Answer:
the numbers are 3, 5, 4
Step-by-step explanation:
The given relations can be written as a system of equations. These are conveniently solved using elimination.
SetupLet the three numbers be represented by x, y, z. The given relations are ...
x +y +z = 12
x -y +z = 2
x +y -z = 4
SolutionSubtracting the second equation from the first gives ...
(x +y +z) -(x -y +z) = (12) -(2)
2y = 10 . . . . . . . . . simplify
y = 5 . . . . . . . . divide by 2
Subtracting the third equation from the first gives ...
(x +y +z) -(x +y -z) = (12) -(4)
2z = 8 . . . . . . . . . simplify
z = 4 . . . . . . . . divide by 2
Using these values of y and z in the first equation lets us find x:
x +5 +4 = 12
x = 3 . . . . . . . . . subtract 9
The numbers, in order, are (3, 5, 4).
The region under the curve with equation y = 1/(2x-1) is rotated through four right angles about the x-axis to form a solid. Find the volume of the solid between x=3 and x = 8.
Using the disk method, the volume of the solid is
[tex]\displaystyle \pi \int_3^8 \left(\dfrac1{2x-1}\right)^2 \, dx = \pi \int_3^8 \frac{dx}{(2x-1)^2}[/tex]
Substitute [tex]u = 2x-1[/tex] and [tex]du=2\,dx[/tex].
[tex]\displaystyle \pi \int_3^8 \frac{dx}{(2x-1)^2} = \frac\pi2 \int_5^{15} \frac{du}{u^2} \\\\ ~~~~~~~~ = -\frac\pi2 \frac1u \bigg|_5^{15} \\\\ ~~~~~~~~ = -\frac\pi2 \left(\frac1{15} - \frac15\right) = \boxed{\frac\pi{15}}[/tex]
A highway patrol officer is seated on a motorcycle on a curvy section of Highway 1. The posted speed limit is 45 miles per hour on this stretch of highway. The officer is monitoring traffic using radar. The next exit is 3.6 miles up the road. The radar picks up a speeding car averaging 68 mph. When the officer tries to start his motorcycle to follow the car, it won’t start. He tries again and again, and soon he fears that he won’t be able to catch the speeding car before it turns off the highway. Finally, his motorcycle starts and he begins the pursuit 30 seconds after the speeding car has passed him on the roadside.
How fast does the officer need to go to catch up to the speeding car? What is his average speed in pursuit?
Answer:
80.7 mph
Step-by-step explanation:
In order to catch the car at the exit, the officer must cover the distance in 30 seconds less time than the car does. The time, speed, distance relation can be used.
Time for car to reach the exitThe relation between time, speed, and distance is ...
time = distance/speed
Here, speed is in miles per hour, and distance is in miles. That means time will be given in hours by the straightforward application of this formula.
time = (3.6 mi)/(68 mi/h) = (3.6/68) h = 9/170 h
Time for the motorcycle to reach the exitThere are 3600 seconds in 1 hour, so 30 seconds represents this fraction of 1 hour:
30/3600 = 1/120
The motorcycle will have this amount of time less than the time the car takes to reach the exit, so ...
(9/170 -1/120) h = (9(120)-170)/(170×120) h = 910/20400 h = 91/2040 h
Motorcycle speedThe speed required to cover 3.6 miles in 91/2040 hours is ...
speed = distance/time
(3.6 mi)/(91/2040 h) = 3.6×2040/91 mph = 7344/91 mph ≈ 80.7 mph
The officer's average speed in pursuit must be 80.7 miles per hour (or faster).
__
Additional comment
There are other ways the problem can be worked. One of them is to consider the remaining distance the car must travel when the officer begins pursuit. That will be 3.6 mi less (1/120 h)(68 mi/h) = 17/30 miles. The ratio of the officer's speed to the car's speed will be the same as the ratio of the officer's miles to the car's miles: 3.6/(3.6 -17/30) × 68 mph ≈ 80.7 mph.
Intermediate values used in the calculations should be kept at full calculator precision. Rounding should only be done at the end. Here, the actual speed required is 80.7032967... mph, rounded down for the above result.
Simplify: (−12az2−2z3)+(−2a3+7a2z)−(−4a2z+8az2)
Answer:
[tex] \large{ \boxed{ \tt{ - 20a {z}^{2} - 2 {z}^{3} - 2 {a}^{3} + 11 {a}^{2} z }}}[/tex]
- Please see the attached picture for full solution!:)
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Find M∠BFE.
