Answer:B
Step-by-step explanation: I took the test
trust me :p
If the discriminant is negative, there are nο real sοlutiοns, but there are twο cοmplex sοlutiοns in the fοrm οf cοmplex cοnjugates.
What is the quadratic equatiοn?In algebra, a quadratic equatiοn is any equatiοn that can be rearranged in standard fοrm as where x represents an unknοwn value, and a, b, and c represent knοwn numbers, where a ≠ 0.
A quadratic equatiοn is a secοnd-degree pοlynοmial equatiοn in οne variable οf the fοrm:
ax² + bx + c = 0
where a, b, and c are cοnstants, and x is the variable. The quadratic equatiοn is used tο sοlve prοblems that can be represented by a secοnd-degree pοlynοmial functiοn.
The general fοrm οf the quadratic equatiοn can be sοlved using the quadratic fοrmula:
x = (-b ± √(b² - 4ac)) / 2a
where the "±" sign means that there are twο pοssible sοlutiοns, οne with the pοsitive square rοοt and the οther with the negative square rοοt.
The quadratic equatiοn can have οne, twο, οr nο real sοlutiοns depending οn the value οf the discriminant b² - 4ac. If the discriminant is pοsitive, there are twο distinct real sοlutiοns. If the discriminant is zerο, there is οne real sοlutiοn with a multiplicity οf 2.
If the discriminant is negative, there are nο real sοlutiοns, but there are twο cοmplex sοlutiοns in the fοrm οf cοmplex cοnjugates.
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which of the following is equal to 9•6 divided by long division?
The solution to the expression 9•6 is 54
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
9•6 divided by long division
The above expression is a product expression
This means that it cannot be evaluated using long division
When the expression is evaluated. we have
9 * 6 = 54
Hence, the solution is 54
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A 16ft pipe has been cut into two parts, one 3 times as long as the other. How long (in ft) is each part?
Answer:
12 feet
Step-by-step explanation:
Let x be the length of the shorter part of the pipe.
According to the problem, the longer part is three times as long as the shorter part. Therefore, the length of the longer part is 3x.
We also know that the sum of the lengths of the two parts is equal to the original length of the pipe, which is 16 feet.
So we can write an equation:
x + 3x = 16
Simplifying this equation, we get:
4x = 16
Dividing both sides by 4, we get:
x = 4
So the length of the shorter part is 4 feet, and the length of the longer part is 3 times as long, or 3 × 4 = 12 feet.
In Exercises 9 to 14, find the limit of each function at the given point, or explain why it does not exist. 10. f(z) = Arg z at Zo--1 11. f(z) = (1-Im z)-1 at z,-8 and then at zo-8 +1 12.f(z) = (z _ 2) log(z-21 at zo = 2 13, f(z) =-, z#0 at zo = 0 14. f(z) = 2+21,
Previous question
The limit of each function at the given point i n the question 10 to 14, is explained below.
Limit Of A function:A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit. Although the right- and left-hand limits are present in this scenario, the limit is not defined.
When a variable approaches its limit from the right, the function's right-hand limit is the value that approaches.a
10). The limit of f(z) = Arg z as z approaches Zo = 1 does not exist. This is because the argument function is not continuous at the point z = 1, where there is a branch cut.
11). The limit of f(z) = [tex](1 - lm z)^{-1}[/tex] as z approaches z0 = -8 does not exist. This is because the function approaches infinity as z approaches -8 from the left, and negative infinity as z approaches -8 from the right.
However, if we consider the limit of f(z) as z approaches z0 = -8 + i from both the left and the right, the limit exists and is equal to 0. This is because in the complex plane, the value of Im z cannot exceed 1, so as z approaches -8 + i, the denominator (1 - Im z) approaches 0, and the function approaches infinity. However, the numerator approaches a finite value of 1, which cancels out the denominator, and the overall limit is equal to 0.
12). The limit of f(z) = (z - 2) log(z - 2) as z approaches z0 = 2 is 0. This is because the term (z - 2) approaches 0 as z approaches 2, and log(z - 2) approaches 0 as well because log(z - 2) is continuous at z = 2. Therefore, the limit is equal to 0.
