Answers
They are not the best factors to use because 12 cannot be simplified further into a perfect square. It is better to factor 48 into perfect squares and simplify each square root separately.
What is factors?Factors can be classified as prime or composite. A prime factor is a factor that is a prime number, meaning it is only divisible by 1 and itself. For example, the prime factors of 12 are 2 and 3. A composite factor is a factor that is not a prime number, meaning it has more than two factors. For example, 4, 6, and 12 are composite factors of 12.
Let's examine the factors 4 and 12 to see if they can be used to simplify the square root of 48:
4 is a perfect square, and its square root is 2. However, 12 is not a perfect square, and its square root cannot be simplified further.
We can write 48 as 4 x 12, so the square root of 48 can be simplified as the product of the square root of 4 and the square root of 12, or 2√12.
However, this is not the simplest form of the square root of 48. We can further simplify √12 by factoring it into perfect squares: √12 = √(4 x 3) = √4 x √3 = 2√3.
Therefore, the simplest form of the square root of 48 is 2√3, not 2√12.
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Related Questions
The formula occurs in the indicated application. Solve for the specified variable.A=P+Prt for r (principal plus interest) r=
Answers
To solve for r, we can divide both sides of the equation by Pt: r = (A-P)/Pt
The formula A=P+Prt is used to calculate the total amount of money (A) after a certain period of time when a principal amount (P) is invested at a certain interest rate (r) for a certain amount of time (t). To solve for the specified variable r, we need to rearrange the formula and isolate r on one side of the equation. Here are the steps to do so:
Step 1: Subtract P from both sides of the equation to get:
A - P = P + Prt - P
Step 2: Simplify the right side of the equation to get:
A - P = Prt
Step 3: Divide both sides of the equation by Pt to get:
(A - P) / Pt = r
Step 4: Simplify the left side of the equation to get:
r = (A - P) / Pt
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Tiana is told to carry out the following polynomial division: (2x^(3)+4x^(2)-9x-18)-:(x+5)
Answers
The final answer is 2x^(2)-6x+21 with a remainder of -123. In polynomial division notation, this can be written as (2x^(2)-6x+21)-123/(x+5).
The polynomial division that Tiana is told to carry out is (2x^(3)+4x^(2)-9x-18)-:(x+5). To carry out this division, we can use long division.
Divide the first term of the dividend, 2x^(3), by the first term of the divisor, x. This gives us 2x^(2), which we write above the division symbol.
Multiply the divisor, x+5, by the first term of the quotient, 2x^(2), to get 2x^(3)+10x^(2).
Subtract this result from the dividend to get -6x^(2)-9x-18.
Repeat the process with the new dividend, -6x^(2)-9x-18. Divide the first term, -6x^(2), by the first term of the divisor, x, to get -6x, which we write above the division symbol next to 2x^(2).
Multiply the divisor, x+5, by the new term in the quotient, -6x, to get -6x^(2)-30x.
Subtract this result from the new dividend to get 21x-18.
Repeat the process with the new dividend, 21x-18. Divide the first term, 21x, by the first term of the divisor, x, to get 21, which we write above the division symbol next to 2x^(2)-6x.
Multiply the divisor, x+5, by the new term in the quotient, 21, to get 21x+105.
Subtract this result from the new dividend to get -123, which is our remainder.
So, the final answer is 2x^(2)-6x+21 with a remainder of -123. In polynomial division notation, this can be written as (2x^(2)-6x+21)-123/(x+5).
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1.5×10^5
bacteria are measured to be in a dirt sample that weighs 11 gram. Use scientific notation to express the number of bacteria that would be in a sample weighing 1919 grams.
Answers
Hence, a 19-gram sample would contain 2.5909 x 10⁵ germs.
How come we use measure?
We can compare unknown amounts to known values with the use of measurement. We can quantify the size, length, and speed of objects with the use of measurement. The final result won't be accurate without measurement.
We may start by calculating the bacterium to dirt sample weight ratio:
bacteria per gram = 1.5 x 10⁵ / 11 = 13636.36...
We are able to employ this ratio to determine how many bacteria are present in a 19-gram specimen:
bacteria = bacteria per gram x weight of sample
bacteria = 13636.36... x 19
bacteria = 259090.91...
