The equation of the line that passes through the point (1, 4) and has a slope of -2 is y = -2x + 6
What is slope-intercept form of a line?
The equation of the line in slope-intercept form is given by:
y = mx + c
Here,
(x, y) = Every point on the line
m = Slope of the line
c = y-intercept of the line
According to the given question:
The given line has slope m = -2 and point (1, 4) passes through the line.
By slope-intercept form general equation of line is y = mx + b where b is
y-intercept.
Substituting values of m and point (1, 4) in this equation to get value of b
y = mx + b
4 = -2(1) + b
b = 6
Hence equation of the line is y = -2x + 6
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Graph the function y=log(x-2)
Which proportion can you use to derive the equation of the line? (4 questions in picture 2)
The proportion that you use to derive the equation of the line is (y+2)/x=4/3.
So, option c is correct.
What is meant by an equation?An equation is something like 3x - 5 = 16. By solving for x, we discover that x equals 7, which is the value for the variable. By deleting parentheses and merging like terms, you can simplify either side of an equation and find its solution.
Identify the variable term on one side of the equation by adding or subtracting. You can find the variable's value by multiplying or dividing. When two expressions are connected with the equals sign (=) in a mathematical formula, it expresses the equality of the two expressions. Depending on the language, the definition of the word equation and its cognates may alter slightly. For instance, an equation is what is meant in French.
Here,
In the given diagram:
The slope of the straight lines is constant
So, DE/AD=CB/AB
(y+2)/x=4/3
Therefore, option c is correct.
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Tanvi Is attending a school orchestra concert. She sees her math teacher seated 5 m ahead of her and her science teacher seated 12 m to her right. How far apart are the 2 teachers
Answer:
The two teachers are 13 feet apart
Step-by-step explanation:
Right Triangles
Ava, her math teacher, and her science teacher form a right triangle in which she is at the 90° vertex.
The distances from the three people must satisfy the Pythagora's theorem, where the distance between the two teachers (D) is the hypotenuse, thus:
D = 13 feet
Step-by-step explanation:
What is the side length rounded to the nearest hundredth
11.18033
let b=x
use pythag and rearrange for side b. Then simply maths.
I need help with the statement and reason part. (Its ok if just one of the questions is answered.)
The triangles consist in rectangles ΔABD and ΔCDB are congruent triangles.
Given that,
To prove ΔABD ≅ ΔCDB.
In congruent geometry, the shapes that are so identical. can be superimposed on themselves.
Here,
consider ΔABD and ΔCDB
1. AB = CD [opposite sides of a rectangle]
2. ∠A = ∠C [each angle of the rectangle is 90°]
3. AD = BC [opposite sides of a rectangle]
ΔABD ≅ ΔCDB
Thus, Both triangles ΔABD ≅ ΔCDB are congruent triangles, hence proved.
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HELP SO EASY!!!!!! ASAP
A polygon is said to be equilateral if all of its sides are the same length. Find the perimeter of the equilateral polygon whose vertices are as follows.
(−2,−4), (1,0), (1,5), (−2,9), (−7,9), (−10,5), (−10,0), (−7,−4)
The perimeter of the equilateral polygon with the given vertices is given as follows:
40 units.
How to obtain the perimeter of the polygon?The perimeter of a polygon is composed by the sum of the lengths of the outer edges of the figure.
From the figure given at the end of the answer, the parameters for the polygon with these given vertices are given as follows:
8 side lengths.Each side length is of 5 units. (as the polygon is equilateral, meaning that the side lengths are equal).Then, considering the 8 side lengths and the fact that they measure 5 inches, the perimeter of the polygon is given as follows:
Perimeter = 8 x 5 = 40 units.
(sum of 8 times the number 5 is equals to the multiplication of eight by five).
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Tyler's savings account pays a simple annual interest rate of 3.25%. Suppose he deposits $5,000 in the
account and makes no additional deposits or withdrawals for 3 years. What will the total value of the account
be after 3 years?
Answer:
The total value of the account after 3 years will be $5,503.52.
Step-by-step explanation:
A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
Tyler's bank account pays a straightforward yearly financing cost of 3.25%. Assume he stores $5,000 in the record and sets aside no extra installments or withdrawals for a long time.
