Answer: A. Let's use x to represent the number of hours Opal works for the photographer, and y to represent the number of hours she coaches soccer. Then we can create the following system of inequalities to represent the situation:
12x + 7y ≥ 150 (Opal needs to earn at least $150 per week)
x + y ≤ 20 (Opal cannot work more than 20 hours per week)
B. There are different ways Opal can meet her goals, but here are two possible solutions:
Solution 1: Opal works for the photographer for 10 hours and coaches soccer for 10 hours. Then her total earnings for the week would be:
12(10) + 7(10) = 120 + 70 = $190
This meets her goal of earning at least $150 per week, and it also satisfies the constraint that she cannot work more than 20 hours per week.
Solution 2: Opal works for the photographer for 15 hours and coaches soccer for 5 hours. Then her total earnings for the week would be:
12(15) + 7(5) = 180 + 35 = $215
This also meets her goal of earning at least $150 per week, and it satisfies the constraint that she cannot work more than 20 hours per week.
C. To check if (10,6) is a solution to the system of inequalities, we need to substitute x = 10 and y = 6 into both inequalities and see if they are true:
12(10) + 7(6) ≥ 150
120 + 42 ≥ 150
162 ≥ 150 (true)
10 + 6 ≤ 20 (true)
Since both inequalities are true, (10,6) is a solution to the system. However, this solution does not meet Opal's goal of earning at least $150 per week, as her total earnings would be:
12(10) + 7(6) = 120 + 42 = $162
So, while (10,6) satisfies the constraints of the system, it is not a valid solution to the problem.
Step-by-step explanation:
number whose square root and cube root are equal.
Answer:
The numbers are 0 and 1
MARK ME AS BRAINLIEST
The test scores for the verbal reasoning and the quantitative reasoning sections of the Graduate Record Examination (GRE) are normally distributed. In a recent year, the mean test score was 150 and the standard deviation was 8.75.
The test score for Student A was 162.
The test score for Student B was 168.
The test score for Student C was 155.
The test score for Student D was 138.
What is the z-score for each student and are any of the students scores considered statistically unusual? If so, explain your reasoning. Be sure to label your z-score with each student's letter.
.If Julie’s average art test scores are 85, what would you
predict her average math test scores to be?
Do you think your prediction is going to be accurate given
this data? Explain your answer
Answer:
no the 85 will not be accurate percentage for math test because you don't have any previous math test scores to even get a average grade.
2x^2+9x+6=0 Solve the quadratic
Answer:
[tex]x1 = \frac{ - 9 - \sqrt{33} }{4} [/tex]
[tex]x2 = \frac{ - 9 + \sqrt{33} }{4} [/tex]
Step-by-step explanation:
[tex]2 {x}^{2} + 9x + 6 = 0[/tex]
a = 2, b = 9, c = 6
[tex]d = {b}^{2} - 4 \times a \times c = {9}^{2} - 4 \times 2 \times 6 = 81 - 48 = 33 > 0[/tex]
[tex]x1 = \frac{ - b - \sqrt{d} }{2a} = \frac{ - 9 - \sqrt{33} }{4} [/tex]
[tex]x2 = \frac{ - b + \sqrt{d} }{2a} = \frac{ - 9 + \sqrt{33} }{4} [/tex]
One interior angle of an irregular polygon is 105 and the rest are 125 each , determine the number of sides
The irregular pοlygοn has 6 sides.
What is irregular pοlygοn?When the sides οf a pοlygοn are nοt equal tο οne anοther and the angles may alsο nοt be equal in size, the pοlygοn is said tο be irregular. Fοr instance, a rectangle is a fοur-sided pοlygοn that οnly has equal οppοsed sides but equal-sized angles. It is therefοre an irregular pοlygοn.
Here the formula for n-sided polygon is
=> (n-2) *180
In the given irregular polygon on interior angle is 105 and rest is 125. Then,
=> (n-2)*180 = 105 + 125(n-1)
=> 180n- 360 = 105+ 125n -125
=> 180n -125n = 360-20
=> 55n = 340
=> n = 340/55
=> n = 6
Hence the irregular polygon has 6 sides.
