7•e^.1t =47 express the solution as a logarithmic in base e

a d

.....................................................

The solution to the exponential equation 8^(x/2)/4^(x/3) = 2^(-5/2) is given as follows:

x = -6/5.

The exponential equation for this problem is defined as follows:

[tex]\frac{8^{\frac{x}{2}}}{4^{\frac{x}{3}}} = 2^{-\frac{5}{2}}[/tex]

Both 8 and 4 are powers of 2, as follows:

Applying the power of power rule (multiplying the exponents), the expression on the left side can be rewritten as follows:

[tex]\frac{2^{\frac{3x}{2}}}{2^{\frac{2x}{3}}} = 2^{-\frac{5}{2}}[/tex]

When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents, hence:

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

The subtraction is obtained as follows:

3x/2 - 2x/3 = 9x/6 - 4x/6 = 5x/6.

(as the least common factor of 2 and 3 is of 6).

Then the simplified expression is of:

[tex]2^{\frac{5x}{6}} = 2^{-\frac{5}{2}}[/tex]

As the exponential function y = 2^x is injective, the solution is obtained as follows:

5x/6 = -5/2.

10x = -12

x = -6/5.

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Answer:

The sum is 2635

Step-by-step explanation:

I did this problem

Answer:

option D

Step-by-step explanation:

Answer:

b < –6 or b > 6

Step-by-step explanation:

The equation of the line in slope-intercept form, with the point (4, -5) and an undefined rate of change is x = 4.

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

In Mathematics, any line that has an undefined slope (rate of change) is a vertical line because it does not have a y-intercept. This ultimately implies that, a vertical line that is parallel to the y-coordinate (y-axis) would have an undefined slope (rate of change).

Generally speaking, the equation of a line that has an undefined slope (rate of change) is given by this mathematical expression;

x = a

Where:

a represents the x-intercept.

At point (4, -5), the required equation with an undefined slope (rate of change) is x = 4.

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Answer:

81/100 is the answer I believe if I'm wrong my bad

Answer:

81/100

Step-by-step explanation:

brainliest pls

The value of x is 8.

Angles are formed whenever two or more straight lines intersect. These angles produced thus have individual and some common properties of which some can add up to form complementary angles, or supplementary angles.

Two angles are said to be supplementary if the value of their sum add up to 180^o.

From the given question, we can deduce that;

m<1 + m<2 = 180^o              (definition of complementary angles)

(17x - 30) + (7x + 18) = 180^o

17x - 30 + 7x + 18 = 180^o

24x - 12 = 180

24x = 180 + 12

24x = 192

x = 192/ 24

  = 8

x = 8

The value of x is 8.

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Answer:

the first bubble is your answer hope it helps

Answer:

y = 3/2x - 3

Step-by-step explanation:

first find slope (m):

m = (-3/2 -(-15/2)) / (1 - (-3)) = (12/2) / 4 = 6/4 = 3/2

plug the point (1, -3/2) into the point-slope form (y-y1) = m(x-x1):

y - (-3/2) = 3/2(x-1)

y + 3/2 = 3/2x -3/2

now put it in slope-intercept form y = mx + b:

y = 3/2x -6/2

y = 3/2x - 3

Answer:

I think its b

Step-by-step explanation:

Answer:

[tex]80^{\circ}[/tex]

Step-by-Step Explanation:

The interior angles of the triangle are [tex]70^{\circ}, (14+6x)^{\circ}[/tex], and [tex](3x-3)^{\circ}[/tex].

Angles in a triangle add to [tex]180^{\circ}[/tex].

[tex]70+14+6x+3x-3=180 \\ \\ 81+9x=180 \\ \\ 9x=99 \\ \\ x=11[/tex]

So, [tex]m\angle A=14+6(11)=80^{\circ}[/tex].

The percent error in the amount of water Rich added is 15.93%.

When compared to the actual value, the percent error is the difference between the estimated and actual values.

The difference between the estimated value and the actual value in relation to the actual value is given as a percentage and is known as the percent error. In other words, the relative error times 100 equals the percent error.

Given that Rich added water to a solution in science class is 26.2 milliliters

Whereas the directions said to add water is 22.6 milliliters

The amount of water that is added more is 26.2 -22.6 = 3.6 milliliters

The percent error is = (3.6/22.6)*100%

The percent error is = 15.9292*100%

Therefore, the correct answer is option b) 15.93%.

