Answer:
1. After multiplying both sides by x you need to subtract 1 from both sides
2. You can assume x ≠ 0 because both sides are undefined if x = 0.
Step-by-step explanation:
Given
[tex]\frac{1}{x} + 3 = \frac{3}{x}[/tex]
Required
Which of the options shows the validity of Beth's action
The first option answers the question and the reason is as follows;
Multiply both sides by x
[tex]x * (\frac{1}{x} + 3) = \frac{3}{x} * x[/tex]
Open the bracket
[tex]1 + 3x = 3[/tex]
As stated in option 1; Subtract 1 from both sides
[tex]1 - 1 + 3x = 3 - 1[/tex]
[tex]3x = 2[/tex]
Divide both sides by 2
[tex]x = \frac{2}{3}[/tex]
Another correct option is the option 2
Because the expression is undefined if x = 0
See Proof by substituting 0 for x
[tex]\frac{1}{0} + 3 = \frac{3}{0}[/tex]
Division by 0 is undefined.
Hence, option 2 is also correct
The other options (3 and 4) are incorrect
A refrigerator sells for $1201. If the sales tax rate is 6.8%, what is the total price that you would pay for the fridge?
The answer is $1282.66
Explanation:
The sales tax rate (in this case 6.8%) is paid as part of selling a product. Also, to find the final price of a product, find the tax rate (percentage) of the price of the product and add this number to the price. The process to know the final price of the fridge is shown below:
1. Determine the 6.8% of $1201
1.1. Write the values
1201 = 100
x = 6.8
1.2. Cross multiply and solve the equation
x100 = 8166
x= 8166 ÷ 100
x = 81.66
2. Add this value to the original price
$1201 + $ 81.66 = $1282.66 (Total price including the sales tax)
Identify the pair of angles shown in the figure. Linear pair Vertical Supplementary Complementary
Answer:
Complementary angles
Step-by-step explanation:
The sum of the 2 angles = 27° + 63° = 90°
This is the definition of Complementary angles
[tex]0.05x^{2}[/tex]how do i evaluate 0.05
Try to make 0.90 cents using exactly 11 coins. What are the coins?
Answer:
3 quartars 2 nickles 4 pennnies 2 half-pennies
Step-by-step explanation:
Add 15,7,.5 step by step please I'll mark u brainlest PLEASE
Answer:
27
Step-by-step explanation:
15+5=20
20+7=27
Answer: 27
Step-by-step explanation:
15+5=20
20+7=27
Plz help would the answer be -30
Answer:
Yes
Step-by-step explanation:
-27+(-3) can be simplified to -27-3
-27-3= -30
Answer: Yes you are correct. The answer is -30
Explanation:
We are adding 2 negatives. So we effectively add the positive versions of each number, and then make the result negative.
You can think of it in terms of money: you start off 27 dollars in debt and then borrow 3 more dollars to be a total of 27+3 = 30 dollars in debt.
Or you can think of it like you're under the ocean. Writing -27 could mean you're 27 feet below sea level. Adding on -3, ie subtracting 3, would then move you down 3 feet to get to 27+3 = 30 feet below sea level.
simplify the expression
Answer:
[tex]\sqrt[3]{215}[/tex]
Decimal Form: 5.99072641
Look down for explanation
Step-by-step explanation:
[tex]\sqrt[3]{215}[/tex]
You have to simplify.
[tex]= \sqrt[3]{215}[/tex].
Decimal Form: 5.99072641
Now you have the answer to your question!
Hope this helps!
In each problem 7 through 14, verify that each given function is a solution of the differential equation. Y" - y = 0; y1(t) = et, y2(t) = cosh t.
Answer:
Since L.H.S = R.H.S = 0, for both [tex]y_{1} (t) = e^{t}[/tex] and [tex]y_{2} (t) = cosh(t)[/tex], y₁ and y₂ both satisfy the equation y" - y = 0 and are thus solutions to the differential equation.
Step-by-step explanation:
To check whether the given functions are solutions the given differential equation, we differentiate the functions and then insert it into the given equation.
So y" - y = 0 and
[tex]y_{1} (t) = e^{t}\\y_{1}' (t) = e^{t}\\ y_{1}" (t) = e^{t}[/tex]
Substituting these values of y and y" into the left hand side of the equation, we have
y" - y
[tex]y_{1}" (t) - y_{1} (t) = e^{t} - e^{t} = 0[/tex]
Since L.H.S = R.H.S
So [tex]y_{1} (t) = e^{t}[/tex] is a solution of the differential equation.