The total value of the account after 3 years will be calculated as,
A = $5,000(1 + 0.0325)³
A = $5,000 x (1.0325)³
A = $5,000 x 1.1007
A = $5,503.52
The total value of the account after 3 years will be $5,503.52.
(a) what sample size is necessary if the 95% ci for p is to have a width of at most 0.15 irrespective of p? people
The sample size is necessary if the 95% ci for p is to have a width of at most 0.15 irrespective of p being 385 people.
In statistics, a confidence interval describes the likelihood that a population parameter will fall between a set of values for a given percentage of the time. Confidence intervals that include 95% or 99% of anticipated observations are frequently used by analysts.
The largest confidence interval occurs when p = .5
The standard error = [tex]\sqrt{\frac{(0.5)^{2} }{x} }[/tex]
The z* for a 95% confidence interval = 1.96
Setting up an equation,
[tex]1.96\sqrt{\frac{(0.5)^{2} }{x} } = 0.05[/tex]
Solving gives x=384.2.
So you need 385 people.
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Write the polynomial so that the powers of x are in descending order, -3x + 8x² - 11 +
9x³
Answer:
9x³+8x²-3x-11
Step-by-step explanation:
1. You can move sections around throughout the equation.
^Note: Be sure to keep the same signs (either positive or negative) for each section.
In this problem, the sections are (-3x), (8x²), (-11), and (9x³).
^Note: I kept the subtraction/negative sign
2. Rearrange the exponents in order from largest to smallest in the equation.
largest 9x³ +8x² -3x -11 smallest
^Note: -3x has an exponent of 1
In a hypothesis test for population proportion, you calculated the p-value is 0.01 for the test statistic, which is a correct statement of the p-value?Group of answer choicesa)The p-value indicates that it is very rare to observe a test statistics equally or more extreme when the null hypothesis is true.b)The p-value indicates that it is very likely to observe a test statistics equally or more extreme when the null hypothesis is true.c)The p-value is calculated assuming the alternative is true.
a) The p-value indicates that it is very rare to observe a test statistics equally or more extreme when the null hypothesis is true.
What is null hypothesis?A null hypothesis is a claim or presumption that there is no association between two observed variables or that observed differences between groups are the result of chance. It is frequently employed in statistical testing, and it is represented by the symbol "H0". The null hypothesis is often the inverse of the alternative hypothesis, which posits a link or difference between the variables. To reject the null hypothesis, the observed data must be statistically significant and unlikely to have occurred by chance. In scientific research, the null hypothesis is crucial because it enables researchers to assess the significance of their data and reach reliable conclusions.
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Amy needs to write a paper that contains more than 3,305 words for school. She has already written 1,450 words and writes at a rate of 265 words per day. Which of the following inequalities could be used to solve for x, the number of days it will take Amy to finish her paper?
Inequality that could be used to solve for x is;
1450 words + (265 words / day)x = 3305 words
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Given that Amy has already written 1450 words out of 3305 words.
And she writes at the rate of 265 words per day.
To establish the inequality which could be used to solve for x,
Then Firstly, we will form an equation for the total number of days required to write her paper,
1450 words + (265 words / day)x = 3305 words.
Simplifying the above expression,
(265 words / day)x = 3305 words - 1450 words
To solve this linear equation, we'll find x = 7.
x = { 3305 words - 1450 words} / 265 words
x = 7 days.
Hence, inequality that could be used to solve for x is;
1450 words + (265 words / day)x = 3305 words
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Graph the line with y-intercept -7 and slope 3/2
We are given the slope and the y-intercept so using the slope-intercept form:
y = mx + b, where m- slope, b- y-intercept.Substitute values to get:
y = (3/2)x - 7To graph a line we need two points, one is given, (0, - 7) - the y-intercept.
Find one more point, take even value of x to cancel the fraction, let it be x = 4, find its y-coordinate:
y = (3/2)*4 - 7 = 6 - 7 = - 1So our points are:
A(0, - 7) and B(4, - 1)Plot the points and connect to graph the line.
See below.
The graph of the linear equation:y = (3/2)*x - 7 can be seen in the image at the end.
