Express the following fraction in simplest form using only positive exponents.

By using Pythagoras theorem, Kyle run for the distance of 210 m.

What is the Pythagorean theorem ?

According to Pythagoras's Theorem, the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides.

                                  Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides.

The given length of the field is 84 m.

And, the width is 35 m.

Now, the diagonal of the field can be calculated using Pythagoras theorem as below,

Diagonal = √((84)² +(35)²)

              = 91

Then, the total length is found by summing the length, width and the diagonal as below,

= 84 + 35 + 91

= 210

Hence, Kyle run for the distance of 210 m.

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Answer:

318.75 miles

Step-by-step explanation:

The best triangle congruent theorem for the image is Angle-Angle-Side (AAS)

Two triangles are congruent if they have exactly the same three sides and exactly the same three angles.

From triangle ABC,

<BAC is given

<ABC=90⁰

<BCA is not given

Also, in triangle ACD,

<ACD is given

<CDA =90⁰

<DAC is not given

Therefore <BAC=<ACD (given)

<CDA=<ABC=90

<DAC=<BCA (not given)

Therefore,  ΔABC=ΔACD (AAS)

In conclusion, The two triangles are congruent with SSA theorem.

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In a Kite ABCD the diagonals AC and BD can be proved perpendicular by linear pair perpendicular theorem.

What is linear pair perpendicular theorem?

This theorem states that if two straight lines intersect at a point, and the linear pair of angles they form have an equal measure, then the two lines are perpendicular to each other.

According to the given question:

ABCD is a Kite        //Given

AB=BC                     //Given

BE=BE                    //Common side, reflexive property of equality

∠ABE ≅ ∠CBE      // in a kite the axis of symmetry bisects the angles at  

                                      those corners

△ABE≅△CBE      //Side-Angle-Side postulate

∠AEB ≅ ∠CEB      //Corresponding angles in congruent triangles (CPCTC)

AC⊥BD     //Linear Pair Perpendicular Theorem

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The expression that is equivalent to the given algebraic expression is; negative 14 over 18 times t minus 5 over 8

We are given the algebraic expression as;

-(10/9)t + (1/8) - [(-6/18)t + (3/4)]

Factorize out 1/72 to get;

(1/72)(-80t + 9 + 24t - 54)

= (1/72)(-45 - 56t)

= (-14/18)t - 5/8

We have used some basic mathematical operations in the expression, it gives us negative 14 over 18 times t minus 5 over 8

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The break even point is at 500 baskets. The company must sell 500 baskets a month, at which point their revenue of $10,000 will cover their total costs of $10,000.

What is break even point?

In economics, business, and particularly cost accounting, the break-even point is the point at which total cost and total revenue are equal, or "even." Although opportunity costs have been paid and capital has received the risk-adjusted, expected return, there is no net loss or gain, and one has "broken even."

In this case we could probably solve the problem from the graph itself, but we can also solve it algebraically by setting the equations equal:

[tex]\begin{gathered}R(n)=C(n) \\20 n=6000+8 n\end{gathered}[/tex]

Subtract 8n from both sides:

[tex]12 n=6000[/tex]

Divide:[tex]n=\frac{6000}{12}=500[/tex]

Evaluate either function at this input: [tex]R(500)=C(500)=10,000[/tex]

The break even point is at 500 baskets. The company must sell 500 baskets a month, at which point their revenue of $10,000 will cover their total costs of $10,000.

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To  have a total mass of 1 googol kilograms, 1.674480911 × 10 ⁷⁵ earths are needed

Given that:

1 googol = 10¹⁰⁰

Earth's mass is 5.972×10²⁴ kilograms

In order to find how many earths are needed to have a total mass of 1 googol kilograms, you need to divide  1 googol kilograms by Earth's mass (5.972×10²⁴ kilograms). Thus:

Number of earths needed =  10¹⁰⁰ / 5.972×10²⁴

Number of earths needed = 1.674480911 × 10 ⁷⁵ earths

Therefore, 1.674480911 × 10 ⁷⁵ earths are needed to have a total mass of 1 googol kilograms

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The total no: of pages needed are 18 pages

A fundamental idea behind the unitary method is using the value of one unit to determine the values of additional units. Study up on the unitary method. With an increase in units, the value of additional units rises.

