Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4x and y = 2x−2 intersect are the solutions of the equation 4x = 2x−2. (4 points)
Part B: Make tables to find the solution to 4x = 2x−2. Take the integer values of x between −3 and 3. (4 points)
Part C: How can you solve the equation 4x = 2x−2 graphically? (2 points)
Answers
Answer:
Part A
One method for solving a system of equations is solving by substitution.
Substitute the variable in one equation with the expression of the variable in the other equation.
Replace the y of "y = 2x - 2" with "y = 4x" to make "4x = 2x - 2".
Part B
\(\large\begin{array}{| c | c | c |}\cline{1-3} x & 4x & 2x-2 \\\cline{1-3} 3 & 12 & 4\\\cline{1-3} 2 & 8 & 2\\\cline{1-3} 1 & 4 & 0\\\cline{1-3} 0 & 0 & -2\\\cline{1-3} -1 & -4 & -4\\\cline{1-3} -2 & -8 & -6\\\cline{1-3} -3 & -12 & -8\\\cline{1-3} \end{array}\)
The only integer for which both equations give the same result is x = -1.
Therefore, the solution is x = -1
Part CTo solve the equation graphically, graph the lines y = 4x and y = 2x - 2.
The x-coordinate of the point of intersection is the solution to the equation 4x = 2x - 2
(see attached)
This is why because
y=4xy=2x-2So y is equal hence both sides are equal
so x values are equal
Tables
#4x=2x-2
\(\boxed{\begin{array}{c|c|c}\bf x&\bf 4x &\sf 2x-2\\ \sf -3 &\sf -12&\sf 4 \\ \sf -2&\sf -8&\sf 6\\ \sf -1&\sf -4&\sf -4\\ \sf 0&\sf 0&\sf -2\\ \sf 1&\sf 4&\sf 0 \\ \sf 2&\sf 8&\sf 2\\ \sf 3&\sf 12&\sf 4 \end{array}}\)
Let's solve
Graph both
The solution is (-1,-4)
The reason is -1 has same y values for both functions
Related Questions
Please. Help quickly
Answers
Answer: it is a
Step-by-step explanation:
In the square pyramid shown, points and are midpoints of the edges of one face. If the figure is sliced through points and and through the base, which best describes the shape of the resulting cross section? The picture shows a triangular prism. M and N are the points on the prism. A. rectangle B. trapezoid C. quadrilateral D. parallelogram
Answers
Based on the given information, we have a square pyramid with points M and N being the midpoints of the edges of one face. and forms a parallelogram. Option D
Since the base of the pyramid is a square, the cross section will consist of a square shape. Additionally, since the slice is made through the midpoints of the edges of the face, the resulting cross section will have parallel sides.
Considering these characteristics, we can conclude that the shape of the resulting cross section is a parallelogram. A parallelogram is a quadrilateral with opposite sides parallel. In this case, the opposite sides of the square cross section will be parallel, as the slice passes through the midpoints of the edges.
Therefore, the correct answer is D. parallelogram.
It's important to note that a triangular prism is not the correct answer because a triangular prism is a three-dimensional figure with two triangular bases and three rectangular faces. The cross section resulting from the given slice will not have the characteristics of a triangular prism. Option D.
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a question was asked by a teacher to a student. She gave the student a jumbled word and told him to make words out of it. The jumbled word is gzeysktqix. Now you know what to do. see ya!
Answers
The teacher's question, the student can provide a List of words including "sixty," "zesty," "skit," "site," "size," "exit," "yeti," "kits," "kite," and "ties."
Let unscramble the jumbled word "gzeysktqix" and find the possible words that can be formed.
Upon unscrambling, we can find several possible words:
1. Sixty
2. Zesty
3. Skit
4. Site
5. Size
6. Exit
7. Yeti
8. Kits
9. Kite
10. Ties
These are some of the words that can be formed from the jumbled letters "gzeysktqix." There may be additional words that can be created, depending on the specific rules or restrictions given by the teacher.
