Please help: What is the inverse of the function below?

Answer: 740 miles

Step-by-step explanation:

You know that [tex]\frac{3}{8}inches[/tex] on the map is actually 60 miles and the distance between these two cities is [tex]4\ \frac{5}{8}inches[/tex].

You can express this distance as a decimal number:

[tex](4+0.625)inches=4.625inches[/tex]

Therefore, let be "d" the distance in miles between these two cities.

Then, you get:

[tex]d=\frac{(4.625inches)(60miles)}{(\frac{3}{8}inches)}\\\\d=740miles[/tex]

Answer:

106

Step-by-step explanation:

VPL=1/2VkP

VKP=148

VPL=74

JPV+VPL=180

JPV=106

The measurement of angle JPV from the considered situation is found as m∠JPV = 106°

The radius which touches the point where the tangent touches too on a specified circle, is perpendicular to the tangent (90 degrees angle with the tangent).

Referring to the image attached below, we're provided that:

m arcVKP = central angle arc VKP subtends = m∠VOP = 148°

The perpendicular from center O on the line VP (VP is a chord) bisects it, and therefore, the triangle ODP and ODV are congruent by SAS congruency [ side OD is common, the angle (the 90 degree) on either side of OD is of same measure, and VD and DP are of same measure due to OD bisecting VP).

Thus, we get:

[tex]m\angle POD = m\angle VOD[/tex]

But since we have:

m∠POD + m∠VOD  = m∠VOP = 148°

thus, m∠POD + m∠POD = 148°

or  m∠POD = 148°/2 = 74° = m∠VOD

Now, as sum of angles in a triangle is 180°, therefore, for triangle OPD, we get:

[tex]m\angle OPD + m\angle ODP + m\angle POD = 180^\circ\\x^\circ + 90^\circ + 74^\circ = 180^\circ\\x = 16[/tex]

Thus, we get the measurement of angle JPV as:

[tex]m\angle JPV = m\angle JPO + m\angle OPD\\ m\angle JPV = 90^\circ + x^\circ = (90 + 16)^\circ = 106^\circ[/tex]

Thus, the measurement of angle JPV from the considered situation is found as m∠JPV = 106°

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Answer:

The lines of symmetry are the diameters, any straight line passing through the origin and touching both ends of the circle.

Step-by-step explanation:

Without graphing, this is the equation of a circle with center at the origin,

(0, 0) and with a radius of 3 units. The general equation of a circle with center (a, b) and with radius r units is given as;

[tex](x-a)^{2}+(y-b)^{2}=r^{2}[/tex]  

The graph of the function is as shown in the attachment below;

A line of symmetry cuts the graph of a function into two equal parts such that these parts become mirror images of each other.

For the case of a circle, the line that divides the circle into two equal portions is the diameter. Any given circle has infinite number of diameters.

Therefore, the lines of symmetry are the diameters, any straight line passing through the origin and touching both ends of the circle.

Answer:

Answer me please??!!

Step-by-step explanation:

Answer:

  550 mm^2

Step-by-step explanation:

A net can be drawn as shown in the first figure attached. Each square represents 5 mm by 5 mm, so is 25 mm^2. Altogether, there are 22 of them, so the total area is ...

  (25 mm^2)·22 = 550 mm^2

The second attachment shows that net folded up to make the given figure.

_____

In the first attachment, the green shades represent the left- and right-side faces. (Darker green is left side.) The red and blue shades represent the front- and back-side faces. The white rectangles represent the top and bottom faces. The dark black lines are the cut lines. If you want to fold the figure up, the lighter lines are the fold lines.

The second attachment is just verification that all faces are accounted for and the net actually corresponds to the given figure.

Answer:

21.5

Step-by-step explanation:

x is the radius of the circle.

If we draw a line from the circle's center to either end of the horizontal line, that line will also be a radius, so it will have length x.  This forms a right triangle with side lengths 10 and 19 and hypotenuse x.

