Simplify by combining like terms step by step
- (3x - 4y) + x
Solve each formula for the indicated variable. step by step
h = vt -5t^2 , for v
Answers
-3x + 4y + x.....combine like terms
-2x + 4y
h = vt - 5t^2....add 5t^2 to both sides
h + 5t^2 = vt....divide both sides by t
(h + 5t^2) / t = v
Related Questions
Choose the best verbal statement for the following inequality: m > 13
Answers
Hope this helps!! :)
If Y is between X and Z, then X, Y, and Z are collinear?
A) Always true
B) Sometimes true
C) Never true ...?
Answers
Yes, its always true that if Y is between X and Z, then X, Y and Z are collinear.
Here,
Given that;
Y is between X and Z.
We have to find X, Y and Z are collinear.
What is Collinear points?
Two or more points are Collinear points if they are lie in one straight line.
Now,
Y is between X and Z.
Clearly, XZ is a line and Y is lie in between X and Z.
So, X, Y and Z are Collinear points.
Therefore, its always true that if Y is between X and Z, then X, Y and Z are Collinear.
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What is the sum of the arithmetic sequence 151, 137, 123,..if there are 26 terms?
A. -676
B.-650
C.-624
D.-598
Answers
common difference: d = -14 (we decrease by 14 each time, eg, 151-14 = 137)
nth term of this arithmetic sequence is...
an = a1+d(n-1)
an = 151+(-14)(n-1)
an = 151-14n+14
an = -14n+165
This will be used in the formula below
Sn = n*(a1+an)/2
Sn = n*(151+(-14n+165))/2
S26 = 26*(151+(-14*26+165))/2 ... replace every n with 26
S26 = -624
The final answer here is choice C) -624
Answer:
option C -624
Step-by-step explanation:
Julia wrote 14 letters to friends each month for y months in a row. Write an expression to show how many total letters she wrote.
Answers
The expression representing the total number of letters that Julia wrote after 'y' months is '14y', as she writes 14 letters each month.
Explanation:This is a mathematics problem related to writing algebraic expressions. In this case, Julia has written 14 letters each month for 'y' months. Hence, the expression to determine the total number of letters Julia has written is '14y'. Let's break this down:
Julia writes 14 letters each month. This is a constant, represented by the number 14. The time period over which she continues this action is variable, represented by 'y'. So, for every month 'y', she writes 14 letters. We multiply 14 (letters per month) by 'y' (number of months) to get the total number of letters, hence the expression 14y.Learn more about Algebraic Expression here:
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The expression to show how many total letters Julia wrote is 14y.
Explanation:To find the total number of letters Julia wrote, we need to multiply the number of letters she wrote each month (14) by the number of months she wrote letters (y). So, the expression to show how many total letters she wrote is 14y.
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find the derivative of y=(2x-7)^3
Answers
To find the derivative of y=(2x-7)^3, use the power rule and chain rule. Differentiate each term individually and apply the chain rule. Add all the terms together to get the derivative.
Explanation:To find the derivative of y=(2x-7)^3, we can use the chain rule. First, we can rewrite the equation using the power rule: y = (2x - 7)(2x - 7)(2x - 7). Next, we differentiate each term individually using the power rule and then apply the chain rule. The derivative of the first term will be 2(2x - 7)(2), the derivative of the second term will be 2(2x - 7)(2), and the derivative of the third term will be 2(2x - 7)(2). Finally, we add all these terms together to get the derivative of the original equation.
You drop a rock off a bridge. The rock’s height, h (in feet above the water), after t seconds is modeled by h = -16t2 + 541. What is the height of the rock after 2 seconds?
Answers
h = - 16(2)² + 541
= - 16(4) + 541
= - 64 + 541
h = 477 feet
From 2006 to 2010, the population of a town declined to 22,000. The population is expected to continue to decline at a rate of 2.8% each year. What will the population be in 2040? Round to the nearest whole number. Enter your answer in the box.
Answers
actually i just took the test and it said the answer was 9384
mary has $500 in her savings account and she buy a pair of shoes every week for $125 write a function
Answers
can't keep that habit up
A hummingbird beats its wings about 75 times in one second. Based on this rate, what is the number of times a hummingbird beats its wings one minute?
Answers
75 × 60 seconds = 4,500 beats a minute
what is the slope of 3x + 4Y = 24
Answers
The slope of the line 3x + 4y = 24 is -3/4.
