According to the question, the given rational expression is as follows:
Rational expression = [tex]\frac{2x}{4x^{2} -2x}[/tex]
To simplify the given expression by performing factors on denominator:
[tex]4x^{2}-2x = 2x(2x-1)[/tex]
Substituting these factors in the final expression, we get:
Rational expression = [tex]\frac{2x}{4x^{2} -2x}=\frac{2x}{2x(2x-1)}=\frac{1}{2x-1}[/tex]
Therefore, the final answer for the given expression is [tex]\frac{1}{2x-1}[/tex].
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The total cost (t) after 8% sales tax is added to an Items price (p): 1.08p=t
It should be noted that the total cost (t) after 8% sales tax is added to an Items price (p): 1.08p. This is true.
How to illustrate the information?It should be noted that tax simply has to do with the compulsory levy that's paid by the individuals and firms to the government.
It should be noted that from the information, the total cost (t) after 8% sales tax is added to an Items price (p): 1.08p. This will be confirmed this:
Price = p
Tax = 8%
New price = Price + Tax
New price = p + (8% × p)
New price = p + 0.08p.
New price = 1.08p
Therefore, it should be noted that the total cost (t) after 8% sales tax is added to an Items price (p): 1.08p. This is true.
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The total cost (t) after 8% sales tax is added to an Items price (p): 1.08p. True or false?
I need help i dont under stand any of this
Answer:
The equation of a line in slope intercept form is
y=mx+c
in integers form y=2x+3
01.07 Operations with Scientific Notation
CCSS.Math.Content.8.EE.A.4
Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
A number that can be expressed in scientific notation will be (2 × 10³) × 4 × 10².
What is scientific notation?Numbers that are either too large or too little to be conveniently stated in decimal form can be expressed using scientific notation. It may also be referred to as standard form, scientific form, or standard index form.
Always set the base to 10. The exponent must be an integer that is non-zero, therefore it can either be positive or negative. The coefficient's absolute value is more than or equal to 1, but it must be less than 10.
It should be noted that the number that can be expressed in scientific notation will be (2 × 10³) × 4 × 10². This will be:
= (2 × 10³) × (4 × 10²)
= 8 × 10^5.
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Estimate the product of 2,456 x 38 by rounding to the nearest thousand and ten.
Answer:93000
Step-by-step explanation:
For the following problem, match the name of the number property that was used to get to each step from the previous step.
37 • 2 • (-5 + + 5)
1. 37 • 2 • (-5 + 5 + )
inverse property of multiplication
2. 37 • 2 • (0 + )
inverse property of addition
3. 37 • 2 •
commutative property
4. 37 • 1
identity property of multiplication
5. 37
identity property of addition
37 • 2 • (0 + 1/2 ) - Inverse property of addition
37 • 2 • 1/2 - Commutative property of addition
37 • 1 - Inverse property of multiplication.
37 - Identity property of multiplication.
What is an algebraic equation?Algebraic expressions include at least one variable and at least one operation addition, subtraction, multiplication or division.
We have,
37 • 2 • (-5+ 5+ 1/2)
= 37 • 2 • (0 + 1/2 ) -Inverse property of addition
The inverse property of addition states that:
a + (-a ) = 0 where a ∈ R
= 37 • 2 • 1/2 - Commutative property/Identity property of addition
The commutative property of real numbers states that:
a + b = b + a where a,b ∈ R
= 37 • 1 - Inverse property of multiplication.
The inverse property of real numbers states that:
a + 1/a = 1 where a ∈ R
= 37 - Identity property of multiplication.
The identity property of multiplication of real numbers states that:
a x 1 = a where a ∈ R
Thus,
37 • 2 • (0 + 1/2 ) - Inverse property of addition
37 • 2 • 1/2 - Commutative property of addition
37 • 1 - Inverse property of multiplication.
37 - Identity property of multiplication.
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The complete question is:
For the following problem, match the name of the number property that was used to get to each step from the previous step.
37 • 2 • (-5+ 5+ 1/2)
37 • 2 • (0 + 1/2 )
37 • 2 • 1/2
37 • 1
37
identity property of addition
commutative property
inverse property of multiplication
inverse property of addition
identity property of multiplication
How many different real solutions are there for the equation 4 x²=-4 x-4 ?
