a) How many times does the line y = -6 intersect with the circle x2+ y2 = 36 ?
b) Hence, use a single word to describe what the line is to the circle.
Answers
we can say that the line is a secant of the circle, meaning it intersects the circle at two distinct points. a) The line y = -6 intersects with the circle x^2 + y^2 = 36 twice.
b) The single word that can describe the relationship between the line y = -6 and the circle x^2 + y^2 = 36 is "intersect." The line and circle intersect at two points, which means they have some common points.
However, the line does not pass through the center of the circle, so it is not a diameter of the circle. Therefore, we can say that the line is a secant of the circle, meaning it intersects the circle at two distinct points.
The points of intersection between the line and the circle can be found by substituting y = -6 into the equation of the circle and solving for x.
This gives us x^2 + (-6)^2 = 36, which simplifies to x^2 = 0. Therefore, x = 0, which gives us the two points of intersection: (0, -6) and (0, -6).
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Related Questions
1. Find the missing values in the equations.
a. -3 x 4 = ?
b. -3 x ? = 12
c. 3 x ? = 12
d. ? X -4 = 12
e. ? x 4 = -12
Answers
Answer:
a. ? = 12
b. ? = -4
c. ? = 4
d. ? = -3
e. ? = -3
Step-by-step explanation:
B. 4
C. 4
D. 3
E.-3
On a coordinate plane, a larger rectangle has a length of 24 and width of 16. A smaller rectangle has a length of 6 and width of 4. How would a scale factor of 4 be used to determine the lengths of the scale figure? The scale factor is added to the original length. The scale factor is subtracted from the original length. The scale factor is multiplied by the original length. The scale factor is divided by the original length.
Answers
The scale factor is multiplied by the original length.
How would a scale factor of 4 be used to determine the lengths of the scale figure?The scale factor is the size by which the shape is enlarged or reduced. It is used to increase the size of shapes like circles, triangles, squares, rectangles, etc.
A scale factor value can used to determine the size of a scale figure by using the value of the scale factor to multiply the original size.
In this case, a scale factor of 4 can be used to determine the lengths of the scale figure using 4 to multiply the original length.
Therefore, the scale factor is multiplied by the original length.
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Let X be the cholesterol level (in mg/dl) in the population of middle-aged American men, so that X follows the N(222, 37) distribution. • The probability in this population of having borderline high cholesterol (between 200 and 240 mg/dl) can be computed as Select ] • In this population, 90% of men have a cholesterol level that is at most [Select] mg/dl In the U.S. adult population, the distribution of BMI values (body mass index) are clearly right-skewed. Which of the following distributions can we nonetheless consider to be approximately Normal? (There may be one or more.) What is your reasoning? (no answer required here) The sample distribution of BMI values in a random sample of 500 adults The sampling distribution of mean BMI for random samples of 60 adults The sampling distribution of mean BMI for random samples of 9 adults
Answers
From the given information, cholesterol level X follows the N(222, 37) distribution.
The probability of having borderline high cholesterol (between 200 and 240 mg/dl) can be calculated by using the z-score formula as follows:
z = (x - μ) / σ
For lower limit x1 = 200, z1 = (200 - 222) / 37 = -0.595
For upper limit x2 = 240, z2 = (240 - 222) / 37 = 0.486
The probability of having borderline high cholesterol (between 200 and 240 mg/dl) can be computed as
P(200 ≤ X ≤ 240) = P(z1 ≤ Z ≤ z2) = P(Z ≤ 0.486) - P(Z ≤ -0.595) = 0.683 - 0.277 = 0.406
In this population, 90% of men have a cholesterol level that is at most X90.The z-score corresponding to a cholesterol level of X90 can be calculated as follows:
z = (x - μ) / σ
Since the z-score separates the area under the normal distribution curve into two parts, that is, from the left of the z-value to the mean, and from the right of the z-value to the mean.
So, for a left-tailed test, we find the z-score such that the area from the left of the z-score to the mean is 0.90.
By using the standard normal distribution table,
we get the z-score as 1.28.z = (x - μ) / σ1.28 = (X90 - 222) / 37X90 = 222 + 1.28 × 37 = 274.36 ≈ 274
The cholesterol level of 90% of men in this population is at most 274 mg/dl.
