Find the angle measure indicated. Assume that lines which appear tangent are tangent. A. 110 degrees B. 175 degrees C. 155 degrees D. 120 degrees
Answers
Therefore, the angle measure indicated 110° that is option A.
What is angle?An angle is the measure of the amount of rotation between two intersecting lines or planes. It is defined as the space between two intersecting lines or planes measured in degrees, radians, or other units of angular measurement. Angles are often represented by a symbol that looks like a small arc, with three letters labeling the points that define the angle, such as "ABC." The vertex of an angle is the point where the two lines or planes intersect, and the sides of an angle are the two rays that extend from the vertex. Angles are used in geometry, trigonometry, and other mathematical fields to measure and analyze the relationships between shapes and objects.
Here,
Since sector PF has a measure of 90 degrees, then angle PAF must also have a measure of 90 degrees since it is an inscribed angle that intercepts the same arc.
To find the angle measure of QSR, we first need to find the measure of angle QPR.
Since sector PF is a 90 degree sector and line QR is tangent to the circle at point R, we know that angle QRP is a right angle (90 degrees).
Similarly, since sector QR is a 150 degree sector and line PS is tangent to the circle at point S, we know that angle QPS is a right angle (90 degrees).
Therefore, angle QPR + angle QPS = 90 + 90 = 180 degrees.
Since angle QPS and angle QRP share ray QR, they are adjacent angles.
So, angle QSR = 360 - (angle QPR + angle QPS)
= 360 - 180 -70
= 110 degrees
Therefore, the measure of angle QSR is 110 degrees, which is equivalent to a straight line.
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Related Questions
(d+3)(d^2-4d+1) solve using the FOIL method
Answers
After solving (d + 3)(d² - 4d + 1) by using the FOIL method we get d³ - d² - 11d + 3.
The foil method is a strategy for organising your memory of the steps
needed to multiply two binomials. First, outer, inner, and last are the
letters that make up the acronym F-O-I-L.
To solve the given expression using the FOIL method, you have to follow the below steps:
F: Multiply the First terms (d x d²)
O: Multiply the Outer terms (d x -4d)
I: Multiply the Inner terms (3 x d²) and
L: Multiply the Last terms (3 x 1)
Finally, combine the like terms to get the answer
(d + 3)(d² - 4d + 1)= d(d² - 4d + 1) + 3(d² - 4d + 1)
= d³ - 4d² + d + 3d² - 12d + 3
= d³ - d² - 11d + 3
Thus, (d + 3)(d² - 4d + 1) equals d³ - d² - 11d + 3.
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Which of the following equations represents a linear function?
Oy=¹1x²
Oy-x-7
Ox=4
3x - 5= 18
Answers
Answer:
O y = 15x + 10 is the only linear function
Hope this helps!!!
After watching the Quest Kickoff video, which examines the work of an astronomer who searches for life on planets outside our solar system, think about the qualities that make for a skilled astronomer. What scientific attitudes are important to the work of an astronomer such as the one in the video? Record your thoughts.
NOTEBOOK
Answers
A deep appreciation for the natural world and a desire to contribute to advancing scientific knowledge is essential for pursuing a career in astronomy.
Astronomers require a combination of scientific attitudes to excel in their work. To begin with, they need to be curious and passionate about exploring the unknown universe. They should also have a strong sense of patience, persistence, and attention to detail, given that astronomical observations can take a long time to produce results. A capacity for critical thinking, creativity, and problem-solving is also crucial in analyzing and interpreting data, developing theories, and testing hypotheses. Additionally, astronomers must be skilled in communication, as they often collaborate with colleagues, present their findings to the scientific community and the public, and engage in public outreach and education efforts.
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Last week, Joi bought the same set of fidget poppers at the regular price of $20, plus 8% sales tax. How much more did Joi pay than Adelyn for each fidget popper?
Answers
Answer:
To find out how much more Joi paid than Adelyn for each fidget popper, we need to know how much Adelyn paid for each fidget popper.
If we assume that Adelyn bought the same set of fidget poppers as Joi at the regular price of $20 without tax, then we can calculate how much Adelyn paid for each fidget popper by dividing the total price by the number of fidget poppers in the set.
Let’s say that there are 10 fidget poppers in the set. Then, Adelyn paid $20 / 10 = $2 per fidget popper.
Joi bought the same set of fidget poppers at the regular price of $20 plus 8% sales tax. To find out how much Joi paid for each fidget popper, we can add the sales tax to the regular price and then divide by the number of fidget poppers in the set.