Using Pythagorean Theorem:

c² = a² + b²

x² = 10² + 19²

x² = 461

x ≈ 21.5

Answer:

The area of the circle is [tex]36\pi\ units^{2}[/tex]

Step-by-step explanation:

we know that

The area of a circle subtends a central angle of [tex]2\pi[/tex] radians

so

By proportion find the area of the circle

[tex]\frac{33\pi }{(11\pi /6)}=\frac{x}{2\pi}\\ \\ x=2\pi*( 33*6)/11\\ \\x=36\pi\ units^{2}[/tex]

Answer:

its just 36 pi

Step-by-step explanation:

just did this one

Check the picture below.

so is filled with those cubes, recall that a cube has all equal sides, in this case 1/3, so the volume of each cube is simply the product of length*width*height.

[tex]\bf \stackrel{\textit{volume of one cube}}{\cfrac{1}{3}\cdot \cfrac{1}{3}\cdot \cfrac{1}{3}\implies \cfrac{1}{27}}\qquad \qquad \stackrel{\textit{if there are \underline{x} cubes inside then their total volume is}}{\cfrac{1}{27}x~~~~=~~~~\stackrel{\textit{volume of prism}}{4}} \\\\\\ x=27\cdot 4\implies x=108[/tex]

[tex]\ln(n+3)-\ln n=\ln\dfrac{n+3}n=\ln\left(1+\dfrac3n\right)[/tex]

We can show the sequence is bounded and monotonic.

Boundedness: [tex]1+\dfrac3n>1[/tex] for all [tex]n>0[/tex], so [tex]\ln\left(1+\dfrac3n\right)>\ln1=0[/tex] for all [tex]n>0[/tex].

Monotonicity: Consider the function

[tex]f(x)=\ln\left(1+\dfrac3x\right)[/tex]

which has derivative

[tex]f'(x)=\dfrac{1+\frac3x}{-\frac3{x^2}}=-\dfrac3{x^2+3x}[/tex]

which has negative sign for all [tex]x>0[/tex], and so [tex]f(x)[/tex] is strictly decreasing.

[tex]\ln(n+3)-\ln n[/tex] is bounded and monotonic, so the sequence converges.

As [tex]n\to\infty[/tex] we have [tex]\dfrac3n\to0[/tex], leaving us with the limit

[tex]\displaystyle\lim_{n\to\infty}(\ln(n+3)-\ln n)=\lim_{n\to\infty}\ln\left(1+\frac3n\right)=\ln\left(1+\lim_{n\to\infty}\frac3n\right)=\ln1=0[/tex]

The sequence an = ln(n + 3) - ln(n) converges with a limit of 0. This is determined by simplifying the expression and observing its behavior as n approaches infinity.

Firstly, the question pertains to the study of the convergence or divergence of a sequence. In this case, we're looking at the sequence an = ln(n + 3) - ln(n). Using logarithmic properties, this can be rewritten as ln((n+3)/n). As n approaches infinity, the sequence converges to the limit ln(1), which equals 0. Therefore, the sequence converges and its limit is 0.

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Answer:

125,970

Step-by-step explanation:

Even if jury are assigned numbers, the order in which they are picked has no importance.  That means that it's a combination, not a permutation.

The formula to calculate possible combinations is:

[tex]C(n,r) = \frac{n!}{(r! (n-r)!)}[/tex]

Where n is the global population, and r is the number of selected items.

In our case, n = 20 and r = 12, so...

[tex]C(20,12) = \frac{20!}{(12! (20-12)!)} = 125970[/tex]

There are 125970 different ways to select 12 jury members out of 20 people.

there are 125970 different 12 person juries that can be chosen from a pool of 20 people.

The question is asking how to determine the number of different ways to choose a 12-person jury from a pool of 20 potential jurors. This type of problem is solved using the concept of combinations in mathematics, specifically the binomial coefficient formula which is given by the following:

C(n, k) = n! / (k!(n - k)!)

where:

n represents the total number of items (in this case, jurors).

k represents the number of items to choose (jurors to be selected for the jury).

n! means factorial of n, which is the product of all positive integers up to n.

In this scenario, n = 20 and k = 12. Therefore, the number of different 12 person juries that can be chosen is calculated as:

C(20, 12) = 20! / (12!(20 - 12)!)

Further calculation yields:

C(20, 12) = 20! / (12!8!) = 125970

Therefore, there are 125970 different 12 person juries that can be chosen from a pool of 20 people.

ANSWER

[tex]Area = 2\sqrt{3} \: {cm}^{2} [/tex]

EXPLANATION

We need to use the Pythagoras Theorem to find the height of the triangle.

