Annabelle apanhou o Polar Express até o Pólo Norte! O Polar Express tem 100 metros de comprimento e leva 30 segundos para atravessar a ponte de gelo de 400 metros do Papai Noel. Qual a velocidade do trem?

Answer:

3V / (pi*r^2) = h

Step-by-step explanation:

V = 1/3 *pi * r^2 h

We want to solve for h so we need to get it alone

Multiply each side by 3.

3*V =3* 1/3 *pi * r^2 h

3V = pi * r^2 h

Divide each side by pi r^2

3V / (pi*r^2) = pi * r^2 h/ (pi *r^2)

3V / (pi*r^2) = h

Answer:

[tex]x=3.5,y=24[/tex]

Step-by-step explanation:

The smaller triangle joining the midpoints of the bigger right angle triangle will also be a right angle triangle.

Midpoint Theorem-

According to this, the segment joining two sides of a triangle at the midpoints is half the length of the third side.

Applying this,

[tex]\Rightarrow x=\dfrac{1}{2}(4x-7)[/tex]

[tex]\Rightarrow 2x=4x-7[/tex]

[tex]\Rightarrow 4x-2x=7[/tex]

[tex]\Rightarrow 2x=7[/tex]

[tex]\Rightarrow x=\dfrac{7}{2}=3.5[/tex]

So, the hypotenuses of the bigger triangle will be,

[tex]=6(3.5)+4=25[/tex]

Applying the mid point theorem, the hypotenuses of the smaller triangle will be,

[tex]=\dfrac{1}{2}\times 25=12.5[/tex]

Applying Pythagoras theorem in the smaller triangle, the leg will be

[tex]=\sqrt{12.5^2-3.5^2}\\\\=\sqrt{156.25-12.25}\\\\=\sqrt{144}\\\\=12[/tex]

Again applying mid point theorem,

[tex]\Rightarrow y=2\times 12=24[/tex]

Answer:

1.  x=6

2.  y=2

Step-by-step explanation:

If x=5, the line is vertical, so we need a vertical line so that we are parallel.  A vertical line is x= a constant

We can choose the value for x as long as it is not 5, that would make it the same line.  I will choose x=6

If y=-3=5, the line is horizontal, so we need a horizontal line so that we are parallel.  A horizontal line is y= constant

We can choose the value for y as long as it is not -3, that would make it the same line.  I will choose y=2

Answer:

[tex]\text{d.}\quad a_n=-2.25(2)^{n-1}[/tex]

Step-by-step explanation:

The common ratio is given as 2, so the base of any exponential must be 2 (not -2 or 2.25). The 4th term is negative, so the initial value must be negative (since the multiplying factor is positive). The only selection matching these requirements is d.

You know the general term is ...

... an = a1·r^(n-1)

so the 4th term is

... -18 = a1·2^(4-1) = 8·a1

Then the first term is ...

... a1 = -18/8 = -2.25 . . . . . confirms our choice of answer d.

Answer:(2x + 9i)(2x - 9i)

Step-by-step explanation:

a^2 - b^2 = (a+b)(a-b)

a^2 + b^2 = (a+bi)(a-bi) = a^2 + abi - abi - b^2 i^2

But -b^2 i^2 = +b^2

Answer:

[tex](4x+9i)(4x-9i)[/tex]

Step-by-step explanation:

Here, we have to apply this complex numbers property:

[tex]a^2 + b^2 = (a+bi)(a-bi)[/tex]

So, the given expression [tex]4x^2+81[/tex], can be rewrite as factor using the property:

[tex]4x^2+81=(4x+9i)(4x-9i)[/tex]

Because, if

[tex]a^2=x^2 \ and \ b^2=81\\\ then \ a=x \ and \ b=9[/tex]  

Therefore, the factors are [tex](4x+9i)(4x-9i)[/tex]

Answer:

domain = real numbers, range = positive real numbers

Step-by-step explanation:

f(x) = a^x

Domain is the set of all real numbers whose values are defined.

Here x is the exponent. There is no restriction for x

So x  can take any value. x  can be positive or negative

Hence, domain is all real numbers.

For range we consider the value of f(x)

For positive x  values , f(x) will be positive

For negative x  values , f(x) will be positive

so , range is positive real numbers

An icosahedron have 20 faces. So the correct Option is D.  

An icosahedron is a three-dimensional geometric shape known as a polyhedron. It is characterized by having 20 faces, making it an interesting and unique structure in geometry.

An icosahedron is one of the five Platonic solids, which are regular polyhedra with equal faces and angles. To understand why an icosahedron has 20 faces, we can break down its construction.

1. Vertices (V): An icosahedron has 12 vertices. Each vertex is a point where three edges of the polyhedron meet.

2. Edges (E): There are 30 edges in an icosahedron. These are the straight lines connecting the vertices.

3. Faces (F):  Now, to find the number of faces, we can use Euler's formula, which states that for any polyhedron, V - E + F = 2. This formula relates the number of vertices, edges, and faces of a convex polyhedron.

