Converting a Repeating Decimal into a Fraction

Answer:

How could the intersection of the graphs of the two equations be located on a coordinate grid?

-From the origin, move three units right and nine units up

What does the solution to a system of two linear equations mean on a graph?

-The point of intersection of the two lines

Can you have more than one solution to a system of linear equations?

-Yes, if both lines are the same exact line

Can you have exactly two solutions to a system of linear equations?

-No, because lines are straight

Can you have no solutions to a system of linear equations?

-Yes, if the lines are parallel

Step-by-step explanation:

Please look at the images attached. Sorry for the bad handwriting, I'm on a computer.

Basically, a linear system of equations has one solution if the equations yield two lines that intersect exactly once.

A linear system of equations has no solutions if the lines are parallel, because they will never intersect.

A linear system of equations has infinite solutions if the system of equations yields two lines that are the same, because they will forever intersect.

If you have any questions about these answers, please tell me in the comments below my answer. I'll be happy to answer them :)

You would need to reach home plate in 1.02 seconds before the ball reaches the catcher.

we need to convert the speed from mph to feet per second, since the distance is given in feet.

40 mph = 58.7 feet per second (rounded to one decimal place)

To calculate the time it takes to get from 3rd base to home plate, we can use the formula:

time = distance / speed

Plugging in the given values, we get:

time = 60 feet / 58.7 feet per second

time = 1.02 seconds

Therefore, you would need to reach home plate in 1.02 seconds before the ball reaches the catcher.

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Answer:

45.75 mph

Step-by-step explanation:

Let's call Sonya's speed before the rest stop "x" (in miles per hour). Then, we know that her speed after the rest stop was "x-5" miles per hour.

We can use the formula: distance = speed x time, to set up two equations based on the given information:

Equation 1: 170 = x * t1 (where t1 is the time Sonya drove before the rest stop)

Equation 2: 320 = (x-5) * (t1+3) (where t1+3 is the time Sonya drove after the rest stop)

We can solve for t1 in Equation 1 by dividing both sides by x:

t1 = 170/x

Now we can substitute this expression for t1 into Equation 2 and simplify:

320 = (x-5) * (170/x + 3)

320 = 170(x-5)/x + 3(x-5)

Multiplying both sides by x gives:

320x = 170(x-5) + 3x(x-5)

320x = 170x - 850 + 3x^2 - 15x

Simplifying and rearranging terms gives a quadratic equation:

3x^2 - 165x + 850 = 0

We can solve for x using the quadratic formula:

x = [165 ± sqrt(165^2 - 4(3)(850))] / (2*3)

x = [165 ± sqrt(27225 - 10200)] / 6

x = [165 ± sqrt(17025)] / 6

x = [165 ± 130.5] / 6

x = 45.75 or x = 9.25

We can ignore the solution x = 9.25 since it doesn't make sense in the context of the problem (Sonya's speed cannot be negative). Therefore, Sonya's speed before the rest stop was 45.75 miles per hour

The probability of rolling a number other than 1 on a standard number cube is 5/6.

When rolling a standard number cube, there are six equally likely outcomes, one for each face of the cube. To find the probability of rolling a number other than 1, we need to determine the number of              favorable outcomes and divide it by the total number of possible outcomes.

In this case, the favorable outcomes are rolling any number from 2 to 6, which gives us five possibilities. Therefore, the probability of rolling a number other than 1 is 5 out of 6.

Expressing this as a fraction, the probability can be written as 5/6. This means that out of all the possible outcomes, there is a 5/6 chance of rolling a number that is not 1.

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The general equation is y=mx+b

where m is the slope and b is the y intercept.

So substitute the m and the b for the equation.

m=2, b = 5 : y = 2x+5

m=3 b = 5: y = 3x + 5

m = 5 b = 4: y = 5x + 4

The equation of the circle with radius 9 and center ( -1,-8 ) is( x + 1 )² + ( y + 8  )² = 81.

The standard form equation of a circle with center (h, k) and radius r is:

( x - h )² + ( y - k )² = r²

Given that the circle has a center of (-1, -8) and the radius is 9.

Hence; from the standard form of the equation of the circle:

Center ( h , k ) = ( -1, -8 )

h = -1

k = -8

And radius r = 9

Plug these values into the above formula and simplify.

