Answer:
to find the value of x
x=(8x28)÷4
Answer: x=56
x/y 28/4=x/8
reduce 28/4 to 7/1
7/1 = x/8
cross multiply
x=56
Step-by-step explanation:
Write 18,25% as a common fraction in its simplest form.
Step-by-step explanation:
1825%
and percentage means 100
so 1825/100=73/4
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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In a bag of 60 candies, 36 are green and 45 have caramel in them. If the events of
picking a green candy and picking a candy with caramel are independent, what
percent of the green candies have caramel in them?
Answer:
9/20
Step-by-step explanation:
Total number of candies =60
Number of Green candies, n(G)=36
Number of candies with caramel, n(C)=45
Since the events are independent, the probability of selecting two candies where the first is green and the second has caramel is given by:
P(GC)=P(G) X P(C)
\begin{gathered}=\dfrac{n(G)}{n(S)} X \dfrac{n(C)}{n(S)} \\=\dfrac{36}{60} X \dfrac{45}{60}\\ =\dfrac{9}{20}\end{gathered}=n(S)n(G)Xn(S)n(C)=6036X6045=209
The probability in its lowest form is 9/20.
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)
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
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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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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Which of the following is the graph of the inequality y-2>-2(x-1)?
A
B
C
(2.1)
(0, -3)
ACE
AD
(2.1)
(4,-1)
UN
(1.2)
(3,-2)
14TH
D
(1.2)
(3,-2)
The graph is shown in the attached image.
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.
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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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 = $360,000
The quick ratio would therefore be:
= ( New Current assets - New inventory) / New current liabilities
= ( (1,260,000 + 360,000) - (285,000 + 360,000) ) / (450,000 + 360,000)
= 1.204
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A cabbage is worth 55 points, an apple is worth 40 points, a potato is worth 45 points and a pumpkin is worth 60 points. How many points is a cauliflower worth?
if you borrow 200$ 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)
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
Of the
50
5050 U.S. states,
4
44 have names that start with the letter
W
Wstart text, W, end text.
What percentage of U.S. states have names that start with the letter
W
Wstart text, W, end text?
The 8% of us states have names that start with the letter w the answer is 8%.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
The complete question is:
Of the 50 us states 4 have names that start with the letter w what percentage of us states have names that start with the letter w.
The percentage of the US states that have names that start with the letter W can be calculated:
Percentage = (No of US states starting with W/Total no of US states)×100
Percentage = (4/50)×100
Percentage = 8%
Thus, the 8% of us states have names that start with the letter w the answer is 8%.
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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]
Find M∠BFE.
A. 116
B. 58
C. 148
D. 164
Answer:
C
Step-by-step explanation:
57+57+34=148
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) ✔✔
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
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.
Can anyone help me solve this question?
Answer:
corresponding angles
Step-by-step explanation:
i dont cap
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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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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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!
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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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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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:
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]
In the parallelogram above what is the value of x?Please explain for brainlest
E.36
F.18
G.6
H.5
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.