Unscrambling words can be a fun and challenging exercise that helps improve vocabulary, word recognition, and problem-solving skills. It allows students to enhance their language abilities and discover new words they might not have known before.
Remember, the key is to rearrange the given letters systematically and try different combinations until meaningful words are formed.
So, in response to the teacher's question, the student can provide a list of words including "sixty," "zesty," "skit," "site," "size," "exit," "yeti," "kits," "kite," and "ties."
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Write a function to convert Celsius to Fahrenheit using F=(9/5)C+32. Find the Fahrenheit value when C=56.7 and when C=−89.2. (The record high and low temperatures ever recorded on Earth.)
If x is the given temperature in Celsius, the function to return the equivalent temperature in Fahrenheit it:
f(x) = 9 / 5 * x + 32
f(x) = 9/5x + 32
f(x) = 9/5 * (x + 32)
f(x) = 9/5c + 32
The value in Fahrenheit at C=56.7 (a record high) is:
?
The value in Fahrenheit at C=−89.2 (a record low) is:
?
Using your function, f(C), to convert Celsius to Fahrenheit, compare the difference at C=20 between the function value and the simpler function: g(C)=2C+30. (In other words, is "double and add 30" a reasonable approximation?)
The difference f(C)−g(C) at C=21 (approximate room temperature) is:
?
Answers
The function used to convert Celsius to Fahrenheit is: 5/9(F - 32)
The Fahrenheit value when C = 56.7 is: 134.06
and when C = 89.2, F = -128.56, as found by basic algebra. If x is the given temperature in Celsius, the function used to return the equivalent temperature in Fahrenheit is: f(x) = 9 / 5 * x + 32 (Option A).
What is basic algebra?Numbers, variables, constants, expressions, equations, linear equations, and quadratic equations are all part of the basics of algebra. Additionally, the algebraic expressions contain the basic arithmetic operations of addition, subtraction, multiplication, and division.(1)
Given:
F = 9/5 × (C) + 32
F - 32 = 9/5 × (C)
5/9 × (F-32) = C(2)
For C = 56.7, in the above formula, by basic algebra, we get:
F = 9/5 × (56.7)+32
F = 102.06 + 32
F = 134.06
For C = -89.2, by basic algebra,
we get: F = (9/5) × (-89.2)+32
F = -160.56 + 32
F = -128.56(3)
We are given:
F = 9/5 (C) + 32
If f(x) represents the temperature in Fahrenheit, we get:
f(x) = 9/5 (C) + 32,
which is equivalent to Option A.
Hence, (1) The function used to convert Celsius to Fahrenheit is:
9/5(F-32)
(2) The Fahrenheit value when C = 56.7 is: 134.06 and when C = 89.2, F = -128.56, as found by basic algebra.
(3) If x is the given temperature in Celsius, the function used to return the equivalent temperature in Fahrenheit is: f(x) = 9 / 5 * x + 32 (Option A).
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5,7,12,20,31 what’s the pattern
Answers
Answer:
To identify the pattern in the given sequence of numbers (5, 7, 12, 20, 31), we can try finding the differences between consecutive terms:
7 - 5 = 2
12 - 7 = 5
20 - 12 = 8
31 - 20 = 11
We notice that the differences themselves form a sequence of consecutive odd numbers: 2, 5, 8, 11. This suggests that the pattern in the original sequence might involve adding consecutive odd numbers to the previous term.
Starting with 5, we can add the first odd number (1) to get 6, then the next odd number (3) to get 9, then the next odd number (5) to get 14, and so on. Continuing this pattern, we get:
5, 7, 12, 20, 31, 45, 62, 82, ...
Therefore, the pattern in the given sequence is that each term is obtained by adding consecutive odd numbers to the previous term, starting with 5 and the first odd number (1).
