in the following coordinate plane, find the image of each of the given points in the transformation that is the composition of a reflection in line m followed by a reflection in line n. a. (4,8)b. (0,1)c. (-1,0)d. (0,0)
Answers
We want to calculate the image of (4,8). So first we identify that line m is line y=2.
To reflect the point around the line m, we need to find the distance between point (4,8) and line y=2. To do so, we will draw a vertical line that passes through point (4,8) and check where it crosses the line y=2. So the line would look like this.
Now, we want to calculate the distance between this two points. To do so, we will use the formula
\(d=\sqrt[]{(a-c)^2+(b-d)^2}\)which would be tghe distance between points (a,b) and (c,d). So using the formula to points (4,8) and (4,2) we get
\(d=\sqrt[]{(8-2)^2+(4-4)^2}=\sqrt[]{(8-2)^2}=(8-2)=6\)Now, we want to find a point over the blue line that is at distance 6 from the red line, but is under the red line. We achieve this by taking the point of intercsection (4,2) and subtract 6 on the y coordiante. So the reflection of point (4,8) on line m is simply given by the point
\((4,2-6)=(4,-4)\)So the reflection of point (4,8) on line m is the point (4,-4).
Now, we want to reflect (4,-4) on line n. First we identify that the vertical line n is the line x=3. Now, we repeat the process as before.
In this case, we draw a horizontal line to identify the point of intersection, it would be
NOw, we calculate the distance. As they are on a horizontal line, we can simply subtract the x coordiantes and then take the absolute value.
This leads to
\(d=|4-3|=1\)So know we subtract the distance from the x coordinate of the intersection. We get
\((3-1,-4)=(2,-4)\)So the reflection of point (4,-4) on line n is (2,-4)
Related Questions
PLS HELP ME ANSWER THIS QUESTION..
Answers
Answer:
b. 4
c. 90⁰
Step-by-step explanation:
a. is in the diagram
Help ASAP, easy 15 points and a brainly for the first one to answer .
Answers
Answer:
It slopes downward from left to right. You can see the downward slope of that gender, which starts at the left and moves to the right.
Step-by-step explanation:
In a bag of Starbursts, 30% of the bag is pink. There are 90 pink starbursts in the bag. How many Starbursts are in the bag?
Answers
Answer:
27
Step-by-step explanation:
3/10 / 30% / .3
3 x
10 90 -use criss cross method so 3 and 90 and x times 10
270 =10x
27=x
you can also go on a calculator and type 90 times 0.3 and get the answer too
A diagnostic test for a disease is such that it (correctly) detects the disease in 90% of the individuals who actually have the disease. Also, if a person does not have the disease, the test will report that he or she does not have it with probability 0.9. Only 1% of the population has the disease in question. If a person is chosen at random from the population and the diagnostic test indicates that she has the disease, what is the conditional probability that she does, in fact, have the disease
Answers
Answer:
8.33% probability that she does, in fact, have the disease
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)
In which
P(B|A) is the probability of event B happening, given that A happened.
\(P(A \cap B)\) is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Positive test
Event B: Has the disease
Probability of a positive test:
10% of 100-1 = 99%
90% of 1%
So
\(P(A) = 0.1*0.99 + 0.9*0.01 = 0.108\)
Positive test and having the disease:
90% of 1%
\(P(A \cap B) = 0.9*0.01 = 0.009\)
What is the conditional probability that she does, in fact, have the disease
\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.009}{0.108} = 0.0833\)
8.33% probability that she does, in fact, have the disease
The graph shows a hypothetical relationship between tons of fertilizer used and crop yields. Which statement is NOT correct?img
A) The slope of the curve between one and two tons of fertilizer is approximately 2.
B) The relationship between fertilizer usage and yield is nonlinear.
C) Because the relationship is nonlinear, it is difficult to create an economic model describing the relationship between the two variables.
D) Using more than three tons of fertilizer has minimal effect on yield.
Answers
The correct answer is C), because it is possible to create an economic model describing the relationship between fertilizer usage and yield.
The economic model would take into account the nonlinear relationship, which is shown in the graph. Specifically, the slope of the curve between one and two tons of fertilizer is approximately 2 (change in yield divided by change in fertilizer usage). This means that for every ton of fertilizer used, the yield increases by two (change in yield / change in fertilizer usage = 2). Although using more than three tons of fertilizer has minimal effect on yield, the economic model would still take this into account and provide a more accurate representation of the relationship between the two variables.
