Three pins are inserted into a cork mat at points c, e, and d. the three pins are collinear. how much string is needed to reach from the pin at e to the pin at d and then to the pin at c? leave your answer as a decimal to the nearest tenth.

Answer: 100 million or 100,000,000

Step-by-step explanation:

Do the exponent in the brackets. Then the one outside of the brackets.

10 to the power of 4=10000(which is 10 x 10 x 10 x10)

Then figure out 10000 the the power of 2.

10000 x 10000 = 100,000,000

Therefore the value of this is 100 million.

The simplification of the given logarithmic functions ln (2x-1)² = 7 is 17.055.

The logarithm of a number is the exponent by which a fixed value referred as the base should always be raised to generate a certain number. For instance, because 1000 is 10 to the third power, a log of 1000 to base 10 is 3.

Some properties of the logarithmic functions are defined as-

As, for the stated log or ln function ln (2 x-1)²=7

Use the power rule on the left side of the equation.

2 ln (2 x-1) = 7

Simplifying the equation.

ln (2 x-1) = 7/2

ln (2 x-1) = 3.5

Using the exponential property of the log.

e∧[ln (2 x-1)] = e∧3.5

2x-1 = 33.11

2x = 33.11 + 1

2x = 34.11

x = 34.11/2

x = 17.055

Therefore, the value of the x for the stated logarithmic functions ln (2x-1)² = 7 is calculated as 17.055.

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Answer: 1.7

Step-by-step explanation:

Answer: 8c + 40

Step-by-step explanation: i did this on OW

The base lengths are (2x + 3) and (x - 4) meters if the area of the base of the statue is 4x² + 12x + 9.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

It is given that:

The quadratic polynomial is:

= 4x² + 12x + 9

After using factor method:

= 2x² - 4x + 3x - 12

= 2x(x + 4) + 3(x - 4)

= (2x + 3)(x - 4)

Thus, the base lengths are (2x + 3) and (x - 4) meters if the area of the base of the statue is 4x² + 12x + 9.

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The area of a rectangular cement walkway of width x meters around a 50m by 25m pool is 4x²+150x sq. meters.

Rectangle area in geometry refers to the area that a rectangle occupies on a two-dimensional plane. A rectangle is a form of a quadrilateral, a two-dimensional object with four sides and four vertices. The four angles of the rectangle are all perfectly right angles or 90 degrees. The opposing sides of the rectangle are equal and parallel.

Area of Rectangle = Length × Breadth

In the given question,

The width of the walkway is x meters.

Width of the pool= 25+2x meters

and the Length= 50+2x.

So the area of the walkway with the pool is

= (25+2x)+(50+2x)

= 1250+100x+50x+4x²

= 4x²+150x+1250 sq. m

Area of the pool= 50x25

= 1250 sq. m

Area of the walkway= 4x²+150x+1250-1250

= 4x²+150x sq. meters.

Hence, the answer is 4x²+150x sq. meters.

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Answer:

5x+40-7<23

5x+33<23

5x<-10

x<-2

Darla can spend the greatest total cost of groceries in order to spend as close to $15 as possible is approximately $14.20.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Let the cost of the groceries be represented as "c", then we have;

Cost price + VAT = c + (5% of c)

In order to get the cost, c, that make him spend as close to $15. Since the tax is 5% of the cost price, then the cost price will be close to $15.

Let c = $14.20, then;

So that,

c + (5% of c) = 14.20 + (5% of 14.20)

                   = 14.20 + 0.71

                   = $14.91

Therefore, the greatest total cost of groceries she can spend in order to spend as close to $15 as possible is approximately $14.20.

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If Lily is sitting 40 feet away from a beautiful waterfall that is 1,000 feet high. The angle of inclination from Lily's location to the top of the waterfall is: 87.7°.

Given data or information:

Feet away=40 feet away

Feet high=1,000 feet high

Now let find or determine  the angle of inclination rom Lily's location to the top of the waterfall

Hence,

tanФ=1,000/40

Ф=tan^-1 (1,000/40)

Ф=87.70°

Therefore If Lily is sitting 40 feet away from a beautiful waterfall that is 1,000 feet high. The angle of inclination from Lily's location to the top of the waterfall is: 87.7°.

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Integers are positive and negative whole number digits, where the set of integers is denoted by capital Z.

Z={-n,...,-2,-1,0,1,2,...,36,37,38,39,...,n}

So 37 is in between 36 and 38

Answer:

In the first image, the triangles are congruent because each side measures equally to the other. The circles are not because they are not the same size. The big circle is 4 by 4 squaes and the small circle is 2 by 2.

