a)
d)
1) Since the zeros of that polynomial were given, then we can write it into the factored form. Note that there are 4 zeros, so we can write:
[tex]\begin{gathered} (x-x_1)(x-x_2)(x-x_3)(x-x_4)=0 \\ (x-(-2i))(x-2i)(x-3)(x-(-4))=0 \\ (x+2i))(x-2i)(x-3)(x+4))=0 \end{gathered}[/tex]2) To find out the corresponding polynomial then we can expand it by rewriting "i" as -1
[tex]\begin{gathered} (x+2i))(x-2i)(x-3)(x+4) \\ (x+2i)(x-2i)=x^2+4 \\ (x-3)(x+4)=x^2+4x-3x-12 \\ (x^2+4)(x^2+x-12) \\ x^4+x^3-8x^2+4x-48 \end{gathered}[/tex]3) Hence, the answers are
a)
d)
[tex]x^4+x^3-8x^2+4x-48[/tex]the question is on the sheet .The shaded region is the area within the figure but not the corner squares
Based on the information given in the exercise, you know that the shaded region has this area:
[tex]6x^2-2xy+3y^2[/tex]And the area of each square region in the corners is:
[tex]4x^2[/tex]Since there are four square regions, you can multiply that the area of any of them by 4, in order to find the total area of them:
[tex]4(4x^2)=16x^2[/tex]Then, in order to find the total area of the figure, you must add the area of the shaded region and the total area of the square regions:
[tex](6x^2-2xy+3y^2)+(16x^2)=22x^2^{}-2xy+3y^2[/tex]Therefore, the total of the figure is:
[tex]22x^2-2xy+3y^2[/tex]DISREGARD THE LAST ONE
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
A company manufactures computer memory chips as circular silicon wafers with a diameter of 10 Inches. The wafers are cut into
different sized sectors. Match each wafer's central angle to the area of that sector.
48°
20°
62°
45°
55°
Answer:
25/18 - 20
155/36 - 62
25/8 - 45
Step-by-step explanation:
can I please get answer quickly I just need to confirm I got it right
SOLUTION
We want to find the magnitude of the vector (-3, 4)
Magnitude of a vector is given as
[tex]\begin{gathered} |v|=\sqrt{x^2+y^2} \\ (x,y)=(-3,4) \\ we\text{ have } \\ =\sqrt{(-3)^2+4^2} \\ =\sqrt{9+16} \\ =\sqrt{25} \\ =5 \end{gathered}[/tex]Hence the answer is 5 units, the last option
through: (-5,4) perpendicular to x=5
First let's calculate the slope of the straight line
For slopes that are perpendicular to each other we can use the following formula
[tex]m1m2=-1[/tex]Where
m1 = original slope
m2 = perpendicular slope
[tex]\begin{gathered} m2=-\frac{1}{m1} \\ m2=-\frac{1}{5} \end{gathered}[/tex]Now for the intersection
[tex]\begin{gathered} b=y-mx \\ b=4-(\frac{-1}{5})\cdot(-5) \\ b=4-1 \\ b=3 \end{gathered}[/tex]The equation of the line that passes through the point (-5,4) with a slope of -1/5 is
[tex]y=-\frac{1}{5}x+3[/tex]What is the area of this rectangle?
3
7b ft
7
3
b+21 ft
Step-by-step explanation:
the area of a rectangle is
length × width.
in our case that is
(7/3 × b + 21) × (3/7 × b) =
= 7/3 × 3/7 × b × b + 21 × 3/7 × b =
= 1 × b² + 3×3 × b = b² + 9b = b(b + 9) ft²
so, the area is
b² + 9b = b(b + 9) ft²
remember, an area is always a square "something".
a volume a cubic "something".
so, when the lengths are given in feet, the areas are square feet or ft².
The perimeter of a rectangle is 48 centimeters. The relationship between the length, the width, and the perimeter of the rectangle can be described with the equation 2⋅length+2⋅width=48. Find the length, in centimeters, if the width is w centimeters
Using the relationship between the dimension of a rectangle and its perimeter, given its perimeter and width, the length is: 20.4 cm.
