A triangle with the given side lengths 6cm , 8cm , and 10cm represents a scalene right angled triangle.
As given in the question,
For the given triangle,
Side lengths of the given triangle is equal to :
6cm , 8cm , and 10cm
Longest side length of the given triangle is equal to 10cm.
Apply Pythagoras theorem to check whether the given triangle is right angled triangle or not.
( longest side ) ² = ( side 1)² + ( Side 2)²
Hypotenuse = longest side
Side 1 = base
Side 2 = Altitude
In the given triangle,
10²
= 100
= 36 + 64
= 6² + 8²
which satisfies the condition of Pythagoras triplets.
All the sides are of different measure so it is a scalene triangle.
Therefore, a triangle with given side lengths is a scalene right angles triangle.
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Question
Points A , B , and C are three vertices of a rectangle. Plot the three points. Then find the coordinates of the fourth point, D , to complete the rectangle. Finally, write the equation of the line that passes through points B and D and forms a diagonal of the rectangle. �
(
−
2
,
3
)
,
�
(
4
,
3
)
,
�
(
4
,
−
1
)
A(−2,3),B(4,3),C(4,−1)
The fourth co-ordinate of the rectangle is D (-2, -1). The equation of the line that passes through the points B and D is 3y = 2x + 3.
The given points are:
A(−2,3), B(4,3), C(4,−1)
When we plot these points on the graph we can easily estimate the fourth point which will be equidistant from A as the point C is from B and from the point C as the point A is from B.
Therefore, the diagonal points are B(4, 3) and D(-2, -1).
The equation of the line between these two points is:
(y - y1) = ((y2 - y1)/(x2 - x1)) (x - x1)
(y - 3) = ((-1 -3)/(-2 - 4)) ( x - 4)
y - 3 = (2/3) (x - 4)
3y - 9 = 2x - 8
3y = 2x + 1
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Ekaterina’s favorite expression is 4x – 4. Alban’s favorite expression is 8x – 24. What value of x makes these two expressions equal?
Answer:
x = 5
Step-by-step explanation:
You are solving for a x that can, when plugged in, equate both given expressions. To do so, set each given expression equal to each other:
4x - 4 = 8x - 24
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& roots)
Multiplications
Divisions
Additions
Subtractions
~
First, subtract 8x and add 4 to both sides of the equation:
4x (-8x) - 4 (+4) = 8x (-8x) - 24 (+4)
4x - 8x = -24 + 4
-4x = -20
Next, divide -4 from both sides of the equation:
(-4x)/-4 = (-20)/-4
x = -20/-4
x = 5
5 is your answer.
Check:
Plug in 5 for x in both given expressions:
4x - 4
4(5) - 4
= 20 - 4
= 16
-
8x - 24
8(5) - 24
= 40 - 24
= 16
~
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how to do distributive law in factorization?
Answer: it’s lar and we can’t compete against each other
Step-by-step explanation:
a mathematical organization is producing a set of commemorative license plates. each plate contains a sequence of five characters chosen from the four letters in aime and the four digits in $2007$. no character may appear in a sequence more times than it appears among the four letters in aime or the four digits in $2007$. a set of plates in which each possible sequence appears exactly once contains $n$ license plates. find $\frac{n}{10}$.
On solving the provided question we can say that there are 7!/(7-5)! potential sequences if 0 appears 0 or 1 times in the sequence.
what is a sequence?A collection of numbers, or "terms," is referred to as a sequence. Examples of terms are 2, 5, and 8. Some sequences can be made endlessly lengthy by taking advantage of a particular pattern they follow. Use the example of 2,5,8 and add 3 to continue the sequence. There are formulas that demonstrate where to look for words within a sequence. A collection of objects that are in some order is known as a sequence in mathematics (or events). It resembles a set in that it contains pieces (also called elements or terms). The entire, perhaps infinite number of ordered objects are referred to as the sequence's length. the act of placing two or more items in a logical order. Chronological.
N/10 has a value of 372.
The letters can be selected from the words "AIME" or "2007."
The only number that can be repeated twice is 0; there are seven different characters that can be chosen.
There are 7!/(7-5)! potential sequences if 0 appears 0 or 1 times in the sequence.
There are 2520 possible sequences if 0 appears 0 or 1 times in the sequence.
