log_8(5x+4)=3x-4
Write the log equation as an exponential equation. You do not need to solve for X

Answer:

Bhāskara was a 7th-century mathematician and astronomer, who was the first to write numbers in the Hindu decimal system with a circle for the zero, and who gave a unique and remarkable rational approximation of the sine function in his commentary on Aryabhata's work. 

Aryabhatta is the father of Indian mathematics. He was a great mathematician and astronomer of ancient India. His major work is known as Aryabhatiya. It consists of spherical trigonometry, quadratic equations, algebra, plane trigonometry, sums of power series, arithmetic.

Step-by-step explanation:

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Answer:

[tex]x = - 3 \: and \: y = - 11[/tex]

Step-by-step explanation:

L

[tex]since \: y = 2x - 5(equation \: 1) \: \\ [/tex]

[tex]substitute \: for \: y \: in \: equation \: 2 \: (6x + 7 = y)[/tex]

[tex]6x + 7 = y \\ 6x + 7 = 2x - 5 \\ collect \: like \: terms \\ 6x - 2x = - 5 - 7 \\ 4x = - 12 \\ x = \frac{ - 12}{4} \\ x = - 3[/tex]

[tex]substitute \: for \: x in \: equation \: 1[/tex]

[tex]y = 2x - 5 \\ y = 2( - 3) - 5 \\ y = - 6 - 5 \\ y = - 11[/tex]

Answer:

[tex]y = 2.x = \frac{1}{11} [/tex]

[tex] \binom{x - 56x + 7 = y}{y = 2} [/tex]

_______________________

1. Substitute y = 2 :

[tex](x - 56x + 7 = 2)[/tex]

2. Simplify :

[tex]( - 55x + 7 = 2)[/tex]

3. Isolate x for [tex]( - 55x + 7 = 2) : x = \frac{1}{11} [/tex]

4. The solution of the system of equations are :

[tex]y = 2.x = \frac{1}{11} [/tex]

Answer:

See below ~

Step-by-step explanation:

Question 6(e) :

⇒ x² ≤ 16

Take square root on each side :

⇒ √x² ≤ √16

⇒ x ≤ 4 and x ≥ -4

⇒ -4 ≤ x ≤ 4

⇒ x² ≤ 16

Apply the absolute rule if x² < a then -√a < x < √a

⇒ -√16 ≤ x ≤ +√16

⇒ -4 ≤ x ≤ 4

First of all, The student should have subtracted both sides by 4

What he should have done:

[tex]\rightarrow \sf \dfrac{3}{x-2} > 4[/tex]

[tex]\rightarrow \sf \dfrac{3}{x-2} -4 > 4 -4[/tex]

[tex]\rightarrow \sf \dfrac{3}{x-2} -\dfrac{4(x-2)}{x-2} > 0[/tex]

[tex]\rightarrow \sf \dfrac{3-4(x-2)}{x-2}} > 0[/tex]

[tex]\rightarrow \sf \dfrac{3-4x+8}{x-2}} > 0[/tex]

[tex]\rightarrow \sf \dfrac{-4x+11}{x-2}} > 0[/tex]

[tex]\sf \large \boxed{\sf {\left \{ {{-4x+11 = 0} \atop {x-2 = 0}} \right. }}[/tex]

⇒ -4x + 11 = 0, x - 2 = 0

⇒ -4x = -11, x = 2

⇒ x = 11/4 , x = 2

Solution satisfying the inequality:

⇒ 2 < x < 11/4

Answer:

Negative thirty

Step-by-step explanation:

The triangle are similar because they satisfy the AAA postulate : Triangle ABC ~ Triangle PQR ( AAA similarity postulate )

A triangle can be defined as a plain shape that has three sides and three angles.

Congruent triangles are triangles that satisfy one or more congruence postulates or laws. The triangles could either be similar based on their angles or sides or angles and side being similar.

In conclusion, The triangle are similar because they satisfy the AAA postulate : Triangle ABC ~ Triangle PQR ( AAA similarity postulate )

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The similarity relationship is  AC / EC = AB / ED.

The length of AB is 157.50m.

When two triangles are similar, the ratio of the known sides of the triangles can be used to determine the length of the side of the unknown length.