There are 0 or no real solutions for the equation 4x²=-4x-4.
What, exactly, is an equation?A mathematical statement composed of two representations joined by an equal sign is known as an equation.3x - 5 = 16 is an example of an equation.We obtain the value for the variable x as x = 7 after solving this equation.So,
Given the equation: 4x²=-4x-4
Then,
4x²=-4x-44x²+4x+44x²+x( + )=44x²+x(2+2)+44x²+2x+2x+42x(2x+1)+2(x+2)No factor for this equation.
Therefore, there are 0 or no real solutions for the equation 4x²=-4x-4.
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factor out the negative sign with the GCF
-4x^3 + 28x^2 - 20x
Answer:
Step-by-step explanation:
-4x^3 + 28x^2 - 20x
= 4x(-x^2 + 7x - 4)
Solve each equation. 3ˣ=243
Answer:
[tex] {3}^{x} = 243 = {3}^{x} = {3}^{5} = 5[/tex]
Which of the following shows the prime factorization of 200 using exponential notation?
02².52
0 23.5²
O8-25
O2-10²
The prime factorization of 200 using exponential notation is [tex]2^3 *5^2[/tex] that is correct option is (b)
First, we decompose the number given on statement by applying prime numbers in ascending order. We see that 200 is an even number, therefore, we infer that smallest prime number within is 2.
1) [tex]200\div2=100[/tex] (Even number)
2) [tex]100\div2=50[/tex](Even number)
3) [tex]50\div2=25[/tex](Even number)
4) [tex]25\div5=5[/tex](Odd number, not a multiple of 3, but a multiple of 5 since last digit is 5)
5) [tex]5\div5=1[/tex](Odd number, not a multiple of 3, but a multiple of 5 since last digit is 5)
Now, we construct the prime factorization using exponential notation:
[tex]200=2^3\cdot5^2[/tex]
The prime factorization of 200 using exponential notation is [tex]2^3\cdot5^2[/tex] that is option (b)
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The prime factorization of 200 using exponential notation is 2^3*5^2 that is correct option is (b)
First, we decompose the number given on statement by applying prime numbers in ascending order. We see that 200 is an even number, therefore, we infer that smallest prime number within is 2.
1) 200/2=100 (Even number)
2) 100/2=50 (Even number)
3)50/2=25 (Even number)
4) 25/5=5 (Odd number, not a multiple of 3, but a multiple of 5 since last digit is 5)
5) 5/5=1 (Odd number, not a multiple of 3, but a multiple of 5 since last digit is 5)
Now, we construct the prime factorization using exponential notation:
200=2^3*5^2
The prime factorization of 200 using exponential notation is 2^3*5^2 that is option (b)
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A contractor purchases 6 dozen pairs of padded work gloves for $89.28 . He incorrectly calculates the unit price at $14.88 per pair for the expense report. What is the correct unit price? Why is the contractor's unit price incorrect?
The correct unit price is $1.24 per pair of padded gloves such that the contractor's unit price is incorrect because total cost was divided by number of dozens bought instead of the number of units in 6 dozens
How many units are in a dozen?
The dozen of pairs of padded gloves contains 6 pairs of padded gloves, in other words, the number of units in 6 dozens is 6 dozens multiplied by 12 units in a dozen
number of units in 6 dozens=6*12
number of units in 6 dozens=72
unit price=total cost/number of units in 6 dozens
unit price=$89.28/72
unit price=$1.24
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Solve the following system of equations. Show all work and solutions.
y = 2x- + 6x + 4
y = -4x- + 4
The system of the equation has x = 0.
The two equations are,
y = 2x + 6x + 4
y = -4x + 4
Now equating the equation, we have
2x + 6x + 4 = -4x + 4
8x + 4 = -4x + 4
12x = 0
x = 0
Therefore the system of the equation has x = 0.
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Find the product. Simplify your answer. 8( – 3v2+2)
Verify -4 x (5+1) = (-4 x 5) + (-4 x 1)
Simplification: -4 x (5+1) = (-4 x 5) + (-4 x 1)
Take LHS,
-4 x (5+1) = -4x6
= -24
Take RHS,
(-4 x 5) + (-4 x 1) = -20 + (-4)
= -20-4
= -24
LHS= RHS
Hence -4 x (5+1) = (-4 x 5) + (-4 x 1) this equation is verified.
