If f(x) = 5x, what is f-1(x)?

Answer:

∠ B = 85°

Step-by-step explanation:

the inscribed angle B is half the measure of its intercepted arc AC , then

∠ B = [tex]\frac{1}{2}[/tex] × 170° = 85°

Answer:

1/3 or 33.33%

Step-by-step explanation:

30000000/90000000

root*324=18

441=21

529=23

hope it helps

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Problem 4

The template of [tex]y = a*b^x[/tex] becomes [tex]y = 10800*0.975^x[/tex] to represent the exponential function.

We want to know when the population reaches half of 10800, so we want to know when the population is 10800/2 = 5400

Plug in y = 5400 and solve for x.

[tex]y = 10800*0.975^x\\\\5400 = 10800*0.975^x\\\\0.975^x = 5400/10800\\\\0.975^x = 0.5\\\\\log(0.975^x) = \log(0.5)\\\\x\log(0.975) = \log(0.5)\\\\x = \log(0.5)/\log(0.975)\\\\x \approx 27.377851\\\\x \approx 28\\\\[/tex]

I rounded up to the nearest whole number because x = 27 leads to y = 5452, which is not 5400 or smaller.

Luckily, x = 28 leads to y = 5315 which gets over the hurdle of being 5400 or smaller.

Add 28 years onto the starting year 2002 and we get to 2002+28 = 2030

The population reaches half of its original amount in the year 2030.

============================================================

Problem 5

If the car loses 12% of its value each year, then it keeps the remaining 88%

Plug those values into [tex]y = a*b^x[/tex].

We find the equation is [tex]y = 28750*0.88^x[/tex] where,

Replace y with 10,000 and solve for x.

[tex]y = 28750*0.88^x\\\\10000 = 28750*0.88^x\\\\0.88^x = 10000/28750\\\\0.88^x \approx 0.347826\\\\\log(0.88^x) \approx \log(0.347826)\\\\x\log(0.88) \approx \log(0.347826)\\\\x \approx \log(0.347826)/\log(0.88)\\\\x \approx 8.261168\\\\x \approx 9\\\\[/tex]

Like in the previous problem, we round up so we clear the hurdle.

Adding 9 years onto 2012 gets us to 2012+9 = 2021

Answer:

Exponential Function

General form of an exponential function: [tex]y=ab^x[/tex]

where:

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

Given:

As the population is decreasing by 2.5% each year, the population will be 100% - 2.5% = 97.5% of the previous year. Therefore, the base is 0.975.

Final equation:  [tex]\large \text{$ y=10800(0.975)^x $}[/tex]

Half of population:  10800 ÷ 2 = 5400

[tex]\large \begin{aligned}y & =5400\\\implies 10800(0.975)^x & =5400\\(0.975)^x & = \dfrac{5400}{10800}\\(0.975)^x & = 0.5\\\ln (0.975)^x & = \ln 0.5\\x \ln 0.975 & = \ln 0.5\\x & = \dfrac{\ln 0.5}{\ln 0.975}\\x & = 27.377785123\end{aligned}[/tex]

2002 + 27.37785... = 2029.37785...

Therefore, the population will reach half during 2029 (by 2030).

Given:

As the value is decreasing by 12% each year, the value will be 100% - 12% = 88% of the previous year. Therefore, the base is 0.88.

Final equation:  [tex]\large \text {$ y=28750(0.88)^x $}[/tex]

Find when the car is worth $10,000:

[tex]\large \begin{aligned}y & = 10000\\\implies 28750(0.88)^x & = 10000\\(0.88)^x & = \frac{10000}{28750}\\(0.88)^x & = \frac{8}{23}\\\ln (0.88)^x & =\ln \left(\frac{8}{23}\right)\\x \ln (0.88) & =\ln \left(\frac{8}{23}\right)\\x & =\dfrac{\ln \left(\frac{8}{23}\right)}{\ln (0.88)}\\x & = 8.26116578\end{aligned}[/tex]

2012 + 8.26116578.. = 2020.26116578..

Therefore, the value of the car will reach $10,000 during 2020 (by 2021).

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

Exact Form:

[tex]1351+780\sqrt{3}[/tex]

Decimal Form:

2701.99962990

Thus, 2,701 is your answer

[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(-4,7)\qquad B(5,1)\qquad \qquad \stackrel{\textit{ratio from A to B}}{1:2} \\\\\\ \cfrac{A\underline{P}}{\underline{P} B} = \cfrac{1}{2}\implies \cfrac{A}{B} = \cfrac{1}{2}\implies 2A=1B\implies 2(-4,7)=1(5,1)[/tex]

[tex](\stackrel{x}{-8}~~,~~ \stackrel{y}{14})=(\stackrel{x}{5}~~,~~ \stackrel{y}{1})\implies P=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-8 +5}}{1+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{14 +1}}{1+2} \right)} \\\\\\ P=\left(\cfrac{-3}{3}~~,~~\cfrac{15}{3} \right)\implies P=(-1~~,~~5)[/tex]

now, the segment AB cut by P in a 1:2 ratio, makes 3 thirds, so the ratio AP/AB is

