We have prοven that the Prοduct Rule fοr expοnents wοrks, and that 4a and 4b are equivalent.
What is the prοduct rule οf expοnent?The prοduct rule οf expοnents states that when multiplying twο terms with the same base, yοu can add the expοnents. Specifically, [tex]a^m * a^n = a^{(m+n)[/tex].
Tο expand the expressiοn [tex]2x^3[/tex] •[tex]5x^2[/tex] using the fact that expοnents are repeated multiplicatiοn, we can write:
[tex]2x^3[/tex] • [tex]5x^2[/tex]= (2 • x • x • x) • (5 • x • x)
Using the cοmmutative prοperty οf multiplicatiοn, we can rearrange the factοrs tο grοup the x's and the numbers:
[tex]2x^3[/tex] • [tex]5x^2[/tex] = 2 • 5 • x • x • x • x
[tex]= 10x^5[/tex]
Nοw, let's prοve why the Prοduct Rule fοr expοnents wοrks. The Prοduct Rule states that when multiplying twο expοnential expressiοns with the same base, we can add their expοnents:
[tex]a^m[/tex] • [tex]a^n = a^{(m+n)[/tex]
Tο see why this is true, let's cοnsider the repeated multiplicatiοn οf a base a with expοnent m and a base a with expοnent n:
[tex]a^m[/tex]• [tex]a^n[/tex] = (a • a • ... • a) • (a • a • ... • a)
We can cοmbine the twο grοups οf factοrs by using the assοciative prοperty οf multiplicatiοn:
[tex]a^m[/tex] •[tex]a^n[/tex] = [tex]a^{(1+1+...+1)[/tex]• (a • a • ... • a) (m times)
[tex]= a^{(m+n)[/tex] • (a • a • ... • a) (m times)
Using the fact that a tο the pοwer οf 1 is just a, we can simplify the expressiοn tο:
[tex]a^m[/tex] • [tex]a^n[/tex] [tex]= a^{(m+n)[/tex]•[tex]a^m[/tex]• [tex]a^n[/tex]
Dividing bοth sides by [tex]a^m[/tex] • [tex]a^n[/tex], we get:
[tex]1 = a^{(m+n)[/tex] / ([tex]a^m[/tex] • [tex]a^n[/tex])
Using the rule fοr dividing expοnential expressiοns with the same base, we get:
[tex]1 = a^{(m+n)[/tex] • [tex]a^{(-m)[/tex] • [tex]a^{(-n)[/tex]
Using the rule fοr adding expοnents with the same base, we can simplify the expressiοn tο:
[tex]1 = a^{(m+n-m-n)[/tex]
Simplifying further, we get:
[tex]1 = a^0[/tex]
Therefοre, we have prοven that the Prοduct Rule fοr expοnents wοrks, and that 4a and 4b are equivalent.
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Three friends, Jessa, Tyree, and Ben, are collecting canned food for a culinary skills class. Their canned food collection goal is represented by the expression 11x2 − 2xy + 6. The friends have already collected the following number of cans:
Jessa: 2xy + 4
Tyree: x2
Ben: 3x2 − 7
Part A: Write an expression to represent the amount of canned food collected so far by the three friends. Show all your work.
Part B: Write an expression that represents the number of cans the friends still need to collect to meet their goal. Show all your work.
The expression that represents the amount of canned food collected so far by the three friends is [tex]$4x^2 + 2xy - 3$[/tex] and the expression that represents the number of cans the friends still need to collect to meet their goal is [tex]7x^2 + 9$.[/tex]
What is an expression?
In mathematics, an expression is a combination of numbers, variables, operators, and/or functions, which when arranged in a meaningful way, represents a mathematical relationship or a quantity.
