Need help on geometry

Answer:

v(9)=2000

V(15)=8000

Step-by-step explanation:

Answer:

Step-by-step explanation:

You are given a function V(t) and asked to find V(9) and V(15). In each case, the number in parentheses replaces "t" in the function expression. After that, it is just arithmetic. (You may want to use a calculator, but it isn't really necessary.)

Given:

  V(t) = 250·2^(t/3)

Find:

  V(9) = 250·2^(9/3)

  = 250·2^3

  = 250·8

  V(9) = 2000

__

  V(15) = 250·2^(15/3)

  = 250·2^5

  = 250·32

  V(15) = 8000

_____

As you know, an exponent signifies repeated multiplication. The exponent tells you the number of times the base is a factor in the product:

  2^3 = 2·2·2 = 8 . . . . . . the exponent of 3 means 2 is a factor 3 times

Answer:

(x) free throw = 8

(y) 2-point = 6

(z) 3-point = 2

x+(y*2)+(z*3)

8+(6*2)+(2*3)

8+12+6

=26

The expression for the given sequence of operations is 2(x-4)+8.

The given statement is "subtract 4 from x, double, and add 8".

We need to write an expression for the sequence of operations.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Now, subtract 4 from x=x-4

Double the difference that is 2(x-4)

Add 8=2(x-4)+8

Therefore, the expression for the given sequence of operations is 2(x-4)+8.

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Answer: Probability that at least two of the triplets will win a medal is19/24

Step-by-step explanation:

Total number of cmpetitors=9

Total number of selecting 3 winners out of 9 competitors=9C3=84

Number of ways of selecting 2 out of 3 triplets=3C2

Number of selecting 1 out of 6 others =6C1

Number of selecting 2 out of 3 triplet and o1 out of 6 others= 3C2 ×6C1=18

Number of selecting 3 out of 3 triplets=3C3=1

Total ways of selecting less than 2 or 2 triplets= 18+1=19

Probability that at least 2 of the triplets will win is 19/84

Answer:

True

Step-by-step explanation:

Müller-Lyer illusion - In this illusion two-line having the same length appear to be different from one another.

the line showing in the file attached, the line with arrow moving outward appears to have large length and line having the arrow pointing inward appear to have a short length. But given lines are equal in length, it is just an illusion that might force to believed you that one is shorter or larger than others.

Answer:

  y = -2

Step-by-step explanation:

Any asymptotes of a rational function will be described by the quotient of the numerator and denominator (excluding any remainder).

  [tex]f(x)=\dfrac{-2x}{x+1}=-2+\dfrac{2}{x+1}[/tex]

The horizontal asymptote is ...

  y = -2

Answer:

Step-by-step explanation:

The given function is

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

An asymptote refers to a restriction in the domain or range set of the function. This happens to rational functions, because there's a scenario where the function is undetermined: when its denominator is zero.

So, in this case, the value that makes the denominator zero is

[tex]x+1=0\\x=-1[/tex]

That means, we need to restrict the domain for [tex]x=-1[/tex]. But this is a vertical asymptote.

To find horizontal asymptotes, we need to find the restrictions for the range of the function, we do that isolating [tex]y[/tex].

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

So, if we analyse the denominator

[tex]y+2=0\\y=-2[/tex]

Therefore, the restriction is [tex]y=-2[/tex]. In other words, the vertical asymptote is the first choice.

Answer: the cost of one adult ticket is $8

the cost of one kid ticket is $4

Step-by-step explanation:

Let x represent the cost of one adult ticket.

Let y represent the cost of one kid ticket.

They sold 64 adult tickets (x) and 132 kid tickets (y) and made $1040. This means that

64x + 132y = 1040 - - - - - - - - - - -1

An adult ticket is double the cost of a kid's ticket. This means that

x = 2y

Substituting x = 2y into equation 1, it becomes

64 × 2y + 132y = 1040

128y + 132y = 1040

260y = 1040

y = 1040/260 = 4

x = 2y = 2 × 4

x = 8

Answer:

The coordinate of [tex]Z=7.3[/tex].

Step-by-step explanation:

To determine:

What is the coordinate of Z?

