The graph of the function f(x)= 5/4 sin(x)+1 is shown. What are the key features of this function?

- The maximum value of the function is....(2pi,2.25,1)
- The minimum value of the function is...(pi/2,-0.25,-1)
- On the interval (0,pi/2), the function is...(increasing, decreasing)
-the range of the function is...([-0.25,2.24],all real numbers, [-1,1])​

Answer:

[tex]y = -\frac{2}{3}x + 490[/tex]

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

y-intercept = [tex]490[/tex]

Step-by-step explanation:

• The slope-intercept form of an equation takes the general form:

[tex]\boxed{y = mx + c}[/tex],

where:

m = slope,

c = y-intercept.

• We are given the equation:

[tex]2x + 3y = 1470[/tex]

To change this into the slope-intercept form, we must make y the subject:

[tex]3y = -2x + 1470[/tex]          [subtract [tex]2x[/tex] from both sides]

⇒ [tex]y = -\frac{2}{3}x + \frac{1479}{3}[/tex]        [divide both sides by 3]

⇒ [tex]y = -\frac{2}{3}x + 490[/tex]

• Comparing this equation with the general form equation, we see that:

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

c = [tex]490[/tex].

This means that the gradient is [tex]\bf -\frac{2}{3}[/tex], and the y-intercept is [tex]\bf 490[/tex].

Since this is the result of the second function, hence equations I and II are inverse of each other.

Inverse of a function

Inverse of a function is s a function that serves to undo another function. That is, if f(x) produces y, then putting y into the inverse of f produces the output x.

Given the function f(x) = 3x

Find its inverse

Replace with y with x

y = 3x

x =3y

Make y the subject of the formula

3y = x

y = x/3

Since this is the result of the second function, hence equations I and II are inverse of each other.

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Answer:

D.

Step-by-step explanation:

Yes, because it passes the vertical line test.

Answer:

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

Conditions we need to meet:

To get the smallest number we'd use all 10 digits in the ascending order:

Here we can't have zero in the beginning as the number becomes 9-digit.

So swapping zero with the closest digit, 1.

Our number should be even, so we should swap 9 with one even digit.

Again it should be the closest one to 9, so it is 8.

We get the following number as a result:

To test you may swap digits, any number you get will be greater than this number.

The sum of the length of the overall pattern in the given cartesian coordinate is calculated as; 44

We are told that The final line on the plan is parallel to the y-axis and passes through x = -10

Now, looking at the pattern, the lengths of each side are as follows;

1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5

Thus, the sum of the length of the overall pattern is calculated as;

1.5 + 2 + 2.5 + 3 + 3.5 + 4 + 4.5 + 5 + 5.5 + 6 + 6.5 = 44

Therefore we can conclude from all the deductions and calculations above that the sum of the length of the overall pattern in the given cartesian coordinate is calculated to be; 44

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Answer:

9

Step-by-step explanation:

let the number be y

5×y - 7 = 3×y + 11

5y-7 = 3y+11

collect like terms

5y-3y = 11+7

2y = 18

y = 18/2

y = 9

Answer:

Step-by-step explanation:

First, you have to multiply. 15x4=60. All you need to do is add a zero to that product. You will get 600. Product means the answer to a multiplication problem. That is why you would have to multiply to get your answer. Your answer to that part is 600. 15*40= 600. Then, you would do 45+15= 60. 600/60= 10. Your answer is 10.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathsf{(x + 3)^0}[/tex]

[tex]\huge\textbf{Simplifying:}[/tex]

[tex]\mathsf{(x + 3)^0}[/tex]

[tex]\text{Anything raised to the 0 power it automatically equal to 1.}[/tex]

[tex]\huge\text{So, this mean that your answer should be: \boxed{\mathsf 1}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

3:10

10:1

8:1

100:7

Step-by-step explanation:

900:3000

300:1000

3:10

80:8

10:1

2000:750

8:1

100:7

The indicated sum for the geometric series is 121.5

The series is given as:

162 − 54 + 18 − 6 + .....

Start by calculating the common ratio of the geometric series.