Choose a postmenopausal woman at random. The probability is 0.46 that the woman chosen has osteopenia (low but not pathologically low bone density ) and 0.09 that she has osteoporosis (pathologically low bone mineral density. Assume that a woman can't have both diseases simultaneously. (a) What is the probability that a randomly chosen postmenopausal woman has a healthy bone density
Answers
Answer:
The probability that a randomly chosen postmenopausal woman has a healthy bone density is 0.45.
Step-by-step explanation:
Probability of the postmenopausal woman having osteopenia = 0.46
Probability of the postmenopausal woman having osteoporosis = 0.09
Probability of having either osteopenia or osteoporosis = 0.55 (0.46 + 0.09).
Therefore, the probability that the postmenopausal woman does not have either osteopenia or osteoporosis, which is the same as having a healthy bone density = 0.45 (1 - 0.55).
Find the x- and y-intercepts of the cubic function f(x) = (x+4)(2x-1)(x-1).
Answers
As a result, the x-intercepts are -4, 1/2, and 1, respectively, while the y-intercept is -4.
What is function?In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. It is a rule or a procedure that assigns to each input value exactly one output value. Functions are often represented as a mathematical equation, a graph, or a table showing the input and corresponding output values. They are used in many branches of mathematics, science, and engineering to model and analyze real-world situations.
Here,
To find the x-intercepts, we need to set f(x) equal to zero and solve for x:
f(x) = (x+4)(2x-1)(x-1) = 0
This means that one or more of the factors (x+4), (2x-1), or (x-1) must be equal to zero. So we have three possible x-intercepts:
x+4 = 0, which gives x = -4
2x-1 = 0, which gives x = 1/2
x-1 = 0, which gives x = 1
To find the y-intercept, we set x = 0 and evaluate f(x):
f(0) = (0+4)(2(0)-1)(0-1) = -4
So the y-intercept is -4.
Therefore, the x-intercepts are -4, 1/2, and 1, and the y-intercept is -4.
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Is F(X) =9 to x power a exponential decay?
Answers
Find the lowest common denominator.
1 1 2
----------- , ------------ , -------------
(x+2)2 (x-2)2 x2-4
Answers
The LCD of 1/(x+2)^2, 3/(x-2)^2, and 4/(x^2-4) is (x+2)^2(x-2)^2(x+2)(x-2) = (x+2)^3(x-2)^3.
To find the lowest common denominator (LCD) of three fractions, we need to identify the factors of each denominator and select those factors that are common to all denominators.The given fractions are: 1/ (x+2)^2, 3/ (x-2)^2, and 4/ (x^2-4).
The first denominator (x+2)^2 can be factored using the formula for the difference of two squares. The denominator of 3/(x-2)^2 can also be factored using the formula for the difference of two squares.
Finally, the denominator of 4/(x^2-4) can be factored using the formula for the difference of two squares and the formula for the sum of two squares.
So, 1/(x+2)^2, 3/(x-2)^2, and 4/(x^2-4) can be rewritten as follows:1/ (x+2)^2 = A/(x+2) + B/(x+2)^2. Multiplying both sides by (x+2)^2 gives:1 = A(x+2) + B ... (1)3/ (x-2)^2 = C/(x-2) + D/(x-2)^2.
Multiplying both sides by (x-2)^2 gives:3 = C(x-2) + D ... (2)4/ (x^2-4) = E/(x-2) + F/(x+2). Multiplying both sides by (x^2-4) gives:4 = E(x-2)(x+2) + F(x+2)(x-2) ... (3)
Now, we need to solve these equations for A, B, C, D, E, and F. First, we will solve equation (1) for A and B by substituting x = -2, which gives A = -1/4. Then we will substitute x = -2 again and solve for B, which gives B = 1/4. Next, we will solve equation (2) for C and D by substituting x = 2, which gives C = 3/4.