The slope of a line is determined by the coefficient of x in the equation of a line written in the form y = mx + b, where m represents the slope.
In the equation 3x + 4y = 24, rearranging it to the slope-intercept form y = mx + b gives 4y = -3x + 24, and then y = -3/4x + 6. Thus, the slope is -3/4.
Chris is calculating his deductions for his tax return. He is filing singly. He can claim $1,813 from property taxes, $1,513 from medical expenses, and $761 from state income tax. The standard deduction for a single filer is $5,700. How does the standard deduction compare to Chris’s deductions? a. Chris’s deductions are $1,437 better than the standard deduction. b. Chris’s deductions are $4,087 better than the standard deduction. c. The standard deduction is $1,613 better than Chris’s deductions. d. The standard deduction is $664 better than Chris’s deductions.
Answers
1,813 + 1,513 + 761 = 4,087
Then you subtract
5,700 - 4,087 = 1,613
It's C. The standard deduction is $1,613 better than Chris's deductions
I just took the test.
Answer:
(C)
Step-by-step explanation:
Chris's deductions for tax return = claim from property taxes +claim from medical expenses+claim form state income tax
= $1813+$1513+$761
= $4087
Standard deductions = $5700
Difference between standard deduction and Chris's deductions = 5700-408
= $1613
Hence standard deductions is better than Chris's deductions by $1613
Therefore, option (C) is correct.
Sarah's craft project uses pieces of yarn that are 1/8 yard long. She has a piece of yarn that is 3 yards long. How many 1/8 yard pieces can she cut and still have 1 1/4 yards left?
Answers
3 - 1/8x = 1 1/4
1/8x = 3 - 1 1/4 = 1 3/4
x = 1 3/4 / 1/8 = 14
Therefore, she can cut 14 pieces of yarn.
Find the key number to the equation, the intervals into which the key numbers divide the number line, and the sign of y over each of these intervals. y=x+1/(x-1)^2
Answers
1) key number
The key number (also called critical values) is where the denominator equals zero.
(x -1)^2 = 0 => x = 1
2) intervals: (-∞,1) ,(1,∞)
3) Sign of the function
The sign of the denominator is always positive, then the sign of the function is the same sign of the numerator
x +1 > 0 => x > - 1
x+ 1 < 0 => x < -1
Then in the interval (-∞,1) the function is negative for (-∞,-1) and positive for (-1,1).
The function is positive for all the values in the interval (1,∞)
Briefle, the functionis negative in (-∞,-1) and positive in (-1,∞).
you can buy an 8 pack of paper towels for $7.92 or 12 pack for $11.64, which is a better buy?
Answers
The first option has a price of $0.99 for one paper towel, and the second option has a price of $0.97 for one paper towel.
The second option is the better buy.
How many square feet of outdoor carpet will we need for this hole
Answers
Answer:
The actual answer is 36. If I am wrong i am sorry
Step-by-step explanation:
Answer:
36 square ft
Step-by-step explanation:
How many solutions does this equation have?
Answers
you randomly draw a marble from a bag of marbles that contains 7 blue marbles, 2 green marbles, and 1 red marble. what is the probability not draw a blue marble
Answers
Answer:
0.3
Step-by-step explanation:
It is given that,
Number of blue marbles = 7
Number of green marbles = 2
Number of red marbles = 1
Total number of marbles = 7+2+1=10
We need to find the probability that we do not draw a blue marble.
[tex]P=\dfrac{\text{Number of non-blue marbles}}{\text{Total number of marbles}}[/tex]
[tex]P=\dfrac{2+1}{10}[/tex]
[tex]P=\dfrac{3}{10}[/tex]
[tex]P=0.3[/tex]
Therefore, the required probability is 0.3.
There are 6 female goldfish for every 10 male goldfish in the aquarium. there are 216 female goldfish in the aquarium. how many male goldfish are in the aquarium?
Answers
cross multiply because we have a proportion
6m = (216)(10)
6m = 2160
m = 2160/6
m = 360...so when there are 216 females, there are 360 males.
