[ INDICES]- Simplify :
1. [tex] \large{ \tt{\frac{ {13}^{ \: 2x + 1} - 5 \times {169}^{x} }{9 \times {169}^{x} } }}[/tex] [ Ans : 2 ]

2. [tex] \large{ \tt{ \frac{ {9}^{ \: n + 2} + 10 \times {9}^{n} }{ {9}^{n + 1} \times 11 - 8 \times {9}^{n} }}}[/tex] [ Ans : 1 ]

- Please show your workings! :)
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Answer:47/12

=3.9167

Step-by-step explanation:

Step-by-step explanation:

I hope this will help you

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Answer:

It's an isosceles triangle equal 2 sides so

it will be x+67 ° +67 ° =180° ( sum of angle in triangle)

x+134 °=180 °

x =180 - 134

x = 46 °

The measurement of the missing angles in the given triangle is 67.

Use the concept of isosceles triangle defined as:

A triangle with two equal-length sides is said to be isosceles.

An isosceles triangle has equal angles on either side of its equal sides.

In the given figure,

One angle is 67 degrees

And two sides are equal.

Let the missing angle is x°

Since the two sides of this triangle are equal,

So this is an isosceles triangle.

Then two opposite angles must be equal.

For a triangle,

The sum of interior angles = 180°

Therefore,

67° + 67° + x° = 180°

x° = 46°

Hence,

The measurement of the missing angle is 46°

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Answer:

3

Step-by-step explanation:

9,8,3,2,5

3

3/5=0.6

0.6

Answer:

Rs 56250

Step-by-step explanation:

Given:

Cost price of laptop (CP) = RS 45000

Profit (P) = 24 % = 0.24

The selling price of dealer (SP) = Cost price of customer,

So,

Selling price of dealer = [tex]\tt CP + Profit \:Percentage \:of \:C.P[/tex]

Selling price of dealer = CP(1+ Profit %)

Substituting value

Selling price of dealer = 45000(1+0.24)

Selling price of dealer = 45000*1.24

Selling price of dealer = 56250

Therefore, the Customer paid Rs 56250 for the laptop.

Answer:

Rs 56,250

Step-by-step explanation:

To calculate how much the customer paid for the laptop, we need to determine the total price after the retailer added a 25% profit margin.

If the dealer purchased the laptop for Rs 45,000, then Rs 45,000 is 100%. If the dealer sells it to a customer at 25% profit, it was sold at 125% of its purchase price.

Therefore, to calculate how much the customer paid for the laptop, we need to find 125% of Rs 45,000:

[tex]\begin{aligned}\sf 125\%\;of\;45000&=\sf\dfrac{125}{100} \times 45000\\\\&=\sf\dfrac{125\times 45000}{100} \\\\&=\sf\dfrac{5625000}{100} \\\\&=\sf56250\end{aligned}[/tex]

Therefore, the customer paid Rs 56,250 for the laptop.

Given:

The two exponential functions are shown in the given table.

To find:

The correct conclusion about the functions f(x) and g(x).

Solution:

The given functions are:

[tex]f(x)=2^x[/tex]

[tex]g(x)=\left(\dfrac{1}{2}\right)^x[/tex]

The function g(x) can be written as:

[tex]g(x)=\dfrac{1}{2^x}[/tex]

[tex]g(x)=2^{-x}[/tex]

[tex]g(x)=f(-x)[/tex]

It means the graphs of f(x) and g(x) are reflections over the y-axis. So, option B is correct.

Since [tex]g(x)\neq -f(x)[/tex], therefore the functions f(x) and g(x) are not the reflections over the x-axis. So, option A is incorrect.

The function f(x) is an increasing function because the base of the exponent is [tex]2>1[/tex]. The function g(x) is a decreasing function because the base of the exponent is [tex]\dfrac{1}{2}<1[/tex]. So, option C is incorrect.

At x=0 the value of f(x) is 1 and the value of g(x) is also 1. It means the functions has same initial values. So, option D is incorrect.

Therefore, the correct option is B.

We can conclude that g(x) is a reflection over the y-axis of f(x).

The two functions are:

You can see the graph of these functions at the end of the answer.

You can also notice that g(x) can be written as:

g(x) = (1/2)^x = 2^(-x) = f(-x)

Then this is a reflection over the y-axis, thing that you can also see in the graph below.

So the correct option is:

"The functions f(x) and g(x) are reflections over the y-axis."

