Answer:
20 hours
5 hours- 25%
10 hours- 50%
15 hours- 75%
20 hours- 100%
100 Points! Geometry question. Photo attached. Determine whether the quadrilateral is a parallelogram. Justify your answer using a theorem. Please show as much work as possible. Thank you!
The prove of the statement is described below.
First of all ,
Labeling the given figure
And draw a diagonal,
In the quadrilateral PQRS,
The side PQ is equal to the side RS.
Therefore,
PQ = RS
And also, the side PQ is parallel to the side RS.
Then,
PQ || RS.
Now, draw the diagonal PR.
We know that a parallelogram's diagonal divides the parallelogram into two congruent triangles.
By the rule of Side-Angle-Side,
we can show that ∆ PQR ≅ ∆ RSP.
Therefore,
The side QR is parallel to PS
Then,
QR || PS.
Hence,
PQRS is a parallelogram.
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Describe the location of point (−7, 6, −4) in three-dimensional coordinate space.
The description of the location of the point, (−7, 6, −4) in three-dimensional coordinate space is this: A. From the origin, move 7 units back, 6 units right, and 4 units down.
What is a three-dimensional coordinate space?The meaning of a three-dimensional coordinate space is a requirement for three units to come together to form a point. In the location of the point above, we are given three units namely, -7, 6, and -4.
The indication of signs in front of them are as follows; -7, means moving 7 units back, 6 means moving 6 units right, ad -4 means moving 4 units down.
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How can graph coloring be applied in real-world situations, and what are the challenges and limitations associated with using graph coloring algorithms? Provide specific examples to support your answer.
Answer:
Graph coloring is a widely used concept in real-world situations, particularly in computer science and engineering. It involves assigning colors to the vertices of a graph, with no adjacent vertices having the same color. One real-world application of graph coloring is in scheduling problems, where tasks must be assigned to resources such as workers or machines, with the constraint that no two tasks requiring the same resource can be scheduled at the same time. Another application is in map coloring, where regions on a map are assigned colors in such a way that no two adjacent regions have the same color.
Challenges and limitations associated with using graph coloring algorithms include the exponential increase in computation time as the size of the graph increases, making it difficult to apply the algorithm to very large graphs. Additionally, some graph coloring problems may be NP-hard, meaning that no polynomial-time algorithm is known that can solve them for all possible inputs. This can make it challenging to find an optimal solution, and instead approximate solutions may need to be used.
For example, in telecommunication networks, channel assignment is a common problem of graph coloring. In mobile networks, different channels must be assigned to different cells to avoid interference and ensure efficient use of resources. The channel assignment problem can be formulated as a graph coloring problem, where the vertices represent cells and the edges represent interference.
Another example is in scheduling of sports leagues. In this case, teams are assigned to play on different days and times in such a way that no two teams play against each other more than once and no team plays two games on the same day. This can be formulated as a graph coloring problem, with vertices representing teams and edges representing games between teams.
In conclusion, graph coloring algorithms have numerous real-world applications. While there are challenges and limitations associated with these algorithms, they continue to be an important tool for solving optimization problems in a wide range of fields.
Step-by-step explanation:
least common denominator of -3/a and 1/4a^2
Answer:
-12a-1/4a2
Step-by-step explanation:
Use the graph to answer the question.
Graph of polygon ABCD with vertices at negative 2 comma negative 1, 0 comma negative 4, 4 comma negative 4, 2 comma negative 1. A second polygon A prime B prime C prime D prime with vertices at 5 comma negative 1, 7 comma negative 4, 11 comma negative 4, 9 comma negative 1.
Determine the translation used to create the image.
7 units to the right
3 units to the right
7 units to the left
3 units to the left
The translation used to create the image of the second polygon is A, 7 units to the right.
How to determine translation?To determine the translation used to create the image of the second polygon (A' B' C' D') from the original polygon (ABCD), compare the corresponding vertices.
Original polygon (ABCD):
A (-2, -1)
B (0, -4)
C (4, -4)
D (2, -1)
Image polygon (A' B' C' D'):
A' (5, -1)
B' (7, -4)
C' (11, -4)
D' (9, -1)
To find the translation, calculate the horizontal and vertical differences between the corresponding vertices.
