0.71428571428 as a fraction in simplest form
To express 0.71428571428 as a fraction, we use a geometric series and find that the simplest form is 713/999.
Explanation:To express 0.71428571428 as a fraction in simplest form, we first note that the fractional part of the decimal is 0.71428571428. Since the decimal has a repeating pattern, we can represent it as a fraction using a geometric series. Let x equal the fraction, then we have:
x = 0.71428571428
Multiplying both sides by 10 gives:
10x = 7.1428571428
Subtracting the original equation from the new equation eliminates the repeating part:
10x - x = 7.1428571428 - 0.71428571428
Simplifying, we get:
9x = 6.42857142852
Dividing both sides by 9, we find:
x = 0.71428571428 = 6.42857142852/9 = 713/999
Therefore, 0.71428571428 as a fraction in simplest form is 713/999.
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A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. 648 feet of fencing is used. find the dimensions of the playground that maximize the total enclosed area.
Write the next three terms and write a rule to describe the number pattern. 0.57, 0.66, 0.75, 0.84, . . .
The next three terms in the number pattern 0.57, 0.66, 0.75, 0.84 are 0.93, 1.02, and 1.11. The rule for the pattern is that each term increases by 0.09 from the previous term.
Explanation:The given sequence is: 0.57, 0.66, 0.75, 0.84, ... The step or difference between each consecutive term is 0.09. Therefore, the next three numbers in the sequence would be: 0.84 + 0.09 = 0.93, 0.93 + 0.09 = 1.02, 1.02 + 0.09 = 1.11. So the answer is 0.93, 1.02, 1.11.
The generalized rule for this series is that each term increases by 0.09 from the previous term. In mathematical terms, if we denote the nth term as Tn, then Tn+1 = Tn + 0.09. This rule tells us that the number pattern involves adding 0.09 for each subsequent term in the sequence.
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What's is the radius of a circle with a circumference of 56.5?
Which graph represents the system of inequalities?
y+2<5xy+3x>4y≥2x
Answer:
The correct option is 2.
Step-by-step explanation:
The given system of inequalities
[tex]y+2<5x[/tex]
[tex]y+3x>4[/tex]
[tex]y\geq 2x[/tex]
Inequality (1) can be written as
[tex]y<5x-2[/tex]
The related equation is
[tex]y=5x-2[/tex]
The slope of line is 5 and y-intercept is -2.
The sign of inequality is < , it means related line of inequality (1) is a dotted line and shaded region is below the line.
Inequality (2) can be written as
[tex]y>-3x+4[/tex]
The related equation is
[tex]y=-3x+4[/tex]
The slope of line is -3 and y-intercept is 4.
The sign of inequality is >, it means related line is a dotted line and shaded region is above the line.
Inequality (3) is
[tex]y\geq 2x[/tex]
The related equation is
[tex]y=2x[/tex]
The slope of line is 2 and y-intercept is 0.
The sign of inequality is ≥, it means related line is a solid line and shaded region is above the line.
In the below graph the common shaded region is the solution region.
Therefore the correct option is 2.
Find the value of x. If necessary, round to the nearest tenth.
A. 11.7 in.
B. 9.7 in.
C. 13.7 in.
D. 6.9 in.
Answer:
B. 9.7 in.
Step-by-step explanation:
We have been given an image of a triangle. We are asked to find the value of x.
We will use area of triangle formula to solve our given problem.
[tex]\text{Area of triangle}=\frac{1}{2}\times \text{Base*Height}[/tex]
[tex]47\text{ in}^2=\frac{1}{2}\times x*x[/tex]
[tex]2*47\text{ in}^2=\frac{1}{2}*2\times x^2[/tex]
[tex]94\text{ in}^2=x^2[/tex]
Taking square root of both sides we will get,
[tex]x=\sqrt{94\text{ in}^2}[/tex]
[tex]x=9.6953597\text{ in}\approx 9.7\text{ in}[/tex]
Therefore, the value of x is 9.7 inches and option B is the correct choice.