Then we will substitute x = 2 again and solve for D, which gives D = -3/4. Finally, we will solve equation (3) for E and F by substituting x = 2 and x = -2, which gives E = 1/2 and F = 1/2.
Now, we have A = -1/4, B = 1/4, C = 3/4, D = -3/4, E = 1/2, and F = 1/2. The LCD is the product of all the factors that appear in the denominators of the fractions, each raised to the highest power that appears.
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What is the difference in length between 1 1/4 inch button and 3/8 inch button
Answers
The price for a pair of jeans was reduced from $40 to $24. By what
percentage was the price of the pair of jeans reduced?
25%
30%
40%
O45%
Answers
Answer:
40%
Step-by-step explanation:
Based on what we have:
\(\frac{40-24}{40}\)
Calculate the fraction above:
= \(\frac{16}{40}\)
Simplify the fraction above:
\(\frac{2}{5}\)
Next convert to a fraction:
\(\frac{2*20}{5*20}\)
Convert the num:
\(\frac{40}{100}\)
Correct option C. 40%
Question 15 (2 points)
The equation 5x-11 = 6x-x-11 has infinite solutions.
O True
O False
Answers
Reason:
The 6x-x on the right hand side simplifies to 5x
This means the right hand side turns into 5x-11, which is an identical copy of the 5x-11 on the left side.
The equation 5x-11 = 5x-11 has infinitely many solutions because we can replace x with any real number to end up with a true statement.
28,401 divided by 0.8
Answers
Answer:
35501.25
Step-by-step explanation:
6 -9x = 5x -10x + 2 solve for x
Answers
+9. +9 -2
4 = 4x
X=1
Write the quadratic function in the form y = a(x - h)^2+ k. (10Points)
Answers
Answer:
D is the correct option.
Step-by-step explanation:
y = x^2 -14x + 39
take 1/2 of the x coefficient (-14) square it then add it and subtract it :
x^2 - 14x + 49 - 49 + 39 Now reduce the three Left terms
(x-7)^2 - 49 +39 simplify the R portion
y = (x-7)^2 - 10 This process is called 'completing the square'
What is the standard deviation of this data set ?Reporting 2 more decimal places than the original data. 69.2,85.2,85.2,73.8,57.9,42.6,59,67.2,85.2,61
Answers
Answer:6.986
Step-by-step explanation:
To find the standard deviation of a set of data I find it easiest to make a chart. First you must find the mean of your data. In this case it is 476.85. Then you must subtract the mean from each data point, and square each number. Now you take your new set of data that has been squared and find the mean of these numbers. This is 48.8006. Lastly, take the square root of this number. In this case your standard deviation is 6.986.
Answer: Standard deviation is 6.986.
Step-by-step explanation:
Given an data 69.2,85.2,85.2,73.8,57.9,42.6,59,67.2,85.2,61 and have to calculate standard deviation
To find the standard deviation of a set of data I find it easiest to make a chart. First you must find the mean of your data. In this case it is 476.85. Then you must subtract the mean from each data point, and square each number.
Now you take your new set of data that has been squared and find the mean of these numbers. This is 48.8006. Lastly, take the square root of this number.
In this case standard deviation is 6.986.
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Help ASAP fist correct answer get Brainly answer
Multiply -3 2/3• (-2 1/4)
Answers
Answer:
8 1/4.
Step-by-step explanation:
What decimal number is halfway between 16 and 17?
Answers
Answer:
16.5?
Step-by-step explanation:
It's halfway between 16 and 17?
PLEASE HELP Two prisms are composed to form a V shape. The thickness of each prism is 1 unit, and width of each prism is 2 units. If the length of one prism is greater than the length of the other prism by 1 unit and the total volume of the figure is 30 cubic units, what are the lengths of the prisms?
Answers
Answer:
7 units, 8 units
Step-by-step explanation:
Apparently, the cross section of each prism is a rectangle 1 unit by 2 units. Hence the total length will be ...
