I need help with this

Answer:

[tex]x = 3[/tex]

Step-by-step explanation:

Given

[tex]\log6^{(4x-5)} =\log6^{(2x+1)}[/tex]

Required

Solve for x

We have:

[tex]\log6^{(4x-5)} =\log6^{(2x+1)}[/tex]

Remove log6 from both sides

[tex](4x-5) = (2x+1)[/tex]

Collect like terms

[tex]4x - 2x = 5 + 1[/tex]

[tex]2x = 6[/tex]

Divide by 2

[tex]x = 3[/tex]

9514 1404 393

Answer:

  9

Step-by-step explanation:

The ordered pair (2, 4) in the relation for function F tells you F(2) = 4.

The ordered pair (2, 5) in the relation for function G tells you G(2) = 5.

Then the sum is ...

  (F+G)(2) = F(2) +G(2) = 4 +5

  (F+G)(2) = 9

Answer:

[tex]{ \tt{ = ( log_{x}16)( log_{2}x) }}[/tex]

Change base x to base 2:

[tex]{ \tt{ = (\frac{ log_{2}16}{ log_{2}x } )( log_{2}x)}} \\ \\ { \tt{ = log_{2}(16) }} \\ = { \tt{ log_{2}(2) }} {}^{4} \\ = { \tt{4 log_{2}(2) }} \\ = { \tt{4}}[/tex]

Answer:

35

Step-by-step explanation:

y = 35x+23 is in the form

y = mx+b  where m is the slope and b is the y intercept

The slope can also be called the rate of change

35 is the slope

there are 12 set of months in a year

Answer:

[tex]{ \tt{hypotenuse = { \boxed{5}}}} \\ { \tt{opposite = { \boxed{3}}}} \\ { \tt{adjacent = { \boxed{4}}}} \\ \\ { \tt{ \sin \angle R = \frac{{ \boxed{3}}}{{ \boxed{5}}} }} \\ \\ { \tt{ \cos \angle R = \frac{{ \boxed{4}}}{{ \boxed{5}}} }} \\ \\ { \tt{ \tan \angle R = \frac{ \boxed{3}}{{ \boxed{4}}} }}[/tex]

Two workers finished a job in 7.5 days.

How long would it take each worker to do the job by himself if one of the workers needs 8 more days to finish the job than the other worker?

let t = time required by one worker to complete the job alone

then

(t+8) = time required by the other worker (shirker)

let the completed job = 1

A typical shared work equation

7.5%2Ft + 7.5%2F%28%28t%2B8%29%29 = 1

multiply by t(t+8), cancel the denominators, and you have

7.5(t+8) + 7.5t = t(t+8)

7.5t + 60 + 7.5t = t^2 + 8t

15t + 60 = t^2 + 8t

form a quadratic equation on the right

0 = t^2 + 8t - 15t - 60

t^2 - 7t - 60 = 0

Factor easily to

(t-12) (t+5) = 0

the positive solution is all we want here

t = 12 days, the first guy working alone

then

the shirker would struggle thru the job in 20 days.

Answer:7 + 17 = 24÷2 (since there are 2 workers) =12. Also, ½(7) + ½17 = 3.5 + 8.5 = 12. So, we know that the faster worker will take 7 days and the slower worker will take 17 days. Hope this helps! jul15

Step-by-step explanation:

Answer:

The slope of this line is 1 and the equation for the line is y=x+1

Step-by-step explanation:

So take 2 points passing through the the line (0,1), (-1,0)

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

First, let's find what m is, the slope of the line...

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (0,1), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=0 and y1=1.

Also, let's call the second point you gave, (-1,0), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-1 and y2=0.

Now, just plug the numbers into the formula for m above, like this:

m=

0 - 1

-1 - 0

So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

y=1x+b

Now, what about b, the y-intercept?

To find b, think about what your (x,y) points mean:

(0,1). When x of the line is 0, y of the line must be 1.

(-1,0). When x of the line is -1, y of the line must be 0.