Find the value of ‘x' and the length of segment ab. if b is between a and c, and ab = 3x – 3 and bc = 4x + 8, and ac = 75, then find the value of ‘x' and ab. answer
To solve for 'x' and the length of segment AB, we use the equation AB + BC = AC, which simplifies to (3x - 3) + (4x + 8) = 75, revealing that 'x' = 10 and the length of AB is 27 units.
Explanation:The question requires us to find the value of 'x' and the length of segment AB given that B is between A and C, with AB = 3x – 3, BC = 4x + 8, and the total length AC = 75. To solve this, we set up an equation using the given lengths of segments AB and BC to equal the total length AC. This gives us the equation AB + BC = AC, which simplifies to (3x – 3) + (4x + 8) = 75.
First, we simplify the equation: 3x + 4x – 3 + 8 = 75, which reduces to 7x + 5 = 75. Subtracting 5 from both sides gives us 7x = 70. Dividing both sides by 7, we find that x = 10. With the value of x, we can find AB by substituting x back into its equation: AB = 3(10) – 3 = 30 – 3 = 27.
Therefore, the value of 'x' is 10 and the length of segment AB is 27 units.
what is 8.525 rounded to 2 decimal place????
two vertices of an isosceles triangle in the coordinate plane have coordinates (0,0) and (2a,0). Where might the third vertex be located?
Decide which of the two points lies on the graph of the line
X= -3
A. 2,-3
B. -3,2
What are the slope and the y-intercept of the linear function that is represented by the equation y=9x-2?
1.)The slope is –2, and the y-intercept is 9.
2.)The slope is 2, and they y-intercept is 9.
3.)The slope is 9, and the y-intercept is –2.
4.)The slope is 9, and the y-intercept is 2.
Answer with explanation:
The equation of line in slope intercept form is :
y= m x +c
Where,m =Slope
c=Y intercept =Distance between origin and point where the line cuts the Y axis
The equation of line is
y= 9 x-2
Comparing with the above equation of line in slope intercept form
Slope =9
Y intercept =2
Option 4
The slope is 9, and the y-intercept is 2.
Explain the axis of symmetry for f(x)=-2(x-4)^2+2
In order from smallest to largest 0.9,75%,4/5
A car recently sold for $32,345. If there's a 6% sales tax on automobile sales, how much tax will be added to the price of the car
Answer:
1940.70
Step-by-step explanation:
1. algebraic expression
2. coefficient
3. constant
4. expression
5. variable
A. the constant preceding the variables in a product
B. a letter or symbol used to represent an unknown
C. a mathematical expression containing one or more variables
D. a numerical value
E. a mathematical phrase that cannot be determined true or false
Answer:3. constant - D. a numerical value
2. coefficient - A. the constant preceding the variables in a product
4. expression -E. a mathematical phrase....
5. variable - B. a letter... representing an unkown
1. algebraic expression - C. a mathematical expression...
hope this helps
Step-by-step explanation:
How many possible solutions are there to a linear equation in one variable?
A valid opinion poll requires random sampling which means
Jonathon created a graph that shows the number of exercises he completes in his workout routine
Which statement summarizes his exercise routine?Jonathon does 3 crunches for every 2 push-ups.Jonathon does 2 push-ups for every 3 crunches.Jonathon does 2 push-ups for every 15 crunches.Jonathon does 15 push-ups for every 2 crunches.
Answer: Hello mate!
in the graph you can see that:
Jonathon does 2 pushups when he does 15 crunches.
then he does 4 = ( 2+ 2) pushups when he does 30 = (15 + 15) crunches
this means that he does 2 pushups more than before, and 15 crunches more than before.
and 6= (2 + 2 +2) pushups when he does 35 =(15 + 15 + 15) crunches.
this, again, means that he does 2 pushups more than before, and 15 crunches more than before.
then you can see that he does 2 pushups for every 15 crunches.
Equation for (1, -6) and (0,3)
7 divided by something = 1204
Which set represents a pythagorean triple (1 point)?