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Which expression is equivalent to 24(807). A 20(8)+4(8)+20(7)+
Answer:
C
Step-by-step explanation:
807 is equal to 800 + 7, and 24 is equal to 20 + 4. Using the distributive property, we get 20(800) + 4(800) + 20(7) + 20(7)
Answer:
C
Step-by-step explanation:
Because 24*807 in distributive property is C
I choose a random integer n between 1 and 10 inclusive. What is the probability that for the n I chose, there exist no real solutions to the equation x(x+5)=−n? Express your answer as a common fractio
The probability is 1/10.
The equation x(x+5) = -n can be rewritten as x^2 + 5x + n = 0. To find the solutions of this equation, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a, where a = 1, b = 5, and c = n.
For there to be no real solutions, the discriminant (b^2 - 4ac) must be negative. The discriminant is 5^2 - 4(1)(n) = 25 - 4n. So for there to be no real solutions, 25 - 4n < 0, or n > 6.25.
Since the integer n is between 1 and 10 inclusive, the only value that would not have a real solution is n = 7. Therefore, the probability that for the randomly chosen n there exist no real solutions is 1/10.
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The double number line shows that Jéssica lives 48 km from the capitol. 0 Distance (km) H Percentage 0% Distance (km) 48 12 60 48 Percentage Complete the table to show different percentages of the distance. + + 100% 1% of 48 km % of 48 km % of 48 km
The different percentages of the distance is 100%, 25% & 125%.
How to find the table to show different percentage of the distance?The Latin word "per centum," which means "by the hundred," served as the basis for the English word "percentage." Percentages are fractions with the denominator 100. In other words, it is the relationship between a part and a whole in which the value of the whole is always assumed to be 100.
A percentage is a fraction or ratio in which the whole value is always 100. For instance, Sam would have received 30 out of a possible 100 points if he had received 30% on his math test. It is expressed as 30/100 in fractional form and 30:100 in ratio form.
48 = 100% of 48
12 = 25% of 48
60 = 125% of 48
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Is the function even, odd, or neither. Use the graph to answer the question
Answer:
A. Even
Step-by-step explanation:
Even Function
A function is "even" when:
[tex]f(x) = f(-x) \;for\; all\; x\\\\[/tex]
Stated in other terms, the function graph is symmetric about the vertical(y-axis). The right part of the function graph about the y-axis is a reflection of the left part of the function graph about the y-axis
Looking at the function graph, we see it is indeed symmetric about the y-axis
Hence an even function
Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 5 hours. Together they charged a total of $1150. What was the rate charged per hour by each mechanic if the sum of the two rates was $95 per hour?
Answer: Let's call the hourly rate of the first mechanic "r1" and the hourly rate of the second mechanic "r2".
We know that the total time they worked is 20 hours + 5 hours = 25 hours.
We also know that the sum of their hourly rates is $95 per hour, so:
r1 + r2 = $95
We can use this information along with the total amount they charged, $1150, to find out how much each mechanic charged. We know that the total amount charged is the product of the number of hours worked and the hourly rate. So we can use the following equation:
(20 hours * r1) + (5 hours * r2) = $1150
Now we can substitute the equation r1 + r2 = $95 into the above equation and solve for r1:
(20 hours * r1) + (5 hours * (95 - r1)) = $1150
20r1 + 475 - 5r1 = 1150
15r1 = 675
r1 = $45/hour
To find out the hourly rate of the second mechanic, we can use the equation r1 + r2 = $95
r2 = $95 - r1
r2 = $95 - $45
r2 = $50/hour
So the first mechanic charges $45 per hour and the second mechanic charges $50 per hour.
Step-by-step explanation:
the hawks won 65% of their 60 games this year . how many games did they win ?
Answer: 24 games
Step-by-step explanation: 60-60%=24
find the inequality represented by the graph
For each pair of triangles below, state
whether the triangles are congruent, not
congruent or if it is impossible to tell.
a)
65°
27 cm
38 cm
19 cm
65°
27 cm
43°
43°
b)
80°
58°
42°
42°
80°
58%
C)
12 cm
82°
12 cm
37°
37%
82°
Answer: all are congruent
Step-by-step explanation:
a. The pair of triangles are not congruent.
b. It is impossible to tell about congruency.
c. The pair of triangles are congruent.
Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.
These triangles can be slides, rotated, flipped and turned to be looked identical.
a. The given triangles are not congruent.
The triangle has same measures but the side lengths are different.
So the pair of triangles are not congruent.
b. The given pair of triangles are might be congruent if they have side lengths same.
But in the given triangles the side lengths are not measured.
So it is impossible to tell.
c. The given pair of triangles have same measures and same side lengths.
By AAS rule the pair of triangles are congruent.
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g eight children are divided into two teams each containing 4 children to play a game against each other. how many different divisions are possible?