How to graph the linear equation?A general linear equation is written as:y = a*x + b
Where a is the slope and b is the y-intercept. Then our linear equation is:y = (3/2)*x - 7
To graph it, we need to know two points in our line, to do so, we evaluate it in two different values of x. if x = 0y = (3/2)*0 - 7y = -7So we have the point (0, -7)
And if x = 2 then:y = (3/2)*2 - 7y = 3 - 7y = -4So we have the point (2, -4)
Now we just need to graph these two points and connect them with a line. You can see the graph below.
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in spain sam pays 27 euros for 18 litres of petrol. in wales leo pays £40.80 for 8 gallons of the same type of petrol. 1
1 euro=85p
4.5 litres=1 gallon
sam thinks petrol is cheaper in spain than wales.
Work out if sam in correct?
The amount for 1 Liter of petrol in Wales is less than the amount for 1 Liter of Petrol in Spain
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 amount of petrol in Spain be = A
Let the amount of petrol in Wales be = B
Now , the total amount Sam paid for 18 Liters of petrol in Spain = 27 euros
1 euro = 0.85 pounds
So ,
Total amount Sam paid for 18 Liters of petrol in Spain = 27 x 0.85 pounds
Total amount Sam paid for 18 Liters of petrol in Spain = 22.95 pounds
So ,
The amount for 1 Liter of petrol in Spain = Total amount Sam paid for 18 Liters of petrol in Spain / 18
Substituting the values in the equation , we get
The amount for 1 Liter of petrol in Spain = 22.95 / 18
The amount for 1 Liter of petrol in Spain = £ 1.275
And ,
Now , the total amount Sam paid for 8 gallons of petrol in Wales = £ 40.80
1 gallon = 4.5 Liters
8 gallons = 4.5 x 8 Liters
8 gallons = 36 Liters
So ,
Total amount Sam paid for 36 Liters of petrol in Wales = £ 40.80
So ,
The amount for 1 Liter of petrol in Wales = Total amount Sam paid for 36 Liters of petrol in Spain / 36
Substituting the values in the equation , we get
The amount for 1 Liter of petrol in Wales = 40.80 / 36
The amount for 1 Liter of petrol in Wales = £ 1.13
£ 1.13 < £ 1.275
Therefore , the amount for 1 Liter of petrol in Wales is less than the amount for 1 Liter of Petrol in Spain
Hence , The amount for 1 Liter of petrol in Wales is less than the amount for 1 Liter of Petrol in Spain
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Examine the parallelogram below. Given m/ABC = (3x + 1) and m /BCD = (8x - 8), then
m
HELP PLEASE IM BEGGING
The value of the angle m ∠ DAB in the parallelogram is 128 degrees
Angles in a ParallelogramIn a given parallelogram, the opposite sides and angles are equal to one another.
In the question given;
m∠ ABC = 3x + 1
m∠ BCD = 8x - 8
m∠ DAB = ?
m ∠ ABC + m∠ BCD = 180°
The sum of the two angles is equal to 180 degrees
3x + 1 + 8x - 8 = 180
11x - 7 = 180
11x = 187
x = 17
However, m∠ DAB = m∠ BCD
Two opposite angles are equal
m∠ DAB = 8x - 8
m ∠ DAB = 8(17) - 8
m ∠ DAB = 128 degrees
The angle is 128 degrees
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PLEASE ANSWER ASAP!
In February, 7 tulips bloom in a garden. In March, 18 tulips bloom. Find the percent change to the nearest percent.
Answer:
Step-by-step explanation:
157.1429% but you can round it down
Find the median and mode of the following data: 34,21,56,33,34,12,53,72,45,23,11
Answer:
see explanation
Step-by-step explanation:
Median -
To find the median: Arrange the data points from smallest to largest. If the number of data points is odd, the median is the middle data point in the list. If the number of data points is even, the median is the average of the two middle data points in the list.
Answer: 34
Mode -
The most frequent number—that is, the number that occurs the highest number of times.
Answer: 34
Answer:
I think
Mode = 34
Median = 34
Step-by-step explanation:
Find the distance between the points $A\left(13,\ 2\right)$ and $B\left(7,\ 10\right)$ .