The general unitary group, also known as the group of unitary similitudes, is simply the product of the unitary group and the group of all positive multiples of the identity matrix. It includes all matrices A such that AA is a nonzero multiple of the identity matrix.

According to the question:-

The no: of pages needed for 6 letters = 6

The no: of pages needed for the other 6 letters= 6*2

                                                                              =12

Total no: of pages are 18

Hence, the total no: of pages are 18

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Answer:

B. none of other works. Only hue rate of change of Function F is higher than Function G

Inequality (A) "y > x-2 represents the given graph when the line passes to 2 and -2 from the x-axis and y;-axis respectively.

In discrete mathematics, more specifically in graph theory, a graph is a structure that resembles a collection of objects where some object pairs are conceptually "connected."

Each pair of connected vertices is referred to as an edge, and the objects are represented by mathematical abstractions known as vertices.

To calculate the slope m and the y-intercept, write the equation y = MX + b.

The slope and y-intercept can then be used to graph the equation (0, b).

So, to find which inequality represents the given graph, simply plot the inequalities on the graph.

After plotting, we can conclude that inequality "y > x-2" represents the graph shown in the question.

(Refer to the image attached below)

Therefore, inequality (A) "y > x-2 represents the given graph when the line passes to 2 and -2 from the x-axis and y'-axis respectively.

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Complete question:
Which inequality does the graph represent?

a. y > x-2

b. y > -X-2

c. y <-x-2

d. y <x-2

Coordinates of the point C after dilation with a scale factor of 5, centered at the origin will be: C'(10, 5)

Given that,

The point C

C(2, 1)

We have to find what are the coordinates of the point D after a dilation with a scale factor of 5, centered at the origin.

We know that,

The point C

The size of the coordinates of the picture of point P will be 5 times larger than the original coordinates of point C in a dilatation with a scale factor of 5.

The following is the scale factor 5 rule of dilation:

(x, y)  →  (5x, 5y)

C(2, 1)  →  (5x, 5y) = (5(2), 5(1)) = C'(10, 5)

Therefore, coordinates of the point C after dilation with a scale factor of 5, centered at the origin will be: C'(10, 5)

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Answer:

Step-by-step explanation:

what

Answer:

x = 11

Explanation:

It looks like the total distance between points I and K is -3 + x. Since I to J and J to K is also the total distance, I to K is also equal to 6 + 2x - 20. You can represent this in an equation and solve for x.

-3 + x = 6 + 2x - 20

-3 + x = 2x - 14

- 3 = x - 14

11 = x

In the given trapezoid, the angle ∠ HMA is 120°.

A closed polygon or geometry with four sides, four corners, and four angles is called a trapezium. Each pair of a trapezium's opposing sides is parallel to the other.

In the given trapezoid AMHT,

The angle H = 60°.

To find the angle ∠ HMA,

Since, the sum of angle MHT and angle HMA is equal to 180°.

∠ HMA + ∠ MHT = 180°

∠ HMA + 60 = 180

∠ HMA = 120

The required angle ∠ HMA is 120°.

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The other information that must prove by the triangle is that ∠A ≅ ∠X.

How do you understand "ABC" and "DEF"?

The triangles are congruent if their included sides are congruent and two of their angles match two of the other triangle's angles. applying labels Triangle ABC is congruent to triangle DEF if, in triangles ABC and DEF, angle A = angle D, angle B = angle E, and angle AB = DE.

By SAS or Side-Angle-Side Postulate, the corresponding two sides and it's included angles should be congruent.

Therefore, based on the illustration, the included angle for ∆ABC is ∠A while the included angle for ∆XYZ is ∠X.

Therefore, the other information that must prove by the triangle is that ∠A ≅ ∠X.

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Answer:

a=4

Step-by-step explanation:

we fill in b to find a

a=2(3a-5)-10

a=6a-10-10

a=6a-20

+20  +20

a+20=6a

-a.    -a

20=5a

/5. /5

4=a

hopes this helps

Answer:

(-4,-7)

Step-by-step explanation:

8x - 3y = -11

2x - 5y = 27

8x - 3y = -11

4(2x - 5y) = 27 (4)

8x - 3y = -11

8x - 20y =108

8x - 8x = 0

-3y - (-20y) = 17y

- 11 - 108 = -119

17y = -119

17/17 y = -119/17

y = - 7

2x - 5(-7) = 27

2x + 35 = 27

2x = 27 - 35

2x = - 8

2/2 x = -8/2

x = -4

The ratio of volumes of Cylinder A to Cylinder B is 1 : 2

What is a Cylinder?