Part A:
To find the amount of canned food collected so far by the three friends, we need to add up the number of cans collected by each friend. So, we can write:
Amount collected [tex]$= \text{Jessa's collection} + \text{Tyree's collection} + \text{Ben's collection}$[/tex]
Substituting the given expressions, we get:
Amount collected [tex]$= (2xy + 4) + x^2 + (3x^2 - 7)$[/tex]
Simplifying the expression, we get:
Amount collected [tex]$= 4x^2 + 2xy - 3$[/tex]
Therefore, the expression that represents the amount of canned food collected so far by the three friends is [tex]$4x^2 + 2xy - 3$[/tex].
Part B:
To find the number of cans the friends still need to collect to meet their goal, we need to subtract the amount collected by the three friends from the goal expression. So, we can write:
Number of cans needed [tex]$= \text{Goal} - \text{Amount collected}$[/tex]
Substituting the given expressions, we get:
Number of cans needed [tex]$= (11x^2 - 2xy + 6) - (4x^2 + 2xy - 3)$[/tex]
Simplifying the expression, we get:
Number of cans needed [tex]$= 7x^2 + 9$[/tex]
Therefore, the expression that represents the number of cans the friends still need to collect to meet their goal is [tex]7x^2 + 9$.[/tex]
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6. The value, V(t), of a new car is decreasing according to the function V(t) = 22,465 (0.88)', where time t is
measured in years and V(t) is given in dollars. Which of the following represents the average rate of decrease
in the value of the car over the first 5 years of ownership?
An expression that represent the average rate of decrease in the value of the car over the first 5 years of ownership is: 3. 11,855.50 per year.
How to determine the average rate of decrease after 5 years?In Mathematics and Statistics, a population or physical asset that decreases at a specific period of time represent an exponential decay. This ultimately implies that, a mathematical model for any population or physical asset that decreases by r percent per unit of time is an exponential equation of this form:
P(t) = I(1 - r)^t
Where:
P(t ) represents the population.t represents the time or number of years.I represents the initial value of car.r represents the decay rate.By substituting given parameters, we have the following:
P(t) = I(1 - r)^t
P(5) = 22,465(0.88)^5
P(5) = 22,465(0.5277319168)
P(5) = 11,855.50 per year.
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What attributes do a right pyramid and a sphere have in common?
Both shapes have 1 apex and a curved surface.
Both shapes have a curved surface and at least 2 edges.
Both shapes have a circular base and a circular face.
These shapes do not share any common attributes.
The common attributes of a right pyramid and a sphere are that they both have an apex and a curved surface.
What is a shape?
Shape can be defined as the external physical outline, structure or form of an object or entity. It refers to the appearance or visual characteristic of an object or entity, and is often determined by its edges, contours, curves, angles, or other physical attributes.
A right pyramid and a sphere have some similarities and differences in their attributes.
Similarities:
Both shapes have a single point at the top which is called the apex.
Both shapes have a curved surface. In the case of the right pyramid, the curved surface is a set of triangles that converge to the apex. In the case of the sphere, the curved surface is a continuous, smooth surface.
Both shapes are three-dimensional objects that occupy space.
Differences:
The base of a right pyramid is a polygon, whereas a sphere has no edges or vertices.
The curved surface of a right pyramid is made up of flat triangles, whereas a sphere's curved surface is continuous and has no flat faces.
A right pyramid has edges where the flat faces meet, whereas a sphere has no edges or corners.
A right pyramid has a finite number of vertices and edges, whereas a sphere has an infinite number of points on its curved surface.
A right pyramid can have different base shapes and sizes, whereas a sphere has only one size and shape.
Therefore, the common attributes of a right pyramid and a sphere are that they both have an apex and a curved surface.
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Use the graph to determine
(a) open intervals on which the
function is increasing, if any.
(b) open intervals on which the
function is decreasing, if any.
(c) open intervals on which the
function is constant, if any.
(a) Select the correct choice below and, if necessary, fil in the answer box to complete your choice.
• A. The function is increasing on the interval(s)
(Type your answer in interval notation. Use a comma to separate answers as needed.)
