The ratio of the area of the shaded part to the unshaded part is______.

Given

[tex]25x^{-4} - 99x^{-2} - 4 = 0[/tex]

consider substituting [tex]y=x^{-2}[/tex] to get a proper quadratic equation,

[tex]25y^2 - 99y - 4 = 0[/tex]

Solve for [tex]y[/tex] ; we can factorize to get

[tex](25y + 1) (y - 4) = 0[/tex]

[tex]25y+1 = 0 \text{ or } y - 4 = 0[/tex]

[tex]y = -\dfrac1{25} \text{ or }y = 4[/tex]

Solve for [tex]x[/tex] :

[tex]x^{-2} = -\dfrac1{25} \text{ or }x^{-2} = 4[/tex]

The first equation has no real solution, since [tex]x^{-2} = \frac1{x^2} > 0[/tex] for all non-zero [tex]x[/tex]. Proceeding with the second equation, we get

[tex]x^{-2} = 4 \implies x^2 = \dfrac14 \implies x = \pm\sqrt{\dfrac14} = \boxed{\pm \dfrac12}[/tex]

If we want to find all complex solutions, we take [tex]i=\sqrt{-1}[/tex] so that the first equation above would have led us to

[tex]x^{-2} = -\dfrac1{25} \implies x^2 = -25 \implies x = \pm\sqrt{-25} = \pm5i[/tex]

Answer:

Here is your answer

Step-by-step explanation:

Step -1: Forming equations.

                  Let, present age of son = x

                  And, present age of father = 3x+3

                  3 years later, age of son = x+3

                  age of father = 3x+3+3=3x+6                                  ...(i)

                  According to the given condition, age of father = 10+2(x+3)        ...(ii)

Step -2: Solving for x

                  From (i) and (ii)

                  ∴3x+6=10+2(x+3)

                  ⇒3x+6=10+2x+6

                  ⇒3x−2x=10+6−6

                  ⇒x=10

                  ∴Present age of son = 10 

                  and present age of father = 3x+3=3×10+3=33

Hence, son’s present age is 10 years and father’s 

Answer:

i think its c wouldve helped if i saw a pic of the triangle tho

Step-by-step explanation:

The length of side AB is 5√3.

Option B is the correct answer.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

We can use trigonometry to solve this problem.

Let's start by finding the length of BC.

sin(30°) = BC/AC

sin(30°) = BC/10

BC = 5

Now, we can use the Pythagorean theorem to find the length of AB.

AB² = AC² - BC²

AB² = 10² - 5²

AB² = 75

AB = 5√3

Therefore,

The length of side AB is 5√3.

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At times, latitudes with values higher than 66.5  degrees can have ~ 24 hours of continuous sunshine.

Locations above the Arctic Circle (north of latitude 66.5 degrees, 90 degrees minus the tilt of the Earth's axis) are exposed to 24-hour sunlight. Below the Arctic Circle (latitude 66.5 degrees south), there is 24-hour darkness.

When at the equator, the sun is directly above – at the poles, the sun is on the horizon. However, regardless of the current location (from the pole to the equator), all parallels are bisected, so we have 12 hours a day and 12 hours a night in all locations.

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Answer:

x/2

Step-by-step explanation:

Madison didn't cancel the common factor of 2 and that 4 that is why she is wrong.

Hope this helps pls brainliest have a nice day :>

The population in the year 2020 is 4628

The given parameters are:

Initial, a = 12910

Rate, r = 5%

Since the population decreases, then we make use of an exponential decay function.

This is represented as:

f(n) = a * (1 - r)^n

So, we have:

f(n) = 12910 * (1 - 5%)^n

Evaluate the difference

f(n) = 12910 * 0.95^n

2020 is 20 years from 2000.

So, we have:

f(20) = 12910 * 0.95^20

Evaluate

f(20) = 4628

Hence, the population in the year 2020 is 4628

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Answer:

No

Step-by-step explanation:

Let's assume that x=2 and y=3.

1/2+1/3≠1/5

Also, when adding fractions, you cannot simply add the denominator. You have to make the denominators of all fractions the same and then add.