  Plugging in the values, we get: 12 (vertices) - 30 (edges) + F (number of faces) = 2

  Solving for F, we get: F = 20

Thus, an icosahedron has 20 faces, represented by 20 flat surfaces, each of which is an equilateral triangle. Each vertex is shared by five triangles, and each edge is shared by two triangles.

The keyword "icosahedron" refers to the specific three-dimensional shape with 20 faces, while "Platonic solids" refers to the family of regular polyhedra with equal faces and angles. Euler's formula is essential for understanding the relationship between vertices, edges, and faces of polyhedra.

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Answer:

mean: 27

median: 25

mode: 25

Step-by-step explanation:

Mean: 297/11 =27

Median: put the values in order; 22,23,24,25,25,25,28,29,31,32,33. the median is 25

Mode: 25

Final answer:

The mean of the data set is 27, the median is 25, the mode is also 25, and the range is 11.

Explanation:

To find the mean, you add up all the numbers and then divide by the number of values. The median is the middle value when the numbers are in order. The mode is the number that appears the most. The range is the difference between the highest and lowest numbers.

First, let's order the data from least to greatest: 22, 23, 24, 25, 25, 25, 28, 29, 31, 32, 33.

Now, we calculate each:

1.The mean is (22 + 23 + 24 + 25 + 25 + 25 + 28 + 29 + 31 + 32 + 33) / 11 which equals 297 / 11 which equals 27.
2.The median is the middle number, which is 25 because there are five numbers on each side of it in the ordered list.

3.The mode is the number that appears most frequently - that's 25, as it appears three times.

4.To find the range, subtract the smallest number from the largest: 33 - 22 equals 11.

Answer:

[tex]g(x)=x^2+7 x+12[/tex]

Step-by-step explanation:

since f(x)=[tex]x^{2}+3 x+2[/tex]

now we are given that this function f(X) is shifted 2 units to the left and we get a function g(x) this means

g(x)=f(x+2) since f(x+2) will shift the function f(x) 2 units to the left.

[tex]g(x)=(x+2)^{2}+3(x+2)+12[/tex]

g(x)=[tex]x^2+4+4 x+3 x+6+2[/tex]

hence, the function g(x)=[tex]x^2+7 x+12[/tex]

Answer:

c. 345 calories

Step-by-step:

We need to create a ratio

There are 230 calories in 4oz

230/4

How many calories are in 6oz

x/6

Let's equate them to solve for x

230/4 = x/6       cross multiply

4x = 1380           isolate x

x = 345

There are 345 calories in 6oz of said icecream

Answer:

Its the 3rd choice.

Step-by-step explanation:

The general form  for this type of parabola is y^ = 4ax where a is the x coordinate of the focus.

So it is y^2 = 4*3 * x

= y^2 = 12 x

or x = 1/12 y^2

Answer:

The standard form would be 5x + 6y = 8

Step-by-step explanation:

To find the equation between these two points, start by finding the slope. You can do this using the slope formula.

m(slope) = (y2 - y1)/(x2 - x1)

m = (3 - -2)/(-2 - 4)

m = 5/-6

m = -5/6

Now that we have the slope, we can use that and a point in point-slope form. Once we have that we can solve for the constant and rationalize the denominator for the standard form.

y - y1 = m(x - x1)

y - 3 = -5/6(x + 2)

y - 3 = -5/6x - 5/3

5/6x + y - 3 = -5/3

5/6x + y = 4/3

5x + 6y = 8

Answer: C

Step-by-step explanation:

[tex]\dfrac{x+2}{15} =\dfrac{x+1}{5}[/tex]

cross multiply: 5(x + 2) = 15(x + 1)

distribute: 5x + 10 = 15x + 15

                -5x          -5x          

                          10 = 10x + 15

                        -15           -15

                          -5  = 10x

                           [tex]\dfrac{-5}{10}=\dfrac{10x}{10}[/tex]

                           [tex]-\dfrac{1}{2} =x[/tex]

Final answer:

The height of the new cones will be 16.5 inches.

Explanation:

To find the height of the new cones, we can use the formula for the volume of a cone:

V = (1/3)πr^2h

Let's denote the radius of the new cones as r2 and the height of the new cones as h2. We know that the volume of the new cones will be the same as the volume of the existing cones:

(1/3)π(r2)^2h2 = (1/3)π(r1)^2h1

Substituting the given values, r1 = 22 inches (radius of existing cones) and h1 = 66 inches (height of existing cones), we can solve for h2:

(1/3)π(44)^2h2 = (1/3)π(22)^2(66)

Dividing both sides by (1/3)π(44)^2, we get:

h2 = h1(r1/r2)^2

Plugging in the values, h1 = 66 inches and r1 = 22 inches, and r2 = 44 inches, we can calculate:

h2 = 66(22/44)^2

h2 = 66(1/2)^2

h2 = 66(1/4)

h2 = 66/4

h2 = 16.5 inches

Answer:

Marta is (2x)+6 older than Ella.