Recall:
Perimeter of a rectangle (P) = 2(L + W) (relationship between the width, length and perimeter)
Given:
Width (W) = 3.6 cm
Perimeter (P) = 48 cm
Length (L) = ?
Using the relationship between the dimension of a rectangle and its perimeter, the following equation would be derived:
48 = 2(L + 3.6)
Solve for the value of L
48 = 2L + 7.2
Subtract 7.2 from each side
48 - 7.2 = 2L
40.8 = 2L
Divide both sides by 2
20.4 = L
L = 20.4 cm
Therefore, using the relationship between the dimension of a rectangle and its perimeter, given its perimeter and width, the length is: 20.4 cm.
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Joe has $6,500 to invest One option is to invest some of his money in an account that earns 3% simple interest and the rest in an account that earns 2% simple interest. Joe would like to make at least $200 in interest this year. The following system of equations can be used to help Joe determine how much of his money he should invest at each rate. x +y = 6500 0.03x + 0.02y ≥ 200 The mathematical solution to this system is x=7000. Explain what the solution means in terms of how much Joe should invest in each account.
Data:
[tex]\begin{gathered} x+y=6500 \\ \\ 0.03x+0,02y\ge200 \end{gathered}[/tex]In this case;
x is the amount of money Joe should invest in first account (with 3% simple interest)
y is the amount of monet Joe should invest in second account (with 2% simple interest)
Then, if the mathematical solution for the given system is x=7000 it means that in order to get at least $200 in interest this year Joe needs to invest a bigger amount of money that he has, in the fisrt account ($7000) and in the second account y Joe shoul take a loan of $500 with 2% simple interest
[tex]\begin{gathered} x=7000 \\ x+y=6500 \\ y=6500-x_{} \\ y=6500-7000=-500 \end{gathered}[/tex]e22. Which expressions have values less than 1 whenx = 47 Select all that apply.(32)xo3x4
To know the expression that is less than 1 when x=4
we will need to check each expression
As for the first one;
[tex](\frac{3}{x^2})^0[/tex]anything raise to the power of zero will give 1, since the o affects all that is in the bracket, then the expression is 1
Hence it is not less than 1
For the second expression;
[tex]\frac{x^0}{3^2}=\frac{4^0}{9}=\frac{1}{9}[/tex]The value is less than 1
For the third expression;
[tex]\frac{1}{6^{-x}}[/tex]substituting x=4 in the above expression
[tex]\frac{1}{6^{-4}}[/tex]The above is the same as;
[tex]undefined[/tex]The dimensions of a rectangular prism are measured in centimeters. What unit will the volume of the prism be measured in?centimeterssquare centimeterscubic centimetersmeters
Given:
The dimensions of a rectangular prism are measured in centimetres.
Required:
What unit will the volume of the prism be measured in?
Explanation:
The volume of the prism will be measured in square centimetres
Final Answer:
Square centimeters
if Em=11, Am=16,CF=27, What are the lengths of the following sides
We will have the following:
First, we calculate AE as follows:
[tex]AE=\sqrt[]{AM^2-EM^2}[/tex]Now, we replace values and solve it:
[tex]AE=\sqrt[]{16^2-11^2}\Rightarrow AE=3\sqrt[]{15}[/tex]From theorem AE = EC therefore EC = esqrt(15); so, the following is true:
[tex]AC=AE+EC\Rightarrow AC=2AE\Rightarrow AC=2(3\sqrt[]{15})\Rightarrow AC=6\sqrt[]{15}[/tex]Knowing this, we then determine FA as follows:
[tex]FA=\sqrt[]{AC^2-CF^2}[/tex]We then determine BE, DM & CM as follows:
solve for y please and thank uou
Similar triangles are triangles that maintain the same ratio even though they are of different scales. Their angles are however equal.
In this case, y is the longest side in triangle 2 as 37.5 is the longest side in triangle 1
The ratio is thus:
[tex]\frac{y}{37.5}=\frac{16.5}{27.5}[/tex]Cross multiplying, we have:
[tex]\begin{gathered} 27.5y\text{ =37.5 x 16.5} \\ to\text{ get y, we divide both sides by 27.5} \\ \frac{27.5y}{27.5}\text{ = }\frac{\text{37.5 x 16.5}}{27.5} \end{gathered}[/tex]y = 22.5
Solve the inequality for x and identify the graph of its solution.|x+ 2] < 2Choose the answer that gives both the correct solution and the correct graph.
| x + 2 | < 2
-2 < x + 2 < 2
-2 - 2 < x + 2 < 2 - 2
-4 < x < 0 This is the inequality
Letter B is the right choice.