So, if you are given 1/x +1/y, you should get (y+x)/xy, not 1/(x+y)

Angles EBA and DBC are congruent. The three angles EBA, EBD, and DBC are together supplementary, so their measures sum to 180°. This means

x + (4x + 11°) + x = 180°

6x + 11° = 180°

6x = 169°

x = (169/6)°

Then the measure of angle D is

2x + 8° = 2 (169/6)° + 8° = (193/3)°

The interior angles of any triangle sum to 180°, so if y is the measure of angle C, we have

(169/6)° + (193/3)° + y = 180°

y = (175/2)° = 87.5°

There is a profit of $39.7.

It is given that there 100 tickets costing $10 per ticket.

You must look first for the probability of the 4 prizes which are $475, $195, $30, and no prize.

P ($475 prize) = 1/100 or 0.01

P ($95 prize) = 2/100 or 0.02

P ($30 prize) = 4/100 or 0.04

P (No prize) = 100/100 – 1+2+4/100 =93/100 .93

Expected gain or loss is computed by: (P(x)* n)

E= (475-10)*.01 + (95-10)*0.02 + (30-10)* 0.04 + (-10)*.93

= 46.5 + 1.70 + 0.8 – 9.3

E = 39.7

There is a profit of $39.7.

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The total amount you have paid from May 2014 to July 2022 is $75,319.86

= 96 + 2

= 98 months

Total amount paid from May 2014 to July 2022 = $768.57 × 98 months

= $75,319.86

The total amount paid so far from May 2014 to July 2022 is $75,319.86

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The polar form of any complex number can be written as

[tex]z = |z| e^{i\arg(z)}[/tex]

where [tex]\arg(z)[/tex] is the argument of [tex]z[/tex], i.e. the angle it makes with the positive real axis in the complex plane.

If [tex]z=\sqrt3+i[/tex], then [tex]z[/tex] has modulus

[tex]|z| = \sqrt{\left(\sqrt3\right)^2 + 1^2} = \sqrt4 = 2[/tex]

and argument

[tex]\arg(z) = \tan^{-1}\left(\dfrac1{\sqrt3}\right) = \dfrac\pi6[/tex]

Then

[tex]\sqrt3 + i = 2e^{i\frac\pi6} = 2 \left(\cos\left(\dfrac\pi6\right) + i \sin\left(\dfrac\pi6\right)\right)[/tex]

The ladder reaches 19.938 foot high from the ground on the wall.

A right angled triangle is a triangle that has one of its angle measure as 90  degree.

It is given that

Ladder Length = 22 foot

The angle between the ladder and the ground is 65 degree.

When the ladder leans on a wall , the wall makes 90 degree with the ground and the ladder is the hypotenuse of the right angled triangle formed.

The figure is attached with the answer.

sin 65 = Height of the wall / Hypotenuse

0.9063 = Height of the wall / 22

Height of the wall = 19.938 foot

Therefore the ladder reaches 19.938 foot high from the ground on the wall.

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Answer:

19.94

Step-by-step explanation:

Answer:

x=58

Step-by-step explanation:

Exterior angle of one interior angle in a triangle is equal to the sum of the other two remote interior angles. (Ext. Angle Th.) So, 3x-32=84+x

2x=116

x=58

Answer: h>0 and k>0

Step-by-step explanation:

If the circle is centered in Quadrant I, then both the x and y coordinates of the center are positive.

This means that h>0 and k>0.

Answer:

C

Step-by-step explanation:

Solution

There are 8 apples in the bowl

There are 8 + 14 = 22 total fruits in the bowl.

Ratio apples / total = 8 / 22. But that is not the answer. You can divide top and bottom of the ratio by 2.

When you do that, you get 4/11 which is C

Answer: 4/11 or C

The ordered pair is (-9, -25) and the word statement is if x is equal to -9, then the value of h(x) is -25

From the given table, f(x) = y means that the corresponding value of y given a value x.

For the function h(-9), we need to find the equivalent value of h(x) when x is -9. Hence h(-9) is -25

The ordered pair is (-9, -25) and the word statement is if x is equal to -9, then the value of h(x) is -25

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The probability that the sample proportion will differ from the population proportion by less than 6% is 0.992.

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

цр = р

The standard deviation of this sampling distribution of sample proportion is:

бр = √ρ(1-ρ)÷n

The information provided is:

ρ = 0.22

ⁿ = 276

As the sample size is large, i.e. n = 276 > 30, the Central limit theorem can be used to approximate the sampling distribution of sample proportion.