The distributions that we can consider to be approximately normal are the sampling distribution of mean BMI for random samples of 60 adults and the sampling distribution of mean BMI for random samples of 9 adults.
The reason for considering these distributions to be approximately normal is that according to the Central Limit Theorem, if a sample consists of a large number of observations, that is, at least 30, then its sample mean distribution is approximately normal.
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A parachutist's rate during
free fall reaches 132 feet per second. What Is this rate in meters per second? At this rate, how many meters will the parachutist fall
during 5 seconds of free fall? In your computations, assume that 1 meter is equal to 3.3 feet. Do not round your answers.
Answers
Answer:
place follow me
thank you
if 1 book cost $7, how much will 3 books cost?
Answers
If 1 book cost $7, 3 books will cost: 3*$7 = $21. (Multiplying)
The answer is $21.
Answer pls! No spam!
Answers
Answer:
Check the attachment.
An ant on top of a tree 23 meters tall directly above her home which is 0.3 meters below the ground.
Answers
Answer:
Can you tell me what they are looking for in the question?
will mark as brainlist!!!!pls include steps
Answers
Step-by-step explanation:
a) 1.16× 10^-6
standard form should be less than 10. therefore, count decimal places from where the decimal point is located to the right until you reach a number less than 10 ....count the number of shifts in the above is 6 shifts to the right. when moving to the right, power will be negative.(-6)
1.157/1.16 ×10^-6
b) 6.79 × 10^10
67890000000....count till a number less than 10.there will be 10 shifts to the left. the 10 will be your power,(positive) since u r moving to the left exponent is positive
6.789/6.79 × 10^10
\(1.157 \times {10}^{ - 6} \)
\(6.79 \times {10}^{10} \)
Step-by-step explanation:
\(mark \: me \: as \: brainliest\)
i need to know all the missing sides and angles in this problem
Answers
Answer:
a = 23
c= 13
this is the answer
Translate into an equation
16 less than twice a number is -
10
Answers
Answer:
2x-16=10
Step-by-step explanation:
16 less is -16
twice a number is 2x because the number is unknown
Answer: 2n-16= 10
Step-by-step explanation:
Let's break this sentence into parts.
"16 less than": always translates to something -16. Hack: Whenever you see "something less than" you put a subtraction sign and that number on the right side. just like "5 less than" becomes something -5.
'twice a number': 2 times a number's value, or 2 times the number. let's say the number is 4. "twice the number" means to double it's value. 4x2=8. In this case, you write 2n.
- 2n translates to "2 times a number". A number next to a letter means they're being multiplied.
"is 10": =10. Hack: "is" always becomes an equals sign.
Combine
16 less than , twice a number, is 10.
2n - 16= 10
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The coordinates of point A are 400 units of X and 40 units of Y. The coordinates of point B are 480 units of X and 60 units of Y. With X on the horizontal axis and Y on the vertical axis, the slope of the line between points A and B is
Answers
Answer:
The slope of the line between points A and B is 0.25
Step-by-step explanation:
Here in this question, we simply aim at calculating the slope of the line between two given points;
The points in question are;
A(400,40) and B(480,60)
Mathematically, the slope of the line can be calculated using the formula:
slope = (y2-y1)/(x2-x1)
Where ;
x1 = 400
y1 = 40
x2 = 480
y2 = 60
Substituting the values, we have;
slope = (60-40)/(480-400) = 20/80 = 1/4 = 0.25
Which system models this situation? y = 26x and y = 8,400(x-500)2 15,900 y = 26x and y = -0.030(x-500)2 15,900 y = x/26 and y = -0.030(x-500)2 15,900 y = x/26 and y =8,400(x-500)2 15,900
Answers
The option B is a correct option which is y = 26x and y = -0.030(x-500)2 15,900 represent the quadratic and linear function.
