convert logx8=2 to exponential form​

The graph of the linear equation is attached below. After 11 months, the total savings will be $237.50.

What is a saving account?

An account in a retail bank is a savings account. Common characteristics include having a finite number of withdrawals allowed, not having check or connected debit card facilities, having few transfer choices, and not being able to become overdrawn.

Given equation is

y = 12.5x + 100

To find points on the linear equation, putting x = 0, 1 and 2 in the given equation:

y(0) = (12.5 × 0) + 100

y(0) = 100

y(1) = (12.5 × (1)) + 100

y(1) = 12.5 + 100

y(1) = 112.5

y(2) = (12.5 × 2) + 100

y(2) = 25 + 100

y(2) = 125.

The points on the linear equation are (0,100), (1, 112.5), (2,125).

Plot the points and join the points to draw the line to get graph the linear equation.

Putting y = 237.50 in the given equation y = 12.5x + 100:

237.50 = 12.5x + 100

Subtract 100 from both sides:

237.50 - 100 = 12.5x + 100 - 100

137.50 = 12.5x

Divide both sides by 12.5:

x = 137.50/12.5

x = 11

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Answer:

53

Step-by-step explanation:

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Answer:

B. 73°

Step-by-step explanation:

mL HLK = ½ × mL HJK = ½×146=73°

Answer:

16 x 12 = 192

192 x 2 = 384

10 x 8 = 80, 80 divided by 2 = 40

40 x 2 = 80

10 x 16 = 160

Add all given areas:

384 + 80 + 160 = 624 cm2 is your answer.

Answer:

120°

Step-by-step explanation:

I drew a picture that will make it easier to understand what's going on. Please see the attached image

In a rhombus, the diagonals bisect the opposite angles, and opposite angles are congruent.

Let's say angle 1 is x. The interior angles of a quadrilateral add up to 360°, so

30+30+30+30+2x=360

2x=240

x=120

angle 1 is 120°.

Answer:

  Truck                 Car              Total

Female           5                      35                40

Male              27                     21                48

Total              32                     56                88

P(buying a car given a male )  =  21/88 = .238 ≈ 24%

Step-by-step explanation:

Let B  = Probability of buying a car and being male    21/88

Let M = Probability of being a male  =  48/88

P(B l M)   =  P(B and M) / P(M)   =   (21/88) / (48/88)  = 21/48  = .4375  = 44%

Answer:

The answer will be 1.53 after dividing and rounding to the nearest tenth 3.5 divided by 2.29.

9514 1404 393

Answer:

  $1800

Step-by-step explanation:

The tax due is ...

  3% × $10,000 + 5% × ($40,000 -10,000)

  = 5% × $40,000 - (5% -3%)($10,000)

  = $2000 - 200

  = $1800 . . . . tax due

_____

Additional comment

The table is structured so you need to compute the amount due in each bracket and add those to find the total due.

I prefer to compute the tax due by applying the appropriate tax rate to the whole amount, then subtracting a "discount" that reflects the fact that the rate doesn't actually apply to the whole amount.

Step-by-step explanation:

Area (A) = (1/2)b×h = (1/2)(10)(6) = 30

Perimeter = 8+ 8 + 10 = 26

Answer:

the answer is 9 hope this helps

Step-by-step explanation:

9514 1404 393

Answer:

  (a)  m = 2

Step-by-step explanation:

The formula tells you the slope is ...

  m = (18 -10)/(5 -1) = 8/4

  m = 2

The function for position x(t) could be x(t) = 3t^2 - 2t + 10.

In mathematics, a function is a relation between two sets that assigns to each element of the first set exactly one element of the second set. In other words, it is a rule that describes how one set of values is related to another set of values. Functions are used to model real-world scenarios and to solve mathematical problems. Examples of functions include linear equations, polynomials, and trigonometric functions.

This is determined by using the equation x'(t) = a(t). Differentiating both sides of the equation, we get x'(t) = 6t - 2. Integrating this equation, we get x(t) = 3t^2 - 2t + C, where C is the constant of integration. Since x(1) = 10, we can substitute this value into the equation and solve for the constant of integration. Therefore, we get x(t) = 3t^2 - 2t + 10.

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Answer:

x=per hour

233=42x+65

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

If Anna's age is represented by A, then 12 more than Anna's age will be ...

  12 + A

Jason's age is said to be 12 more than Anna's age, so ...

  J = 12 + A

__

The sum of their ages will be J + A. That is said to be 50, so ...

  J + A = 50

_____

These equations can be solved by using the first to substitute for J in the second.

  (12 +A) +A = 50

  2A = 38 . . . . . . . . subtract 12

  A = 19 . . . . . . . . . . divide by 2

  J = 12 +19 = 31 . . . find Jason's age

Jason is 31; Anna is 19.

Answer:

4

Step-by-step explanation:

How many 2/5s are in 1 1/2? To make it easier and simpler , I would change these fractions into decimals . Our answer is there are ALMOST 4 of 2/5ths in 1 and a half .

Answer:

Part A:

This data is modeling an exponential function because the y-values are increasing at an increasing rate. For example, between station 1 and station 2, the time increased by 2 minutes, and between station 2 and station 3, the time increased by 4 minutes. The time between each station is increasing by a multiple of the time between the previous two stations. This indicates that the data follows an exponential curve.

Part B:

To represent this data as a function, we can use the formula y = ab^x, where a and b are constants and x is the input (station number).

Substituting in the values from the first data point, we get: 2 = ab^1

Substituting in the values from the second data point, we get: 4 = ab^2

We can then solve for a and b by dividing these equations:

4/2 = (ab^2)/(ab^1)

2 = b

Substituting this value back into the first equation, we get:

2 = a*2^1

1 = a

Therefore, the function that represents this data is y = 2^x.