A. 116
B. 58
C. 148
D. 164
Answer:
C
Step-by-step explanation:
57+57+34=148
Find a real number c such that the line cx-5y+8=0 has x-intercept 4
Using the x-intercept concept, the function has x-intercept of 4 when c = -2.
What are the x-intercepts of a function?The x-intercepts of a function are the values of x when y = 0.
In this problem, the function is:
cx - 5y + 8 = 0.
When y = 0, we have that:
cx + 8 = 0
x = 4, hence:
4c = -8
c = -2.
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32 randomly picked people were asked if they rented or owned their own home, 8 said they rented. Obtain a point estimate of the proportion of home owners.
Group of answer choices
0.250
0.600
0.750
0.200
0.500
Answer:
.750
Step-by-step explanation:
triangle ABC is isosceles, angle B is vertex angle , AB = 20x -2, AC =25x, and BC =12 x +20. Find x and the length of each side of the triangle?
Length of AB = 18. 92
Length of AC = 26. 15
Length of BC = 32. 552
How to determine the sides of the triangleUsing the Pythagorean theorem, we have that
[tex](20 x-2)^2 = (12x + 20)^2 + (25x)^2[/tex]
Expand the bracket
[tex]400x^2- 4 = 144x^2 + 400 + 625x^2[/tex]
Collect like terms
[tex]400x^2 - 144x^2 - 625x^2 = 400 + 4[/tex]
[tex]-369x^2 = 404[/tex]
Make x^2 subject
[tex]x^2 = \frac{404}{369}[/tex]
[tex]x = \sqrt{1.0948}[/tex]
[tex]x = 1. 046[/tex]
Thus,
Length of AB = 20x -2 = 20(1. 046) - 2 = 18. 92
Length of AC = 25x = 25* 1.046 = 26. 15
Length of BC = 12x + 20 = 12(1. 046) + 20 = 32. 552
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Find the interval in which the function is positive. f(x) = x2 - 7x + 10 I. (-, 2) II. (2, 5) III. (5,)
Step-by-step explanation:
f(x) = x2-7x+10
f(x) = -5x+10 = -5(x-2)
= 10-5x
Let, f(x) = 0
0 = 10-5x
5x = 10
x = 2
f(2) = 10 - 10 = 0
f(5) = 10-5(5) = 10-25 = -15
Let, f(y) = f(x)
= 10-5x
y = -0
So, the correct answer is I. (- , 2) ✔✔
I need help setting up my problem
The measure of angle A is 144.3 degrees and the angle to cut the molding is 54.3 degrees
How to solve for angle A?Start by solving the acute part of angle A using the following sine function
sin(Ax) = (30 - 4)/32
Evaluate the quotient
sin(Ax) = 0.8125
Take the arc sin of both sides
Ax = 54.3
The measure of angle A is then calculated as:
A = 90 + Ax
This gives
A = 90 + 54.3
Evaluate
A = 144.3
Hence, the measure of angle A is 144.3 degrees
The angle to cut the moldingIn (a), we have:
Ax = 54.3
This represents the angle where the molding would be cut
Hence, the angle to cut the molding is 54.3 degrees
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if you borrow 200$ for 12 years at an annual interest rate of 2%,how much will you pay altogether!!!!!!HURRY
Answer:
248.00
Step-by-step explanation:
A = P(1 + rt)
A = the future value
P = the initial principal
r = annual interest rate (decimal)
t = the time in years
A=200(1+0.2*12)
Juan got 4 questions incorrect out of the 80 questions on his exam. Express the number of questions that he got correct as a fraction of the total number of questions on the exam, and reduce the fraction to the lowest terms
Answer:
19/20
Step-by-step explanation:
He got 4 incorrect, meaning he got 80-4 correct.
80-4 = 76.
Fraction = 76/80 = 38/40 = 19/20.
Answer:
19/20
Step-by-step explanation:
[tex]\frac{80-4}{80} =\frac{76}{80} =\frac{19}{20}[/tex]
Hope this helps
The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is twice the measure of the first angle. The third angle is fourteen more than the second. Find the measures (in degrees) of the three angles.
A parallelogram has sides measuring 200mm by 150mm. what would be the length of side of a square having the same perimeter?
