The sides of the triangle ABC are 6, 10, and 8. The sides of the triangle LMN are 12, 20, and 16. The ratio of the respective sides is the same for the two triangles because they are comparable. Therefore, BC is 10 miles long.
Due to the equal ratio of their corresponding sides, the triangles ABC and LMN are comparable. This indicates that the lengths of the sides of LMN may be obtained by multiplying the lengths of the sides of ABC by the same factor. For instance, side AB in ABC is 6 inches long, whereas side LM in LMN is 12 inches long. The lengths are 6:12, or 1:2, apart. The ratio remains the same for all matching. We can examine the other two sides of ABC to verify this response. Ten is the length of AC, and twenty is the length of MN. These two sides must likewise be multiplied by the same factor (1/2), since the ratio of the corresponding sides is the same. This results in AC and MN having lengths of 10 and matching ABC's dimensions. This demonstrates that BC is eight miles long.
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the complete question is
triangles abc and lmn are similar with measurements as shown. what is the measurement of bc, rounded to an integer find BC?
25. There were 13 gummies in a packet. Mrs. Sooklal bought a few packets of gummies. After giving 3 sweets to each of her 27 students, she has 10 gummies remaining, how many packets of gummies did she purchase?
the measure of the angle represented by the expression (7x+12)=1.?
The measure of the angle represented by the expression (7x+12) is 61°.
What is the measure of the angle represented by the expression (7x+12)?The measure of the angle represented by the expression (7x+12) is determined as follows:
The same-side interior angles are supplementary and their sum is 180°.
7x + 12 and 17x are same-side interior angles and are, therefore, supplementary.
7x + 12 + 17x = 180°
solving for x by summing similar terms:
24x + 12 = 180
24x = 168
Dividing both sides by 24
x = 7
Therefore,
7x + 12 = 7 * 7 + 12
7x + 12 = 61°
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Look at the steps for solving the equation and choose a true statement.
3x-9x + 1 = 2(-3x + 1) - 1
-6x + 1 = -6x + 2-1
-6x + 1 = -6x + 1
C
There are infinitely many solutions to the equation.
There is no way to know if there is a solution to this equation.
The only solution to the equation is 1.
There are no solutions to the equation.
The only solution to the equation is -6.
Based on the steps for solving the equation, a true statement include the following: A. there are infinitely many solutions to the equation.
What is no solution?In Mathematics, no solution is sometimes referred to as zero solution, and an equation is said to have no solution when the left hand side and right hand side of the equation are not the same or equal.
What are infinitely many solutions?In Mathematics, an equation is said to have an infinitely many solution when the left hand side and right hand side of the equation are the same or equal:
3x - 9x + 1 = 2(-3x + 1) - 1
-6x + 1 = -6x + 2 - 1
-6x + 1 = -6x + 1
When x = 1, we have:
-6(1) + 1 = -6(1) + 1
-5 = -5.
When x = 2, we have:
-6(2) + 1 = -6(2) + 1
-11 = -11.
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Choose the blanks
The linear relationship is or is not
And the graph passes or does not pass
Because the ratios between each set of numbers are equal, and the graph passes through the point, the linear relationship is proportionate (0,0).
What does the word "proportional" mean?Proportional connections are those in which the ratios of the two variables are equal. Another way to think about them is that one variable is always a constant value multiplied by the other in a proportional relationship. The "constant of proportionality" is the name given to this variable.
The origin, points (2,14.5), (4,29), and (6,43.5) are provided (0,0).
We are aware that the ratios are equivalent in a proportional connection, i.e.
So,
⇒ 14.5/2 = 29/4 = 43.5/6 = 7.25
The linear relationship is a proportionate relationship since the ratios are equal.
The given situation's graph has been drawn, and it is evident that the graph passes through its origin, or "zero," which is (0,0)
Since the ratios between each set of data are equal, the linear relationship can only be a proportional relationship because the graph passes through the point (0,0).
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use the definition of continuity and limits to find values of the constants a and b so that the piece-wise cubic function
The constants a and b can be found by ensuring the function is continuous and that the limits at each point match. This can be done by setting the values of a and b so that the function and its derivative are equal at each point.