We must write the number in scientific notation because it is more than 10⁵. This can be achieved by adding a factor of 10⁵ and shifting the decimal place five places to a left:
bacteria = 2.5909 x 10^5
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the table gives information about the lengths of time spent in minutes, it took some pupil to do their maths homework last week.
Answers
Using the lengths of the time spent we can plot the histogram by the values in the table.
What is a histogram how to draw a histogram?A histogram is a visual depiction of a frequency distribution with continuous classes that has been categorised.
To create a histogram, follow the steps shown below.
Mark the class intervals on the X-axis and the frequencies on the Y-axis to get started.
Both axes must have the exact same scales. Intervals between classes must be exclusive. Create rectangles with appropriate frequencies as the heights and bases acting as class intervals.
As the class limits are shown on the horizontal axis and the frequencies are shown on the vertical axis, a rectangle is constructed on each class interval.
If the intervals are identical, the height of each rectangle is proportional to the associated class frequency.
From the given information, we have the following:
Length of time (t) Frequency
0 ≤ t < 10 5
10 ≤ t < 25 24
25 ≤ t < 30 12
30 ≤ t < 50 8
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The complete question is:
Bobbi bought two text books that cost 120 dollars, but paid 130
dollars because of the sales tax.What was the sales tax?
Answers
The sales tax that Bobbi paid was 10 dollars. Below, you will learn how to solve the problem.
To find the sales tax, we can simply subtract the cost of the text books from the total amount paid:
Sales tax = Total amount paid - Cost of text books
Sales tax = 130 dollars - 120 dollars
Sales tax = 10 dollars
Therefore, the sales tax that Bobbi paid was 10 dollars.
In mathematics, subtraction (also called subtraction) is an arithmetic operation that removes quantities from any kind of operation.
After subtracting, we will always have a smaller value than the one we had before.
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At the point where the cost is the same, how much will it cost to bowl at both bowling centers?
Answers
Part A: The cost of bowling will be the same at both centers if 4 games are bowled. Part B: It will cost $10 to bowl at both Fannin Lanes and Fun Time Lanes for 4 games.
Describe Bowling Games Cost?The cost of bowling games can vary depending on a number of factors, including the location, time of day, and day of the week. Generally, bowling alleys charge per game or per hour, with additional fees for shoe rentals and any other amenities or services.
The cost per game can range from a few dollars to upwards of $10 or more, depending on the location and other factors. Some bowling alleys also offer discounted rates for children, seniors, or members of certain groups.
Part A:
Let's assume that the number of games to be bowled is 'x'. The total cost of bowling at Fannin Lanes is 2.5x + 2, and at Fun Time Lanes it is 2x + 4. We need to find the number of games where the cost of bowling at both centers is the same.
2.5x + 2 = 2x + 4
0.5x = 2
x = 4
Therefore, the cost of bowling will be the same at both centers if 4 games are bowled.
Part B:
Using the value of 'x' found in Part A, we can find the cost of bowling at both centers.
At Fannin Lanes: 2.5(4) + 2 = 10
At Fun Time Lanes: 2(4) + 4 = 12
Therefore, it will cost $10 to bowl at both Fannin Lanes and Fun Time Lanes for 4 games.
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The complete question is:
Discrete Math I already saw the responses to this question but I want another way. Please don't copy and past it! Please show all work.
Dijkstra's algorithm to find the length of the shortest path between vertices a and z in the following weighted graph. Please show your distinguished vertex set and distances for each iteration.
Answers
Dijkstra's algorithm is a useful tool for finding the length of the shortest path between two vertices in a weighted graph.
To solve this problem, we can start by creating a distinguished vertex set Q that contains all of the vertices in the graph, and assigning a distance of ∞ to each vertex in the set. Then, we can assign the starting vertex, a, a distance of 0.
Next, we can choose the vertex in Q with the shortest distance from the source vertex, a. This vertex is then removed from the set Q, and all of its adjacent vertices are evaluated and added to the set Q if they are not already in it. We then assign each adjacent vertex the distance of the selected vertex, plus the weight of the edge connecting it to the selected vertex.
Finally, we continue this process until the destination vertex, z, is removed from the set Q. At this point, the length of the shortest path between vertices a and z can be found by looking at the distance of the destination vertex.
