ - y₂) ]
We have a triangle ABC in coordinate plane in above figure. The coordinates of triangle are A( 4,5) , B(1,2) and C( 6,2). Here, x₁ = 4 , y₁ = 5 , x₂ = 1 , y₂ = 2 ,x₃ = 6 , y₃ = 2. So, Area of ∆ABC
= 1/2[ 4( 2 - 2)+ 1( 2 - 5) + 6(5 - 2)
= 0 + (-3) + 18 = 15
Hence, the required area is 15 unit².
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Complete question:
What is the area of this triangle in the coordinate plane? See the above figure.
a)25. 0 units²
b) 27. 5 units²
c) 50. 0 units²
d) 15. 0 units²
How do you teach division to Year 3?.
Chunking is a good way to introduce your child to some of the more basic concepts of division, and once they have come to terms with this they can then move onto the short method of division.
Now, According to the teaching Ideas:
Start with a clear definition of division. Reinforce Mathematical language expectations with clear definitions for dividend, divisor and quotient. Explore word problems with pictorial support.Model how to use manipulatives to represent the grouping in the word problem.We have four basic arithmetic operations i.e., addition, subtraction, multiplication, and division. Amongst these four operations, the division is one of the major operations we use in our daily activities. It is the process of splitting a large group into equal smaller groups. For example, divide 25 by 5. Division fact for this example will be, 25 ÷ 5 = 5.
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please show the Mod base Work
Pretend that it's 3:00 now. Answer the following
questions, but don't worry about AM/PM.
A
What time will the clocks minutes show 220 minutes from
now?
Time after 220 minutes will be 6:40 on the clock.
Add 60 minutes to the end minutes and take an hour off the end time hours if the start minutes are greater than the end minutes. Subtract the start time minutes from the final minutes as you go. Add the hours from the start to the end. To find the solution, combine the results for hours and minutes.
1 hour = 60 mins
220 minutes = hours?
⇒ 220 / 60
⇒ 3 4/6
⇒ 3 hours and 40 minutes
At present, it's 3:00,
The time after 220 minutes will be -
⇒ 3 + 3.7 hours
⇒ 6.7 hours
The clock will show time 6: 40.
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Julianne and Vito caught 6 flounders, which was 75% of the fish they caught. How many fish did Julianne and Vito catch altogether?
Answer:
8 FISHES
Step-by-step explanation:
There are several ways to solve this but lets use proportion cus I feel it's easier. So what you are looking for is simply 100% of the fish they caught.!
So therefore, 75% = 6
100% = (100 × 6) ÷ 75
= 600 ÷ 75
= 8 FISHES
Geometry 6.2
What is m∠N
Check the picture below.
Periodical Express is a newspaper printing company. They printed 450 copies of The Informer in just 15 seconds! They next need to print 300 copies of the Sport Report.
If they print at the same rate, how many seconds will it take to print the Sport Report?
Answer:
10 seconds
Step-by-step explanation:
create a proportion
450 copies over 15 seconds = 300 copies over 't' seconds
cross-multiply to get:
450t = 4500
t = 10
it will take 10 seconds for Periodical Express to print 300 copies of the Sports Report if they maintain the same printing rate.
What are arithmetic operations?
Arithmetic operations are basic mathematical operations that include addition, subtraction, multiplication, division, and others.
Periodical Express printed 450 copies of The Informer in 15 seconds, which means they printed 450/15 = 30 copies per second.
To find out how long it would take to print 300 copies of the Sports Report, we just need to divide the number of copies by the rate of printing.
So, the calculation is 300 / 30 = 10 seconds
Therefore, it will take 10 seconds for Periodical Express to print 300 copies of the Sports Report, if they maintain the same printing rate.
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The um of Joy' age and her brother' age i $24. Her brother' age i $3 year older than twice Joy' age. What i the difference, in year, between Joy' age and her brother' age?
To determine their ages, the substitution approach is used.
Joy's age and her brother's age are differed by 10 years.
What is linear system?
It is an system of equation where the maximum power of the variable is consistently 1. a single-dimensional object with no breadth. It consists of an endless number of dots placed side by side.
Given
The combined ages of Joy and her brother total 24.
Joy's older brother is three years older than twice his age she is.
To locate
Joy's age as compared to that of her brother.
Assume that Joy is x years old and her brother is y.
then in line with the first circumstance.
x + y = 24 ...(1)
And according to the second condition.
2x + 3 = y ...(2)
On solving equations 1 and 2. We get
x + 2x + 3 = 24
x = 7
Then
y = 2x + 3
y = 17
Then, the difference between Joy's age and her brother's age.
y - x = 17 - 7 = 10
Thus, the difference between Joy's age and her brother's age is 10.
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soit B(x)=4x²-12x. Résoudre dans R l'équation B(x)=-9
Answer:
B(-9) = 432
Step-by-step explanation:
B(x) = 4x² - 12x
B(-9) = 4(-9)² - 12(-9)
B(-9) = 4(81) + 108
B(-9) = 324 + 108
B(-9) = 432
Answer:
432
Step-by-step explanation:
B(x) = - 9
Replacing the value of x in the equation,
4x² - 12x
= 4 * (-9)² - 12 * (-9)
= 4 * 81 + 108
= 324 + 108
= 432
_________
hope this helps!
How do you find no solution?.
We can find no solution by the condition; if (a₁/a₂) = (b₁/b₂) ≠ (c₁/c₂), then there will be no solution.
A linear equation in two variables is a type of equation in the form ax + by + c = 0 where a, b, c ∈ R, a, and b ≠ 0. A linear equation with no solution is named an inconsistent pair of linear equations.
Suppose the pair of linear equations is in two variables, x and y.
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂ = 0
Where a₁, b₁, c₁, a₂, b₂, c₂ are all real numbers.
Note that, a₁² + b₁² ≠ 0, a₂² + b₂² ≠ 0
If (a₁/a₂) = (b₁/b₂) ≠ (c₁/c₂), then there will be no solution.
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The square root parent function is translated so that the endpoint is located at (-7,7). Write an equation that represents this new function
The square root function is translated so that the endpoint is located at (-7,7), [tex]g(x)= \sqrt{x+7} +7[/tex] and this can be determined by using the transformation.
The square root parent function is translated so that the endpoint is located at (-7,1).
The following steps can be used to determine the equation that represents this new function:
Write the square root parent function.[tex]f(x) =\sqrt{x}[/tex]
The graph of the above function is translated by a factor of 7 in the negative x-axis that is in the left direction.Then the graph obtained in the above step is translated by a factor of 7 in the positive y-axis in the upward direction.Write the equation of the function that obtains in step 3.[tex]g(x)= \sqrt{x+7} +7[/tex]
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