Fetching Information and Solution Steps:

The distance [tex]XY[/tex] = [tex]3.8-1.3 = 2.5[/tex]

As

Y is [tex]\frac{5}{12}[/tex] of the way from [tex]X[/tex] to [tex]Z[/tex]

So,

[tex]YZ[/tex] is [tex]\frac{7}{5}[/tex] as big as [tex]XY[/tex]

Therefore,

[tex]Z = 3.8 + (\frac{7}{5} )(2.5)[/tex]

[tex]Z=3.8+\frac{17.5}{5}[/tex]

[tex]Z=7.3[/tex]

Therefore, the coordinate of [tex]Z=7.3[/tex].

Keywords: coordinate, point, length, ratio

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The coordinate of Z is (4.43, 11.57)

The coordinate of X is (1, 3)

The coordinate of Y is (3, 8)

Let the coordinate of z be (x₂, y₂)

The ratio of division is 5:7

m = 5, and n = 7

Let the coordinate of y be (a, b)

a = 3, b = 8

[tex]a=\frac{mx_1+nx_2}{m+n}\\\\3= \frac{5(1)+7x_2}{5+7}\\\\3(12)=5+7x_2\\\\7x_2=36-5\\\\7x_2=31\\\\x_2=4.43[/tex]

[tex]ab=\frac{my_1+ny_2}{m+n}\\\\8= \frac{5(3)+7y_2}{5+7}\\\\8(12)=15+7y_2\\\\7y_2=96-15\\\\7y_2=81\\\\y_2=11.57[/tex]

The coordinate of Z is (4.43, 11.57)

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Answer:

His diagonal brace need to be 15.55 feet long in the kitchen.

Step-by-step explanation:

Given : The wall of the kitchen is in the shape of a square.

Area of the wall = 121 sq ft

Let us assume the each side of  wall = a ft

Now, AREA OF THE SQUARE = Side x Side

⇒   a x  a = 121 sq units

[tex]\implies a ^2 = 121\\\implies a = 11[/tex]

So, each side of the  kitchen wall is 11 ft.

Now,as  we know in a square : EACH ANGLE IN THE  SQUIRE IS A RIGHT ANGLE.

So, by Pythagoras Theorem, Diagonal D is:

[tex]D^2 = a^2 + a^2\\\implies D^2 = 11^2 + 11^2 = 121 + 121\\\implies D^2 = 242\\\implies D = 15.55[/tex]

Hence,  his diagonal brace need to be 15.55 ft long in the kitchen.

Answer: 15.07°

Step-by-step explanation:

Sin^-1 0.26= 15.07°

Therefore:

Cos15.07= 0.9656

Tan 15.07 = 0.2692

Csc15.07= 1/(Sin15.07)= 3.846

Sec15.07=1/cos15.07=1.0356

Cot15.07=1/tan15.07= 3.7147

We can use the trigonometric identity sin² θ + cos² θ = 1 to find cos θ in a first quadrant triangle where sin θ = 0.26, and get cos θ = 0.966. Then, we calculate tan θ with the formula tan θ = sin θ / cos θ, and get tan θ = 0.269 after rounding.

In trigonometry, there are three primary ratios called trigonometric ratios: sine (sin), cosine (cos), and tangent (tan). These ratios can be defined using the sides of a right triangle, and they relate the angles of a triangle to the lengths of its sides. If we know one of these ratios in a right triangle, we can find the others.

In this case, we know that sin θ = 0.26 and θ is in Quadrant I. In the first quadrant, all the trigonometric ratios are positive.

So, firstly we find cos θ. Remember that sin² θ + cos² θ = 1, we can solve for cos θ using the calculator with the square root of (1 - sin² θ), which results in cos θ = 0.966 approximately.

Next, to find tan θ, we use the relationship tan θ = sin θ / cos θ. So, tan θ = 0.26 / 0.966 = 0.269 approximately, after rounding to the nearest hundredth.

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Answer:

-5/6

Step-by-step explanation:

covert the mixed number into a improper fraction

4/3 + (- 13/6) =

Find LCD which is 6 so

[tex]\frac{4}{3} * 2[/tex]

8/6 + (-13/6) =

Which is -5/6

Answer:  The required equation for points P is [tex]4x+2y=17.[/tex]

Step-by-step explanation: We are give two points A(0, 1, 2) and B(6, 4, 2).