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

[tex] ({2 \sqrt{3}) }^{2} + {b}^{2} = {4}^{2} [/tex]

[tex]12 + {b}^{2} = 16[/tex]

[tex] {b}^{2} = 16 - 12[/tex]

[tex]{b}^{2} = 4[/tex]

Take positive square root to get;

[tex]b = \sqrt{4} = 2[/tex]

Area =½bh

[tex]Area = \frac{1}{2} \times 2\sqrt{3} \times 2[/tex]

[tex]Area = 2\sqrt{3} \: {cm}^{2} [/tex]

Answer: [tex]x=-11[/tex]

Step-by-step explanation:

You can use the Method of substitution.

Substitute the equation [tex]y=3-\frac{1}{2}x[/tex] into the equation [tex]3x + 4y = 1[/tex] and then you must solve for the variable x:

[tex]3x + 4y = 1\\\\3x + 4(3-\frac{1}{2}x) = 1\\[/tex]

Apply Distributive property:

[tex]3x + 12-\frac{4}{2}x = 1\\3x+12-2x=1[/tex]

Subtract 12 from both sides of the equation and then add the like terms. Then you get:

[tex]3x+12-2x-12=1-12\\3x-2x=-11\\x=-11[/tex]

Answer:

m∠DAB = 90°

Step-by-step explanation:

* Lets revise some facts about the circle

- If two tangent segments drawn from a point outside the circle, then

 the two tangent segments are equal in length

- The radius and the tangent perpendicular to each other at the point

 of contact

* Lets solve the problem

∵ AB and AD are two tangent segments to circle C at B and D

 respectively

∴ AB = AD ⇒ (1)

∵ CD and CD are two radii

∴ AB ⊥ BC and AD ⊥ DC

∴ m∠ABC = m∠ADC = 90°

∵ m∠BDC = 45°

∵ ∠BDC + m∠ADB = m∠ADC

∴ 45° + m∠ADB = 90° ⇒ subtract 45° from both sides

∴ m∠ADB = 45° ⇒ (2)

- In Δ ABD

∵ AB = AD ⇒ proved in (1)

∴ m∠ABD = m∠ADB ⇒ isosceles triangle

∵ m∠ADB = 45° ⇒ proved in (2)

∴ m∠ABD = 45°

- The sum of the measure of the interior angles of a Δ is 180°

∴ m∠DAB + m∠ABD + m∠ADB = 180°

∴ m∠DAB + 45° + 45° = 180° ⇒ simplify

∴ m∠DAB + 90° = 180° ⇒ subtract 90° from both sides

∴ m∠DAB = 90°

Answer:

A = (16π -32) in²

P = (4π +8√2) in

Step-by-step explanation:

The area is that of a quarter-circle of radius 8 inches less half the area of a square with side length 8 inches. Two formulas are useful:

area of a circle = πr² . . . . .r = radius

area of a square = s² . . . . s = side length

Then your area is ...

A = (1/4)π(8 in)² - (1/2)(8 in)² = (64 in²)(π/4 -1/2)

A = (16π -32) in²

____

The applicable formulas for the side lengths of your figure are ...

arc BD = (1/4)(2πr) = π(r/2) = π(8 in)/2 = 4π in

segment BD = (8 in)√2

The perimeter is the sum of these lengths, so is ...

P = (4π +8√2) in

_____

Of course, you are very familiar with the fact that an isosceles right triangle with side lengths 1 has a hypotenuse of length √(1²+1²) = √2. Scaling the triangle by a factor of 8 inches means the segment AB will be 8√2 inches long.

She will take 6 weeks.

Answer:

She will take 6 weeks.

hope this helps

Answer:

A. 10

Step-by-step explanation:

This is a right triangle with a hypotenuse between the vertices (-4,-2) and (4,4). You can now solve for the length to get 10.

The solution to the equation -3(h + 5) + 2 = 4(h + 6) - g is h = -12 and g = -18.