The sales tax is 8% of $20, which is $1.60. So, Joi paid a total of $20 + $1.60 = $21.60 for the set.
If there are 10 fidget poppers in the set, then Joi paid $21.60 / 10 = $2.16 per fidget popper.
To find out how much more Joi paid than Adelyn for each fidget popper, we can subtract Adelyn’s price per fidget popper from Joi’s price per fidget popper:
$2.16 - $2 = $0.16
Therefore, Joi paid $0.16 more than Adelyn for each fidget popper
Answer:
Nn
Step-by-step explanation:
help asap!!!!!!!!!!!!!!!
Answers
LA = 4(1/2)sl = 2(4 m)(8 m) = 64 m^2
B = s^2 = (4 m)^2 = 16 m^2
SA = 64 m^2 + 16 m^2 = 80 m^2
So the answer is 80 m^2.
#1 Original price: $50
Discount: 30%
What is the sale price?
Answers
To find the sale price, we need to apply the discount to the original price:
Discount = 30% = 0.30
Original price = $50
Discount amount = Discount x Original price
= 0.30 x $50
= $15
Sale price = Original price - Discount amount
= $50 - $15
= $35
Therefore, the sale price after a 30% discount on an original price of $50 is $35.
Answer:
$35
Step-by-step explanation:
70% of 50 is 35
Find the range of the given data
95.5,65.7,78.2,68.3,95.4,11.2,78.5,55.4,23.6,37.5,95.3,16.9,64.2,11.8,77.1,23.1,90,78.7,22.5,11.6,87.8,95.1,63,78.1
Answers
Answer:
84.3.
Step-by-step explanation:
To find the range of the given data, we need to subtract the smallest value from the largest value in the set.
The smallest value in the set is 11.2 and the largest value is 95.5. Therefore, the range is:
Range = Largest value - Smallest value
= 95.5 - 11.2
= 84.3
the range of the given data is 84.3.
Consider the diagram below. Which of the variables (consumer surplus, producer surplus, and deadweight loss) have decreased due to the price floor of $9.00 set by the government?
Answers
Consumer surplus and deadweight loss have decreased due to the price floor of $9.00 set by the government. The correct option is c.
To answer this question, we need to first understand what a price floor is and how it affects the market.
A price floor is a government-imposed minimum price that must be paid for a good or service.
In the context of a market, a price floor that is set above the equilibrium price will create a surplus of the good or service.
This is because the price floor creates a situation where the quantity supplied exceeds the quantity demanded.
Now, let's examine the diagram:
^
| P=$9.00 <- price floor
S | / \
| / \
$10 | / \
|/ \
$8 / \
| \
$6 /|_________\
| \
| Qd Qs |
|___________|
Q
In this diagram, the price floor is set at $9.00, which is above the equilibrium price of $8.00.
As a result, there is a surplus of the good, with quantity supplied (Qs) exceeding quantity demanded (Qd).
Now, let's consider the impact on consumer surplus, producer surplus, and deadweight loss:
Consumer surplus is the difference between the price consumers are willing to pay and the actual price they pay. In this case, the price consumers are willing to pay is below the price floor, so consumer surplus is reduced. Therefore, option c.) "Consumer surplus and deadweight loss" is the correct answer.
Producer surplus is the difference between the price producers receive and the minimum price they are willing to accept. In this case, the price producers receive is above the equilibrium price, so producer surplus is increased. Therefore, option b.) "Consumer surplus and producer surplus" is incorrect.
Deadweight loss is the loss of economic efficiency that occurs when the quantity of a good that is bought and sold is below or above the equilibrium quantity. In this case, the price floor creates a surplus, which leads to deadweight loss. Therefore, option d.) "Only deadweight loss" is incorrect.
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Consider the diagram below. Which of the variables (consumer surplus, producer surplus, and deadweight loss) have decreased due to the price floor of $9.00 set by the government?
a.) Producer surplus and deadweight loss
b.) Consumer surplus and producer surplus
c.) Consumer surplus and deadweight loss
d.) Only deadweight loss
which of the following statements about quadratic functions are true? select all that apply. a quadratic function is either concave up or concave down, but never both. a quadratic function must have a vertex and that is where either the maximum or minimum value is attained. a quadratic function can never change from increasing to decreasing, or from decreasing to increasing. if the leading term of a quadratic has a negative coefficient, then the quadratic must have a minimum. a quadratic function always attains both a maximum and a minimum value. all quadratic functions have two real roots. if a quadratic function has two real roots, then the x -value that corresponds to the max/min
Answers
The Statements 1,2 and 4 are true about quadratic function. So, the right answer for this problem is options (1), (2) and (4).