To find the equation for points P such that the distance of P from both A and B are equal.

We know that the distance between two points R(a, b, c) and S(d, e, f) is given by

[tex]RS=\sqrt{(d-a)^2+(e-b)^2+(f-c)^2}.[/tex]

Let the point P be represented by (x, y, z).

According to the given information, we have

[tex]PA=PB\\\\\Rightarrow \sqrt{(x-0)^2+(y-1)^2+(z-2)^2}=\sqrt{(x-6)^2+(y-4)^2+(z-2)^2}\\\\\Rightarrow x^2+y^2-2y+1+z^2-4z+4=x^2-12x+36+y^2-8y+16+z^2-4z+4~~~~~~~[\textup{Squaring both sides}]\\\\\Rightarrow -2y+1=-12x-8y+52\\\\\Rightarrow 12x+6y=51\\\\\Rightarrow 4x+2y=17.[/tex]

Thus, the required equation for points P is [tex]4x+2y=17.[/tex]

Answer:

August D is the fastest rapper. XD

Step-by-step explanation:

Answer:

Based on this info I would say that Mark Lee does because he is at 90.0 sps.

Step-by-step explanation:

Answer:

[tex]4x+9+4x^2[/tex]

Step-by-step explanation:

The given functions are:

[tex]f(x)=4x+9[/tex] and [tex]g(x)=4x^2[/tex]

We want to find [tex](f+g)(x)[/tex].

Recall that:

[tex](f+g)(x)=f(x)+g(x)[/tex]

We substitute the functions to get:

[tex](f+g)(x)=4x+9+4x^2[/tex]

We now write in standard form to obtain:

[tex](f+g)(x)=4x^2+4x+9[/tex]

Answer:

Step-by-step explanation: The brains are very similar insofar that they function in almost the same way when it comes to controlling physical aspects of our existence. Our brains regulate our organs and our body parts just like a sheep's brain.

Answer:

A) [tex]2x[/tex]

Step-by-step explanation:

Given:

Number of calculator made by Adnan in this week = [tex]'x'[/tex]

We need to write an algebraic expression for the number of calculators that Maya made this week.

Solution:

Now given:

Maya made twice as many calculators.

So we can say that;

Number of calculators made by Maya this week is equal to 2 times Number of calculator made by Adnan this week.

framing in equation form we get;

Number of calculators made by Maya this week = [tex]2\times x = 2x[/tex]

Hence an algebraic expression for the number of calculators that Maya made this week is [tex]2x[/tex].

Answer:

65.83

Step-by-step explanation:

The total amount Mr. And Mrs. Kingsley have to leave if Their dinner bill came to $57.24, If they wish to leave, a 15% tip is $65.83.

As it is clear from the term per cent means measuring anything per hundred. For example, you get marks per 100 marks, so you get the percentage.

Given:

The dinner bill is $57.24,

The tip percentage = 15%,

Calculate the amount of the tip as shown below,

The amount of the tip = 15% of 57.24

The amount of the tip = 15 / 100 × 57.24

The amount of the tip = 0.15 × 57.24

The amount of the tip = 8.586

Hence, total amount = tip amount + bill amount

Total amount = 57.24 + 8.586

Total amount = 65.83

Thus, the total amount is $65.83.

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Answer:a) C = 2πr

b) 37.68feet

c) r = C/2π

d) 5.89feet

Step-by-step explanation:

The answers are a) 2πr, b) 37.68 ft, c) r = C/2π and d) 5.8 ft

The circumference is the distance around the edge of a circle.

Given that, a circle whose size can vary. The circumference of the circle is always 2π times as large as its radius and r represent the radius of the circle (in feet) and let C represent the circumference of the circle (in feet).

a) C = 2πr

b) C = 2*3.14*6 = 37.68ft

c) C = 2πr, r = C/2π

d) r = 37/2*3.14 = 5.8 ft

Hence, The answers are a) 2πr, b) 37.68 ft, c) r = C/2π and d) 5.8 ft

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Answer:it will take 0.25 years

Step-by-step explanation:

Let x represent the number of years that it will take for type A and tree B to be the same height.