Therefore , the solution of the given problem of function comes out to be
a.(5, 7) ,b.(4, 5). and c. (1, 2).
What does function actually mean?The midterm exam covers a wide range of topics, including building, geometry, integers, ones personal divisions, and both actual and hypothetical geographic locations. A work describes the relationships between different elements that all variable cooperate to create the same outcome. A utility is composed of numerous unique elements that work together to produce unique outcomes for each input.
Here,
(a) On the intervals (2, 4) and, the function is growing (5, 7).
(b) On the intervals (0, 2) and (c), the algorithm decrements (4, 5).
(c) On intervals (0, 1) and, the function is constant (1, 2).
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Three sisters are saving for a special trip.
The ratio of Helga's savings to Nora's savings is 7 : 2 and the ratio of Nora's savings to Gertrude's savings is 2 : 3
Together all 3 sisters have saved $48
How much has each girl saved?
Nοra has $8 saved, Helga has $28 saved, and Gertrude has $12 saved.
What is ratiο ?A ratiο is a way οf cοmparing twο quantities οr numbers by divisiοn. It is a relatiοnship between twο numbers that tells us hοw many times οne value is cοntained in the οther. Ratiοs can be written in different fοrms such as a:b, a tο b, οr a/b. In a ratiο, the first number is usually referred tο as the "antecedent" and the secοnd number is referred tο as the "cοnsequent".
Fοr example, if we have a ratiο οf 2:3, it means that the first number is twο-thirds οf the secοnd number. Ratiοs can alsο be simplified οr expressed in different units, but the relatiοnship between the twο quantities remains the same. Ratiοs are cοmmοnly used in many different areas οf mathematics, such as in geοmetry, prοpοrtiοn, and statistics.
Let x be the amοunt οf savings that Nοra has
Then, Helga has 7x/2 (since the ratiο οf Helga's savings tο Nοra's savings is 7:2)
And, Gertrude has 3/2x (since the ratiο οf Nοra's savings tο Gertrude's savings is 2:3)
We knοw that the sum οf their savings is $48, sο we can write an equatiοn:
x + 7x/2 + 3/2x = 48
Tο sοlve fοr x, we can first simplify the left side οf the equatiοn:
(2x + 7x + 3x)/2 = 48
12x/2 = 48
6x = 48
x = 8
Nοw that we knοw Nοra has $8 saved, we can find hοw much Helga and Gertrude have:
Helga has 7x/2 = 7(8)/2 = $28 saved
Gertrude has 3/2x = 3/2(8) = $12 saved
Therefοre, Nοra has $8 saved, Helga has $28 saved, and Gertrude has $12 saved.
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9. If AFGH-AKJH, find FH.
F
G
x+8
4x-25
H
32
52
J
K
Answer:The required length of FH is obtained as 64.68.
What is the criteria for similarity of two triangles?
Two triangles are said to be similar when either the ratio of their corresponding sides are equal or all the corresponding angles are equal.
Two similar triangles are the same in shape but not in size.
The given diagram shows two similar triangles as ΔFGH and ΔKJH.
Since the ratios of the corresponding sides of the two triangles are equal, the following equation can be written for the given case as,
(x + 8)/32 = (4x - 25)/52
=> 52(x + 8) = 32(4x - 25)
=> 52x - 128x = -32 × 25 - 52 × 8
=> -76x = -1716
=> x = 22.42
Thus FH = 4x - 25 = 4 × 22.42 - 25 = 64.68
Hence, the length of FH for the given case is 64.68.
Step-by-step explanation:
Preston and Kim are fostering homeless kittens. Together they have fostered 47 kittens. Preston has fostered one less than one third as many kittens as Kim. How many kittens has Preston and Kim each fostered?
Answer:
Let's use variables to represent the number of kittens each person has fostered.
Let x be the number of kittens Kim has fostered.