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what type of data would best be displayed in a box plot
Answers
Answer:(2x+7)+(2x+7)
Step-by-step explanation:
what you do is put 2x on the top and on the side and then seven on the top and on the side and then you got your answer
(A LOT OF POINTS) Given the linear equation 2x + y = 6, perform the necessary operations to put the equation into the proper general form. Explain in complete sentences how you knew that the equation was in the proper general form. Complete your work in the space provided or upload a file that can display math symbols if your work requires it. Include the entire process for establishing the general form of the equation and the general form.
Answers
Answer:
\(\huge\boxed{2x + y - 6 = 0}\)
Step-by-step explanation:
2x + y = 6
Subtracting both sides by 6
2x + y - 6 = 0
Comparing it with the general form of equation \(\sf Ax+By +C = 0\) , we get:
A = 2, B = 1 and C = -6.
So, the equation is in proper general form.
Answer:
\(\boxed{2x+y-6=0}\)
Step-by-step explanation:
\(\sf The \ general \ form \ for \ the \ equation \ of \ a \ line \ is \ given \ as \ Ax+By+C=0.\)
\(2x+y=6\)
\(\sf Subtract \ 6 \ from \ both \ sides.\)
\(2x+y-6=6-6\)
\(2x+y-6=0\)
\(\sf A=2 \ \ \ B = 1 \ \ \ C=-6\)
\(\sf The \ equation \ is \ in \ general \ form.\)
\(\sf Graph \ equation:\)
Ez or not? Help bros.
Answers
Answer:
11 ft
Step-by-step explanation:
a dilation has center (0,0). Find the image of the point L(-4,0) for the scale factor 7.
Answers
The image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7 is the point L'(-28,0).
A dilation with a center of (0,0) and a scale factor of 7 means that every point in the plane will be multiplied by a factor of 7 from the origin.
To find the image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7, we can simply multiply the coordinates of L by the scale factor.
The coordinates of the image point L' will be:
L' = (-4 × 7, 0 × 7) = (-28, 0)
Therefore, the image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7 is the point L'(-28,0).
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8. The first three terms of a geometric sequence are ( x-6), 3x, and y. If the common ratio is 6, then the value of y is.
Answers
Answer:
The value of y is 216
(and the value of x is 12)
Step-by-step explanation:
The general formula for a geometric sequence is,
\(a_n = a_1(r)^{n-1}\)
Where n represents the nth term, a_1 is the first term and r is the common ratio,
we see that,
r = 6,
the first term is,
a_1 = (x-6)
the 2nd term is,
a_2 = 3x,
the 3rd term is,
a_3 = y, finding y,
first we find x, using the above given formula we have,
\(a_2 = a_1(6)^{2-1}\\3x = (x-6)(6^1)\\3x = 6x -36\\36 = 6x - 3x\\36 = 3x\\x=36/3\\x=12\)
x = 12,
Now, for y we can use the relation between a_3 and a_2,
\(a_3 = a_1(6)^{3-1}\\y = (x-6)(6)^2\\y = (12-6)(6^2)\\y = 6(6^2)\\y = 6^3\\y = 216\)
y = 216
Select the correct answer
Consider functions f. g. and h below
f(x)=x²+2x+3
X
-1
0
1
2
3
h(x) -7 4 -1 2 5
Order the above functions, from least to greatest, by the rate of change of functions over the interval 10. 21.
A g.h.f
B. th.g
C g.f.h
D Lg.h
Answers
The order of the functions from least to greatest rates is (a) g(x), h(x), f(x)
How to order the functions, from least to greatestFrom the question, we have the following parameters that can be used in our computation:
f(x) = x² + 2x + 3
x -1 0 1 2 3
h(x) -7 4 -1 2 5
The interval is given as [0, 2]
For the functions, we have
f(0) = 0² + 2(0) + 3 = 3
f(2) = 2² + 2(2) + 3 = 11
h(0) = 4
h(2) = 2
So, we have the average rates of change at this interval to be
f(x) = (11 - 3)/(2 - 0) = 4
h(x) = (2 - 4)/(2 - 0) = -1
When ordered, we have
h(x), f(x)
Hence, the order is (a) g(x), h(x), f(x)
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Find the sum of the geometric series.
/3-3/2+3|3/4-9/8+...
Answers
Answer:
none of these
Step-by-step explanation:
it's infinite series so answer is in appox.