Simplify to create an equivalent expression. 2(3r + 7) - (2 +r) Over Choose 1 answer: Intro INCORRECT (SELECTED 4r + 12 You might have confused terms. Sub B 5r + 13 809 C 5r + 12
The frist step in simplifying the expression is expanding the term on the left. This gives
[tex]2(3r+7)=6r+14[/tex]therefore, the expression becomes
[tex]2(3r+7)-(2+r)=6r+14-(2+r)[/tex]and since
[tex]-(2+r)=-2-r[/tex]the above becomes
[tex]6r+14-2-r[/tex]Adding/subtracting the like terms gives
[tex]6r-r+14-2[/tex][tex]5r+12[/tex]which is our answer!
The roots of unity (1) may be calculated from the equation x3-1=0. What are they?
we find the root of x² + x + 1 has it can't be factorized
Using quadratic formula:
[tex]x\text{ = }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]for a² + bx + c = 0
comparing: x² + x + 1
where a = 1, b = 1, c = 1
[tex]\begin{gathered} x\text{ = }\frac{-1\pm\sqrt[]{(1)^2^{}-4(1)(1)}}{2(1)} \\ x\text{ = }\frac{-1\pm\sqrt[]{1^{}-4}}{2} \end{gathered}[/tex][tex]\begin{gathered} x\text{ = }\frac{-1\pm\sqrt[]{-3}}{2}\text{= }\frac{-1\pm\sqrt[]{-1(3)}}{2} \\ Since\text{ we can't find the square root of a negative number, we apply complex root} \\ \text{let i}^2\text{ = -1} \\ x\text{ = }\frac{-1\pm\sqrt[]{3i^2}}{2} \end{gathered}[/tex][tex]\begin{gathered} x\text{ = }\frac{-1\pm\sqrt[]{3i^2}}{2}\text{ = }\frac{-1\pm i\sqrt[]{3^{}}}{2} \\ x\text{ = }\frac{-1+i\sqrt[]{3^{}}}{2}or\text{ }\frac{-1-i\sqrt[]{3^{}}}{2} \\ \end{gathered}[/tex][tex]\begin{gathered} \text{The roots of x}^3\text{ - 1 = 0 are:} \\ 1\text{ and }\frac{-1\pm i\sqrt[]{3^{}}}{2} \\ 1\text{ and }\frac{\text{-1 }}{2}\pm\text{ }\frac{i\sqrt[]{3^{}}}{2}\text{ (option C)} \end{gathered}[/tex]State whether the given set of lines are parallel, perpendicular or neither.3x-2y=56y-9x=6The lines are Answer
Two lines are parallel if:
[tex]m1=m2[/tex]Two lines are perpendicular if:
[tex]m1\cdot m2=-1[/tex]---------------------
Let's rewrite the given equations in the slope-intercept form:
[tex]\begin{gathered} 3x-2y=5 \\ y=\frac{3}{2}x-\frac{5}{2} \\ -------- \\ 6y-9x=6 \\ y=\frac{3}{2}x+1 \end{gathered}[/tex]Since:
[tex]\begin{gathered} m1=m2 \\ \frac{3}{2}=\frac{3}{2} \\ \end{gathered}[/tex]We can conclude that the lines are parallel.
Pete Corporation produces bags of peanuts. Its fixed cost is $18,200. Each bag sells for $3.43 with a unit cost of $1.83. What is Pete’s breakeven point?
Let's call x to the bags of peanuts. One bag has a variable cost of $1.83, then the variable cost of x bags is 1.83x dollars.
The total cost of production for the corporation is obtained by adding fixed and variable costs. In this case, the total cost is 18,200 + 1.83x dollars.
The revenue for the corporation of 1 bag is $3.43, then of x bags is 3.43x dollars.
