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The cost price of the cycle is Rs.3240

Represent the cost price of the cycle with x and the selling price with y

A gain of 5% when the marked price is at a discount of 10% implies that:

[tex]5\%=\frac{(1 - 10\%)y-x}{x}[/tex]

Express 10% as decimal

[tex]5\%=\frac{(1 - 0.10)y-x}{x}[/tex]

[tex]5\%=\frac{0.90y-x}{x}[/tex]

Express 5% as decimal

[tex]0.05=\frac{0.90y-x}{x}[/tex]

Cross multiply

[tex]0.05x=0.90y-x[/tex]

Collect like terms

[tex]x + 0.05x=0.90y\\[/tex]

This gives

[tex]1.05x=0.90y[/tex]

Make y the subject of the formula

[tex]y = \frac{1.05x}{0.90}[/tex]

Also, when the discount is 5% and the profit is 351, we have:

[tex]351=(1 - 5\%)y -x[/tex]

Express 5% as decimal

[tex]351=(1 - 0.05)y -x[/tex]

This gives

[tex]351=0.95y -x[/tex]

Make y the subject

[tex]0.95y = 351 + x[/tex]

Substitute [tex]y = \frac{1.05x}{0.90}[/tex]

[tex]0.95 \times \frac{1.05x}{0.90} = 351 + x[/tex]

[tex]\frac{0.9975x}{0.90} = 351 + x[/tex]

Subtract x from both sides

[tex]\frac{0.9975x}{0.90} -x= 351[/tex]

Take LCM

[tex]\frac{0.9975x - 0.9x}{0.90}= 351[/tex]

[tex]\frac{0.0975x}{0.90}= 351[/tex]

Multiply both sides by 0.90

[tex]0.0975x= 315.9[/tex]

Divide both sides by 0.0975

[tex]x= 3240[/tex]

Hence, the cost price of the cycle is Rs.3240

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Answer:

[tex]\sqrt{8}----- 2units,2units[/tex]

[tex]\sqrt{7} ------\sqrt{5}units,\sqrt{2}units[/tex]

[tex]\sqrt{5}-------1unit,2units[/tex]

[tex]3------2units, \sqrt{5}units[/tex]

Step-by-step explanation:

Use pythagorean's theorem to solve each pair individually.

The instructions say that you have the two sides (a and b) and you have to match it with their hypothenuse.

[tex]Formula: c^2=a^2+b^2[/tex]

1. [tex]a=\sqrt{5}, b=\sqrt{2}[/tex]

Plug this into the formula.

[tex]c=\sqrt{(\sqrt{5} )^2+(\sqrt{2})^2 }[/tex]

The square here eliminates the roots.

[tex]c=\sqrt{5+2}\\ c=\sqrt{7}[/tex]

2. [tex]a=\sqrt{3}, b=4[/tex]

[tex]c=\sqrt{(\sqrt{3} )^2+(4)^2}\\ c=\sqrt{3+16}\\ c=\sqrt{19}[/tex]

3. [tex]a=2, b=\sqrt{5}[/tex]

[tex]c=\sqrt{(2)^2+(\sqrt{5})^2 }\\ c=\sqrt{4+5}\\ c=\sqrt{9}\\ c=3[/tex]

4. [tex]a=2, b=2[/tex]

[tex]c=\sqrt{(2)^2+(2)^2}\\ c=\sqrt{4+4}\\ c=\sqrt{8}[/tex]

5. [tex]a=1, b=2[/tex]

[tex]c=\sqrt{(1)^2+(2)^2}\\ c=\sqrt{1+4}\\ c=\sqrt{5}[/tex]

Answer:

[tex]y=1,\:y=-1[/tex]

Step-by-step explanation:

[tex]y^2+14=3y^2\cdot \:5\\\y^2+14-14=3y^2\cdot \:5-14\\y^2=15y^2-14\\y^2-15y^2=15y^2-14-15y^2\\-14y^2=-14\\\frac{-14y^2}{-14}=\frac{-14}{-14}\\y^2=1\\\\y=\sqrt{1},\:y=-\sqrt{1}\\y=1,\:y=-1[/tex]

Answer:

y = ± 1

Step-by-step explanation:

Given

y² + 14 = 3y² × 5, that is

y² + 14 = 15y² ( subtract y² from both sides )

14 = 14y² ( divide both sides by 14 )

1 = y² ( take the square root of both sides )

± [tex]\sqrt{1}[/tex] = y , that is

y = ± 1

Thus y = - 1 or y = 1

Question :

The triangular prism shown below is 6 cm wide and 4 cm deep. The vertical height is 7 cm. What is the length of the side edge, s, of the triangular prism? Round your answer to the nearest tenth.

