solve the inequality 4x-18<_6x-16

Step-by-step explanation:

We are going to use the following properties of logarithms to solve this problem:

[tex]\log{\dfrac{a}{b}} = \log{a} - \log{b}[/tex]

and

[tex]\log{ab} = \log{a} + \log{b}[/tex]

So we can rewrite the given equation as

[tex]\log{2x^3} - \log{x} = \log{\left(\dfrac{2x^3}{x}\right)} = \log{2x^2}[/tex]

Also,

[tex]\log{16} + \log{x} = \log{(16x)}[/tex]

So we can write

[tex]\log{2x^2} = \log{(16x)}[/tex]

or eliminating the log symbols, we get

[tex]2x^2 = 16x[/tex]

The solutions for the equation above are

[tex]x = 8\:\text{and}\: 0[/tex]

The path between each building is an illustration of Pythagoras theorem.

See attachment for a copy of the given image.

The sidewalk between library and humanities

This is represented with (a).

The value of (a) will be calculated using Pythagoras theorem.

So, we have:

[tex]a^2 = 15^2 + 15^2[/tex]

[tex]a^2 = 450[/tex]

Take square roots

[tex]a = 21.21[/tex]

Sidewalk between chemistry and library

This is represented with (d).

First calculate the value of (b) and (c)

[tex]c + 15 = 30[/tex]

So:

[tex]c = 15[/tex]

Also:

[tex]b + 15 = 40[/tex]

So:

[tex]b = 25[/tex]

The value of (d) will be calculated using Pythagoras theorem.

[tex]d^2 = b^2 + c^2[/tex]

[tex]d^2 = 25^2 + 15^2[/tex]

[tex]d^2 = 850[/tex]

Take square roots

[tex]d = 29.15[/tex]

The sidewalk between chemistry and humanities

This is represented with (e).

The value of (e) will be calculated using Pythagoras theorem.

[tex]e^2 = d^2 + a^2[/tex]

[tex]e^2 = 850 + 450[/tex]

[tex]e^2 = 1300[/tex]

Take square roots

[tex]e = 36.06[/tex]

Learn more about Pythagoras theorem at:

https://brainly.com/question/343682

Answer:

A. y = |x - 5| - 4

Step-by-step explanation:

The shape of the graph is a V with slope 1 on the right side and slope -1 on the left side. The parent function is y = |x|. The vertex of the V in the parent function is at (0, 0). Here, there has been a translation of the vertex to (5, -4).

The x-coordinate shifted 5 units right, or a shift of +5, and the y-coordinate shifted 4 units down, or a shift of -4.

y - k = |x - h| shows a shift of h units in x and k units in y when compared to the parent function y = |x|.

y - (-4) = |x - 5|

y + 4 = |x - 5|

y = |x - 5| - 4

Answer: A. y = |x - 5| - 4

9514 1404 393

Answer:

  264x³-66x

Step-by-step explanation:

The order of operations requires this be evaluated as ...

  11x(96x÷4x -6) . . . . given

  11x(24x·x -6) . . . . . . division inside parentheses

  11x(24x² -6) . . . . . . multiplication inside parentheses

  264x³ -66x . . . . . multiply by outside factor (use the distributive property)

_____

Additional comment

The appearance of the expression in parentheses may induce you to evaluate it as (96x)÷(4x) = 24. The order of operations requires that you do the division before the multiplication, left to right, so this must be evaluated as ...

  ((96x)÷4)x = 24x²

You need to be very careful with division and with exponents to make sure to follow the Order of Operations exactly. If you have an appropriate calculator, it will do that automatically. For example, if you tell your calculator ...

  (for x=2) 11×2×(96×2÷4×2-6)

it should give you the result 1980, not 396.

Answer:

= 198x

Step-by-step explanation:

11x × { 96x ÷ 4x -6}

11x × { 24x -6}

264x - 66x

= 198x

You got the correct answer

Step-by-step explanation:

[tex]A(2)=A(2-1)+6=A(1)+6=12+6=18[/tex]

Answer:

-11

Step-by-step explanation:

if you put the numbers of the variebles in, it would be

-6-9+9-5

Answer:

9

-6a = 54

9x = -45

54 + (-45) = 9

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The triangle will have the noted sides the same length. It is best if they are marked as having the same length. The names of the same-length segments tell you the a.pex is point Y.

Answer:

= 77

Step-by-step explanation:

{3 × [tex]2^{2}[/tex] - 3} -2 × 11

Solve the brackets first

{ 3 × 4  - 3} -2 × 11

{12 - 3 }  -2 × 11

9  -2 × 11

9  -22

= -13

Answer:

-13

Step-by-step explanation:

Solve in the bracket first

(3*4 -3) -2 * 11

(12 - 3) -22

9 - 22

-13 is the final answer

Answer:

what is statistics ???

explain !!!

Step-by-step explanation:

Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data. ... Probability is a mathematical language used to discuss uncertain events and probability plays a key role in statistics.Please mark me as brainliest

Answer =1267.2

Step-by-step explanation:

6(3+5)26.4

6×8×26.4

48×26.4

1267.2 is the answer

Answer:

3/4 hours I believe so??