The fundamental guidelines and procedures to simplify any algebraic statement are as follows: By multiplying factors, remove any grouping symbols like brackets and parenthesis. If the words contain exponents, use the exponent rule to eliminate grouping. Add or remove like words to combine them.
Start by resolving all of the terms included in parenthesis to simplify mathematical equations using the order of operations. The exponents should then be solved, followed by any necessary multiplication. Division problems are next, followed by adding and subtracting to wrap things out.
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solve the equation 5(2x+1)=25
Answer: x = 2
Step-by-step explanation:
Answer:
x = 2
Step-by-step explanation:
Given equation,
→ 5(2x + 1) = 25
Solving for the value of x,
→ 5(2x + 1) = 25
→ 10x + 5 = 25
→ 10x = 25 - 5
→ x = 20/10
→ [ x = 2 ]
Hence, the value of x is 2.
a) In a field
number of cows: number of sheep = 12:5
Which two of the following statements must be correct about
the sheep and cows in the field?
A there are exactly 5 sheep
B there are more than twice as many cows as there are sheep
C the number of cows is a multiple of 12
D there are 7 more cows than sheep
Since the ratio is 12 : 5, the statement which is true is there are more than twice as many cows as there are sheep.
The ratio between the number of cows to number of sheep in a field is given as:
12 : 5
Now,
let the number of sheep be 5 x.
So, the number of cows will be 12 x.
So, we get that:
12 x > 2 ( 5 x)
12 x > 10 x
So, the statement which is true will be:
there are more than twice as many cows as there are sheep
Therefore, since the ratio is 12 : 5, the statement which is true is there are more than twice as many cows as there are sheep.
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Which value is NOT defined?
(A) tan 0
(B) tan π
(C) tan 3π/2
(D) 1 / tanπ/4
Answer:
(C) tan 3pi/2
Step-by-step explanation:
See image. You can use the Unit Circle to help you find these answers. The Unit Circle looks like scary math chaos pizza, but it really is just a great big giant answer key. It has all the trig answers on it.
(If you use your calculator instead be sure to change it to radian mode.)
See image.
Tangent for any angle is the y/x.
Only tan 3pi/2 is undefined.
At 3pi/2 the x and y are (0,1) so tangent is 1/0 which is undefined.
Find the range of the function y=1/2x+3 when the domian is {-2, 0, 2, 4}
The range of the function y=1/2x+3 when the domain is {-2, 0, 2, 4} is {-1 , 0.33 , 0.14 , 0.090}
The set of all attainable values that qualify as inputs to a operate thought because the domain of the operate, or it may also be outlined because the entire set of values attainable for freelance variables.The domain is outlined because the entire set of values attainable for freelance variables.The vary is found when work the attainable x- values to search out the y-values.The domain of a operate is that the set of values that we have a tendency to are allowed to plug into our operate. This set is that the x values in a very operate like f(x). The vary of a operate is that the set of values that the operate assumes. This set is that the worth that the operate shoots out when we have a tendency to plug Associate in Nursing x value in.We have given a function y = 1/2x+3 .....(1) and domain {-2, 0, 2, 4} .
In order to find the range putting x = -2 in equation (1) , we get
y=1/(2(-2)+3
y=1/-4+3
y=1/-1
y = -1
Putting x = 0 in equation (1) , we get
y=1/2(0)+3
y=1/0+3
y=1/3
y = 0.33
Putting x = 2 in equation (1) , we get
y=1/2(2)+3
y=1/4+3
y = 1 / 7
y = 0.14
Putting x = 4 in equation (1) , we get
y=1/2(4)+3
y=1/8+3
y= 1 / 11
y = 0.090
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Find Victoria's debt to income ratio of her monthly expenses are 1280 and her monthly salary is 2 thousandand 500 express your answer in a decimal
Victoria's debt to income ratio is 0.51 when her monthly expenses are compared to her monthly salary
What is debt to income ratio?
The debt to income ratio compares the monthly expenses(monthly obligations) of Victoria to her monthly salary to determine the portion of her salary that would be used in paying her bills
debt to income ratio=monthly expenses/monthly salary
monthly expense=1280
monthly salary=2,500
debt to income ratio=1280/2,500
debt to income ratio=0.51
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Identify the range of the function shown in the graph. what’s the answer?