Let y represent the height of type A after x years.

Let z represent the height of type B after x years.

Type A is 5 feet tall and grows at a rate of 13 inches per year. This means that

y = 5 + 13x

Type B is 3 feet tall and grows at a rate of 21 inches per year. This means that

z = 3 + 21x

To determine the number of years it will take both trees to be of the same height, we would equate equation y to z. It becomes

5 + 13x = 3 + 21x

21x - 13x = 5 - 3

8x = 2

x = 2/8 = 0.25 years

Answer: a) Length of wire to replace old one=9ft

b) Length of wire=3.09ft

Leftover wire=0.91ft

Step-by-step explanation: from the right angle triangle, Tan&=20/15

&=53.13°

Length of wire,x=cos 31.13=x/15

15cos31.13

X=9

b) Tan&=10/6

Tan^-110/6

&=59.05

Length= 6cos59.04

X=3.09

4-3.09=.91= leftover wire

Using the Pythagorean theorem, the length of the guy wire needed for a 20-foot flagpole with a 15-foot distant anchor point is 25 feet, and for a 10-foot flagpole with a 6-foot distant anchor point, a 12-foot guy wire is needed, leaving approximately 4 inches of wire leftover.

The question involves applying the Pythagorean theorem to determine the lengths of guy wires needed to support flagpoles. For the first scenario, a 20-foot tall flagpole with a 15-foot distant anchor point, the guy wire's length can be found using the equation a^2 + b^2 = c^2, where 'c' is the hypotenuse (the guy wire), 'a' is one leg (the height of the flagpole which is 20 feet), and 'b' is the other leg (the distance from the base of the pole to the anchor point which is 15 feet). After calculation, the guy wire's length is found to be 25 feet.

For the second scenario with a 10-foot tall flagpole and a 6-foot distant anchor point, using the same theorem gives us the equation 10^2 + 6^2 = c^2. Estimating using perfect squares, we get c as the square root of 136, which is approximately 11.66 feet. Since guy wires can only be purchased in whole foot lengths, we would purchase a 12-foot guy wire, leaving approximately 0.34 feet (about 4 inches) of wire leftover.

Answer:

2.

Step-by-step explanation:

Healthy baby.

Answer:

y=22000x+40000

Answer:

The answer to your question is below

Step-by-step explanation:

a) x² = 196

   x = ±√196

  x = ± 14       or     x = -14  and x = 14

b) 9x² = 49

      x² = 49/ 9

      x = √(49/9)

      x = ±7/3

      x = ± 2.3      or  x = 2.3 and  x = -2.3

c)  4x² - 8 = 56

    4x² = 56 + 8

    4x² = 64

      x² = 64/4

      x² = 16

      x = ±√16

     x = ±4        or   x = 4 and   x = -4

d) x² = 160

   x = ± √160

Find the prime factors of 160

          160    2

            80    2

             40   2

             20   2

              10   2

               5   5

                1                  160 = 2⁵5      

 x = √2⁴10      

x =  ±4√10

e) x² = 72

    Find the prime factor of 72

    72 = 2²3²6

   x = √2²3²6

   x = ±6√6 or  

   x = ±8.5

Answer:

a). 170 miles

b). Planes will be 500 miles apart after 1.1 hours.

Step-by-step explanation:

a). Two planes heading towards North and South when passed each other were 80 miles apart.

Distance between these planes after 20 minutes or [tex]\frac{1}{3}[/tex] hours.

From the figure attached,

In right angle triangle DEC,

DE = 80 miles

BE = (Speed × duration) = [tex]300\times \frac{1}{3}=100[/tex] miles

Similarly, BC = [tex]150\times \frac{1}{3}=50[/tex] miles

By Pythagoras theorem,

DC² = EC² + DE²

       = (EB + BC)² + DE²

       = (100 + 50)² + (80)²

       = 28900

DC = √28900 = 170 miles

b). Now we have to evaluate the duration after which distance between the planes is 500 miles.

Let after t hours planes will be 500 miles apart.