This is calculated using

r = -54/162

Evaluate

r = -1/3

The indicated sum for the geometric series is then calculated as:

S = a(1 - r^n)/1 - r

Substitute the known values in the above equation

S = 162(1 - (-1/3)^7)/1 + 1/3

Evaluate the exponent and the sum

S = 162(1 + 1/2187)/4/3

Evaluate the sum

S = 162(2188/2187)/4/3

Express as products

S = 162 * (2188/2187)* 3/4

Evaluate the product

S = 162 * 547/729

Evaluate the product

S = 121.5

Hence, the indicated sum for the geometric series is 121.5

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if two occurrences A and B are unrelated to one another. Then, 3/4 or 0.75 is the likelihood of event B.

The field of mathematics known as probability studies numerical descriptions of the likelihood of an event occurring or of a statement being true.. The probability of an event is a number between 0 and 1, with 0 generally signifying the event's impossibility and 1 generally signifying its certainty.

These occurrences are referred to as independent events when the occurrence or non-occurrence of one event has no bearing on the occurrence or non-occurrence of any other events.

Figuratively, we have:

If we have the following, two events A and B are said to be independent.

                            [tex]\mathrm{P}(\mathrm{A} \cap \mathrm{B})=\mathrm{P}(\mathrm{A}) \mathrm{P}(\mathrm{B})[/tex]

Events A and B happen apart from one another. P(A) = 1/6, while P(A and B) = 1/8.

The likelihood of the event B will then be.

                            [tex]\begin{aligned}&\mathrm{P}(\mathrm{A} \cap \mathrm{B})=\mathrm{P}(\mathrm{A}) \mathrm{P}(\mathrm{B}) \\&\mathrm{P}(\mathrm{B})=\frac{\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{\mathrm{P}(\mathrm{A})} \\&\mathrm{P}(\mathrm{B})=\frac{1 / 8}{1 / 6} \\&\mathrm{P}(\mathrm{B})=\frac{6}{8} \\&\mathrm{P}(\mathrm{B})=\frac{3}{4}=0.75\end{aligned}[/tex]

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I understand that the question you are looking for is:

Two events, A and B, are independent of each other. P(A) = 1/6 and P(A and B) = 1/8. What is P(B) written as a decimal? Round to the nearest hundredth, if necessary.

Answer:8 feet

Step-by-step explanation:

Using a linear function, it is found that Sarah can use 3.7 gigabytes while staying within her budget.

A linear function is modeled by:

y = mx + b

In which:

Considering the flat cost as the y-intercept and the cost per gigabyte as the slope, the cost of using g gigabytes is:

C(g) = 4g + 69.

She wants to keep her bill at $83.80 per month, hence:

C(g) = 83.80

4g + 69 = 83.80

4g = 14.80

g = 14.80/4

g = 3.7.

Sarah can use 3.7 gigabytes while staying within her budget.

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Answer:

The other person is correct!

Step-by-step explanation:

Yes

Answer:

7.52 m^3

Step-by-step explanation:

This is like compound interest in a banking calculation

Future volume = 5 (1 + .06)^7 = 7.52 m^3

Answer:

read below or other answer

Step-by-step explanation:

2 [{2-2(2÷2-2)} ÷2]÷2​

2 [ { 2 - 2 ( 1 - 2 ) } ÷ 2 ] ÷ 2

2 [ { 2 - 2 ( - 1 ) } ÷ 2 ] ÷ 2

2 [ { 2 + 2 } ÷ 2 ] ÷ 2

2 [ 4 ÷ 2 ] ÷ 2

2 ( 2 ) ÷ 2

4 ÷ 2

2 divided by 2

Answer: 2

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

Fraction of total area of the circle each color occupies in the spinner.

purple = 1/8

red = 1/4

orange = 1/8

yellow = 1/8

green = 1/4

blue = 1/8

Landing on yellow or purple: 1/8 + 1/8 = 1/4

Not landing on yellow or purple = 1 - 1/4 = 3/4

Answer:

Area = (a² -5a) in²

Perimeter = (4a -10) in

Step-by-step explanation:

Let the length of the rectangle be a.

Given that, its width is 5 in less than the length.

So,

length ⇒ a

width ⇒ (a - 5)

First, let's find the area of the rectangle.

Area = length × width

Area = a ( a - 5 )

Solve the brackets.

Area = (a² -5a) in²

Now, let us find the perimeter of the rectangle.

