Answer:
x(x - 5)(x + 2)
Step-by-step explanation:
[tex]x^3 - 3x^2 - 10x = x(x^2 - 3x - 10)[/tex]
x² - 3x - 10
Now, we look for two integers which when added give (-3) and when multiplied give (-10). The factors are 2 and (-5).
Sum = -3
Product = -10
Factors = 2 , (-5) {2*(-5) = -10 and 2 + (-5) = -3}
x² - 3x - 10 = x² - 5x + 2x - 10 {Rewrite the middle term using the factors}
From the first and second term, take out the common factor 'x' & take out the common factor 2 from the third and fourth term.
= x(x - 5) + 2(x - 5)
= (x -5)(x + 2)
[tex]x^3 - 3x^2 - 10x = x(x -5)(x + 2)[/tex]
I need help on this now!
thank you
The safe distance between the supports to carry the load of 1500 pounds is found to be 8 meters.
Explain about the inverse proportion?One kind of proportionality relationship is inverse proportion. If two quantities remain inversely related, one will increase while the other will decrease.
The area of a circle is proportional to its radius, which serves as an illustration of direct proportion.
The equation for inverse proportion of the weight carried along with distance is:
P = 5400 /D
P is load in pounds (lb)
D is the safe distance.
Then, distance to carry 1500 lb of load is:
1500 lb = 1500*0.45 kg
1500 lb = 675 kg
675 = 5400 /D
D = 5400/675
D = 8 meters
Thus, safe distance between the supports to carry the safe load of 1500 pounds is found to be 8 meters.
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You want to buy a triangular lot measuring 1360 feet by 1850 feet by 2430 feet. The price of the land is $2200 per acre. How much does the land cost? (Hint: 1 acre =43,560 square feet. Round your answer to two decimal places.)
The land will cost approximately $52,800.00.
What is triangle ?
A triangle is a polygon with three sides and three angles. It is one of the simplest and most basic shapes in geometry. The three sides of a triangle can be of different lengths, and the three angles can also be of different sizes. The sum of the angles in a triangle is always 180 degrees.
To find the area of the triangular lot, we can use Heron's formula for the area of a triangle:
s = (1360 + 1850 + 2430)/2 = 2820
A = √[s(s-1360)(s-1850)(s-2430)] ≈ 1,046,482.74 square feet
To convert this to acres, we divide by 43,560:
A ≈ 24.00 acres
Finally, we can calculate the cost of the land by multiplying the area in acres by the price per acre:
cost = 24.00 acres × $2200/acre ≈ $52,800.00
Therefore, the land will cost approximately $52,800.00.
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A pharmaceutical company has developed a new drug to reduce cholesterol. A regulatory agency will recommend the new drug for use if there is convincing evidence that the mean reduction in cholesterol level after one month of use is more than 20 milligrams/deciliter (mg/dl), because a mean reduction of this magnitude would be greater than the mean reduction for the current most widely used drug.
The pharmaceutical company collected data by giving the new drug to a random sample of 50 volenteers having high cholestrol. The reduction in cholestrol level after one month was recorded for each individual, resulting in a sample mean reduction of 24 mg/dl and a standard deviation of 15 mg/dl.
(a) The regulatory agency decided o use a confidence interval estimate for the population mean reduction in cholestrol level for the new drug. Provide a 95% confidence inerval for the mean reduction in cholestrol level
A 95% confidence interval for the population mean reduction in cholesterol level is (19.78, 28.22) mg/dl, based on a sample mean of 24 mg/dl and a standard deviation of 15 mg/dl.
Using the information, we can compute a confidence interval for the population mean decrease in cholesterol level as follows:
1. Calculate the standard error of the mean:
standard error = standard deviation/sqrt(sample size)
= 15/sqrt(50)
= 2.12
2. Calculate the margin of error using a t-distribution with (n-1) degrees of freedom at 95% confidence level:
margin of error = t_(n-1, 0.025) * standard error
= t_(49, 0.025) * 2.12 (using a t-table)
= 2.009 * 2.12
= 4.26
3. Calculate the confidence interval by subtracting and adding the margin of error to the sample mean:
CI = sample mean +/ - margin of error
= 24 +/ - 4.26
= (19.74, 28.26)
In this manner, we can say with 95% certainty that the true mean reduction in cholesterol level following one month of drug of the new medication is between 19.74 mg/dl and 28.26 mg/dl. Since the lower limit reaches the confidence interval (19.74 mg/dl) is greater than 20 mg/dl, we can reason that there is persuading proof that the new medication is powerful in lessening cholesterol level following one month of purpose.