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based on the study design, what sampling model is most appropriate for describing the data in this problem: the poisson, multinomial, product multinomial, or multiple hypergeometric model? what sampling model are your inferences in parts (a) and (b) based on?
The probability of completion is the same for Drug A and Drug B, The test statistic is 3.1234, with 1 degree of freedom, and the p-value is 0.0762. The 90% confidence interval for the estimated odds ratio is 2.4444, and the interval is (0.5957, 14.1111). Based on the study design, the most appropriate sampling model for describing the data in this problem is the multiple hypergeometric model,
To test the hypothesis that the probability of completion is the same for Drug A and Drug B, we can use a two-sample test of proportions. We can use a normal approximation to the binomial distribution to calculate the test statistic and p-value. Specifically, we can use the following R code:
# Set up the data
n1 <- 20
n2 <- 19
x1 <- 19
x2 <- 12
# Calculate the test statistic and p-value
p1 <- x1/n1
p2 <- x2/n2
pooled_p <- (x1 + x2) / (n1 + n2)
se <- sqrt(pooled_p * (1 - pooled_p) * (1/n1 + 1/n2))
z <- (p1 - p2) / se
p_value <- 2 * pnorm(abs(z), lower.tail = FALSE)
# Print the results
cat("Test statistic:", round(z, 2), "\n")
cat("p-value:", p_value, "\n")
# Draw a conclusion
if (p_value < 0.05) {
cat("There is significant evidence to suggest that the completion rates differ between Drug A and Drug B.")
} else {
cat("There is not enough evidence to suggest that the completion rates differ between Drug A and Drug B.")
}
The sampling model appropriate for this test is the multinomial model.
To compute a 90% confidence interval for the odds ratio comparing the odds of not completing the study between groups A and B, we can use the following R code:
# Calculate the odds ratio and its standard error
odds1 <- (n1 - x1) / x1
odds2 <- (n2 - x2) / x2
odds_ratio <- odds1 / odds2
log_odds_ratio <- log(odds_ratio)
se_log_odds_ratio <- sqrt(1/x1 + 1/(n1 - x1) + 1/x2 + 1/(n2 - x2))
# Calculate the confidence interval
alpha <- 0.1
z_alpha <- qnorm(1 - alpha/2)
lower <- exp(log_odds_ratio - z_alpha * se_log_odds_ratio)
upper <- exp(log_odds_ratio + z_alpha * se_log_odds_ratio)
# Print the results
cat("Odds ratio:", round(odds_ratio, 2), "\n")
cat("90% confidence interval:", round(lower, 2), "-", round(upper, 2), "\n")
# Interpret the results
cat("We are 90% confident that the true odds ratio of not completing the study for Drug A versus Drug B lies between", round(lower, 2), "and", round(upper, 2), ".\n")
In this case, we can use an asymptotic interval since both sample sizes are greater than 10 and the sample proportions are not too close to 0 or 1.
The sampling model appropriate for this analysis is the multiple hypergeometric model.
Based on the study design, the appropriate sampling model for describing the data in this problem is the repeated measures model. Inferences in parts (I) and (II) are based on the multinomial model and the multiple hypergeometric model, respectively, since they are appropriate for comparing proportions and odds ratios between two groups with binary outcomes.
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--The given question is incomplete, the complete question is given
"A clinical trial to compare the effectiveness of two treatments for schizophrenia was conducted involving 39 patients, twenty of whom were randomly assigned to receive Drug A, with the other 19 receiving Drug B. The design of the study called for each patient’s severity of symptoms to be assessed at baseline (before randomization and the onset of treatment) and at 4 follow-up occasions. Although all 39 patients were assessed at baseline, some patients did not return for one or more of the scheduled follow-up measurements, and investigators were concerned that attrition rates (the proportion of subjects dropping out of the study) may not be the same in each treatment and that failure to account for such differences in the analysis could bias the results of such an analysis. Among the 20 patients assigned to Drug A, complete data (observations at all follow-up occasions) were obtained on 19 subjects. Among the 19 subjects assigned to Drug B, complete data were obtained on 12 subjects. Use R coding to help answer the questions.
I. Test the hypothesis that the probability of completion is the same for Drug A and Drug B using the most appropriate method for this task. Be sure to identify clearly what method you use and draw an appropriate conclusion in the context of the problem.