Then, according to the problem, Preston has fostered one less than one third as many kittens as Kim, so Preston has fostered:
(1/3)x - 1
We know that the total number of kittens fostered is 47. Therefore, we can write an equation:
x + (1/3)x - 1 = 47
Simplifying and solving for x:
(4/3)x = 48
x = 36
So Kim has fostered 36 kittens.
To find out how many kittens Preston has fostered, we can substitute x = 36 into the expression we found earlier:
(1/3)x - 1 = (1/3)(36) - 1 = 11
Therefore, Preston has fostered 11 kittens.
In summary, Kim has fostered 36 kittens and Preston has fostered 11 kittens.
Answer:
36, 11
Step-by-step explanation:
Preston and Kim 47 kittens
Kim has fostered X number of kittens
Preston has fostered X/3 - 1 ( 1/3 of Kim - 1)
Total number of kitten will be Preston +Kim
X +1/3X - 1 = 47
Add 1 to both sides
X + 1/3X = 48
If 4/3X is 48, X is 36
If Kim has 36kittens, Preston fostered 47- 36 =11
To check
1/3 of 36 = 12
Subract 1 = 11
The population of some bacteria increases by 15% every day. If the original
population was 6000 bacteria, calculate the size of the population after 10 days
Answer:
To solve this problem, we can use the formula for exponential growth:
N = N0 * (1 + r)^t
Where:
N0 = the initial population size
N = the population size after t time periods
r = the growth rate per time period
t = the number of time periods
In this case, we know that the initial population (N0) is 6000, the growth rate (r) is 15% per day, and we want to find the population size (N) after 10 days (t = 10).
First, we need to convert the growth rate from a percentage to a decimal:
r = 15% / 100% = 0.15
Now we can plug in the values and solve for N:
N = 6000 * (1 + 0.15)^10
N = 6000 * 3.439
N ≈ 20,634
Therefore, the population of bacteria after 10 days would be approximately 20,634.
Which is a potential rational root of f(x) at point p
The potential rational root of a polynomial f(x) at point p is the value of x for which the result of evaluation of f(x) at that point is zero.
A potential rational root of a polynomial f(x) at point p is a value of x where the result of evaluation of f(x) at that point is zero. By Rational Roots Theorem To find a potential rational root of a polynomial f(x), we first factorize f(x) into its factors and then identify the factors which are of the form (x-p). The value of x for which the result of evaluation of f(x) at that point is zero, is the potential rational root of the polynomial f(x).
For example, consider a polynomial f(x) = x^3 + 4x^2 + 7x +2.
To find a potential rational root of this polynomial at point p, we factorize f(x) as follows:
f(x) = (x - 1)(x^2 + 5x + 2)
The factor (x - 1) is of the form (x-p) and hence, 1 is a potential rational root of the polynomial f(x). To verify that 1 is indeed a potential rational root, we evaluate f(1):
f(1) = 1^3 + 4(1^2) + 7(1) + 2
= 1 + 4 + 7 + 2
= 14
Since f(1) ≠ 0, 1 is not a rational root of the polynomial f(x).
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Complete question:
What is a potential rational root of the polynomial f(x) at the point p?
Ricardo spends $80 to buy x hamburgers and y French fries to share with his family. A burger cost $8 and French fries cost $2.
Answer:
8 burgers and 8 french fries
Step-by-step explanation:
8x+2y=80
x=8
y=13
8x8=64
80-64=16
16/2=8
Kenny saved $10 every week. Which expression represents the amount of money, in dollars, Kenny will save in x weeks?
Please help
The equation represents the amount of money, in dollars, Kenny will save in x weeks is y = $10*x
Which expression represents the amount of money Kenny will save in x weeks?We know that Kenny saved 10 dollars every week.
Then, if we define the variable y as the savings, after one week we know that:
y = 10
After another week:
y = 20
And so on.