70 different divisions are possible when eight children are divided into two teams each containing 4 children to play a game against each other
so this is what's known as a combination. a combination is a group where the order does not matter. to solve a combination, you use this equation:
n! / (r! *(n-r)!)
n is the total number of objects being sorted (8)
r is the group you need to sort them into (4)
(i know it's 2 groups of 4 but if you solve this for 1 group, the other group is automatically made of the remaining kids)
definition of !:
a number with a ! means 1*2*3...*that number (so that number multiplied by every number smaller than it all the way to one)
so we put 8 and 4 in this equation:
8! / (4! *(8-4)!)
simplify:
8! / *(4! 4!)
multiply out:
(8*7*6*5*4*3*2*1) / (4*3*2*1 * 4*3*2*1)
and put that in your calculator
you will get 70 different divisions are possible
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______ are measures of center that summarize a typical data point
in a data set.
A. Mean and median
B. Median and interquartile range
C. Mean and mean absolute deviation
D. Mean absolute deviation and interquartile range
How do you solve ratio word problems in 7th grade?
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other
What is an equivalent ratios?
A ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.
Two ratios are equivalent to each other if one of them can be expressed as the multiple of the other. Hence, to get the equivalent ratio of another ratio, we have to multiply the two quantities (antecedent and consequent) by the same number.
Given ratios are 2:1 and 3:1
we can write it as 2/1 and 3/1.
The lcm of 2 and 3 is 6.
Multiply denominator of both ratio with 6, we get
2/6 and 3/6 And we can see both the ratios are not equal.
Hence, there are not equivalent ratios.
4:1 and 8:3 are equivalent ratios -----> is false, because 4:1 is equivalent to 8:2
11:2 and 2:11 are equivalent ratios------> is false (because, are reciprocal ratios, not equivalent ratios)
3:1 and 9:3 are equivalent ratios ------> is true
because 3:1 multiply both sides by 3 -----> 3*3:1*3=9:3
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Which statement is the best interpretation of the value 29,864 in the quadratic regression equation?
The company has an initial loss of about $29,864.
The company has an initial profit of about $29,864.
The company needs to sell about 29,864 units to break even.
The company needs to sell about 29,864 units to maximize its profit.
The interpretation of the value, 29,864, in the quadratic regression equation is the initial loss incurred by the company. The correct option is therefore;
The company has an initial loss of about $29,864What is a quadratic regression equation?A quadratic regression equation is the equation of the parabola that corresponds of best fits the points of the dataset on the coordinate plane.
The points on the graph of the question, obtained from a similar question, posted online are;
Number of units [tex]{}[/tex] Profits ($)
500 [tex]{}[/tex] -10000
1200 [tex]{}[/tex] 3000
2500 [tex]{}[/tex] 27000
3200 [tex]{}[/tex] 40000
3600 [tex]{}[/tex] 45000
4300 [tex]{}[/tex] 47000
5000 [tex]{}[/tex] 45000
6750 [tex]{}[/tex] 20000
The polynomial regression equation that corresponds to the points in the above table, obtained with MS Excel is presented as follows;
y = -0.004·x² + 34.637·x - 29864
Where;
y = The profit made
x = Number of units
When the company produces 0 units, x = 0, we get;
y = -0.004 × 0² + 34.637 × 0 - 29864 = -29864The 29864 is therefore the loss of $29864, of the company when the company produces zero units.
The correct option is therefore;
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A study selected independent random samples of 50 dogs and 60 cats and found that 38 of the dogs and 15 of the cats could be trained to fetch a ball. Do these data provide convincing evidence that the proportion of all dogs that can be trained to fetch a ball is greater than the proportion of all cats that can be trained to fetch a ball
On solving the provided question, we can say that 10% condition is met,
There are two separate random samples available.
what is random sample?selected at random (purely random, unpredictable). Every member of the population being polled ought to have an equal probability of getting chosen. She randomly selected 25 names from a pool of 250 employees as an example of a simple random sample. Since there are 250 of her employees in total, and each one has an equal probability of being chosen, the sample in this instance is random. Using simple random sampling, which is a form of probability sampling, researchers choose individuals at random from a population. There is an equal opportunity for selection for every person in the population.
There are two separate random samples available.
The 10% requirement is satisfied.
For both samples, 24, 26, 29, and 31 triumphs and failures are anticipated.