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Which table of values is defined by the function y=4-7x
The table of values for the function y=4-7x can be found by choosing any real value of x and we will get real value output from the function. So the table C is found to be correct for the function f(x)=4-7x.
For example, let's choose some values of x and calculate the corresponding values of y:
When x = 0, y = 4 - 7(0) = 4
When x = 1, y = 4 - 7(1) = -3
When x = 2, y = 4 - 7(2) = -10
When x = 3, y = 4 - 7(3) = -17
We can continue this process to find more values of y for different values of x.
The resulting table of values is:
x y
0 4
1 -3
2 -10
3 -17
So, this is the table of values defined by the function y=4-7x.
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The complete question is :
Which table of values is defined by the function y=4-7x
Table A Table B Table C Table D
x y x y x y x y
0 4 0 0 0 4 0 -4
1 3 1 1 1 -3 1 -3
2 10 2 2 2 -10 2 -10
3 17 3 3 3 -17 3 -17
The diameter of a circle is 8 cm. Find its area to the nearest whole number.
Answer:
≈ 50 cm²
Step-by-step explanation:
Use the equation [tex]A= \frac{1}{4} \pi d^{2}[/tex] Where d is the diameter.
Answer:
The answer that you're looking for is approximately 50 (rounded), In terms of π, it is 16π.
Step-by-step explanation:
In order to find the area you need to use the formula: Area = [tex]\pi r^{2}[/tex].
Since The Diameter is double the amount of the radius you need to make sure to divide the diameter by 2 and replace "r" in the equation with the equation given.
8/2 gives you 4. Now you have the equation Area of Circle = [tex]\pi 4^{2}[/tex].
Following the rules of PEMDAS we do exponents since there is no parenthesis.
[tex]4^{2}[/tex] is the same as 16. In terms of pi, you just put pi next to your result giving 16π.
However, if you want to find out normally you can multiply with either 3.14 or π.
Both cases will give you different decimals, but when rounded to the nearest whole number they all give you 50.
Area of Circle = [tex]\pi r^{2}[/tex].
Area of Circle = [tex]\pi 4^{2}[/tex]
Area of Circle = 16π
Area of Circle = 50 (rounded).
I hope this was helpful!
Help me pls
The circumference of a circle is 171 cm.
What is exact the area of the circle?
Do not round. Include correct units.
Show all your work.
Answer:
72.25π cm²
Step-by-step explanation:
C = 2πr
17π cm = 2πr
Divide both sides by 2π.
8.5 cm = r
r = 8.5 cm
A = πr²
A = π × (8.5 cm)²
A = 72.25π cm²
Find the following characteristics about the linear function 30x + 5y = -80. X-intercept: y-intercept: slope: m = f(3) = when f(x) = 110, x =
After calculating we get, x-intercept is (-8/3, 0), y-intercept is (0, -16), slope is -6, f(3) = (-34) and So when f(x) = 110, x = -21.
To find the characteristics of the linear function 30x + 5y = -80:
To find the x-intercept, we set y = 0 and solve for x:
30x + 5(0) = -80
30x = -80x = -8/3
So the x-intercept is (-8/3, 0).
To find the y-intercept, we set x = 0 and solve for y:
30(0) + 5y = -80
5y = -80y = -16
So the y-intercept is (0, -16).
To find the slope, we solve for y in terms of x by rearranging the equation to slope-intercept form, y = mx + b:
30x + 5y = -80
5y = -30x - 80y = -6x - 16
So the slope is -6.
To find f(3), we substitute x = 3 into the equation and solve for y:
30(3) + 5y = -80
90 + 5y = -80
5y = -170y = -34
So f(3) = (-34).
To find x when f(x) = 110, we substitute y = 110 into the equation and solve for x:
30x + 5(110) = -80
30x + 550 = -80
30x = -6
30x = -21
So when f(x) = 110, x = -21.
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15 The table shows values of s and t.
S
t
0.2
7.5
0.5
1.4
0.9
Is s inversely proportional to f? Explain why.
(2 marks)
Answer:
s is not inversely proportional to t
Step-by-step explanation:
This is an edited response. My first answer was incorrect.s is not inversely proportional to t. I had responded that they were, based on the fact that as s went up, t went down. But the question was not simply is there an inverse relationship, but are they inversely proportional.