( x - h )² + ( y - k )² = r²

( x - ( -1 ) )² + ( y - ( -8 ) )² = 9²

Simplify

( x + 1 )² + ( y + 8  )² = 81

Therefore, the equation of the circle is ( x + 1 )² + ( y + 8  )² = 81.

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Based on the Supermarkets Agreement 2012, the normal weekly pay for an adult aged 21 and over is $565.90.

The wage rates for a junior employee are based on a percentage of the adult rate, but the exact percentage is not provided. Therefore, it is impossible to determine how many people aged 16 and under 17 years can be employed for the same cost as one adult employee without knowing the specific percentage and calculating the wages accordingly  Based on the Supermarkets Agreement 2012, the normal weekly pay for an adult aged 21 and over is $565.90. To determine how many people aged 16 and under 17 years can be employed for the same cost as one adult employee, we need to know the percentage of the adult rate for junior employees. Once we have that information, we can calculate the number of junior employees that can be employed for the same cost as one adult employee.

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Answer:

5

Hope this helps!

Step-by-step explanation:

Plug in m = 1 into the equation.

m = 1  :  [tex]\frac{4}{m} +1[/tex]  =>  [tex]\frac{4}{(1)} +1[/tex] = 4 + 1 = 5

The equation of L2 is y = 2x/3 + 23/3.

The equation of L3 is y = -3x/2 - 7.

The equation of L2 in standard form is 2x/3 - y = -23/3.

The x and y intercepts of L3 are (-4.667, 0) and (0, -7) respectively.

The point of intersection between L2 and L3 is (-6.769, 3.154).

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

Based on the information provided about line 1 (L1) and line 2 (L2), we have the following equation;

Equation of line 1 (L1): 3x + 2y = 12

y = -3x/2 + 12

Since line L2 is perpendicular to L1 at (2, 9) and a slope of 2/3, the equation of L2 can be calculated as follows;

y - y₁ = m(x - x₁)

y - 9 = 2/3(x - 2)

y = 2x/3 + 23/3

Since L3 is parallel to L1 and passes through point (-4, -1), the equation of L2 can be calculated as follows;

y - y₁ = m(x - x₁)

y + 1 = -3/2(x + 4)

y = -3x/2 - 6 - 1

y = -3x/2 - 7

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a. The z-score for a value of 25 is -0.57, to the nearest hundredth.

b. The percent of the data is greater than 34 is about 2%.

To find the z-score for a value of 25, we can use the following formula;

z = (x - μ) /σ

where;

z = (25 - 27) / 3.5

z = -0.57

Rounding to the nearest hundredth, we get the z-score of -0.57.

The z-score for x = 34 is calculated as follows;

z = (x - μ) / σ

z = (34 - 27) / 3.5

z = 2

Using a standard normal distribution table, we find that the percentage of data that is greater than 34 = 2.28%.

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It is true that the functions f(x) and h(x) share a common x-intercept.

On the definition of a function, the x-intercept is given by the value/values of x for which the function assumes a value of zero.

Function f(x) is defined as follows:

x² + 4x.

Hence the x-intercepts are obtained as follows:

x² + 4x = 0

x(x + 4) = 0

x = 0 and x + 4 = 0 -> x = -4.

On a graph, the x-intercept of a function is the value of x at which the graph of the function crosses the x-axis.

Hence the x-intercept of function h(x) is given as follows:

x = -4.

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The resulting image of Triangle ABC after reflecting it across the line y=-x and rotating it 90 degrees clockwise is Triangle A''B''C'' with vertices at (2, 3), (1, 4), and (5, 1).