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Answer:

C:The set of all possible outcomes

Answer:  C. Trey, Susie, Tucker, Jordan, Ashton

========================================================

Explanation:

The random sub-sequence 52197 66082 helps directly determine who we pick.

The digit 5 is first of that sequence, so we pick Trey first (as he's the 5th student). Then we pick student #2 next, who is Susie.

Up next is student #1, and that would be Tucker

Up next is student #9, but the list only goes high as 7. So we skip over 9

Jordan is next up since 7 is the next digit

Finally, the last selection is Ashton because 6 follows after.

--------------

In other words, the sequence 52197 6 will lead to these selections in the order provided.

Side note: if we wanted a 6th student, then we'd have to skip over the next 6 since we cannot pick Ashton twice. The 6th selection would be Jack since he's student #0

Answer:

[tex]x1 = - 4.525[/tex]

[tex]x2 = 5.525[/tex]

Step-by-step explanation:

[tex]x1 = \frac{1 - \sqrt{101} }{2} [/tex]

[tex]x2 = \frac{1 + \sqrt{101} }{2} [/tex]

Answer:

60

Step-by-step explanation:

Step 1:

3 x 5 = 15

Step 2:

15 x 4 = 60

Answer:

well 3. x 5 is 15, then multiply by 4 to get 60.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello!

(x +x+7)*2 = 50

(2x+7)*2 = 50

4x+14= 50

4x= 50-14

4x= 36

x= 36/4

x= 9

9 et 16cm

Answer:

Step-by-step explanation:

4). a). If the diagonals of a parallelogram are congruent, then it must be a RECTANGLE.

b). If the diagonals of a parallelogram are perpendicular, then it must be a SQUARE.

c). If the diagonals of a parallelogram bisect the angles of the parallelogram, then it must be a RHOMBUS.

d). If the diagonals of a parallelogram are perpendicular and congruent, then it must be a SQUARE.

e). If a parallelogram has four congruent sides, then it must be a SQUARE.

5). Given quadrilateral SELF is a rhombus.

a). All sides of a rhombus are equal,

   Therefore, ES = EL = 25

b). Diagonals of a rhombus bisects the opposite angles,

   Therefore, m∠ELS = m∠FLS

    3x - 2 = 2x + 7

    3x - 2x = 7 + 2

    x = 9

c). Diagonals of the rhombus bisect the opposite angles, and adjacent angles are supplementary.

m∠ELF = 2(m∠ELS) = 2(2y - 9)

m∠LES = 2(m∠LEF) = 2(3y + 9)

And 2(2y - 9) + 2(3y + 9) = 180

(2y - 9) + (3y + 9) = 90

5y = 90

y = 18  

Answer:

(B) mn+3

Rule of algebra: *INTEGERS*

like sign➡ add

unlike sign➡ subtract

Step-by-step explanation:

Because the m2n2 is got subtract by m and n that's why it bacames a constant mn.

Answer:

[tex](m^{2} n^{2} -7)-(mn+4)[/tex]

[tex]=m^{2} n^{2} -7-mn-4[/tex]

[tex]m^{2} n^{2} -mn-11[/tex]

Option C is your answer

----------------------------------

Hope it helps...

Have a great day!!

Answer:

x = 6

Step-by-step explanation:

log2(x + 5) + log2(x − 5) = log2 11.

We know that loga (b) + log a(c) = log a( bc)

log2(x + 5) (x − 5) = log2(11)

Multiply

log2(x^2 -25) = log2(11)

Raise each side to the power of 2

2^log2(x^2 -25) = 2^log2(11)

x^2 - 25 = 11

Add 25

x^2 -25 +25 = 25+11

x^2 = 36

Taking the square root of each side

x = ±6

But x cannot be negative because then the log would be negative in log2(x-5) and that is not allowed

x = 6

Answer:

x = 6

Step-by-step explanation:

[tex] log_2[/tex] ( x + 5 ) + [tex] log_2[/tex]( ( x - 5 ) = [tex] log_2[/tex] 11

Determined the define range.

[tex] log_2[/tex] ( x + 5 ) + [tex] log_2[/tex]( ( x - 5 ) = [tex] log_2[/tex] (11), x ∈ ( 5, + ∞ )

We know that [tex] log_a ( b ) + log_a ( b ) [/tex] = [tex] log_a( bc) [/tex]

[tex] log_2[/tex] ( x + 5 ) ( x - 5 ) = [tex] log_2[/tex] ( 11).