Answer:

125

Step-by-step explanation:

400÷2 = 200

300÷2 = 150

so,

250÷2 = 125

Answer:

Ans; 10⁴ —> 10, 000

Ans; 10-⁴ / 10² —> 1/ 10⁶ = 0. 000 001

Ans; 10-⁴ × 10² —> 1/ 10² = 0.01

Ans; 10-⁴ —> 1/ 10⁴ = 0. 000 1

I hope I helped you^_^

Answer:

A=a

B=d

C=c

D=b

Step-by-step explanation:

Answer:

[tex]u + xy \\ 18 + 10 \times 8 \\ 10 + 80 \\ 90[/tex]

Answer:

Solution,

here,

u=18

x =10

y= 8

=u+xy

=18+(10×8)

=18+80

=98

9514 1404 393

Answer:

  t(n) = -n^2 -n +102

Step-by-step explanation:

We can use the first 3 terms to find a, b, c.

  a(1)^2 +b(1) +c = 100

  a(2)^2 +b(2) +c = 96

  a(3)^2 +b(3) +c = 90

Subtract the first equation from the other two:

  3a +b = -4 . . . . . . [eq4]

  8a +2b = -10 . . . . [eq5]

[eq5] can be reduced to

  4a +b = -5 . . . . . . [eq6]

Subtracting [eq4] from [eq6] gives ...

  (4a +b) -(3a +b) = (-5) -(-4)

  a = -1 . . . . . . . . simplify

Filling that into [eq4], we get

  3(-1) +b = -4

  b = -1 . . . . . . . add 3

Putting the values for 'a' and 'b' into the first equation gives ...

  -1 +-1 +c = 100

  c = 102

Then the n-th term t(n) of the sequence is ...

  t(n) = -n^2 -n +102

_____

Additional comment

As you might guess, there is a generic solution for quadratic sequences. In terms of the first term (a1), first first difference (d1), and second difference (d2), the coefficients can be written as ...

This sequence has first differences of -4, -6, -8, -10, and second differences of -2. Putting the sequence values into the above formulas, we find ...

9514 1404 393

Answer:

Step-by-step explanation:

Consider a zero at x=1.

If it has multiplicity 1, the corresponding factor is (x -1). Now consider the sign of that factor for x = 1.1. The value is (1.1 -1) = 0.1, a positive number.

When the value of x is 0.9, the factor is (0.9 -1) = -0.1, a negative number.

This tells you that values to the left of a zero make the factor(s) associated with that zero be negative. For x-values to the right of the zero, the factor(s) will be positive.

If the multiplicity is even, the product of those factors is positive on either side of the zero. (A negative number to an even power is a positive number.) That is, the graph will not change sign from one side of an even-multiplicity factor to the other. At an odd-multiplicity factor, the graph changes sign.

__

For the problem at hand, the only even-multiplicity factor is (x -1), so the graph will not change sign at x=1. It will touch the axis (be tangent to the x-axis), but will not cross. The other zeros have odd multiplicity (1 or 3), so the graph will change sign there.

It is worthwhile to note that the higher the multiplicity, the "flatter" the graph is at the zero. You can see this in the attachment by comparing the shape of the graph at x=6 with the shape at x=2 (also an upward zero crossing).

_____

Additional comment

You may wonder why the curve is below the x-axis at x=1 when the product of the factors in that neighborhood is always positive. The reason is that there are an odd number of zeros to the right of x=1, so the product of those factors is negative.

[tex]\text{CJ}=3\text{x}+6\\\\\text{CT}=37\\\\\text{JT}=3\text{x}+7\\\\\text{CJ}+\text{JT}=\text{CT}\\\\3\text{x}+6+3\text{x}+7=37\\\\6\text{x}+13=37 \ \ /-13\\\\6\text{x}=24 \ \ /:6\\\\\text{x}=4\\\\\text{JT}=3\cdot4+7=12+7=\boxed{19}[/tex]

Answer:

[tex]\huge\boxed{-2}[/tex]

Step-by-step explanation:

Use any two points from the line.

Let them be:

(x1,y1) = (0,-2)

(x2,y2) = (-1,0)

Now,

[tex]\displaystyle Slope = \frac{y_2-y_1}{x_2-x_1} \\\\Slope = \frac{0-(-2)}{-1-0} \\\\Slope = \frac{2}{-1} \\\\Slope = -2\\\\\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

x = 5.5 inches.

Step-by-step explanation:

The perimeter is the sum of the 3 sides, so:-

x + x + 3 + 2x + 5 = 30

4x + 8 = 30

4x = 22

x = 5.5.

Step-by-step explanation:

17 nickels and 5 quarters I just thought way to much for such a simple question

Answer:

21 loads

Step-by-step explanation:

357/17=21

Answer:

Set the denom to 0 and solve.

x^2 - 16 = 0 --> x = -4,4

This means the vertical asymptote is 4, -4.

Therefor, the domain is for all real numbers that are not 4, -4.

We ignore the top because if the numerator was 0, it's still a number. But if the denom was 0, then it would be impossible (you can't divide by 0). So for all numbers that can go into the denom that aren't 0, is your domain.

Answer:

[tex] {x}^{2} + 4b = 0 \\ {x}^{2} = - 4b \\ x = \sqrt{ - 4b} \\ x = 2 \sqrt{b} i \\ thank \: you[/tex]

Answer:

600,000+80,000+700+5

Answer:

36.8

Step-by-step explanation:

I think A=36.8

Hope it will help you (:

9514 1404 393

Answer:

  C.  (x -1)/(x +7)

Step-by-step explanation:

The factor (x +1) in the numerator cancels the same factor in the denominator, leaving the ratio (x -1)/(x +7). This matches choice C.

_____

Additional comment

Even though (x+1)/(x+1) = 1 and can be removed from the expression, the fact that it is undefined at x=-1 means the reduced ratio (x-1)/(x+7) is only a valid representation of the original ratio when x≠-1. The factor (x+1) may be gone, but the domain restriction associated with it remains.