13). The limit of f(z) = -1/z as z approaches z0 = 0 does not exist. This is because as z approaches 0, the magnitude of 1/z approaches infinity, but the direction of approach depends on which quadrant the limit is approached from. Since the limit does not approach a unique value from all directions, the limit does not exist.
14). The limit of f(z) = 2 + [tex]2^{1/z}[/tex] as z approaches infinity does not exist. This is because as z approaches infinity, the term [tex]2^{1/z}[/tex] approaches 1, and the limit approaches 2 + 1 = 3. However, if we approach infinity along the real axis, the limit of [tex]2^{1/z}[/tex] approaches 1, but if we approach infinity along the imaginary axis, the limit of [tex]2^{1/z}[/tex] approaches infinity. Therefore, the limit of f(z) does not exist.
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A basketball player makes 39% of her shots from the free throw line. Suppose that each of her shots can be considered independent and that she throws 5 shots. Let x = the number of shots that he makes. What is the sample space for x?.
The sample space for x, where x is the number of shots the basketball player makes out of 5 free throws, is,{SSSSS, FSSSS, SFSSS, SSFSS, SSSF S, SSSSF, FSSF S, FSFSS, FSSSF, SFFSS, SFSSF, SSFFS, FSSFS, FSFSS, FFSSS, SFFSF, SFSSF, SSFSF, FSSSF, FSFSS, SFSFS, FSSFS, FSSSF, SFFFS, SSFFS, FFSFS, FFSFF, FSFFS, SFSFF, SFSSS}There are 32 possible outcomes in the sample space.
The sample space for x is the set of all possible outcomes of the experiment of shooting 5 free throws. Since each shot can either be made or missed, there are 2 possible outcomes for each shot. Therefore, there are 2^5 = 32 possible outcomes for the experiment.
To enumerate the sample space, we can use the notation S for made shots and F for missed shots. Then, each outcome of the experiment can be represented by a string of 5 letters, where each letter represents the outcome of a single shot.
Using this notation, the sample space for x is:
{SSSSS, FSSSS, SFSSS, SSFSS, SSSF S, SSSSF, FSSF S, FSFSS, FSSSF, SFFSS, SFSSF, SSFFS, FSSFS, FSFSS, FFSSS, SFFSF, SFSSF, SSFSF, FSSSF, FSFSS, SFSFS, FSSFS, FSSSF, SFFFS, SSFFS, FFSFS, FFSFF, FSFFS, SFSFF, SFSSS}
Note that there are 6 outcomes where the player makes 0 shots, 5 outcomes where the player makes 1 shot, 10 outcomes where the player makes 2 shots, 10 outcomes where the player makes 3 shots, 5 outcomes where the player makes 4 shots, and 1 outcome where the player makes all 5 shots.
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Determine the set of x-values where f(x) =
The set of x-values where f(x) is continuous is all real numbers except x=1, interval notation is (-∞, 1) U (1, ∞).
What are the set of x-values?
The function f(x) is a rational function, which is continuous for all x-values except those that make the denominator 0.
Thus, to find the set of x-values where f(x) is continuous, we need to find the values that make the denominator x-1 equal to 0:
x - 1 = 0
x = 1
Therefore, the set of x-values where f(x) is continuous is all real numbers except x=1. We can write this set in interval notation as:
(-∞, 1) U (1, ∞)
which means the set of all x-values less than 1, combined with the set of all x-values greater than 1.
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Roger will pour concrete to make a sidewalk with the dimensions, in feet, shown in the figure below. He will pour the concrete to a depth of 4 inches. One bag of concrete mix makes 0.6 cubic feet of concrete. What is the least whole number of bags of concrete mix that Roger needs in order to make the sidewalk?
F. 16
G. 44
H. 50
J. 58
K. 67
Answer:
The least whole number of bags of concrete mix that Roger needs in order to make the sidewalk is G, 44. To calculate this, we must first convert the cubic feet of the sidewalk into cubic inches, which would be 345,600 cubic inches. Then, we need to divide this by the amount of cubic inches in one bag (0.6 cubic feet = 630 cubic inches). This gives us 550 bags of concrete mix, but since Roger will be using a whole number, the closest he can get is 44 bags.