Horizontal difference:
For point A: A'x - Ax = 5 - (-2) = 7
For point B: B'x - Bx = 7 - 0 = 7
For point C: C'x - Cx = 11 - 4 = 7
For point D: D'x - Dx = 9 - 2 = 7
Vertical difference:
For point A: A'y - Ay = -1 - (-1) = 0
For point B: B'y - By = -4 - (-4) = 0
For point C: C'y - Cy = -4 - (-4) = 0
For point D: D'y - Dy = -1 - (-1) = 0
From the calculations, see that the horizontal difference is 7 units for all the corresponding vertices, while the vertical difference is 0 units for all the corresponding vertices.
Therefore, the translation used to create the image of the second polygon is 7 units to the right.
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Mathematical form of the question:
Use the graph to answer the question.
Graph of polygon ABCD with vertices at A (-2, -1), B (0, -4), C (4, -4), D (2, -1). A second polygon A' (5, -1), B' (7, -4), C' (11, -4), D' (9, -1).
Determine the translation used to create the image.
7 units to the right
3 units to the right
7 units to the left
3 units to the left
Calculate the unknown length, x, in the shape below.
If your answer is a decimal, give it to 1 d.p.
8
8 cm
area = 55 cm²
area=178.2 cm²
15 cm
The triangles are similar triangles. Then the value of 'x' will be 27 cm.
The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
From the above theorem, the equation is given as,
(x/15)² = 178.2 / 55
Simplify the equation, then we have
(x/15)² = 3.24
x/15 = 1.8
x = 27 cm
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Copy and complete the pattern in the table
The pattern in the table should be completed as follows;
Number of 1 3 9 27 81
students with pets
Total number 3 9 27 81 243
of students
A ratio that compares the number of blue squares to the total number of squares is 3 : 4.
What is a proportional relationship?In Mathematics and Geometry, a proportional relationship can be modeled or represented by the following mathematical equation:
y = kx
Where:
y represents the x-variable.x represents the y-variable.k is the constant of proportionality.Next, we would find the constant of proportionality (k) by using various data points as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 3/1 = 9/3
Constant of proportionality, k = 3.
y = 3x
81 = 3x
x = 27
x = 9/3
x = 3
y = 3(81)
y = 243
For the ratio of blue squares to total squares, we have:
18/24 = 3/4 = 3 : 4
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Help with my school work, I spend 80 points on this question. I will give brainiest for correct answer.
If 1 + 2 = 3, then why does 4 + 5 not = 6?
And if 2 x 2 = 4, then why does 4 x 4 not = 8?
Answer:
Because equations is not counting, and multiply is not addition.
Step-by-step explanation:
Addition is: a process of combining two or more numbers. Addends are the numbers being added, and the result or the final answer we get after the process is called the sum. It is one of the essential mathematical functions we use in our everyday activities. There are many situations in which we add numbers.
Like lets say you have 1 apple, and your friend gives 2 more, then you have 3. If you have 4 apples, and your friend gives 5 more, then you have 9 apples.
Its always better to start with the bigger number, it makes it easier, like 2 + 1 = 3, or 5 + 4 = 9.
Now multiplication is harder. Multiplication is: the basic explanation of multiplication is adding a number, with respect to another number, repeatedly. For example, if we are multiplying 2 by 3, that means 3 is added to itself two times, i.e. 3 + 3 = 6. This is a simple technique for kids to multiply numbers.
(Answer) 2 x 2 would equal 4. (Explanation) Add a 2, with respect to 2, repeatedly, would equal 4.
(Answer) 4 x 4 would equal 16. (Explanation) Add a 4, with respect to 4, repeatedly, would equal 16.
I hope it helps you out!Mark me as brainiest please. HAVE A GREAT REST OF YOUR DAY/NIGHT!!!Answer: Step-by-step explanation:
because 1 + 2 does equal 3 but 4 + 5 does not equal to 6 because it equals to 9.
and 2 x 2 does equal to 4 but 4 x 4 does not equal to 8 because it equals to 16.