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is

Volume of Cylinder = πr²h

where r is the radius of the cylinder

h is the height of the cylinder

Given data ,

Let the volume of the first cylinder be = A

Let the volume of the second cylinder be = B

Now,

The diameter of first cylinder = 7 cm

Radius of the first cylinder r = 7/2 = 3.5 cm

Height of the first cylinder h = 14 cm

And ,

The diameter of second cylinder = 14 cm

Radius of the second cylinder R = 14/2 = 7 cm

Height of the second cylinder H = 7 cm

To find the ratio between the volumes of both cylinders

Volume of Cylinder A = πr²h

Substituting the values in the equation , we get

Volume of Cylinder A = π x ( 3.5 ) x ( 3.5 ) x ( 14 )

Volume of Cylinder B = πR²H

Substituting the values in the equation , we get

Volume of Cylinder B = π x ( 7 ) x ( 7 ) x ( 7 )

The ratio between volumes of A and B is given by = Volume of Cylinder A / Volume of Cylinder B

So , the ratio is

Volume of Cylinder A / Volume of Cylinder B = π x ( 3.5 ) x ( 3.5 ) x ( 14 ) /  π x ( 7 ) x ( 7 ) x ( 7 )

On simplifying the equation , we get

Volume of Cylinder A / Volume of Cylinder B = 2/4

Therefore , the ratio is

Volume of Cylinder A / Volume of Cylinder B = 1 : 2

Hence , The ratio of volumes of Cylinder A to Cylinder B is 1 : 2

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The calculations for the slope-intercept forms of the equations are (1) m=-[tex]\frac{3}{4}[/tex],B=2  (2)m=1, B=5  (3) m=-1, B=6

How to use the Slope -intercept form?

Slope of a line is a number that describes both the direction and the steepness of the line.

The intercept of a line is defined as the point at which it intersects the y-axis in a graph.

The equation of a line is expressed as follows;

Y=MX+B

Where M=slope and B=intercept

From the equations:

(1) y<[tex]\frac{-3x}{4}[/tex]+2

Applying the equation of slope-intercept form,

m=[tex]\frac{-3}{4} , B=2[/tex]

(2) Y[tex]\leq 5[/tex]

Applying the equation: Y=MX+B

m=1,  B=5

(3) x+y>6

Applying the formula: Y=MX+B

Re-arrange the equation

y>-x+6(1)

⇒ m=-1, B=6

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Answer:

To find out how much Laura earns each week, you can set up an equation using the information given. Let's call Laura's weekly pay "W".

You know that Laura has saved 5 times her weekly pay, so you can write this as 5W.

You also know that she spent less than 2 times her weekly pay this week, so you can write this as 2W - X, where X is the amount that she spent less than 2 times her weekly pay.

Finally, you know that she has 156 left after spending some money, so you can write this as 156.

You can now set up the equation:

5W + (2W - X) = 156

Combining like terms, you get:

7W - X = 156

Adding X to both sides, you get:

7W = 156 + X

Dividing both sides by 7, you get:

W = (156 + X) / 7

Thus, Laura's weekly pay is equal to (156 + X) / 7. You know that she spent less than 2 times her weekly pay this week, so X must be less than 2W. However, you don't know the exact value of X, so you can't find the exact value of Laura's weekly pay.

:

If laura has saved her babysitting money for the past two weeks then Laura earns 52 dollars per week.

Two or more expressions with an Equal sign is called as Equation.

Let Laura earns x dollars per week.

According to the problem, after two weeks of saving, she has 5 times her weekly pay, which means she has saved 5x dollars.

This week, she spent less than 2 times her weekly pay, which means she spent less than 2x dollars.

Now, she has 156 dollars left, so we can set up the equation:

5x -  2x = 156

Simplifying this equation, we get:

3x= 156

Divide both sides by 3

x = 52

Hence, Laura earns 52 dollars per week.