Write the solution using interval notation
The solution to the inequality is [-∝, -6]
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
2/3x + 9 ≤ -2/3x + 1
Using the above as a guide, we have the following:
Evaluate the like terms
4/3x ≤ -8
Cross multiply
4x ≤ -24
Divide by 4
x ≤ -6
As an interval notation, we have
[-∝, -6]
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Does anyone know the missing statement?
We are proving that two triangles are congruent by an ASA (angle-side-angle).
In the process of proof we already have two congruent angle pairs and the missing bit is the included side.
In order to complete the proof we need to show that AE and CF are congruent segments.
We can show this as:
Statement Reason
AE ≅ CF Segment addition property, two segments consisting of congruent part are congruent A.F + FE = CE + FEWhat is the slope of the line on the graph?
C)2
The slope of the line on the given graph in the image below is: 2.
How to Find the Slope of a Line on a Graph?To find the slope of the line in a graph, use any two points on the line and plug in the coordinates of the two points in the slope formula which is given as:
Slope (m) = change in y / change in x = rise/run = y2 - y1 / x2 - x1
Picking two points on the line, (0, 1) and (1, 3):
Slope (m) = change in y / change in x = (3 - 1) / (1 - 0)
Slope (m) = 2/1
m = 2
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in an experiment to learn whether substance m can help restore memory, the brains of 20 rats were treated to damage their memories. first, the rats were trained to run a maze. after a day, 10 rats (determined at random) were given substance m and 7 of them succeeded in the maze. only 2 of the 10 control rats were successful. the two-sample z test for the difference in the true proportions. Gives z= 2.25, P< 0.02
The z-value obtained from the test was 2.25, and the p-value was less than 0.02.
What is probability ?
Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.
Based on the experiment described, a two-sample z-test for the difference in proportions was conducted to determine if there is a significant difference between the proportion of rats that succeeded in the maze after being given substance m and the proportion of rats in the control group that succeeded in the maze.
This suggests that the difference in proportions between the two groups is statistically significant at the 0.05 level of significance (since the p-value is less than 0.05).
In other words, the results of the experiment suggest that substance m may be effective in helping to restore memory, as a greater proportion of rats in the substance m group succeeded in the maze compared to the control group. However, it's important to note that further experiments and analyses would be necessary to confirm these findings and determine the extent of the effect of substance m on memory restoration.
Therefore, The z-value obtained from the test was 2.25, and the p-value was less than 0.02.
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given a set of data that is skewed-right, there is at least % of the data within 3 standard deviations. use either chebyshev's theorem or the empirical rule to fill in the blank with the best answer:
The set of data that is skewed-right, there is at least 99.7% of the data within 3 standard deviations.
What Is the Empirical Rule?A statistical principle known as the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, holds that with a normal distribution, almost all observed data will lie within three standard deviations (denoted by ) of the mean or average (denoted by ).
Some points about standard deviation using Empirical Formula:
In accordance with the Empirical Rule, 99.7% of data that are found to have a normal distribution fall within 3 standard deviations of the mean.According to this formula, 68% of the data are within one standard deviation of the mean, 95% are within two standard deviations, and 99.7% are within three standard deviations.Learn more about Empirical Formula here:
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what is the y intercept when the coordinate is -3,-3 and the slope is -1!! quick answers needed
When the coordinate is (-3, -3) and the slope is -1, the y-intercept is -4.
What is slope?Slope is a measure of the stainless of a line what is surface and it represent by the letter m. It is calculated by dividing the vertical change in the line or surface by the horizontal change in the line or surface. Slope is used in mathematics engineering and other science to measure the rate of change between two point.
The y-intercept is the point at which a line crosses the y-axis when plotting coordinates on a graph. To find the y-intercept, you need to use the equation y = mx + b, where m is the slope and b is the y-intercept. In this case, the equation would be y = -1x - 4. This equation can be used to solve for the y-intercept when the coordinate is (-3, -3). By substituting -3 for x and -3 for y, the equation can be rearranged to -3 = -1(-3) - b, which simplifies to -4 = -b. Therefore, the y-intercept is -4.