Distribute the negative signs:

-3(h + 5) + 2 = -3h - 15 + 2

Combine constant terms:

-3h - 15 + 2 = 4(h + 6) - g

-3h - 13 = 4h + 24 - g

Isolate h on one side:

-7h - 13 = 24 - g

-7h = 37 - g

h = (37 - g) / -7

Substitute h back into the original equation to solve for g:

-3(h + 5) + 2 = 4(h + 6) - g

-3((37 - g) / -7 + 5) + 2 = 4((37 - g) / -7 + 6) - g

-3(-12 - g + 35) + 2 = 4(-12 - g + 42) - g

Simplify both sides:

11g + 66 = -36g + 108

47g = 42

g = -18

Therefore, the solution is h = -12 and g = -18.

Answer:

  x = 12 cm

Step-by-step explanation:

The product of lengths from the secant intersection point to the "near" and "far" circle intersection points is the same for both secants. When one "secant" is a tangent, the lengths to the circle intersection points are the same (so their product is the square of the tangent segment length).

  8^2 = 4·(4 +x) . . . . . . measures in centimeters

  16 = 4 +x . . . . . . divide by 4

  12 = x . . . . . . . . . subtract 4

Answer:$76

Step-by-step explanation:

JEANS: (5x8)= 40

SHIRTS:(4x6)= 24

SHOES BUY ONE GET ONE FREE: (12x2 - 12)= 12

40 + 24 + 12 = 76

Answer:

$726.02 I had to guess cause I used a calculator but it didn't get to an exact number this is the closet

Answer:

$726.02

Step-by-step explanation:

Answer:

Your Awnser would be 597,000

Step-by-step explanation:

Answer:

The actual answer for this question should be 200.

Step-by-step explanation:

The scale factor of the lengths of two similar octagons with areas 4 m² and 9 m² is obtained by taking the square root of the ratio of their areas, yielding a scale factor of 1.5.

The subject of this question is Mathematics, particularly dealing with geometry and scale factors. For two similar shapes, the ratio of their areas is equal to the square of the scale factor of their lengths.

Given the areas of the two similar octagons as 4 m² and 9 m², we find the square root of the ratio of the areas to obtain the scale factor of the lengths. That is, √(9/4) = √2.25 = 1.5.

Therefore, the scale factor of the lengths of the two similar octagons is 1.5.

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The scale factor of the lengths of the two similar octagons is 1.5.

To find the scale factor of the lengths of two similar octagons, we can use the formula:

Scale factor = sqrt(Area2 / Area1)

Where Area1 is the area of the first octagon, and Area2 is the area of the second octagon.

Plugging in the given values, we get:

Scale factor = sqrt(9 m² / 4 m²) = sqrt(2.25) = 1.5

Therefore, the scale factor of the lengths of the two octagons is 1.5.

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Answer:

We have to prove

sin⁡(α+β)-sin⁡(α-β)=2 cos⁡ α sin ⁡β

We will take the left hand side to prove it equal to right hand side

So,

=sin⁡(α+β)-sin⁡(α-β)      Eqn 1

We will use the following identities:

sin⁡(α+β)=sin⁡ α cos⁡ β+cos⁡ α sin⁡ β

and

sin⁡(α-β)=sin⁡ α cos ⁡β-cos ⁡α sin ⁡β

Putting the identities in eqn 1

=sin⁡(α+β)-sin⁡(α-β)

=[ sin⁡ α cos ⁡β+cos⁡ α sin⁡ β ]-[sin⁡ α cos ⁡β-cos ⁡α sin ⁡β ]

=sin⁡ α cos⁡ β+cos⁡ α sin ⁡β- sin⁡α cos⁡ β+cos ⁡α sin ⁡β

sin⁡α cos⁡β will be cancelled.

=cos⁡ α sin ⁡β+ cos ⁡α sin ⁡β

=2 cos⁡ α sin ⁡β  

Hence,

sin⁡(α+β)-sin⁡(α-β)=2 cos ⁡α sin ⁡β

Answer:

6.9

Step-by-step explanation:

12 x 4 = x^2

48 = x^2

x = 6.9

Answer:

6.9

explanation:

I did the test.

hope this helps you!

:D

Answer:

square; 60; 225.

Step-by-step explanation:

1) using the vectors rules to calculate the lengths of the sides AB; BC; CD and AD. When AB=BC=CD=AD it means, the shape is a square of rhombus.

2) using the vectors rules to calculate the lengths of the diagonales AC and BD. When AC=BD it means, the shape is a square.