In the second image the first image is congruent, and in the second image the figures are not congruent because the image to the right is thinner than the left.

Step-by-step explanation:

Hope it helps! =D

Answer: Ok for the first screen shot (the one with the triangles) its yes then the circles no

the upside down L 's yes

and the quadrilaterals no

Step-by-step explanation: congruent means the same or identical.

Hope it helped :D

Answer:

-85

Step-by-step explanation:

(-60) + (-25) = (-85)

Answer:

Step-by-step explanation:

the fish is 85 feet bellow the surface

explanation 60+25 is 85 so therefor -60-25 would be -85

[tex]{\huge\color{yellow}{\boxed{\fcolorbox{blue}{black}{꧁ANSWER ꧂}}}} \\ \\ \frac{3}{4} + ( - \frac{1}{4} ) \\ \\ = \frac{9 - 3}{12} = \frac{6}{12} = \frac{2}{4} \\ \\ \frac{3}{8} + ( - \frac{3}{8}) = 0(cancel \: \: out)[/tex]

Answer:

3/4 + (-1/4)

-1/4 = -0.25

3/4 = 0.75

3/8 + (-3/8)

-3/8 = -0.375

3/8 = 0.375

Answer:

Step-by-step explanation:

w(t)  =  F(t) - D(t) = water into (or out of the pool)

        =  t^2 + 8t+9      -   (t^2 +11t+4)

 w(t)        = -3t + 5       <===== shows all of the water will leak out after 5/3 hr

the two functions intersect at 5/3 hr    this is where water in = water out = dry pool

After expanding logarithm equation is : [tex]\frac{t^{\frac{2}{3}}(\frac{1}{2} log_7(r)+9)}{s^2t}[/tex]

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as  .

   [tex]log_ax=N[/tex]

where, a is the base of function or equation

           x define expression

Mathematically, if  [tex]a^N=x[/tex]  is an exponential function then, this can be converted to logarithmic function as  [tex]log_ax=N[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms are :

The given expression can be written as,

[tex]\frac{log_7(\sqrt{r} )+9}{s^2t^\frac{1}{3} }[/tex]

as, log (√x) = 1/2 log (x), equation becomes

[tex]= \frac{\frac{1}{2} log_7(r) + 9}{s^2t^\frac{1}{3} } \\[/tex]

now, after rationalize this equation

[tex]= \frac{t^{\frac{2}{3}}(\frac{1}{2} log_7(r)+9)}{s^2t}[/tex]

Thus, after expanding the logarithm equation is : [tex]\frac{t^{\frac{2}{3}}(\frac{1}{2} log_7(r)+9)}{s^2t}[/tex]

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The correct option is (x²- 2x + 4) for the quotient.

For the given question;

The equations are given as;

(x³ + 8) = (x + 2)

For finding the quotient; this could be written as,

(x³ + 8)/ (x + 2) = 1

Thus, we have

= (x³ + 8)/ (x + 2)

Rewriting the equation as;

=  (x³ + 2³)/ (x + 2)

Apply the formula of (a³ + b³) = (a+b)(a² - ab + b²) at the numerator;

= (x + 2)(x² -2x + 4)/  (x + 2)

Cancel the value of (x+ 2)

= (x² -2x + 4)

Thus, the quotient of the division is obtained as (x² -2x + 4).

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Answer:

1. E K H and F K G

2. E K F and H K G

3. E K F or G K H

4. F K G and G K J

5. G K J

Step-by-step explanation:

The solution to the inequality expression 22 >= -3x + 7 and -3x + 7 >-17 is -5 <= x  < 8

A number line is a  vertical or horizontal line that has endpoints and it is used to represent numbers at a constant interval

The expression is given as

22 >= -3x + 7 and -3x + 7 >-17

The above expression is an inequality expression

As a general rule:

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

So, we have

22 >= -3x + 7 and -3x + 7 >-17

Evaluate the like terms

15 >= -3x  and -3x  >-24

Divide through by -3

So, we have

-5 <= x  and x  < 8

Combine the expressions

-5 <= x < 8

Hence, the solution to the inequality expression 22 >= -3x + 7 and -3x + 7 >-17 is -5 <= x  < 8

See attachment for the number line

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Answer:

A. x < $20 or x > $150

B. x [tex]\geq[/tex] $25

C. x [tex]\leq[/tex] 35mph

D. x [tex]\leq[/tex] $4

Step-by-step explanation:

Not sure of the format desired for item A but this is what I came up with.