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The total price of 3 mangoes and 6 apples is $42. If the price of a mango is $2 less than 2 times that of an apple, find the price of an apple.
Answer:
$4
Step-by-step explanation:
Let's denote the price of an apple by "a" and the price of a mango by "m". Then we can set up two equations based on the information given in the problem:
"The total price of 3 mangoes and 6 apples is $42"
mangoes are three times apples in this case.
3m + 6a = 42
"The price of a mango is $2 less than 2 times that of an apple"
m = 2a - 2
Now we can substitute equation 2 into equation 1 and solve for "a":
3(2a - 2) + 6a = 42
6a - 6 + 6a = 42
12a = 48
a = 4
Therefore, the price of an apple is $4.
꧁༒αηѕωєяє∂ ву gσ∂кєу༒꧂
100 POINTS HELP A company buys equipment for $625 to help increase sales. What is the shareholder's equity if $450 was put on credit?
A. $450
B. $1075
C. $625
D. $175
The shareholder's equity if $450 was put on credit is $175. Option D
How to find the shareholder's equityThe purchase of equipment for $625 represents a decrease in the company's shareholder equity, since assets have increased while the equity has not changed.
If $450 was put on credit, this means that the company has only paid $625 - $450 = $175 towards the equipment.
The shareholder's equity is reduced by this amount, so the new shareholder's equity is:
Shareholder's equity = Initial equity - Decrease in equity
Shareholder's equity = 0 - $175
Shareholder's equity = -$175
Since the shareholder's equity is negative, it means that the company owes more than it owns. Therefore, the answer $175.
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CAN SOMEONE HELP WITH THIS QUESTION?✨
The marginal revenue is 909 dollars per unit.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
R(q) = -2q² + 1000q _____(1)
Where q is the unit sold.
Now,
Substitute q = 91 in (1).
R(q) = -2q² + 1000q
R(q) = -2 x 91² + 1000 x 91
R(q) = -8281 + 91000
R(q) = $82719
Now,
91 units = $82719
1 unit = 82719/91
1 unit = $909
Thus,
909 dollars per unit is the marginal revenue.
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is this problem a one solution,no solution or all real numbers
The equation is true for all real numbers, and therefore the solution set is (C) all real numbers.
What is the solution to the equation?In arithmetic, a solution to the equation expresses can be replaced for the variable to provide a piece of real number information.
We can start simplifying the equation using the distributive property:
4(6x - 4) = 8(3x - 2)
24x - 16 = 24x - 16
We can see that both sides of the equation are identical, so the equation is an identity. This means that the equation is true for all real numbers, and therefore the solution set is all real numbers.
In other words, any value we choose for x will make the equation true.
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The complete question would be as:
How many solutions have the below equation?
4(6x - 4) = 8(3x - 2)
A. one solution.
B. no solution.
C. all real numbers.
Question content area top
Part 1
The line models the cost of renting a kayak. Write an equation in slope-intercept form for the line, where x is the number of hours the kayak is rented and y is the total cost of renting the kayak.
The equation of the line that models the cost of renting a kayak in slope-intercept form is: y = 5x + 10
The slope and y-intercept of the line that predicts the price of renting a kayak must be identified in order to formulate the equation for the line.
We can observe from the provided graph that the line traverses points (0, 10) and (6, 40). We may determine the slope of the line using these two points:
Slope = (Y Change/X Change) = (40 - 10)/(6 - 0) = 30/6 = 5
The equation of a line can also be expressed in the slope-intercept form, which is as follows:
y = mx + b
where m denotes the line's slope and b its y-intercept.
The slope of the line is previously known to be 5. One of the points the line passes through can be used to determine the y-intercept, for instance (0, 10). When we enter these numbers into the equation, we obtain:
10 = 5(0) + b
If we simplify, we get:
b = 10
Thus, the slope-intercept form equation of the line that represents the cost of renting a kayak is as follows:
y = 5x + 10
where x represents the duration of the kayak rental and y represents the entire cost.
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2 A representative sample of 60 students from a high school is surveyed
which elective he or she is taking. The table shows the respons Elective Dance Music Art Photography Electronics Number of Stud 19 7 15 11 8
The Accurate Prediction of the data:
In a group of 120 students, it is expected that 16 of them are taking electronics.