Quadratic function is defined as a function whose highest power of exponent is 2.
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how many lists of length 3 can be made from the letters u, v, w, x, y, z if repetitions are not allowed, and each list has a w or u in the second entry?
Answers
If repeats are forbidden, the provided letters u, v, w, x, y, and z can be used to create 8 lists of length 3, each of which has a w or u in the second entry.
We can apply the inclusion-exclusion concept to resolve this issue.
First, let's determine how many total lists of length three can be created using the provided letters without any limitations. There are six options for the first submission, five for the second (since it must be either w or u), and four for the third (since no characters can be repeated). Thus, there are a total of the following lists:
6 × 5 × 4 = 120
Next, let's count the number of lists of length 3 that do not have a w or u in the second entry. We have 6 choices for the first entry, 4 choices for the second entry (since we can't choose w or u), and 4 choices for the third entry (since we can't repeat any letters). Thus, the total number of such lists is:
6 × 4 × 4 = 96
Similarly, we can tally the number of lists of length 3 lacking a w or u in the first entry as well as the number of lists of length 3 lacking a w or u in either the first or second entry. Which are:
4 × 5 × 4 = 80 (no w or u in first entry)
4 × 4 × 4 = 64 (no w or u in first or second entry)
Finally, we can use the principle of inclusion-exclusion to count the number of lists that have a w or u in the second entry. This is:
120 - 96 - 80 + 64 = 8
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What is the equation of the circle in standard form?
(x-4)² + (y− 1)² = 3
(x-4)² + (y - 1)² = 9
(x + 4)² + (y + 1)² = 3
(x+4)² + (y + 1)² – 9
Answers
The calculated value of the equation of the circle in standard form is: (x - 4)^2 + (y - 1)^2 = 9
What is the equation of the circle in standard form?The equation of a circle with center (h, k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
In this case, the center of the circle is (4, 1) and the radius is 3.
So we can plug in these values to get:
(x - 4)^2 + (y - 1)^2 = 3^2
Simplifying and expanding, we get:
(x - 4)^2 + (y - 1)^2 = 9
So the equation of the circle in standard form is: (x - 4)^2 + (y - 1)^2 = 9
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Solve for x. Round your answer to the nearest tenth
Answers
The numerical value of x rounded to the nearest tenth is 7.5.
What is the numerical value of x?The Midsegment Theorem states that the segment joining the midpoints of two sides of a triangle is parallel to and half the length of the third side.
Hence:
the smaller segment = half the third side
From the diagram;
The smaller segment = x
The larger third side = 15
Using the Midsegment Theorem
x = half of 15
Solve for x
x = 1/2 × 15
x = 15/2
x = 7.5
Therefore, the value of x is 7.5.
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Patty is building a rope ladder for a tree house. She needs two 4-foot pieces of rope for the sides of the
ladder. She needs 6 pieces of rope, each 15 inches long, for the steps.
How many feet of rope does Patty need to make the ladder?
Enter your answer in simplest form.
Answers
Answer:
15.5 feet
Step-by-step explanation:
12 (each foot have 12 inches) × 8 (two 4-foot pieces of rope) = 96
6 (six pieces of rope) × 15 (each rope have fifteen inches long) = 90
90 + 96 = 186
186 ÷ 12 = 15.5
12 × 15.5 = 186
Patty need 15.5 feet.
of the respondents, 517 support same-sex marriage. what is the 95 % confidence interval for the proportion of all american adults who support same-sex marriage?
Answers
The 95% confidence interval for the proportion of all American adults who support same-sex marriage is 0.485 to 0.549.
The following formula is used to calculate a confidence interval for the proportion of all American adults who support same-sex marriage
KI = p ± z*(√(p*(1-p)/n))
where:
p = percentage of respondents who support same-sex marriage
n = sample size (total number of respondents)
z = z-score for the desired confidence level
substitute all the values in the above formula,
CI = 0.517 ± 1.96*(√(0.517*(1-0.517)/n))
To compute confidence intervals, we need to know the sample size (n). the sample size is large, so we can use the normal distribution.
the random sample size of 1000 is taken as no sample size is specified.