Step-by-step explanation:

Y should have a negative side in front of it.

[tex]2x - y = 5 \\ - y = - 2x + 5 \\ y = 2x - 5[/tex]

the equation of the line that has a slope of 1/5 and passes through (-5, -6) is: y = 1/5x - 5.

Given that the line passes through (-5, -6), and has a slope (m) = 1/5, to find the equation of the line, do the following:

Substitute (x, y) = (-5, -6) and m = 1/5 into y = mx + b to find the value of b:

-6 = 1/5(-5) + b

-6 = -1 + b

Add 1 to both sides

-6 + 1 = -1 + b + 1

-5 = b

b = -5

Substitute m = 1/5 and b = -5 into y = mx + b

y = 1/5x + (-5)

y = 1/5x - 5

Thus, the equation of the line that has a slope of 1/5 and passes through (-5, -6) is: y = 1/5x - 5.

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Answer:

(1, 1) , (5, 2), (6, 4), (4, 7) and (2, 3)

Step-by-step explanation:

When a point is rotated 180° about the origin(either clockwise or anticlockwise), the transformed coordinates are the negatives of the original coordinates.

Thus when a point (x, y) is rotated about the origin, its new coordinates become (-x, -y)

Given the original 5 vertices of the pentagon, the vertices of the rotated pentagon are transformed as follows

Original Vertex    ==>     Transformed Vertex

(-1, -1)                      ==>          (1, 1)
(-5, -2)                    ==>          (5, 2)
(-6, -4)                    ==>          (6, 4)
(-4, -7)                    ==>          (4, 7)
(-2, -3)                    ==>          (2, 3)

Answer:

1/8

Step-by-step explanation:

144 ÷ 18 = 8

so, it 1/8

The function y = (x + 3)² is the result of translating the function y = x² 3 units in the -x direction.

In this question we have a function of the form y = f(x), which is modified by transformation rules. The statement defines the original function as y = x² and we see that the resulting expression is y = (x + 3)². By direct observation, we that the latter function is the consequence of using an horizontal translation of the form:

g(x) = f(x - k), where k < 0.

This transformation rule indicates a horizontal translation in the - x direction. To be specific, a horizontal translation 3 units in the -x direction. Graphically specific, the graph of f(x) is moved 3 units in the - x direction.

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The answer to the present question is: log(a²b³/c⁴) = 2log(a) + 3log(b) - 4log(c)

For solving this kind of question, we are going to use these three identities:

log(x*y) = log(x) + log(y)   ....(1)

log(x/y) = log(x) - log(y)    ....(2)

log(xⁿ) = nlog(x)                ....(3)

So, using (2), log(a²b³/c⁴) may be written as: log(a²b³) - log(c⁴)  ....(4)

Again, using (1), log(a²b³) are often written as: log(a²) + log(b³)  ....(5)

Now, Putting equation (4) in equation (3), we get:

log(a²) + log(b³) - log(c⁴)   ....(5)

Now, using (3), expanding all the terms, we get:

log(a²) = 2log(a)log(b³) = 3log(b)log(c⁴) = 4log(c)

Putting of these in equation 5, we get:

2log(a) + 3log(b) - 4log(c)

Therefore,  log(a²b³/c⁴) = 2log(a) +3log(b) - 4log(c)

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Answer:

  2√10

Step-by-step explanation:

You want the simplest radical form of 6.32455532034.

In order for the given decimal value to have a "simplest radical form," we must assume it is an approximation of an irrational root. The given rational number is approximately equal to √40, differing in the 12th decimal place and beyond.

  6.32455532034 ≈ √40 = 2√10

__

Additional comment

The radical is simplified by removing all of the perfect squares from under the radical.

  40 = 2^3 × 5 = (2^2)(2×5) = (2^2)(10)

  √40 = 2√10

The value of the stock after 2 years was 0.6497xx.

What is Mathematical expression?

The combination of number and variable by using addition, subtraction, multiplication and division is called Mathematical expression.

Given that;

Christopher bought stock in a company two years ago that was worth xx dollars.

In the first year that he owned the stock, then it decreased by 11%.

In the second year the value of the stock decreased by 27%.

Now,

The multiplier of value for the first year was (1 - 11%) = 0.89

The multiplier of value for the second year was (1 - 27%) = 0.73

Then the multiplier of value for the two years was = 0.89 * 0.73

                                                                             = 0.6497

Hence, The value of the stock after 2 years was 0.6497xx.

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Answer:

[tex]\mathrm{88 + v}[/tex]