In summary, to find m z1, we need to know the relationship between the rail lines and the angles formed by their intersection.
What is equation?An equation is a mathematical statement that shows the equality of two expressions. It is composed of two sides, separated by an equals sign (=), indicating that the two sides are equivalent in value. An equation may contain variables, which are unknown values represented by letters, as well as constants, which are known values. Equations are used in many areas of mathematics and science to model and solve problems. For example, the equation y = mx + b is a linear equation that describes the relationship between the variables x and y in a straight line, where m is the slope of the line and b is the y-intercept. Equations can be solved by manipulating the variables and using mathematical operations to isolate the unknown value.
Here,
In order to help Carmen find m z1, we need some additional information about the rail lines and the angles involved.
Assuming that z1 is an angle formed by the intersection of two rail lines, we can use the following steps to find its measure:
Identify the other angles formed by the two rail lines. If the rail lines are perpendicular, then z1 is a right angle and has a measure of 90 degrees. If the rail lines are not perpendicular, then they form two pairs of opposite angles, each with a measure of x degrees.
Use the fact that the sum of the measures of all angles formed by the intersection of two rail lines is 360 degrees. This means that the sum of the measures of the two pairs of opposite angles is 360 degrees.
Solve for x by setting the sum of the measures of the two pairs of opposite angles equal to 360 degrees and then solving for x. Once you have x, you can find the measure of any of the angles formed by the intersection of the rail lines, including z1.
For example, let's say that the two rail lines form two pairs of opposite angles, each with a measure of x degrees. Then, we have:
2x + 2z1 = 360 (since the sum of the measures of all angles formed by the intersection of two rail lines is 360 degrees)
Simplifying this equation, we get:
2z1 = 360 - 2x
z1 = (360 - 2x)/2
Now we need more information to find x, such as the measure of one of the opposite angles or the relationship between x and another angle in the figure. Once we know x, we can substitute it into the equation for z1 to find its measure.
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Mr. Anderson needs to work on the farm for at least 27 hours every week.
He worked 4 hours a day for the last 6 days.
He worked 5 hours today.
Mr. Anderson says that 4 × 6 is less than 27, so he has not worked enough during the week.
Is Mr. Anderson correct?
PLEASE HELP ASAP I NEED IT !!!
Ahmed and his brother went to the gym together today. Ahmed goes to the gym every 6 days and his brother goes to the gym every 9 days . After how many days will they go to the gym together again ?
Answer:
18
Step-by-step explanation:
To determine the number of days until they both work out at the gym on the same day again, Find the lowest common multiples of 6 days and 9 days.
Ahmed (6-days)=6,12,18,24
Brother(9-days)=9,18,24
pls right answer worth 100 points and brainlest
Answer: 204 ft
Step-by-step explanation: First lets find the area of the triangle, the formula for area of a triangle is base times height divided by 2. Now the height isn't given but we can find it by subtracting 18 by 10 which gives us 8. 8 times 6 is 48 divided by 2 is 24. Therefore, the area of the triangle is 24 ft. Now we find the area of the rectangle which is length times width. 18 times 10 is 180. Now we add the area of both shapes, 180 plus 24 is 204, so your answer is 204 ft.
Answer:
Step-by-step explanation:
The following two-way table shows the distribution of high school students categorized by their grade level and music-listening preference.
A 4-column table with 3 rows. Column 1 has entries junior, sophomore, total. Column 2 is labeled Earbuds with entries 4, 4, 8. Column 3 is labeled Speakers with entries 12, 12, 24. Column 4 is labeled total with entries 16, 16, 32. The columns are titled music-listening preferences and the rows are titled grade level.
Suppose a high school student is selected at random. Let event A = junior and event B = earbuds. Are events A and B independent?
Yes, P(A) = P(A|B).
Yes, P(A) = P(B|A).
No, P(A) ≠ P(A|B).
No, P(A) ≠ P(B|A).
edge 2023
Since two-way table shows the distribution of high school students The correct option is C: No, events A and B are not independent because P(A) ≠ P(A|B).