According to the statement
we have given that Vertex
(h,k) = (500, 15900)
And One of the points on the graph
(x,y) = (0,8400)
FIRST PART: we have to find the quadratic function
We can find the quadratic function by parabola's equation formula
y = a (x - h)² + k -(1)
Input the numbers to the formula, to find the value of a
y = a (x - h)² + k
8400 = a(0 - 500)² + 15900
8400 = a (500)² + 15900
8400 = 250000a + 15900
-250000a = 15900 - 8400
-250000a = 7500
a = 7500/-250000
a = 0.03
Now,
Submit a to the formula (1)
y = a (x - h)² + k
y = 0.03 (x - 500)² + 15900
this is the quadratic equation.
SECOND PART: Find the linear function
the total cost = cost each helmet × the number of helmet
y = 26x
So,
The option B is a correct option which is y = 26x and y = -0.030(x-500)2 15,900 represent the quadratic and linear function.
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Disclaimer: This question was incomplete. Please find the full content below.
Question: A company plans to sell bicycle helmets for $26 each. The company's business manager estimates that the cost, y, of making x helmets is a quadratic function with a y-intercept of 8,400 and a vertex of (500, 15900)
x= number of helmets
y = amount in dollars
Which system models this situation?
a) y = 26x and y = 8,400(x-500)2+15,900
b) y = 26x and y = -0.030(x-500)2+15,900
c) y = x/26 and y = -0.030(x-500)2+15,900
d) y = x/26 and y =8,400(x-500)2+15,900
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Answer:
B. y = 26x and y = -0.030(x-500)2+15,900
Step-by-step explanation:
There is a rectangular lot in the garden, with 6 ft in length and 4 ft in width. You plan to expand the lot by an equal length around its four sides, and make the area of the expanded rectangle 48 ft^2. How long should you expand the original lot in four directions?
You should expand the original lot by…
Please type ft to represent feet.
Answers
Answer:
2 ftStep-by-step explanation:
Given:
l = 6 ftw = 4 ftExtended area = 48 ft²Extension= xFind x:
(6 + x)(4 + x) = 48x² + 10x + 24 = 48x² + 10x + 25 = 49(x + 5)² = 49x + 5 = 7x = 7 - 5x = 2To explore how often families eat at home, Harris Interactive surveyed adults living with children under the age of 18. (USA Today, Jan. 3, 2007). The survey results are given in the following table:
Answers
The survey aimed to understand how frequently families eat at home and the results provide an indication of the reported frequency of family meals in households with children under the age of 18. This information can be valuable for understanding the prevalence of family meals at home during the given time period.
According to a survey conducted by Harris Interactive, adults living with children under the age of 18 were surveyed to explore the frequency of family meals at home. The survey results, presented in the table, provide insights into this aspect. To summarize the findings, the table showcases the percentage of respondents who reported eating meals together at home either rarely, occasionally, often, or always. It is important to note that the data was collected by Harris Interactive and reported by USA Today on January 3, 2007.
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A line passes through the points (8,5) and (4,4). What is its equation im slope-intercept from?
Answers
Given the points ( 8 , 5 ) and ( 4 , 4 )
The general slop-intercept form of the equation of the line is:
y = mx + c
where m is the slope and c is y-intercept
The slope will be calculated as following:
\(\text{slope}=m=\frac{y2-y1}{x2-x1}=\frac{5-4}{8-4}=\frac{1}{4}\)So, the equation of the line will be:
\(y=\frac{1}{4}x+c\)Using the one of the given points to find the value of c
Let , we will use the point ( 4 , 4 )
so, when x = 4 , y = 4
\(\begin{gathered} 4=\frac{1}{4}\cdot4+c \\ 4=1+c \\ c=4-1=3 \end{gathered}\)So, the slope - intercept equation of the line is:
\(y=\frac{1}{4}x+3\)Need help with properties if dilations homework
Answers
With a dial action, although the dilated image may get smaller or larger the angles/ slope of lines would remain the same.
Slope = change I. Y over the change in X
Slope = (5-4) /(3-2) = 1/1 = 1
Slope = 1
Help!!!
a $52 item is marked up 10% and then markdown 10% what is the final price
Answers
Answer: $51.48
Step-by-step explanation:
If a $52 item is marked up by 10%, its new price will be:
$52 + 10% of $52 = $52 + $5.20 = $57.20
Then, if this new price is marked down by 10%, the final price will be:
$57.20 - 10% of $57.20 = $57.20 - $5.72 = $51.48
Therefore, the final price of the item after the markup and markdown is $51.48.
