(b) A shopkeeper gives 20% discount on the marked price of a television set. The VAT amount at the rate of 13% is Rs. 2,600. Find the marked price and the amount of discount.​

Answer:

x = 46

Step-by-step explanation:

Assuming DE is an angle bisector , then it divides the opposite side into segments that are proportional to the other 2 sides, that is

[tex]\frac{HD}{DG}[/tex] = [tex]\frac{EH}{EG}[/tex] , substitute values

[tex]\frac{x+4}{58}[/tex] = [tex]\frac{55}{63.8}[/tex] ( cross- multiply )

63.8(x + 4) = 3190 ( divide both sides by 63.8 )

x + 4 = 50 ( subtract 4 from both sides )

x = 46

Answer:

see below

Step-by-step explanation:

11a   -2(x^2 -3)

Distribute

-2*x^2 -2(-3)

-2x^2 +6

11b  2x(x+4)

 Distribute

2x*x +2x*4

2x^2 +8x

12 The perimeter is the sum of all sides

The top is equal to the bottom and the left side is equal to the right

x-10 + x+20+x-10+x+20

Combine like terms

4x +20

Answer:

O I, II, and III only

Step-by-step explanation:

x-3 < 2

Add 3 to each side

x-3+3< 2+5

x<5

-3 is less than 5

0 is less than 5

2 is less than 5

5 is not less than 5

I , II , II are true

Answer:

Therefore 3/10 is closer to ½

Step-by-step explanation:

We've to get the difference:

» with 3/10 :

[tex] \frac{1}{2} - \frac{3}{10} = { \boxed{\frac{1}{5} }}[/tex]

» with 5/7

[tex] | \frac{1}{2} - \frac{5}{7} | = { \boxed{ \frac{3}{14} }}[/tex]

but:

[tex] \frac{3}{14} > \frac{1}{5} [/tex]

Among both the given fractions, the one that is closer to a ½ is 3/10.

A number that is stated as a quotient in mathematics, when the numerator and denominator are split in half. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction.

An element of a whole or, more broadly, any number of equal pieces, is represented by a fraction. When used in conversational English, a fraction indicates the number of components of a particular size, as in one-half, eight-fifths, and three-quarters.

A fraction is a number that represents a portion of a whole. In order to evaluate it, a whole is divided into a number of components.  A correct fraction has a numerator that is lower than its denominator.

Required calculations are done with both the fractions,

1/2 - 3/10 = 1/5

1/2 - 5/7 = 3/14

3/14 ≥ 1/5

Therefore, among both the given fractions, the one that is closer to a ½ is 3/10.

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Answer:

M = sin ^-1 (5/11)

M = 27 degrees

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hyp

sin M = 5/11

Taking the inverse sin of each side

sin ^-1 sin M = sin ^-1 (5/11)

M = sin ^-1 (5/11)

M=27.03569

To the nearest degree

M = 27

The steps to create attached screenshot of the inscribed circle of triangle ΔABC using GeoGebra tools includes;

1) Clicking on the Geometry link, under Powerful Math Apps group

2) On the opened Geometry page click on the Polygon icon and follow the instructions that come up, which is Select all vertices and then the first vertex (selected) again (a second time)

3) Once the triangle is created, select the Angle Bisector icon, under the Construct group; A message will appear, asking to Select three points or two lines, select three vertex, of the triangle created with a mouse click, with the vertex A in the center, such as BAC, or CAB a straight line representing the angle bisector of angle ∠A is created

4) Repeat the above to create the angle bisector of angle ∠B

5) Click on the Point button under the Basic Tools group, then click on the intersection of the two angle bisectors created above, the point will be automatically labelled point D

6) Click on the Perpendicular Line, icon under the Construct group, then click on point D, and then the line AB to draw the perpendicular from D to AB

7) Click on the point Point icon and then the intersection point of the perpendicular from D and AB to label the point E

8) Click on the Circle with Center basic tool and then points D and E above, to create the inscribed circle of triangle ΔABC

9) Select the Segment tool, then select the center of the circle and a point

on the circumference. Click on the label, from the pop up options, select

the label option AA then change the label of the segment created to Radius

and select Show Label and Show Value. The inscribed circle of ΔABC created with GeoGebra tools is attached

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Answer:

Step-by-step explanation: from edmentum

Answer:

jejejjejejr

Step-by-step explanation:

uejejjejejjsjs

Using Pythagorean theorem

[tex]\\ \sf\longmapsto P^2=H^2-B^2[/tex]

[tex]\\ \sf\longmapsto P^2=11^2-9^2[/tex]

[tex]\\ \sf\longmapsto P^2=121-81[/tex]

[tex]\\ \sf\longmapsto P^2=40[/tex]

[tex]\\ \sf\longmapsto P=\sqrt{40}[/tex]