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Last week, Cindy's Diner sold 7 milkshakes with whipped cream on top and 18 milkshakes without whipped cream. What percentage of the milkshakes had whipped cream?
Answers
Answer: The total number of milkshakes sold is 7 + 18 = 25.
The number of milkshakes sold with whipped cream is 7.
To find the percentage of milkshakes with whipped cream, we can use the formula:
percentage = (part/whole) x 100
Substituting the values, we get:
percentage = (7/25) x 100
percentage = 28
Therefore, 28% of the milkshakes had whipped cream.
Step-by-step explanation:
From Monday through Friday, Earl works in the Tutoring center on another day. On another day Earl cleans bathrooms and in the on another. On Saturday and Sunday, 50% of the days. How many days does work in a week? What percent of Monday through Friday does work?
Answers
Earl works 5 days a week, which is 50percentage of Monday through Friday. He works in the Tutoring center one day, cleans bathrooms one day, and has another day for unspecified work.
Earl works 5 days a week. He works in the Tutoring center one day, cleans bathrooms one day, and has another day for unspecified work. This means that he is working 50% of Monday through Friday. On Saturday and Sunday, he has no work. His work schedule is a great example of how one can balance work with free time. It also shows how one can make the most out of their working hours by doing different activities each day. It provides variety and prevents boredom from setting in. The days off also give Earl time to rest and relax, allowing him to be productive the other days. His weekly schedule is a great example of how one can efficiently manage their time.
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1. (7 points) Find the minima and maxima of the following function at a given interval:y=x4−32x3−2x2+2xin the interval[0,3]. Hints: You may want to use conditional statement to gatekeep the values. However, do not use solveset () function.
Answers
The minima and minima of the function y=x^4-(32/3)x^3-2x^2+2x in the interval [0,3] are:
Maxima: x=2
Minima: None
The minima and maxima of a function are the lowest and highest points on the function within a given interval. To find these points, we need to take the derivative of the function and set it equal to zero to find the critical points. The critical points are where the function changes direction, and are potential minima or maxima. We can then use a conditional statement to determine if the critical points are within the given interval and if they are minima or maxima.
The derivative of the function is:
y'=4x^3-3(32/3)x^2-4x+2
Setting the derivative equal to zero, we get:
4x^3-32x^2-4x+2=0
We can use the Rational Root Theorem to find the potential rational roots of this equation. The potential rational roots are ±1, ±2, ±1/2, and ±1/4. Using synthetic division, we find that x=2 is a root. This gives us the factor (x-2), and we can use synthetic division again to find the other factors. The factored form of the equation is:
(x-2)(4x^2-12x+1)=0
Using the quadratic formula, we can find the other two roots:
x=3±√(3^2-4(4)(1))/2(4)
x=3±√(9-16)/8
x=3±√(-7)/8
x=3±i√7/8
The only real root is x=2, so this is the only critical point. We can use a conditional statement to determine if this critical point is within the given interval and if it is a minima or maxima. The critical point x=2 is within the interval [0,3], so we need to determine if it is a minima or maxima. We can do this by taking the second derivative of the function and plugging in the critical point:
y''=12x^2-6(32/3)x-4
y''(2)=12(2^2)-6(32/3)(2)-4
y''(2)=48-64-4
y''(2)=-20
Since the second derivative is negative at the critical point, this means that the critical point is a maxima. Therefore, the maxima of the function is at x=2.
In conclusion, the minima and maxima of the function y=x^4-(32/3)x^3-2x^2+2x in the interval [0,3] are:
- Maxima: x=2
- Minima: None
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Consider the scale drawing and actual drawing of an
office.
Original
1.5 in.
3 yd
Enlargement
2.5 in.
5 yd
Compare the scale drawing to the actual drawing. What
information is needed to find the area?
1. The scale factor is (1) (2) (3) or (4)
2. The area of the scale drawing is (3.75) (4) (8) or (11.5)
3. To find the area of the actual drawing, multiply the
area of the scale drawing by the (inverse) (multiple) (reciprocal) or (square)
of the scale factor.
Answers
The answers to each part about the scale factor is given above.
What is scale factor?Scale factor is the ratio of final dimensions to the initial dimensions.