Help !!!! heres the picture for it
Answers
Using the proportional rule of Similar Triangles, the length of SD is 12 m.
Given a truss bridge.
From it,
The triangles BCD and RSD are similar.
For similar triangles, corresponding sides are proportional.
Corresponding sides are,
BC and RS, CD and SD, BD and RD.
BC / RS = CD / SD = BD / RD.
Consider BC / RS = CD / SD.
2 / 1 = 24 / SD
2 (SD) = 24
SD = 12
Hence the length of SD is 12 m.
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Work out the angle marked x in each diagram you must show your working
Answers
Anwser: 41°
Okay so every triangle is 180° degrees in total.
We need to find the angle of x in the triangle BDC.
We know that the angle of x is 180 - ( x + 15)
We also have another triangle named BAD
Which angles are 90 + 56 + x
the angle of D in the triangle BDC is 180 -58 = 124
So 124 + 15 = 139
180 - 139 = 41
Triangle EFG is rotated and dilated by a scale factor other than 1 to create triangle E'F'G'. Do triangle EFG and triangle EFG' have the same area? Justify your answer.
Respond in the space provided.
Answers
Answer:
yes
Step-by-step explanation:
it was just rotated not dilated
The area of triangle ΔEFG changes after rotation and dilation.
What is Scale factor?The scale factor is a type of measurement which is used to increase or decrease the size of an object keeping its shape as the same. It can be determined by taking the ratio of the new and the original dimension of the object.
Suppose the scale factor is k for the dilation of triangle.
Now, new dimensions of ΔE'F'G' is k times the dimension of ΔEFG.
Area of triangle ΔEFG = 1/2 × b × h
Then, triangle area for ΔE'F'G' = 1/2 × kb × kh = k²(1/2 × b × h)
Thus, the area becomes k² times.
Hence, the given triangles ΔEFG and ΔE'F'G' do not have the same area.
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6. There are 45 cans of mixed nuts. Each
can has 338 nuts. Below is Mary's work
to find the total number of nuts.
Answers
The total number of nuts is 15210 and the missing number is 5
Number of cans of mixed nuts = 45 cans
Number of nuts in each can = 338 nuts
The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors.
Finding the total number of nuts we get:
Total number of nuts = Number of cans*Number of nuts in each can
\(338\\*45\\= 1690\\+ 13520\\= 15210\)
So, the missing number is 5
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Please help me answer this.
Answers
Answer:
D. 4,-1
Step-by-step explanation:
The mathmatical way to solev it is to find the linear equation and plug in the points, but i just looked at the graph to see which point was in the shaded region.
The price of an item has been reduced by 80%. The original price was $60. What is the price of the item now?
Answers
Answer:
48
Step-by-step explanation:
Simplify 80% to 0.8
Simplify=48
We could find the price of the item now by multiplying 80% by 60.
263,000,700,000 in scientific notation I'm wondering will the exponent will be negative or positive
]
Answers
Consider the following hypotheses: H0: p ≥ 0.47 HA: p < 0.47 Compute the p-value based on the following sample information. (You may find it useful to reference the appropriate table: z table or t table) (Round "z" value to 2 decimal places. Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)
p-value
a. x = 52; n = 130
b. x = 118; n = 329
c. p⎯⎯ = 0.41; n = 48
d. p⎯⎯ = 0.41; n = 406
Answers
p-value : c will have a fairly high p-value because of the smaller sample size and b will have a small p-value.
To compute the p-value for each scenario, we can use the standard normal distribution (z-distribution) since the sample size is sufficiently large.
The formula for calculating the test statistic (z-score) is given by:
z = (p¬ - p) / sqrt(p * (1 - p) / n)
where p¬ is the sample proportion, p is the hypothesized proportion, and n is the sample size.