Then EB = 300t

BC = 150t

Therefore, EC = EB + BC = 450t

It's given that DC = 500 miles

By Pythagoras theorem again,

DC² = EC²+ DE²

(500)²=  (450t)²+ (80)²

250000 = 202500t² + 6400

2500 = 2025t² + 64

2025t² = 2436

t² = 1.20297

t = 1.097 hours ≈ 1.1 hours

Therefore, both the planes will be 500 miles apart after 1.1 hours.

Answer:

False

Step-by-step explanation: Are you asking whether or not its false? If so then yes f(x) is not a function because the x's on the left side repeat. Example the six points to two different numbers on the right side. I hope i helped!

Answer:

  your answer is correct

Step-by-step explanation:

When a relation has an input that maps to more than one output, it is not a function.  Both 6 and 12 map to two different outputs, so the relation is not a function. Your answer choice is correct.

Answer:

A= 1132.8 m^2

Step-by-step explanation:

l=19.1m

b=18m

h=12m

s=15m

The formula to find surface area of the triangular prism is:

A = bh + 2ls + lb

A = (18×12) + 2(19.1×15) + (19.1×18)

A = 216 + 573 + 343.8

A= 1132.8 m^2

Answer: surface Area of triangular prism = 502.5m^2

Step-by-step explanation:

Formular for surface area of a prism is given as: SA=bh+(S1 +S2+S3)H

Given base =18m, length=19.1, h=12, w=15

S1=1/2bh =1/2×18×12 =108m

S2=108m . This is because the dimensions of the two ends of the triangular prism.

S3=lw=19.1×15=286.5m

Surface area=108+108+286.5=502.5m^2

Answer:

four numbers are 1, 3, 5, 7

Step-by-step explanation:

The sum of four numbers in arithmetic progression is 16

a, a+d, a+2d, a+3d are the four arithmetic series

sum of 4 numbers are

[tex]a+a+d+a+2d+a+3d=4a+6d[/tex]

[tex]4a+6d= 16[/tex]

divide both sides by 2

[tex]2a+3d=8[/tex]

[tex]3d= 8-2a[/tex]

The square of the last number is the square of the first number plus 48.

[tex](a+3d)^2=a^2+48[/tex]

solve for  a  and d

[tex](a+3d)^2=a^2+48\\(a+8-2a)^2=a^2+48\\(8-a)^2=a^2+48\\a^2-16a+64=a^2+48\\-16a=48-64\\-16a=-16\\a=1[/tex]

Now find out 'd'

[tex]3d=8-2a\\3d=8-2\\3d=6\\a=2[/tex]

a, a+d, a+2d, a+3d

four numbers are 1, 3, 5, 7

Answer:

Side of 22 and height of 11

Step-by-step explanation:

Let s be the side of the square base and h be the height of the tank. Since the tank volume is restricted to 5324 ft cubed we have the following equation:

[tex]V = s^2h = 5324[/tex]

[tex]h = 5324 / s^2[/tex]

As the thickness is already defined, we can minimize the weight by minimizing the surface area of the tank

Base area with open top [tex]s^2[/tex]

Side area 4sh

Total surface area [tex]A = s^2 + 4sh[/tex]

We can substitute [tex]h = 5324 / s^2[/tex]

[tex]A = s^2 + 4s\frac{5324}{s^2}[/tex]

[tex]A = s^2 + 21296/s[/tex]

To find the minimum of this function, we can take the first derivative, and set it to 0

[tex]A' = 2s - 21296/s^2 = 0[/tex]

[tex]2s = 21296/s^2[/tex]

[tex]s^3 = 10648[/tex]

[tex]s = \sqrt[3]{10648} = 22[/tex]

[tex]h = 5324 / s^2 = 5324 / 22^2 = 11[/tex]

To find the dimensions of the rectangular tank with a square base and minimum weight, we set up the volume and surface area formulas in terms of the base's side length and the tank's height, then use calculus to find the dimensions that minimize the surface area.

The problem is a typical unconstrained optimization problem in calculus. The volume of the tank is given as 5324 cubic feet. Since it's a rectangular tank with a square base, we can let x be the length of the side of the base and h be the height of the tank. Then, the volume of the tank is x^2*h = 5324.