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=x+b. b is what we want, the 1 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (0,1) and (-1,0).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.

You can use either (x,y) point you want..the answer will be the same:

(0,1). y=mx+b or 1=1 × 0+b, or solving for b: b=1-(1)(0). b=1.

(-1,0). y=mx+b or 0=1 × -1+b, or solving for b: b=0-(1)(-1). b=1.

In both cases we got the same value for b. And this completes our problem.

The equation of the line that passes through the points

(0,1) and (-1,0)

is

y=x+1

Answer:

A cable that weighs 6 lb/ft is used to lift 600 lb of coal up a mine shaft 500 ft deep. Find the work done. Show how to approximate the required work by a Riemann sum.

Step-by-step explanation:

Answer:

25/3 ft/s

Step-by-step explanation:

Height of pole , h=15 ft

Height of man, h'=6 ft

Let BD=x

BE=y

DE=BE-BD=y-x

All right triangles are similar

When two triangles are similar then the ratio of their corresponding sides are equal.

Therefore,

[tex]\frac{AB}{CD}=\frac{BE}{DE}[/tex]

[tex]\frac{15}{6}=\frac{y}{y-x}[/tex]

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

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

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

[tex]3y=5x[/tex]

[tex]y=\frac{5}{3}x[/tex]

Differentiate w.r.t t

[tex]\frac{dy}{dt}=\frac{5}{3}\frac{dx}{dt}[/tex]

We have dx/dt=5ft/s

Using the value

[tex]\frac{dy}{dt}=\frac{5}{3}(5)=\frac{25}{3}ft/s[/tex]

Hence, the tip of  his shadow moving  with a speed 25/3 ft/s when he is 45 feet from the pole.

Answer:

The tip pf the shadow is moving with speed 25/3 ft/s.

Step-by-step explanation:

height of pole = 15 ft

height of man = 6 ft

x = 45 ft

According to the diagram, dx/dt = 5 ft/s.

Now

[tex]\frac{y-x}{y}=\frac{6}{15}\\\\15 y - 15 x = 6 y \\\\y = \frac{5}{3} x\\\\\frac{dy}{dt} = \frac{5}{3}\frac{dx}{dt}\\\\\frac{dy}{dt}=\frac{5}{3}\times 5 =\frac{25}{3} ft/s[/tex]

Answer:

[tex]\displaystyle 51[/tex]

General Formulas and Concepts:

Algebra I

Algebra II

Calculus

Limits

Limit Rule [Variable Direct Substitution]:                                                             [tex]\displaystyle \lim_{x \to c} x = c[/tex]

Limit Property [Addition/Subtraction]:                                                                   [tex]\displaystyle \lim_{x \to c} [f(x) \pm g(x)] = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)[/tex]

Limit Property [Multiplied Constant]:                                                                     [tex]\displaystyle \lim_{x \to c} bf(x) = b \lim_{x \to c} f(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle f(x) = \left \{ {{3\sqrt{2x - 1}, \ x \leq 2} \atop {6(2x - 1)^2 - 3, \ x > 2}} \right.[/tex]

Step 2: Solve

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

Book: College Calculus 10e

Answer:

BẠN BỊ ĐIÊN À

Step-by-step explanation:

CÚT

Answer:

In picture.

Step-by-step explanation:

To do this answer, you need to count the boxes up to the mirror line. This will give us the exact place to draw the triangle.

The picture below is the answer.

Answer:

60

Step-by-step explanation:

10 x 6 = 60

Hope this helped! :)

Answer:

The new coordinates are [tex]A'(x,y) = (3, 0)[/tex], [tex]B'(x,y) = (6, -3)[/tex] and [tex]C'(x,y) = (2, -3)[/tex].

Step-by-step explanation:

Vectorially speaking, the translation of a point can be defined by the following expression:

[tex]V'(x,y) = V(x,y) + T(x,y)[/tex] (1)

Where:

[tex]V(x,y)[/tex] - Original point.