(30 units³)/((1 unit)(2 units)) = 15 units
Two numbers that differ by 1 and have a sum of 15 are 7 and 8.
The lengths of the prisms are 7 units and 8 units.
A farmer has two equal-size fields. He plants corn in 11/12 of the first field and in 6/12 of the second field. How much more of the first field does he plant with corn than the second field?
Answers
Answer:
41.66% more than 2nd ..........
Which triangle is a translation of triangle P? On a coordinate plane, triangle P is shifted 5 units to the right and 7 units up to form triangle C. triangle A triangle B triangle C triangle D Mark this and return
Answers
Answer: Triangle C.
Step-by-Step Explanation:
To solve this problem, we need to understand what it means for a triangle to be a translation of another triangle. A translation for a triangle means that it is the same shape and size as the original triangle, but it has shifted (or moved) a specific number of units either up, down, left, or right.
In this problem, we have Triangle P, which has been shifted 5 units to the right and 7 units up to form Triangle C. To determine which triangle is a translation of Triangle P, we can look at the coordinates of the different triangles.
Triangle A: (1, 4), (3, 7), (5, 6)
Triangle B: (2, 3), (4, 6), (6, 5)
Triangle C: (6, 11), (8, 14), (10, 13)
Triangle D: (3, 5), (5, 8), (7, 7)
If we compare the coordinates of each triangle with those of Triangle P, we can see that Triangle C, with coordinates (6, 11), (8, 14) and (10, 13), is the translation of Triangle P because all of the coordinates of Triangle P have been shifted 5 units to the right, and 7 units up. Therefore, the answer is Triangle C.
...................................................................
Answers
Answer:
29 degrees
Step-by-step explanation:
Note how both triangles are isosceles triangles, which mean two angles will be equivalent. In the triangle with the marked angle measurement, since the total of angles in a triangle is 180, then the measurement of the unmarked angles have a sum of 180-64, which is 116. Then, as stated before, this triangle is isosceles, so the measurement of each unmarked angle is 116/2, which is 58.
Next, notice how the angle below angle x in that triangle shares a line with one of the 58 degree angles. This means that angle is 180-58, which is 122. Now, since the total of angles in a triangle is 180 and the triangle is isosceles, then angle x is (180-122)/2, which is 58/2, or 29 degrees
- 12. What is the greatest common factor of 120 and 84?
e.
a. 3
b. 6
12
18
d.
Answers
Answer:
12 (the third one is the greatest common factor of 120 and 84)
Answer:
12
Step-by-step explanation:
factors of 120. 1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,80,120
factors of 84: 1,2,3, 4,6,7,12,14,28,42,84
greatest common factor=12
Here are the shopping times (in minutes) of ten shoppers at a local grocery store.
Complete the grouped frequency distribution for the data.
In the distribution, the frequency of a class is the number of shopping times in that class.
(Note that we are using a class width of 5.)
Answers
The frequency which is to filled in the table is 1, 4, 2 and 4.
Given that;
All shopping time of ten shopkeeper:
25, 29, 25, 18, 24, 28, 36, 25, 33, 37
We have to complete the frequency in the table. Frequency of something is the number of times that number is coming.
Since, Shopping time is given as ,
25, 29, 25, 18, 24, 28, 36, 25, 33, 37
And, Intervals for which frequency is given is ,
18 to 22, 23 to 27, 28 to 32, 33 to 37.
Hence, WE get;
Numbers in the range 18 to 22 = 18 therefore 1
Numbers in the range 23 to 27 = 25, 25, 24, 25 therefore 4
Numbers in the range 28 to 32 = 29, 28 therefore 2
Numbers in the range 33 to 37 = 36, 33, 37, therefore 3
Hence, the frequency which is to filled are 1, 4, 2 and 4.