Mathematically, we can write -
K = {final dimension/initial dimension}
Given are the dimensions of the drawing as -
Original 1.5 in. 3 yd
Enlargement 2.5 in. 5 yd
{ 1 } -
We can write the scale factor as -
K = 3/1.5
K = 2
{ 2 } -
Area of the scaled drawing -
A = 2.5 x 5
A = 2.5 x 180
A = 450 square inches
{ 3 } -
To find the area of the actual drawing, multiply the area of the scale drawing by the multiple of the scale factor.
Therefore, the answers to each part about the scale factor is given above.
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Three baby penguins and their father were sitting on an iceberg
0.5
0.50, point, 5 meters above the surface of the water. The father dove down
4.7
4.74, point, 7 meters from the iceberg into the water to catch dinner for his kids.
What is the father penguin's position relative to the surface of the water?
Answers
Answer:The father's position relative to the surface of the water is 4.2 meters below the surface of the water.
Step-by-step explanation:
What is an expression?
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The height relative to the water surface is calculated as:-
Height from iceberg to water surface = 0.5 meters
The height from iceberg to deep inside the water is = 4.7 meters
Father's height relative to the water surface is,
H= 4.7 - 0.5 = 4.2 meters.
The image of the condition is also attached with the answer below.
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Two ships B and C are both due east of a point A at the bas is 130 metres high. The ship at C is 350 metres from the bottom of the cliff. (a) (b) (ii) Calculate the distance from the top of the cliff to the ship at C. Calculate the angle of depression from the top of the cliff to the ship at C. 130 m A (33 B 350 m The angle of elevation of the top of the cliff from the ship at B is 33°. Calculate the distance BC.
Answers
The distance from the top of the cliff to the ship at C 373.4 m.
The angle of depression from the top of the cliff to the ship at C is 20.4 degrees
The distance BC = 200.2m
How to find the distancethe distance is given as
[tex]\sqrt{130^{2} +350^{2} }[/tex]
= 373.4 m
The distance of the top of the cliff to the ship at c is 373.4 m
angle of depression is tan ∅ = 130 / 350
∅ = tan⁻¹ 130 / 350
= 20.4 degrees
b. The distance BC
tan 33 = 130 / AB
AB = 130 / tan 33
= 200.2 m
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Why do we use standard units when measuring an object? (Select all that apply) A. Standard units are used because they are relatively permanent. B. Standard units enable communication over time. C. Standard units enable communication over distance. D. Standard units are exact.
Answers
We use standard units when measuring an object because :
A. Standard units are used because they are relatively permanent.
B. Standard units enable communication over time.
C. Standard units enable communication over distance.
D. Standard units are exact.
We use standard units when measuring an object because they are relatively permanent and enable communication over time, distance, and exactness.
Standard units are used because they are relatively permanent. This means that they do not change over time and are consistent. Standard units enable communication over time. Since they are consistent, they allow for accurate communication of measurements even if they are taken at different times.
Standard units enable communication over distance. They allow for accurate communication of measurements even if the people communicating are in different locations. Standard units are exact. This means that they are precise and accurate, allowing for consistent measurements.
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Roland and Vickie are salespeople who earned the same amount this week, although Vickie made 8 more sales than Roland. Roland earns a base of $49 plus $15 per sale. Vickie earns a base of $145 plus $6 per sale. How many sales did Roland make this week?
Answers
Roland made 16 sales this week, while Vickie made 8 more sales than Roland.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.
Let x represent the number of sales Roland has.
Roland earns a base of $49 plus $15 per sale. HenceL
Total earning by Roland = 15x + 49
Vickie made 8 more sales than Roland. Vickie earns a base of $145 plus $6 per sale.
Total earning by Vickie = 6(x + 8) + 145 = 6x + 193
Roland and Vickie are salespeople who earned the same amount this week, Therefore:
15x + 49 = 6x + 193
9x = 144
x = 16
Roland made 16 sales this week.
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running track in the shape of an oval is shown. The ends of the track form semicircles. A running track is shown. The left and right edges of the track are identical curves. The top and bottom edges of the track are straight lines. The track has width 56 m and length of one straight edge 130 m. What is the perimeter of the inside of the track? HELP PLEASE INEED THIS
Answers
The perimeter of the inside of the track is approximately 354.36 meters.
What is the circumference?
In geometry, the circumference is the perimeter of a circle or ellipse.
To find the perimeter of the inside of the track, we need to find the length of the inside edge of the track and add it to twice the length of the semicircles at each end.