We can define x as the number of weeks, and now we know that after x weeks, the amount of money that Kenny has saved is x times $10, this gives the linear equation.
y = $10*x
That is the equation we wanted.
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Which equation would be the best to solve by completing the square?
3x^2 + 4x = -2
x^2 + 8x = 20
x^2 + 11x = 40
x^2 = 36
The equation [tex]x^2 + 4x + 4 = 0[/tex] can be solved by completing the square.
To solve an equation by completing the square, first move the constant term to the other side of the equation. So for the equation [tex]x^2 + 4x + 4 = 0[/tex], we can move the 4 to the right side to get [tex]x^2 + 4x = -4[/tex]. Then divide the coefficient of the x-term (4 in this case) by 2, and square the result. 4 divided by 2 is 2, and 2 squared is 4, so we add 4 to both sides: [tex]x^2 + 4x + 4 = -4 + 4[/tex], which simplifies to [tex]x^2 + 4x = 0[/tex]. Then divide the coefficient of the x-term (4 in this case) by 2, and square the result. 4 divided by 2 is 2, and 2 squared is 4, so we add 4 to both sides.
[tex]x^2 + 4x + 4 = 0[/tex]
[tex]x^2 + 4x = -4[/tex]
[tex]x^2 + 4x + 4 = -4 + 4[/tex]
[tex]x^2 + 4x = 0[/tex]
[tex]x^2 + 4x + 4 = 0[/tex]
[tex](x + 2)^2 = 0[/tex]
This gives us [tex]x^2 + 4x + 4 = 0[/tex]. Next, we can factor the left side of the equation: [tex](x + 2)^2 = 0[/tex]. Then we can take the square root of both sides and solve for x: x + 2 = 0 or x = -2.
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4.02 Lesson check ! (10)
Answer:
yes
d = -30.
the difference between each successive term will give you -30, that's the common difference.
E.g -62 - ( -32) = -62 + 32 = -30
Answer:
Yes (choice 1)
d = - 30 (choice 4)
Step-by-step explanation:
It is an arithmetic sequence because the difference between successive terms is -30
-32 - (-2) = -32 + 2 = -30
-62 - (-32) = -62 + 32 = -30 etc.
Therefore the common difference is -30
Use your calculator to work out the exact value of 13822 x 623/14 Using approximations to 1 significant figure check that your answer to part a) makes sense I did part a and it is 615079
We may type the following expression into a calculator to calculate 13822 x 623/14: 13822 * 623/14 = 615079. 6 x 105 is equal to 1.4 x 104 x 4.4 x 101. Our response to part a) makes sense because 615079 is not far from 6 x 105.
We may type the following expression into a calculator to calculate 13822 x 623/14: 13822 * 623/14 = 615079
As a result, 615079 is the precise value of 13822 x 623/14.
Using approximations to 1 significant figure, we may determine whether the response makes logical.
The difference between 13822 and 623/14 is around 1.4 x 104 and 4.4 x 101, respectively.
Hence, 6 x 105 is equal to 1.4 x 104 x 4.4 x 101.
Our response to part a) makes sense because 615079 is not far from 6 x 105.
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Estimate the fraction of students who take more than 10 minutes to get to school
We estimate the fraction that 1,080 / 1,500 equals to 0.72 or 72% of all students take more than 10 minutes to get to school.
We can use the proportion of the surveyed students who take less than 10 minutes to estimate the fraction of all students who take less than 10 minutes to get to school. Then, we can subtract this fraction from 1 to estimate the fraction of all students who take more than 10 minutes to get to school.
The fraction of surveyed students who take less than 10 minutes to get to school is:
21/75 = 0.28
Assuming that the surveyed students are representative of all students in the school, we can use this proportion to estimate the fraction of all students who take less than 10 minutes to get to school. If there are 1,500 students in the school, then we can estimate the number of students who take less than 10 minutes to get to school as:
0.28 x 1,500 = 420
Therefore, we can estimate the fraction of all students who take more than 10 minutes to get to school as:
(1,500 - 420) / 1,500 = 1,080 / 1,500 = 0.72
So, we estimate that 72% of all students take more than 10 minutes to get to school.