Compute the value of P(р-p<0.06) as follows:

P(р-p<0.06) = P(р-p ÷ бp<0.06 ÷√0.22(1 - 0.22) ÷ 276

= P ( Z < 2.41 )

= 0.99202

≈ 0.992

Thus, the probability that the sample proportion will differ from the population proportion by less than 6% is 0.992.

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The interquartile range is 12.

The interquartile range is the difference between the third quartile and the first quartile. The first quartile is the first line on the box while the third quartile is the third line on the box.

First quartile = 11

Third quartile = 23

Interquartile range = 23 - 11  = 12

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Step-by-step explanation for each question:

For Question 6, the range of a function is all the possible outputs of the function. Since the function can only take the inputs 0, 4, and 7, we can just plug in each into the formula and find their corresponding outputs.

g(0) = 0² - 9 = 0 - 9 = -9

g(4) = 4² - 9 = 16 - 9 = 7

g(7) = 7² - 9 = 49 - 9 = 40

Therefore the only possible outputs of function g, or the range, is {-9, 7, 40}.

For question 4, the input t is a given time, and h(t) is the height of the football at that time.

Hence, h(2.5) is the height of the football (in feet) at 2.5 seconds. The value 2.5 can be plugged into the function [tex]-16t^2+58t+2[/tex] to get the height. This gives us

[tex]-16(2.5)^2 + 58(2.5) + 2[/tex]

[tex]-16(6.25) + 58(2.5) + 2[/tex] [Squaring 2.5]

[tex]-100 + 145 + 2[/tex] [Multiplying]

[tex]47[/tex] [Combining all terms]

We find that the height of the football at 2.5 seconds is 47 feet.

For Question 5, the table of values show all the possible values x can be (or the domain), and what the output of the function f(x) would give for each.

A) f(-3) = 5, as the row with -3 for x has -5 for y.

B) f(0) = 0, as the row with 0 for x has 0 for y.

C) f(1) = -3, as the row with 1 for x has -3 for y.

The range of the function will be -9,7 and 40.

The domain denotes all potential x values, while the range denotes all possible y values.

Given equation;

g(x) = x²-9

The range of the given domain is found by putting the values one by one in the above equation as;

g(x) = x²-9

a)For x = 0

g(x) = 0²-9

g(x) =-9

b)For x =4

g(x) = 4²-9

g(x) =16-9

g(x) = 7

c)For x =7

g(x) = 7²-9

g(x) =49-9

g(x) = 40

Hence, the range of the function will be -9,7 and 40.

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Answer:

14.52% are unicyclists

Step-by-step explanation:

First, we can use proportions to find the number of unicyclists at the convention. Since we know that the ratio of unicyclists to aerial artists is 9:11, and there are 88 aerial artists, we can set up the following equation:

[tex]\frac{9}{11}=\frac{x}{88}[/tex]

If we cross multiply, we get that 11x = (88)(9). After we divide through by 11 to isolate x, we get that x = (8)(9) = 72

Second, we have to figure out the number of mimes at the convention to figure out the total number of people there. We know that the ratio of unicyclists to mimes is 3:14, and the number of unicyclists is 72. So, we can set up the following proportion:

[tex]\frac{3}{14}=\frac{72}{y}[/tex]

If we cross multiply, we get that 3y = 1008, or y = 336 mimes

The total number of people at the convention is 336 mimes + 72 unicyclists + 88 unicyclists = 496. Now we have to figure out what percent of 496 is 72 (the number of unicyclists). If we let z = the percentage, we can simply set up an equation that says that 72 is z% of 496:

[tex]72=0.01z*496\\0.01z=0.14516\\z=14.52[/tex]

This means that approximately 14.52% of the performers are unicyclists.

Answer:

14.52%

Step-by-step explanation:

U/A = 9/11       and   A = 88      multiply by  8/8   ( to get A=88 as given)

9/11 * 8/8 = 72/88  = U / A       so U = 72

Then U/M = 3/14    multiply by  24/24   ( to get U = 72 as found above)

  then  U/M=    72 / 336     M = 336

U / ( A + U + M )  x  100% = 14.52 %

Answer:

AC = 6√3 in

Step-by-step explanation:

Join OC. Now ΔAOC is an isosceles triangle as OA = OC =radius.

 ∠A = ∠C = 30.

