The justification for each step in the solution of the equation (5x−4)/2=2x−1 is:
Step 1: (5x-4)/2 = 2x-1 (As Given)
Step 2: ((5x-4)/2) × 2 = 2 × (2x-1)
The Multiplication Property of Equality asserts that when both sides of an equation are multiplied by the same number, the two sides remain equal.
Step 3: (5x-4) = 4x-2
The Distributive Property of Equality asserts that equality holds after distributing by multiplication.
Step 4: 5x - 4 + 4 = 4x - 2 + 4
The Addition Property of Equality states adding the same number on both sides of an equation yields equivalent results.
⇒ 5x = 4x + 2
Step 5: 5x - 4x = 4x + 2 - 4x
The Subtraction Property of Equality states that you can get an equivalent equation by subtracting the same integer from both sides of an equation.
⇒ x = 2
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According to the solving each step in the solution of the equation (5x−4)/2=2x−1 is:
Step 1: (5x-4)/2 = 2x-1
Step 2: ((5x-4)/2) × 2 = 2 × (2x-1)
Step 3: (5x-4) = 4x-2
Step 4: 5x - 4 + 4 = 4x - 2 + 4
Step 5: 5x - 4x = 4x + 2 - 4x
What are the four mathematical equality properties?The four properties of equality—addition, subtraction, multiplication, and division—can be used to solve an equation. To get the value of an equation's unknown variable, we can easily add, subtract, multiply, or divide the two sides of the equation.
According to the given equation:(5x-4)/2 = 2x-1 (As Given)
((5x-4)/2) × 2 = 2 × (2x-1)
According to the Multiplication Property of Equality, an equation's two sides stay equal even after being multiplied by the same number.
Step 3: (5x-4) = 4x-2
According to the distributive property of equality, multiplicative distribution still maintains equality.
Step 4: 5x - 4 + 4 = 4x - 2 + 4
According to the Addition Property of Equality, an equation produces equivalent outcomes when the same integer is added to both sides.
⇒ 5x = 4x + 2
Step 5: 5x - 4x = 4x + 2 - 4x
According to the "Subtraction Property of Equality," subtracting the same number from both sides of an equation will result in an identical equation..
⇒ x = 2
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question the radius of a circle is decreasing at a constant rate of 0.1 centimeter per second. in terms of the circumference c, what is the rate of change of the area of the circle, in square centimeters per second?
The rate of the area of the circle, expressed in terms of the circumference C, is 0.1C square centimeters per second.
What is known as a circle?
A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the center.C=2πr
A=πr²
dA/dr=2πr=C
dr/dt=-0.1 cm/sec
dA/dt
= dA/dr * dr/dt
= 2πr (-0.1) cm²/s
= -0.1C cm²/s
As a result, a circle's radius is reducing at a steady rate of 0.1 centimeters each second. The rate of the area of the circle, expressed in terms of the circumference C, is 0.1C square centimeters per second.
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Tyreke has $5000 to put into an account that earns compound interest. Which of the following is the BEST advice you can offer so that he can maximize interest?
The BEST advice you can offer so that he can maximize interest is : b Deposit your money as early as possible in an account with the highest interest rate possible.
What is compound interest?Compound interest can be defined as the interest a person earn on the money they saved in their account as well as the money earn on the interest the bank gives them which implies that a person tend to earn interest on the money saved and the interest giving on the money saved.
A person can tend to earn more interest when they deposit their money earlier into an account that pay more interest rate as this will enables them to accumulate more interest.
Therefore the correct option is b.
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The complete question is:
Tyreke has $5000 to put into an account that earns compound interest. Which of the following is the BEST advice you can offer so that he can maximize interest?
a. It's ok to open an account with a low interest rates as long as you deposit your money early
b. Deposit your money as early as possible in an account with the highest interest rate possible
c. Wait for interest rates to rise above 5%, otherwise compounding doesn't have any effect
d. Compound interest will not have any effect at such a low dollar amount. Find different opportunities to earn interest on your savings.
determine the average rate of change, in mph, from 2 to 4 hours on the graph shown below
Answer:
maybe, probably 20mph
Step-by-step explanation:
The average rate of change is equal to 10 miles per hour.
What is the average rate of change?It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.