Mark me brainiest pls.Have good day.Ms. Edwards is redecorating her office. She has a choice of 8 colors of paint, 5 kinds of curtains, and 6 colors of carpet. How many different ways are there to redecorate?
240 ways
297 ways
357 ways
19 ways
Answer:
To determine the total number of different ways Ms. Edwards can redecorate her office, we need to multiply the number of choices for each item:
Number of paint color choices = 8
Number of curtain choices = 5
Number of carpet color choices = 6
To calculate the total number of ways, we multiply these choices together:
Total number of ways = Number of paint color choices × Number of curtain choices × Number of carpet color choices
= 8 × 5 × 6
= 240
Therefore, there are 240 different ways for Ms. Edwards to redecorate her office. So, the answer is 240 ways.
19
Evaluate the following:
25 (23 +8÷4) +5
16
B) 20
27
D) 28
pls pls help, will give brainliest answer!!
Answer:
Equation of the triangle: (x + 74) + 73 + (37 + x) = 180°
Solve for x: x = -2
Find the measure of angle A: A = 35°
Step-by-step explanation:
Step 1: We know that the 73° angle and the angle inside the triangle that lies opposite it are vertical angles ,so this angle is also 73° .
Step 2: Similarly, the (x + 74)° angle and the angle inside the triangle that lies opposite it are also vertical angles, so this angle is also represented by the expressions (x + 74)°
Equation of the triangle: The triangle sum theorem states that the sum of the interior angles of a triangle equals 180°. Thus, the equation of the triangle is (x + 74) + 73 + (37 + x) = 180
Solving for x:
Step 1: Rearrange and combine like terms:
(x + 74) + 73 + (37 + x) = 180
(x + x) + (74 + 73 + 37) = 180
2x + 184 = 180
Step 1: Subtract 184 from both sides:
(2x + 184 = 180) - 184
2x = -4
Step 3: Divide both sides by 2 to solve for x:
(2x = -4) / 2
x = -2
Finding the measure of angle A: Now we can plug in -2 for x in the expression representing the measure of angle A to find the actual measure:
A = 37 - 2
A = 35
Thus, the measure of angle A is 35°.
Optional Step: We can check that our equation of the triangle, the value we've found for x, and the measure of angle A is correct by simply plugging in -2 for x in the equation of the triangle and checking that we get 180 on both sides:
(-2 + 74) + 73 + (37 - 2) = 180
72 + 73 + 35 = 180
145 + 35 = 180
180 = 180
Thus, all of our answers are correct.
4. Higher Order Thinking A national TV
news show conducted an online poll to find
the nation's favorite
comedian. The
website showed
the pictures of
5 comedians and
asked visitors of the
site to vote. The news
show inferred that
the comedian with
the most votes was
the funniest comedian
in the nation.
a. Is the inference valid? Explain.
b. How could you improve the poll? Explain.
No, the inference is not necessarily valid. The fact that a comedian received the most votes in an online poll does not guarantee that they are the funniest comedian in the nation.
Is the inference valid? Explain.The poll's results are influenced by various factors such as the sample size, the demographics of the voters and potential biases in the voting process.
Also, humor is subjective and what one person finds funny may not be the same for someone else. Therefore, determining the funniest comedian based solely on the number of votes in an online poll is an oversimplified and flawed approach.
To improve the poll, several steps can be taken which are:
Increase sample sizeUse random samplingImplement multiple criteriaConduct a live event or competition.Read more about inference
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
An auto body shop repaired 22 cars and trucks. There were 8 fewer cars than trucks. How many trucks were repaired. URGENT PLEASE HELP
If an auto body shop repaired 22 cars and trucks and there were 8 fewer cars than trucks, 15 trucks were repaired.
Let's assume the number of trucks repaired is "x". We know that the total number of cars and trucks repaired is 22. Since there were 8 fewer cars than trucks, the number of cars repaired must be x-8. Therefore, we can set up the following equation:
x + (x-8) = 22
Simplifying, we get:
2x - 8 = 22
Adding 8 to both sides:
2x = 30
Dividing by 2:
x = 15
We can check this by plugging x back into the equation and verifying that the number of cars repaired is 7, which is 8 fewer than 15.