About 25% of the students in the school are taking art.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. With the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
Total students = 60
let x% of students chose Arts
So, x% of 60 = 15
x/ 100 (60) = 15
x = 1500 / 60
x = 25%
and, if there 120 students then number of students choose electronics
= 8/60 x 120
= 16
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som3one please help me solve this
Answer:
see explanation
Step-by-step explanation:
using the rules of radicals
• [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
• [tex]\sqrt{\frac{a}{b} }[/tex] ⇔ [tex]\frac{\sqrt{a} }{\sqrt{b} }[/tex]
(1)
[tex]\sqrt{108}[/tex]
= [tex]\sqrt{36(3)}[/tex]
= [tex]\sqrt{36}[/tex] × [tex]\sqrt{3}[/tex]
= 6[tex]\sqrt{3}[/tex]
(2)
[tex]\sqrt{14}[/tex] × [tex]\sqrt{35}[/tex]
= [tex]\sqrt{14(35)}[/tex]
= [tex]\sqrt{490}[/tex]
= [tex]\sqrt{49(10)}[/tex]
= [tex]\sqrt{49}[/tex] × [tex]\sqrt{10}[/tex]
= 7[tex]\sqrt{10}[/tex]
(3)
[tex]\sqrt{\frac{28}{64} }[/tex]
= [tex]\frac{28}{\sqrt{64} }[/tex]
= [tex]\frac{\sqrt{28} }{8}[/tex]
= [tex]\frac{\sqrt{4(7)} }{8}[/tex]
= [tex]\frac{\sqrt{4}(\sqrt{7}) }{8}[/tex]
= [tex]\frac{2\sqrt{7} }{8}[/tex]
= [tex]\frac{\sqrt{7} }{4}[/tex]
At the Crown Interior Pizza Hat location in Faridabad, a report showed that 431 out of 778 orders were for delivery. What is the minimum sample size needed to have a 4 percentage point error for the proportion of orders that were carry-out?
*If you used a program on the graphing calculator or formula can you specify which ones please?
Answer:
Step-by-step explanation:
To determine the minimum sample size needed to have a 4 percentage point error for the proportion of orders that were carry-out, we can use the following formula:
n = (Z^2 * p * q) / E^2
where:
n is the sample size we want to determine
Z is the z-score associated with the desired level of confidence (let's assume a 95% confidence level, so Z = 1.96)
p is the estimated proportion of orders that were carry-out (we don't know this yet, so we'll use 0.5 as a conservative estimate)
q is 1 - p (i.e., the estimated proportion of orders that were delivery)
E is the desired margin of error (in this case, 0.04)
Using the given information, we can estimate that the proportion of orders that were carry-out is:
p = 1 - 431/778 = 0.446
Then, plugging in the values into the formula, we get:
n = (1.96^2 * 0.446 * 0.554) / 0.04^2 ≈ 602.25
Rounding up to the nearest whole number, the minimum sample size needed is 603.
Note that I used the formula for sample size calculation based on a finite population, since the total number of orders is known (778). If we used the formula for an infinite population, the result would be very similar (around 604). I calculated this by hand, without using any calculator program, but you could use a calculator or a spreadsheet to perform the calculations more efficiently.
The point A ( 3 , − 2 ) is reflected over the point ( 4 , 0 ) and its image is point B . What are the coordinates of point B ?
The coordinates of point B are (1,2).
How to find Reflection of a point?
When a point is reflected across the X-axis, the x-coordinates remain the same. But the Y-coordinates are transformed into their opposite signs. Therefore, the reflection of the point (x, y) across X-axis is (x, -y).
The reflected point will be equidistant from the point over which it is reflected as the original point and in the same line as the original point and the reflected point.
Find the difference between the x and y values of the given points and add that value (distance) to the reflection point.
x-values: 4-3 = 1 y-values: 0-(-2) = 2
Add to reflection point x: 4-3 = 1 y: 0 -(-2)= 2
Hence, The coordinates of point B are (1,2).