The inside edge of the track is formed by two parallel lines, each offset by a distance of 56 m from the outer edge. The length of this edge is equal to the length of the long straight edge minus twice the offset distance:
length of inside edge = 130 m - 2(56 m)
length of inside edge = 18 m
The length of each semicircle at each end is equal to half the circumference of a full circle with a radius equal to the width of the track (56 m). Therefore, the length of both semicircles is:
2 x (1/2 x 2π x 56 m) = 2π x 56 m
Adding the length of the inside edge to twice the length of the semicircles, we get:
perimeter of inside track = 18 m + 2π x 56 m
perimeter of inside track = 18 m + 112π m
the perimeter of the inside track ≈ 354.36 m (rounded to two decimal places)
Hence, the perimeter of the inside of the track is approximately 354.36 meters.
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so thit i \( \mathrm{A}_{4} \) is targer than a \( \mathrm{B}_{2} . \mathrm{H} \) \[ \begin{array}{l} a=34, c=45, \quad A=194 \\ \rightarrow B_{1}=7 \cdot 3 \cdot \sim B_{2}= \\ -C_{1}= \\ b_{1}= \\ \
Answers
(\mathrm{A}_{4}\) is larger than \(\mathrm{B}_{2}\)
Yes, \(\mathrm{A}_{4}\) is larger than \(\mathrm{B}_{2}\). To show this, we can use the following equation:
\[\mathrm{A}_{4} = a \cdot c \cdot \mathrm{H}\]
and
\[\mathrm{B}_{2} = b_{1} \cdot c_{1}\]
Given that \(a = 34\), \(c = 45\), \(\mathrm{H} = 194\), \(b_{1} = 7\), and \(c_{1} = 3\), then \(\mathrm{A}_{4} = 34 \cdot 45 \cdot 194 = 291930\) and \(\mathrm{B}_{2} = 7 \cdot 3 = 21\). As \(291930 > 21\), \(\mathrm{A}_{4}\) is larger than \(\mathrm{B}_{2}\).
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The diameter of a quarter is about 1
in.
You trace around the edge of the quarter on a sheet of paper.
What is the area of the circle on the paper?
Use 3.14
as an approximation for π
. Round your answer to the nearest tenth.
Answers
The area of the circle which is drawn by tracing around the edge of the quarter on a sheet of paper is 0.78 in.²
What is meant by a quarter of a circle?All points in a plane that are at a specific distance from a specific point, the centre, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
Each of the four equally sized pieces that make up a circle is known as a quarter of a circle. The quadrant of the circle is the name given to each quarter. One-fourth of the total area of the circle is represented by the area of a quarter circle.
Given,
the diameter of the quarter = 1 in.
When we trace around the edge of the quarter on a sheet of paper, we get a circle of diameter 1 in.
So the radius of the circle r = 1/2 = 0.5 inches
Area of the circle on the paper = πr² = 3.14 × 0.5² = 0.78 in.²
Therefore the area of the circle which is drawn by tracing around the edge of the quarter on a sheet of paper is 0.78 in.²
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Jean-Luc deposits $625 in a savings account which pays 1.6% interest, compounded continuously (A = Pe^rt). How much will his account be worth in 5 years?
Answers
Jean-Luc's account will be worth approximately $740.55 after 5 years of continuous at a compounding annual interest rate of 1.6%.
What is Compound interest?Compound interest is the addition of interest to the principal amount of a loan or investment. In other words, it is the interest earned on both the principal amount and any accumulated interest from previous periods.
What is interest rate?Interest rate is the amount charged by a lender to a borrower for the use of money or the amount earned by an investor for lending money or investing in an asset. It is usually expressed as a percentage of the principal amount and is typically calculated on an annual basis.
In the given question,
The formula for continuous compounding is:
A = Pe^(rt)
where A is the amount of money in the account after t years, P is the principal amount (the initial deposit), r is the annual interest rate (as a decimal), and e is the mathematical constant approximately equal to 2.71828.
Plugging in the given values, we get:
A = 625 * e^(0.016*5)
Simplifying this expression, we get:
A = 625 * e^(0.08)
Using a calculator, we can evaluate this expression to get:
A ≈ $740.55
Therefore, Jean-Luc's account will be worth approximately $740.55 after 5 years of continuous compounding at an annual interest rate of 1.6%.