To find the resulting image of Triangle ABC after reflecting it across the line y=-x and rotating it 90 degrees clockwise, we can follow these steps:
1. Draw Triangle ABC and the line y=-x on a coordinate plane.
2. Reflect Triangle ABC across the line y=-x to get its image, Triangle A'B'C'.
3. Draw the image Triangle A'B'C' on the coordinate plane.
4. Rotate Triangle A'B'C' 90 degrees clockwise around the origin to get its final image.
5. Draw the final image of Triangle ABC, which is Triangle A''B''C''.
To find the coordinates of the image points, we can use the transformation rules for reflections and rotations.
First, let's find the image points after reflecting Triangle ABC across the line y=-x:
- The point A(-2, 3) is reflected to the point A'(-3, 2) by swapping the x and y coordinates and changing their signs.
- The point B(4, 1) is reflected to the point B'(-1, -4) by swapping the x and y coordinates and changing their signs.
- The point C(1, 5) is reflected to the point C'(-5, -1) by swapping the x and y coordinates and changing their signs.
Now, let's find the image points after rotating Triangle A'B'C' 90 degrees clockwise around the origin:
- To rotate a point (x, y) 90 degrees clockwise around the origin, we can use the formulas (-y, x).
- Applying this formula to each image point, we get:
 - A''(2, 3)
 - B''(1, 4)
 - C''(5, 1)
Therefore, the resulting image of Triangle ABC after reflecting it across the line y=-x and rotating it 90 degrees clockwise is Triangle A''B''C'' with vertices at (2, 3), (1, 4), and (5, 1).

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The water level in the aquarium will rise by 18 cm.

The volume of water in the aquarium before adding the sand is given by:

Volume = (1/2) x 23 cm x 15 cm = 172.5 cm³

When the sand is added, its volume is 2350 cm³. Therefore, the new volume of water and sand in the aquarium is:

 = 172.5 cm³ + 2350 cm³

 = 2522.5 cm³

Let h be the height of the water level after adding the sand. The new volume of water in the aquarium is given by:

Volume = (1/2) x 23 cm x 15 cm x h

Setting this equal to the new total volume, we can solve for h:

(1/2) x 23 cm x 15 cm x h = 2522.5 cm³

h = 2522.5 cm³ / (1/2 x 23 cm x 15 cm) = 18 cm

Therefore, the water level in the aquarium will rise by 18 cm.

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The population of the patch land in 50 years is given as follows:

13,547.

An exponential function has the definition presented as follows:

[tex]y = ab^\frac{x}{n}[/tex]

In which the parameters are given as follows:

The parameter values in this problem are given as follows:

a = 42, b = 2, n = 6.

Hence the function for the population after x years is given as follows:

[tex]y = 42(2)^\frac{x}{6}[/tex]

The population in 50 years is given as follows:

[tex]y = 42(2)^\frac{50}{6}[/tex]

y = 13,547.

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The subtraction of the two matrix is   [31    6     12    -14     57 ]

                                                               [-19  -27  -18     18     27 ]

                                                               [ 47    14     -1    -40     9 ]

                                                               [10     12    -19    -15   -58]

                                                               [-14   -23    10     4       19]

The subtraction of the two matrix is calculated as follows;

The result to 4 multiplied by D is calculated as;

4[D] = [28   -24    12    -32     -36]

        [8      -36   -24     24      36]

        [32     8      20     -40     -12]

        [40   -12      -16    12     - 28]

        [4      -8       16     -20     -8 ]

The result to 3 multiplied by B is calculated as;

3[B] = [-3    -30  -24   -18     21]

        [27    -9    -6      6       9]

        [-15    -6    21     0      -21]

        [30    -24   3    27      30]

        [18     15     6   -24     -27]

The subtraction of the two matrix is calculated as follows;

4[D] - 3[B] =  [31    6     12    -14     57]

                   [-19  -27  -18     18     27 ]

                   [ 47    14     -1    -40     9 ]

                   [10     12    -19    -15   -58]

                   [-14   -23    10     4      19]

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The length of segment WK is given as follows:

B. [tex]2\sqrt{5}[/tex]

Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].

The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The endpoints of the segment in this problem are given as follows:

K(-2,0) and W(-6,-2).

Hence the length of the segment is given as follows:

[tex]\sqrt{(2 - (-6))^2 + (0 - (-2))^2} = \sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5}[/tex]

Meaning that option B is the correct option in the context of this problem.

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The proportion is solved and value of a = 9 and constant is k =45

Given data ,

If a is inversely proportional to b, it means that their product remains constant

a * b = k

where "k" is the constant of proportionality.

Given that a = 1.5 when b = 30, we can substitute these values into the equation:

1.5 * 30 = k

k = 45

Now, we can use the value of k to determine the value of "a" when b = 5:

a * 5 = 45

Dividing both sides by 5:

a = 45 / 5

a = 9

Hence , proportionality constant is k = 45 and when b = 5, the value of "a" is 9

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The ratio which represents the ratio of paperback books to hardcover books is 6 : 5.