Answer:
175mmStep-by-step explanation:
To find the total perimeter of the parallelogram we must add 200+200+150+150
This equals 700. Then, since squares have side lengths that are all equal, we have to divide by 4.
700 / 4 = 175
So, the length of a side of a square having this perimeter would be 175mm
Hope this helps!
f(x) = -3x³ + x² - 3, find f(1).
Answer:
Step-by-step explanation:
hello :
f(x) = -3x³ + x² - 3, find f(1).
f(1) = -3(1)³ +(1)² - 3=-3+1+3 = -5
A cabbage is worth 55 points, an apple is worth 40 points, a potato is worth 45 points and a pumpkin is worth 60 points. How many points is a cauliflower worth?
Which expression is
equivalent to the following complex fraction?
Answer:
(y - x)/(y + x)
Step-by-step explanation:
(1/x - 1/y)/(1/x + 1/y) =
= (1/x - 1/y)/(1/x + 1/y) × (xy)/(xy)
= (y - x)/(y + x)
Given f(x) = 4x + 2, find f-1(3).
Answer:
1/4
Step-by-step explanation:
The inverse function tells you the input value that corresponds to the given output value of the function.
ApplicationYou want f^-1(3), which is the value of x such that f(x) = 3.
f(x) = 3 = 4x +2
1 = 4x . . . . . . subtract 2
1/4 = x . . . . . divide by 4
The inverse function of 3 is 1/4:
[tex]\boxed{f^{-1}(3)=\dfrac{1}{4}}[/tex]
Betty wants to put new cabinets in her kitchen. She measures one side of her kitchen and finds it measures 181818 meters.
Which measurement did Betty find?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Area
(Choice B)
B
Perimeter
(Choice C)
C
Length
Answer:
lenght
Step-by-step explanation:
I think it is that because it says ONE SIDE and for area and perimeter of a square/ rectangle you need more than one side
hope it helps
What will be the firm's quick ratio after Nelson has raised the maximum amount of short-term funds? Do not round intermediate calculations. Round your answer to two decimal places.
Based on the short-term debt that Nelson raises, the firm's quick ratio will be 1.204.
What is the firm's quick ratio?First, find the maximum amount of short-term funds that Nelson can raise?
Assuming this amount is x, we can find it with the current ratio formula:
Current ratio = Current assets / Current liabilities
2 = (1,260,000 + x) / ( 450,000 + x)
x = $360,000
The quick ratio would therefore be:
= ( New Current assets - New inventory) / New current liabilities
= ( (1,260,000 + 360,000) - (285,000 + 360,000) ) / (450,000 + 360,000)
= 1.204
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2.1 If 5 + 3 = 0 and < 0, evaluate (without using a calculator):
2.1.1 22 − 1 (4)
2.1.2 2 + 2 (3)
2.1.3 1 − 2
1. 18
2.8
3.-1
What is expression?An expression is a set of terms combined using the operations +, – , x or ,/.
Given:
1. 22 − 1 (4)
=22- 1*4
= 22-4
= 18
2. 2 + 2 (3)
=2+2*3
=2+6
=8
3. 1 − 2
= -1
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A person invested $7700 for 1 year, part at 8%, part at 9%, and the remainder at 12%. The total annual income from these investments was $811. The amount of money invested at 12% was $1100 more than the amounts invested at 8% and 9% combined. Find the amount invested at each rate.
The amount invested at 8% was $1400, $1900 was invested at 9% and $4400 was invested at 12% making a total annual income of $811.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the amount of money invested at 8%, y represent the amount of money invested at 9% and z represent the amount of money invested at 12%
x + y + z = 7700 (1)
Total interest is:
(x * 1 * 0.08) + (y * 1 * 0.09) + (z * 1 * 0.12) = total interest
0.08x + 0.09y + 0.12z = 811 (
Also:
z = 1100 + x + y (3)
From equation 1, 2 and 3:
x = 1400, y = 1900 and z = 4400
T
The amount invested at 8% was $1400, $1900 was invested at 9% and $4400 was invested at 12% making a total annual income of $811.
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Can anyone help me solve this question?
Answer:
corresponding angles
Step-by-step explanation:
i dont cap
Complete the following, using ordinary interest. (Use Days in a year table.) (Do not round intermediate calculations. Round the "Interest" and "Maturity value" to the nearest cent.)