For n = 1000,
CI = 0.517 ± 1.96*(√(0.517*(1-0.517)/1000))
= 0.517 ± 0.032
Therefore, the 95% confidence interval for the proportion of all American adults who support same-sex marriage is 0.485 to 0.549.
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A movie theater wanted to determine the average rate that their diet soda is purchased. An employee gathered data
on the amount of diet soda remaining in the machine, y, for several hours after the machine is filled, x. The following
scatter plot and line of fit was created to display the data.
Soda Machine
Amount of Diet Soda
Find the y-intercept of the line of fit and explain its meaning in the context of the data.
The y-intercept is -4.8. The machine starts with 4.8 ounces of diet soda.
O The y-intercept is -4.8. The machine loses about 4.8 fluid ounces of diet soda each hour.
O The y-intercept is 40.98. The machine starts with 40.98 ounces of diet soda.
O The y-intercept is 40.98. The machine loses about 40.98 fluid ounces of diet soda each hour.
Answers
Option D is incorrect because it gives a value that is not consistent with the scatter plot and the line of fit. The correct answer is: The y-intercept is 40.98. The machine starts with 40.98 ounces of diet soda.
What is y-intercept?In the context of a graph, the y-intercept is the point where a straight line or curve intersects the y-axis. It is the value of the dependent variable (y) when the independent variable (x) is equal to zero. Mathematically, it is the value of y when x = 0 in the equation of the line or curve. The y-intercept is also known as the initial value or starting point of the graph. It is often denoted as (0, b), where b is the y-coordinate of the intercept point.
The y-intercept of the line of fit represents the starting point of the relationship between the two variables, in this case, the amount of diet soda in the machine and the time after the machine is filled. Therefore, the y-intercept value of 40.98 means that the machine starts with 40.98 ounces of diet soda when it is filled.
Option A is incorrect because the y-intercept is a starting value, and it does not represent a rate of change.
Option B is also incorrect because it suggests that the machine loses 4.8 fluid ounces of diet soda every hour, which is not what the y-intercept represents.
Option D is incorrect because it gives a value that is not consistent with the scatter plot and the line of fit.
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According to the general equation for conditional probability, if P (A|B = 3/10 and P(B)= 2/5 , what is P(A|B) ? A.3/8 B.1/2 C. 1/16 D. 3/4
Answers
The solution is A. 3/8. We can calculate it in the following manner.
According to the general equation for conditional probability,
P(A|B) = P(A and B) / P(B)
We are given that P(A|B) = 3/10 and P(B) = 2/5.
We need to find P(A and B) to solve for P(A|B).
Using the formula for conditional probability, we can rearrange the equation as:
P(A and B) = P(A|B) * P(B)
Substituting the given values, we get:
P(A and B) = (3/10) * (2/5) = 6/50 = 3/25
Now, we can find P(A|B) using the first equation:
P(A|B) = P(A and B) / P(B) = (3/25) / (2/5) = (3/25) * (5/2) = 3/10
Therefore, the answer is A. 3/8.
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For annual compound interest what are the rate would result in a single investment doubling in 3years?
Answers
The rate that would result in a single investment doubling in 3 years with annual compound interest can be calculated using the rule of 72.
How is the rule of 72 used in this context?The rule of 72 states that if you divide 72 by the annual interest rate (as a percentage), you get the approximate number of years it takes for an investment to double in value.
So, to find the annual interest rate that would result in a single investment doubling in 3 years, we need to solve the equation: 72 / r = 3 where the r is the annual interest rate (as a percentage).
Simplifying the equation, we get:
r = 24
Therefore, the annual interest rate that would result in a single investment doubling in 3 years is 24%.
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assume that the traffic to the web site of made by charmz, llc which sells customized mugs, follows a normal distribution, with a mean of 8.5 million visitors per day and a standard deviation of 610,000 visitors per day. what is the probability that the web site has fewer than 8 million visitors in a single day?
Answers
The probability that the website has fewer than 8 million visitors in a single day is 0.2061 or 20.61%.Hence, option C is correct.
The traffic to the web site of Made by Charmz, LLC which sells customized mugs, follows a normal distribution,
with a mean of 8.5 million visitors per day and a standard deviation of 610,000 visitors per day.
The problem asks us to find the probability that the website has fewer than 8 million visitors in a single day.
Therefore, we need to find P(X < 8 million).
Using the Z-score formula, we have;
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
Where X = 8 million, μ = 8.5 million and σ = 610,000.