Perimeter = 2 ( l + w )

Perimeter = 2 ( a + a - 5 )

Perimeter = 2 ( 2a - 5 )

Perimeter = (4a -10) in

Answer:

[tex]\frac{-1}{4}[/tex]

Step-by-step explanation:

Perpendicular lines have opposite reciprocal slopes. This means you change the sign and flip the numerator and denominator.

If the original slope is 4, the perpendicular slope is [tex]\frac{-1}{4}[/tex]

Answer:

  9

Step-by-step explanation:

The 79-digit number of interest can be formulated as a sum of shorter numbers whose remainders can be computed.

The expanded form of the number can be written as ...

  a_44 = 01×10^78 +23×10^76 +45×10^74 +67×10^72 +89×10^70 +...

  +10×10^68 +11×10^66 +... +43×10^2 +44×10^0

Each number except the last is multiplied by a power of 10. Powers of 10 modulo 45 are ...

  10 mod 45 = 10

  100 mod 45 = 10

This lets us conclude that any positive power of 10 mod 45 is 10.

In short, all of the multiplication by powers of 10 can be collapsed to a single multiplication by 10. Hence, the mod 45 value of a_44 will be ...

  a_44 mod 45 = (((01 +23 +45 +67 +89) +10 +11 +12 +... +43)×10 +44) mod 45

  = (((01 +23 +45 +67 +89) mod 45 + sum(10 .. 43) mod 45)×10 +44) mod 45

  = (((225 mod 45) +(901 mod 45))×10 +44) mod 45

  = ((0 +1)×10 +44) mod 45

  a_44 mod 45 = 54 mod 45 = 9

__

Additional comment

The result can be confirmed by a suitable calculator.

__

The sum of the 34 numbers from 10 to 43 is the product of their average value (10+43)/2 = 26.5 and their number, 34. (26.5×34) = 901.

Answer: 9

Step-by-step explanation:

we can manually do this by dividing 1234567891011121314151617181920212223242526272829303132333435363738394041424344

on the calculator. I saw multiple hate comments on the answer above, and I wanted to test it manually - it still is 9.

Answer:

140°

Step-by-step explanation:

The exterior angle is equal to the sum of the 2 remote interior angles. (The 2 angles farthest from the angle on the outside of the triangle)

20 + 120 = 140

Answer:

y= 140

Step-by-step explanation:

first you find x by using the sum of angles in a triangle(180-120-20). so x is 40.and then you do 180-40 ( adjustment angles on a straight line. let me know if it makes sense.

Answer:

x>4

Step-by-step explanation:

3x - 2 >10  add 2 to both sides

3x > 12  Divide both sides by 3

x >4

Answer:

[tex]x > \bf 4[/tex]

Step-by-step explanation:

To find a solution to this inequality, we have to rearrange this equation to make [tex]x[/tex] its subject:

[tex]3x - 2 > 10[/tex]

⇒ [tex]3x - 2 + 2 > 10 + 2[/tex]      [Add 2 to both sides]

⇒ [tex]3x > 12[/tex]

⇒ [tex]\frac{3x}{3} > \frac{12}{3}[/tex]                         [Divide both sides by 3]

⇒ [tex]x > \bf 4[/tex]

Step-by-step explanation:

clearly divergent.

the elements of the series are getting bigger and bigger intercepted by some constant "1" (but they don't help here - after every intercepting "1" are 2 numbers that are larger by 1 than the 2 numbers before the intercepting "1", and that continues into infinity, so, the numbers will go to infinity, and that shows that the series is divergent).

The perpendicular bisector of a chord passes through the center of a circle.

In geometry, a chord is a straight line segment that connects two points on the circumference of a circle. It is the longest possible segment within the circle.

The perpendicular bisector of a chord is a line that passes through the midpoint of the chord, creating two equal halves, and is perpendicular to the chord.

Notably, for any chord in a circle, its perpendicular bisector always intersects at the center of the circle, making it a significant geometric property.

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The height of the pyramid is [tex]16ft.[/tex]

The centroid of the base sits just above the right pyramid. Oblique pyramids are non-right pyramids. A right pyramid is typically assumed to be a regular pyramid because it has a regular polygon base.

To find the height of the pyramid:

l=the slant height of the right pyramid.

b=the length side of the square base of the right pyramid.

h=the height of the right pyramid.