Answer: 7.62cm

Step-by-step explanation:

Given the following :

Width = 6cm

Depth = 4cm

Vertical height = 7cm

Splitting the face of the prism into two:

Thus the width becoming 6cm/2 = 3cm and vertical height = 7cm

Using Pythagoras ;

The side edge 's' equals

s^2 = width^2 + height^2

s = √(width^2 + height^2)

s = √(3^2 + 7^2

s = √9 + 49

s = √58

s = 7.62cm

Answer:

7.6

Step-by-step explanation:

the person above is correct, i took the test on khan, but you have to round to the nearest tenth

Answer:

73°

Step-by-step explanation:

the measure of two complementary angles add up to 90

so We need to solve this equation to get the measure of its complementary angle :

x + 17 = 90

then

x = 90 - 17

  = 73

Answer:

1. Option A is correct (A = length x width)

2. Option B is correct ( A = base x height/2)

Hope this helps

:)

Answer:

12

Step-by-step explanation:

Answer:

82 cm is the area of trapezoid

Answer:

about 904.78

Step-by-step explanation:

πr^2h pi(6)^2 * 8

Answer:

14 did this lesson rn

Step-by-step explanation:

The required change in Dana's profit is given as $12, as of the given condition.

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,
On Saturday Dana's profit = -$2
On Sunday Dans;s profit = $12
Change in Dana's profit = 12 - 2 = $12

Thus, the required change in Dana's profit is given as $12.

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Answer:

The house value increase by $17,040 in dollar terms

The current value of the house $ 230,040

Step-by-step explanation:

The increase in value of the house can be determined as the difference between the value of the house now after 8% increase in value and the earlier value of $213,000

new value=earlier value *(1+% increase in value)

% increase in value is 8%

new value=$213,000*(1+8%)

                 =$213,000*1.08=$230,040.00  

increase in value= $230,040-$213,000=$17,040

The increase in value of the house of 8% translated into a dollar value of $17,040

Answer:

4

Step-by-step explanation:

Answer:

GCF=4

Step-by-step explanation:

It's 4

24/4=6

40/4=10

60/4=15

You can't go any higher because there is no GCF of 6, 10, and 15.

Answer: - √2

Step-by-step explanation:

Answer:

1/36

Step-by-step explanation:

If the cubes are numbered from 1 to 6 there is just one way that the sum of both of them equals 12 and this is when Marsha gets 6 in the first cube and 6 in the other.

Thus, to know what the probability that the total of numbers facing up will equal 12 we would have to calculate the probability that the first cube is 6 AND the second one is also 6.

The probability that the first cube has the number 6 is: 1/6

The probability that the second cube has the number 6 is: 1/6

We need to multiply this numbers because they both have to be 6 (rule of multiplication),

so: [tex]\frac{1}{6}(\frac{1}{6} )= \frac{1}{36}[/tex]

Thus, the probability that the sum of them equals 12 is 1/36

Answer:[tex]\frac{1}{64}^{th}[/tex]

Step-by-step explanation:

Given

Suppose V is the original volume of cone having r as radius and h as height

If we multiply all the linear dimensions of ac one by [tex]\frac{1}{4}^{th}[/tex]

the [tex]r'=\frac{r}{4}[/tex]

[tex]h'=\frac{h}{4}[/tex]

Therefore new volume is

[tex]V'=\frac{1}{3}\pi r'^2h'[/tex]

[tex]V'=\frac{1}{3}\pi (\frac{r}{4})^2(\frac{h}{4})[/tex]

[tex]V'=\frac{1}{64}\times \frac{1}{3}\pi r^2h[/tex]

[tex]V'=\frac{V}{64}[/tex]

So new volume becomes [tex]\frac{1}{64}^{th}[/tex] of the original one

Answer: [tex]17.33ft[/tex]

Step-by-step explanation:

We need to go from area to radius to circumference.

Formula for the area:

[tex]A=\pi r^2[/tex]

Solve for r;

Divide by pi

[tex]r^2=\frac{A}{\pi}[/tex]

Extract the square root.

[tex]r=\sqrt{\frac{A}{\pi} }[/tex]

Plug in the value of the area.

[tex]r=\sqrt{\frac{24ft^2}{3.14} } \\r=2.76ft[/tex]

Now that you've found the radius, use the circumference formula to calculate it.

[tex]C=2\pi r\\C=2(3.14)(2.76ft)\\C=17.33ft[/tex]

Answer:

$555,765.76

Step-by-step explanation:

1

2

4

8

16

32

64

128

256

512

1024

2048

4096

8192

16282

32564

65128

13256

26512

53024

106048

212096

424192

868384

1736768

3473536

6947072

13894144

27788288

55576576=

555,765.76

The money would you have after 30 days is  $555,765.76.

A penny that doubles each day for 30 days.

We have to determine the money would you have after 30 days.