The term proportional means that the relationship between s and t is a constant. That is:
t = s*(1/x)
Let's rewrite that to y*x = k and then check the numbers. See the attached spreadsheet. If the relationship were inversel proportioanl, thaen the product of t*s would be a contant for the series. The third set is different from the first two. The data has an is inverse relationship, but it is NOT proportional.
Help with this math problem theres no 550
Answer:
A. 450 trucks
Step-by-step explanation:
Given
Totally the parking lot can hold 1000 vehiclesOnly 2/5 of the spaces are for carsAnswer
A. 450 trucks
Saving Sally makes $15 an hour, h, and spends $125 on her bills each week. Which expressions show how much Sally will have after 10 weeks? Select all that apply.
15(10h - 125)
150h - 1875
10(15h - 125)
150h - 1250
-1250 + 150h
10(15h + 125)
Answer:
10(15h-125)
Step-by-step explanation:
In this question, h is represented for hours. we want to see how much money sally will have after 10 weeks. We know each hour she makes $15 per h. This will look like 15h. We also know her bills cost $125 each week so we have to subtract 125 from 15h which the equation will now look like
15h-125.
Now we want to know how much she will have after 10 weeks so we will now the equation will look like 10(15h-125).
Answer: Pls I don't know this
Step-by-step explanation:
Pls I don't mean to hurt your feelings but my brother knows this and I have sent it to him
Draw a rectangle that is 3 squares long and 1/2 of a square wide. Then add up the partial squares to find the area. Multiply to check your answer
According to the image, we can see that 3 rectangles are half-shaded= 1.5 units²,
A square is a quadrilateral with four equal sides and four equal angles that is a regular quadrilateral. The square's angles are at a straight angle or 90 degrees. The square's diagonals are also equal and split at a 90-degree angle.
A rectangle with two opposite sides that have the same length can also be referred to as a square.
P.S: Rectangle attached in image.
According to the image, we can see that 3 rectangles are half-shaded.
This means that:
Half-shaded square + Half-shaded square + Half-shaded square
=> 0.5 + 0.5 + 0.5
=> 1.5 units²
Check:
To check our answer:
3 x 0.5 = Area of rectangle
=> 1.5 units² = Area of rectangle
Hence, our explanation is correct.
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An element wIth mass 420 grams decays by 11.8% per minute. How much of the element is remainifg after 16 minutes, to the nearest 1oth of a gram?
Answer: To calculate the amount of the element remaining after 16 minutes, we can use the formula:
A = P * (1 - r)^t
where:
A = amount remaining after time t
P = initial amount
r = rate of decay per unit time (as a decimal)
t = time elapsed
In this case, we have:
P = 420 grams
r = 0.118 per minute
t = 16 minutes
Substituting these values into the formula, we get:
A = 420 * (1 - 0.118)^16
A ≈ 123.82 grams
Rounding this answer to the nearest tenth of a gram, we get:
A ≈ 123.8 grams
Therefore, approximately 123.8 grams of the element remain after 16 minutes.
A health survey was conducted at a company with 6,480 employees. Through "mild threats" they got 4860 to answer. One question asked was how often the respondent exercised in their free time. 1296 people stated that they exercised at least 3 times a week.
In order to better estimate the percentage of employees who exercised at least 3 times a week, a sample of the absentees was called. In this sample of 80 people, 7 stated that they exercised at least 3 times a week. Using this information, estimate the total percentage of the company that exercised at least 3 times a week by using the Hansen-Hurwitz dropout plan (method)
The estimated total percentage of the company that exercised at least 3 times a week is approximately 20.5%.
Using the Hansen-Hurwitz dropout plan (method), the estimated total percentage of the company that exercised at least 3 times a week is approximately 20.5%. This can be calculated by multiplying the response rate of the survey (4860/6480) by the response rate of the sample (7/80).
The response rate of the survey is 0.7479 and the response rate of the sample is 0.0875. To get the estimated total percentage of the company that exercised at least 3 times a week, you would multiply these two numbers together to get 0.205 (0.7479 x 0.0875 = 0.205).
So, the percentage is 20.5%.
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a man spent one-eighth of his spare change for a package of cigarettes, three times as much for a meal, and then had eighty cents left. how much money did he have at first?
The man had $1.60 at first.
What is an equation?