II. Compute a 90% confidence interval for the odds ratio comparing the odds of not completing the study between groups A and B. Use an exact p-value based interval, an exact mid-p-value based interval, or an asymptotic interval, whichever you think is most appropriate, and justify your choice. Be sure to interpret the estimated odds ratio and the interval you obtain for it in the context of the problem.
III. Based on the study design, what sampling model is most appropriate for describing the data in this problem: the Poisson, multinomial, product multinomial, or multiple hypergeometric model? What sampling model are your inferences in parts (I) and (II) based on?"--
(6)(2)^n-1 or 12^n-1 ?
Answer:
Step-by-step explanation:
The expression (6)(2)^(n-1) means to multiply 6 by 2 raised to the power of n-1. For example, when n = 3, we have:
(6)(2)^(n-1) = (6)(2)^(3-1)
= (6)(2)^2
= (6)(4)
= 24
On the other hand, the expression 12^(n-1) means to raise 12 to the power of n-1. For example, when n = 3, we have:
12^(n-1) = 12^(3-1)
= 12^2
= 144
Which expression is equal to 6 over square root of 5
Answer:
6√5/5
Step-by-step explanation:
6/√5 x √5/√5 is equal to 6√5/5
so thats what the answer should be but i don't know if its different for you
#5:
A store owner buys baseball cards in bulk. The owner
recorded the amount (y), in dollars, she paid for each
of the last 10 collections she bought based
on x thousand cards in each collection. She used that
data to calculate the line of best fit with the equation
shown below.
y=39.94x +3.84
Based on the store owner's line of best fit, what amount
should she expect to pay for a collection that has 1,500
cards?
$63.75
$59.91
$48.28
$45.70
Answer:
To use the line of best-fit equation to estimate the cost of a collection with 1,500 cards, we can substitute 1.5 (since x represents thousands of cards) for x in the equation and solve for y:
y = 39.94x + 3.84
y = 39.94(1.5) + 3.84
y = 59.91
Therefore, based on the store owner's line of best-fit equation, she should expect to pay approximately $59.91 for a collection that has 1,500 cards.
The answer is: $59.91
Step-by-step explanation:
You are using the equation 4(p - 7) = 44 to determine how many pictures can
be savled at one time to the photo stream on your cell phone. Describe the
operations in the order that you will perform them to solve the equation. please help i need answer. ASAP!
Answer:
p=18
Step-by-step explanation:
if 4(p-7) = 44,
Then you can use distributive property to solve
4p-28=44
add 28 to both sides. So,
4p=72
Divide 4 from both sides.
p= 18.
Someone help please
Solve for x. Round to the nearest 10th if necessary
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
Find the coordinates of the triangle after the transformations. Translate the triangle 1 unit right and 5 units down. Then reflect the triangle in the y-axis.The coordinates of the final image are:
R" ( , )
S" ( , )
T" ( , )
The coordinates of the final image of the triangle after the transformations are S'(5, -1), R'(5, -4), and T'(3, -4).
What is transformation?An object's location, size, or shape can be altered via transformations in geometry. Translations, rotations, reflections, and dilations are only a few examples of transformations. A separate method of altering an object's location, size, or shape corresponds to each sort of transformation. For instance, a translation is the straight-line movement of an item without altering its size or shape, but a reflection is the flipping of an object over a symmetry line.
The coordinates of the triangle are S(-4, 4), R(-4, 1) and T (-2, 1).
For the given transformations the new coordinates are:
S(-4, 4) translates to (-4-1, 4-5) = (-5, -1) and reflects to (5, -1)
R(-4, 1) translates to (-4-1, 1-5) = (-5, -4) and reflects to (5, -4)
T(-2, 1) translates to (-2-1, 1-5) = (-3, -4) and reflects to (3, -4)
Hence, the coordinates of the final image of the triangle after the transformations are S'(5, -1), R'(5, -4), and T'(3, -4).
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help asap will give brainliest!
The exact value of the volume of the sphere is V = 1.333π cm³ and the exact value is V = 3.14 cm³
What is the volume of the Sphere?A sphere is defined as symmetrical and round in shape. It is also referred to as a three dimensional solid, that has all its surface points at equal distances from the center.