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Aldo and Lena are standing on a riverbank 220 meters apart at points A and B respectively (see the figure below). They want to know the distance from Aldo to a house located across the river at point C. Aldo measures angle A to be 51 and Lena measures angle B to be 65. What is the distance from Aldo to the house? Round your answer to the nearest tenth of a meter.
When Aldo and Lena are standing on a riverside 220 meters apart at certain points, the distance between Lena and the home is 240.8 meters.
what is distance ?Displacement is the overall, purposeless movement of an object. Speed can be characterized as the amount of area an object has covered, disregarding of the origin or ending location. Distance has characterized by the extent or size of the distance between two places. The gap between adjacent positions and the distance moved between them are not exactly the same thing, it should be emphasized. The travelled is the entire length of a path that join different places. Distance is the average trip distance of a body. It is also known as distance. For instance, OP = 360 m would indicate the length of the path for an object traveling from 0 ° to point P.
given
BC/sin 53 = 250/sin 56
BC = 250 * sin 53 /sin 56
=240.8 m
When Aldo and Lena are standing on a riverside 220 meters apart at certain points, the distance between Lena and the home is 240.8 meters.
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Pls answer and show me how you got that answer
The mass of the radioactive sample at the beginning of the 13th day of the experiment will be around 424.7 grams.
What does one gramme represent?A metric weight measurement unit. A gramme is one thousandth of a kilogramme, or about 30 times smaller than an ounce. Leave a space between the word "gramme" (or the symbol "g") and the number that comes before it when a specific number is provided. In technical and scientific writing, the unit name and the number are either written together in full (for example, ten grammes) or a numeral is used with the sign ( e.g. 10 g ).
When we find the mass of radioactive, we obtain:
m₀=initial mass=1500 grams, r = 13% and n =12 days
⇒m = m₀ x [tex](1 - \frac{r}{100} )^{n}[/tex]
⇒m =1500×[tex](1-\frac{13}{100}) ^{12}[/tex]
⇒m=424.7 grams.
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PLEASE HURRY
A. Plot the circles x^2+y^2=4 and x^2+y^2=1 on the same coordinate plane.
B. Find the image of any point on x^2+y^2=4 under the transformation (x,y) to (1/2x,1/2y). The point (2,0) will go to the ordered pair___.
C. What do you notice about x^2+y^2=4 and x^2+y^2=1? The small circle is a __ of the larger one using the origin as a center and a scale factor of __.
PLEASE HURRY
Answer:
Step-by-step explanation:
A. To plot the circles x^2+y^2=4 and x^2+y^2=1 on the same coordinate plane, we can use the standard form of the equation of a circle:
For x^2+y^2=4, the radius is 2 and the center is at the origin (0,0).
For x^2+y^2=1, the radius is 1 and the center is also at the origin (0,0)
B. To find the image of any point on x^2+y^2=4 under the transformation (x,y) to (1/2x,1/2y), we can substitute the values of x and y from the original equation into the transformation rule. Let's take the point (2,0) as an example:
(1/2x,1/2y) = (1/22, 1/20) = (1,0)
Therefore, the point (2,0) will go to the ordered pair (1,0).
C. We can notice that x^2+y^2=1 is a smaller circle that is completely contained within x^2+y^2=4, which is a larger circle. The smaller circle is a dilation of the larger one using the origin as a center and a scale factor of 1/2. This means that every point on the smaller circle is half the distance from the origin as the corresponding point on the larger circle. In other words, the smaller circle is a scaled-down version of the larger one.
The same hammer is available from an online retailer. if a customer uses a discount code fhat offercs a 25% discount and free shipping, the hammer will cost $17.25. There is no sales tax if the customer buys the hammer online
Therefore , the solution of the given problem of percentage comes out to be the original price of the hammer is $23, and the customer saved $5.75 with the discount code.
What is a percentage?In mathematics, a percentage is any value that can be represented as a fraction of 100. There are also sporadic uses of the abbreviations "pct.," "pct," or "pc." Nonetheless, it is typically denoted by the "%" symbol. The proportional amount is flat and lacks any dimensions. As percentages have a numerator of 100, they can be thought of as fractions. The percent symbol (%) must come after a number to denote that it is a percentage. .
Here,
Let x be the original price of the hammer.