When the revenue and the total cost are equal, the breakeven point is reached, in this case:
18,200 + 1.83x = 3.43x
18,200 = 3.43x - 1.83x
18,200 = 1.6x
18,200/1.6 = x
11375 = x
The cost of production of 11375 bags is:
Total Cost = 18,200 + 1.83*11375
Total Cost = 18,200 + 20816.25
Total Cost = 39016.25
Pete’s breakeven point is (11375, 39016.25), or, 11375 bags and $39,016.25
Bobby was making a road trip to visit his parents. He stopped for gas and bought x number of gallons for $2.25 per gallon and a soda for $1.75. How much did he spend at the gas station if her purchased 15 gallons of gas?
Answer:
$35.5
Explanation:
If Bobby purchased 15 gallons of gas and each gallon cost $2.25, the total cost of the gallons of gas is:
15 x $2.25 = $33.75
Adittionally, Bobby bought a soda for $1.75, so he spend a total of:
$33.75 + $1.75 = $35.5
So, he spends $35.5
Solve for x. Round to the nearest tenth ofa degree, if necessary.5.3HGto8.5F
We have a rigth triangle, where we have to find the measure of x.
We can use trigonometric ratios to relate the lengths of the sides and the measure of x.
The lengths we know are from the hypotenuse and the adyacent side of x, so we can use the following trigonometric ratio:
[tex]\begin{gathered} \cos (x)=\frac{\text{Adyacent}}{\text{Hypotenuse}} \\ \cos (x)=\frac{5.3}{8.5} \\ x=\arccos (\frac{5.3}{8.5})\approx\arccos (0.623)\approx51.4\degree \end{gathered}[/tex]Answer: x = 51.4°
Covert1 1/4 percent to a decimal 5 bill has received a wage increased. His new hourly wage is $14.30 compared to previous wage of $12.95 find the percentage increase in bill hourly wage. Round it off to 2 decimal places
The percentage increase in bill hourly wage is 10.42%
Given,
Bill has received a wage increased.
His new hourly wage is $14.30
and, compared to old wage of $12.95
To find the percentage increase in bill hourly wage.
Now According to the question:
New bill is = $14.30
Old bill is = $ 12.95
= ($14.30 - $12.95) / $12.95
= $1.35 / $12.95
= 10.42%
Hence, The percentage increase in bill hourly wage is 10.42%
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Answer ASAP please and thank you :)
We can see the pairs (-1, 4) and (1, 4), so the function is not invertible.
Is the function g(x) invertible?
Remember that a function is only invertible if it is one-to-one.
This means that each output can be only mapped from a single input (the outputs are the values of g(x) and the inputs the values of x).
In the table, we can see the pairs (-1, 4) and (1, 4).
So both inputs x = -1 and x = 1 have the same output, this means that the function is not one-to-one, so it is not invertible.
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(b) Construct a 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone. Round the answers to at least three decimal places.
A 90% confidence interval for the proportion of cell phone owners aged 18 - 24
who have an Android phone is
SEE PHOTO
A 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone is 0.503 < p < 0.397.
In the given question,
We have to construct a 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone.
A 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone is
..............< p <...............
We have to construct the 90% confidence interval.
From the given question we know that among 240 cell phone owners aged 18 - 24 surveyed, 108 said their phone was an android phone.
So the total number of cell phone owners aged 18 - 24 is 240.
So n=240
From them 108 have an android phone.