If there are 6 female goldfish for every 10 male goldfish in the aquarium and if there are 216 female goldfish in the aquarium then there are 360 male goldfish in the aquarium.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Let us use a proportion to represent the relationship between the number of female and male goldfish in the aquarium
6 female goldfish / 10 male goldfish = 216 female goldfish / x male goldfish
We know that there are 216 female goldfish in the aquarium, so we can substitute that value into the equation:
6 / 10 = 216 / x
Let us solve for x by cross-multiply:
6x = 10 × 216
6x = 2160
Divide both sides by 6
x = 360
Therefore, there are 360 male goldfish in the aquarium.
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what is the difference between all real numbers and no solution how do you know when these situations occur
Answers
example
simplifying results in x=x or 8=8 or 0=0 or something liek that
an example equation would be 2(x+1)=2x+2, simplifies to x=x or 2=2 or 0=0
no solution is when you get a false statement from simplifying
example, 3=4 or -1=0
an example equation could be 2(x+1)=2x+3, it simplifies to 2=3 which is false
The difference between 'all real numbers' and 'no solution' is that the former means any real number satisfies the equation while the latter means no real number satisfies it. These concepts are essential in understanding and solving mathematical problems, which is a skill developed through practice.
Explanation:The difference between 'all real numbers' and 'no solution' in mathematical equations is significant. When an equation has all real numbers as its solution, it means that any real number can be substituted for the variable and the equation would still hold true. This situation typically occurs when both sides of the equation are identical after simplification. For example, if we simplify an equation and end up with a statement like 5 = 5, it implies that all real numbers are solutions since the statement is always true, regardless of the value of the variable.
On the other hand, 'no solution' means that there are no real numbers that satisfy the equation, often arising when a statement is made that is logically false after simplification, such as 0 = 5. Identifying knowns and unknowns and checking if an answer is reasonable are part of the problem-solving process, where we also look for unreasonable results that might suggest 'no solution'.
The occurrence of these situations during problem solving reflects the complexity of real-world problems, where we must determine which information is relevant and sort out the possible from the impossible. This discernment can be developed through consistent practice in evaluating and solving various types of problems. In some cases, particularly in systems of equations, if the number of unknowns is larger than the number of equations, it may indicate that there could be infinite solutions or no unique solution.
Peaches are being sold for $2 per pound if X represents the number of pounds of peaches bought and Y represents the total cost for the peaches which best describes the value of X and Y
Answers
Answer:
Y = 2X is the expression which describes the value of X and Y.
Step-by-step explanation:
Peaches are being sold at the rate = $2 per pound
If X represents the number of pounds of peaches purchased then the total cost of the peaches = 2X
Total cost of the peaches is represented by Y, then the expression will be
Y = 2X
Therefore, expression which shows the relation between X and Y is
Y = 2X
It took morry 2 and 5/6 hours to drive to the beach. it took jason twice as long. about how long did it take jason to drive to the beach?
Answers
x 2
-------
5 2/3
need answers............
Answers
_______________________________________________
This answer, "Answer choice [D]", is the converse of the conditional statement given: "If x = -10, then [tex] x^{2} [/tex] = 100 . "
_________________________________________
As such, this is the correct answer choice.
Write a real- world problem that you can solve by writing an equation. the answer to the problem must be 6.
Answers
The difference of two numbers is more than 12,and one of the numbers is 3
Answers
x-y = 3
x = 3+y
Substitute it in 1st equation,
3+y+y=12
2y = 9
y = 4.5
Substitute it in 1st eq.,
x = 12-4.5 = 7.5
So, the two numbers are 7.5 & 4.5
Hope this helps!
Inequality for the other number x > 15.
What is inequality?An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The most frequent application is to size-compare two numbers on a number line.
Given,
Difference of two numbers is greater than 12
One number is 3
Let the other number be x
Then, inequality becomes
x - 3 > 12
Adding 3 on both sides
x > 12 + 3
x > 15
Hence, x>15 represents the other number so that difference of two numbers is greater than 12.
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What are the different mathematical relationships in data?
Answers
What is the solution of the system?
Use the substitution method.
{y−2x=8
{16+4x=2y
The only solution is (24, 0)
The only solution is (1, 10)
There is no solution.
There are an infinite number of solutions.
Answers
solve for y in first equation
add 2x to both sides
y=2x+8
sub 2x+8 for y in second equation
16+4x=2(2x+8)
divide both sides by 2
8+2x=2x+8
true
there are infinite solutions for x
therefor infinite soltions for y
there are an infinite number of solutions
The hypotenuse of a right triangle has endpoints A(4, 1) and B(–1, –2).