Given that the function is changing from point (30,2) to (20,1). The average rate of the change will be calculated as,
The average rate of change = ( 30 - 20) / ( 2 - 1)
Average rate of change = 10 miles per hour
Therefore, the average rate of change is equal to 10 miles per hour.
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is 1over2xsquared - 7y a polynomial? if it is a polynomial, state the degree of the polynomial
The expression 1/(2x²) - 7y is not a polynomial because it has a negative exponent
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
A polynomial is an expression that involves only the operations of addition, subtraction, multiplication, and positive exponent powers of variables. If the expression has a negative exponent, it is not a polynomial.
Given:
1/(2x²) - 7y = 0.5x⁻² - 7y
1/(2x²) - 7y is not a polynomial
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Rewrite 7 − 8 using the additive inverse and display the new expression on a number line.
Answer: A.)
Step-by-step explanation: if you start at 7 and take 8 away your left with a negative
A is correct purple line to 7 and red line to -1
Hope this helps
Any blank on a line is a blank of the equation
Answer:
Yeah
Step-by-step explanation:
but i can also do it in opposite
6. Ron pays 6 payments of $4 each to a game store. He returns one game and receives
$10 back. What is the change to the amount of money she has?
The change to the amount of money she has = $10
what is amount ?
Amount is defined as to add up to a total .the bill for four people at a restaurant that is 50 dollars is an example of the costs of four meals that amount to 50 dollars.
A amount is a number, or quantity of something
she made 6 payments of $4each = 6(4) =$ 20 spent
she got $ 10 back = 20-10 =$10
the change to the amount of money she has is -$10 because
she has $10 less than she started with
so the change to the amount of money she has $10
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In trapezoid abcd with the legs ab and cd, point o is the intersection of the diagonals. Is the area of triangle abo =6in,find area if triangle cod
the area of triangle cod is 6 sq. inch
what is trapezoid ?A trapezoid is also as a trapezium, is a flat closed shape having 4 straight
sides, with one pair of parallel sides . a trapezium can also a parallel legs .
Point O (the point of intersection of diagonals )divides two diagonals AC and BD into parts that are proportional:
AO/CO = DO/BO
Then AO x BO = CO xDO
Consider triangle ABO. The area of this triangle is
Aabo = 1/2 x AO x BO x sin ∠AOB
Consider triangle COD. The area of this triangle is
Acod = 1/2 x CO x DO x sin ∠COD
Since AO x BO = CO x DO and angles AOB and COD are congruent as vertical angles
Acod = 1/2 x BO x AO x sin ∠ AOB = Aaob = 6. inc.sq.
hence ,
the area of traiangle cod is 6 sq. inc.
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An item costs $490 before tax, and the sales tax is 39.20. Find the sales tax rate
Answer:8%
Step-by-step explanation:
Expand and simplify (x+3)(2x-1)(x+4)
The expansion and simplified form of the expression [(x+3)(2x-1)(x+4)] will be (2x³ + x² - 25x - 12).
As per the question statement, we are provided with the expression of [(x+3)(2x-1)(x+4)] where three separate factors of the variable "x" are multiplied with each other.
We are required to expand and simplify the above-mentioned expression to obtain our desired answer.
Given, [(x + 3)(2x - 1)(x + 4)]
= [{(x + 3)*(2x - 1)}(x + 4)]
= [{(x*2x) - (x*1) + (3*2x) - (3*1)}(x + 4)]
= [(2x² - x - 6x -3)(x + 4)]
= [(2x² - 7x -3)(x + 4)]
= [(2x²*x) + (2x²*4) - (7x*x) - (7x*4) - (3*x) - (3*4)]
= [2x³ + 8x² - 7x² - 28x - 3x - 12]
= [2x³ + (8x² - 7x²) - (28x + 3x) - 12]
= (2x³ + x² - 25x - 12)
Expression: Expressions are mathematical statements that have two or more terms containing numbers or variables, or both, connected by operators in between.To learn more about Expressions, click on the link below.
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A brave leaves home and travels four blocks east then two blocks south and three blocks west how many blocks has he travel
Answer:
he has travelled nine blocks
Step-by-step explanation:
four blocks + two blocks + three blocks
=nine blocks
Janelle and Samantha are at an arcade. Janelle scored 83,452 points on a video game. Samantha scored 59,237 points on the same game. How many more points did Janelle score than Samantha?
what is 1 5/8 and 5/6 as a decimal? and more importantly, do i have to turn it into a bar notation?
what is the 7th term of sequence -4,16,-64,256,-1,024
Answer:
a,b,coeiiggjfj
jrjjunr
Nine months ago Alexa deposited 5,000 in a three year CD. She has received $124.16 in interest. She withdraws $500. This is before the CD matures, so she pays a $250 penalty. What is her balance after the withdrawal and fee(s)?