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seems appropriate for further analysis. f(x)=1.3x^(4)-5.7x^(2)+3.71,[-4,4,-8,14]
Answers
To further analyze the function f(x)=1.3x^(4)-5.7x^(2)+3.71 on the interval [-4,4,-8,14], we can find the critical points, relative extrema, and inflection points of the function.
First, let's find the critical points by taking the derivative of the function and setting it equal to zero:
f'(x)=5.2x^(3)-11.4x
0=5.2x^(3)-11.4x
0=x(5.2x^(2)-11.4)
x=0, x=±√(11.4/5.2)
So the critical points are x=0, x=±1.4656
Next, let's find the relative extrema by using the second derivative test:
f''(x)=15.6x^(2)-11.4
f''(0)=-11.4<0, so x=0 is a relative maximum
f''(1.4656)=11.4>0, so x=1.4656 is a relative minimum
f''(-1.4656)=11.4>0, so x=-1.4656 is a relative minimum
Finally, let's find the inflection points by setting the second derivative equal to zero:
0=15.6x^(2)-11.4
x=±√(11.4/15.6)
x=±0.8544
So the inflection points are x=±0.8544
Overall, the function f(x)=1.3x^(4)-5.7x^(2)+3.71 has a relative maximum at x=0, relative minimums at x=±1.4656, and inflection points at x=±0.8544 on the interval [-4,4,-8,14].
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(c) \( (35)^{3} \) (the composition of the permutation (3 5 ) three times); (d) \( \left(\begin{array}{ll}1 & 2 \\ 4\end{array}\right)^{2023} \).
Answers
The composition of the permutation (3 5 ) three times is (3 5) and the permutation (1 2 4) to the power of 2023 is (1 2 4)
The composition of the permutation (3 5 ) three times is (3 5) and the permutation (1 2 4) to the power of 2023 is (1 2 4).For part (c), we can find the composition of the permutation (3 5) three times by applying the permutation to itself three times. The first time we apply it, we get (5 3), the second time we get (3 5), and the third time we get (5 3) again. Since the permutation (5 3) is the same as the original permutation (3 5), the composition of the permutation (3 5) three times is (3 5).For part (d), we can find the permutation (1 2 4) to the power of 2023 by applying the permutation to itself 2023 times. Since the permutation (1 2 4) is a cycle of length 3, applying it to itself 3 times will give us the identity permutation (1 2 4)(1 2 4)(1 2 4) = (1)(2)(4). Therefore, we can reduce the exponent of 2023 to 2023 mod 3 = 1, and the permutation (1 2 4) to the power of 2023 is the same as the permutation (1 2 4) to the power of 1, which is (1 2 4).
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I have no clue how to do this
Answers
Put the function y=10x(x+1) in factored form f(x)=a(x-r)(x-s) and state the values of a,r, and s. (Assume r ≤ x)
Answers
The function y=10x(x+1) is already in factored form, with a=10, r=0, and s=-1.
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The set X is termed the domain of the function and the set Y is called the codomain of the function. Initially, functions represented the idealized relationship between varied quantities and other variables.
To see this, we can rewrite the function as f(x)=10(x-0)(x-(-1)), which matches the form f(x)=a(x-r)(x-s). Therefore, the values of a, r, and s are:
a = 10
r = 0
s = -1
It is important to note that the values of r and s are the x-intercepts of the function, or the values of x that make the function equal to zero. In this case, the x-intercepts are 0 and -1, which correspond to the values of r and s.
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Solvex + 4 - 5 = 6.