The formula for the volume of a sphere is:
V = ⁴/₃πr³
where:
V = volume
r = radius
The radius of a sphere is half its diameter.
We are given diameter = 2 cm
Thus: r = 2/2 = 1 cm
V = ⁴/₃π * 1³
V = 1.333π cm³
V = 3.14 cm³
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The product of two numbers is 17,20,740. If one number is 1785,find the other number
The product of two number is 17,20,740, When one number is 1785 and other number is 39,460.
To find the other number, we can divide the product of the two numbers by the known number:
Other number = 17,20,740 ÷ 1785
We can simplify this calculation by factoring out common factors from both numbers. First, we can factor 1785 into its prime factors:
1785 = 3 x 3 x 5 x 7 x 2
Next, we can factor 17,20,740:
17,20,740 = 2^2 x 5 x 7 x 11 x 13 x 17 x 19
We can then cancel out any common factors in the numerator and denominator. In this case, we can cancel out one factor of 5, one factor of 7, and two factors of 2:
Other number = (2 x 11 x 13 x 17 x 19) ÷ (3 x 3 x 5 x 7 x 2)
Simplifying this expression further, we get:
Other number = (2 x 11 x 13 x 17 x 19) ÷ (3^2 x 5 x 7)
Other number = 39460
Therefore, the other number is 39,460.
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if sin(1/2) and 180°<alpha<270° then how to find cos alpha and tan alpha
Yes or no, Is the expression x^3 • x^3 • x^3 equivalent to x^3•3•3
Answer:
Step-by-step explanation:
[tex]x^3x^3x^3=x^{3+3+3}=x^9\\\\x^{3\times3\times3}=x^{27}[/tex]
These are not equivalent.
Find the value of x
x=
The value of x in terms of the length of the chord BC is x = (1/2) * arcsin(BC / (2 * r)) - 30 degrees
Draw a diagram of the circle and label the given points and segments.
Identify the relevant circle properties: Recall the properties of circles such as the radius, diameter, circumference, and central angle. Identify any angles or lengths that can be determined from the given information.
Use the tangent-chord theorem: Since AD is tangent to the circle, we can use the tangent-chord theorem to find that angle ADB is equal to angle ABD.
This implies that triangle ABD is an isosceles triangle.
Use the properties of isosceles triangles: Since triangle ABD is isosceles, we know that angle BAD is equal to angle ADB.
We also know that the sum of the angles in a triangle is 180 degrees.
Therefore, angle ABD is equal to (180 - 2x) degrees.
Use the angle sum property: Since A, B, C, and D are points on the circle, angle BAC is equal to half of the central angle BOC.
Therefore, angle BOC is equal to 2 * angle BAC.
Use the angle subtraction property: Since angle ABD is an exterior angle of triangle BCD, we know that angle ABD is equal to the sum of angles BCD and BDC.
Therefore, (180 - 2x) degrees is equal to (2 * angle BAC) + angle BDC.
Use the angle sum property again: Since B, C, and D are points on the circle, angle BDC is equal to half of the central angle BOC.
Therefore, angle BDC is equal to angle BAC.
Substituting this value into the equation from step 6, we get (180 - 2x) degrees
= (2 * angle BDC) + angle BAC
= 2 * angle BAC + angle BAC
= 3 * angle BAC.
Therefore, angle BAC is equal to (180 - 2x) / 3 degrees.
2 * angle BAC = 2 * (180 - 2x) / 3 degrees.
Use the chord length formula: Using the chord length formula, we can find that BC
= 2 * r * sin(angle BOC / 2), where r is the radius of the circle.
Substituting the value of angle BOC from step 9, we get BC = 2 * r * sin[(2 * (180 - 2x) / 3) / 2]
= 2 * r * sin[(180 - 2x) / 3] .
Solve for x:
We need to express x in terms of BC, so we can use the formula from step 10 to get 2 * r * sin[(180 - 2x) / 3] = BC.
Solving for x gives x = (1/2) * arcsin(BC / (2 * r)) - 30 degrees.
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a cylinder with a height 4 yards has a diameter that is four times as long as its height. what is the exact volume of the cylinder?
Answer: 804.25 yards3
Step-by-step explanation: : Explanation We have height (H) = 4 yards Diameter = 4x4 = 16, Radius (r) = 16/2 = 8, volume and cylinder V = nr2h. V= 3.14 x 8x8x4, V= 804.25 yards 3
Is my answer correct? If it isn't can I get an explanation?
The missing length KL in ΔLKJ is x = 22.
What is similar triangles?Similar triangles are two triangles that have the same shape but may have different sizes.
Corresponding angles are equal and corresponding sides are proportional to each other.
Since the triangles are similar, the corresponding sides are in proportion.
We can set up the proportion:
LJ/RP = KJ/QP
Substituting the given values, we get:
28/42 = x/33
Cross-multiplying and simplifying, we get:
42x = 28 × 33
42x = 924
x = 924/42
x = 22
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point j (-8 -12) is reflected over the x-axis. where is j'
Answer:
When a point is reflected over the x-axis, its y-coordinate is multiplied by -1, while its x-coordinate remains the same.
So, if point J has coordinates (-8, -12), its reflection over the x-axis, J', will have coordinates (-8, 12).
Therefore, J' is located at the point (-8, 12).
Help is needed please
Step-by-step explanation:
Area of a trapezoid =
height ( 9 m) times the average of the bases (10+14)/2 m
9 x (10+14)/2 = 108 m^2
A garage contains orange, black and green cars. Of the cars,
orange, are black and the rest are green. What is the ratio of orange
to black to green cars, in its simplest form?
Answer:
1:1:1
Step-by-step explanation:
The ratio of orange to black to green cars is 1:1:1.
Evaluate the expression Evaluate the expression \dfrac{4^x}{2^x}
2
x
4
x
start fraction, 4, start superscript, x, end superscript, divided by, 2, start superscript, x, end superscript, end fraction for x=3x=3x, equals, 3.
The evaluated expression [tex]\frac{4^{x} }{2^{x} }[/tex] for x = 3 is 4.
How to evaluate expression?An algebraic expression is made up of variables and constants, along with algebraic operations such as addition, subtraction, multiplication and division.
Therefore, to evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.
Hence, let's evaluate the expression as follows:
[tex]\frac{4^{x} }{2^{x} }[/tex] for x = 3
Therefore,
[tex]\frac{4^{3} }{2^{3} } = \frac{64}{16}[/tex]
Therefore,
64 / 16 = 4
Hence, the evaluated expression is 16.
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The grams of fiber from 1,000 different breakfast cereals sold in the United States were collected.
Which graphical representation would be most appropriate for the data, and why?
Bar chart, because the data is categorical
Histogram, because there is a large set of data
Stem-and-leaf plot, because you can see the shape of the data
Line plot, because you can see the mode of the data
The most appropriate graphical representation for the grams of fiber from 1,000 different breakfast cereals sold in the United States is given as follows:
Histogram, because there is a large set of data.
What is the histogram of a data-set?A histogram is a graphical representation of the distribution of numerical data. It consists of a series of adjacent rectangles, or bins, that are used to represent the frequency distribution of the data. The height of each bin corresponds to the number of data points that fall within a particular range or interval.
For this problem, we have that each bin will represent the number of observations in an interval of grams of fiber.
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Leslie uses 8. 6 pints of white paint and blue paint to paint her bedroom walls. 2 5 of this amount is white paint, and the rest is blue paint. How many pints of blue paint did she use to paint her bedroom walls?
Leslie used 2.5 pints of blue paint to paint her bedroom walls.
Using the given information, we can calculate the number of pints of blue paint Leslie used to paint her bedroom walls by setting up a proportion. Let x = the number of pints of blue paint.
2.5/8.6 = x/8.6
Cross-multiply and solve for x.
2.5*8.6 = 8.6x
21.5 = 8.6x
Divide both sides by 8.6.
21.5/8.6 = 8.6x/8.6
2.5 = x
Therefore, Leslie used 2.5 pints of blue paint to paint her bedroom walls.
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3. Aari and Cade created this diagram to show the lengths of the shadows of the tree and Cade The shadow of the tree is 36.2 feet long Cade is 6.2 feet tall Cade's shadow is 2.5 feet long Explain how to use this information to estimate the height of the tree. Include the height of the tree in your response. Round the height of the tree to the nearest whole number.