Substituting the given values in the formula, we get:
[tex]Z=\frac{8-8.5}{0.61}=-0.8197[/tex]
Using a standard normal table, the probability corresponding to Z-score = -0.8197 is 0.2061.
Therefore, the probability that the website has fewer than 8 million visitors in a single day is 0.2061 or 20.61%.Hence, option C is correct.
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A rectangular prism is 4 meters long, 5 meters wide, and has a height of 7 meters. What is its surface area?
Answers
Answer:The surface area of rectangular prism is 166 m².
Step-by-step explanation:
Given that,
length l= 4 m
Width b= 5 m
Height h=7 m
Using the formula of surface area of rectangular prism
We substitute the value into formula
Hence, The surface area of rectangular prism is 166 m².
Please answer this test is due in 30 mins please help meeee
Answers
The value of x from the given triangle is 55°.
What is an exterior angle?
The angle between any side of a shape and a line that extends from the next side is known as the exterior angle. the angle formed by a shape's side and a line that extends from another side.
Here, we have
Given: A side of the triangle below has been extended to form an exterior angle of 125°.
We have to find the value of x.
From the given figure, the exterior angle of the triangle is 125° and x is the exterior angle to that.
Now, 125°+x=180°
x=180°-125°
x=55°
Hence, the value of x from the given triangle is 55°.
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What are the coordinates of each point after quadrilateral EFGH is translated 3 units right and 2 units down?
Answers
Point E: (7, 3), Point F: (1, 3), Point G: (1, -2) and Point H: (7, -2) are the coordinates of each point.
To translate a point in the (x, y) coordinate plane, we add the translation distances to the x-coordinate and the y-coordinate of the point.
For each point in the quadrilateral EFGH, we can apply this translation as follows:
Point E: (4, 5) + (3, -2) = (7, 3)
Point F: (-2, 5) + (3, -2) = (1, 3)
Point G: (-2, 0) + (3, -2) = (1, -2)
Point H: (4, 0) + (3, -2) = (7, -2)
Therefore, after the translation of 3 units right and 2 units down, the coordinates of the points in quadrilateral EFGH are:
Point E: (7, 3)
Point F: (1, 3)
Point G: (1, -2)
Point H: (7, -2)
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HELPPPPPPP ME PLS IM BEING TIMED ALSO PLS EXPLAIN HOW YOU FIGURE IT OUT STEP BY STEP PLSSS
Answers
Answer:
I think second one is the answer
Step-by-step explanation:
if a number is raised to a negative power u put 1 as the numerator and the number with a positive power and for p3 it stays the same
Answer:
[tex]\frac{p^3}{n^6}[/tex]
Step-by-step explanation:
using the rule of exponents
[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]
given
[tex]n^{-6}[/tex] p³
= [tex]\frac{1}{n^{6} }[/tex] × p³
= [tex]\frac{p^3}{n^6}[/tex] ( with positive exponents )
In the figure above, what is the area of the shaded region? PLEASE HELP ASAP TIMED
Answers
With little knowledge of the square shape, we know that the area of the shaded region is (B) x² - 2y².
What is a square?A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles.
It can alternatively be explained as a rectangle with two neighboring sides that are of equal length.
As we previously stated, a square is nothing more than a rectangle with equally long neighboring sides.
The area of a rectangle is therefore expressed as Area = Length Breadth.
So, according to the given figure:
The area of the shaded region would be:
x² - y²
But as we know that 2 triangles make up 1 small square, so the formula can be molded as:
x² - 2y²
Therefore, with little knowledge of the square shape, we know that the area of the shaded region is (B) x² - 2y².
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Which expressions are equivalent to the one below? Check all that apply.
5x
A. 15^x/3
B. 5.5^x+1
C. (15/3)^x
D. 5^x
E. 5.5x-1
F.15^x/3^x
Answers
Answer:
C and D
Step-by-step explanation:
The expression 5x cannot be simplified further, but we can check which expressions are equivalent to it.The expressions that are equivalent to 5x are:
C. (15/3)^x = 5^xD. 5^xTherefore, the expressions that are equivalent to 5x are C. (15/3)^x and D. 5^x.None of the other expressions listed are equivalent to 5x.
A. 15^x/3 = (3*5)^x/3 = 3^x * 5^x/3, which is not equivalent to 5x.B. 5.5^(x+1) = 5.5^x * 5.5^1 = 5.5^x * 5.5, which is not equivalent to 5x.E. 5.5x-1 = 5x * 5^-1 = 5x/5, which is not equivalent to 5x.F. 15^x/3^x = (3*5)^x/3^x = 3^x * 5^x/3^x, which is not equivalent to 5x.y=-2x^2+5 different from the graph of y=-2x^2 ?