What is the distribution about?To determine whether events A and B are independent, we need to compare the probability of event A occurring without any knowledge of event B (i.e., P(A)) to the probability of event A occurring given that event B has occurred (i.e., P(A|B)).
From the table, we see that P(A) = 8/32 = 1/4, since there are 8 juniors out of a total of 32 students. Also, P(B) = 8/32 = 1/4, since there are 8 students who prefer earbuds out of a total of 32 students.
From the table, we see that the probability of both events A and B occurring is P(A and B) = 4/32 = 1/8, since there are 4 juniors who prefer earbuds out of a total of 32 students.
Now, to calculate P(A|B), we use the formula:
P(A|B) = P(A and B) / P(B)
Substituting the values we have, we get:
P(A|B) = (1/8) / (1/4) = 1/2
Since P(A) = 1/4 and P(A|B) = 1/2, we can see that P(A) ≠ P(A|B). Therefore, events A and B are not independent.
Therefore, the answer is No, P(A) ≠ P(A|B).
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Six empty cans weighs 3.5 ounces. How many cans equal 200 pounds
Approximately 342,857 empty cans would weigh 200 pounds.
What is the ratio and proportion ?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as 1 : 3 (for every one boy there are 3 girls).
According to given information :To solve this problem, we need to use proportional reasoning. We know that six empty cans weigh 3.5 ounces, so we can set up a proportion to find out how many cans are needed to weigh 200 pounds:
6 cans : 3.5 ounces = x cans : 200 pounds
To solve for x, we need to cross-multiply and simplify:
6 cans * 200 pounds = 3.5 ounces * x cans
1200 pounds = 3.5 ounces * x cans
x cans = 1200 pounds / 3.5 ounces
x cans = 342857.14 cans (rounded to two decimal places)
Therefore, approximately 342,857 empty cans would weigh 200 pounds.
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Answer this question please
The single translation that maps shape A onto shape C is given as follows:
Translation one unit right.Translation ten units down.What is a translation?A translation happens when either a figure or a function are moved horizontally or vertically on the coordinate plane.
The four translation rules for coordinates are defined as follows:
Translation left a units: (x,y) -> (x - a, y).Translation right a units: (x,y) -> (x + a, y).Translation up a units: (x,y) -> (x, y + a).Translation down a units: (x,y) -> (y - a).Translations can often be composed, that is, a combination of multiple translations can result in a single translation, as is the case for this problem.
Considering the translation of 3 units left(shape B) and then 4 units right(shape C), the horizontal translation is given as follows:
-3 + 4 = 1 -> 1 unit right.
Considering the translation of 7 units down(shape B) and then 3 units down(shape C), the vertical translation is given as follows:
-7 - 3 = 10 units down.
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An crate weighing 530 N is resting on a plane inclined 35° above the horizontal.
(a) Calculate the magnitude of the acceleration (ignore friction).
(b) After 4.00 s, how fast will the crate be moving?
Answer:
(a) 5.62 m/s²
(b) 22.5 m/s
Step-by-step explanation:
You want the magnitude of the acceleration of a crate on a frictionless plane inclined at 35° from the horizontal. And you want the speed after 4 seconds.
(a) AccelerationThe acceleration will be the component of the acceleration due to gravity that is in the direction down the plane.
(9.8 m/s²)·sin(35°) ≈ 5.62 m/s²
(b) SpeedThe speed of the crate will be the product of the acceleration and time:
v = at = (5.6 m/s²)(4 s) = 22.5 m/s
<95141404393>
Need help with this problem 1
By the given definition of matrix A, the value of the matrix A⁻¹ is [tex]\left[\begin{array}{ccc}-1&0&1&2&-1&-2&0&0&-1\end{array}\right][/tex] and it is true that AA⁻¹ = I₃.
Calcuting the matrix A⁻¹Given that
[tex]A = \left[\begin{array}{ccc}1&0&2\\1&1&0\\1&0&1\end{array}\right][/tex]
To find the inverse of A, we can use the following formula:
A⁻¹ = (1/|A|) adj(A)
where |A| is the determinant of A and adj(A) is the adjugate matrix of A.
First, let's calculate the determinant of A:
|A| = 1(1×1 - 0×0) - 0(1×0 - 0×1) + 2(1×0 - 1×1)
|A| = -1
Next, we need to find the adjugate matrix of A.