Given that,

Michelle had 6 paperback books and 5 hardcover books on the shelf by her bed.

We have to find the ratio of the paperback books to hardcover books.

We have,

Number of paperback books = 6

Number of hardcover books = 5

We need to find the ratio of the paperback books to hardcover books.

Ratio = Number of paperback books / Number of hardcover books

         = 6/5

Hence the ratio is 6/5.

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Answer:

6 small baskets

Step-by-step explanation:

Ms smith has decided to split 45 apples among 5 learners. So, 45/5=9 apples.

However, she realizes only 8 apples can be held in a small basket, She will need to use at least two baskets to give 9 apples to each learner.

So, the number of baskets required can be calculated as:

45 apples ÷ 8 apples per basket = 5.625 baskets

Since we can't use a fraction of a basket, 5.625 is approximately equal to 6.

Therefore, Ms. Smith will need 6 small baskets to divide the apples equally among her learners

We can see here that the 90% confidence interval will be: 420.2 to 585.8.

An interval of values known as a confidence interval is one that is likely to include the real value of a population parameter. A confidence interval of 95%, for instance, indicates that there is a 95% likelihood that the population parameter's real value falls inside the interval.

We will find the sample mean first:

Sample mean = sum of data points / number of data points

Sample mean = 8551 / 17 = 503

Then the standard error will be:

Standard error = population standard deviation / square root of number of data points

Standard error = 190 / √(17) = 41.7

Confidence interval = Sample mean ± 1.645 × standard error.

where 1.645 is the z-score for a 90% confidence interval.

Confidence interval = 503 ± 1.645 * 41.7 = 420.2 to 585.8

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Answer: Most Data takes 10 seconds to download. (sorry if this answer is very vague its hard to explain)

The nearest Whole percent, the percent increase of women students is approximately 21%.

The percent increase of women students, we need to compare the number of women students in 2005 and 2006.

In 2005, the number of women students was 123.

In 2006, the number of women students was 149.

To find the increase, we subtract the initial value (2005) from the final value (2006):

Increase = Final Value - Initial Value

Increase = 149 - 123

Increase = 26

Next, we need to calculate the percent increase. The percent increase is given by the formula:

Percent Increase = (Increase / Initial Value) * 100

Plugging in the values:

Percent Increase = (26 / 123) * 100

Calculating the percent increase:

Percent Increase ≈ 21.14%

Rounding to the nearest whole percent, the percent increase of women students is approximately 21%.

Therefore, the answer is 21%.

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Answer:

  x = -5 2/3

Step-by-step explanation:

You want the solution to the rational equation ...

  (x+5)/(x+8)=1+(6)/(x+1)

Casting this into the form f(x) = 0, we have ...

  [tex]\dfrac{x+5}{x+8}=1+\dfrac{6}{x+1}\\\\\\1-\dfrac{3}{x+8}=1+\dfrac{6}{x+1}\\\\\\\dfrac{6}{x+1}+\dfrac{3}{x+8}=0\\\\\\\dfrac{3(2(x+8)+(x+1))}{(x+1)(x+8)}=0\\\\\\3x+17=0\qquad\text{the numerator is zero when the fraction is zero}\\\\\\\boxed{x=-\dfrac{17}{3}}[/tex]

__

Additional comment

The attachment shows the left side and right side expressions are equal when x = -17/3 = -5 2/3.

<95141404393>

Applying the tangent and the circle theorems, we have:

22. x ≈ 9.4;   23. Perimeter of triangle GHI = 168 units

24. m<NSR = 110°;    25. x = 10

22. Based on the tangent theorem, the triangle is a right triangle since the line is tangent to the radius of the circle. Therefore, based on the Pythagorean theorem, we have:

x = √[(7.4 + 4.6)² - 7.4²]

x ≈ 9.4

23. JH and HK are tangents, therefore they are equal. Thus:

7x + 4 = 13x - 20

7x - 13x = -4 - 20

-6x = -24

x = 4

Perimeter = GI + GJ + JH + HK + KI

GI = 52

HK = JH = 7x + 4 = 7(4) + 4 = 32

KI = 15

GJ = 52 - 15 = 37

Perimeter of triangle GHI = 52 + 37 + 32 + 32 + 15 = 168 units

24. Based on the angle of intersecting chords theorem, we have:

m<NSR = 1/2(170 + 50)

m<NSR = 110°

25. Based on the inscribed angle theorem, we have:

2(4x - 5) + 290 = 360

Solve for x:

8x - 10 + 290 = 360

8x = 360 - 280

8x = 80

x = 10

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Answer:

Step-by-step explanation:

This is a triangle with sides 15.2 cm, 6.6 cm, and 15.6 cm. To solve for the angles, we can use the Law of Cosines:

c^2 = a^2 + b^2 - 2ab cos(C)

where a = 6.6 cm, b = 15.6 cm, c = 15.2 cm, and C is the angle opposite side c.

Using this formula, we can solve for the cosine of angle C:

cos(C) = (a^2 + b^2 - c^2) / 2ab

cos(C) = (6.6^2 + 15.6^2 - 15.2^2) / (2 * 6.6 * 15.6)

cos(C) = 0.748

Taking the inverse cosine of 0.748, we get:

C = 41.5 degrees

To find the other angles, we can use the Law of Sines:

a/sin(A) = b/sin(B) = c/sin(C)

Using this formula, we can solve for angle B:

sin(B) = (b/sin(C)) * sin(A)

sin(B) = (15.6/sin(41.5)) * sin(A)

sin(B) = 0.614 * sin(A)

Using the fact that sin(A) + sin(B) + sin(C) = 1, we can solve for sin(A) and sin(B):

sin(A) = (sin(C) - sin(B)) / (1 + cos(C))

sin(A) = (sin(41.5) - 0.614 * sin(A)) / (1 + cos(41.5))

Solving for sin(A), we get:

sin(A) = 0.266

Using this value of sin(A), we can solve for sin(B):

sin(B) = 0.614 * sin(A)

sin(B) = 0.157

Taking the inverse sine of these values, we get:

A = 15.4 degrees

B = 123.1 degrees

Therefore, the triangle has angles of approximately 15.4 degrees, 123.1 degrees, and 41.5 degrees.

The measures of the arcs are: 16. m(MN) = 72°;  17. m(NQR) = 180°; 18. m(NQ) = 108°; 19. m(MRP) = 265°; 20. m(QR) = 72°; 21. m(MR) = 108°; 22. m(QMR) = 288°; 23. m(PQ) = 13°; 24. m(PRN) = 265°; 25. m(MQN) = 288°

To determine the measures of each of the arcs, note that the central angle will have the same measure as the arc.

16. m(MN) = m<QRN

Substitute:

m(MN) = 72°

17. m(NQR) = 180° [semicircle is equal to 180 degrees]

18. m(NQ) = 180 - 72

m(NQ) = 108°

19. m(MRP) = 180 + (180 - 95)

m(MRP) = 180 + 85

m(MRP) = 265°

20. m(QR) = 72° [central angle is equal to intercepted arc measure)

21. m(MR) = 180 - 72

m(MR) = 108°

22. m(QMR) = 360 - 72 = 288°

23. m(PQ) = 180 - 95 - 72 = 13°

24. m(PRN) = 360 - 95

m(PRN) = 265°

25. m(MQN) = 360 - 72

m(MQN) = 288°

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Answer: 3. Prism

explanation: An apex is basically, the point where all lines meet at one point, and a prism is the one shape that doesn't have a apex. Hope this helps!

A reading that is not possible is given as follows:

A. 0.102cal/g*f

The possible readings are obtained applying the proportions in the context of the problem.

The percent error is of 20%, hence the minimum reading is given as follows:

0.8 x 0.174 = 0.1392 cal/gf

The maximum reading is given as follows:

1.2 x 0.174 = 0.2088 cal/gf.

The reading from option A is the only reading that is not between the minimum and the maximum values.

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The probability that the product is a multiple of 3 is given as follows:

p = 7/16.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

There are four numbers, hence the total number possible products are given as follows:

4² = 16.

The products that are multiples of 3 are given as follows:

7 products are multiples of 16, out of the 16 products, hence the probability is given as follows:

p = 7/16.

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