Answers
Answer:
Yes, the graph of y = -2x^2 + 5 is different from the graph of y = -2x^2. Both equations are quadratic functions with a leading coefficient of -2, which means that they have the same shape of a downward-facing parabola.
However, the graph of y = -2x^2 + 5 is shifted upwards by 5 units compared to the graph of y = -2x^2. This means that for any given value of x, the y-value of y = -2x^2 + 5 will be 5 units higher than the y-value of y = -2x^2.
Ernesto takes a sheet of paper and makes a diagonal cut from one corner to the opposite corner, making two triangles. The cut he makes is 20 inches long and the width of the paper is 16 inches. What is the paper's length?
Answers
Answer:
3`1
Step-by-step explanation:
Answer: 12 inches
Step-by-step explanation:
The 20 inches is the hypotenuse whereas 16 inches is the height of the triangle respectively.
So,
let keep the paper's length as x inches.
20² = 16² + x²
x² = 20² - 16²
x = [tex]\sqrt{20^{2}-16^{2} }[/tex]
x = 12
I am not sure if this is right because i have never done a sum in inches before but I hope this helps sorry if it is not right.
Solve the problem by finding m angle C
Answers
Answer:
angleC = 35°
Step-by-step explanation:
Because AC is the diameter of the circle, angle B = 90°
Then we can use the idea that there are 180° in a triangle to find angle C.
55 + 90 + c = 180
145 + c = 180
c = 35
The measure of angleC = 35°
brown v board of education was passed in 1954. six years later in 1960, what was the percentage of black students attending integrated schools in the south? group of answer choices 2% 40% 20% 60%
Answers
In 1960, the percentage of black students attending integrated schools in the South was approximately 2%.
Brown v Board of Education was a landmark decision in 1954 that declared segregation in public schools unconstitutional. However, it took several years for this decision to be implemented in Southern states, and in 1960, only 2% of black students in the South attended integrated schools. This highlights the resistance to desegregation in Southern states and the slow pace of change. It also underscores the ongoing struggles for civil rights and the continued efforts to address systemic racism in education and other aspects of American society.
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which describes the relationship between a tangent line to a circle and the radius of the circle drawn to the point of tangency?
A. The tangent line and the radius are parallel
B. The tangent line and the radius are perpendicular
C. The tangent line is the perpendicular bisector of the radius
D. The radius is the perpendicular bisector of the tangent line.
Solve for x. Assume that lines which appear tangent are tangent.
A. 8
B. 10
C. 7
D. 9
Answers
The tangent line and the radius are perpendicular. and the value of x is 8
Describing the relationshipThe correct answer is B. The tangent line and the radius are perpendicular.
In a circle, the tangent line at a point on the circle is perpendicular to the radius drawn to that point. This is a fundamental property of circles.
Calculating the value of xThe value of x is calculated as
9 * x = 12 * 6
So, we have
9x = 72
Divide
x = 8
Hence, the value of x is 8
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For what values of x and y are the triangles to the right congruent by HL?
Answers
Based on the Hypotenuse-Length Theorem of Congruence (HL), the values of x and y that will make both right triangles congruent are:
x = 8 and y = 4
Two triangles are said to be congruent if the three sides and three angles are equal in all directions.
Two right triangles are congruent to each other by the Hypotenuse-Length Congruence Theorem (HL) if the hypotenuse length and one leg of a right triangle are congruent to the hypotenuse length and leg of the other right triangle.
Thus, for both right triangles to be congruent, it means that their hypotenuse and one of their corresponding legs must be equal to each other.
Use this to create two equations and solve them to get the value of x and y.
Equal Hypotenuse:
x + y = 3y
⇒ x +4 -4 = 3y -4
⇒ x = 3y -4 ------------------------ (1)
Equal legs:
x = y +4 _______________ (2)
Find the value of y, by substituting x = (y + 4) into eqn. 1.
y + 4 = 3y - 4
⇒ -2y = -8
⇒ y = 4
Find the value of x, by substituting y = 4 into eqn. 2.
x = y + 4
⇒ x = 4 +4
⇒ x = 8
Therefore, based on the Hypotenuse-Length Theorem of Congruence (HL), the values of x and y that will make both right triangles congruent are: x = 8 and y = 4.
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