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Sienna used the scale drawing above to create a pool that is 14 ft wide x 22 ft long. She then decided to make pool with a final length of 33 ft. Which expression finds the change in scale factor for the longer pool with a final length of 33 ft which expression finds the change in scale factor for the longer pool Sierra is building
Answers
A scale factor allows a shape to be changes into another shape by changing the linear dimensions to the multiples of the initial dimension and a constant
The expression that finds the change in scale factor for the longer pool with a final length of 33 ft. Sierra is building is the option;
\(\dfrac{2 \, ft.}{3 \, ft.}\)Reason:
Known parameters are;
Dimensions of the pool created = 14 ft. wide × 22 ft. long
Final length of the pool = 33 ft.
Let x represent the length of the drawing using the initial scale factor, we have;
\(The \ initial \ scale \ factor = \dfrac{22 \, ft.}{x \, in.}\)The scale factor of the drawing following a final length of 33 ft. is therefore;
\(New \ scale \ factor = \dfrac{33 \, ft.}{x \, in.}\)The change in scale factor is given as follows;
\(Change \ in \ scale \ factor = \dfrac{Initial \, scale \, factor}{Final \, scale \, factor}\)
Therefore;
\(Change \ in \ scale \ factor = \frac{\left( \dfrac{22 \, ft.}{x \, in.} \right)}{\left( \dfrac{33 \, ft.}{x \, in.} \right)} = \dfrac{2 \, ft.}{3 \, ft.}\)Learn more here;
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Answer:
its c
Step-by-step explanation:
Help pls! I don't really know if there should be a < or no!
Answers
Answer:
yes
Step-by-step explanation:
Six bands and five comics are performing for a student talent show how many different programs can be arranged if the comics must perform between bands
Answers
120 different programs can be arranged.
What is permutation?
A permutation is a specific arrangement of objects. Set members or elements are arranged in a sequence or linear order here.
Since we are dealing with arrangements, this is a permutation problem.
Given: In the first question we have the choice of 5 acts to appear first, 4 acts to appear second, 3 acts to appear third, and so on.
So, you get 5! = 5 * 4 * 3 * 2 * 1
⇒ 120 different programs.
In the second question we have 3 choices for the first act (bands), 2 choices for the second act (comics), 2 choices for the third act (bands), 1 choice for the fourth act (comic), and 1 choice for the fifth act (band).
So, you get 3 * 2 * 2 * 1 * 1
⇒ 12 different programs.
Hence, 120 different programs can be arranged if the comics must perform between bands.
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Jim’s total bill for lunch is $20. The cost of his drink is 15% of the bill. What is the percent of the total food cost? What was the cost of his food?
Answers
Answer:
Percent of the total food cost: 85%
Cost of the food: $17
Step-by-step explanation:
If the drink is 15% of the bill, then the other 85% is the cost of the food.
85% of 20 is 17
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Given the equation cosx = x^2 prove that it has at least one root in the [0, pi] interval. Justify answer by indicating the theorem used.
Answers
1 is the root of the equation cosx = x² in the interval [0, pi]/
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The given equation is cosx = x²
cosx-x²=0
y(x)=cosx-x²
y(0)=1
y(π)=-1-π²
y(π)<0<y(0) and y is continuous, there must be a value of x in [0, pi]
where
cosx−x²=0.
Hence, 1 is the root of the equation cosx = x² in the interval [0, pi].
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8(2x - 7) = 8 how to show work
Answers
Step-by-step explanation:
8(2x-7) =8
16x - 56 = 8
16x = 64
x = 4
1). Distribute 8 and multiply.
2). Add 56 to both sides.
3). Divide both sides by 16.
Let me know of you have any questions!
Answer: Divide both sides by 88.
2x-7=1
2x−7=1
2 Add 77 to both sides.
2x=1+7
2x=1+7
3 Simplify 1+71+7 to 88.
2x=8
2x=8
4 Divide both sides by 22.
x=\frac{8}{2}
x=
2
8
5 Simplify \frac{8}{2}
2
8
to 44.
x=4
x=4
Step-by-step explanation: