To calculate equivalent form of an algebraic expression we can use the following :
1) distributing property
2) factoring.
Two mathematical expressions are said to be equivalent if they yield the same result upon solving them. To represent equivalent form an equality (=) sign is used. 3(x + 2) and 3x + 6 are equivalent expressions because the value of both the expressions remains the same for any value of x. To calculate equivalent form by using Distributive Property :
Start with an algebraic expression. Let's take an example 2x(3y + 2).Distribute the multiple 2x throughout the rest of the equation. That is multiplying 2x by 3y and by 2, we get 6xy + 4x.This is our equivalent expression. It can be represent as equality : 2x(3y + 2) = 6xy + 4x.To calculate equivalent form Using Factoring :
Identify the common factors in the expression. If possible divide the equation to find an equivalent expression.Let the expression 5xy + 4x, in this case, both numbers 4 and 5 are co-prime. As we see that there is common factor, x. Take the other common factors: x(5y + 4).This gives you an equivalent form . Again, the equality form, 5xy + 4x = x(5y + 4). Thus, the required equivalent form is determined.
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help pls mathematics
Therefore , the solution of the given problem of inequality comes out to be 13 and 17 is the number of hikers.
What does inequality really mean?In mathematics, an inequality is a linear connection or a collection of numbers even when there is no equal sign. Equity always comes after equilibrium. When two numbers are not equal, inequality exists. Between equality and inequality, there exist differences. The most common symbol was chosen because when parameters aren't the same or comparable (). Values can be compared using a variety of disparities, no matter how few or numerous they are.
Here,
Given :
a) The minimum number of hikers
who walks between 8 miles and 19 miles :
=> 8 < x < 19
=> 7 +6
=> 13
b) The maximum number of hikers
who walks between 8 miles and 19 miles :
=> 8 < x < 19
=> 7+6+4
=> 17
Therefore , the solution of the given problem of inequality comes out to be 13 and 17 is the number of hikers.
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find the solution set x^2 -8x+ 7=0
Step-by-step explanation:
x²-8x+7=0
x²-7x-x+7=0
x(x-7) -1(x-7)=0
(x-7) (x-1)=0
Either, x-7=0 i.e x=7
or, x-1=0 i.e x=1
How to determine if a differential equation is linear?
It is linear if and only if the coefficients of y (the dependent variable) and all order derivatives of y are functions of t or constant terms.
What is equation?An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.
Here,
It is linear if and only if all order derivatives of y (the dependent variable) are functions of t or constant terms.
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How do you find the opposite side of a triangle?.
Multiply the hypotenuse of triangle by sinθ to determine the length of the side opposite the angle (θ). Alternatively, to obtain the side next to the angle, multiply the hypotenuse by cos(θ).
Scalene triangles are typically described as triangles with no two sides that are equal. Isosceles triangles are those triangles whose two sides are equal. An equilateral triangle is one with equal lengths on each of its three sides. Clearly, all equilateral triangles are isosceles, but not the opposite.
The side across from the right angle is always the hypotenuse of a right triangle. The opposite and neighboring sides are the other two sides.
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Kim went to the store and bought 4 items: $32.45, $46.78, $12.91, and $52.38. How much did Kim spend if the sales tax is 8%?
To find out how much Kim spent in total with the 8% sales tax included, we first need to add up the cost of all 4 items: $32.45 + $46.78 + $12.91 + $52.38 = $144.52
Next, we'll multiply that total cost by the sales tax rate as a decimal (8% expressed as 0.08) to find out how much tax Kim had to pay: $144.52 x 0.08 = $11.56
Finally, we'll add the total cost of the items and the tax to find out how much Kim spent in total: $144.52 + $11.56 = $156.08
Solve this equation for the given domain.
cos(2x + 45°) = 0.8 for 0° ≤ x ≤ 180°
The solution to the equation cos(2x + 45°) = 0.8 in the domain of 0° to 180° is x = 15° and X=139° or X=176 °
How to find the solution?Because Cos (±37° +360k) = 0.8
0≤2X ≤ 360°
0+45°=2x+45° 360°+45° 45°≤ 2x+45°< 405°
50 2x+45° = 360°-37° or 2x+45° = 360° + 37°
{list the equation} 397° -45°=2X = 323-45°
2X = 323-45°. 2x=397° -45°
2x= 278°. 2x= 352°
X = 139°. X=176°
So , x = 139° or x = 176°
To discover the solution set of an equation with a particular domain, first insert each domain value into the equation to obtain the associated range values. Make ordered pairs out of these values and put them down as a set. That set is your solution!
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Two hiker walk on a trail in the direction of increaing mile marker number. Mandy tart at mile marker 1 and hike at a rate of 2. 5 mile per hour. At the ame time, Rita tart at mile marker2 and hike at a rate of 3 mile per hour. The equation 2. 5h1= 3h 2 repreent the number of hour h it will take Mandy to catch up with Rita
Mandy will catch up Rita at 0.5 hour after they start walking.
When will Mandy catch up Rita?As per data given are Mandy start = 1, Rita start = 2, Mandy speed = 5 and Rita speed = 2. Based on this explanation we can determine the formula for Mandy time to catch up Rita as follow
s1 = s2
Rita start + Rita speed x t = Mandy start + Mandy speed x t
2 +3 x t = 1 + 5 x t
2 + 3t = 1 + 5t
2 - 1 = 5t - 3t
1 = 2t
t = 0.5 h
Hence, Mandi will catch up with Rita at 0.5h after start.
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Geometry
A jar contains 5 red balls and 3 white balls. A ball is selected and its color is noted, then the ball is replaced. A second ball is selected and its color is noted. Find the probability of each of the following.
a. What is the probability of selecting 2 red balls?
b. What is the probability of selecting 1 red ball and then 1 white ball?
Answer:awnsers below
Step-by-step explanation:
a. The probability of selecting 2 red balls is (5/8) * (5/8) = 25/64. This is because the probability of selecting a red ball on the first draw is 5/8, and the probability of selecting a red ball on the second draw is also 5/8, since the ball is replaced after each draw.
b. The probability of selecting 1 red ball and then 1 white ball is (5/8) * (3/8) = 15/64. This is because the probability of selecting a red ball on the first draw is 5/8, and the probability of selecting a white ball on the second draw is 3/8, since the ball is replaced after each draw.
Answer:
Step-by-step explanation:
a)
P(Red)=5/8
(5/8)^2=25/64
b)
P(Red)=5/8 P(White)=3/8
5/8*3/8=15/64
What is the slope of 3x 4y =- 12?.
The slope of the equation 3x + 4y = -12 is -3/4
Slope in math is defined as the ratio of the amount that y increases as x increases some amount
Here we have given the equation 3x + 4y = -12.
As we all know that the general form of the equation of the line is written as,
y = mx + c
here m refers the slope of the line and c refers the y intercept of the line.
Now, we have to convert the given equation into the general form then it can be look like the following,
=> 4y = -12 - 3x
=> y = -12/4 - 3x/4
It can be rewritten as,
=> y = -3x/4 - 12/4
Then the resulting slope is -3/4.
Complete Question:
What is the slope of the equation 3x + 4y = -12?
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Divide 1 hour in the ratio 1:5
Answer: ratio of 1: 10mins
ratio of 5: 50mins
Step-by-step explanation:
The ratio of 1:
[tex]\frac{1}{6}[/tex] x 60 (hours should be converted to minutes therefore it is 60 mins and
the denominator seen here is taken by adding the two values in the
given ratio and since we're still finding 1 you should divide 1 by the
added denominator and the same applies when finding the ratio 5)
Answer= 10mins
The ratio of 5:
[tex]\frac{5}{6}[/tex] x 60 (refer to the underlined explanation above)
answer= 50mins
so if you want to verify you add the two values you got to see if you got 60 as 60mins in hours was divided in ratio so when you add it will be 60 which means your answer is correct!
Answer: 12:60
Step-by-step explanation: To find the ratio, we must take 1 h and turn it into minutes. So as we know, it's 60 minutes. So next, we shall change the ratio into fraction form (don't worry it's the same basic format)
[tex]\frac{1}{5} = \frac{?}{60}[/tex]
So with that given information, we know that 60 would be our denominator. So, we need to divide both denominators, and then whatever we get from that, multiply that by the given numerator. So, we would do:
60 / 5
= 12
12 * 1
= 12
Therefore we now know that 1/5 = 12/60 as a ratio. I hope this helped :)
(Attachment included)
An artist makes pottery. The artist earns the same amount for each piece of pottery sold
but must pay a fee to rent a booth at a local fair. After analyzing data from recent sales,
the artist finds the equation y=42x-200 models the profit, y, earned for selling x
pieces of pottery after the expense of renting the booth. Which statement is true?
a)
The slope of the equation is -200, and it represents the $200 the artist earns, on
average, for every piece of pottery sold.
b)
The slope of the equation is -200, and it represents the cost of renting the
booth.
c) The slope of the equation is 42, and it represents the $42 the artist earns, on
average, for every piece of pottery sold.
d) The slope of the equation is 42, and it represents the cost of renting the booth.
The slope of the equation is 42, and it represents the $42 the artist earns, on is true after analyzing data from recent sales.
What is sales?Sales in mathematics is the process of exchanging goods or services for money. It is a vital part of the economy and involves the transfer of ownership from the seller to the buyer. In mathematical terms, sales can be expressed as a function where the input is the amount of money paid for goods or services and the output is the goods or services received. Sales can also be expressed as an equation in which the variables are the cost of goods or services, the number of goods or services sold, and the total sale amount.
The slope of the equation is 42, and it represents the $42 the artist earns, on average, for every piece of pottery sold.
The constant -200 represents the cost of renting the booth.
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The American with Diabilitie Act tate that ramp mut have an angle le than or equal to 4. 8 degree. Remember, a 4. 8 degree angle in a right American with Diabilitie Act requirement
The designs that meet the condition have leg lengths that are in the ratio of 1: 12.
Two ramps that meet the Americans Disabilities Act are;
A ramp has leg lengths of 3 feet by 36 feet.A ramp with leg lengths of 5 inches by 60 inches.The needed measure of the angle of a ramp according to the Americans with Disability Act is θ ≤ 4.8°.
The ratio of the legs of a right triangle having a 4.8° angle is 1: 12Given, the ratio of the leg lengths is 1: 12, we have;
Expressed as a fraction, we have;
The required ratio of leg lengths = [tex]\frac{1}{12}[/tex]
Probable leg lengths are seen by multiplying the numerator and denominator of the above fraction by a constant as follows;
Possible leg length for the ramp = [tex]\frac{1 * 3}{12 * 3} = \frac{3}{36}[/tex]
That gives a ramp with having leg length of 3 feet and 36 feet.A second possible combination of leg length for the ramp = [tex]\frac{1 * 5}{12 * 5} = \frac{5}{60}[/tex]
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The complete question is:
The Americans with Disabilities Act states that ramps must have an angle less than or equal to 4.8 degrees. Remember, a 4.8-degree angle in a right triangle has a 1: 12 ratio for the legs. Design 2 ramps that meet the Americans with Disabilities Act requirements.
What is a 1 in 3 angle?.
1 in 3 angle of slope in degree is 18.435°.
In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located.
The inverse tangent function is called arctangent, often known as arctan or tan-1. Tangent only has a limited domain for its inverse function.
So to find the 1 in 3 angle we have to put the value 1/3 in arctan function
∴ arctan (1/3) = 18.43494882° ≈ 18.435.
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What is the product of 7x 6 2?.
The product of (7x - 6)² is 49x² - 84x + 36.
Equation is (7x - 6)²,
⇒ We will solve the given problem using the algebraic identity
(a - b)² = a² + b² - 2ab
Here a = 7x and b = 6
⇒ (7x - 6)² = (7x)² + 6² - 2(7x)(6)
⇒ (7x - 6)² = 49x² + 36 - 84x
⇒ 49x² - 84x + 36
The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable.
A product is the outcome of multiplication in mathematics, or an expression that specifies the factors (numbers or variables) to be multiplied.
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Is 999 a cube number?.
=> 999 is not a perfect cube.
Because cube root of 999 is 3 [tex]\sqrt[3]{37}[/tex] .
Now, According to the question:
A cube number is the result when a number has been multiplied by itself twice. The symbol for cubed is 3. For example, 8 is a cube number because it's 2 x 2 x 2 (2 multiplied by itself twice); this is also written as [tex]2^3[/tex] (“two cubed”).
It is the real solution of the equation [tex]x^3[/tex] = 999.
The cube root of 999 is expressed as [tex]\sqrt[3]{999}[/tex] or 3 [tex]\sqrt[3]{37}[/tex] in the radical form and as[tex](999)^\frac{1}{3}[/tex] or [tex](999)^0^.^3^3[/tex] in the exponent form.
The prime factorization of 999 is 3 × 3 × 3 × 37, hence, the cube root of 999 in its lowest radical form is expressed as 3 [tex]\sqrt[3]{37}[/tex].
Cube root of 999: 9.996665555Cube root of 999 in Exponential Form: [tex](999)^\frac{1}{3}[/tex]Cube root of 999 in Radical Form: [tex]\sqrt[3]{999}[/tex] or 3 [tex]\sqrt[3]{37}[/tex] .Learn more about Cube Number at:
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Dennis and Gail Schultz are looking over the repayment schedule for their $5,500 loan for lake house remodeling at 15% interest for 42 months with a monthly payment of $168.85. They note that the balance after payment 18 is $3,493.39, after 24 is $2,718.43, and after 30 is $1,883.50. How much would they save by paying off the loan earlv at payment (a) 19, (b) 25, or (c) 31?
Answer:
c)31
Step-by-step explanation:
The goal of this exercise is to determine the total savings by paying the debt early at
�
)
a)
19
19th payments
�
)
b)
25
25th payments and
�
)
c)
31
31st payments.
If Ellen is X years old.in thirteen years she will be twenty-four years old why’s the answer to that
For each graph, determine the y-intercept using the slope formula. Write the y-intercept in coordinate form.
y = 8/3x + 100 exists the equation of the line in slope-intercept form.
What is meant by Slope of Line?The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line.
A line's slope and y intercept are represented in the slope intercept form as y = mx + b.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) contains
m = y₂-y₁/x₂-x₁
At two of the points the line passes through in the accompanying graph.
Let the two points be (0, 100) and (42, 148)
Let the equation be m = y₂-y₁/x₂-x₁
substitute the values in the above equation, we get
Slope = 148-100/42
= 48/42 = 8/3
To find y intercept, we get
100 = 8/3(0) + b
b = 100
So slope intercept form exists y = 8/3x + 100
Therefore, y = 8/3x + 100 exists the equation of the line in slope-intercept form.
The complete question is:
Examine the linear graph. Determine the y-intercept and write the y-intercept in coordinate form. Then write the equation of the line in slope-intercept form.
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Plssss help!!!! I need to finish this and it is really difficult:
The result of addition and subtraction is
5 (2/3) - 1 (1/4) = 58 (5/12) + 31 (1/6) = 393 (1/4) + 3 (3/5) = 79 (1/10) - 6 (7/10) = 27 (5/8) + 2 (1/7) = 1020 (9/11) - 18 (3/10) = 310 (3/7) + 22 (2/9) = 321 (5/6) + 5 (1/6) = 7113 (1/13) + 86 (9/11) = 20065 (17/20) + 19 (3/25) = 8571 (41/50) + 25 (5/24) = 9712 (13/15) + 18 (2/5) = 31The directions to solve these problems are to round each fraction to the nearest whole number and then add or subtract. We have to round each fraction into the nearest whole number.
If the fraction is more than 1/2 we round it up to 1.If the fraction is less than 1/2 we round it down to 0.1. 5 (2/3) - 1 (1/4) = (5 + 1) - 1 = 6 - 1 = 5
2/3 = 4/62. 8 (5/12) + 31 (1/6) = 8 + 31 = 39
5/123. 3 (1/4) + 3 (3/5) = 3 + (3 + 1) = 3 + 4 = 7
1/44. 9 (1/10) - 6 (7/10) = 9 - (6 + 1) = 9 - 7 = 2
1/105. 7 (5/8) + 2 (1/7) = (7 + 1) + 2 = 8 + 2 = 10
5/86. 20 (9/11) - 18 (3/10) = (20 + 1) - 18 = 21 - 18 = 3
9/11 = 18/227. 10 (3/7) + 22 (2/9) = 10 + 22 = 32
3/7 = 6/148. 1 (5/6) + 5 (1/6) = (1 + 1) + 5 = 2 + 5 = 7
5/69. 113 (1/13) + 86 (9/11) = 113 + (86 + 1) = 113 + 87 = 200
1/13 = 2/2610. 65 (17/20) + 19 (3/25) = (65 + 1) + 19 = 66 + 19 = 85
17/2011. 71 (41/50) + 25 (5/24) = (71 + 1) + 25 = 72 + 25 = 97
41/5012. 12 (13/15) + 18 (2/5) = (12 + 1) + 18 = 13 + 18 = 31
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make x the subject of the formula 13x=6y
The formula which represents the solution of the given equations; 13x = 6y for variable, x is; x = 6y / 13.
What is the solution of the given equation for x?It follows from the task content that the solution of the given equation for variable, x is to be determined.
Since the given equation is; 13x = 6y.
It follows that the equation can be solved as follows;
13x = 6y
Divide both sides of the equation by 13 so that we have;
x = 6y / 13.
Ultimately, the formula for x is; x = 6y / 13.
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What is the value of x in the triangle?
What are the two types of indirect proof in geometry?.
There are two methods of indirect proof:
Proof of the contrapositive and proof by contradiction.
Now, According to the question:
Let's know:
An indirect proof, also called a proof by contradiction, is a roundabout way of proving that a theory is true. When we use the indirect proof method, we assume the opposite of our theory to be true. In other words, we assume our theory is false.
Hence, There are two methods of indirect proof:
Proof of the contrapositive and proof by contradiction.
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How much is a domestic letter stamp?.
The First Class Mail (1 oz.) letter rate for postage purchased at the Post Office will increase two cents to $0.60 from $0.58.
Domestic shipping refers to shipping a package via a carrier within a country's borders.
Now, According to the question:
Media Mail rates will increase by 9%. Rates will start at $3.49 (previously $3.19).NEW: Priority Mail will now include $100 of insurance for free (previously $50 of insurance was provided for free).NEW: Cubic pricing is being introduced for Parcel Select Ground.Parcel Select Ground will see a rate decrease of 12.1% for Commercial Base (online postage) in 2022, with rates starting at $7.22 (previously $7.01).The “Metered Mail” rate for First Class Mail (1 oz.) letters which includes online postage and postage meters, will increase 4 cents to $0.57 from $0.53.
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what is the highest fraction that is reduced to 1/2
I WILL MARK U BRAINLIST
Answer:
I think its two
Step-by-step explanation:
If I am wrong sorry
Is linear equations in two variables easy class 10?.
Linear equations in two variables can be relatively easy to understand and work with, as they represent straight lines in the xy-plane. The slope-intercept form of a linear equation, y = mx + b, is a simple way to represent a line with a specific slope and y-intercept.
Graphing linear equations is also straightforward, as you can find the x-intercept and y-intercept and plot the line using these points.
However, solving linear equations in two variables can become more challenging when the equations involve multiple terms or are presented in a different form. Also, understanding the concept of slope, y-intercept, and how to graph the line can be challenging for some students.
Overall, linear equations in two variables can be considered as a fundamental concept in algebra and mathematics and it requires practice to gain mastery over it.
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what is the following product? Assume x>0 3root x^2 times 4 root x ^3
The product is 3x * 4x^(3/2) = 12x^(5/2)
How to do the product of root?
When multiplying two terms with the same base and different exponents, you can add their exponents.
For example, √(a^m) * √(a^n) = √(a^m * a^n) = √(a^(m+n)) = a^((m+n)/2)
The product of 3√(x^2) * 4√(x^3) is equal to:
12x^(5/2)
This is because when you multiply two terms with the same base, you can add their exponents:
3√(x^2) * 4√(x^3) = (3*4)√(x^(2+3/2)) = 12x^(5/2)
This is because
√(x^2) = x^(2/2) = x
√(x^3) = x^(3/2) = x^(3/2)
so we can write 3root x^2 = 3x and 4root x^3 = 4x^(3/2)
Hence, the product is 3x * 4x^(3/2) = 12x^(5/2)
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How do you change improper fractions to mixed numbers for kids?.
The way to change improper fractions to mixed numbers for kids is solved by using the division operation.
In math the term called fraction is defined as a part of a whole number, and a way to split up a number into equal parts
Here we need to identify the way to change improper fractions to mixed numbers for kids.
As from the definition of fraction we have identified that the way to solve the improper fraction into mixed fraction is written as follows:
Here we have to convert an improper fraction to a mixed number,
Then we have to work out how many whole numbers there are by dividing the numerator by the denominator.
And then we have to make the remainder the new numerator and leave the denominator as it was.
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A family ha two car. During one particular week, the firt car conumed 30 gallon of ga and the econd conumed 40 gallon of ga. The two car drove a combined total of 1850 mile, and the um of their fuel efficiencie wa 55 mile per gallon. What were the fuel efficiencie of each of the car that week?
The fuel efficiency of the first car was 40.72 miles per gallon and the fuel efficiency of the second car was 14.28 miles per gallon.
The problem can be solved by using a system of equations.
We can call the fuel efficiency of the first car x and the fuel efficiency of the second car y.
From the problem, we know:
x + y = 55 (the combined fuel efficiency of the two cars is 55 miles per gallon)
We can also use the information about the amount of gas consumed and the distance has driven to set up another equation:
(30 gallons) * (x miles per gallon) + (40 gallons) * (y miles per gallon) = 1850 miles
Now we have a system of two equations with two variables (x and y):
x + y = 55
(30)x + (40)y = 1850
We can solve this system of equations using any method of solving such as substitution or elimination.
x = 55 - y
and substitute it in the second equation
(30)(55-y) + (40)y = 1850
1650 - 30y + 40y = 1850
-14y = -200
y = 14.28
x = 55 - 14.28 = 40.72
So the fuel efficiency of the first car was 40.72 miles per gallon and the fuel efficiency of the second car was 14.28 miles per gallon.
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what does x^2 + 12 -35 equal
Answer:
x^2-23
Step-by-step explanation:
Which value of x is the solution to this equation 5x^2 -3x+45
This means that the solution to the equation x is 6.
What is equation?An equation is a mathematical statement that expresses the relationship between two values. It typically consists of an equal sign (=) and two expressions that are related to each other. Equations are used to describe how one value depends on another, or how two values are related to each other.
To solve this equation, use the Quadratic Formula,
which states that for an equation of the form ax2 + bx + c = 0,
the solution is x = [-b ± √(b2 - 4ac)] / 2a.
Plugging in the given equation,
we have a = 5, b = -3, and c = 45.
This means that the solution to the equation is x = [-(-3) ± √((-3)2 - 4*5*45)] / 2*5, or x = 6.
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