Principal: 1,000
Interest rate: 8%
Date borrowed: March 8
Date repaid: June 9
Exact time:
Interest:
Maturity value:
Answer:
75
Step-by-step explanation:
An artist sells her sculptures for $250. Each piece costs her $150 to make, and she spends $11000 per year for her studio and other fixed costs. How many sculptures must she sell if she wants to make $10000 in profit
l don't know if you know it tell please
Expand. Your answer should be a polynomial in standard form. -p^2(p^2-p-1) =
Answer:
[tex]\huge\boxed{\sf -p^4+p^3+1}[/tex]
Step-by-step explanation:
Given expression:[tex]=-p^2(p^2-p-1)\\\\Distribute \\\\= -p^4+p^3+1\\\\\rule[225]{225}{2}[/tex]
If you know this please help
1) given
2) given
3) Definition of linear pair
4) If alternate interior angles are congruent, then the lines are parallel.
For a certain company, the cost for producing x items is 50x+300 and the revenue for selling x items is 90x−0.5x^2 .
Part a: Set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratic polynomial.)
Part b: Find two values of x that will create a profit of $300 .
Part c: Is it possible for the company to make a profit of $15,000 ?
a. The expression for profit is p(x) = -0.5x² + 40x - 300
b. The two values of x that will create a profit of $300 is 20 and 60
c. it is not possible for the company to make a profit of $15,000
What is profit?The profit is the selling price minus the cost price.
Therefore,
Profit = revenue - cost
a.
The expression for profit is as follows;
p(x) = 90x − 0.5x² - (50x + 300)
p(x) = 90x − 0.5x² - 50x - 300
p(x) = -0.5x² + 40x - 300
b.
The two values of x that will create a profit of $300 is as follows;
-0.5x² + 40x - 300 = 300
-0.5x² + 40x - 600 = 0
0.5x² - 40x + 600 = 0
x² - 80x + 1200 = 0
(x - 20)(x - 60) = 0
x = 20 and 60
Therefore, the two value of x are 20 and 60
c.
-0.5x² + 40x - 300 = 15000
-0.5x² + 40x - 300 - 15000 = 0
-0.5x² + 40x - 15300 = 0
x² - 80x + 30600 = 0
There is no real solution. Therefore, it is not possible for the company to make a profit of $15,000
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Below are the weekly salaries, in dollars, of nine recent college graduates. Utilize the data to calculate the midrange.
833 692 1057 955 749 1113 857 946 907
The midrange of the weekly salaries is $902.50.
What is the midrange?Midrange is a measure of variation of a data set. Midrange is the mean of the lowest and highest salary.
Midrange + (lowest salary + highest salary) / 2
(692 + 1113) / 2 = $902.50
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PLS ANSWER THESE TWO QUESTIONS
EXPLANATION IS NOT NEEDED
MAKE SURE IT IS CORRECT
The answers to the following word problems are given below:
(C). [tex]1\frac{1}{2}[/tex](C). 0Meaning of word problemA Word problem can be defined as a mathematical problem that is given in a sentence format.
A word problem needs the student to decipher it and then translate it to a normal arithmetic problem.
In conclusion, The answers to the word problems are given
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Interpret, in a written description, what the graph is saying about the relationship between the variables. A graph has time (hours) on the x-axis, and distance (miles) on the y-axis. A line increases to 2 hours, is constant through 3 hours, and then increases through 6 hours. a. You leave home and drive for 6 hours with no stops. b. You leave home, drive for 1 hours at a constant speed, stop for 30 minutes, continue at the same speed, stop for 1 hour and then continue at the same speed as before. c. You leave home, drive for 2 hours at a constant speed, and then stop for 1 hour. Finally you continue at a slower (but constant) speed than before. d. You leave home, drive for 3 hours at a constant speed, and then stop for 2 hours. Finally you continue at the same speed as before. Please select the best answer from the choices provided
An interpretation of the relationship between the variables in this graph is that: C. you leave home, drive for 2 hours at a constant speed, and then stop for 1 hour. Finally, you continue at a slower (but constant) speed than before.
What is a graph?A graph can be defined as a type of chart which is used to graphically represent the relationship between the variables in a data set, on both the horizontal and vertical lines of a cartesian coordinate i.e x-axis and y-axis.
By critically observing the graph attached in the image below, we can infer and logically deduce that an interpretation of the relationship between the variables in this graph is that you drove at a constant speed for 2 hours, and then stopped for 1 hour. Finally, you continued at a slower, but constant speed than before.
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