[tex] log_2[/tex] ( ( x + 5 ) × ( x - 5 ) ) = [tex] log_2[/tex] ( 11).

Use indentity :- ( a + b ) ( a - b ) = a² - b².

[tex] log_2[/tex] ( x² + 25) = [tex] log_2[/tex] ( 11).

Since , the base of the logarithm are the same. set the arguments equal.

x² - 25 = 11.

Move constant to the right-hand side and change their sign.

x² = 11 + 25

x² = 36.

Take square root of each side.

√x² = √36

x = ± 6

x = 6

x = -6, x ∈ ( 5, + ∞ )

Check if the solutions is in determine range.

x = 6

Answer:

x = 10

The both line crosses with a little hyphen, meaning those are same

Answered by GAUTHMATH

Answer:

D makes sense. I think the answer is D.

Answer:  70  and -16

==========================================================

Explanation:

For now, we'll assume x is the largest value (aka the max)

Let's sort the values from smallest to largest.

7, 20, 26, 27, 34, 41, 47, x

We see that 7 is the smallest item, so,

range = max - min = x - 7

Set this equal to 63 and solve for x

x-7 = 63

x = 63+7

x = 70

So x could be equal to 70.

---------------------------

Next, we'll assume that x is the smallest value

That means the min is x and 47 is now the max

max - min = range

47 - x = 63

-x = 63-47

-x = 16

x = -16

So if x is the smallest value, then it must be -16

----------------------------

Finally, we'll let x be somewhere between 7 and 47

Unfortunately, we can't pin down a specific value here since we could have lots of possible values. Three such examples are x = 8, x = 9, and x = 10. There are many others.

If your teacher is looking for 2 values only, then I would refer to the previous two sections and ignore this section entirely.

Answer:

[tex]m\widehat{MP}=118^{\circ}[/tex]

Step-by-step explanation:

In any circle, the measure of an inscribed angle (an angle created when the intersection of two chords is on the circle) is equal to half of the arc it forms. In this case, [tex]\angle MPN[/tex] is an inscribed angle that forms [tex]\widehat{MN}[/tex]. Therefore, the measure of arc MN must be twice the measure of angle MPN:

[tex]m\widehat{MN}=2\cdot m\angle MPN,\\m\widehat{MN}=2\cdot 31^{\circ}=62^{\circ}[/tex]

Since we want to find the measure of arc MP, we need to know that there are 360 degrees in a circle. Since [tex]\overline{PN}[/tex] is a diameter of the circle (line that has two endpoints on the circle and that passes through the center of the circle), each side of [tex]\overline{PN}[/tex] must be 180 degrees.

Therefore, we have:

[tex]m\widehat{MN}+m\widehat{MP}=180^{\circ},\\62^{\circ}+m\widehat{MP}=180^{\circ},\\m\widehat{MP}=\boxed{118^{\circ}}[/tex]

Answer:

h = 8 sqrt(2)

Step-by-step explanation:

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

sin theta = opp / hyp

sin 45 = 8 / h

h sin 45 = 8

h = 8 / sin 45

h = 8 / (1 sqrt(2)

h = 8 sqrt(2)

Answer:

right answer is option D

Step-by-step explanation:

tan 45 = BC/8. ; BC - Lower side

BC = 8

h = 8sq. + 8sq = √128 = 8√2

Answer:

x:-4,-3,-2,-1,0,1

f(x):-10,0,0,-4,-6,0

from the table we can see when x=0, y=-6

Therefore the y-intercept will be (0,-6)

OAmalOHopeO

The y intercept of the continuous function in the table is given by the relation f ( 0 ) = -6

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given data ,

Let the function be represented as A

Now , the value of A is

Let the values of x be x = { -4 , -3 , -2 , -1 , 0 }

Let the values of y be y = { -10 , 0 , 0 , -4 , -6 }

Now , the y intercept of the function is when the value of x = 0

So , when x = 0 , the value of y = -6

And , f ( 0 ) = -6

Therefore , the y intercept is ( 0 , -6 )

Hence , the y intercept of the function is ( 0 , -6 )

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The predicted value of Y when X = 0. Therefore, option D is the correct answer.

Regression analysis is one of the sophisticated statistical modeling techniques in which we try and establish a relationship between variables, the dependent or response variable, and one or more independent or explanatory variables.

The linear regression equation of a single variable can be written down as: Y=a+bX

According to the definition of the equation of regression analysis, the Y-intercept represents the predicted value of Y when X = 0.