To do this, we need to find the matrix of cofactors of A, then take its transpose:
[tex]C = \left[\begin{array}{ccc}1&-2&0&0&1&0&-1&2&1\end{array}\right]\\[/tex]
adj(A) = [tex]C^T = \left[\begin{array}{ccc}1&0&-1&-2&1&2&0&0&1\end{array}\right][/tex]
Now we can calculate A⁻¹ using the formula:
A⁻¹ = (1/|A|) adj(A)
So, we have
[tex]A^{-1} = (-1) \left[\begin{array}{ccc}1&0&-1&-2&1&2&0&0&1\end{array}\right] = \left[\begin{array}{ccc}-1&0&1&2&-1&-2&0&0&-1\end{array}\right][/tex]
Checking whether AA⁻¹ = I₃Finally, we can check whether AA⁻¹ = I₃ using
[tex]A^{-1}A = \left[\begin{array}{ccc}-1&0&1&2&-1&-2&0&0&-1\end{array}\right] \left[\begin{array}{ccc}1&0&2&1&1&0&1&0&1\end{array}\right] = \left[\begin{array}{ccc}1&0&0&0&1&0&0&0&1\end{array}\right] = I_3[/tex]
Therefore, we have found the inverse of A and verified that AA⁻¹ = I₃.
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1.3 1.4 Thabang save money by putting coins in a money box. The money box has 600 coins that consist of 20 cents and 50 cents. 1.3.1 1.3.2 Determine the total amount of cents in the money box. Convert the amount in 1.3.2 to rands (R). Thabang and his friend Ndivhu share a job of cleaning a neighbours yard and they were paid R400. Thabang worked three hours and Ndivhu worked for two hours. 1.4.1 Calculate how many 50 cents pieces are in the container if there are 220 pieces of 20 cents. 1.3.3 Determine the amount Thabang will receive if they decided to share their morey according to hours.
Let the number of 50 cents coins in the container be "x".
We know that the total number of coins in the container is 600, so we can write:
[tex]x + 220 = 600[/tex]
Solving for x, we get:
[tex]x = 600 - 220[/tex]
[tex]x = 380[/tex]
Therefore, there are 380 50 cents pieces in the container.
Hope you can understand :)
15. Blaine works for a battery manufacturing company. He wants to develop a method to test the batteries made each day to determine if they work.
Which method would provide the most valid results?
A. sampling the first 25 batteries made each day and testing to see if they work
B. sampling the last 25 batteries made each day and testing to see if they work
C. sampling the first 50 batteries made each day and testing to see if they work
D. randomly sampling 50 batteries throughout the day and testing to see if they work
The most reliable results would come from randomly selecting 50 batteries throughout the day and testing to determine if they function.
What battery testing techniques are there?A voltage reading, a pulse or AC impedance measurement of internal resistance, coulomb counting, and electrochemical impedance spectroscopy are some of the test techniques available (EIS).
How can a battery's energy be tested?The red probe should be connected to the positive terminal of the battery, and the black probe should be connected to the negative terminal. Take the multimeter's reading. The battery is still safe to use if the reading for a 9V battery is greater than 7V.
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Hello, If 1lb - $3.40 would 0.274lb equal 2.647? I was struggling with this question, At first I did 0.34(y) and 0.1(x) but I learned that going up from 0.34 every 0.1 decimal will not help because I am trying to figure out 0.274 so then I am trying to see if $2.4 would work. Thank you. Oops, I am in middle school not college, Apologies.
If. Sin0 + cos0 = √₂cos0 show that cos0-sin0 = √₂ sin0
Therefore, we have proven that cos (0) - sin (0) = √2 sin (0), given that sin (0) + cos (0) = √2 cos (0).
What is trigonometry?Trigonometry is a branch of mathematics that deals with the study of the relationships between the angles and sides of triangles. It explores the properties and functions of angles, as well as the relationships between them in various geometrical shapes.
Given by the question.