Let's calculate the p-value for each scenario:
a. x = 52, n = 130
p¬ = x / n = 52 / 130 = 0.4
z = (0.4 - 0.47) / sqrt(0.47 * (1 - 0.47) / 130) ≈ -1.732
Looking up the z-value in the standard normal distribution table, the corresponding p-value is approximately 0.0418.
b. x = 118, n = 329
p¬ = x / n = 118 / 329 ≈ 0.3589
z = (0.3589 - 0.47) / sqrt(0.47 * (1 - 0.47) / 329) ≈ -3.3656
The p-value corresponding to z = -3.3656 is extremely small, approaching 0.
c. p¬ = 0.41, n = 48
z = (0.41 - 0.47) / sqrt(0.47 * (1 - 0.47) / 48) ≈ -1.3872
The p-value associated with z = -1.3872 is approximately 0.0837.
d. p¬ = 0.41, n = 406
z = (0.41 - 0.47) / sqrt(0.47 * (1 - 0.47) / 406) ≈ -2.5128
The p-value corresponding to z = -2.5128 is around 0.0060.
Therefore, the p-values for each scenario are:
a. p-value ≈ 0.0418
b. p-value ≈ 0.0001
c. p-value ≈ 0.0837
d. p-value ≈ 0.0060
Therefore, p-value : c will have a fairly high p-value because of the smaller sample size and b will have a small p-value.
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The work that Ryan did to find the greatest common factor of 48 and 72 is shown below.
Prime factorization of 48: 2 x 2 x 2 x 2 x 3
Prime factorization of 72: 2 x 2 x 2 x 3 x 3
The greatest common factor is 2 ´ 2 ´ 2 ´ 3 x 3
What is Ryan’s error?
Answers
Answer:
there will only be one 3
Step-by-step explanation:
see cause the first 3 of both numbers are 2 but only the last one of both numbers are 3 .
Determine if the following triangles are right triangles. Prove your answers using the
Pythagorean Theorem.
12 ft
7 ft
10 ft
Please help
Answers
Answer:
not a right triangle
Step-by-step explanation:
Using the converse of Pythagoras' identity
If the square of the longest side is equal to the sum of the squares on the other 2 sides then the triangle is right.
longest side = 12 and 12² = 144
7² + 10² = 49 + 100 = 149 ≠ 144
Then triangle is not right
Examine ABC below. B Determine which of the following relationships is true. O mcBCA=2(m
Answers
Answer:
Your answer should be option 2
Step-by-step explanation:
those || lines mean parallel and the lines DE and AC are parallel.
I really need help with this question . Please and thank you . I got 136 but I do not know the square root of 136.
Answers
Answer:
It's the other way around, subtract 36 from 100, and you will get 8
Step-by-step explanation:
a^2+b^2=c^2
a and b are the sides, and c is the longest side.
6x6=36
10x10=100
100-36=64
square root of 64 is 8
A warehouse worker wearing a dosimeter has recorded the following noise level data: Station 1: 82 dBA at 3.5 hours Station 2: 97 dBA at 1.5 hour Station 3: 85 dBA at 2 hours Using Table of Equivalent values: Steady Sound Level (dBA) Duration 82 16 hours 85 8 hours 88 4 hours 91 2 hours 94 1 hours 97 30 minutes 100 15 minutes 103 7.5 minutes 106 3.75 minutes 109 1.88 minutes 112 0.94 minutes 115 28.12 seconds Determine the percentage exposure. Is it within the OEL value? Explain
Answers
The percentage exposure needs to be calculated by converting the duration of each noise level and comparing it to the OEL (Occupational Exposure Limit) value to determine if it is within the acceptable range.
The percentage exposure is [to be calculated]. It needs to be compared to the OEL (Occupational Exposure Limit) value to determine if it is within the acceptable range.
In order to calculate the percentage exposure, we need to convert the duration of each noise level into hours and sum them up. For Station 1, the duration is 3.5 hours, for Station 2 it is 1.5 hours, and for Station 3 it is 2 hours. We can then use the table of equivalent values to find the corresponding steady sound levels and their durations. By multiplying each steady sound level by its duration and summing them up, we can calculate the total exposure.
Once we have the total exposure, we can compare it to the OEL value, which represents the maximum allowable exposure. If the percentage exposure is within the OEL value, it means that the worker's exposure to noise is within the acceptable limit. If the percentage exposure exceeds the OEL value, it indicates that the worker has been exposed to noise levels that exceed the recommended limit, which may have potential health and safety implications.
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