An equation is a statement that shows that two expressions are equal. It contains an equals sign "=" and may include variables, constants, coefficients, and mathematical operations such as addition, subtraction, multiplication, and division.
Let's assume the man had x amount of money at first.
Then he spent 1/8x on a package of cigarettes and 3 times as much, or 3/8x, on a meal.
So he spent a total of 1/8x + 3/8x = 1/2x of his money.
If he had 80 cents left, that means he spent x - 0.8.
So we can set up an equation:
1/2x = x - 0.8
Solving for x:
1/2x - x = -0.8
-1/2x = -0.8
x = (-0.8)/(-1/2)
x = 1.6
Therefore, the man had $1.60 at first.
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This is 1/6 problems finish them all each is 10 points 60 total.
The cosine of θ is the ratio of the length of the adjacent side to the length of the hypotenuse
What is the cosine of an angle?The cosine of an angle is a trigonometric function that relates the length of the adjacent side of a right triangle to the length of the hypotenuse. Specifically, it is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.
In mathematical terms, if we have a right triangle where one of the angles is labeled as theta (θ), then the cosine of theta is given by the formula:
cos(θ) = adjacent side / hypotenuse
1) Cos R =30/34 =15/17
Cos S = 16/34 = 8/17
2) Cos R = 24/26 = 12/13
Cos S = 10/26 = 5/13
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For each of the following gas-phase reactions, indicate how the rate of disappearance of each reactant is related to the rate of appearance of each product.
Part A
H2O2(g)→H2(g)+O2(g)
Express your answer as an integer.
−Δ[H2O2]Δt =
Δ[H2]Δt
SubmitMy AnswersGive Up
Part B
Express your answer as an integer.
−Δ[H2O2]Δt = Δ[O2]Δt
SubmitMy AnswersGive Up
Part C
2N2O(g)→2N2(g)+O2(g)
Express your answer as an integer.
−Δ[N2O]Δt = Δ[N2]Δt
SubmitMy AnswersGive Up
Part D
Express your answer as an integer.
−Δ[N2O]Δt = Δ[O2]Δt
SubmitMy AnswersGive Up
Part E
N2(g)+3H2(g)→2NH3(g)
Express your answer using one decimal place.
−Δ[N2]Δt = Δ[NH3]Δt
SubmitMy AnswersGive Up
Part F
Express your answer using one decimal place.
−Δ[H2]Δt = Δ[NH3]Δt
SubmitMy AnswersGive Up
Part G
C2H5NH2(g)→C2H4(g)+NH3(g)
Express your answer as an integer.
−Δ[C2H5NH2]Δt = Δ[C2H4]Δt
SubmitMy AnswersGive Up
Part H
Express your answer as an integer.
−Δ[C2H5NH2]Δt = Δ[NH3]Δt
Part A: −Δ[[tex]H2O2[/tex]]/Δt = Δ[[tex]H2[/tex]]/Δt + Δ[[tex]O2[/tex]]/Δt
Part B: −Δ[[tex]H2O2[/tex]]/Δt = Δ[[tex]O2[/tex]]/Δt
Part C: −Δ[[tex]N2O[/tex]]/Δt = 1/2 Δ[[tex]N2[/tex]]/Δt + Δ[[tex]O2[/tex]]/Δt
Part D: −Δ[[tex]N2O[/tex]]/Δt = Δ[[tex]O2[/tex]]/Δt
Part E: −Δ[[tex]N2[/tex]]/Δt = 1/2 Δ[[tex]NH3[/tex]]/Δt
Part F: −Δ[[tex]H2[/tex]]/Δt = Δ[[tex]NH3[/tex]]/Δt
Part G: −Δ[[tex]C2H5NH2[/tex]]/Δt = Δ[[tex]C2H4[/tex]]/Δt + Δ[[tex]NH3[/tex]]/Δt
Part H: −Δ[tex][C2H5NH2][/tex]/Δt = Δ[tex][NH3][/tex]/Δt
The rate of disappearance of [tex]H2O2[/tex]is equal to the sum of the rates of appearance of H2 and O2.
Part B: −Δ[[tex]H2O2[/tex]]/Δt = Δ[[tex]O2[/tex]]/Δt
The rate of disappearance of [tex]H2O2[/tex] is equal to the rate of appearance of O2.