[tex]V'(x,y)[/tex] - Translated point.

[tex]T(x,y)[/tex] - Translation vector.

If we know that [tex]A(x,y) = (-3,4)[/tex], [tex]B(x,y) = (0,1)[/tex], [tex]C(x,y) = (-4,1)[/tex] and [tex]T(x,y) = (6, -4)[/tex], then the resulting points are:

[tex]A'(x,y) = (-3, 4) + (6, -4)[/tex]

[tex]A'(x,y) = (3, 0)[/tex]

[tex]B'(x,y) = (0,1) + (6, -4)[/tex]

[tex]B'(x,y) = (6, -3)[/tex]

[tex]C'(x,y) = (-4, 1) + (6, -4)[/tex]

[tex]C'(x,y) = (2, -3)[/tex]

The new coordinates are [tex]A'(x,y) = (3, 0)[/tex], [tex]B'(x,y) = (6, -3)[/tex] and [tex]C'(x,y) = (2, -3)[/tex].

Answer:

32

Step-by-step explanation:

they will each age two years, 3x2 is 6, add 6 to 26

Answer:

32

Step-by-step explanation:

they will each age two years, 3x2 is 6, add 6 to 26

Answer:

260% is the correct answer

Step-by-step explanation:

i hope i helped

Answer:

6

Step-by-step explanation:

First, we can expand the function to get its expanded form and to figure out what degree it is. For a polynomial function with one variable, the degree is the largest exponent value (once fully expanded/simplified) of the entire function that is connected to a variable. For example, x²+1 has a degree of 2, as 2 is the largest exponent value connected to a variable. Similarly, x³+2^5 has a degree of 2 as 5 is not an exponent value connected to a variable.

Expanding, we get

(x³-3x+1)²  = (x³-3x+1)(x³-3x+1)

= x^6 - 3x^4 +x³ - 3x^4 +9x²-3x + x³-3x+1

= x^6 - 6x^4 + 2x³ +9x²-6x + 1

In this function, the largest exponential value connected to the variable, x, is 6. Therefore, this is to the 6th degree. The fundamental theorem of algebra states that a polynomial of degree n has n roots, and as this is of degree 6, this has 6 roots

y'' - 6y' + 9y = 0

If y = C₁ exp(3x) + C₂ x exp(3x), then

y' = 3C₁ exp(3x) + C₂ (exp(3x) + 3x exp(3x))

y'' = 9C₁ exp(3x) + C₂ (6 exp(3x) + 9x exp(3x))

Substituting these into the DE gives

(9C₁ exp(3x) + C₂ (6 exp(3x) + 9x exp(3x)))

… … … - 6 (3C₁ exp(3x) + C₂ (exp(3x) + 3x exp(3x)))

… … … + 9 (C₁ exp(3x) + C₂ x exp(3x))

= 9C₁ exp(3x) + 6C₂ exp(3x) + 9C₂ x exp(3x))

… … … - 18C₁ exp(3x) - 6C₂ (exp(3x) - 18x exp(3x))

… … … + 9C₁ exp(3x) + 9C₂ x exp(3x)

= 0

so the provided solution does satisfy the DE.

Answer:

The answer is 17

Step-by-step explanation:

-15-2= -17

9514 1404 393

Answer:

Step-by-step explanation:

1. Input 3 for x and do the arithmetic.

  z(x) = x+1

  z(3) = 3+1 = 4 . . . . . the output is 4

__

2. The expression for n(x) has x in the denominator. The expression will be undefined when the denominator is zero, so x=0 cannot be used.

-3w-6p when w=2 and p=-7

-3(2)-6(-7)

= -6 + 42

= 36

Answer:

48

Step-by-step explanation:

-3w-6p when w=2 and p--7

you want to plug in the numbers to their letters

-3(2)-6(-7)

then you want to times the numbers.