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Currently it is estimated that 3 out of every 1000 Californians are infected with
coronavirus. The so-called rapid "antigen" test for coronavirus has a very low false
positive rate of just 0.05, but has a high false negative rate of 0.2. The so-called
PCR test is more reliable: it has an even lower false positive rate than the antigen
test, namely only 0.001, but even more importantly its false negative rate is much
lower at 0.01.
What is the probability that you have a coronavirus infection conditional on your
PCR test has coming back positive?
The probability that an antigen test comes back positive is approximately 0.05225, or about 5.225%.
We have,
To find the probability that an antigen test comes back positive, we need to consider both the true positive rate (probability of a positive test given that the person is infected) and the false positive rate.
Now,
Prevalence of coronavirus in California: 3 out of 1000
False positive rate of the antigen test: 0.05 (5 out of 100)
Let's calculate the probability of a positive test result.
The true positive rate can be calculated as 1 minus the false negative rate (probability of a negative test given that the person is infected):
True positive rate = 1 - 0.2 = 0.8 (or 80 out of 100)
The probability of a positive test result can be calculated using Bayes' theorem:
P(Positive test) = P(Positive test | Infected) x P(Infected) + P(Positive test | Not Infected) x P(Not Infected)
P(Positive test) = (0.8 x 3/1000) + (0.05 x 997/1000)
P(Positive test) = 0.0024 + 0.04985
P(Positive test) = 0.05225
Therefore,
The probability that an antigen test comes back positive is approximately 0.05225, or about 5.225%.
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Halle planted mint and basil seeds in her herb garden. She measured the height of each herb plant at the end of each week for six weeks. The results are shown in the line graph below.
What is the difference to the nearest tenth in the mean growth per week for both herbs during the six weeks shown in the graph?
A. 0.7cm/week
B. 0.6cm/week
C. 3.7cm/week
The difference in mean growth per week is 3.7cm/week
From the graph given :
Growth per week for Basil = 2, 6, 9, 10, 14, 16
Growth per week for Mint = 1, 2, 4, 7, 9, 12
Mean growth per week = (2+6+9+10+14+16) / 6 = 9.5 cm/week
Mean growth per week (Mint) = (1+2+4+7+9+12)/6 = 5.83 cm/week
The difference cannbe obtained by subtracting the mean Values thus ;
Difference in average growth = 9.5 - 5.83 = 3.67 cm/week
Therefore, the difference in mean growth per week is 3.7cm/week
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Find the area of the parallelogram with given points.
(7,4)
(3,0)
(-4,9)
(13,0)
The area of the parallelogram with given points is 8√26 or 40.79 square units.
How to calculate the area of this parallelogram?In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:
Area of a parallelogram, A = b × h
Where:
b represents the base area of a parallelogram.h represents the height of a parallelogram.Height = √[(x₂ - x₁)² + (y₂ - y₁)²]
Height = √[(3 - 7)² + (0 - 4)²]
Height = √32 units.
Base = √[(13 - 7)² + (0 - 4)²]
Base = √52 units
By substituting the given parameters into the formula for the area of a parallelogram, we have the following;
Area of a parallelogram = √32 × √52
Area of a parallelogram = 8√26 or 40.79 square units.
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Katrina wants to make a cover for her laptop to fit into her bag in order to protect it. She measured the top of her laptop and found it was 57,000 mm2. “No one sells covers using square millimeters,” her friend noted. Describe the area of the top of Katrina’s laptop using square centimeters.
Answer:
To convert square millimeters to square centimeters, we need to divide the area in square millimeters by 100 (since there are 100 square millimeters in a square centimeter).
So, the area of the top of Katrina's laptop in square centimeters would be:
57,000 mm² ÷ 100 = 570 cm²
Therefore, the area of the top of Katrina's laptop in square centimeters is 570 cm².
NEED THIS SOLVED ASAP!!!!!!!!!!!! I AM GIVING 15 POINTS
Arm Span (inches) / Height (inches)
58 60
49 47
51 55
19 25
37 39
44 45
47 49
36 35
41 40
46 50
58 61
Using graphing software of your choice, create a scatter plot of your data. Predict the line of best fit, and sketch it on your graph.