So x=108
Estimation of sample proportion([tex]\hat p[/tex]) = x/n
Now putting the value
Estimation of sample proportion([tex]\hat p[/tex]) = 108/240
Estimation of sample proportion([tex]\hat p[/tex]) = 0.45
Now the construct a 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone
C.I. = [tex](\hat p \pm z_{\alpha /2}\sqrt\frac{\hat p(1-\hat p)}{n}})[/tex]
As we know that
[tex]\hat p=0.45[/tex]
Now finding the value of [tex]z_{\alpha /2}[/tex]
We have to find the 90% confidence interval. We can write 90% as 90/100 = 0.90
So [tex]\alpha[/tex] = 1-0.90
So [tex]z_{\alpha /2}=z_{0.10 /2}[/tex]
[tex]z_{\alpha /2}=z_{0.05}[/tex]
From the standard z table
[tex]z_{0.05}[/tex] = 1.645
Now putting the value in the
C.I. = [tex](\hat p \pm z_{\alpha /2}\sqrt\frac{\hat p(1-\hat p)}{n}})[/tex]
C.I. = [tex](0.45 \pm 1.645{\sqrt\frac{0.45(1-0.45)}{240}})[/tex]
Simplifying
C.I. = [tex](0.45 \pm 1.645{\sqrt\frac{0.45\times0.55}{240}})[/tex]
C.I. = [tex](0.45 \pm 1.645{\sqrt\frac{0.2475}{240}})[/tex]
C.I. = [tex](0.45 \pm 1.645\sqrt{0.001031})[/tex]
C.I. = [tex](0.45 \pm 1.645\times0.0321)[/tex]
C.I. = [tex](0.45 \pm 0.053)[/tex]
We can write it as
C.I. = {(0.45+0.053),(0.45-0.053)}
C.I. = (0.503,0.397)
Hence, a 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone is
0.503 < p < 0.397.
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The selling price of a refrigerator, is $537.60. If the markup is 5% of the dealer's cost, what is the dealer's cost of the refrigerator?
The cost price of dealer is $512.
We have to find the dealer's cost of refrigerator.
We know that mark up is on dealer's cost.
We have been given the markup as 5%
Let the dealer's cost of refrigerator be x,
Now, we know that there is a markup on it
So, we will calculate the marked up price
Marked up price = (Cost price * Markup percent)/100 + cost price
Marked up price = x*5/100 + x
Marked up price = 5x/100 + x
Marked up price = x/20 + x = (x+20x)20
Marked up price = 21x/20
We know that marked up price is the selling price and we have been given the selling price of the refrigerator
537.60 = 21x/20
537.60*20 = 21x
10752 = 21x
x = 10752/21
x = 512
The dealer's cost price is $512.
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Identify the composition that is represented by:r (90, O). T (-2, 4)A translation left 2, up 4 and then a reflection of 90°O A rotation of 90° and then a translation left 2, up 4.A reflection of 90° and then a translation left 2, up 4.O A translation of left 2, up 4 and then a rotation of 90°.
ANSWER:
A rotation of 90° and then a translation left 2, up 4.
STEP-BY-STEP EXPLANATION:
Since r (90, 0) is the first and means a 90 ° rotation and that T (-2, 4) is a translation of 2 units to the left (because it is negative) and 4 units up (because it is positive) , the answer is the option "A rotation of 90° and then a translation left 2, up 4."
in this problem you will use a ruler to estimate the length of AC. afterwards you will be able to see the lengths of the other two sides and you will use the pythagorean theorem to check your answer
Answer:
5.124
Explanation:
Given the following sides
AB = 6.5cm
BC = 4.0cm
Required
AC
Using the pythagoras theorem;
AB^2 = AC^2 + BC^2
6.5^2 = AC^2 + 4^2
42.25 = AC^2 + 16
AC^2 = 42.25 - 16
AC^2 = 26.25
AC = \sqrt{26.25}
AC = 5.124
Hence the actual length of AC to 3dp is 5.124
I need help with system B. I have one right. And if the answer is infinitely. It asks to satisfy and it has Y=
We have the next system of equations
[tex]\begin{gathered} -5x-y=5 \\ -5x+y=5 \end{gathered}[/tex]We can sum both equations we can eliminate one variable
[tex]\begin{gathered} -10x=10 \\ \end{gathered}[/tex]then we isolate the x
[tex]x=\frac{10}{-10}=-1[/tex]Therefore x=-1 then we substitute the value of x in order to find the value of y in the second equation
[tex]-5(-1)+y=5[/tex]Then we simplify
[tex]5+y=5[/tex]Then we isolate the y
[tex]y=5-5[/tex][tex]y=0[/tex]ANSWER
x=-1
y=0
5) 40,20,10,5, _,_,_a) Explain and Complete the sequence.B) write an explicit and recursive formula for the sequence
We have the sequence: 40, 20, 10, 5,...
Each term is half the previous term, so it is a geometrical sequence with common ratio r = 0.5.