To find the constants a and b for the given piece-wise cubic function, we must consider the definition of continuity and limits. Firstly, for the function to be continuous, the function and its derivative must be equal at each point. Thus, we need to set the values of a and b so that the function and its derivative are equal at the points x=1, x=2 and x=3. We can use this to create a system of equations to solve for a and b. Once we have determined the values of a and b, we can then check that the limits at each point match. This can be done by computing the left and right hand limits at each point, and ensuring they are equal. If the limits are equal, then the function is continuous and the constants a and b are correct.
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When u and v are nonzero vectors, Spanlu,v) contains only the line through u and the line through v and the origin.
A. False. Span(u,v) includes linear combinations of both u and v. B. False. Span(u,v) will not contain the origin. C. True. Span(u,v) is the set of all scalar multiples of u and all scalar multiples of v
Span(u,v) is the set of all linear combinations of u and v, including scalar multiples of both. It does not include the origin.
Span(u,v) is the set of all linear combinations of u and v, meaning any combination of u and v multiplied by scalars. This includes scalar multiples of both u and v, but does not include the origin. To calculate Span(u,v), first write u and v as vectors u = (u1,u2,...,un) and v = (v1,v2,...,vn). Then, any linear combination of u and v can be written as c1u + c2v, where c1 and c2 are scalars, and the set of all such linear combinations is Span(u,v). For example, if u = (1,2) and v = (3,4), then Span(u,v) = {(1,2), (3,4), (4,6), (5,8), (7,10), ...}. In other words, Span(u,v) is the set of all scalar multiples of u and all scalar multiples of v.
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Part B: What is the probability that a randomly chosen person is a child? (3 points)
Part C: What is the probability that a randomly chosen person prefers running and is a child? (3 points)
Part D: What is the probability that a person prefers running given that the person is a child? (3 points)
Part E Are being a child and preferring running independent events? Explain. (5 points)
The probability that a randomly chosen person is a child, that a randomly chosen person prefers running and is a child is 12/25 , 1/ 6 respectively.
What is probability ?
Probability can be defined as the ratio of number of favourable outcomes and number of total outcomes.
Given in the table ,
Probability that a randomly chosen person is a child
= 48 / 100
= 12/25
Probability that a randomly chosen person prefers running and is a child
= 6/48
= 1/8
Probability that a person prefers running given that the person is a child
= 6/48
=1/8
Therefore, The probability that a randomly chosen person is a child, that a randomly chosen person prefers running and is a child is 12/25 , 1/ 6 respectively.
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1.) Leila wants to sell her homemade candles at the Linwood Street Craft Fair. She decides to
sell her candles for $12 apiece. The materials for one candle cost Leila $2. If she also pays
$40 to rent the booth for the day, how many candles must Leila sell to cover all of her
expenses? How much will her sales and expenses be at that point?
The total cost of materials for one candle is $2 and she pays $40 for the booth for the day.
Therefore, the total cost for making and selling one candle is $2 + $12 + $40 = $54
To cover all her expenses, Leila must sell enough candles to make $54 from each candle.
She must sell 54/$12 = 4.5 candles
Therefore, Leila needs to sell at least 5 candles to cover all her expenses.
At that point, her sales and expenses will be 5 candles x $12/candle = $60
Therefore, Leila's sales and expenses will be $60 at that point.
X
%
60°
4
Z
30%
Y
Given right triangle XYZ, what is the value of tan(Y)?
02/0
O
O
O
3
√3
2
O2p
The value of tan 30 degrees is √3 / 3
How to solve for tan 30We are to solve this problem using SOH CAH TOA
We are to find the tangent of Y
Tan (Y) = opposite / adjacent
the value of y is 30 degrees
In this question, we can name opposite and adjacent as a and b respectively. No value is given for both
To get the value of a , we have to use sine
sin (y) = opposite / hypotenuse
sin 30 = opposite / 4
4 * 0.5 = opposite
opposite = 2
Cosine Y = opposite / hypotenuse
cos 30 = adjacent / 4
4 * 0.8660 = adjacent
3.464 or 2√3 = adjacent
Then tan 30 = opp / adj
tan 30 = 2 / 3.464
tan 30 = 0.5773
or tan 30 = √3 / 3
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NO LINKS!!
Please help me with #14.
Answer:
a) Domain: (-∞, 10)
b) k⁻¹(8) = 6
c) CBD
d) Range: (-∞, 7)
e) k⁻¹(0) = 4
f) x = -5
Step-by-step explanation:
Part aThe domain of the inverse of a function is the same as the range of the original function.