We have:
sin (0) + cos (0) = √2 cos (0)
Simplifying the left-hand side:
sin (0) + cos (0) = 1
Substituting back into the original equation:
1 = √2 cos (0)
Dividing both sides by √2:
1/√2 = cos (0)
Now we need to prove that:
cos (0) - sin (0) = √2 sin (0)
Substituting our value for cos (0):
1/√2 - sin (0) = √2 sin (0)
Multiplying both sides by √2:
√2/2 - √2 sin (0) = 2 sin (0)
Adding √2 sin (0) to both sides:
√2/2 = 3 sin (0)
Dividing both sides by 3:
sin (0) = √2/6
Substituting back into the equation we were trying to prove:
cos (0) - sin (0) = cos (0) - √2/6
We can now use our earlier equation to substitute for cos (0):
cos (0) - √2/6 = √2/2 - √2/6
Simplifying:
cos (0) - sin (0) = √2 sin (0)
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I really need help ASAP
-9p+9c
Answer:
it cant be if the term 9p and 9c is together but if it 9p and 9c both are in product form then your answer is -p+c
find cos{a} in the triangle side lengths 20,29,21
Check the picture below.
This figure is made from a part of a square and a part of a circle.
What is the area of this figure, to the nearest square unit?
Perimeter of the given polygon figure will be 38 units.
What exactly is a polygon in mathematics?
A closed, two-dimensional, flat, closed polygon is a shape that is constrained by geometry and has straight sides. Its sides don't curve inward at all. Another term for a polygon's sides is its polygonal edges. The points where two sides converge are known as a polygon's vertices (or corners).
Perimeter of a polygon = Measure of the circumference of the polygon
From the figure attached,
Perimeter of the figure = measure of the three straight lines + measure of the circumference of the quarter circle
Measure of linear sides = 5 + 10 + 10 + 5 = 30 units
Circumference of the quarter circle = 1/4(2πr)
= 1/2(π)(5)
= 7.85 units
Perimeter of the figure = 30 + 7.85
= 37.85
≈ 38 units
Therefore, perimeter of the given figure will be 38 units.
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HELP ME ASAP
Owen's Muffin Extravaganza recorded how many of each type of muffin it recently sold.
bran muffins 25
blueberry muffins 12
poppy seed muffins 3
chocolate chip muffins 10
Considering this data, how many of the next 16 muffins sold would you expect to be bran muffins?
Answer:
Step-by-step explanation:
A hands-on experience is the only modality that would give visitors a complete understanding of the plight of modern enslaved people.
A triangle with vertices (2, 3), (4, 7), and (3, 3) is translated a distance of 5 units to the right. What are the new coordinates?
(-3, 3), (-1, 7), (-2, 3)
(2, -2), (4, 2), (3, -2)
(2, 8), (4, 12), (3, 8)
(7, 3), (9, 7) and (8, 3)
The answer is (D) (7, 3), (9, 7) and (8, 3) when A triangle with vertices (2, 3), (4, 7), and (3, 3) is translated a distance of 5 units to the right.
To translate a two-dimensional figure such as a triangle, we move all its points a certain distance in a certain direction. In this case, we need to move the triangle 5 units to the right. This means we need to add 5 to the x-coordinate of each vertex, while leaving the y-coordinate unchanged.
In this case, we need to add 5 units to the x-coordinates of each vertex of the triangle.
The new coordinates of the triangle's vertices would be:
(2+5, 3) = (7, 3)
(4+5, 7) = (9, 7)
(3+5, 3) = (8, 3)
Therefore, the answer is (D) (7, 3), (9, 7) and (8, 3).
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The complete question is :
A triangle with vertices (2, 3), (4, 7), and (3, 3) is translated a distance of 5 units to the right. What are the new coordinates?
A.(-3, 3), (-1, 7), (-2, 3)
B.(2, -2), (4, 2), (3, -2)
C.(2, 8), (4, 12), (3, 8)
D.(7, 3), (9, 7) and (8, 3)
18-34 35-44 45-5455+
206 388 393 410
26 9 21 13
Neither more nor less likely 283 220 153 137
Total
In a recent poll, a random sample of adults in some country (18 years and older) was asked, "When you see an ad emphasizing that a product is "Made in our country," are you m
buy it, or neither more nor less likely to buy it?" The results of the survey, by age group, are presented in the following contingency table. Complete parts (a) through (c).