We can not complete the sequence, as it becomes infinitely smaller and does not have a last term.
But we can write the three next terms to complete the blank spaces: 2.5, 1.25, 0.625.
We can start by writing the recursive formula. We know that each term is half the value of the previous term, so we wil have:
[tex]a_n=0.5\cdot a_{n-1}[/tex]From this recursive formula, we can deduce the explicit formula (in terms of n) as:
[tex]\begin{gathered} a_1=40 \\ a_2=0.5\cdot40=20 \\ a_3=0.5\cdot20=0.5\cdot(0.5\cdot40)=0.5^2\cdot40=10 \\ a_4=0.5\cdot10=0.5\cdot(0.5^2\cdot40)=0.5^3\cdot40 \\ \Rightarrow a_n=40\cdot0.5^{n-1} \end{gathered}[/tex]Answer:
a) Geometric sequence with r = 0.5.
The sequence first terms are: 40, 20, 10, 5, 2.5, 1.25, 0.625.
b) The recursive formula is a(n) = 0.5*a(n-1).
The explicit formula is a(n) = 40*0.5^(n-1).
12) A row of roses is planted in a repeating pattern of "red, red, yellow, yellow, pink, pink
There is a total of 56 roses planted in the row. How many red roses are there?
Answer:
********
Answer:
22
Step-by-step explanation:
XXxxxxXXxxxxXXxxxxXXxxxxXXxxxxXXxxxxXXxxxxXXxxxxXXxxxxXX
Each of the capital X's are red roses, and there are 56 x's in total.
The table shows the outcome of car accidents in a certain state for a recent year by whether or not the driver wore a seat belt. Find the probability of wearing a seat belt, given that the driver did not survive a car accident. Part 1: The probability as a decimal is _ (Round to 3 decimal places as needed.) Part 2: The probability as a fraction is _
Conditional probability is a measure of the probability of an event occurring, given that another event has already occurred.
The table shows the outcome of car accidents by whether or not the driver wearing a seat belt.
Let's call:
A = The event of the driver wearing a seat belt in a car accident.
B = The event of the driver dying in a car accident
The conditional probability is calculated as follows:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]The conditional probability stated in the formula is that for the driver wearing a seat belt knowing he did not survive the car accident.
The numerator of the formula is the probability of both events occurring, i.e., the driver wore a seat belt and died. The denominator is the simple probability that the driver died in a car accident.
From the table, we can intersect the first column and the second row to find the number of outcomes where both events occurred. The probability of A ∩ B is:
[tex]P(A\cap B)=\frac{511}{583,470}[/tex]The probability of B is:
[tex]P(B)=\frac{2217}{583,470}[/tex]The required probability is:
[tex]P(A|B)=\frac{\frac{511}{583,470}}{\frac{2217}{583,470}}[/tex]Simplifying the common denominators:
[tex]P(A|B)=\frac{511}{2217}=0.230[/tex](2, -3) (4, -2)
Slope intercept
The slope of the given coordinates is m = 1/2.
What is the slope?A line's steepness can be determined by looking at its slope. The slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the point where the y-intercept is located (0, b). For instance, the slope and y-intercept of the equation y = 3x - 7 are 3 and 0, respectively.So, the slope of (2, -3) (4, -2):
The slope formula: m = y₂ - y₁/x₂ - x₁Now, solve for slope by putting the values as follows:
m = y₂ - y₁/x₂ - x₁m = -2 - (-3)/4 - 2m = -2 + 3/2m = 1/2Therefore, the slope of the given coordinates is m = 1/2.
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The correct question is shown below:
Find the slope using the coordinates (2, -3) (4, -2).
Name a postulate or theorem that can be used with the given information to prove that the lines are parallel<3 ~ <7
Postulates and Theorems of Parallel Lines
First, we need to know what type of angles are <3 and <7. Following the definition:
If two lines are crossed by another line, the angles in matching corners are called Corresponding Angles.
Angles 3 and 7 are corresponding angles and they are told to be congruent.
Now we apply the postulate that reads:
The Converse of the Corresponding Angles Postulate. If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.
The postulate that can be used to prove that the lines are parallel is The Converse of the Corresponding Angles Postulate