Part C: −Δ[[tex]N2O[/tex]]/Δt = 1/2 Δ[[tex]N2[/tex]]/Δt + Δ[[tex]O2[/tex]]/Δt
The rate of disappearance of N2O is equal to half the rate of appearance of N2 plus the rate of appearance of O2.
Part D: −Δ[[tex]N2O[/tex]]/Δt = Δ[[tex]O2[/tex]]/Δt
The rate of disappearance of [tex]N2O[/tex] is equal to the rate of appearance of O2.
Part E: −Δ[[tex]N2[/tex]]/Δt = 1/2 Δ[[tex]NH3[/tex]]/Δt
The rate of disappearance of N2 is equal to half the rate of appearance of[tex]NH3.[/tex]
Part F: −Δ[[tex]H2[/tex]]/Δt = Δ[[tex]NH3[/tex]]/Δt
The rate of disappearance of H2 is equal to the rate of appearance of NH3.
Part G: −Δ[[tex]C2H5NH2[/tex]]/Δt = Δ[[tex]C2H4[/tex]]/Δt + Δ[[tex]NH3[/tex]]/Δt
The rate of disappearance of[tex]C2H5NH2[/tex] is equal to the sum of the rates of appearance of[tex]C2H4[/tex] and [tex]NH3.[/tex]
Part H: −Δ[tex][C2H5NH2][/tex]/Δt = Δ[tex][NH3][/tex]/Δt
The rate of disappearance of [tex]C2H5NH2[/tex] is equal to the rate of appearance of [tex]NH3.[/tex]
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A. What is your bi-weekly gross paycheck based on 40 hours a week at a rate of $18.25
per hour? Show your work.
Bi-weekly gross paycheck based on 40 hours a week at a rate of $18.25 per hour is $1,460.
What is multiplication ?
Multiplication is a basic arithmetic operation that involves combining two or more numbers to find their product or the total number of items when a certain number is repeated a certain number of times. In multiplication, the numbers being combined are called factors, and the result is called the product.
To calculate your bi-weekly gross paycheck, you need to multiply your hourly rate by the number of hours you work per week and then multiply that by 2 to account for two weeks in a pay period.
Hourly rate: $18.25
Weekly hours: 40
Bi-weekly hours: 40 x 2 = 80
Bi-weekly gross paycheck: Hourly rate x Bi-weekly hours
Bi-weekly gross paycheck: $18.25 x 80 = $1,460
Therefore, your bi-weekly gross paycheck based on 40 hours a week at a rate of $18.25 per hour is $1,460.
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Which graph is defined by the function given below?
y=(x-2)(x+5)
-10
10
A.
10
V
-10
OA. Graph A
OB. Graph B
OC. Graph C
OD. Graph D
-10-
B.
10
-10
10
-10
C.
10
-10
10
D.
10
3
Answer:
graph A is the correct graph.
The graph of the function is plotted by graph A
What is Equation of Graph of Polynomials?Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.
Identify the even and odd multiplicities of the polynomial functions' zeros.
Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.
The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = ( x - 2 ) ( x + 5 )
To find the x-intercepts (or zeros) of the function f(x) = (x - 2)(x + 5), we need to set the function equal to zero and solve for x.
f ( x ) = ( x - 2 ) ( x + 5 ) = 0
This product is zero if and only if one of the factors is zero. So we can set each factor equal to zero and solve for x.
x - 2 = 0 or x + 5 = 0
x = 2 or x = -5
Hence , the x-intercepts of the function are x = 2 and x = -5 and the graph is plotted
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A cylinder has the net shown.
net of a cylinder with diameter of each circle labeled 3.4 inches and a rectangle with a height labeled 3 inches
What is the surface area of the cylinder in terms of π?
13.09π in2
15.98π in2
20.4π in2
33.32π in2
The surface area of the cylinder in terms of π is 15.98π in².
What is surface area ?
Surface area is the measure of the total area that the surface of a three-dimensional object covers. In other words, it is the sum of the areas of all the faces or surfaces of the object. For example, the surface area of a rectangular prism is the sum of the areas of its six rectangular faces.
To find the surface area of the cylinder, we need to find the area of each of its faces and add them up.