-6-42

=48

Answer:

B) All real numbers except 0 and integer multiples of 8π∕5

Step-by-step explanation:

Cotangent function:

The cotangent function is given by:

[tex]y = \cot{ax} = \frac{\cos{ax}}{\sin{ax}}[/tex]

Domain:

All real values except those at which:

[tex]\sin{ax} = 0[/tex]

The sine is 0 for 0 and all integer multiples of [tex]\frac{1}{a}[/tex]

In this question:

[tex]a = \frac{5}{8}[/tex], so the values outside the domain are 0 and the integer multiples of [tex]\frac{8}{5}[/tex]. Then the correct answer is given by option b.

Answer:

10x8=80 that would be the area for the picture 14x11=154 for the boards area

Answer:

[tex]8x^{-10}y^6 - 2x^2y^{-8} = \frac{8y^{14} - 2x^{12}}{x^{10}y^8}[/tex]

Step-by-step explanation:

Given

[tex]8x^{-10}y^6 - 2x^2y^{-8}[/tex]

Required

Simplify

Rewrite as:

[tex]8x^{-10}y^6 - 2x^2y^{-8} = \frac{8y^6}{x^{10}} - \frac{2x^2}{y^8}[/tex]

Take LCM

[tex]8x^{-10}y^6 - 2x^2y^{-8} = \frac{8y^6*y^8 - 2x^2 * x^{10}}{x^{10}y^8}[/tex]

Apply law of indices

[tex]8x^{-10}y^6 - 2x^2y^{-8} = \frac{8y^{14} - 2x^{12}}{x^{10}y^8}[/tex]

Answer:

The volume is increasing at a rate of 33929.3 cubic millimeters per second.

Step-by-step explanation:

Volume of a sphere:

The volume of a sphere of radius r is given by:

[tex]V = \frac{4\pi r^3}{3}[/tex]

In this question:

We have to derivate V and r implicitly in function of time, so:

[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]

The radius of a sphere is increasing at a rate of 3 mm/s.

This means that [tex]\frac{dr}{dt} = 3[/tex]

How fast is the volume increasing when the diameter is 60 mm?

Radius is half the diameter, so [tex]r = 30[/tex]. We have to find [tex]\frac{dV}{dt}[/tex]. So

[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]

[tex]\frac{dV}{dt} = 4\pi (30)^2(3) = 33929.3[/tex]

The volume is increasing at a rate of 33929.3 cubic millimeters per second.

Answer:

Blair & Rosen (B&R) Plc.

Recommendation for moderate investor:

Internet fund = 96/240 * $500,000 = $200,000

Blue-chip fund = 144/240 * $500,000 = $300,000

Annual return for the portfolio:

Internet fund = $200,000 * 12% =  $24,000

Blue-chip fund = $300,000 * 9% = $27,000

Total portfolio returns =                  $51,000

Annual returns of portfolio = $51,000/$500,000 * 100 = 10.2%

Recommendation for aggressive investor:

Internet fund = 192/320 * $500,000 = $300,000

Blue-chip fund = 128/320 * $500,000 = $200,000

Step-by-step explanation:

a) Data and Calculations:

Maximum investible savings = $500,000

Projected annual return of the internet fund = 12%

Projected annual return of the blue-chip fund = 9%

Maximum determined amount to invest in the internet fund = $350,000

Risk rating for the internet fund = 6/1,000

Risk rating for the blue-chip fund = 4/1,000

Maximum risk rating for a moderate investor = 240

Maximum risk rating for an aggressive investor = 320

Recommendation for moderate investor:

Internet fund = 96/240 * $500,000 = $200,000

Blue-chip fund = 144/240 * $500,000 = $300,000

Annual return for the portfolio:

Internet fund = $200,000 * 12% = $24,000

Blue-chip fund = $300,000 * 9% = $27,000

Total returns = $51,000

Annual returns of portfolio = $51,000/$500,000 * 100 = 10.2%

Recommendation for aggressive investor:

Internet fund = 192/320 * $500,000 = $300,000

Blue-chip fund = 128/320 * $500,000 = $200,000