Copy and paste your scatter plot into a word-processing document. (Recommend me this software so I can do this part).
Using graphing software of your choice, create a scatter plot of your data. Predict the line of best fit, and sketch it on your graph.
Copy and paste your scatter plot into a word-processing document.
The scatter plot for the above data and it's line of best fit is attached accordingly. You may achieve this result using Microsoft Excel.
How to plot scatter plot on Microsoft ExcelEnter your data into two columns in an Excel worksheet. For example, in columns A and B, enter the years and corresponding life expectancies from your given data.
Select the data range by clicking and dragging over the cells containing the data.
Go to the "Insert" tab in the Excel ribbon.
In the "Charts" group, click on the "Scatter" chart type. Choose the scatter plot style that suits your preference (e.g., "Scatter with Straight Lines").
A scatter plot will be created on your worksheet.
Right- click on any data point on the scatter plot and choose "Add Trendline" from the context menu.
In the "Format Trendline" pane that appears on the right side of the screen, select the "Linear" trendline option.
Check the box for "Display Equation on Chart" if you want to show the equation of the line of best fit on the chart.
You can further customize the appearance of the scatter plot and the trendline using various chart formatting options in Excel.
Your scatter plot with the line of best fit is now plotted on Excel.
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1/5 ( x - 10 ) = 4/5
The value of x is 14
What are fractions?Fractions are described as expression that shows the part of a whole number, a whole variable. a whole element.
The different types of fractions are listed as;
Improper fractionsProper fractionsMixed fractionsSimple fractionsComplex fractionsFrom the information given, we have that;
1/5 ( x - 10 ) = 4/5
This is written as;
(x -10)/5 = 4/5
cross multiply the values, we have;
5(x-10) = 20
expand the bracket
5x - 50 = 20
Collect like terms
5x = 70
Divide the values
x =14
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Write and solve an equation to find the value of x.
The value of x for each item is given as follows:
28. x = 5.
29. x = 3.44.
How to obtain the value of x in each item?For item 28, we apply the crossing chord theorem, which states that the products of the parts of the chords are equal, hence the value of x is obtained as follows:
16x = 10 x 8
16x = 80
x = 5.
For item 29, we apply the two secant theorem, hence the value of x is obtained as follows:
10(x + 10) = 12(12 + 25)
10x + 100 = 444
10x = 344
x = 3.44.
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Question 5 Joy is a 52-year-old nurse who earns a salary of R286 500 per annum. She contributes 7% of her annua salary to a pension fund. She only has her 2 daughters listed as a dependents on her medical aid. Sh is concerned that the R4000 monthly income tax deduction is too much.
Determine Joy's annual income tax liability. If the amount is significantly different from the R4000 monthly deduction, she may need to consult a tax advisor to ensure accurate tax planning.
To assess whether the monthly income tax deduction of R4000 is too much for Joy, we need to calculate her annual income tax liability and compare it to the deduction.
First, let's calculate the amount Joy contributes to her pension fund annually:
Pension fund contribution = 7% of annual salary
Pension fund contribution = 7/100 * R286,500
Pension fund contribution = R20,055
Next, we need to determine Joy's taxable income by subtracting her pension fund contribution from her annual salary:
Taxable income = Annual salary - Pension fund contribution
Taxable income = R286,500 - R20,055
Taxable income = R266,445
Now, we can calculate the income tax liability based on the South African income tax brackets for the 2023 tax year. Please note that tax brackets are subject to change, so it's essential to verify with the latest tax regulations.