[tex]\cfrac{AP}{AB}\implies \cfrac{1}{1+2}\implies \cfrac{1}{3}[/tex]

Answer:

9

Step-by-step explanation:

The least number of packages she should buy is 9 because 9 x 6 is 54 so she would have 4 extra ducks but she would still have enough for the carnival game

Step-by-step explanation:

length × width = 24

2×length + 2×width = 22

length + width = 11

length = 11 - width

this we use in the first equation again :

(11 - width) × width = 24

11×width - width² = 24

width² - 11×width + 24 = 0

the general solution to an quadratic equation :

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = width

a = 1

b = -11

c = 24

and so we get

width = (11 ± sqrt((-11)² - 4×1×24))/2×1) =

= (11 ± sqrt(11² - 96))/2 = (11 ± sqrt(121-96))/2 =

= (11 ± sqrt(25))/2 = (11 ± 5)/2

width1 = (11 + 5)/2 = 16/2 = 8 cm

width2 = (11 - 5)/2 = 6/2 = 3 cm

and teenaged to this is then

length1 = 11 - width1 = 11 - 8 = 3 cm

length2 = 11 - width2 = 11 - 3 = 8 cm

so, it is clear. one dimension has to be 8 cm, and the other one 3 cm. it does not matter which is which.

Answer:

23/5

Step-by-step explanation:

* means multiply

4 3/5

5 * 4 = 20

20 + 3 = 23

23/5

Answer:

[tex]\frac{23}{5}[/tex]

Step-by-step explanation:

The type of fraction we are dealing with is called a mixed fraction

In order to convert this fraction into a fraction greater than 1, we will have to convert it into an improper fraction

So we keep the denominator

Multiply the whole number by the denominator and add that to the numerator

The measure of angle ACB for circle centered at point O is 21°

An equation is an expression that shows the relationship between two or more numbers and variables.

∠AOB = 2 * ∠ACB (angle at center is twice the angle at circumference)

42 = 2 * ∠ACB

∠ACB = 21°

The measure of angle ACB for circle centered at point O is 21°

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Answer:

B

Step-by-step explanation:

Monthly Payment Formula

[tex]\sf PMT=\dfrac{Pi(1+i)^n}{(1+i)^n-1}[/tex]

where:

Given:

[tex]\implies \sf PMT=\dfrac{195000(0.066)(1+0.066)^{360}}{(1+0.066)^{360-1}}[/tex]

Answer:

x= 27.71281 = 16√3

y= 13.85641 = 8√3

Step-by-step explanation:

hope it helps :)

Answer:

  x = -2

Step-by-step explanation:

The function is decreasing where the first derivative is negative.

That is, the function is decreasing on the interval (-2, 5), except at x=2, where there is a flat spot. That means the maximum value is found at the left end of that interval, at x=-2.

__

The maximum value might be found at x = 6, at the right end of the interval (5, 6) on which the function is increasing. However, we judge the area under the first derivative curve between x=5 and x=6 to be less than the total area under the curve between x=-2 and x=5. That means the function does not increase enough from its minimum at x=5 to make up for the decrease over the longer interval.

__

The attachment shows an approximation of the derivative function given in the problem statement (dashed line) and its integral (solid line). Not all of the curvature of f'(x) is accounted for in the approximation, but the overall result is consistent with the above analysis.

The unknown sides of the right angle triangle using trigonometric ratios are as follows;

PR = 13.2 units

RQ = 17.6 units

A right angle triangle is a triangle that has one of its angles as 90 degrees.

The sides of the triangle can be found using trigonometric ratios.

Therefore,

sin 37° = opposite / hypotenuse

sin 37° = PR / 22

cross multiply

PR = 22 sin 37

PR = 22 × 0.60181502315

PR = 13.2399305093

PR = 13.2 units

cos 37 = adjacent / hypotenuse

cos 37 = RQ / 22

RQ = 22 cos 37

RQ = 17.569981221

RQ = 17.6 units

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The tangent, cosine and sine ratios of angles X & Y in the reduced faction form is 3/4, 4/5 and 3/5 respectively.

For a right angle triangle, the trigonometry ratios can be given as,

[tex]\rm \sin \theta=\dfrac{b}{c}\\\rm \cos \theta=\dfrac{a}{c}\\\rm \tan \theta=\dfrac{b}{a}[/tex]

Here, a is base side, b is perpendicular side and c is the hypotenuse side of the triangle.

In the given triangle, the length of base side is 8 units, perpendicular side is 6 units and hypotenuse side is 10 units.

[tex]a=8\\b=6\\c=10[/tex]

Thus, the  tangent, cosine and sine ratios of angles X & Y are,

[tex]\rm \sin \theta=\dfrac{6}{10}=\dfrac{3}{5}\\\rm \cos \theta=\dfrac{8}{10}=\dfrac{4}{5}\\\rm \tan \theta=\dfrac{6}{8}=\dfrac{3}{4}[/tex]

Thus, the tangent, cosine and sine ratios of angles X & Y in the reduced faction form is 3/4, 4/5 and 3/5 respectively.