Purchase likelihood
More likely
Less likely
Question 7 of 11 >
Total
1397
69
793
515 617 567 560 2259
Yes, more likely
No, less likely
This quiz: 11 point(s) possible
This question: 1 point(s) possible
(a) What is the probability that a randomly selected individual is at least 55 years of age, given the individual is
The probability is approximately 0.2934.
(Round to three decimal places as needed.)
(b) What is the probability that a randomly selected individual is more likely to buy a product emphasized as "Made in our country." given the individual is at least 55 years of age?
The probability is approximately.
(Round to three decimal places as needed.)
(c) Are 18-to 34-year-olds more likely to buy a product emphasized as "Made in our country than individuals in general?
likely to buy a product emphasized as "Made in our country"?
Answer:
(a) To find the probability that a randomly selected individual is at least 55 years of age, we need to add up the values in the last row of the contingency table corresponding to the age group 55+ and divide it by the total number of respondents:
P(age 55+) = (515 + 617 + 567 + 560) / 2259 ≈ 0.2934
So the probability is approximately 0.2934.
(b) To find the probability that a randomly selected individual is more likely to buy a product emphasized as "Made in our country," given the individual is at least 55 years of age, we need to add up the values in the second row of the contingency table (corresponding to "Yes, more likely") for the age group 55+ and divide it by the total number of respondents in that age group:
P(more likely|age 55+) = 515 / (515 + 617 + 567 + 560) ≈ 0.2281
So the probability is approximately 0.2281.
(c) To determine whether 18-34-year-olds are more likely to buy a product emphasized as "Made in our country" than individuals in general, we need to compare the proportion of respondents who answered "Yes, more likely" in the 18-34 age group to the proportion in the entire sample. We can calculate these proportions by adding up the values in the second row of the contingency table for the 18-34 age group and for the entire sample, respectively, and dividing each by the total number of respondents in each group:
P(more likely|age 18-34) = 206 / (206 + 388 + 393 + 410) ≈ 0.1913
P(more likely|entire sample) = 1397 / (1397 + 69 + 793) ≈ 0.6251
The proportion of 18-34-year-olds who are more likely to buy a product emphasized as "Made in our country" is approximately 0.1913, while the proportion in the entire sample is approximately 0.6251. Therefore, it appears that individuals in general are more likely to buy a product emphasized as "Made in our country" than 18-34-year-olds.
Step-by-step explanation:
Rewrite in the simplest form 7(−8f−2)+10(−5f+7)
Answer:
-106f+56
Step-by-step explanation:
7(-8f-2)= -56f-14
10(-5f+7)= -50f+70
-56f-14. +. 50f+70
=-106f+56
Answer:
-2(53f-28)
Step-by-step explanation:
Distribute7(−8f−2)+10(−5f+7)
7x-8f=-56f 7x-2=-14
10x-5f=-50f 10x7=70
-56f-14+-50f+70 Adding a negative to something means to subtract. Like right here at -14 + -50 is the same as -14 - 50
2. Add the numbers
-56f-14+-50f+70 -14+70=56
-56f+56-50f
3. Combine like terms
-56f+56-50f -56+ -50= -106
-106f +56
4. Common Factor
-106f + 56
-2(53f-28)
Which best describes the relationship between the line that passes through the points (–6, 5) and (–2, 7) and the line that passes through the points (4, 2) and (6, 6)?
A. same line
B. neither perpendicular nor parallel
C. parallel
D. perpendicular
Answer:
B
Step-by-step explanation:
calculate the slopes m of the 2 lines using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 6, 5 ) and (x₂, y₂ ) = (- 2, 7 )
m = [tex]\frac{7-5}{-2-(-6)}[/tex] = [tex]\frac{2}{-2+6}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]
repeat with
(x₁, y₁ ) = (4, 2 ) and (x₂, y₂ ) = (6, 6 )
m = [tex]\frac{6-2}{6-4}[/tex] = [tex]\frac{4}{2}[/tex] = 2
• Parallel lines have equal slopes
[tex]\frac{1}{2}[/tex] ≠ 2 , then lines are not parallel
the product of the slopes of perpendicular lines equals - 1
[tex]\frac{1}{2}[/tex] × 2 = 1 ≠ - 1 , thus lines are not perpendicular
the lines are neither perpendicular nor parallel
N=6, p=0.3, x<4
P(x<4) =
Answer:
Step-by-step explanation:
To find P(x<4), we need to use the cumulative distribution function (CDF) of the binomial distribution.