The similarity relationship is : AC / EC = AB / ED

AC = 160 + 50 = 210

210 / 160 = AB / 120

AB = (210 X 120) / 160 = 157.50

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To solve the theorem, we will  take the square of the longest side of a right triangle and equate to the sum of the squares of the other two sides

Pythagoras theorem states that the square of the longest side of a right triangle is equal to the sum of the squares of the other two sides

For instance, let;

According to the theorem above, mathematically;

c² = a² + b²

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Multiply the top equation by -3 and then adding both the equations one variable will be eliminated. So the correct answer is option D.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

We are having two equations:-

2x - 4y = 5

6x - 3y=10

When we multiply the first equation by -3 the equation will become as follows:-

-6x  +  12y = - 15

6x   -  3y  =   10

By adding both the equations one variable will be eliminated:-

9y = - 5

Therefore Multiply the top equation by -3 and then add both the equations one variable will be eliminated. So the correct answer is option D.

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Answer:

1347 hours

Step-by-step explanation:

Assuming the income is net income (total after taxes etc.):

To calculate the number of hours to be worked to save enough to buy the car, divide the cost of the car by hourly net income:

[tex]\begin{aligned}\implies \textsf{Number of hours to work} & = \dfrac{\textsf{Cost of car}}{\textsf{hourly net income}}\\\\& = \sf \dfrac{17500}{13}\\\\& = \sf 1346.1538...\end{aligned}[/tex]

We have to round the number up to 1347 hours, as only $17,498 will be saved if 1346 hours are worked.

The average working week is approximately 40 hours, therefore to calculate how many weeks it would take to earn enough money to purchase the car, divide the number of hours by 40:

⇒ 1347 ÷ 40 = 33.675

So it would take 34 weeks, working an average of 40 hours a week and not spending any of the money earned, to save enough to purchase the car.

Total hours

Round to the next whole instead of nearest whole to avoid depicit

In most of the countries the average working hours per week is

Total weeks

Answer:

3-x is the inverse of f(x)=x-3

The tangent of an angle is the ratio of perpendicular to the base. The angle will the guy wire makes with the ground will be 80.91°.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

A tower, 50 feet high, is secured with a guy wire anchored 8 feet from the base of the tower.

The angle will the guy wire makes with the ground will be given by the tangent.

The tangent of an angle is the ratio of perpendicular to the base.

Then we have

tan θ = 50/8

tan θ = 6.25

     θ = tan ⁻¹ (6.25)

     θ = 80.9097

     θ ≅ 80.91°

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Answer:

the probability is %25 percent :P

Step-by-step explanation:

The probability that the student was NOT a female that got a "C" is 15 / 32.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that the student was NOT a female that got a "C" = number of males that got a C / total number of people that got a C =  15 / 32.

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Answer:

Step-by-step explanation:

Identity used:  (a +b)³ = a³ + b³ + 3ab(a +b)

       p + q = -2  ------------------(I)

Both sides take cube,

        (p +q)³ = (-2)³          

a = p and b =q

  p³ + q³ + 3pq(p +q) = -8

  p³ + q³ + 3pq*(-2)   = - 8        {From (I)}

  p³ + q³  - 6pq         = -8

                  p³ + q³    = -8 + 6pq

             p³ + q³   + 8 = 6pq

Hence, proved.

Answer:

[tex] \text{C.} \: f(x) \: = \: |x| [/tex]

Step-by-step explanation:

To identify the absolute value of a number, it will always be represented between two sticks.

The answer is A

[tex]y = - x - 6 \\ 0 = - x - 6 \\ x = - 6[/tex]

so x intercept : (-6,0)

and slope is negative

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The equation of line which a slope is -1 and an x-intercept of (-6,0) will be;

⇒ y = - x - 6

The equation of line in point-slope form passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The slope of the line = - 1

And, The x-intercept = (- 6, 0)

Now,

Let the equation of line;

⇒ y = - x - 6

Slope (m) = dy/dx = - 1

And, The x - intercept is find as;

Put y = 0;

⇒ y = - x - 6

⇒ 0 = - x - 6

⇒ x = - 6

Thus, The correct equation is,

⇒ y = - x - 6

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The answer to your question would be 43/15 or 2.866 and ongoing.

Answer:

if I am awake then it is 9 am.

Step-by-step explanation:

if p then q the converse is if q then p.

The volume of the cylinder will be equal to 1017.87 cubic feet.

Volume is defined as the space occupied by any object in the three-Dimensions. For the cylinder, the volume will be calculated by radius and the height of the cylinder.

Given that:-

The volume of the cylinder will be calculated by using the formulas below:-

V = πr²h

V = π ( 9 )² 4

V = 1017.87 cubic feet.

Therefore the volume of the cylinder will be equal to 1017.87 cubic feet.

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Answer:

10.5 miles.