Therefore, the domain of the inverse function is:
(-∞, 10)Part bThe inverse of a function is its reflection in the line y = x.
Therefore, given that function k(6) = 8 then:
k⁻¹(8) = 6Part cThe inverse of a function is its reflection in the line y = x.
We cannot find k⁻¹(-9) since we have not been given the value of x when k(x) = -9.
Part dThe range of the inverse of a function is the same as the domain of the original function.
Therefore, the range of the inverse function is:
(-∞, 7)Part eThe inverse of a function is its reflection in the line y = x.
Therefore, given that function k(4) = 0 then:
k⁻¹(0) = 4Part fThe zero of the inverse function is the y-intercept of the original function. Therefore, given that k(0) = -5 then:
k⁻¹(-5) = 0Therefore, x = -5 is a zero of k⁻¹(x).
bought a bag of candy for five dollars there were 20 pieces of candy in the bag what is the unit cost of each piece of candy in the bag
Which graph represents an exponential decay function?
The graph that represents an exponential decay function is the second graph.
For you to determine which of the graphs represents an exponential decay, we will need to check the curve that passes through or lies on the x-axis.
we can draw a graph by putting the value of x and we are getting the value of y in this way we get the coordinates of a point
From both figures, we can see that the curve of the second graph almost lies on the x-axis as it curves downwards. This makes it an exponential decay function.
Hence the graph that represents an exponential decay function is the second graph.
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complete question is
Which description matches the function represented by this graph?
A. exponential growth
B. linear growth
C. linear decay
D. exponential decay
Answer:
B or 2
Step-by-step explanation:
The answer above is correct.
please help will mark BRAINLIEST
What is the linear velocity in miles per hour for a particle moving in a circular path at 200 revolutions per minute on a circle of radius 60 feet?
Answer: 1,200. None of the above.
Step-by-step explanation:
200 revolutions per minute times 60 feet. 1,200
City A and City B had two different temperatures on a particular day. On that day, five times the temperature of City A was 8° C more than three times the temperature of City B. The temperature of City A minus twice the temperature of City B was −4° C. The following system of equations models this scenario: 5x = 8 + 3y x − 2y = −4 What was the temperature of City A and City B on that day?
The temperature of city A is 4°C.
The temperature of city B is 4°C.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4= 6 is an equation.
We have,
5x = 8 + 3y ______(1)
x − 2y = −4 _______(2)
Where x is the temperature of city A and y is the temperature of city B.
Now,
From (2),
x = -4 + 2y
Substitution in (1).
5 (-4 + 2y) = 8 + 3y
-20 + 10y = 8 + 3y
-20 - 8 = 3y - 10y
-28 = -7y
y = 4
Now,
x = -4 + 2y
x= -4 + 2 x 4
x = -4 + 8
x = 4
Thus,
The temperature of both city A and city B is 4°C.
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Two angles of a quadrilateral measure 130° and 195°. The other two angles are in a ratio of 2:5. What are the measures of those two angles?
The measure of other two angles in the given quadrilateral are 10° and 25°.
What is quadrilateral?A quadrilateral is a polygon with four sides four angles and four vertices. Whenever we name a quadrilateral, we need to keep in mind the order of the vertices.
Given that, two angles of a quadrilateral measure 130° and 195°.
The other two angles are in a ratio of 2:5.
So, the other two angles are 2x and 5x
Now, 130°+195°+2x+5x=360°
325°+7x=360°
7x=360°-325°
7x=35°
x=5
So, 2x=10° and 5x=25°
Therefore, the measure of other two angles in the given quadrilateral are 10° and 25°.
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$155 $267 $284 $194 $299 $284 $287 $179 What is the mean, median, and mode of this data set?
Answer:
Mean = 243.625
Median = 275.5
Mode = 284
Each value is exact without any rounding.
=================================================
Original data set:
$155 $267 $284 $194 $299 $284 $287 $179
Let's remove the dollar signs, and separate each item with a comma:
155,267,284,194,299,284,287,179
Then sort the values from lowest to highest.
155,179,194,267,284,284,287,299
---------------------
To find the mean, we add up the values and divide by n = 8 since there are 8 items in the list.
(155+179+194+267+284+284+287+299)/8 = 243.625 is the mean
----------------------
Refer to the sorted data set.
The median is the middle-most value. Because the sample size n = 8 is even, we'll have two values tied for the middle.
n/2 = 8/2 = 4
The items in slot 4 and 5 are tied for the middle.