The weight of the tank is proportional to the amount of steel used, which, in turn, is proportional to the surface area of the tank. The surface area of the tank is x^2 + 4*x*h. From the volume formula, we can express h in terms of x: h = 5324 / x^2. Substituting it to the surface area formula, we get the surface area is a function of x, such that "A = x^2 + 4x * 5324 / x^2".

To find the dimensions that minimize the weight, we find the derivative of A with respect to x and set it equal to 0. This will give the x that minimizes the surface area. Then substitute this value back into the equation h = 5324 / x^2 to get the optimal height.

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The answer is

[tex](-9+3\sqrt{2})+(3\sqrt{2}-2)i[/tex]

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

Work Shown:

[tex](-3+\sqrt{-2})(3-\sqrt{2})[/tex]

[tex](-3+\sqrt{-1*2})(3-\sqrt{2})[/tex]

[tex](-3+\sqrt{-1}*\sqrt{2})(3-\sqrt{2})[/tex]

[tex](-3+i\sqrt{2})(3-\sqrt{2})[/tex]

[tex]x(3-\sqrt{2})[/tex] let [tex]x=-3+i\sqrt{2}[/tex]

[tex]3x-x*\sqrt{2}[/tex] distribute

[tex]3(x)-\sqrt{2}(x)[/tex]

[tex]3(-3+i\sqrt{2})-\sqrt{2}(-3+i\sqrt{2})[/tex]

[tex]-9+3i\sqrt{2}+3\sqrt{2}-i*\sqrt{2}*\sqrt{2}[/tex]

[tex]-9+3i\sqrt{2}+3\sqrt{2}-2i[/tex]

[tex]-9+3\sqrt{2}+3i\sqrt{2}-2i[/tex]

[tex](-9+3\sqrt{2})+(3\sqrt{2}-2)i[/tex]

The use of parenthesis in the last step is to help separate out the terms.

The last expression shown above is in the form a+bi where

[tex]a=-9+3\sqrt{2}[/tex]

[tex]b=3\sqrt{2}-2[/tex]

Answer:

There is enough evidence to conclude that the number of minutes spent online per day is related to gender

Step-by-step explanation:

Given that a researcher wants to determine whether the number of minutes adults spend online per day is related to gender. A random sample of 315 adults was selected and the results are shown below.

Gender     0-30   30-60   60-90    90+    total

Males         75         45         25       35       180

Females     30         45         45        15       135

H0: there is no association between gender and spending time online

Ha: There is association

(Two tailed test)

Expected for each cell is calculated as row total*grand total/column total

<30 30-60 60-90 >90  Row Totals

Males 75  (60.00)  [3.75] 45  (51.43)  [0.80] 25  (40.00)  [5.62] 35  (28.57)  [1.45]  180

Females 30  (45.00)  [5.00] 45  (38.57)  [1.07] 45  (30.00)  [7.50] 15  (21.43)  [1.93]  135

chi square -= 27.125

p value <0.0001

Since p is less than 1% (significance level) we reject the null hypothesis

There is enough evidence to conclude that the number of minutes spent online per day is related to gender

Answer:

The answer would be 18.146

Step-by-step explanation:

Given that a researcher wants to determine whether the number of minutes adults spend online per day is related to gender. A random sample of 315 adults was selected and the results are shown below.Gender     0-30   30-60   60-90    90+    totalMales         75         45         25       35       180Females     30         45         45        15       135H0: there is no association between gender and spending time onlineHa: There is association(Two tailed test)Expected for each cell is calculated as row total*grand total/column total<30 30-60 60-90 >90  Row TotalsMales 75  (60.00)  [3.75] 45  (51.43)  [0.80] 25  (40.00)  [5.62] 35  (28.57)  [1.45]  180Females 30  (45.00)  [5.00] 45  (38.57)  [1.07] 45  (30.00)  [7.50] 15  (21.43)  [1.93]  135chi square -= 27.125p value <0.0001Since p is less than 1% (significance level) we reject the null hypothesisThere is enough evidence to conclude that the number of minutes spent online per day is related to gender