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Answer:

Below

Step-by-step explanation:

3% loss means 97% (.97 in decimal ) remains

after 2 years :

 27 900 ( .97)^2 = £  26251 .11

Answer: D.

Step-by-step explanation:

1. Look at the range/IQR of each box-plot

2. The smaller the range = the less variability

Answer:

Step-by-step explanation:

original equation equivalent to 7x+5-3x-2 = 7x-3x+5-2=4x+3

the answer is 4x+3

Answer:

The answer is 4x+3

x

2

−3x−10

x

2

−(5x+x)−10

x

2

−5x+2x−10

x(x−5)+2(x−5)

(x−5)(x+2)

x=5

x=−2

sumofzeroes

=αβ=5×−2=−10

α+β=

9

−b

=−

1

(−3)

=3

productofzeroes

=αβ=5×−2=−10

αβ=

a

c

=

1

−10

=−10

proved

________________________

mark me brainliest........proved

On solving the provided question, we cans ay that - the value of the each unit in this time will be from unitary method is 85.

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

here,

value of the 20 unit is 1700

value of the each unit will be 1700/20 = 85

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Mrs. Smith will be responsible for paying $75.00

The normal monthly charge is $40.00 and the current balance is $110.00,

so the difference is $110.00 - $40.00 = $70.00.

Mrs. Smith negotiated a 50% credit, so she will receive

$70.00 x 0.50 = $35.00 credit.

To find the amount she is responsible for paying, we subtract the credit from the current balance

$110.00 - $35.00 = $75.00

Thus, the amount Mrs. Smith will be responsible for paying is $75.00

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Answer:

5,859,375

Step-by-step explanation:

a10 = 3×5^9 = 3×1,953,125

= 5,859,375

Answer:

5,859,375

Step-by-step explanation:

Given :-

And we need to find out the 10th term of the sequence. Here firstly we should find the Common Ratio and then we can substitute the respective values in the formula to find the nth term of a geometric sequence .

Common Ratio :-

[tex]:\implies[/tex] CR = 15 ÷ 3 = 5

The 10 th term :-

[tex]:\implies[/tex] T_n = arⁿ - ¹

[tex]:\implies[/tex] T_10 = 3 × 5 ¹⁰ - ¹

[tex]:\implies[/tex] T_10 = 3 × 5⁹

[tex]:\implies[/tex] T_10 = 3 × 1953125

[tex]:\implies[/tex] T_10 = 5859375

Hence the 10th term is 5,859,375

The 3 types of terms in quadratic equation:

1) quadratic term,

2) linear term,

3) constant term.

We know that the second degree algebraic equation in x is a quadratic equation.

The standard form of quadrtic equation is ax^2 + bx + c = 0, where a, b, c are integers.

As thise is a quadratic equation, the value of a can not be zero. a ≠ 0

The term ax^2 is called the quadratic term.

From this term, the name given to the equation(quadrtic equation)

The term bx is called the linear term.

And the term c is called the constant term.

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Answer:

A, b, d

Step-by-step explanation:

Answer:

neither

Step-by-step explanation:

when slopes are the same its parallel

when slopes are multiplied and it equals -1 they are perpendicular

Answer:

1) 12.2425 square meters

2)$288

Step-by-step explanation:

According to the problem, we have a rectangle bedroom with 415cm long by 295cm width.

We know that 1cm = 0.01 m

Length of bedroom: 415 x 0.01 = 4.15m

of bedroom: 295 x 0.01 = 2.95m

area of rectangle: Length x Width

Area: 4.15 x 2.95 = 12.2425 square meters

We have a cost of carpet 24 per square meter is given from the problem.

we now know that it is in a whole number so we divide by 2 to get it square

A= 12m (squared)

now we multiply 12 and 24

we get $288

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Answer:

x = 15.8

Step-by-step explanation:

Answer:

Points identify starting and ending positions, and a line (in this case line segment) connects such points to show the distance between the two points.

Step-by-step explanation:

Answer:

n0p = 120°

Step-by-step explanation:

m0n + n0p = 180°

60° + n0p = 180°

n0p = 120°

Answer:

A) 24

B) 10

C) 4

Step-by-step explanation:

i multiplied for each question