The distance between the two points is
The distance between the two points is 10 units
How to determine the distance between the two points?From the question, we have the following parameters that can be used in our computation:
A = (13, 2) and B =(7, 10)
The distance between the two points can be calculated using the following distance equation
distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where
(x, y) = (13, 2) and (7, 10)
Substitute (x, y) = (13, 2) and (7, 10) in distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
distance = √[(13 - 7)² + (2 - 10)²]
Evaluate
distance = 10
Hence, the distance is 10 units
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the scatter plot shows the number of days since several people filled their cars with gas and the gallons of gas in their tank. which is the most reasonable estimate of the gallons of gas in a tank if it has been 3 days since filling up?
The most reasonable estimate of the gallons of gas in a tank if it has been 3 days since filling up is 17 gallons.
On plotting the graph we will get ,
The most reasonable value of y corresponding to x = 3 is approximately 17 gallons.
A plot is a graphical technique for representing a data set, typically in the form of a graph that depicts the relationship between two or more variables. The plot can be created either by hand or by computer. Previously, mechanical or electronic plotters were used.
Graphs are a visual representation of the relationship between variables that are very useful for humans because they allow them to quickly derive an understanding that would not have been possible from lists of values. Graphs can also be used to read off the value of an unknown variable plotted as a function of a known variable given a scale or ruler, but this can also be done with data presented in tabular form. Function graphs are used in mathematics, science, engineering, and technology.
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1/3 Marks
These cards are put into a bag:
1 2 3 4
5 6 7 8 9 10
One card is chosen at random.
a) What is the probability of choosing the card with the number 4?
b)
What is the probability of choosing a card that has a digit 1 on it?
c) What is the probability of choosing a card that does not have a digit 1 on it?
Give your answers as fractions.
Answer:
Below
Step-by-step explanation:
a) there are 10 cards only one '4' so 1 out of 10 = 1/10
b) there are 2 cards out of 10 with a '1' on them 2/10 = 1/5
c) 8 out of 10 = 8/10
Formula: B1+B2=2(Midsegemt) Solve for X
2x-4+3x+2=2(2x+4)
if possible please explain/ show work!
thank you so so much!
The mid term is 2,Accordingly, if n is even, there will only be one middle term, and if n is odd, there will be two middle terms.
How does the Midsegment Theorem work?According to the midsegment theorem, the third side of a triangle is parallel to the first two sides, and the length of the third side's midsegment is equal to half of that side's length.The Binomial Expansion is in its middle term. We are aware that (a + b)n has an extension that has (n + 1) words. We can write the middle term(s) of (a + b)n depending on the value of n. Accordingly, if n is even, there will only be one middle term, and if n is odd, there will be two middle terms.Explanation:
2x - 4 + 3x + 2 = 2(2x+4)
The mid term is 2.
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12, 18,27,...
Find the 8th term.
Check the picture below.
Answer:
205.03125
Step-by-step explanation:
You want the 8th term of the sequence that begins 12, 18, 27, ....
DifferencesThe first differences of the given terms are ...
18 -12 = 6
27 -18 = 9
These are not constant, so the sequence is not an arithmetic sequence.
RatiosThe ratios of sequential terms are ...
18/12 = 1.5
27/8 = 1.5
These are constant, suggesting the sequence is an exponential sequence. The equation for the n-th term is ...
an = 12(1.5^(n-1))
Then the 8th term is ...
a8 = 12(1.5^7) = 205.03125
__
Additional comment
The sequence could be quadratic if the second differences are all 9-6=3. In that case, the equation for the n-th term is ...
an = 1.5n(n +1) +9
and the 8th term is ...
a8 = 1.5·8(8+1) +9 = 117
<95141404393>
someone help me I need a good grade my mom gonna yell at my if i don't get it ):
Y==-2x+8 find x, if y is 16
Answer:
x = –4
Step-by-step explanation:
y = –2x + 8
16 = –2x + 8
2x = 8 – 16
2x = –8
x = –4
The table shows the side length and approximate area of an octagonal stop sign. Area of a stop sign a 2-column table with 5 rows. The first column is labeled side length (inches), x with entries 5, 10, 15, 20, 25. The second column is labeled area, f(x) with entries 120; 480; 1,080; 1,920; 3,000. Which function can be used to compute the approximate area, in square inches, of a stop sign if it has a side length of x inches? f(x) = 4. 8x2 f(x) = 4x2 f(x) = (4. 8)x f(x) = (4)x.
f(x) = 4. 8x² function can be used to compute the approximate area, in square inches, of a stop sign if it has a side length of x inches.