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Find the stable distribution for the regular stochastic matrix. [0.5 0.2 0.5 0.8 ]
As per the given matrix, the stable distribution for the regular stochastic matrix is [tex]\begin{bmatrix}x \\y\end{bmatrix}=\begin{bmatrix}0.40 \\0.10\end{bmatrix}[/tex]
The term matrix is defined as a set of numbers arranged in rows and columns so as to form a rectangular array.
Here we have given that the matrix is written as
[tex]\begin{bmatrix}0.5 & 0.2 \\0.5 & 0.8\end{bmatrix}[/tex]
In order to find the stable distribution for the regular stochastic matrix, we must know what does it means in matrix.
The term stable distribution for the regular stochastic matrix in math is defined as a square matrix whose columns are probability vectors. And the probability vector is a numerical vector whose entries are real numbers between 0 and 1 whose sum is 1.
Here in order to find the solution, we have to equate the value with x and y and then we have to cross multiply the terms, then we get,
=> [tex]\begin{bmatrix}x \\y\end{bmatrix}=\begin{bmatrix}0.5\times0.8 \\0.2\times0.5\end{bmatrix}[/tex]
When we simplify this we get the solution as,
[tex]= > \begin{bmatrix}x \\y\end{bmatrix}=\begin{bmatrix}0.40 \\0.10\end{bmatrix}[/tex]
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Hey, so as you can see I know what the slope is, but i can't figure out the y intercept. Could someone please help me? Thanks!
Answer: (0, -1/3)
Step-by-step explanation: The answer is: (0, -1/3)
y=mx+b
Slope being "m"
And the y intercept being "b"
I think it's (0, -1/3)
......
..
Find at least three different sequences starting with 1. 2, 4 where the terms are generated by a simple rule.
Here are three different sequences starting with 1, 2, and 4, where the terms are generated by a simple rule:
1, 2, 4, 8, 16, 32, ...
The rule for this sequence is to multiply the previous term by 2.
1, 2, 4, 7, 11, 16, 22, ...
The rule for this sequence is to add the previous two terms.
1, 2, 4, 8, 14, 24, ...
The rule for this sequence is to multiply the previous term by 2 and then subtract it from the previous term.
Note that there is an infinite number of different sequences that can be generated by simple rules.
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a right rectangular prism 3 in by 4.25 in by 18.25 in what is the total surface area of the prism
The total surface area of the prism will be 290.125 Square units.
What is a surface area of a rectangular prism?The surface area of a rectangular prism is the measure of how much-exposed area a prism has. Surface area is expressed in square units.
The surface area of a rectangular prism is given by:
SA = 2 (lh +wh + lw )
where
l = 3
w = 4.25
h = 18.25
SA = 2 (3x18.25 + 4.25x18.25 + 3x4.25)
SA = 2 (54.75 + 77.5625 + 12.75)
SA = 2 (146.0625)
SA = 290.125 square units
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After\ flying\ at\ an\ altitude\ of\ 600\ meters,\ a\ hot\ air\ balloon\ starts\ to\ descend.\ its\ g\operatorname{round}\ \operatorname{distance}\ from\ the\ landing\ pad\ is\ 10,000\ meters.\ What\ is\ the\ angle\ of\ depression,\ in\ degrees,\ \operatorname{for}\ this\ part\ of\ the\ flight\
Using the tangent side from trigonometric ratio, the angle of depression is 86.6 degrees
What is Angle of DepressionThe angle created between the line of sight to a location below the horizontal line and the horizontal line of sight is known as the angle of depression.
The angle of depression that the balloon makes with the launch pad can be calculated using the trigonometric ratio.
Data;
Opposite = 10000madjacent = 600angle = ?Since we have the opposite and adjacent side, we can use the tangent of the angle to find the angle of depression.
tanθ = opposite / adjacent
substituting the values into the formula
tan θ = 10000 / 600
tan θ = 100 / 6
tan θ = 16.666
θ = tan⁻¹(16.666)
θ = 86.6°
The angle of depression is 86.6°
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2.If the sum of three integers is a negative integer, we can say WITH CERTAINTY that A all the three integers are equal. B two of the three integers are positive and one is negative. C one of the three integers is positive and two are negative. D at least one of the three integers is negative.
Answer:
D)
That is the only one we can be certain with.
1st option is obviously incorrect
2nd option is wrong as it can also be two are negative one is positive
3rd option is wrong as it can also be one is negative two are positive
4th option is correct as u can't get negative values without a negative numberl.
Determine the reactions at the roller A and pin B.B. 4 m 450 N 600 NmA. 2 m 3 m
The reaction at Roller A is 1800 N and the reaction at Pin B is 2450 N. To calculate the reaction at Pin B, you need to multiply the length of the pin (3 m) by the load (450 N) and add the additional load (600 N).