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Answer:

the answer will be the option b

hope this helps you

Answer: 19.5

Step-by-step explanation:

obtuse + acute = 180

131 + t = 180

t = 49 degrees for the top angle

49 + 61 + 4x-8 = 180 degrees in a triangle

110 + 4x - 8 = 180

102 + 4x = 180

4x = 78

x = 19.5

Answer:

x = 19.5

Step-by-step explanation:

The interior angles of a triangle will ALWAYS have a sum of 180°

The solutions of the equation are given as,
1. 7,  2. 5,  3. 5, 4. 5, 5. 7, 6. -4, 7. 8,  8. 3.

Given that,
A number of equations are given we have to determine the solution of the equaiton,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here
1) 3x + 4 = 25
simplify,
3x + 4 = 25
3x = 25 - 4
x = 21 / 3
x = 7
Similarly, the Solution of the other equation is given as,
2. 5,  3. 5, 4. 5, 5. 7, 6. -4, 7. 8,  8. 3.

Thus, the solutions of the equation are given as,
1. 7,  2. 5,  3. 5, 4. 5, 5. 7, 6. -4, 7. 8,  8. 3.

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Step-by-step explanation:

52×7 = 50×7 + 2×7

why?

because 52 = 50 + 2

so,

52×7 = (50 + 2)×7 = 50×7 + 2×7

Answer

The third option 52 x 7 = 50 x 7 + 2 x 7

Step-by-step explanation:

First of 52 x 7 = 364, so whichever other equation is equal to 364 is the correct option

50 x 7 + 2 x 7

350 + 2 x 7

350 + 14

= 364

After a comparison of females and males on the number of hours of a day that the subject watched the TV.

The hypotheses of a significance test to analyze whether the population means differ for females and males would be as follows:

(a) H0: μ1 = μ2 (the population means are equal for females and males)

Ha: μ1 ≠ μ2 (the population means are not equal for females and males)

(b) In order to conduct the significance test, we would need to calculate the t-statistic and the P-value. However, the question does not provide the necessary information to do so (e.g. sample means, standard deviations, sample sizes). Without this information, we cannot conduct the significance test and interpret the P-value(c) Without conducting the significance test, we cannot conclude anything about whether there is a gender difference in TV watching.

(d) Similarly, without conducting the significance test and calculating the confidence interval, we cannot determine whether the confidence interval would contain 0 or not.

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If a figure is dilated by a scale factor of 10, the area of the figure will change by a factor of 100.

The size of a two-dimensional form or a region in a plane is described by the mathematical notion of area. Square units like square inches, square feet, or square metres are frequently used figure to measure it. The total space a form takes up in a plane is known as its area. The length and breadth of the shape may be multiplied to compute it, or intricate forms like circles, triangles,  formulae can be used. Finding the dimensions of a form, calculating area ofcircle or rectangle, or  area of three-dimensional object are just a few of the many issues that may be solved using the geometry concept of area.

How to solve?

If a figure is dilated by a scale factor of 10, its area will change by a factor of 100.

When a figure is dilated, its area changes by the square of the scale factor. In this case, the scale factor is 10, so the area will change by a factor of 10^2 = 100.

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Answer: t = 11

Step-by-step explanation:

f(11)= 5(11) -7

f(11) = 55 - 7

f(11) = 48

Answer:

f(11) = 48

Step-by-step explanation:

f(t) = 5t-7

we have to find out what t is

5t - 7 =48

    +7    +7

5t = 55

  /5   /5

t = 11

Answer:

A. (3,-1)

Step-by-step explanation:

A reflection of y = x would be:

[tex](x,y)\rightarrow(y,x)[/tex]

Therefore:

[tex](-1, 3) \rightarrow (3, -1)[/tex]

The correct option should be A.

Hope this helps.

The probability that the engineer has to test at least 5 computers in order to find 2 defective ones is 0.985.

Given :

A quality control engineer tests the quality of produced computers. suppose that 5% of computers have defects, and defects occur independently of each other.

So the probability of getting 0 defective computers out of 4 is :

= ( 1 - 0.05 )^4

= 0.95^4

= 0.814.

The probability of getting exactly 1 defective computer out of 4 is :

= 0.05 * ( 1 - 0.05 )^3 * 4! / ( 1! ( 4 - 1 )!)

= 0.05 * 0.95^3 * 24/ ( 1!3! )

= 0.05 * 0.857375 * 24/6

= 0.171.

So the probability of getting only 0 or 1 defective computers out of the 1st 4 is :

= 0.814 + 0.171

= 0.985

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