When
[tex]y_{2} (t) = cosh(t)\\ y_{2}'(t) = sinh(t) \\y_{2}"(t) = cosh(t)[/tex]
Substituting y and y" into the left hand side of the equation, we have
y" - y
[tex]y_{2}"(t) - y_{2} (t) = cosh(t) - cosh(t) = 0[/tex]
Since L.H.S = R.H.S
So, [tex]y_{2} (t) = cosh(t)[/tex] is a solution of the differential equation.
what is the constant of the polynomial 2x3 - 8x2 + 3x - 7
Answer:
-7
Step-by-step explanation:
A constant number is a number that contains no variables like x and y. The only constant in that problem is -7.
A constant is a number which independent of anything and never changes thus the constant in the given expression 2x³ - 8x² + 3x - 7 is -7.
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
An expression is a mathematical proof of the equality of two mathematical expressions.
As per the given expression,
2x³ - 8x² + 3x - 7
Here, x is a variable.
The constant multiplied by a variable is said to be the coefficient.
Thus, 2,-8,3 are the coefficient.
A number independent constant is -7 will be constant.
Hence "A constant is a number which is independent of anything and never changes thus the constant in the given expression 2x³ - 8x² + 3x - 7 is -7."
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A scientist creates a colony of bacteria in a dish. This type of
bacteria duplicates itself per minute.
If at 9am the experiment started with a single cell and at 9:13
the dish was half-full, at what time will the dish be full?
Answer: 9:14
Step-by-step explanation: So if he started if 1 bacteria, it becomes 2 bacteria at 9:01, etc. So at 9:13, it is 2^13 and if that is half, that means 2^14 is when it is full so 9:14.
The dish will be full at 9:14 am.
Given, the bacteria duplicates itself per minute.
The experiment started with a single cell at 9 am and at 9:13 am the dish was half full.
So it is clear that after 13 minutes of experiment started the dish was half full.
Now, let here is only 1 bacteria in the dish which is duplicating per minute,so after 1 minute it becomes 2 after that it becomes 4 and after that it becomes 8. Hence it is clear from the example the bacteria doubles itself in powers of her minute. ([tex]2^x[/tex]) here x is the number of minute.
Since after 13 minutes the dish was half full, it means there are [tex]2^{13}[/tex] bacteria in the dish. hence the full dish is [tex]2^{14}[/tex] bacteria. so the bacteria will take 1 more minute for the dish to be full.
Hence at 9:14 am the dish was full.
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Identify the property of equality that makes Equation 1 and Equation 2 equivalent.
Equation 1
4.2x – 1.5 = 1.7x + 8.3
Equation 2
42x - 15 = 17x + 83
We use the multiplicative property of equality to make Equation 1 and Equation 2 equivalent.
Given,
Equation 1 - 4.2x – 1.5 = 1.7x + 8.3
Equation 2 - 42x - 15 = 17x + 83
We have to Identify the property of equality that makes Equation 1 and Equation 2 equivalent.
We have,
Equation 1 - 4.2x – 1.5 = 1.7x + 8.3
Equation 2 - 42x - 15 = 17x + 83
If we multiply 10 on both sides of the equation, we get
10 (4.2x – 1.5) = 10 (1.7x + 8.3)
10 x 4.2x - 10 x 1.5 = 10 x 1.7x + 10 x 8.3
42x - 15 = 17x + 8.3
We get,
42x - 15 = 17x + 8.3 which is equivalent to equation 2.
This property is called the multiplicative property of equality.
Thus we use the multiplicative property of equality to make Equation 1 and Equation 2 equivalent.
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The graph shows the speed of a ball in free fall for 10 seconds. Which is the constant of proportionality shown in the graph? It's on TTM.
Answer:A
Step-by-step explanation:
2x² - (5 + 2x) + 6x²
Answer: 8x^2-2x-5
Step-by-step explanation:
What number divided by 9 is greater than 700?
Answer:
Any number greater than 6,300
Step-by-step explanation:
[easy points] what is the verbal expression to this equation
Answer:
b
Step-by-step explanation:
BECAUSE x-25 = 3
shows something mines 25 that equals 3
People drive, on average, 11,979 miles per year. About how many miles each week is that?
(Type a whole number or decimal rounded to the nearest tenth as needed)
Answer:
230.4
Step-by-step explanation:
11,979 divided by 52 is 230.365384615.
230.365384615 Rounded gets the answer
Please help me with my homework :(
13. -5/6
14. -7/8
15 -7/10
Step-by-step explanation:
you are playing an online game with your friend and they are on level four. You are on level 6 and can beat, on average, four levels per hour. if your friend can beat five levels per hour, how many hours will it take for you and your friend to be on the same level?
Answer:
2 hours
Step-by-step explanation:
at one hour, you would be on lvl 10 and he would be on lvl 9, at 2 hour you would be on lvl 14, and he would be on lvl 14.