The cylinder has two circular faces, each with a diameter of 3.4 inches. The formula for the area of a circle is A = πr², where r is the radius of the circle. The radius of each circle is half of the diameter, so r = 1.7 inches. Therefore, the area of one circular face is:
A1 = π(1.7 in)² = 9.05π in²
Since there are two circular faces, their total area is:
A1_total = 2 × A1 = 18.1π in²
The cylinder also has a rectangular face, which is the curved surface between the two circular faces. The height of this rectangle is given as 3 inches. The length of this rectangle is the same as the circumference of one of the circular faces, which is πd (where d is the diameter). Therefore, the length of the rectangle is:
L = πd = π(3.4 in) = 10.64 in
The area of the rectangular face is:
A2 = L × h = 10.64 in × 3 in = 31.92 in²
Therefore, the total surface area of the cylinder is:
A_total = A1_total + A2 = 18.1π in² + 31.92 in² = 49.02π in²
Rounding to two decimal places, we get:
A_total ≈ 15.98π in²
So the answer is: 15.98π in².
Therefore, the surface area of the cylinder in terms of π is 15.98π in².
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Answer: 15.98π in²
Step-by-step explanation:
did test and it is right
Please help will give brainliest
The solution to the system of equations is (3, -7).
How to find the solution of equation of lines?To find the solution of these two equations, we need to find the values of x and y that satisfy both equations simultaneously.
We can set the two equations equal to each other to get:
-5x + 8 = x/3 - 8
Multiplying both sides by 3, we get:
-15x + 24 = x - 24
Simplifying, we get:
-16x = -48
Dividing both sides by -16, we get:
x = 3
Now that we know x = 3, we can substitute it into either of the original equations to find y. Let's use the equation y = -5x + 8:
y = -5(3) + 8 = -7
Therefore, the solution to the system of equations is (3, -7).
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The 15 overseas investors own 16/25 of the business Rewrite the fraction in the sentence below as a percentage.
Answer:
64 %
Step-by-step explanation:
To change a fraction to a percent, we need the denominator as 100.
16 4
---- * -----
25 4
64
-----
100
Percent means out of 100, so the percent is 64 %
The original price of a chair was $450.00. The tax on the chair was 5.5%. What is the exact price of the chair including tax?
The exact price of the chair including tax is $425.25. The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
The four fundamental operations, also referred to as "arithmetic operations," are said to be able to explain all real numbers. The four mathematical operations following division, multiplication, addition, and subtraction are quotient, product, sum, and difference.
We are given that the original price of a chair was $450.00 and on it, there was tax of 5.5%.
So, using the arithmetic operations, we get
⇒Exact price = 450 - 5.5% of 450
⇒Exact price = 450 - 24.75
⇒Exact price = $425.25
Hence, the exact price of the chair including tax is $425.25.
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Find the distance between points A (2, 4) and B (-4, 0).
distance A B =
Answer:
7.21 units-------------------------
Use the distance formula to find the distance between two points.
[tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]Substitute coordinates and find the length of AB:
[tex]AB=\sqrt{(0-4)^2+(-4-2)^2}=\sqrt{16+36}=\sqrt{52} =7.21[/tex]Question :-
Find the distance between points A(2, 4) and B(-4, 0).Answer :-
The distance between the two points is 7.21 units.[tex] \rule{200pt}{3pt}[/tex]
Solution :-
As per the provided information in the given question, we have been given that :-
[tex](x_1, y_1) = (2, 4)[/tex][tex](x_2, y_2) = (-4, 0)[/tex]To calculate the distance between the two points, we will apply the formula below :-
[tex] \bigstar \: \: \: \boxed{ \sf{ \: \: AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \: \: }}[/tex]
Substitute the given values into the above formula and solve for AB :-
[tex]\sf:\implies{ AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}}[/tex]
[tex]\sf:\implies{AB = \sqrt{( - 4 - 2)^2 + (0 - 4)^2}}[/tex]
[tex]\sf:\implies{AB = \sqrt{(-6)^2 + (-4)^2}}[/tex]
[tex]\sf:\implies{AB = \sqrt{36 + 16}}[/tex]
[tex]\sf:\implies\bold{AB = \sqrt{52} \approx 7.21 \: units}[/tex]
Therefore :-
The distance between the two points is 7.21 units.[tex]\\[/tex]
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Find the
coordinates of the points on the graph of
ƒ(x) = ½ x³ − ¹⁄2x² − 8x + 7 where the gradient is 4.
Answer:
(-8/3, 19/27) and (3, -17/2).
Step-by-step explanation:
To find the coordinates of the points on the graph of ƒ(x) = ½x³ − ¹⁄₂x² − 8x + 7 where the gradient is 4, we need to find the points where the derivative of ƒ(x) is equal to 4.