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____The given question is incomplete, the complete question is given below:
In a school of 1,500 students, 75 students were surveyed about their time to go to school. 21 of those students say they spend less than 10 minutes on to go to school. Estimate the fraction of students who take more than 10 minutes to get to school.
Is the function y= 7(2/3)^x exponital growth or exponential decay
Answer: The function y = 7(2/3)^x is an example of exponential decay.
This is because the base of the exponential function, 2/3, is between 0 and 1, which means that the function is decreasing as x increases. As x increases, the value of (2/3)^x becomes smaller and smaller, which causes the overall value of the function y to decrease over time.
Exponential decay is a type of exponential function where the value of the function decreases over time. In contrast, exponential growth is a type of exponential function where the value of the function increases over time, and the base of the function is greater than 1.
Step-by-step explanation:
Find the total amount given the original price and tax or tip
123. 28,7. 5%
If the total amount given the original price and tax or tip are 123.28,7. 5%, the total amount including tax is $132.52.
To find the total amount given the original price and tax or tip, we need to add the amount of tax or tip to the original price.
In this case, the original price is $123.28 and the tax is 7.5%. To find the amount of tax, we can multiply the original price by the tax rate expressed as a decimal.
Tax = 0.075 x $123.28 = $9.24
Therefore, the amount of tax is $9.24. To find the total amount, we simply add the original price and the amount of tax:
Total amount = $123.28 + $9.24 = $132.52
Note that if the 7.5% was a tip instead of a tax, we would calculate it in the same way by multiplying the original price by the tip rate expressed as a decimal.
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You have 24 juice cans.
Show all of the ways you
can arrange these cans into
arrays. Draw the arrays on a
separate sheet of paper.
Teyo has 25 juice cans. Show all
of the ways he can arrange his
cans into arrays. Draw the
arrays on a separate sheet of
paper.
1. For your 24 cans of juice, the possibilities of organizing them in arrays can be:
24 cans in a single row12 cans in two rows of 68 cans in three rows of 3, with two cans left6 cans in four rows of 2, with six cans left4 cans in six rows of 1, with 8 cans left3 cans in eight rows of 1, with 0 cans left2 cans in twelve rows of 1, with 0 cans left1 can in twenty-four rows of 1, with 0 cans left2. For Teyo's 25 cans of juice, the possible arrays are:
25 cans in a single row12 cans in two rows of 6, with 1 can left10 cans in two rows of 5, with 5 cans left8 cans in three rows of 2, with 1 can left6 cans in four rows of 1, with 1 can left5 cans in five rows of 1, with 0 cans left2 cans in twelve rows of 1, with 1 can left1 can in twenty-five rows of 1, with 0 cans left over.How to find these possible arrays?You must first consider the factors of the total number of juice cans you own. For activity 1, you must consider the factors of the 24 cans of juice, that is, the factors of 24, which are 1,2,3,4,6,8,12 and 24, and then find the combinations of these factors to sort them into arrays.
Using the information above, you can effectively draw the arrays on a separate sheet of paper.
Therefore, matrices are meant to represent a set of objects or values in a rectangular shape, arranged in rows and columns and are intended to represent a variety of numerical data, text and images.
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On a map, 2 cm = 40 miles. If two cities on the map are 4.8 cm apart, determine the actual distance between the two cites. Show how you determined your answer.
In reality, [tex]96[/tex] miles distance separate the two cities.
In one words, define distance.We kept an eye on them from afar. Compared to earlier, she perceives a gap between her and her brother. They had been close friends earlier, but now there was a great distance between them. He desires to disassociate himself from his old employer.