Step-by-step explanation:
my name is my name is mikiyas
What is the conjecture? 1,1,2,3,5,8 _, _, _, _, _,
Answer:
13, 21, 34, 55, 89 are the next five numbers in the sequence.
Step-by-step explanation:
It's known as the Fibonacci sequence. Every term is the sum of the previous two. If you add the terms of the sequence then the result of each of the sums will form a sequence as well. For this sequence 1+1=2, 2+3=5, 5+3=8, 8+5=13, 13+8=21, 21+13=34, 34+21=55, 55+34=89 and so on.
If two times a number is decreased by 8, the result is 5 more than the number.
Choose the equation that could be used to find this number, x.
Answer:
Step-by-step explanation:
equation: 2x-8=5x
x=-8/3
Suppose you have a population with mean 25 and standard deviation 20. You take samples of size 100 and consider the distribution of the means of those samples. What is the mean of the sample means?.
The value of the z-score for the sample mean is estimated as 0.5.
What is meant by the term z-score?A Z-score is a statistical assessment that explains a value's relationship to a mean of a group of values. The Z-score is measured in aspects of standard deviations from a mean. A Z-score of zero indicates that the information point's score is the same as the mean score.As per the stated question;
The formula for calculating the z-score is;
z = (x - μ)/σ
x = sample size
μ = population mean
σ = standard deviation population.
The vales given in the question;
μ = 25σ = 20x = 35Substitute the value in the z-score.
z = (35 - 25)/20
z = 10/20
z = 0.5
Thus, the value of the z-score for the sample mean is estimated as 0.5.
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The correct question is-
Suppose you have a population with mean 25 and standard deviation 20. You take samples of size 100 and consider the distribution of the means of those samples. What is the z-score for the of the sample means for the sample less than 35?.
A company installs triangular pools at hotels. All of the pools are congruent and triangle JKL is congruent to triangle MNP in the figure. What is the perimeter of each pool?
The perimeter of each pool is 92 ft.
What is perimeter?
A perimeter is a closed route that covers, surrounds, or outlines a two-dimensional form or length. The circumference of a circle or an ellipse is its perimeter.
Given, the triangles are congruent so,
20x-15 = 15x+15
=> 20x-15x = 15+15
=> 5x = 30
=> x = 30/5 = 6
Therefore, perimeter = (4x-4) + (5x+1) + 41
= (4x6 - 4) + (5x6 + 1) + 41
= 20 + 31 + 41
= 92
Hence, the perimeter of each pool is 92 ft.
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what are the coordinates of the roots of the equation 3+2x-x^2=0?
The coordinates of the roots of the equation 3+2x-x^2=0 is (- 1, 0 ) and (3, 0 ).
What is a quadratic equation?A quadratic equation can be described as the algebraic equation that posses the second degree of x which can be seen in the form of ax2 + bx + c = 0 and this can be followed in solving the equation.
We were given:
3+2x-x^2=0
This equation can be re arranges as :
-x^2 + 3+2x=0
This can be factorized as :
(x + 1)(x - 3)
Hence the coordinates of the roots can then be written as (- 1, 0 ) and (3, 0 ).
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Twice a number t decreased by eight equals seventy.
EARNINGS The graph shows the amount of money Ryan
earns. Use the graph to estimate the x- and y-intercepts of
the function, where the function is positive and negative,
and interpret the meanings in the context of the situation.
The most appropriate choice for equation of line in slope intercept form will be given by-
x intercept = 0 and y intercept = 0
This means that if Ryan do not work at all, he will not be paid.
The graph is positive throughout
This means to get paid, Raid will have to spend some time doing .
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Here,
x intercept = 0 and y intercept = 0
This means that if Ryan do not work at all, he will not be paid.
The graph is throughout positive.
This means to get paid, Raid will have to spend some time doing .
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A cell phone company charges a monthly fee plus $0.25 for each text message. The monthly fee is $30.00 and you owe $59.50. Write and solve an equation to find how many text messages x you had.