Isamu decided to use blocking to deal with an extraneous factor in his experiment. what will blocking do to the subject in his experiment?
a. divide them into groups randomly
b. divide them into groups based on similarities
c. divide them into groups based on an alphabetized list
d. divide them into groups based on whether he likes them
Answers
Answer:
b. divide them into groups based on similarities
Step-by-step explanation:
Blocking is a method in statistics used to reduce the effect of nuisance variables in an experiment. Nuisance variables are those factors that could result in variations during the experiment. During blocking, subjects with similar features are grouped in the same block, and treatment is then administered to each of these subjects. In order to form blocks, blocking factors are used.
Blocking factors can affect the results of an experiment but they are of no importance to the experimenter. An example of a blocking factor is age. So, for Isamu who seeks to use blocking to deal with an extraneous factor in his experiment, blocking would enable him to divide his subjects into groups based on similarities.
Answer:
Divide them into groups based on similarities!
Determine whether the rule represents an exponential function. Explain why or why not.
Answers
Since the independent variable x is not the base\(, y=-10.2^x\) does not represent an exponential function. Option A
To determine whether a function is exponential, we need to examine the form of the function and how the independent variable, in this case, x, is related to the dependent variable, y.
In an exponential function, the independent variable is typically the exponent, and the base is a constant. However, in the given function y = \(-10.2^x\), the independent variable x is not the base of the exponent. The base is actually the constant -10.2.
In an exponential function, the variable x represents the exponent, and as x increases, the value of the function grows or decays at an exponential rate. However, in this case, the variable x is not in the exponent position. Instead, it is multiplied by -10.2.
Let's consider an example using different values of x:
For x = 1, y =\(-10.2^1\)= -10.2
For x = 2, y =\(-10.2^2\) = 104.04
For x = 3, y =\(-10.2^3\) = -1061.208
As we can see, the values of y are not growing or decaying at an exponential rate as x increases. Therefore, the given function does not represent an exponential function.
It's important to note that the presence of an exponent alone does not make a function exponential. The relationship between the base, the exponent, and how the values change as the exponent varies determines whether a function is exponential or not.
In this case, since x is not the base and the values do not exhibit exponential growth or decay, the given function\(y = -10.2^x\) does not represent an exponential function.
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When entering a power, you can use a caret (SHIFT-6).
Enter
as w^5:
Use the fraction tool (fraction tool) to enter the numerator and denominator.
Enter
:
Answers
The power expression "w^5" can be entered as "w^5".
To represent a power using the caret symbol, follow these steps:
Start with the base variable or term, in this case, "w".
Type the caret symbol (^), which can be accessed by pressing SHIFT-6 on your keyboard.
Immediately after the caret symbol, enter the exponent or power value, in this case, "5".
The resulting power expression "w^5" represents the variable "w" raised to the power of 5.
Regarding the use of the fraction tool, it is not required to represent the power "w^5" as it does not involve any fraction. The fraction tool is typically used to enter fractions or rational expressions in the form of numerator/denominator.
Therefore, to represent the power "w^5", simply write it as "w^5" without using the fraction tool.
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1. You biked 12 miles and then a fourth of that again
2. Sarah biked 10 miles and then a fourth of that again
3. John biked 7 miles and then a fourth of that again
Case
Initial Distance
Total Distance
1
12
2
10
151
3
7
Answers
Answer:
5 mile/8 km 238 357
10 mile/16.1 km 476 714
15 mile/24.2 km 714 1,072
20 mile/32.2 km 953 1,429
Step-by-step explanation:
Identify the y-intercept of the graph of the equation:
y = ½ x – 8
Question 1 options:
-8
1/2
-1/2
8
Answers
Answer:
-8
Step-by-step explanation:
This function is in slope intercept form, y=mx+b.
m being the slope, b being the y-intercept.
Notice -8 stands for b in this problem.
Thus, the y-intercept of this function is -8.
Find median for average life of a particular brand of a T.V sets from the following data
life in years : 0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40
No. of sets : 2 16 26 39 43 21 8 4
Answers
The median for average life of a particular brand of a T.V sets from the following data is given as follows:
17.5.
How to obtain the median of a data-set?The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than.
The total number of observations in this problem is given as follows:
2 + 16 + 26 + 39 + 43 + 21 + 8 + 4 = 159.
This is an odd cardinality, hence the median is found in the class when the counter hits:
(159 + 1)/2 = 80.
Which is the class 15-20, as 2 + 16 + 26 < 80 and 2 + 16 + 26 + 39 > 80, and the median value is given as follows:
(15 + 20)/2 = 17.5.