Answer:
(- 1 , 1 )
Step-by-step explanation:
Factor the expression. 3 x²+11 x-4
The required factor for the given expression is (x + 4)(3x - 1).
In mathematics, factorization or factoring refers to the process of composing a number or other mathematical object from numerous factors, usually smaller or simpler counterparts.
The given expression is 3x² + 11x - 4.
To factor a general quadratic expression of the form ax² + bx +c, we need to consider the product "ac" and find two factors for this number such that their sum is equal to b. during this case, a = 3, b = 11, and c = -4..
Therefore we need to consider the product ac = 3 × (-4) = -12.
Consider the 2 factors 12 and -1 for the product -12.
Then we have the sum is equal to 12 + (-1) = 12 - 1 = 11.
Therefore the expression 3x² + 11x - 4= 3x² + 12x + (-1)x -4= 3x² +12x - x - 4= 3x(x + 4) - (x + 4)= (x + 4)(3x - 1)
Therefore, the required factor for the given expression is (x + 4)(3x - 1).
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what is 9871 rounded to the nearest ten?
Answer:9870
Step-by-step explanation:
Answer:
Step-by-step explanation:
So we have our 9871
For rounding when a number is four and below if I am remembering correctly you drop the number down. If 5 and up you bump it up to the next number in front of it.
9871
7 = tens
7 > 5
9881
Zalaria
5. For each pair of shapes, decide whether or not Shape A is congruent to Shape B.
Explain your reasoning.
a. First pair:
Answer: Shape A is congruent to Shape B because If you were to rotate one of the two and flip it, it would match.
Step-by-step explanation:
hope it helps :)
Use the Change of Base Formula. What is the value of each expression?
a. log₈32
The value of the expression log₈32 by using the change of base formula is 1.67.
Given that the expression is log₈32.
We are required to find the value of the expression using change of base formula.
The change of base formula is basically used at a time when we have to re-write a logarithm operation as a fraction of logarithms with a new base to find the value of the logarithm.
The result given by it is [tex]log_{a}b[/tex]=log b/log a.
The expression is log₈32.
log₈32=log 32/log 8
=log [tex]2^{5}[/tex]/ log [tex]2^{3}[/tex]
=5log 2/3log 2
=5/3
=1.67
Hence we can say that the value of the expression log₈32 by using the change of base formula is equal to 1.67.
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Two parallel lines are cut by a transversal as shown below.
Suppose m2 = 97°. Find m5 and m<8
Answer: m<8=97 degrees.
m<5=83 degrees
Step-by-step explanation:
m<8=m<2 ==> Angles 8 and 2 are alternate interior angles, meaning that they're equal.
m<8=97 degrees.
m<8+m<5=180 degrees ==> Both angles 8 and 5 add up to a straight line, and straight lines measure 180 degrees and are called straight angles.
97+m<5=180
97-97+m<5=180-97
m<5=83 degrees
find the value of asquare + b square
a-b=7 , ab=8
Answer:
Step-by-step explanation:
As we know that a-b=7 and ab=8(a times b is equal to 8) If we find the factors of 8 we know that 8 times 1 make 8 and if u try 8-1= 7 so 1 squared is 1 and 8 squared is 16 so 16+1=17
Answer:
A = 8
B = 1
A squared + B squared = 65
Step-by-step explanation:
8 - 1 = 7
A - B = 7
8 x 1 = 8
A x B = 8
8 x 8 = 64
1 x 1 = 1
64 + 1 = 65
A squared + B squared = 65
Center = (6,15)
Radius = 2
The equation of the circle where the given parameters are Center = (6, 15) and Radius = 2 is (x - 6)^2 + (y - 15)^2 = 4
How to determine the equation of the circle?The given parameters are
Center = (6, 15)
Radius = 2
Rewrite the above parameters properly as
Center, (h, k) = (6, 15)
Radius, r = 2
The equation of the circle is represented as
(x - h)^2 + (y - k)^2 = r^2
Substitute the known values in the above equation
So, we have
(x - 6)^2 + (y - 15)^2 = 2^2
Evaluate the exponent of 2
So, we have
(x - 6)^2 + (y - 15)^2 = 4
Hence, the equation of the circle where the given parameters are Center = (6, 15) and Radius = 2 is (x - 6)^2 + (y - 15)^2 = 4
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Complete question
Write an equation of the circle with Center = (6,15) and Radius = 2
At a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of 40 minutes and a standard deviation of 4 minutes. what percentage of customers have to wait longer than 49 minutes, to the nearest tenth?