A chemist has 42 grams of aluminum. There are for aluminum. How many milliliters of aluminum does the chemist have?
Answer:
4,200 g. of aluminum
Step-by-step explanation:
42x100=4,200
The 42 grams of aluminum implies that the chemist has 0.06429ml of aluminum
How to determine the amount of aluminum?The mass is given as:
Mass = 42 grams
The density of aluminum is:
Density = 2.7 g/cm³
So, we have:
Volume = Density/Mass
This gives
Volume = 2.7/42
Evaluate
Volume = 0.06429cm³
Convert to ml
Volume = 0.06429ml
Hence, the chemist has 0.06429ml of aluminum
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Please help :) which angles are supplementary
Answer:
The first one BED and DEA. AEC and BEC.
Step-by-step explanation:
Supplementary angles are 2 angles that when added equals 180. Also, if there are no numbers given, the 2 angles should make a straight line when next to each other.
Timothy has three friends. The following table shows the distance and time it takes him to drive to each of his friends’ houses. 5 km 11 km 18 km to 10 min 15 min 20 min. Is the time it takes Timothy to drive to his friends’ houses proportional to the distance
Answer:
No
Step-by-step explanation:
The time it takes Timothy to drive to his friends' houses is not proportional. This is because when going to the first house, he is going at 4km per minute, but when visiting the second and third houses he is no longer traveling at that speed.
In a directly proportional relationship, increasing one variable will increase another. The given relationship is not proportional.
What is the directly proportional and inversely proportional relationship?In a directly proportional relationship, increasing one variable will increase another.
This directly proportional relationship between p and q is written as
p∝q where that middle sign is the sign of proportionality.
Inversely proportional relationship increasing one variable will decrease the other variable if both are inversely proportional.
This directly proportional relationship between p and q is written as
p∝1/q where that middle sign is the sign of proportionality.
Given that the table shows the distance and time it takes him to drive to each of his friends’ houses.
Now, to know if the time it takes Timothy to drive to his friends’ houses proportional to the distance, find the ratio of distance to time for each row. Therefore, the ratios can be written as,
R₁ = 5km / 10 min = 0.5 km per min
R₂ = 11 km / 15 min = 0.7334 km per min
R₃ = 18 km / 20 min = 0.9 km per min
Since the ratio of distance and time in different cases is different, therefore, the given relationship is not proportional.
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What is the solution to this equation?
5x + 9 - 3x = 18 + 15
A. x= 3
B. x = 8
C. x = 12
D. x = 21
Answer:
21
Step-by-step explanation:
5x-3x=18+15-9
2x=42 /:2
x=21
What is the point-slope form given the following slope and a point on the line? m = 3/7 , (7, -4)
Answer:
The equation is y = (3/7)x - 7.
Step-by-step explanation:
Given that the point slope form of an equation is y = mx + b where m represents the gradient and b is the y-intercept. Then, you have to substitute the following values into the equation :
[tex]y = mx + b[/tex]
[tex]let \: m = \frac{3}{7} ,x = 7,y = - 4[/tex]
[tex] - 4 = \frac{3}{7} (7) + b[/tex]
[tex] - 4 = 3 + b[/tex]
[tex] - 4 - 3 = b[/tex]
[tex]b = - 7[/tex]
What type of number is pie/2 ?
Answer:
its a irrational number
What is 910 in scientific notation?
Answer:
9.1 x 10²
Step-by-step explanation:
-2x+11+6x help please ASAP
Evaluate the expression if x = 3, y = 4 and z = 5. 6y - 2xy
Answer:
the answer is 0
Step-by-step explanation:
6 (4) -2 (3)(4)
24-24=0
The difference between a number x and 17 is 22
Answer:
X-17=22
X=22+17
X=39 this is the answer
3. A drone takes off from the base of a mountain at a height of 27 ft below sea level. The drone
then flies up 642 ft before landing at the top of the mountain. How tall is the mountain?
Answer:
669ft high
Step-by-step explanation:
642+27=669ft
The height of the mountain is 669 ft.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
+ Addition operation: Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
For example 4 -2 = 2
A drone takes off from the base of a mountain at a height of 27 ft below sea level.
To determine the height of the mountain.
Using the arithmetic operations of addition and subtraction,
The drone then flies up 642 ft before landing at the top of the mountain.
Assume that distance below sea level is positive,
So the height of the mountain as
⇒ 642 + 27
⇒ 669 ft
Hence, the height of the mountain is 669 ft.
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Solve the system of equations below.
x - y = 5
2x - 3y = 4
(5,0)
(7,2)
(9,4)
(11,6)
Answer:
Step-by-step explanation:
-2x + 2y = -10
2x - 3y = 4
-y = -6
y = 6
2x - 18 = 4
2x = 22
x = 11
(11, 6)