Reaction at Roller A:
2 m * 900 N = 1800 N
Reaction at Pin B:
3 m * 450 N + 600 N = 2450 N
To calculate the reaction at Roller A, you need to multiply the length of the roller (2 m) by the load (900 N). This gives you 1800 N.
To calculate the reaction at Pin B, you need to multiply the length of the pin (3 m) by the load (450 N) and add the additional load (600 N). This gives you 2450 N.
The reaction at Roller A is 1800 N and the reaction at Pin B is 2450 N.
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In the isosceles triangle has an interior angle measuring 134 degrees, what is the measure of each of the other two?.
Answer:
23°Step-by-step explanation:
In the isosceles triangle has an interior angle measuring 134 degrees, what is the measure of each of the other two?.the sum of the interior angles in a triangle is 180°, take away the know angle and divide by 2, it's an isosceles triangle so 2 side and 2 equal angles
(180 - 134) : 2 = (remember PEMDAS)
46 : 2 =
23°
----------------------------
check23 + 23 + 134 = 180°
the answer is goodconcept check 1. another word for mean is . margin centric statistic average product 2. which measure of central tendency is affected by outliers? mean median both mean and median mean, median, and mode 3. when would you calculate an expected value? when you need to know the exact outcome of a future, unknown event when your data points occur on different dates when you only have one data point when your data points have various probabilities of occurring 4. what is the median of the following set of numbers: 4, 0, -3, 5, 1, 3, -2? 3 5 1.14 1 5. true or false: the mode is universally an accurate representation of data sets because it captures the number that occurs most often. true false
Answer:
Another word for the mean is "average".
Which measure of central tendency is affected by outliers? Mean.
When would you calculate an expected value? when your data points have various probabilities of occurring.
What is the median of the following set of numbers: 4, 0, -3, 5, 1, 3, -2? 3.
True or false: The mode is universally an accurate representation of data sets because it captures the number that occurs most often. False. Mode is not always an accurate representation of data sets and it may not exist in certain data sets.
Step-by-step explanation:
I need help with this problem ?
Answer:
398.32
Step-by-step explanation:
647.82 - 249.50 = 398.32
HELP can all regular polygons fit in a larger polygon?
The property of square depicted is not common for all regular polygon
What is a regular polygon?If a polygon's sides and angles are equal, it is said to be regular. As a result, an equilateral triangle is a regular triangle, and a regular quadrilateral is a square.
The property showed how the square was merged with every two sides fully overlapping to form a bigger square
The trapezium which can also be a regular polygon (quadrilateral) lacks such property of arranging four trapeziums side by side, making overlaps that will form a bigger trapezium.
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Solve for X, Leave in simplest radical form
Answer: X = [tex]\frac{1}{\sqrt{2} }[/tex]
Step-by-step explanation: Because the two angles are equal (You circled them, also 45 degs), and there is a right triangle, which means that the 90-degree angle's adjacent sides are equal, in this case, both sides equal to X.
Using the special triangle ratio ( 1, 1, [tex]\sqrt{2}[/tex]), in this case, the "2" is equal to [tex]\sqrt{2}[/tex] times [tex]\sqrt{2}[/tex], so you have to divide the "1" (X) by [tex]\sqrt{2}[/tex], you simply get [tex]\frac{1}{\sqrt{2} }[/tex].
Sorry for my bad english
a rectangle has its upper two vertices on the graph of and its lower two vertices on the -axis. what is the maximum possible area of the rectangle?
The maximum area of the rectangle is determined by the distance between the two points on the graph and the -axis.
What is rectangle?A rectangle is a four-sided shape with four right angles and two pairs of parallel sides. It is one of the most common shapes in the world, found in everything from building designs to artwork. Rectangles are also used in math, specifically to measure area and perimeter. Rectangles can also be classified according to their sides, with squares being a special type of rectangle with four equal sides.
To calculate the maximum possible area of the rectangle, we can use the formula A = (x2 - x1)(y2 - y1).
In this case, the two points on the graph have the same -coordinate, so the x2 - x1 part of the equation is zero. This means that the y2 - y1 part of the equation gives the maximum possible area of the rectangle. To calculate this, we need to take the difference between the two points on the graph.
For example, if the two points on the graph were (2,4) and (2,6), the maximum area of the rectangle would be (6 - 4) = 2.
Therefore, the maximum possible area of the rectangle is equal to the difference between the two points on the graph.
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