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Name the special angle relationship between angle∠ 1 and angle∠ 2 .
1. Alternate Exterior
2. Alternate Interior
3. Corresponding
4. Same Side Interior
Answers
Answer:
corresponding angels
Step-by-step explanation:
Corresponding angles are angles that have the same relative position as one another. In other words, it's what you see here.
A store is having a sale on walnuts and chocolate chips. For 4 pounds of walnuts and 8 pounds of chocolate chips, the total cost is 21$. For 2 pounds of walnuts and 3 pounds of chocolate chips, the total cost is $9. Find the cost for each pound of walnuts and each pound of chocolate chips.
Answers
The cost for each pound of walnuts is $ 2.25 and each pound of chocolate chips is $ 1.5.
We are given that:
Cost of 4 pounds of walnuts and 8 pounds of chocolate chips = $ 21.
Cost of 2 pounds of walnuts and 3 pounds of chocolate chips = $ 9.
Let the cost of pounds of walnuts be x and the cost of pounds of chocolate chips be y.
So, we get the following equations:
4 x + 8 y = 21 …(1)
2 x + 3 y = 9
2 x = 9 - 3 y
x = 1 / 2 (9 - 3y) …(2)
Put the value of x in (1)
4 ( 1 / 2 (9 - 3y) ) + 8 y = 21
2(9 - 3y) + 8 y = 21
18 - 6 y + 8 y = 21
2 y + 18 = 21
2 y = 21 - 18
2 y = 3
y = 3 / 2
y = 1.5
x = 1 / 2 (9 - 3y)
x = 1 / 2 ( 9 - 4.5)
x = 1 / 2 ( 4.5)
x = 2.25
Therefore, we get that, the cost for each pound of walnuts is $ 2.25 and each pound of chocolate chips is $ 1.5.
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Which is a coeffecient
Answers
Answer:
B is a coefficient
Step-by-step explanation:
Coefficient of 2O2 is 2.
B = 2
im so dumb i cant solve it for my sis cause i dont remember TwT
Answers
Answer:
The third answeer
Step-by-step explanation:
Also nice talk
How many degrees if any are in the angle between the hour and the minute hand of a clock when the time is 3:15 pm
Answers
After answering the given query, we can state that As a result, at 3:15 angles pm, there is no inclination between the hour and minute hands.
what are angles?An angle is a shape in Euclidean geometry made up of two rays, referred to as the angle's sides, that converge at a center spot known as the angle's vertex. In the plane where they are positioned, two rays may come together to create an angle. A planar collision produces an angle as well. Dihedral angles are what these are known as. A potential configuration of two rays or lines that share a termination is called an angle in plane geometry. The Latin word "angulus," which means "horn," is where the English word "angle" originates. The intersection of the two beams, also referred to as the angles' sides, is known as the vertex.
To calculate the inclination between a clock's hour and minute hands,
30°/hour multiplied by 3 hours equals 90°
The minute hand's location in degrees will then be found. Each minute on a clock face, which is a circle with 60 minutes, depicts an angle of 360/60, or 6 degrees. The minute needle will be at because it is 15 minutes past the hour at:
15 minutes at 15 degrees per minute equals 90 degrees.
By deducting the smaller angle from the bigger angle, we can now determine the angle between the hour and minute hands:
90 degrees minus 90 degrees equals 0 degrees.
As a result, at 3:15 pm, there is no inclination between the hour and minute hands.
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Nathan usually drinks 35 ounces of water per day. He read that he should drink 68 ounces of water per day. If he starts drinking 68 ounces, what is the percent increase? Round to the nearest percent. Please help me
Answers
Answer:
It’s 61.40 percent so rounding to the nearest percent would be 61% he needs to increase
given that 32✓2=2^a , find the value of a
Answers
Answer:
Step-by-step explanation:
All you need is something that when you divide the right side (the way I've written it) by 2, you get 32 sqrt(2). So a must also have sqrt(2) in it. In addition, it must also have 16 as well so that when you multiply by 2, you get 32.
2a = 32*sqrt(2) Divide by 2
a = 16*sqrt(2)
Answer:
a = 5.5Step-by-step explanation:
\(32\sqrt{2} = 2^a\)\(2^52^{1/2} = 2^a\)\(2^{5+1/2}=2^a\)a = 5.5Circle A has been transformed to Circle B.
What is the scale factor of Circle A to Circle B?