3) The perimeter of the square ABCD is 15*4=60.

4) The area of the square ABCD is 15*15=225.

All the details are in the attached picture; answers are marked with colour.

Answer:

y = 700 (0.969)^t

Step-by-step explanation:

Using the depreciation formula after a given period of time.

A = P (1- r/100)^n

Where, A is the initial value

P is the original value

r is the rate of depreciation and

n is the time taken in years

Therefore;

A will be the new mass of the sample after decay,y

P is the original mass of the sample before decay, 700 mg

r is the rate of decay each year, 3.1% and

n is the number of years, t

Hence;

y = 700 (1- 3.1/100)^t

y = 700 (96.9/100)^t

y = 100(0.969)^t

The relationship between the mass of the radioactive sample (y) and the number of years since the start of the study (t) can be represented by the exponential function y = 700 * (1 - 0.031) ^ t.

This is a problem related to exponential decay. In general, the formula for an exponential decay is given as Y = A * (1 - r) ^ t where 'A' represents the initial amount, 'r' is the rate of decay (as a decimal), and 't' is the time period.

For this problem, the initial amount of the radioactive substance is 700 milligrams (A = 700), the rate of decay is 3.1% per year (r = 0.031), and 't' is represented as the number of years since the start of the study.

Using these values, we can write the exponential function showing the relationship between the mass of the sample 'y' and the number of years 't' as follows:

y = 700 * (1 - 0.031) ^ t

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The answer is -- 10 days

Answer:

  2. 90°

  3. 65°

Step-by-step explanation:

2. Points A, B, and D are on a semicircle centered at C. The angle A is inscribed in that semicircle, so is 90°. Then angles B and D sum to 90°.

__

3. Triangle ABC is similar to triangle EDC by SAS, so angle x has the same measure as the third angle of triangle EDC: 180° -80° -35° = 65°.

___

The relevant relationship in both cases is that the sum of angles in a triangle is 180°. Also, for problem 2, you need to know that an inscribed angle has half the measure of the arc it subtends. And for problem 3, it helps to understand the relationships in similar triangles.

Answer:

ΔADB~ΔCDB; SAS~

Step-by-step explanation:

Due to the tick marks on AD and DC, we know that those sides are congruent

We also know that the angle D is congruent due to the marks

As they share line BD, that side is also congruent.

This means that we have a side, an angle, and another side.

This leaves us with the last two options

The only difference between them is what angle corresponds to which

In the case of this triangle, A and C correspond with each other and B and D are shared. This means we are looking for when the locations of A and C, and B and D are matched

This would mean that the 4th option

ΔADB~ΔCDB; SAS~

Answer: 1,7 and 1,5 on coefficient

Step-by-step explanation:

Equation at the end of step  1  :

 (((5•(x4))+(x3))+3x2)-7

Step  2  :

Equation at the end of step  2  :

 ((5x4 +  x3) +  3x2) -  7

Step  3  :

Checking for a perfect cube :

3.1    5x4+x3+3x2-7  is not a perfect cube

Trying to factor by pulling out :

3.2      Factoring:  5x4+x3+3x2-7  

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  3x2-7  

Group 2:  5x4+x3  

Pull out from each group separately :

Group 1:   (3x2-7) • (1)

Group 2:   (5x+1) • (x3)

3.3    Find roots (zeroes) of :       F(x) = 5x4+x3+3x2-7

Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  5  and the Trailing Constant is  -7.

The factor(s) are:

of the Leading Coefficient :  1,5

of the Trailing Constant :  1 ,7

The factor of the constant is [tex]\rm (x+1) (5x^3-4x^2+7x-7) =0\\\\[/tex].

Given

Expression; [tex]\rm 5x^4+x^3+3x^2-7[/tex]

The leading coefficient of the polynomial of the term has the highest degree of the polynomial.

The factors of the constant term;

[tex]\rm 5x^4+x^3+3x^2-7=0\\\\ 5x^4-4x^3+7x^2-7x+5x^3-4x^2+7x-7=0\\\\(x+1) (5x^3-4x^2+7x-7) =0\\\\[/tex]

Hence, the factor of the constant is [tex]\rm (x+1) (5x^3-4x^2+7x-7) =0\\\\[/tex].

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