First, we need to find the derivative of ƒ(x):
ƒ'(x) = 3/2x² - x - 8
Next, we need to set ƒ'(x) = 4 and solve for x:
3/2x² - x - 8 = 4
3/2x² - x - 12 = 0
Multiplying both sides by 2 to eliminate the fraction:
3x² - 2x - 24 = 0
Factoring the quadratic equation:
(3x + 8)(x - 3) = 0
So x = -8/3 or x = 3.
Now we can find the corresponding y-coordinates:
When x = -8/3:
ƒ(-8/3) = 1/2(-8/3)³ - 1/2(-8/3)² - 8(-8/3) + 7 = 19/27
So one point on the graph with gradient 4 is (-8/3, 19/27).
When x = 3:
ƒ(3) = 1/2(3)³ - 1/2(3)² - 8(3) + 7 = -17/2
So another point on the graph with gradient 4 is (3, -17/2).
Therefore, the coordinates of the points on the graph of ƒ(x) = ½x³ − ¹⁄₂x² − 8x + 7 where the gradient is 4 are (-8/3, 19/27) and (3, -17/2).
NO EXPLANATION JUST ANSWER!
Answer: 364 cm^3
Step-by-step explanation: Please mark brainliest and give thanks!
Answer:
[tex]364cm^3[/tex]
Hope this helps!
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Area of quadrant of a circle with side 8cm and base 6cm
Answer:
A = (1/4)πr^2
where r is the radius of the circle.
If the side and base mentioned in the question refer to the radius of the circle, then the area of the quadrant can be calculated as follows:
Given, radius (r) = 8 cm
The area of the quadrant = (1/4)πr^2
= (1/4)π(8)^2
= 16π square cm
= 50.27 square cm
Turner needs to buy a bathroom mirror that is 4 feet wide and 5 feet long. If the mirror sells for $0.49 per square foot, what will the total cost of the mirror be?
The total cost of the mirror based on its area is obtained as $9.80.
What is area?
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.
The area of the bathroom mirror can be found by multiplying its length and width -
Area = Length × Width
Area = 5 feet × 4 feet
Area = 20 square feet
Since the mirror sells for $0.49 per square foot, we can find the total cost of the mirror by multiplying the area of the mirror by the cost per square foot -
Total Cost = Area × Cost per square foot
Total Cost = 20 square feet × $0.49 per square foot
Total Cost = $9.80
Therefore, the total cost of the bathroom mirror will be $9.80.
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How much would you have to deposit now to be able to withdraw $650 at the end year for 20 years from an account that earns 11% compounded annually?
Please solve this step by step
Answer:
information provided:
ordinary annuity = $650
Number of periods (n) = 20 years
Interest rate (r)= 11 percent
3/2 = 5d - 1/2 (two step equations with fractions)
Answer:
d = [tex]\frac{2}{5}[/tex]
Step-by-step explanation:
[tex]\frac{3}{2}[/tex] = 5d - [tex]\frac{1}{2}[/tex]
multiply through by 2 to clear the fractions
3 = 10d - 1 ( add 1 to both sides )
4 = 10d ( divide both sides by 10 )
[tex]\frac{4}{10}[/tex] = d , then
d = [tex]\frac{2}{5}[/tex]
6m^2-5my-y^2/12m+2y
Simplify the following rations expression and express in expanded form
The simplified expression, expressed in expanded form, is (3m - y)/(12m + 2y).
To simplify the expression (6m² - 5my - y²)/(12m + 2y), we can factor the numerator and denominator, if possible, and then simplify the expression by canceling out common factors.
The numerator can be factored as follows:
6m² - 5my - y² = (3m - y)(2m + y)
The denominator can also be factored by factoring out a common factor of 2:
12m + 2y = 2(6m + y)
Now we can substitute these factorizations back into the original expression:
(6m² - 5my - y²)/(12m + 2y) = [(3m - y)(2m + y)]/[2(6m + y)]
We can now cancel out the common factor of (2m + y) in the numerator and denominator:
[(3m - y)(2m + y)]/[2(6m + y)] = (3m - y)/(2(6m + y))
Expanding this expression, we get:
(3m - y)/(2(6m + y)) = (3m - y)/(12m + 2y)
Therefore, the simplified expression, in expanded form, can be written as (3m - y)/(12m + 2y).
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