[tex]\\ \sf\longmapsto P=6.2cm[/tex]

Step-by-step explanation:

Given,

Hypotenuse = 11 cm

Base (One of the given leg) = 9 cm

Therefore,

According to Pythagoras Theorem,

[tex] {base}^{2} + {height}^{2} = {hypotenuse}^{2} [/tex]

[tex] = > {(9)}^{2} + {height}^{2} = {(11)}^{2} [/tex]

[tex] = > {height}^{2} = {(11)}^{2} - {(9)}^{2} [/tex]

[tex] = > {height}^{2} = 121 - 81[/tex]

[tex] = > {height}^{2} = 4 0[/tex]

[tex] = > height = \sqrt{40} [/tex]

=> height = 6.3245553203

When rounded to nearest tenth,

=> height = 6.3

Hence,

Required length of other leg is 6.3 (Ans)

Answer:-3\2

Step-by-step explanation:

slope is difference y axis by x axis

4-12/-2+6=-6/4=-3\2

Hi there!

[tex]\large\boxed{y = \frac{x + 4}{7}}[/tex]

f(x) = 7x - 4

Rewrite f(x) with y:

y = 7x - 4

Swap the x and y variables:

x = 7y - 4

Solve for y:

x + 4 = 7y

y = (x + 4)/7

Answer:

The Empty set............

Answer:

There is no solution for the intersection of these two sets, as they do not intersect! They don't have any numbers in common and thus form an empty set. The correct answer choice is option D. the empty set.

Step-by-step explanation:

The solution for { x | x <-5} is ---> x < -5

The solution for { x | x >5 } is ---> x > 5

If you placed the two sets on a number line close to each other, you would see that they do not intersect. Thus there is no solution for the intersection of set A and set B as defined in the given problem.

See the graph for better understanding. You see how there's an empty space or area between -5 and 5? Yeah, this is called the empty set which is option D from your answer choices.

Answer:

4746

Step-by-step explanation:

Answer:

y = 3x-10

Step-by-step explanation:

When lines are parallel, they have the same slope

y = 3x+2 is in slope intercept form

y = mx+b where m is the slope and b is the y intercept

The slope is 3

y = 3x+b

We have a point on the line

-1 = 3(3)+b

-1 = 9+b

-10 = b

y = 3x-10

Answer:

x > 5

Step-by-step explanation:

-5-7x < -40

Add 5 to each side

-5+5-7x < -40+5

-7x < -35

Divide by -7, remembering to flip the inequality

-7x/-7 > -35/-7

x > 5

Open circle at 5, going to the right

Answer:

Step-by-step explanation:

The shorter arc is 22 cm.

Arc length formula:

Circumference formula:

Use the first formula to work out the value of C:

Length of arc=L=22cm

We know

[tex]\boxed{\sf L=\dfrac{\Theta}{360}\times πr}[/tex]

[tex]\\ \sf\longmapsto 22=\dfrac{45}{360}\times 2πr[/tex]

[tex]\\ \sf\longmapsto \dfrac{2πr}{8}=22[/tex]

[tex]\\ \sf\longmapsto {2πr=176}[/tex]

[tex]\\ \sf\longmapsto Circumference=176cm[/tex]

1.  - 62.34

2. - 1.4997

3. - $76.49

4. - 23.29

5. - 0.27

6. - $28.26

7. - 0.378

8. - 7.08

9. - 0.3

10. - 1.64

Answer:

1. 62.34

2. 1.4997

3. $76.49

4. 23.29

5. 0.27

6. $28.26

7. 0.378

8. 7.08

9. 0.3

10. 1.64

Answer:

b1=7

Step-by-step explanation:

If we deal with geometric series, we should use the formulas for it. If there is the last term, it is not infinite geometric series. The sum of geometric series which isn't infinite is equal to b1(r^n-1)/(r-1)   where b1 is the first term and r is the common ratio.

So 280= b1(3^n-1)/(3-1)

560= b1(3^n-1)

560= b1*3^n-b1

Then express bn=b1*r^(n-1)

189= b1*3^(n-1)

189= b1*3^n*1/3

567= b1*3^n when

560= b1*3^n-b1

560=567-b1

b1=7

I would go with C as a first step

The correct answer is C (that is equating f(x) and g(x))

A quadratic polynomial has highest degree 2 and a linear polynomial has highest degree 1.

In geometric sense, solving them means finding the point of intersection of curves:

In X-Y plane, these polynomials can be written as:

[tex]y=-x^{2} +2x+3\\y=-2x+3[/tex]

Taking the value of y from second equation and substituting it in first equation we get,

[tex]-x^{2} +2x+3=-2x+3[/tex]

Therefore, with the above procedure, we got the first step of solving the equations with the help of substitution.