Part C:

To find the average rate of change between station 2 and station 4, we can use the formula: (y2 - y1)/(x2 - x1).

Substituting in the values from the data, we get: (16 - 4)/(4 - 2) = 12/2 = 6.

Therefore, the average rate of change between station 2 and station 4 is 6.

Answer:

x = 32

Step-by-step explanation:

• any lower base angle is supplementary to any upper base angle.

here base angle = 2(x - 10) and upper base angle = 4x + 8

supplementary angles sum to 180°

sum the base and upper base angles and equate to 180

2(x - 10) + 4x + 8 = 180

2x - 20 + 4x + 8 = 180

6x - 12 = 180 ( add 12 to both sides )

6x = 192 ( divide both sides by 6 )

x = 32

In the geometric series 2, 4, 6, 8, 10, 12,..., 24 is the 12th term. Each number in this series is separated by a factor of two.

the total of a geometric sequence's terms. Sn=a1(1rn)1r, r1 denotes the sum of the first n terms in a geometric series. an infinite geometric series whose total is provided by the expression S=a11r and where |r|1.

A geometric sequence is a set of numbers that follows a pattern in which the next term is determined by multiplying the previous one by a factor known as the common ratio, r.

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The equilateral triangle ABC have a side length of 2 units of the radius length of the circle tangent to the line AB.

An equilateral triangle have all its side lengths equal so;

line AB = line BC = line AC

At points B and C where the lines AB and AC are tangent to the circle is the a side length BC of the equilateral triangle

Line BC form the diameter of the circle which is 2 radius of the circle so;

line BC = 2 × radius of the circle

line BC = 2 × 1

line BC = 2

Therefore, the side length of the equilateral triangle is 2 units of the radius of the circle tangent at point B and C.

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Answer:

The area of the rhombus is 25.83 cm².

Step-by-step explanation:

The area of a rhombus is given by:

[tex] A = \frac{d_{1} \times d_{2}}{2} [/tex]

Where:      

d₁: is one diagonal      

d₂: is the other diagonal = d₁ + 4 cm

We know that one side length of the rhombus is equal to d₁. We can imagine a right triangle inside the rhombus, with the following dimensions:

h: hypotenuse of the right triangle  

a: one side of the right triangle

b: is the other side of the right triangle  

From the above we know that:

h = d₁                                

[tex] a = \frac{d_{2}}{2} = \frac{d_{1} + 4}{2} [/tex]

[tex] b = \frac{d_{1}}{2} [/tex]            

We can find d₁ with Pitagoras:

[tex] h^{2} = a^{2} + b^{2} [/tex]  

[tex] d_{1}^{2} = (\frac{d_{1} + 4}{2})^{2} + (\frac{d_{1}}{2})^{2} [/tex]

[tex] d_{1}^{2} = \frac{1}{4}(d_{1}^{2} + 8d_{1} + 16 + d_{1}^{2}) [/tex]

By solving the above quadratic equation for d₁ and taking the positive solution we have:

[tex] d_{1} = 5.46 cm [/tex]    

So, d₂ is:

[tex] d_{2} = d_{1} + 4 = 5.46 cm + 4 cm = 9.46 cm [/tex]

Now, we can find the area:

[tex] A = \frac{d_{1} \times d_{2}}{2} = \frac{5.46 cm \times 9.46 cm}{2} = 25.83 cm^{2} [/tex]

Therefore, the area of the rhombus is 25.83 cm².

I hope it helps you!  

Answer:

[tex]5h^3- h - 3[/tex]

Step-by-step explanation:

Given

[tex](2h^3 + 6h) + (3h^3 - 7h - 3)[/tex]

Required

Standard form

We have:

[tex](2h^3 + 6h) + (3h^3 - 7h - 3)[/tex]

Remove bracket

[tex](2h^3 + 6h) + (3h^3 - 7h - 3) =2h^3 + 6h + 3h^3 - 7h - 3[/tex]

Collect like terms

[tex](2h^3 + 6h) + (3h^3 - 7h - 3) =2h^3 + 3h^3+ 6h - 7h - 3[/tex]

[tex](2h^3 + 6h) + (3h^3 - 7h - 3) = 5h^3- h - 3[/tex]

Hence, the standard form is:

[tex]5h^3- h - 3[/tex]

Answer:

A. (x - 4)² + (y + 7)² = 81

Step-by-step explanation:

The general equation for a circle is given by the formula;

x² + y² + 2hx + 2ky + c = 0  ......equation 1.

Where the center is C(-h, -k)

Also, the standard form of the equation of a circle is;

(x - h)² + (y - k)² = r²  ......equation 2.

Where;

Given the following data;

h = 4

k = -7

r = 9

Substituting into eqn 2, we have;

(x - 4)² + (y - {-7})² = 9²

Simplifying further, we have;

(x - 4)² + (y + 7)² = 81

Answer:

C, definitely two sides are different in the triangle.

A, it looks as if the bottom is a right triangle if you look at it in a different way.

The polygons that would be used in a net isosceles triangle & right triangle

A pyramid is a structure whose outer surfaces are triangular and converge to a single step at the top,

As, we need a triangular pyramid whose base has all the three sides equal in length.

We can have a net in the form of isosceles triangle whose two are equal

i.e., two sides are different in the triangle.

and also, bottom with the right angle

i.e.,  the bottom is a right triangle if you look at it in a different way.

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Answer:

9

Step-by-step explanation:

It’s a ratio.

5/30=x/54

reduce

1/6=x/54

cross multiply

54=6x

x=9

Answer:

2.5

Step-by-step explanation:

Decimeter is 0.1 meter (10 centimeters). That means 25 decimeters is 2.5 meters.