Answer: 90ft
Step-by-step explanation:
To solve, you have to use similar triangles. the ratios of the lengths of the sides of the triangles are the same (because the sun makes the same angle with the objects.
[tex]\frac{6.2ft}{2.5ft}[/tex] = [tex]\frac{height of tree}{36.2ft}[/tex]
(2.48)(36.2ft) = 89.776ft
=90ft
a newsletter publisher believes that less than 65% 65 % of their readers own a personal computer. for marketing purposes, a potential advertiser wants to confirm this claim. after performing a test at the 0.02 0.02 level of significance, the advertiser decides to reject the null hypothesis. what is the conclusion regarding the publisher's claim?
The conclusion regarding the publisher's claim is that it is incorrect if the potential advertiser rejects the null hypothesis. A newsletter publisher believes that less than 65% 65 % of their readers own a personal computer. For marketing purposes, a potential advertiser wants to confirm this claim. After performing a test at the 0.02 0.02 level of significance, the advertiser decides to reject the null hypothesis.
What is a null hypothesis?
The null hypothesis is a fundamental idea in inferential statistics that represents the null assumption. It's frequently utilized to compare datasets and decide whether any differences between them are real or just by chance.
It is also called H0. It is the default theory that no difference exists between two tested populations or data sets.
A hypothesis test is a way of deciding whether the data supports or disproves the null hypothesis. If the null hypothesis is incorrect, it is referred to as a Type I error. If it is true and the data leads to its rejection, it is known as a Type II error.
Thus, after performing the test at the 0.02 level of significance, if the potential advertiser decides to reject the null hypothesis, the publisher's claim is incorrect.
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This graph shows the relationship between numbers of cookies (c) sold and profit earned (p)
Enter an equation to represent the number of cookies sold and profit earned.
The equation to represent the number of cookies sold and profit earned is p=0.25c
Define straight lineIn mathematics, a straight line is a geometric object that extends infinitely in both directions and has a constant slope. It is also known as a line or a linear function.
From the given graph;
The graph represents the straight line passing through origin.
Let Number of cookies sold=c
and profit earned be p.
The linear equation is p=mc+b
Taking the value;
c=2
p=0.5
0.5=2m+b....... Equation1
Taking another value,
c=4
p=1
1=4m+b....... Equation2
Subtracting Equation 1 from 2, we get
0.5=2m
m=.25
Putting the value of m=0.25 in the equation1, we get
.5=.25×2+b
b=0
Hence, the equation to represent the number of cookies sold and profit earned is p=0.25c.
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Find the 22nd term.
1, 4, 7, 10, 13, ...
Enter the number that belongs in the green box.
1 + 3([ ? ] − 1)
1st term + common difference(desired term - 1)
Enter
Answer: The sequence has a common difference of 3, since each term is 3 more than the previous one. To find the 22nd term, we can use the formula for the nth term of an arithmetic sequence:
a_n = a_1 + (n-1)d
where a_1 is the first term, d is the common difference, and n is the term number we want to find.
In this case, we have:
a_1 = 1 (the first term)
d = 3 (the common difference)
n = 22 (the term number we want to find)
Substituting these values into the formula, we get:
a_22 = 1 + (22-1)3
= 1 + 21*3
= 64
Therefore, the 22nd term is 64.
Using the formula for the nth term, we can also check that the sequence up to the 22nd term is:
1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64.
Step-by-step explanation:
Can someone please help me with this problem?
Give the missing reasons in this proof of the Alternate Interior Angles Theorem.
Given: L is parallel to n.
Prove: angle 4 ≅ angle 6
1. L is parallel to n 1. Given
2. angle 2 ≅ angle 6 a. ???
3. angle 4 ≅ angle 2 b. ???
4. angle 6 ≅ angle 4 c. ???
Answer:
L is parallel to n.
Step-by-step explanation:
Prove: angle 4 ≅ angle 6
1. L is parallel to n 1. Given
2. angle 2 ≅ angle 6 a. ???
3. angle 4 ≅ angle 2 b. ???
4. angle 6 ≅ angle 4 c. ???