How is multiplying radicals so similar to just simplifying them?
I REALLY NEED HELP 100 POINTS PLEASE ANSWER HONESTLY!!!
9. Is the statement a good definition? If not, find a counterexample. "An airplane is a vehicle that flies."
1 point
10. Write the converse of the following statement. "If you live in the capital of Georgia, then you live in Atlanta."
1 point
11. Write the TWO conditional (if-then) statements that make up the biconditional. "A parallelogram is a figure with two pairs of parallel sides."
2 points
sorry if im wrong
9) yes
10) If you live in Georgia, then you live in Atlanta
11) If three points are collinear, then they are coplanar.
if three points are coplanar, the they are collinear.
What is the value of 5^3? A.125 B.25 C.15 D.8
The perimeter of a rectangular garden is 126 meters. the length is 6 meters longer than twice the width. find the dimensions of the garden
Answer:
Step-by-step explanation:
width - 19m
length - 44m
Which graph represents a function?
Answer:
1st and last one
Step-by-step explanation:
the first and the last one are the only ones that represent a function because for each value of x there is only one corresponding value of y.
A graph represents a function if each value of x corresponds uniquely to a value of y. These graphs, often called line graphs, can depict various types of functions like linear, quadratic, etc. The slope and position of the line will vary depending on the function's formula.
Explanation:
In the subject of Mathematics, specifically when dealing with functions and graphs, a graph represents a function if each value of x corresponds to a unique value of y. This means that different values of x will produce different values of y. Graphs can be produced using specific pairs of (x,y) data points.
These graphs may be named line graphs as they showcase the relationship between two variables: one measured on the horizontal axis (x) and the other on the vertical axis (y). An example could be a function where y = a + bx. If b > 0, the line of the graph slopes upward to the right. If b = 0, the line is horizontal. If b < 0, the line slopes downward to the right.
Graphs may also represent other types of functions like linear, quadratic, inverse, or exponential, depending on the equation of the relation between x and y. It's also important to note that there can be other types of graphs, such as a specific type of line graph shown, where the x-axis consists of data values and the y-axis consists of frequency points.
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In a salsa recipe, the number of tomatoes added is proportional to the amount of salt added. This graph shows the relationship.
What is the unit rate for the number of tomatoes to the tsp of salt?
Answer:
The unit rate for the number of tomatoes to the tsp of salt is 3.
Step-by-step explanation:
Consider the provided graph.
The equation of the line is [tex]y=3x[/tex]
A unit rate is a rate with 1 in the denominator.
Here, the meaning of unit rate is how much tomatoes to the tsp of salt.
As we know the slope intercept form is:
[tex]y = mx + b[/tex]
Where, m is the slope of the line or rate and b is y intercept.
By the comparison we can say that the slope of the line is 3. Here, the denominator is 1.
This shows that 3 tomatoes are added for each teaspoon of salt.
Hence, the unit rate is 3.
The design on Santana’s wall includes 16 pink stripes and 20 green stripes. Find the ratio of pink stripes to green stripes.
The ratio of pink stripes to green stripes on Santana's wall is 4:5.
To find the ratio of pink stripes to green stripes on Santana's wall, we need to compare the two quantities. Santana has 16 pink stripes and 20 green stripes. The ratio can be simplified by finding the greatest common divisor of the two numbers and then dividing both by that number to find the simplest form.
In this case, the greatest common divisor of 16 and 20 is 4. We divide both numbers by 4 to simplify the ratio:
16 / 4 = 4
20 / 4 = 5
Therefore, the simplified ratio of pink stripes to green stripes is 4:5.
2/3 x 5/7 =? A. 7/10 B. 14/15 C. 10/21 D. 7/21
HELP ME
2/3 * 5/7 =
multiply the 2 top numbers and then the 2 bottom numbers
2*5 =10
3*7 = 21
so you get 10/21
answer is C
Identify the relative minimum point of the graph. Select all that apply.