The values in slot 4 and 5 are 267 and 284 in that exact order.
Compute the midpoint: (267+284)/2 = 275.5 is the median
----------------------
The mode is the most frequent value. Look through the sorted data set to see that 284 shows up twice. This is the most frequent compared to the other values (that show up only once).
Therefore, the mode is 284
Side note: It's possible to have multiple modes. It's also possible to not have any modes at all.
Solve pls this equation
Hey there!
If you are solving for x, then your final solutions are [tex]x=\sqrt{-y},-\sqrt{-y}[/tex].
Hope this helps!
Evaluate the expression using the given value of the variable:[pr2]; use [p = 3], and [r = 3] .
Answer:
(pr²)
given,
p=3 r=3
(3 X 3²)
(3 X 9)
27
when ur answering please just give the answer! thank uuu! :)
The equation of the exponential function is y = 0.2⋅2^x
Find the equation of the exponential functionThe steps for this process are as follows:
Step 1: Set up the equation.
The equation of an exponential function has the form y = a⋅b^x
where a and b are constants and b is greater than 0 and not equal to 1.
Step 2: Find the constants.
We can use the given points to find the constants in the equation. For example, when x = 0, y = 0.2.
So we can set 0.2 = a⋅b^0.
This means that a = 0.2 and b^0 = 1,
so b = 1.
Step 3: Write the equation.
Substituting a = 0.2 and b = 1 into the equation gives us y = 0.2⋅2^x.
This is the equation of the exponential function represented by the table.
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Part B
In part A, you used the exact lengths of the sides to find the exact area of the rectangle.
Suppose this rectangle represents a piece of fabric that needs to be cut for a sewing project. Which type of measurement do you think would be more appropriate to use in this situation: the exact side lengths as given in part A or decimal approximations of the side lengths?
Use complete sentences to explain your reasoning.
Approximation of decimals is a mathematical technique for finding or measuring approximations and minimizing the number of decimal places.
What is meant by decimal approximations?A fractional representation of a real number that comes close to representing it. Any real number a can be represented by an endless number of decimal fractions.
The number of decimal places in a decimal number is the number of digits following the decimal point. A mathematical method for locating or measuring approximations and reducing the number of decimal places is known as approximation of decimals.
Any comparison that is close but not accurate to another entity is called an approximation. By rounding, one can get a good idea of a number. By rounding the values in a computation before performing the operations, a calculation can be approximated.
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Problem Gregory forms two different numbers with the digits 1, 2, 3, 4, 5, and 6. Both numbers have 3 digits, and each digit is used only once. If he adds these two numbers, what is the greatest sum Gregory can get? Show your work.
The numeric value of the greatest sum that can be obtained by Greg is given as follows:
1173.
How to obtain the greatest sum?When two n digit numbers are added, the numbers in the equivalent positions are added with each other, that is, starting from the end of the number to the begining.
The first digit is added with the other first digits.The second digit is added with the other second digits.For example, 21 + 32:
1 + 2 = 3.2 + 1 = 5.Hence the sum is of 54.
Hence the greatest sum would be obtained as follows:
The first digits would be of 5 and 6.The second digits would be of 3 and 4. The third digits would be of 1 and 2.Hence the sum would be given as follows:
642 + 531 = 1173.
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whoever can get this i will mark them brainiest
The first diagram of the triangle DEF correctly represents the transformation.
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
The preimage of the triangle is ABC and the image is DEF.
Therefore, ∠A = ∠D, ∠B = ∠E and ∠C = ∠F>
A 90° rotation counterclockwise will rotate the vertex C one-quarter left of a complete circle.
Therefore, The first triangle represents the correct transformation.
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PLEASE THIS IS DUE SOON AND I NEED HELP
Select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x + 5)4 + 2x2 + 5 = 0 6(2x + 4)2 = (2x + 4) + 2 6x4 = -x2 + 5 8x4 + 2x2 – 4x = 0
The answer is x4 – 6x2 – 27 = 0 and this is a quadratic equation in the polynomials .
How to calculate and What is Quadratic equation?This is a quartic equation because the highest degree is 4
In the second option, we have 3x⁴ = 2x, this is also another quartic equation.