With the 25% discount, the customer pays 75% of the original price:
0.75x
And since there is free shipping, the customer pays only the price of the hammer:
0.75x = 17.25
Solving for x, we have:
x = 17.25 / 0.75 = 23
Therefore, the original price of the hammer is $23, and the customer saved $5.75 with the discount code.
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please help working out the area of the shaded shape
so the whole rectangle has an area of 22x18, now there's a tiny triangle on the corner, that we can say it has a base of 22 - 19 = 3, and a height of 18 - 14 = 4, so let's get both areas and subtract that of the triangle's from the rectangle's.
[tex]\stackrel{ \textit{\LARGE Areas} }{\stackrel{ rectangle }{(22)(18)}~~ - ~~\stackrel{ triangle }{\cfrac{1}{2}(\underset{b}{3})(\underset{h}{4})}}\implies 396-6\implies \text{\LARGE 390}~m^2[/tex]
If the area of a rectangle with width x can be represented with the expression A(x) = x(14 – x), what is the perimeter of the rectangle?
A
28
B
56
C
56 – 4x
D
4x + 28
Answer: D
Step-by-step explanation:
To find the perimeter of the rectangle, we need to know both the length and width of the rectangle. Since we are given the expression for the area, which is A(x) = x(14 – x), we can use this expression to find the length of the rectangle that corresponds to a given width x.
The area of a rectangle is equal to its length multiplied by its width. So we have:
A(x) = x(14 – x)
We can rewrite this equation as a quadratic equation in standard form:
A(x) = -x^2 + 14x
To find the maximum value of A(x), we can use the formula for the x-coordinate of the vertex of a quadratic function:
x = -b / 2a
where a = -1 and b = 14 in this case.
x = -14 / 2(-1) = 7
So the maximum area occurs when the width of the rectangle is 7.
To find the length of the rectangle, we can substitute x = 7 into the expression for the area:
A(7) = 7(14 – 7) = 49
So the length of the rectangle is 49/7 = 7.
Now we can find the perimeter of the rectangle by using the formula:
P = 2(l + w)
where l is the length and w is the width.
Substituting l = 7 and w = x, we get:
P = 2(7 + x)
So the correct answer is (D) 4x + 28.
In a lab, a substance was heated by 2°C each hour for 10 hours. What was the total change in temperature?
Answer:20
Step-by-step explanation:2 times with 10 hours becase per hour the temperature 2 degree celsius
Find the equation of the line through the points (−2,−10)
and (−2,−5).
Answer:
x = -2
Step-by-step explanation:
The line passing through the points (-2, -10) and (-2, -5) is a vertical line because both points have the same x-coordinate (-2).
Therefore, the equation of the line is simple:
x = -2
This means that for any value of y, the corresponding value of x is always -2. Visually, this line looks like a straight vertical line passing through the point (-2, -10) and (-2, -5) on the coordinate plane.
Answer:
Step-by-step explanation:
find derivative of f(x) = 4x³ using first Principre and F(x) = 2x²-3x
Answer:
12x^2.
Step-by-step explanation:
let y = 4x^3
If y is increased by a small amount Δy then x is increased by a small amount Δx, so we write:
y + Δy = 4(x + Δx)^3
y + Δy = 4(x^3 + 3x^2 Δx + 3x(Δx)^2 + (Δx)^3)
y + Δy = 4x^3 + 12x^2 Δx + 12x(Δx)^2 + 4(Δx)^3
Δy = 4x^3 + 12x^2 Δx + 12x(Δx)^2 + 4(Δx)^3 - y
= 4x^3 + 12x^2 Δx + 12x(Δx)^3 + 4(Δx)^2 - 4x^3
Δy/Δx = (4x^3 + 12x^2 Δx + 12x(Δx)^3 + 4(Δx)^2- 4x^3 ) / Δx
= (12x^2 Δx + 12x(Δx)^3 + 4(Δx)^2) / Δx
= 12x^2 + 12x(Δx)^2 + 4Δx
Now as Δx approaches zero, the limit ( that is the derivative) of f(x)
= 12x^2
- as we can neglect the last 2 terms.
The second part can be solved by the same process.