What do function and example exactly mean?A function, which produces single output from either a single input, is an illustration of a rule. Alex Federspiel was contacted to collect the image. An illustration of this is the equation y=x2. For each input of x, there is simply one output of y. Considering that x is actually the input value, we would claim that y is just a rational number.
Briefing:area = (# of sides * side length^2) / [4 * tan (180/n)]
area = (8 * x^2) / 4 * tan (22.5)
area = 8 x^2 / (4 * 0.41421)
area = 8 x^2 / 1.65684
area = 4.8 x^2
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Kay uses 4 pints of broth to make a soup. How many quarts of broth does Kay use to make the soup?
Answer:
2 quarts
Step-by-step explanation:
1 quart = 2 pints
4 pints × (1 quart)/(2 pints) = 2 quarts
Answer:
2 quarts
Step-by-step explanation:
1 quart=2 pints
2 quarts=4 pints
Have a great day
Ive friend go to a movie. Each movie ticket cot $11. 75. They hare a large popcorn for $7. 75. If they divide the total cot equally, how much will each friend pay?
We know that each friend will pay $13.3 using simple mathematical operations.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.
The operation's arity is determined by the number of operands.
The rules that specify the order in which we should solve an expression involving many operations are known as the order of operations.
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition Subtraction (from left to right).
So, we know that:
There are 5 friends.
Each ticket costs $11.75.
They have a large popcorn for $7.75.
Then, the amount that each friend will pay:
[(11.75*5)+7.75]/5
[58.75+7.75]/5
66.5/5
$13.3
Therefore, we know that each friend will pay $13.3 using simple mathematical operations.
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Correct question:
Five friends go to a movie. Each movie ticket cost $11. 75. They have a large popcorn for $7. 75. If they divide the total cost equally, how much will each friend pay?
Answer:
Step-by-step
Each friend pays $3.9 each.
1. $11.75 + $7.75 = 19.50.
2. 19.50 divided by 5 (friends) is equal to 3.9.
Multiplications of 2 matrices
The product of matrix A and matrix B is matrix C
a) [tex]C = \begin{pmatrix}23\end{pmatrix}[/tex]
b) [tex]C = \begin{pmatrix}5\end{pmatrix}[/tex]
What is multiplication of matrices?
The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. The first matrix must have the same number of columns as the second matrix has rows. The number of rows of the resulting matrix equals the number of rows of the first matrix, and the number of columns of the resulting matrix equals the number of columns of the second matrix
Given data ,
a)
Let the first matrix be A
The value of A is
[tex]A = \begin{pmatrix}2&3\end{pmatrix}[/tex]
The value of second matrix B is
[tex]B = \begin{pmatrix}4\\ \:5\end{pmatrix}[/tex]
Now , the product of matrix A and matrix B is matrix C
The value of matrix C is
[tex]C = \begin{pmatrix}2&3\end{pmatrix}\begin{pmatrix}4\\ 5\end{pmatrix}[/tex]
On simplifying the value of matrix C , we get
[tex]C = \begin{pmatrix}2\cdot \:4+3\cdot \:5\end{pmatrix}[/tex]
[tex]C = \begin{pmatrix}23\end{pmatrix}[/tex]
Therefore , the value of matrix C is [tex]C = \begin{pmatrix}23\end{pmatrix}[/tex]
b)
Let the first matrix be A
The value of A is
[tex]A = \begin{pmatrix}1&2\end{pmatrix}[/tex]
The value of second matrix B is
[tex]B = \begin{pmatrix}-3\\ \:4\end{pmatrix}[/tex]
Now , the product of matrix A and matrix B is matrix C
The value of matrix C is
[tex]C = \begin{pmatrix}1&2\end{pmatrix}\begin{pmatrix}-3\\ 4\end{pmatrix}[/tex]
On simplifying the value of matrix C , we get
[tex]C =\begin{pmatrix}1\cdot \left(-3\right)+2\cdot \:4\end{pmatrix}[/tex]
[tex]C = \begin{pmatrix}5\end{pmatrix}[/tex]
Therefore , the value of matrix C is [tex]C = \begin{pmatrix}5\end{pmatrix}[/tex]
Hence , the matrix multiplication is
The product of matrix A and matrix B is matrix C
a) [tex]C = \begin{pmatrix}23\end{pmatrix}[/tex]
b) [tex]C = \begin{pmatrix}5\end{pmatrix}[/tex]
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If you rent a car from Caleb's Cars, you'll pay a $61 fee
and $24 per day. At Vinny's Vehicles, you'll pay a $105 fee and $20 per day. Determine the number of days you can rent a car from either place and pay the same amount. Use substitution or elimination.