For N = 6 and p = 0.3, the probability mass function (PMF) is:
P(X = k) = (6 choose k) * 0.3^k * 0.7^(6-k)
where (6 choose k) is the binomial coefficient.
Using this formula, we can find the probabilities for each value of X less than 4:
P(X = 0) = (6 choose 0) * 0.3^0 * 0.7^6 ≈ 0.1176
P(X = 1) = (6 choose 1) * 0.3^1 * 0.7^5 ≈ 0.3025
P(X = 2) = (6 choose 2) * 0.3^2 * 0.7^4 ≈ 0.3241
P(X = 3) = (6 choose 3) * 0.3^3 * 0.7^3 ≈ 0.1852
Therefore, P(x<4) is the sum of these probabilities:
P(x<4) = P(X=0) + P(X=1) + P(X=2) + P(X=3) ≈ 0.9294
So the probability of getting less than 4 successes in 6 trials with a success probability of 0.3 is approximately 0.9294.
A bakery sells chocolate cupcakes and mocha cupcakes. One day it sold 162 chocolate and 138 mocha. What percent of the cupcakes sold that day were chocolate?
Find the value of x..
Answer:
x = 16
Step-by-step explanation:
∠1 + ∠2 = 90
42 + 3x = 90
3x = 90 - 42
x = 48/3 = 16
DUE TODAY! PLEASE HELP! SHOW WORK
I NEED HELP ON PART B, IF PART A IS WRONG, PLEASE FIX IT!
The value of x is equal to: B. 12.
The measure of <BCD, in degrees is 143 degrees.
What is the vertical angles theorem?In Geometry, the vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.
By applying the vertical angles theorem to the geometric figure, we have the following:
37 = 3x + 1
3x = 37 - 1
3x = 36
x = 36/3
x = 12.
For the measure of ∠BCD, in degrees, we have:
∠BCD + (3x + 1) = 180
∠BCD + (3(12) + 1) = 180
∠BCD + 37 = 180
∠BCD = 143°.
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You want to determine the savings for using a battery that can be recharged. The battery costs sixteen dollars. You save four dollars each time you recharge the battery. Represent the cost of the rechargeable battery as a negative number and savings as a positive number.
Define a unit for the net savings of the rechargeable battery.
What is your net savings if you recharge the battery ten times?
If your net savings is twelve dollars, how many times did you recharge the battery?
Complete the rows for the amount you save each time you recharge the battery and the cost of a rechargeable battery. Then, enter a variable for the number of rechargings and use this variable to write an expression for the net savings of the rechargeable battery.
Answer this question please
Either a rotation of a reflection is used to transform Shape P so that exactly one vertex is invariant.
What are transformations on a figure?The possible transformations on a figure are listed as follows:
Translation: Translation left/right or down/up, moving all vertices.Reflections: Over one of the axes or over a line.Rotations: Over a degree measure.Dilation: Coordinates of the vertices of the original figure are multiplied by the scale factor, hence all vertices are changed.An invariant vertex means that the coordinates of the vertex remain constant even after the transformation.
A translation and a dilation will always change the coordinates of every vertex, as:
The translation means that at least one of the x-coordinate of the y-coordinate is added/subtracted.The dilation means that both the x-coordinate and the y-coordinate of each vertex is multiplied by the scale factor.For reflection and rotation, they can happen over one vertex of the shape, hence that vertex would remain constant.
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You travel in a car at an average rate of 55 miles per hour on the highway and 35 miles per hour in the city.
a. How long does it take you to travel 16.5 highway miles and 7 city miles?
b. How long does it take you to travel 44 highway miles and 28 city miles?