Scale Factor
=
Image Radius
Pre- Image Radius
Answers
Answer: 21
Step-by-step explanation: im not guessing im a certified expert at calculus and have a masters degree in mathmatics so yeah
Answer:
21
Step-by-step explanation:
I did the test
Hope this helps :)
A list of 10 numbers contains 6 prime numbers. What is the probability that a prime number will be randomly
selected from the list?
1/6
2/5
1/2
3/5
Answers
Answer:3\5
Step-by-step explanation:since there is 10 numbers in all 10 will be you denominator then there are 6 prime numbers so 6 will be your numerator,so then you get 6/10,but don’t forget to simplify!!! 6/10=3/5
Someone please help
Answers
Answer:
Angle 1 and angle 8
angle 2 and angle 7
angle 3 and angle 6
angle 4 and angle 5
I think its tat.
Step-by-step explanation:
A town's population has been growing linearly. In 2003, the population was 24000, and the population has been growing by 700 people each year.
Write an equation for the population
x
years after 2003.
P
=
Answers
Answer:
the equation for the population is add 700 to the previous term
100 POINTS
A gazebo in the shape of a regular octagon has equal sides of 9 feet and an apothem of 10.9 feet.
a. If one side of a gazebo is open, and the other sides have a railing, find the cost of the railing if it sells for $7.90 per foot.
b. Find the area of the gazebo in square feet.
c. Find the cost of the gazebo's flooring if it costs $3 per square foot. Round to the nearest hundred dollars.
Answers
Answer:
a) $497.70
b) 392.4 square feet
c) $1,200
Step-by-step explanation:
Part (a)A regular octagon has 8 sides of equal length.
Given each side of the octagon measures 9 feet in length, and one side does not have a railing, the total length of the railing is 7 times the length of one side:
\(\textsf{Total length of railing}=\sf 7 \times 9\; ft=63\;ft\)
If the railing sells for $7.90 per foot, the total cost of the railing can be calculated by multiplying the total length by the cost per foot:
\(\textsf{Total cost of railing}=\sf 63\;ft \times \dfrac{\$7.90}{ft}=\$497.70\)
Therefore, the cost of the railing is $497.70.
\(\hrulefill\)
Part (b)To find the area of the regular octagonal gazebo, given the side length and apothem, we can use the area of a regular polygon formula:
\(\boxed{\begin{minipage}{6cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{n\;s\;a}{2}$\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the length of one side.\\ \phantom{ww}$\bullet$ $a$ is the apothem.\\\end{minipage}}\)
Substitute n = 8, s = 9, and a = 10.9 into the formula and solve for A:
\(\begin{aligned}\textsf{Area of the gazebo}&=\sf \dfrac{8 \times 9\:ft \times10.9\:ft}{2}\\\\&=\sf \dfrac{784.8\;ft^2}{2}\\\\&=\sf 392.4\; \sf ft^2\end{aligned}\)
Therefore, the area of the gazebo is 392.4 square feet.
\(\hrulefill\)
Part (c)To calculate the cost of the gazebo's flooring if it costs $3 square foot, multiply the area of the gazebo found in part (b) by the cost per square foot:
\(\begin{aligned}\textsf{Total cost of flooring}&=\sf 392.4\; ft^2 \times \dfrac{\$3}{ft^2}\\&=\sf \$1177.2\\&=\sf \$1200\; (nearest\;hundred\;dollars)\end{aligned}\)
Therefore, the cost of the gazebo's flooring to the nearest hundred dollars is $1,200.
a. To find the perimeter of the gazebo, we can use the formula P = 8s, where s is the length of one side. Substituting s = 9, we get:
P = 8s = 8(9) = 72 feet
Since one side is open, we only need to find the cost of railing for 7 sides. Multiplying the perimeter by 7, we get:
Cost = 7P($7.90/foot) = 7(72 feet)($7.90/foot) = $4,939.20
Therefore, the cost of the railing is $4,939.20.
b. To find the area of the gazebo, we can use the formula A = (1/2)ap, where a is the apothem and p is the perimeter. Substituting a = 10.9 and p = 72, we get:
A = (1/2)(10.9)(72) = 394.56 square feet
Therefore, the area of the gazebo is 394.56 square feet.
c. To find the cost of the flooring, we need to multiply the area by the cost per square foot. Substituting A = 394.56 and the cost per square foot as $3, we get:
Cost = A($3/square foot) = 394.56($3/square foot) = $1,183.68
Rounding to the nearest hundred dollars, the cost of the flooring is $1,184. Therefore, the cost of the gazebo's flooring is $1,184.
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