Step-by-step explanation:

If she walks 7/10 of a mile each morning, and 1, 4/10 of a mile each day, Belle walks a total of 2 1/10 of a mile each day (2.1) miles each day)

We can just multiply the amount of miles per day by 5, (2.1 x 5) and we get 10.5 miles total.

Answer:

10 1/2

Step-by-step explanation:

divide 7/10 which is 0.7 then multiply that by 5 which is 3.5

then divide 4/10 which is 0.4 then multiply that by 5 which is 2, but add 5 which is 7.

then combine all of that together which is 3.5+7= 10.5

then convert that into a fraction which is 10 1/2

Answer:

a

x

2

+

b

x

+

c

=

0

the two roots of the equation take the form

x

1

,

2

=

−

b

±

√

b

2

−

4

a

c

2

a

So, start by adding

−

5

to both sides of the equation to get

2

x

2

+

x

−

5

=

5

−

5

2

x

2

+

x

−

5

=

0

Notice that you have

a

=

2

,

b

=

1

, and

c

=

−

5

. This means that the two solutions will be

x

1

,

2

=

−

1

±

√

1

2

−

4

⋅

2

⋅

(

−

5

)

2

⋅

2

x

1

,

2

=

−

1

±

√

41

4

You can simplify this if you want to get

x

1

=

−

1

+

√

41

4

≅

1.35078

and

x

2

=

−

1

−

√

41

4

≅

−

1.85078

Answer:

(2x-2)=

     +2 =+2

(2x)=2

----------

    2

x= 1

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

(x+5)=

   -5=-5

x= -5

Step-by-step explanation:

You just need to separate the variable from the numbers

By using the midpoint approach, the price elasticity of demand between each of the given prices are:

The price elasticity of demand measures the responsiveness of the quantity demanded by a consumer with respect to a specific change in price of the product, all things being equal (ceteris paribus).

By using the midpoint approach, the price elasticity of demand between each of the given prices is given by:

Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]

Price elasticity of demand = (15 - 5)/[(15 + 5)/2]/(25 - 30)/[(25 + 30)/2]

Price elasticity of demand = 1/-0.1818

Price elasticity of demand = 5.50.

Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]

Price elasticity of demand = (25 - 15)/[(25 + 15)/2]/(20 - 25)/[(20 + 25)/2]

Price elasticity of demand = 0.5/-0.2222

Price elasticity of demand = 2.25.

Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]

Price elasticity of demand = (35 - 25)/[(35 + 25)/2]/(15 - 20)/[(15 + 20)/2]

Price elasticity of demand = 0.33/-0.2857

Price elasticity of demand = 1.17.

Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]

Price elasticity of demand = (45 - 35)/[(45 + 35)/2]/(10 - 15)/[(10 + 15)/2]

Price elasticity of demand = 0.25/-0.4

Price elasticity of demand = 0.63.

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The given polygon isa pentagon and the sum of its exterior angle is  360°. The value of x from the given polygon is 8

The given polygon isa pentagon and the sum of its exterior angle is  360°.

Take the sum of the angles and equate to  360° as shown;

77 + 66 + 62+ 59 + 12x =  360°

264 + 12x = 360

12x = 96

x = 8

Hence the value of x from the given polygon is 8

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The value of the length DF is 17

The statement Triangle ABC = Triangle ADF means that the triangles ABC and ADF are congruent triangles.

So, we have:

AB = AD

AC = A F

BC = DF

Given that BC = 17;

The equation BC = DF becomes

17 = DF

Rewrite as:

DF = 17

Hence, the value of the length DF is 17

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Answer:

6

Step-by-step explanation:

Answer:

2 or A

Step-by-step explanation:

Correct on edge22

Any proper CDF [tex]F(x)[/tex] has the properties

• [tex]\displaystyle \lim_{x\to-\infty} F(x) = 0[/tex]

• [tex]\displaystyle \lim_{x\to+\infty} F(x) = 1[/tex]

so we have to have a = 0 and b = 1.

This follows from the definitions of PDFs and CDFs. The PDF must satisfy

[tex]\displaystyle \int_{-\infty}^\infty f(x) \, dx = 1[/tex]

and so

[tex]\displaystyle \lim_{x\to-\infty} F(x) = \int_{-\infty}^{-\infty} f(t) \, dt = 0 \implies a = 0[/tex]

[tex]\displaystyle \lim_{x\to+\infty} F(x) = \int_{-\infty}^\infty f(t) \, dt = 1 \implies b = 1[/tex]