A. x = -7 and x
-15
B. x = 7 and x = -7
C. x = -7 and x = 15
D. x = 7 and x = -15
Answers
Option:-
[tex] \underline{\sf \color{brown}{ B ) x = 7 nd \: x = -7}}[/tex][tex] \: [/tex]
Given:-
[tex] \sf x + 4 - 5 = 6[/tex][tex] \: [/tex]
Solution:-
[tex] \sf \: x + 4 - 5 = 6[/tex][tex] \: [/tex]
[tex] \sf \: x + 4 = 6 + 5[/tex][tex] \: [/tex]
[tex] \sf \: x + 4 = 11[/tex][tex] \: [/tex]
[tex] \sf \: x = 11 - 4[/tex][tex] \: [/tex]
[tex] \boxed { \sf \blue{x = 7}}[/tex][tex] \: [/tex]
or
[tex] \sf \: x + 4 - 5 = 6[/tex][tex] \: [/tex]
[tex] \sf \: x - 1 = 6[/tex][tex] \: [/tex]
[tex] \sf \: x = 6 + 1[/tex][tex] \: [/tex]
[tex] \boxed{ \sf { \color{skyblue}x = 7}}[/tex][tex] \: [/tex]
━━━━━━━━━━━━━━━━━━━━━━━━━━
hope it helps! :)
Select all the equations that are equivalent to 52 = -4 (2n + 1)
A. -4n = 56
B. 52 = -8n - 4
C. -4n - 4 = 62
D. 52 + 4 = -8n
E. n = -7
Answers
Answer:
B, D, E
Step-by-step explanation:
52= -4(2n+1)
= -8n-4
52= -8n-4
8n= -4-52
8n= -56
n= -7
-8n= 52+4
= 56
Nancy needs her to mark the numbers
and
on the number line. How many parts does she need between 1 and 2, and between -1 and -2, so that she can mark
and
?
Answers
If we consider the number line with rational number marked on it, then the number of parts to be present between 1 and 2 and -1 and -2 will be one part each.
A number line is a pictorial representation or drawing of numbers in which there are equal intervals between each number and is used to represent the real numbers on it. Real numbers are those numbers which may be positive or negative integers, rational numbers or irrational numbers. In general, a quantity which can be expressed as an infinite decimal expansion is called as a real number.
If we draw a number line and mark the points as 1, 2, 3,...,∞ and -∞,..., -3, -2, -1 on the right and left hand side of 0, then the intervals between each real number is equal to 1. Hence the number of parts between 1 and 2 is one part and -1 and -2 is one part. However, these parts may be subdivided into more parts to get more fine value (smaller value).
This value will be a fractional value between 1 and 2 or -1 and -2. Hence parts between two numbers on a number line can be infinity, but for sake of simplicity, one is taken in general case.
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8 is 14% of what number? Round your answer to the nearest hundredth if necessary.
Answers
Answer:
I think the answer is 57.14
Answer:
57.14
Step-by-step explanation:
57.14 is the result of rounding 57.14 to the nearest 0.01
Assume that y = C(a)^x is an exponential function. Why can a not equal zero?
Answers
Answer:
In the exponential function y = C(a)^x, the value of a is the base of the exponent, which determines how fast the function grows or decays. If a were equal to zero, then any value of x would result in y being equal to zero, which would make the function flat and unchanging. Therefore, a cannot be equal to zero in an exponential function, as this would result in an undefined or meaningless expression. Additionally, any number raised to the power of zero is equal to 1, so an exponential function with a base of zero would also violate this mathematical rule.
What is the slope of the line that passes through the points ( 4 , − 6 ) and ( − 2 , 3)
Answers
Answer:
m = -3/2
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Points (4, − 6) and (− 2, 3)
We see the y increase by 9 and the x decrease by 6, so the slope is
m = - 9/6 = -3/2
So, the slope of the line is -3/2
Describe the transformation of the equation below from the parent function of y = I x I
y = -2 I x - 3 I + 3
Answers
The transformation of the equation y = -2 I x - 3 I + 3 from the parent function y = I x I includes a horizontal shift of 3 units to the right, a vertical stretch by a factor of 2, a reflection across the x-axis, and a vertical shift of 3 units up.
The transformation of the equation y = -2 I x - 3 I + 3 from the parent function y = I x I can be described as follows:
The parent function is shifted 3 units to the right. This is indicated by the "-3" inside the absolute value bars in the equation.
The parent function is vertically stretched by a factor of 2. This is indicated by the "-2" in front of the absolute value bars in the equation.
The parent function is reflected across the x-axis. This is indicated by the negative sign in front of the "2" in the equation.
The parent function is shifted 3 units up. This is indicated by the "+3" outside the absolute value bars in the equation.
In summary, the transformation of the equation y = -2 I x - 3 I + 3 from the parent function y = I x I includes a horizontal shift of 3 units to the right, a vertical stretch by a factor of 2, a reflection across the x-axis, and a vertical shift of 3 units up.
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