In the third equation, we have 2(x + 5)⁴ + 2x² + 5 = 0, this is a quartic equation because the highest degree is 4
In the fourth equation, 6(2x + 4)² = (2x + 4) + 2
This is a quadratic equation because the highest degree is 2
In the fifth equation, we have 6x⁴ = -x² + 5 which is also another quartic equation
An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term. First, there must be a term other than zero in the coefficient of x2 (a 0) for an equation to be a quadratic equation. The x2 term is written first when constructing a quadratic equation in standard form, then the x term, and finally the constant term. The numerical values of a, b, and c are typically expressed as integral values rather than fractions or decimals.
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What is an equation of the line that passes through the point (2, 3) and is parallel to
the line x + y = 4?
The equation of the line that is parallel to x + y = 4 and passes through (2, 3) is expressed as: y = -x + 5.
How to Determine the Equations of Parallel Lines?Two lines are parallel if and only if their slopes are equal. The equation of the line x + y = 4 is in slope-intercept form (y = mx + b), where m is the slope. The slope of this line is m = -1, as the coefficient of x is -1.
An equation of a line that is parallel to the line x + y = 4 and passes through the point (2, 3) can be written in the form y = mx + b, where m = -1.
Substituting the point (2,3) and the slope -1 into the point-slope form of a line gives:
y - 3 = -1(x - 2)
Expanding the right hand side gives:
y - 3 = -x + 2
And rearranging the equation gives the final form of the equation of the line:
y = -x + 5
So, the equation of the line that passes through the point (2, 3) and is parallel to the line x + y = 4 is y = -x + 5.
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∠FGK and ∠KGH form a linear pair. Find m∠KGH.
Applying the linear pair definition, m<KGH = 60°.
What is a Linear Pair?In geometry, a linear pair is a pair of adjacent angles that are supplementary, meaning that their measures add up to 180 degrees. The two angles must be adjacent, meaning that they share a common side or vertex, and they must be linear, meaning that they are formed by two intersecting lines.
Therefore:
m<FGK + m<KGH = 180
Substitute
120 + m<KGH = 180
m<KGH = 180 - 120
m<KGH = 60°
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Ages of Dogs The ages of 20 dogs in a pet shelter are shown. Construct a frequency distribution using 7 classes.
7
9
6
8
7
6
8
6
9
5
7
7
Send data to Excel
6
89
8
8
6 4 8
9
6 3
Class limits Class boundaries Frequency
3
2.5-3.5
4
3.5-4.5
4.5-5.5
5.5-6.5
6.5-7.5
7.5-8.5
8.5-9.5
Total
5
The frequency table is added below
How to determine the frequency distributionFrom the question, we have the following parameters that can be used in our computation:
7 9 6 8 7 6 8 6 9 5 7 7
6 8 9 8 8 6 4 8
When represented on a frequency table, we have
Class limits Class boundaries Frequency
2.5 - 3.5 3.0 - 4.0 0
3.5 - 4.5 4.0 - 5.0 1
4.5 - 5.5 5.0 - 6.0 1
5.5 - 6.5 6.0 - 7.0 5
6.5 - 7.5 7.0 - 8.0 4
7.5 - 8.5 8.0 - 9.0 6
8.5 - 9.5 9.0 - 10.0 3
Total 20
The class boundary is calculated as
class boundary = Class limits ± 0.5
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5x - y = -5
3x - 6y = 24
Solve using substitution
Answer:
x = -2
y = -5
Step-by-step explanation:
5x - y = -5
3x - 6y = 24
First, multiply the first equation by -6
-30x + 6y = 30
3x - 6y = 24
-27x = 54
x = -2
Now, put in -2 for x and solve for y
5(-2) - y = -5
-10 - y = -5
-y = 5
y = -5
Let's Check
5(-2) -(-5) = -5
-10 + 5 = -5
-5 = -5
So, x = -2 y = -5 is the correct answer.
Zac and Malcolm each wrote short stories. Zac’s story is 273 lines long. Malcolm’s story is 145 lines longer than Zac’s. How long is Malcolm’s story? Explain what operation you used to solve this problem.
Length of malcom's story is 418lines, the operation used to solve this problem is; lines of zac story+ extra lines of malcom story.
What is simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression. Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form. Simplification usually involves making the expression simple and easy to use later.
Given;
Number of lines in zac story=273
Number of lines in malcom story= 273+145
Now.
Total number of lines in malcom story
=273+145
=418
Therefore, the answer after simplification will be 418
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