Answer:
x = 118 text messages
Step-by-step explanation:
Since the total cost of $59.50 is comprised of the flat fee of $30 plus $0.25 for each text message, we can write
$59.50 = $30 + $0.25x
$29.50 = $0.25x
x = 118 text messages
(EASY POINTS)
What is the measure of an exterior angle of a regular octagon?
(Read carefully)
The measure of an exterior angle of a regular octagon is 45 degrees
What are angles?Angles are formed when two or more lines intersect.
This in other words means that angles is the measure of space between the intersection of rays or lines
How to determine the measure of the exterior angle?The given parameters are:
Shape: regular octagon
A regular octagon has 8 sides, and the total sum of angles is 360
So, we have
Exterior angle = Total sum of angles/Number of sidee
This gives
Exterior angle = 360/8
Evaluate the quotient
Exterior angle = 45
Hence, the measure of the angle is 45 degrees
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The area of a rectangular yard is 5,063 square feet and its length is 61 feet. What is its width? Explain or show your reasoning.
The points X, Y, and Z are on the same directed line segment XYZ. The ratio of XY:XZ is 2:3. If point X is located at (6,10) and point Y is located at (-1,8), what are the coordinates of point Z?
The coordinates of Z are (-11.5, 5)
What is section formula?When a point on a line segment divides it into two segments, the formula used to determine the coordinates of that point is known as the section formula. Let us say, we have a point P(x,y) that divides the line segment with marked points as A (x1,y1) and B(x2,y2). To find the coordinates, we use the section formula, which is mathematically expressed as:
P(x, y) = (m[tex]x_2[/tex] + n [tex]x_1[/tex] / m+ n, m [tex]y_2[/tex] +n[tex]y_1[/tex] /m+ n)
Given coordinates:
XY:XZ is 2:3
X is located at (6,10) and Y is located at (-1,8).
let the coordinates of Z(x, y)
using section formula
-1 = (2x + 18)/ 5
-5 = 2x +18
2x = -23
x= -11.5
and, 8 = 2y + 30 /5
40 = 2y + 30
2y= 10
y=5
Hence, the coordinates of Z are (-11.5, 5)
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Find all the integer solutions of each system of inequalities.
The integer solutions of the system of inequalities are x >= 1 and b <= 0
What are inequality expressions?Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal
What are the integer solutions of the system of inequalities expressions?System of inequalities 1
Here, we have
3 - 18x < 0
0.2 - 0.1x > 0
Rewrite as
0 < 0.2 - 0.1x
The above means that
3 - 18x < 0.2 - 0.1x
Collect the like terms
So, we have
3 - 0.2 < 18x + 0.1x
Evaluate the like terms
So, we have
2.8 < 18.1x
Divide both sides by 18.1
So, we have
0.155 < x
Rewrite as
x > 0.155
The integer value greater than 0.155 is at least one
Hence, the integer solution of the system is x >= 1
System of inequalities 2
Here, we have
6 - 4b > 0
3b - 1 > 0
The above means that
6 - 4b > 0 < 3b - 1
Collect the like terms
So, we have
-4b > - 6 + 0 + 1< 3b
Evaluate the like terms
So, we have
-4b > -5 < 3b
Solve for b
b < -1.25 or -1.67 < b
The integer values in this case are 0
So, we have
b <= 0
Hence, the integer solution of the system is b <= 0
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what is the circumference if the diameter is 10/pi
Answer:
31.42cm
Step-by-step explanation:
We know that C = πd. Since the diameter is 10cm, we know that C = π x 10cm = 31.42cm (to 2 decimal places).
Answer:
31.42 centimeters.
Step-by-step explanation:
Are we in the same class? I had this same question and its due.
I got 165 but it says it wrong ?
help with this question
The surface area of the given pyramid is equivalent to 760 square inches.
Surface area of a pyramidThe surface area of a figure is the sum of the area of the surfaces of such figure.
The given pyramid is made up of 5 big rectangles and 2 small rectangles
Surface area = Area of 4 large rectangles + 2(area of small rectangles)
Surface area = 2(22 * 10) + 2(22 * 5) + 2(10 * 5)
Surface area = 440 + 220 + 100
Surface area = 760 square inches
Surface area = 760 square inches
Hence the surface area of the rectangular based pyramid is 760 square inches
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