According to the current tax brackets, the tax rates for the 2023 tax year are as follows:
18% on the first R216,200 of taxable income
26% on the portion of taxable income between R216,201 and R337,800
31% on the portion of taxable income between R337,801 and R467,500
36% on the portion of taxable income between R467,501 and R613,600
39% on the portion of taxable income above R613,601
Using these tax rates, we can calculate the income tax liability:
Tax liability = (18% * amount within first bracket) + (26% * amount within second bracket) + (31% * amount within third bracket) + (36% * amount within fourth bracket) + (39% * amount within fifth bracket)
First, let's calculate the amounts within each tax bracket:
Amount within first bracket = min(Taxable income, R216,200)
Amount within second bracket = min(max(Taxable income - R216,200, 0), R337,800 - R216,201)
Amount within third bracket = min(max(Taxable income - R337,800, 0), R467,500 - R337,801)
Amount within fourth bracket = min(max(Taxable income - R467,500, 0), R613,600 - R467,501)
Amount within fifth bracket = max(Taxable income - R613,600, 0)
Now, let's substitute the values and calculate the income tax liability:
Tax liability = (18% * min(Taxable income, R216,200)) + (26% * min(max(Taxable income - R216,200, 0), R337,800 - R216,201)) + (31% * min(max(Taxable income - R337,800, 0), R467,500 - R337,801)) + (36% * min(max(Taxable income - R467,500, 0), R613,600 - R467,501)) + (39% * max(Taxable income - R613,600, 0))
By calculating this equation, you can determine Joy's annual income tax liability. If the amount is significantly different from the R4000 monthly deduction, she may need to consult a tax advisor to ensure accurate tax planning.
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Why can you not have 1 imaginary solution?
You cannot have 1 imaginary solution because the quadratic equation must have either two real solutions or two complex solutions
What is an imaginary solution?In mathematics, the discriminant (D = b2 - 4ac) aids in identifying the kind of solutions to quadratic equations of the form ax2 + bx + c = 0.
There are two unique real solutions if the discriminant is positive. There is only one viable option if the discriminant is zero. There are no practical solutions, however, if the discriminant is negative.
The quadratic equation in this instance has two complex solutions that are conjugates of one another. Because the quadratic equation must have either two real solutions or two complex solutions, there can never be just one hypothetical solution.
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Help me please! Thanks
The identification of the polygon that are given in the diagram above would be =
Polygon 1 = Isosceles trapezoid
polygon 2 = parallelogram
polygon 3 = Rectangle
polygon 4 = Rhombus
polygon 5 = Square
polygon 6 = trapezoid
What are the properties of the polynomials given above?Isosceles trapezoid : This is the type that of polygon in which the the top and base are not equal in length, but they are parallel to each other.
Parallelogram : This is defined as the type of polygon that has two pairs of parallel sides.
Rectangle : This has two pairs of sides that are equal and opposite.
Rhombus: All the sides are equal in length with its opposite angles equal .
Square: All sides are equal in length but and all angles are equal to 90°.
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What is the quotient of the expression
O7a³ + ab + 3
O7a³ + ab - 3
O7a³ + 4ab+
+8
O7a³+4ab-8
28a b+4a²b²-12ab?
4ab
The quotient of the expression (7a³ + ab + 3) / (7a³ + ab - 3) divided by 4ab is (7/4a²) + (1/4b) + (3/4ab).
How to find the quotientBy dividing each term of the numerator by 4ab:
(7a³ + ab + 3) / (7a³ + ab - 3) ÷ 4ab
= (7a³ / 4ab) + (ab / 4ab) + (3 / 4ab)
Simplifying each term individually:
= (7/4a²) + (1/4b) + (3/4ab)
Thus, the quotient of the expression (7a³ + ab + 3) / (7a³ + ab - 3) divided by 4ab is (7/4a²) + (1/4b) + (3/4ab).
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Lines y and z are parallel.
Parallel lines are cut by transversals s and t. The angles formed by lines s, t, and y, clockwise from top left, are blank, blank, (10 x + 5) degrees, blank, (4 x minus 7) degrees, blank; formed by s and z are 65 degrees, 1, blank, blank; formed by z and t are 2, blank, blank, blank.
What is the measure of angle 2?
6 degrees
11 degrees
28 degrees
37 degrees
The measure of Angle 2 is 17 degrees.
The measure of angle 2, the relationships between the given angles formed by the parallel lines and transversals.
1. The angles formed by lines s, t, and y, clockwise from top left, are:
- Blank
- Blank
- (10x + 5) degrees
- Blank
- (4x - 7) degrees
- Blank
2. The angles formed by s and z are:
- 65 degrees
- 1
- Blank
- Blank
3. The angles formed by z and t are:
- 2
- Blank
- Blank
- Blank
From the given information, we can deduce the following:
- Angle 1 is congruent to the angle formed by z and t (corresponding angles).