Class 6 distance: what is it?Mileage is a vector variable that quantifies "how much space an object has travelled through" while in motion. An object's dependent and independent variables in position is referred to as displaced, a vector variable that measures "the extent to which place an item is."
Using the scale provided, we can establish the proportion:
[tex]2 cm / 40 miles = 4.8 cm / x[/tex]
where [tex]x[/tex] is the actual distance between the two cities in miles.
To solve for [tex]x[/tex], we can cross-multiply:
[tex]2 cm * x = 40 miles * 4.8 cm[/tex]
Simplifying:
[tex]2x = 192[/tex]
[tex]x = 96[/tex]
Therefore, the actual distance between the two cities is [tex]96[/tex] miles.
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Write 16 over 28 in simplest form
Answer:
4/7
Step-by-step explanation:
16/28= 8/14= 4/7
100 points please help
Answer:
(8x + 1) (8x - 1)
Step-by-step explanation:
64x² - 1
Rewrite 64x² as (8x)²
(8x)² - 1
Rewrite 1 as 1²
(8x)² - 1²
Since both terms are perfect squares, factor using the difference of squares formula, a² - b² = (a + b) (a - b) where a = 8x and b = 1
So, our answer is (8x + 1) (8x - 1)
Tshepiso decides to invest P560 at 8% per annum simple interest for 3 years. Thando also decides to invest R560 at 7% per annumi compound interest for 3 years. Which investment is more profitable? Show all your calculations.
you have $30.00 in your wallet when you drive through Steak-n-Shake. You want to order 5 meals from the $4 per meal menu. You also want to buy as many shakes as possible. The shakes are $3 each. Write and solve an equation that represents the situation. How many shakes can you afford? Round appropriately.
Answer:
Let x be the number of shakes you can buy.
The cost of 5 meals is:
5 * $4 = $20
The total cost of the meals and shakes is:
$20 + $3x = $30
Subtracting $20 from both sides of the equation:
$3x = $10
Dividing both sides of the equation by $3:
x = 3.33
Rounding down to the nearest whole number, you can buy 3 shakes.
I hope this helps!
the function f(x)=6x^2-180x=1000 represents the profit f(x) in thousands of dollars of selling x items. what is the meaning of the extreme value
Answer:
To find the extreme value of the function f(x) = 6x^2 - 180x + 1000, we can first take the derivative of the function and set it equal to zero:
f'(x) = 12x - 180 = 0
Solving for x, we get x = 15. Substituting this value back into the original function, we get:
f(15) = 6(15)^2 - 180(15) + 1000 = 1250
So the extreme value of the function is 1250, which represents the maximum profit in thousands of dollars that can be earned by selling a certain number of items.
More specifically, the value x = 15 is the value of x that maximizes the profit, and the maximum profit is $1,250,000. This means that if the company sells 15 items, they will make the most profit possible.
Step-by-step explanation:
Select the correct triangle.
Which triangle represents a reflection of triangle A across line m?
A
B
m
D
с
Answer:
Step-by-step explanation:
(D)
Solve the equation. Check your solutions.
∣2x+1∣=∣3x−11∣
To solve this equation, we need to consider two cases, one where 2x + 1 is positive and another where it is negative. We will then solve for x in each case and check our solutions to make sure they satisfy the original equation.
Case 1: 2x + 1 ≥ 0
In this case, we have:
|2x + 1| = 2x + 1
and
|3x - 11| = 3x - 11
Substituting these expressions into the original equation, we get:
2x + 1 = 3x - 11
Solving for x, we get:
x = 12
Checking our solution, we have:
|2x + 1| = |2(12) + 1| = 25
and
|3x - 11| = |3(12) - 11| = 25
Therefore, x = 12 is a valid solution to the equation.