Solving for the probability using the z-table, the percentage of customers that have to wait longer than 49 minutes is 1.2 %.
For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.
First, solve for the z-score using the formula below.
z-score = (x – μ) / σ
where x = individual data value = 49
μ = mean = 40
σ = standard deviation = 4
z-score = (49 - 40) / 4
z-score = (9) / 4
z-score = 2.25
Find the probability that corresponds to the z-score in the z-table. (see attached images)
x = (0.9861 + 0.9893)/2
x = 1.9754/2
x = 0.9877
Subtract it from 1 and multiply by 100 to get the percentage.
% = (1 - 0.9877) x 100
% = 0.0123 x 100
% = 1.23%
% = 1.2 %
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Two sides of a triangle have lengths 5 and 12. Which inequalities represent the
possible lengths for the third side, x?
The inequality that represent the possible length of the third side is
7 < x < 17
According to the triangle inequality theorem, the sum of any two sides of a triangle must be greater than the measure of the third side of the triangle.
We have been given measure of two sides which are 5 and 12. Then the possible length for the third side has two condition
Let the third side be x unit.
First condition, x + 5 > 12
x > 7
Second condition, 12+ 5 > x
17 > x
Hence the inequality that represent the possible length of the third side is
7 < x < 17
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Which situation is represented by the inequality?
7x + 50 > 4x + 100
Responses
A Molly has $50 and Mary has $100. Molly saves $7 per week and Mary saves $4 per week. How long will it be before Molly has more money than Mary?Molly has $50 and Mary has $100. Molly saves $7 per week and Mary saves $4 per week. How long will it be before Molly has more money than Mary?
B Molly has $50 and Mary has $100. Molly saves $4 per week and Mary saves $7 per week. How long will it be before Molly has more money than Mary?Molly has $50 and Mary has $100. Molly saves $4 per week and Mary saves $7 per week. How long will it be before Molly has more money than Mary?
C Molly has $50 and Mary has $100. Molly saves $4 per week and Mary saves $7 per week. How long will it be before Molly and Mary have the same amount of money?Molly has $50 and Mary has $100. Molly saves $4 per week and Mary saves $7 per week. How long will it be before Molly and Mary have the same amount of money?
D Molly has $50 and Mary has $100. Molly saves $7 per week and Mary saves $4 per week. How long will it be before Molly and Mary have the same amount of money?Molly has $50 and Mary has $100. Molly saves $7 per week and Mary saves $4 per week. How long will it be before Molly and Mary have the same amount of money?
The situation which is represented by the inequality (7x + 50 > 4x + 100) is: A. Molly has $50 and Mary has $100. Molly saves $7 per week and Mary saves $4 per week. How long will it be before Molly has more money than Mary?
What is an inequality?An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments:
Less than (<).Greater than (>).Less than or equal to (≤).Greater than or equal to (≥).In this scenario, the number of week for saving money by each person is represented by the variable x. Therefore, the situation which is represented by the inequality (7x + 50 > 4x + 100) is that "Molly has $50 and Mary has $100. Molly saves $7 per week and Mary saves $4 per week. How long will it be before Molly has more money than Mary?"
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The average distance from earth to the moon is approximately 238,855 miles. which expression is the best estimate of this distance? 2 x 105 3 x 105 2 x 106 3 x 106
2 x 10^5 miles is the correct answer.
A power of ten in mathematics is defined as one of the integer powers of a number multiplied by ten. Integers can be both positive and negative. To find the multiple of ten, we need to add 10 to itself several times (if the power is a positive integer).
if we have a value that says ten ^5,
then this value is equal to:
= 10 x 10 x 10 x 10 x 10
= 10,0000
Also, by the definition of a multiple of ten, the number 1 is a power of 10 as well if we take the 0th power of 10.
10^0 = 1
Whatever the integer is, it is multiplied by 10 n times. So, the long form of a power of 10 is the number 1, followed by n zeros, where the n number is greater than the 0 value.
Here the distance that is given to us is:
238,855
We can also write it as,
2 x 10 ^ 5.
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