- Angle (10x + 5) degrees is congruent to angle 65 degrees (alternate interior angles).
- Angle (4x - 7) degrees is congruent to angle 2 (alternate interior angles).
Therefore, we can set up the following equations:
65 = 10x + 5 (Equation 1)
2 = 4x - 7 (Equation 2)
Solving Equation 1:
65 - 5 = 10x
60 = 10x
x = 6
Substituting x = 6 into Equation 2:
2 = 4(6) - 7
2 = 24 - 7
2 = 17
Hence, the measure of angle 2 is 17 degrees.
Therefore, the correct answer is:Angle 2 = 17 degrees.
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17. Find m2NSR=
Segment AB is tangent to circle C. Find r.
18. r=
176
40°
35
25
Need help. Please show work and answer 17 and 18
1. The value of angle NSR is 110°
2. The value of r 12
What is arc angle relationships?If two secants or chords intersect inside a circle, then the measure of the angle formed is equal to half the sum of the measures of the intercepted arcs.
Therefore;
S = 1/2( 170+40)
S = 1/2 ( 210)
S = 110
Therefore the value of angle NSR is 110°
2. There is a theorem that states that the angle between a radius and tangent is 90°
Using Pythagorean theorem
(25+r)² = r² +35²
= 625 + 50r + r² = r² +35²
625 +50r = r² - r² +35²
50r = 1125-625
50r = 600
r = 600/50
r = 12
therefore the value of r is 12
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An equilateral triangle has a perimeter of 36 inches. What is the height of the triangle? Express your answer as a simplified radical.
Answer: the height of the equilateral triangle is 6√3 inches.
Step-by-step explanation:
To find the height of an equilateral triangle, we can use the formula:
height = (√3/2) * side
In this case, we are given the perimeter of the triangle, which is 36 inches.
Since an equilateral triangle has three equal sides, each side would be 36 inches divided by 3, which is 12 inches.
Now we can substitute the side length into the formula:
height = (√3/2) * 12
Simplifying:
height = (√3/2) * 12
height = (√3 * 12)/2
height = (12√3)/2
height = 6√3
Therefore, the height of the equilateral triangle is 6√3 inches.
Answer:
RG
Step-by-step explanation:
Expand & simplify.
23p - 3( 2k + 14p ) + 5( 6k - p )
Answer:
23p -6k - 42p + 30k - 5p
23p - 42p - 5p + 30k - 6k
23p - 47p + 24k
-24p + 24k
24(- p + k)
24( k - p)
Answer:
The answer is
60p + 24k
Step-by-step explanation:
1: Expand
=23p - 6k + 42p + 30k - 5p
step2: collect like terms
=42p + 23p - 5p - 6k + 30k
step 3: add/subtract them to get your answer
=60p + 24k
your answer☝
What is the equation of the line that passes through (4, 3) and (-4, -1)?
Choices:
2x+1
y=2x+7
y=x/2 +1
y= -x/2 +7
The equation of the line that passes through (4, 3) and (-4, -1) is y = -x/2 + 5. So, correct option is A.
To find the equation of the line that passes through two given points, we use the slope-intercept form of a linear equation, which is:
y = mx + b
where m is the slope of the line and b is the y-intercept.
First, we need to find the slope of the line using the two given points. The formula for finding slope between two points is:
m = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.
Substituting the given points into the formula, we get:
m = (-1 - 3) / (-4 - 4) = -4/8 = -1/2
Now we know the slope, we can use one of the given points (4, 3) and substitute the slope into the slope-intercept form of the equation and solve for b.
y = mx + b
3 = (-1/2)(4) + b
3 = -2 + b
b = 5
Therefore, the equation of the line that passes through (4, 3) and (-4, -1) is:
y = -x/2 + 5
So, correct option is A.
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Complete question is:
What is the equation of the line that passes through (4, 3) and (-4, -1)?
Choices:
y = -x/2 + 5
y=2x+7
y=x/2 +1
y= -x/2 +7