Case 2: 2x + 1 < 0
In this case, we have:
|2x + 1| = -(2x + 1) = -2x - 1
and
|3x - 11| = -(3x - 11) = -3x + 11
Substituting these expressions into the original equation, we get:
-2x - 1 = -3x + 11
Solving for x, we get:
x = -10
Checking our solution, we have:
|2x + 1| = |2(-10) + 1| = 21
and
|3x - 11| = |3(-10) - 11| = 41
Therefore, x = -10 is not a valid solution to the equation.
Therefore, the only solution to the equation |2x + 1| = |3x - 11| is x = 12.
Write the expression as a single power using only positive exponents, if possible. Assume no denominator equals zero. D^5/d^-3
PLS ANSWER ASAP, I need to know in at least under 3 minutes, your help would be very much appreciated
The expression d^5/d^(-3) simplified as a single power with only positive exponents is d^8.
The expression we're given is d^5 / d^(-3), which can also be written as d^5 × d^3 (using the rule that a/b = a × ( 1/b )).
Recall that when we multiply two terms with the same base, we add their exponents. In this case, the base is d, so we add the exponents of 5 and -3 (or, equivalently, add 3 to 5 and subtract 3 from 5). This gives us:
d^5 × d^3 = d^ (5+3) = d^8
So the simplified expression with only positive exponents is d^8.
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Lety=f(x)be a function with domainD=[−12,−8]and rangeR=[−16,−10]. Find the domainDand rangeRfor each function. (Enter your answers using interval notation. If there is no solution, enter NO SOLUTION.) (o)y=21f(x)domainD=rangeR=(b)y=f(2x)domainD=rangeR=(c)x=f(x−2)+5domainD=rangeR=(d)y=(x+4)−1domain0=rangeft=(d)y=f(x+4)−1domainD=rangeR=(e)y=f(−x)domainD=rangeR=(f)y=−f(x)domainD=rangeR=(g)y=∣f(x)∣domainD=rangeR=
Answer:Park rangers released 4 fish into a pond in year 0. Each year, there were three times as many fish as the year before. How many fish were there after x years? Write a function to represent this scenario.
Step-by-step explanation:
An function which best represent the given scenario is, 4 x 3ˣ. So option B is correct.
What is geometric progression?
In algebra, in sequence we study various progressions, one of the progression is geometric, in this progression for every two consecutive terms, the common ratio is the same.
Formula for nth term of G.P.,
Tₙ = a×rⁿ
where a is first term and r is common ratio
Given that,
Park rangers released 4 fish into a pond in year 0.
Each year, there were three times as many fish as the year before.
The number of fish after x years = ?
After 1 year,
the number of fish = 4 x 3
After 2 year,
the number of fish = 4 x 3 x 3
= 4 x 3²
After 3 year,
the number of fish = 4 x 3² x3
= 4 x 3³
Similarly, after x years
the number of fish = 4 x 3ˣ
Hence, the expression is 4 x 3ˣ
It takes Andrew
720
720720 seconds to take a shower. He spends an additional
420
420420 seconds eating breakfast.
start fraction, 4, divided by, 5, end fraction of the distance to the hole. On his second stroke, the ball traveled
79
7979 meters and went into the hole
To convert the total time from seconds to minutes, we need to divide by 60. So, the total time in minutes would be: (720 + 420) / 60 = 1140 / 60 = 19 minutes.
To find the total time it takes Andrew to take a shower and eat breakfast, we need to add the time it takes for each activity. Andrew takes 720 seconds to take a shower and 420 seconds to eat breakfast. To convert seconds to minutes, we divide the total time in seconds by 60. So the total time it takes Andrew to take a shower and eat breakfast is (720 + 420) / 60 = 19 minutes. Therefore, it takes Andrew 19 minutes to take a shower and eat breakfast.
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Complete question:
It takes Andrew 720 seconds to take a shower. He spends an additional 420 seconds eating breakfast. How many minutes does it take Andrew to take a shower and eat breakfast?
–69u − 47 =
i just need an answer asp
Answer:
-116u
Step-by-step explanation:
-69-47 is 116. The varblie stays making it -116u