At which points could the vertex of the right angle in the triangle be located? Check all that apply.
(–1, 1)
(4, –2)
(1, 1)
(2, –2)
(4, –1)
(–1, 4)
Answers
Answer:
(–1, 1)
(4, –2)
Step-by-step explanation:
Let
(x,y) ----> the coordinates of point C
Applying the Pythagoras Theorem
[tex](-1-4)^2+(-2-1)^2=(x-4)^2+(y-1)^2+(x+1)^2+(y+2)^2[/tex]
step 1
Find the possibles values of x
[tex](-1-4)^2=(x-4)^2+(x+1)^2\\\\25=x^{2}-8x+16+x^{2}+2x+1\\\\2x^{2}-6x-8=0[/tex]
Simplify
[tex]x^{2}-3x-4=0[/tex]
Solve the quadratic equation
[tex]x^{2}-3x-4=(x+1)(x-4)[/tex]
The values of x are
x=-1 and x=4
step 2
Find the possibles values of y
[tex](-2-1)^2=((y-1)^2+(y+2)^2\\\\9=y^{2}-2y+1+y^{2}+4y+4\\\\2y^{2}+2y-4=0[/tex]
Simplify
[tex]y^{2}+y-2=0[/tex]
Solve the quadratic equation
[tex]y^{2}+y-2=(y+2)(y-1)[/tex]
The values of y are
y=-2, y=1
therefore
The possibles coordinates of point C are
(-1,1),(4,-2)
Answer:
(–1, 1)
(4, –2)
Step-by-step explanation:
Given that the hypotenuse of a right triangle has endpoints A(4, 1) and B(–1, –2), then two triangles can be formed (see figure attached).
The vertex of the right angle in each triangle are on points (-1, 1) and (4, -2), as can be seen in the figure.
When rewriting y = 2x + 1 in function notation, what do you replace with f(x)?
Answers
Answer:
You replace y with f(x)
Step-by-step explanation:
- Function is a relation between two sets of numbers, with every element
in the first set has only one corresponding element in the second set
- The first set is called the domain of the function (input)
- The second set is called the range of the function (output)
- If the first set is set X and the second set is set of Y, then each value
of x has only one value of y and x is the input and y is the output
- Function notation is the way to write a function f(x) = y, where f(x)
represents the values of y
∵ y = 2x + 1
∵ f(x) = y
- Replace y by f(x)
∴ f(x) = 2x + 1
* You replace y with f(x)
Answer:
That is what I got off of USA Test Prep
Step-by-step explanation:
For function notation you are saying that you have a relation that is a function of another variable. To correctly rewrite using function notation you replace y with f(x).
write 42.5% as a fraction in simplest form
Answers
The fraction of 42.5% in its simplest form is 17/40.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
42.5%
= 42.5/100
= 425/1000
= 85/200
= 17/40
Thus,
The fraction is 17/40.
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42.5% can be expressed as the fraction 17/40 in simplest form.
To express 42.5% as a fraction in the simplest form, we need to convert the percentage to a fraction with the numerator and denominator in their simplest form. Here's the step-by-step process:
Recognize that a percentage is a fraction out of 100. In this case, 42.5% can be written as 42.5/100.
Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor. In this case, the greatest common divisor of 42.5 and 100 is 2. Dividing both the numerator and denominator by 2 gives us 21.25/50.
Continue simplifying the fraction by dividing both the numerator and denominator by any common factors. In this case, we can divide both by 25: 21.25/50 = 0.85/2.
Finally, express the fraction in simplest form by dividing both the numerator and denominator by their greatest common divisor, which is 5 in this case: 0.85/2 = 17/40.
Therefore, 42.5% can be expressed as the fraction 17/40 in simplest form.
This means that 42.5% is equivalent to 17 parts out of 40 parts.
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The sum of three consecutive integers is 303. If n is the smallest of the three, which equation represents this situation?
Answers
Answer:
The correct equation is 3n + 3 = 303
Correct value of n is 100
Step-by-step explanation:
The sum of three consecutive integers is 303.
Consecutive integer is next number of previous one.
Let n be smallest integer.
Next two integer: n+1, n+2
Sum of n, n+1 and n+2 is 303
Therefore,
n + n + 1 + n + 2 = 303
3n + 3 = 303
3n = 300
n = 100
Hence, The correct equation is 3n + 3 = 303