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Answer:

12 mathletes is needed to solve 30 problems in 5 minutes

Step-by-step explanation:

8 athletes can solve 20 problems in 10 minutes

30-20=10

now we need 10 more problems to be solved so

20/2=10. 8/2=4 so we need more 4 mathletes to solve all the problems

Answer:

f(9) = - 59

Step-by-step explanation:

Substitute x = 9 into f(x) , that is

f(9) = - (9)² + 9 + 13

     = - 81 + 22

    = - 59

Answer:

-59

Step-by-step explanation:

f(x) =-x^2+x+13

Let x = 9

f(9) = - (9)^2 +9+13

       = -81 +9+13

      = -59

Answer:

13 and 17 units

Step-by-step explanation:

explaination is in pic.

The length of the diagonals of the quadrilateral AC and BD are 13 units and 17 units respectively, as per length between two points.

The length between two given points (x₁, y₁) and (x₂, y₂) will be:

√[(x₂ - x₁)² + (y₂ - y₁)²] units

Given, the vertices of a quadrilateral are A(4,-3),B(7,10),C(-8,2)and D(-1,-5).

Therefore, the diagonals of the quadrilateral will be AC and BD.

The coordinates of the diagonal AC are (4, - 3) and (- 8, 2).

Now, the length of the diagonal AC will be:

= √[(-8 - 4)² + (2 - (- 3))²] units

= √[(- 12)² + (5)²] units

= √[144 + 25] units

= √(169) units

= 13 units                                  (length can't be negative)

Similarly, the coordinates of the diagonal BD are (7, 10) and (- 1, - 5).

Now, the length of the diagonal BD will be:

= √[(-1 - 7)² + (- 5 - 10)²] units

= √[(- 8)² + (- 15)²] units

= √[64 + 225] units

= √(289) units

= 17 units                                  (length can't be negative)

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Answer:

(-150, 45)

Step-by-step explanation:

The solution to the system is where the two graphs intersect

My best guess from the graph is

(-150, 45)

Answer:

-19 = b

Step-by-step explanation:

76 = -4b

Divide each side by -4

76/-4 = 4-b/-4

-19 = b

Answer:

b = -19

Step-by-step explanation:

76 = -4b

shift -4 to the left hand side and when you shift -4 divides 76

76/-4 = b

-19 = b

Answer:

126 was removed.

Step-by-step explanation:

The total before division took place was

Total = mean * 14

mean = 49

Total = 49 * 14

Total = 685

Now you subtract x from the total

685 - x

And divide by 13 [one number is missing]

(685 - x)/13

and the result = 43

(685 - x ) / 13 = 43                Multiply both sides by 13

685 - x  = 43 * 13

685 - x = 559                       Subtract 685 from both sides

- x = - 126                             Multiply by - 1

x = 126

Answer:

The perimeter of a shape is the length around it.

Step-by-step explanation:

We will be using the x and y values and add them together to find the total perimeter.

To do this, let's find all the values of the 2 axis:

(2 to 4) = 2

(1 to 3) = 2

(4 to 10) = 6

(3 to 1) = 2

(10 to 12) = 2

(1 to 8) = 7

(12 to 2) = 10

(8 to 1) = 7

We now add these values together which gives us 38. Don't forget to add the units afterwards (cm, m and so forth).

Answer:

1) a³b⁴/ ab³ = a²b

2)2 (x³ )² = 2x^6

3)3x*2x³ y² = 6x⁴y²

Answer:

Option D, 52

Answered by GAUTHMATH

Answer:

(a square +7a+12) ÷(a+3)

Answer:

73

Step-by-step explanation:

Answer:

[tex]h^{-1}[/tex] (t) = [tex]\frac{7-t}{6}[/tex]

Step-by-step explanation:

let y = h(t) and rearrange making t the subject

y = - 6t + 7 ( add 6t to both sides )

6t + y = 7 ( subtract y from both sides )

6t = 7 - y ( divide both sides by 6 )

t = [tex]\frac{7-y}{6}[/tex]

Change y back into terms of x with t = [tex]h^{-1}[/tex] (t)

[tex]h^{-1}[/tex] (t) = [tex]\frac{7-t}{6}[/tex]

Answer:

yes it is the 10th term in the series

Step-by-step explanation:

The nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

Here a₁ = 7 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{14}{7}[/tex] = 2 , then

[tex]a_{n}[/tex] = 7 [tex](2)^{n-1}[/tex]

Equate [tex]a_{n}[/tex] to 3584 and solve for n

7 [tex](2)^{n-1}[/tex] = 3584 ( divide both sides by 7 )

[tex]2^{n-1}[/tex] = 512 , that is

[tex]2^{n-1}[/tex] = [tex]2^{9}[/tex]

Since the bases on both sides are equal, both 2 , then equate the exponents

n - 1 = 9 ( add 1 to both sides )

n = 10

3584 is the 10th term in the series