The Y-intercept, as the name suggests, is the point when the regression line crosses the y axis. This happens only when the value of the x variable is zero:

Y-intercept = Y(0)=a+b(0)

Y-intercept=a

Therefore, option D is the correct answer.

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Answer:

Al inicio Iván tenía 8.1 litros de agua hervida.

Step-by-step explanation:

Dado que Iván sabe que por su salud debe tomar agua hervida, y llenó 3 botellas de agua hervida para empezar con 7,2 L usando 3 botellas grandes y 5 botellas pequeñas, y no llenó otra botella ya que le faltaba 0,5L pero llenó una pequeña mas y le quedaron 0,3L de agua hervida para tomar, para determinar cuánta agua hervida tenia al inicio Iván se debe realizar el siguiente cálculo:

Botella grande = -0.5 litros

Botella chica = +0.3 litros

0.5 + 0.3 = 0.8

Así, la diferencia entre una botella grande y una botella chica es de 0.8 litros.

3X + 5(X - 0.8) = 7.2

3X + 5X - 4 = 7.2

8X = 7.2 + 4

X = 11.2 / 8

X = 1.4

3 x 1.4 + 5 x 0.6 = 7.2

7.2 + 0.6 + 0.3 = 8.1

Por lo tanto, al inicio Iván tenía 8.1 litros de agua hervida.

Answer:

6, permutation

Step-by-step explanation:

Book 1, CD 1

Book 1, CD 2

Book 1, CD 3

Book 2, CD 1

Book 2, CD 2

Book 2, CD 3

There are 6 permutations.

Answer: B

Step-by-step explanation:

Using slope formula, change in y (3) over change in x (2) is 3/2. So the equation would be y=3/2x.

Answer:

(e) (27, 2) and (243, 18)

(g) (63, 9) and (84, 12)

(d) (45, 15) and (60, 20)

(c) (27, 12) and (72, 32)

(a) (15, 30) and (20, 40)

(b) (12, 32) and (18, 48)

(f) (18, 63) and (24, 84)

Step-by-step explanation:

Required

Arrange in increasing order of slope

Slope (m) is calculated using:

[tex]m = \frac{y_2 -y_1}{x_2 - x_1}[/tex]

So, we have:

(a) (15, 30) and (20, 40)

[tex]m = \frac{40 -30}{20- 15}[/tex]

[tex]m = \frac{10}{5}[/tex]

[tex]m =2.00[/tex]

(b) (12, 32) and (18, 48)

[tex]m = \frac{48 -32}{18- 12}[/tex]

[tex]m = \frac{16}{6}[/tex]

[tex]m = 2.67[/tex]

(c) (27, 12) and (72, 32)

[tex]m = \frac{32-12}{72- 27}[/tex]

[tex]m = \frac{20}{45}[/tex]

[tex]m = 0.44[/tex]

(d) (45, 15) and (60, 20)

[tex]m = \frac{20-15}{60- 45}[/tex]

[tex]m = \frac{5}{15}[/tex]

[tex]m = 0.33[/tex]

(e) (27, 2) and (243, 18)

[tex]m = \frac{18-2}{243- 27}[/tex]

[tex]m = \frac{16}{216}[/tex]

[tex]m = 0.07[/tex]

(f) (18, 63) and (24, 84)

[tex]m = \frac{84-63}{24- 18}[/tex]

[tex]m = \frac{21}{6}[/tex]

[tex]m = 3.50[/tex]

(g) (63, 9) and (84, 12)

[tex]m = \frac{12 -9}{84- 63}[/tex]

[tex]m = \frac{3}{21}[/tex]

[tex]m = 0.14[/tex]

From least to greatest slope, the pair of points are:

(e) (27, 2) and (243, 18)

(g) (63, 9) and (84, 12)

(d) (45, 15) and (60, 20)

(c) (27, 12) and (72, 32)

(a) (15, 30) and (20, 40)

(b) (12, 32) and (18, 48)

(f) (18, 63) and (24, 84)

Answer:

From least to greatest slope, the pair of points are:

(e) (27, 2) and (243, 18)

(g) (63, 9) and (84, 12)

(d) (45, 15) and (60, 20)

(c) (27, 12) and (72, 32)

(a) (15, 30) and (20, 40)

(b) (12, 32) and (18, 48)

(f) (18, 63) and (24, 84)

Step-by-step explanation:

Answer:

7.9ft

Step-by-step explanation:

Cos44 x 11

= 7.912737804

≈ 7.9 ft

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