 ∠A + ∠C +  ∠AOC = 180 {angle sum property of traingle}

 30 + 30 + ∠AOC  = 180°

                 ∠AOC = 180 -60

                 ∠AOC = Ф = 120°

Find the length of radius using the bellow formula.

         [tex]\sf \boxed{\bf Arc \ length = \dfrac{\theta}{180}\pi r}[/tex]

            Ф = 120°

                Arc length = 4π

            [tex]\sf 4\pi =\dfrac{120}{180}*\pi *r\\\\ r =\dfrac{4\pi * 180}{120*\pi }\\\\ r = 6 \ in[/tex]

[tex]\sf \boxed{\bf chord \ length = 2rSin \ \dfrac{\theta}{2}}[/tex]

                         [tex]\sf b = 2*6*Sin \ \dfrac{120}{2}\\\\ b = 2 *6 * Sin \ 60^\circ\\\\ b = 2 * 6 * \dfrac{\sqrt{3}}{2}\\\\ \b = 6\sqrt{3}[/tex]

[tex]\sf \boxed{\bf AC = 6\sqrt{3} \ in}[/tex]

The point-slope equation of the line is y-2=-2(x-7)

How will we find the equation of line?

First, we will find the slope of line using the given points then put slope and point in the formula to get equation of line.

We can find the equation as shown below:

Given points (6,4) and (7,2)

slope(m)= (2-4)/ (7-6)

m=-2/1

m=-2

The point slope form:

(y-y1) = m(x-x1)

y1=2, x1=7

putting in formula

(y-2) = -2(x-7)

y-2=-2(x-7)

Hence, the point-slope equation of the line is y-2=-2(x-7)

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Answer:

Step-by-step explanation:

The component form of the vectors shown is (-6, -5)

In order to determine the component of the vectors shown, we will subtract the coordinate points from both each other.

Given the vector coordinates on the line. as (-5, -3) and (1, 2). Take the difference;

Difference = [(-5-1), (-3-2])

Difference = (-6, -5)

Hence the  component form of the vectors shown is (-6, -5)

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Answer:

D

Step-by-step explanation:

the answer is D because the range is the lowest possible value up to the highest possible value and when listed it doesn't repeat

The number of boxes renita and Vanessa has unpacked each is 6 and 9 boxes respectively.

x + (2x - 3) = 15

x + 2x - 3 = 15

3x = 15 + 3

3x = 18

x = 18/3

x = 6

Therefore,

Number of boxes renita has unpacked = x

= 6 boxes

Number of boxes Vanessa has unpacked = 2x - 3

= 2(6) - 3

= 12 - 3

= 9 boxes

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Answer:

Step-by-step explanation:

The number of boxes renita and Vanessa has unpacked each is 6 and 9 boxes respectively.

Equation

Number of boxes renita has unpacked = x

Number of boxes Vanessa has unpacked = 2x - 3

Total boxes both unpacked = 15

x + (2x - 3) = 15

x + 2x - 3 = 15

3x = 15 + 3

3x = 18

x = 18/3

x = 6

Therefore,

Number of boxes renita has unpacked = x

= 6 boxes

Number of boxes Vanessa has unpacked = 2x - 3

= 2(6) - 3

= 12 - 3

= 9 boxes

The statement which is true about the given graph is  that f(x)<0 in the interval (-∞,3) which is option 3.

Given Graph of a function

We have to choose a statement which is correct about the function whose graph is given.

The graph of a function tells us about the domain and range of the function. The values on y axis are the codomain of the function and the values on x axis are the values of domain.

When we see the graph we can find that x=-∞ to x=3 the values are negative means when we put the values of x less than 0 we will get negative number. For example if we put the value of x=-1, we will get -20 which is a negative number.

Hence the third statement is true for the given graph which is that it has values less than zero in the interval (-∞,3).

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Deposit: $1,000

Annual interest: 4% = 0.04

Years: 3

For this type of question, when the question asks you to "continuously compound", you use this formula: [tex]Pe^{rt}[/tex]

Solving:

[tex]1000e^{(0.04)(3)} \\1000e^{0.12} \\=1127.50[/tex]

The value of Joaquin's investment after 3 years = 1,127.50$

Answer: A

Step-by-step explanation:

The angle opposite the shortest side in a triangle has the smallest measure.