According to the given information, it takes 0.5 hours to travel 16.5 highway miles and 7 city miles and 1.6 hours to travel 44 highway miles and 28 city miles.
What is the average rate?
The average rate is a measure of the average speed at which something occurs over a period of time. It is calculated by dividing the total amount of something by the total time it took to occur.
The formula for the average rate or average speed is:
Average speed = Total distance traveled / Total time taken
a. To find the time it takes to travel 16.5 highway miles and 7 city miles, we can use the formula:
time = distance/speed
The time it takes to travel 16.5 highway miles is:
time on highway = 16.5 / 55 = 0.3 hours
The time it takes to travel 7 city miles is:
time in city = 7 / 35 = 0.2 hours
The total time it takes to travel both distances is:
total time = time on highway + time in city = 0.3 + 0.2 = 0.5 hours
Therefore, it takes 0.5 hours (or 30 minutes) to travel 16.5 highway miles and 7 city miles.
b. To find the time it takes to travel 44 highway miles and 28 city miles, we can use the same formula:
time on highway = 44 / 55 = 0.8 hours
time in city = 28 / 35 = 0.8 hours
total time = time on highway + time in city = 0.8 + 0.8 = 1.6 hours
Therefore, it takes 1.6 hours (or 96 minutes) to travel 44 highway miles and 28 city miles.
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Im really struggling with please help quickly
Therefore, the values of a and b are:
[tex]a = 2[/tex]
[tex]b = 9[/tex]
[tex]So, the functionf(x)=2x+9.[/tex]
What do you mean by the function?In programming and mathematics, a function is a set of instructions or a block of code that performs a specific task or calculation. A function takes in one or more input values, performs a series of operations on them, and then returns a single output value. Functions are used to modularize code, making it easier to read, understand, and maintain. They can be defined and called within a program to perform repetitive tasks, manipulate data, or solve complex problems. Functions can also be used to create reusable code that can be called from multiple parts of a program or shared between different programs.
To find the values of a and b, we need to use the given information to create a system of two equations.
Let's start by using the first two rows of the table:
[tex]f(0) = a(0) + b = 7[/tex]
[tex]f(1) = a(1) + b = 9[/tex]
Simplifying these equations, we get:
[tex]b = 7\\a + b = 9[/tex]
Substituting b = 7 into the second equation, we get:
[tex]a + 7 = 9[/tex]
Solving for a, we get:
[tex]a = 2[/tex]
Now we can use this value of a to find b. Let's use the third and fourth rows of the table:
[tex]f(2) = a(2) + b = 11\\f(3) = a(3) + b = 13[/tex]
Substituting a = 2 into these equations, we get:
[tex]2 + b = 11\\3 + b = 13[/tex]
Solving for b, we get:
[tex]b = 9[/tex]
Therefore, the values of a and b are:
[tex]a = 2\\b = 9[/tex]
[tex]So, the functionf(x)=2x+9.[/tex]
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What are the roots of y = x² – 3x – 10? O-3 and -10 0-2 and 5 O2 and -5 O3 and 10
Answer:
x = - 2 , 5
Step-by-step explanation:
to find the roots let y = 0 , that is
x² - 3x - 10 = 0 ← in standard form
(x + 2)(x - 5) = 0 ← in factored form
equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x - 5 = 0 ⇒ x = 5
which of the following has the slowest growth of rate?
5(e)^x
6(1.03)^x
2(3)^x
(0.3)^x
Answer:
(0.3)^x has the slowest growth rate.
Step-by-step explanation:
Out of the given functions, the function with the slowest growth rate is (0.3)^x.
To see why, we can compare the growth rates of each function as x increases.
For 5(e)^x, the base e is approximately equal to 2.718, which means that the function grows very quickly as x increases.
For 6(1.03)^x, the base is slightly greater than 1, which means that the function grows at a moderate rate as x increases.
For 2(3)^x, the base is greater than 1, which means that the function grows more quickly than (1.03)^x, but less quickly than (e)^x.
For (0.3)^x, the base is less than 1, which means that the function decreases as x increases. Therefore, this function has the slowest growth rate out of the given functions.
So, (0.3)^x has the slowest growth rate.