Pythagorean Theorem: [tex]l^{2} =h^{2} +(\frac{b}{2} )^{2}[/tex]

Solve:h

[tex]h^{2} =l^{2} +(\frac{b}{2} )^{2}[/tex]

[tex]h^{2} =20^{2} -12^{2}[/tex]

[tex]h^{2} =256[/tex]

[tex]h=16ft[/tex]

Therefore, The height of the pyramid is [tex]16ft.[/tex]

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Answer:

The height of the pyramid is 16ft

Step-by-step explanation:

Answer:

F

Step-by-step explanation:

There are 6 digits in the repeating pattern.

279 / 6 = 46.5 remainder 3.

we care about the remainder as this is how many digits in. it is the 3rd digit in so is 3.

Answer:

[tex]\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x=\dfrac{x}{9\sqrt{9-x^2}} +\text{C}[/tex]

Step-by-step explanation:

Fundamental Theorem of Calculus

[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given indefinite integral:

[tex]\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x[/tex]

Rewrite 9 as 3²  and rewrite the 3/2 exponent as square root to the power of 3:

[tex]\implies \displaystyle \int \dfrac{1}{\left(\sqrt{3^2-x^2}\right)^3}\:\:\text{d}x[/tex]

Integration by substitution

[tex]\boxed{\textsf{For }\sqrt{a^2-x^2} \textsf{ use the substitution }x=a \sin \theta}[/tex]

[tex]\textsf{Let }x=3 \sin \theta[/tex]

[tex]\begin{aligned}\implies \sqrt{3^2-x^2} & =\sqrt{3^2-(3 \sin \theta)^2}\\ & = \sqrt{9-9 \sin^2 \theta}\\ & = \sqrt{9(1-\sin^2 \theta)}\\ & = \sqrt{9 \cos^2 \theta}\\ & = 3 \cos \theta\end{aligned}[/tex]

Find the derivative of x and rewrite it so that dx is on its own:

[tex]\implies \dfrac{\text{d}x}{\text{d}\theta}=3 \cos \theta[/tex]

[tex]\implies \text{d}x=3 \cos \theta\:\:\text{d}\theta[/tex]

Substitute everything into the original integral:

[tex]\begin{aligned}\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x & = \int \dfrac{1}{\left(\sqrt{3^2-x^2}\right)^3}\:\:\text{d}x\\\\& = \int \dfrac{1}{\left(3 \cos \theta\right)^3}\:\:3 \cos \theta\:\:\text{d}\theta \\\\ & = \int \dfrac{1}{\left(3 \cos \theta\right)^2}\:\:\text{d}\theta \\\\ & = \int \dfrac{1}{9 \cos^2 \theta} \:\: \text{d}\theta\end{aligned}[/tex]

Take out the constant:

[tex]\implies \displaystyle \dfrac{1}{9} \int \dfrac{1}{\cos^2 \theta}\:\:\text{d}\theta[/tex]

[tex]\textsf{Use the trigonometric identity}: \quad\sec^2 \theta=\dfrac{1}{\cos^2 \theta}[/tex]

[tex]\implies \displaystyle \dfrac{1}{9} \int \sec^2 \theta\:\:\text{d}\theta[/tex]

[tex]\boxed{\begin{minipage}{5 cm}\underline{Integrating $\sec^2 kx$}\\\\$\displaystyle \int \sec^2 kx\:\text{d}x=\dfrac{1}{k} \tan kx\:\:(+\text{C})$\end{minipage}}[/tex]

[tex]\implies \displaystyle \dfrac{1}{9} \int \sec^2 \theta\:\:\text{d}\theta = \dfrac{1}{9} \tan \theta+\text{C}[/tex]

[tex]\textsf{Use the trigonometric identity}: \quad \tan \theta=\dfrac{\sin \theta}{\cos \theta}[/tex]

[tex]\implies \dfrac{\sin \theta}{9 \cos \theta} +\text{C}[/tex]

[tex]\textsf{Substitute back in } \sin \theta=\dfrac{x}{3}:[/tex]

[tex]\implies \dfrac{x}{9(3 \cos \theta)} +\text{C}[/tex]

[tex]\textsf{Substitute back in }3 \cos \theta=\sqrt{9-x^2}:[/tex]

[tex]\implies \dfrac{x}{9\sqrt{9-x^2}} +\text{C}[/tex]

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Answer:

Step-by-step explanation:

13