Therefore ,the total number of days to rent a car at both locations for the same price is 11 days.
Simultaneous equation is defined.Two or more algebraic equations can be simultaneous if they share variables, such as x and y. Due to the simultaneous solution of the equations, they are known as simultaneous equations.
Here,
Let x be the number of days to repay after a down payment and y be the total amount due.
Consequently, equation 1 is 61+24x=y.
Eq. 2: 105 + 20x = y
Equation 1 minus equation 2
105-61+20x-24x= 0
44-4x= 0
4x = 44
multiply both sides by 4.
x= 44/4
x= 11 days
the total number of days to rent a car at both locations for the same price is 11 days.
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AABC ~ AQRS
Find the missing side length, m.
R
B
3/
A
C
1
m = [?]
m
5
S
The value of missing side length(m) in ΔQRS is 15 cm.
How to solve the sides of triangle?
Congruent triangles are two triangles that are the same size and shape. Two congruent triangles remain congruent even if we flip, turn, or rotate one of them.Two triangles must have the same angles and, as a result, must be congruent if their sides are the same. If two triangles are congruent or not, we may determine this simply by looking at their sides.These two triangles are also equivalent if we know that two sides of one triangle and the angle between them are congruent to two sides and the angle between them of another triangle.ΔABC ~ ΔQRS
The sides of the triangle will be in equal ration of one another.
i.e., AB/AC = QR/QS
3/1 = m / 5
m = 15 cm
Hence, The value of missing side length(m) in ΔQRS is 15 cm.
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AB¯¯¯¯¯¯¯¯ with endpoints A(4,4) and B(5,−1) is reflected in the line y=x to create its image A′B′¯¯¯¯¯¯¯¯¯¯. Graph A′B′¯¯¯¯¯¯¯¯¯¯. Then find the perimeter of the figure formed by the segments AB¯¯¯¯¯¯¯¯, B′B¯¯¯¯¯¯¯¯¯, and AB′¯¯¯¯¯¯¯¯¯ to the nearest tenth.
The perimeter of the figure is 5.0.
What is a perimeter?
The perimeter of a two-dimensional shape is the distance around the outside of the shape. It is the sum of the lengths of all the sides of the shape. For example, the perimeter of a rectangle is the sum of the lengths of all four sides. The perimeter of a triangle is the sum of the lengths of all three sides.
To reflect a point across the line y=x, we can use the following formula:
(x', y') = (y, x)
Where (x', y') is the reflected point and (x, y) is the original point.
Using this formula, we can find the coordinates of the reflected points A' and B':
A' = (4, 4) -> (4, 4) -> (4, 4)
B' = (5, -1) -> (-1, 5) -> (-1, 5)
Therefore, the image of AB is A'B' with endpoints A'(4, 4) and B'(-1, 5).
To find the perimeter of the figure formed by the segments AB, B'B, and A'B', we can add up the lengths of these three segments. The length of AB can be found using the distance formula:
[tex]AB = \sqrt{((5-4)^2 + (-1-4)^2)}\\\\= \sqrt{(1^2 + (-5)^2)}\\\\= \sqrt{(1 + 25)}\\\\= \sqrt{26}[/tex]
The length of B'B can be found using the same formula:
[tex]B'B = \sqrt{((-1-(-1))^2 + (5-5)^2)}\\\\= \sqrt{(0^2 + 0^2)}\\\\= 0[/tex]
The length of A'B' can also be found using the distance formula:
[tex]A'B' = \sqrt{((-1-4)^2 + (5-4)^2)}\\\\= \sqrt{(-5)^2 + (1)^2}\\\\= \sqrt{25 + 1}\\\\= \sqrt{26}[/tex]
The perimeter of the figure is AB + B'B + A'B' = √26 + 0 + √26 = 2√26. To the nearest tenth, this is 5.0.
Hence, the perimeter of the figure is 5.0.
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