We have to determine for 30 days,

1

2

4

8

16

32

64

128

256

512

1024

2048

4096

8192

16282

32564

65128

13256

26512

53024

106048

212096

424192

868384

1736768

3473536

money, a commodity accepted by general consent as a medium of economic exchange. It is the medium in which prices and values are expressed as currency,

6947072

13894144

27788288

55576576=555,765.76

Therefore we get the money would you have after 30 days $555,765.76.

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Step-by-step explanation:

Step 1:  Convert degrees into radians

[tex]\frac{degrees}{1}*\frac{\pi }{180}[/tex]

[tex]\frac{52}{1}*\frac{\pi}{180}[/tex]

[tex]\frac{52\pi}{180}[/tex]

[tex]\frac{13\pi}{45}[/tex]

Step 2:  Find the arc length

[tex]S = r\theta[/tex]

[tex]S=(3)(\frac{13\pi}{45})[/tex]

[tex]S = \frac{39\pi}{45}[/tex]

[tex]S=\frac{13\pi}{15}[/tex]

Answer: Option B

Answer:

16.67

Step-by-step explanation:

Answer:

16.67

Step-by-step explanation:

70:420*100 =

(70*100):420 =

7000:420 = 16.67

Answer:

-17

Step-by-step explanation:

1w= -17

(1)(-17)=

-17

Answer:

-17

Step-by-step explanation:

in this situations, we normally divide both sides by the number next to the unknown.

1w is the same as saying w

so,

w = -17

Answer:

n=42

Step-by-step explanation:

Answer:

1. 5

2. 1

3. 2

4. 23

Step-by-step explanation:

If y=6x+5, you can plug in the known x or y value to get the other with this function. For the first row, y=6(0)+5=5. For the second row, 11=6x+5, and that x=1. For the third row, x is 2, and for the fourth row y is 23. Hope this helps!

The number of possible combinations of 8 objects taken 6 at a time is 28. Then the correct option is D.

Combinations are the way of selecting objects or elements from a group of objects or collections, in such a way the order of the objects does not matter.

The number of possible combinations of 8 objects taken 6 at a time.

Then the number of the combination is given as

[tex]\rm ^8C_6 = \dfrac{8!}{(8-6)! 6!}\\\\\\^8C_6 = \dfrac{8 \times 7 \times 6!}{2 \times 1 6!}\\\\\\^8C_6 = 7 \times 4\\\\\\^8C_6 = 28[/tex]

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Answer:

[tex]y = 18 \: \: degrees[/tex]( vertically opposite angles)

[tex]x = 64 \: \: degrees[/tex]

[tex]y + z + x = 180 \\ 18 + z + 64 = 180 \\ 82 + z = 180 \\ z = 180 - 82 \\ z = 98 \: \: degrees[/tex]

Answer:

-30

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Distance = √(x2-x1)² + (y2-y1)²

d = √(10-4)² + (13-5)²

d = √6² + 8²

d = √36+364

d = √100

d = 10

Answer: D is a function.

Step-by-step explanation:

A function need to have exactly one output to each input.

Answer: D. (2, 3), (4, 3), (-2, -3), (-4,-3)

Step-by-step explanation: This represents a function because they're the opposing of each other. Hope this helps happy holidays! :)

Answer:

D) as x approaches neg. infinity, y approaches neg. infinity

Step-by-step explanation:

This is because you get to negative x infinity which is towards the right, you see that the y value is going down sharply as well towards the direction of negative infinity in y direction (x direction is right to left and y direction is up and down)

Answer:

D one Edge 2021 ;))

Step-by-step explanation:

Answer:

The domain of f is x > 0.

The range of f is all real numbers.

The domain of the inverse function is all real numbers.

The range of the inverse function is y > 0.

The domain of f is the same as the

range of the inverse function.

The range of f is the same as the

the domain of the inverse function.

Step-by-step explanation:

this is the sample answer, make sure you rewrite in your own words!

The domain and the range of a function are the set of input and output values of the function

The domain and the range of the function are set of real numbers greater than 0

The function is given as:

[tex]f(x) = log_7(x)[/tex]

The above function is a logarithmic function.

From the properties of a logarithmic function, we have:

This means that, the domain and the range of the function are set of real numbers greater than 0

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Answer:

The center is at (3,1) and the radius is [tex]\sqrt{8}[/tex]

Step-by-step explanation:

I am going to assume you meant to write

[tex](x-3)^2+(y-1)^2 = 8[/tex]

Since if both variables were x it would not be a circle:

Then you can find the center and radius using the general formula of a circle:

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

where the center is at (h,k) and r is the radius

Therefore:

The center is at (3,1) and the radius is [tex]\sqrt{8}[/tex]

Answer:

He scored 65 points in his last two games

Step-by-step explanation:

Here, we want to calculate the number of points Benny scored in his last two games.

We must understand that his last two games correspond to the games he played on Monday and on Friday

So to get his total points in the last two games, what we do is that we add both points together

Mathematically, that would be 19 + 46 = 65 points