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Answer:

I believe the answer is 0.7813

Step-by-step explanation:

Find the difference between 400 and 200, as they are first and second terms. This is going to be 0.5 since it is being divided.

The formula is: a∨n=a∨1(r)^(n-1)

n= the number of the sequence you are looking for

r=0.5

a∨1=400

a∨2=200

400(0.5)^(10-1)

Answer:

250

Step-by-step explanation:

Bulb box and carton both are of cuboidal shape.

For bulb box the dimensions are:

For Carton the dimensions are:

To find the number of bulbs packed in the carton, divide the [tex]V_{Carton}[/tex] by [tex] V_{Bulb\: box}[/tex]

So, 250 bulbs will be packed in one carton.

Answer:

B. 3.114 > 3.112

D. 0.541 > 0.145

E. 0.141 < 0.19

Step-by-step explanation:

In order to determine which decimal is greater or less than another, compare the place values from left to right. First, compare the whole numbers to the left of the decimal point. If they are not the same, the smaller decimal number is the one with the smaller whole number. This applies to the rest of the places.

----------------------------------------------------

32.3 has a greater tenths value than 32.03, so 32.03 < 32.3. Option A is false.

----------------------------------------------------

3.114 has a greater thousandths value than 3.112, so 3.114 > 3.112. Option B is true.

----------------------------------------------------

4.003 has a greater whole number than 3.996, so 4.003 > 3.996. Option C is false.

----------------------------------------------------

0.541 has a greater tenths value than 0.145, so 0.541 > 0.145. Option D is true.

----------------------------------------------------

0.19 has a greater hundredths value than 0.141, so 0.141 < 0.19. Option E is true.

hope this helps!

The inequalities which are truly compared are B, D and E.

Given certain inequalities.

We have to find the true comparisons.

We have to look at the corresponding digits of numbers which are compared from left to right. Greater numbers on the left will be the greater number.

A. 32. 03 > 32. 3

This is false since 32.3 is greater. In 32.03, 0 is in the tenth place, while 3 is in the tenth place for 32.3.

B. 3. 114 > 3. 112

This is true since in the thousandths place, 4 is greater than 2.

C. 4. 003 < 3. 996

This is clearly false, since in the whole part, 4 is greater than 3.

D. 0. 541 > 0. 145

This is true, since in the tenths place, 5 is greater than 1.

E. 0. 141 < 0. 19

This is also true, since in the hundredths place, 9 is greater than 4.

Hence the true comparisons are B, D and E.

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Answer:

90 in²

Step-by-step explanation:

First,check the figure I provided .

Area of the figure = area1 + area2 + area3 + area4

= (3×2) + (7×7) + (7×2) + (7×6)÷2

= 6 + 49 + 14 + 21

= 90

Answer:

D one is the answer

Step-by-step explanation:

Answer:

If I am not mistaken, the new figure will be here (view attachment, bright blue figure is the new transformation)

Answer:

For each of the following equations determine the output values Corresponding to the input value

(-2;-1;0;1;2;3)

Answer:

x + y = 4.5

Step-by-step explanation:

x + y = 1.5 + 3 = 4.5

Step-by-step explanation:

there are some pieces of information missing like the price of apples and flour. or the selling prices. or any restrictions like a fixed budget to buy ingredients or how many pies and cobblers he can make in a certain available time.

all we can say based on the given information :

one pie = 4a + 3f (a = apples, f = flour)

one cobbler = 2a + 3f

P(x, y) = 3x + 2y =

= x(selling price - 4a - 3f) + y(selling price - 2a - 3f)

the max. of P(x, y) is the maximum profit by selling pies and cobblers, which is without any further information +infinity.

the more pies and cobblers he sells, the bigger the profit - no limit.

The arithmetic sequence has a common difference, and a first term and the 17th term in the arithmetic sequence is -21

The given parameters are:

The nth term of an arithmetic progression is:

Tn = a + (n - 1)d

So, we have:

T17 = a + 16d

Substitute the given values

T17 = 11 - 16 * 2

Evaluate

T17 = -21

Hence, the 17th term in the arithmetic sequence is -21

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Using the Factor Theorem, it is found that the correct option regarding the complex zeros of f(x) is given by:

D The function has one real zero and two nonreal zeros.

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

In this problem, the function is given by:

f(x) = x³ - 3x² + 16x + 48.

Using a calculator, the roots are given by:

[tex]x_1 = -1.89767, x_2 = 2.44884 + 4.39288i, x_3 = 2.44884 - 4.39288i[/tex]

The first root is real, while the second and third are complex(nonreal), hence option D is correct.

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Answer:

x=90°

Step-by-step explanation:

Too much work............. ....

Answer:

Gretta would be 2500 meters tall

Step-by-step explanation:

2km=2000 and the 1/2 would be 1/2=500 so the answer it 2500

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Answer:

x =6

Step-by-step explanation:

17x + 8 + 66 + 74 +110 = 360

17x + 258 =360

17x = 360 -258

17x =102

x =6

Apply angle sum property