The three girl's average age is (w)+(w/2)+(w/2-6)/3

Step-by-step explanation:

Marta's Age: w

Felicia's Age: w/2

Ella's Age: (w/2)-6

The age difference between Marta and Elle is Felicia's age plus 6 years. The expression for the average age of the three girls is (2*w - 6) / 3, where w is Marta's age and Felicia's age is half of w.

To solve the problem involving the ages of Elle, Felicia, and Marta, we use algebraic expressions. Marta is w years old.

Part a)

Let's denote Felicia's age as f. Since Elle is 6 years younger than Felicia, Elle's age is f - 6. Given that Marta is twice as old as Felicia, Marta's age, w, is equal to 2f. To find the age difference between Marta and Elle, we subtract Elle's age from Marta's age:

Age difference = w - (f - 6)

Since w = 2f, we can substitute 2f for w:

Age difference = 2f - (f - 6) = 2f - f + 6 = f + 6

Part b)

To find the average age of the three girls, we add their ages and divide by 3:

Average age = (Elle's age + Felicia's age + Marta's age) / 3

Average age = (f - 6 + f + 2f) / 3

Average age = (4f - 6) / 3

Since Marta's age is w and w = 2f, we can substitute 2f for each f in the equation:

Average age = (2*w - 6) / 3

Answer:

8

Step-by-step explanation:

We will use the math operation division to find the answer. Division takes a total and divides it into equal amounts. We have a total of 96 and need equal amounts in to each of the 12 groups.

96/12=8 students per group

Answer:

a. [tex]y=830*(0.87)^x[/tex]

b. The value of stereo system after 2 years will be $628.23.

c. After approximately 4.98 years the stereo will be worth half the original value.

Step-by-step explanation:

Let x be the number of years.

We have been given that you purchased a stereo system for $830. The value of the stereo system decreases 13% each year.

a. Since we know that an exponential function is in form: [tex]y=a*b^x[/tex], where,

a = Initial value,

b = For decay b is in form (1-r), where r is rate in decimal form.

Let us convert our given rate in decimal form.

[tex]13\%=\frac{13}{100}=0.13[/tex]

Upon substituting our given values in exponential decay function we will get

[tex]y=830*(1-0.13)^x[/tex]

[tex]y=830*(0.87)^x[/tex]

Therefore, the exponential model [tex]y=830*(0.87)^x[/tex] represents the value of the stereo system in terms of the number of years since the purchase.

b. To find the value of stereo system after 2 years we will substitute x=2 in our model.

[tex]y=830*(0.87)^2[/tex]

[tex]y=830*0.7569[/tex]

[tex]y=628.227\approx 628.23[/tex]

Therefore, the value of stereo system after 2 years will be $628.23.

c. The half of the original price will be [tex]\frac{830}{2}=415[/tex].

Let us substitute y=415 in our model to find the time it will take the stereo to be worth half the original value.

[tex]415=830*(0.87)^x[/tex]

Upon dividing both sides of our equation by 830 we will get,

[tex]\frac{415}{830}=\frac{830*(0.87)^x}{830}[/tex]

[tex]0.5=0.87^x[/tex]

Let us take natural log of both sides of our equation.

[tex]ln(0.5)=ln(0.87^x)[/tex]

Using natural log property [tex]ln(a^b)=b*ln(a)[/tex] we will get,

[tex]ln(0.5)=x*ln(0.87)[/tex]

[tex]\frac{ln(0.5)}{ln(0.87)}=\frac{x*ln(0.87)}{ln(0.87)}[/tex]

[tex]\frac{ln(0.5)}{ln(0.87)}=x[/tex]

[tex]\frac{-0.6931471805599}{-0.139262067}=x[/tex]

[tex]x=4.977286\approx 4.98[/tex]

Therefore, after approximately 4.98 years the stereo will be worth half the original value.

To find when a stereo system purchased for $830 and depreciating at 13% per year will be worth half of its value, use the exponential decay formula V(t) = [tex]P * (1 - r)^t[/tex]. After 2 years, the stereo is worth approximately $627.77, and it will be worth half its original value after about 5.42 years.

An exponential decay model can represent the value of an asset decreasing over time. For a stereo system purchased for $830 with a yearly depreciation of 13%, the model takes on the form of V(t) = [tex]P * (1 - r)^t[/tex], where:

V(t) is the value of the stereo system after t years.

P is the initial purchase price, which is $830.

r is the rate of decay per year, which is 13% or 0.13.

t is the number of years since the purchase.

The value of the stereo system after 2 years can be calculated using the above model:
[tex]V(2) = 830 * (1 - 0.13)^2 = 830 * 0.87^2[/tex]
= 830 * 0.7569
= $627.77 approximately.

To find when the stereo will be worth half the original value, we set [tex]V(t) = rac{P}{2}[/tex] and solve for t:

415 = [tex]830 * (1 - 0.13)^t[/tex]
[tex]0.5 = (1 - 0.13)^t[/tex]
[tex]Log_0.87(0.5) = t[/tex]
t
t = 5.42

The stereo will be worth half its original value after approximately 5.42 years.

Answer:

Value of h(2y+6) = -18y -57

Step-by-step explanation:

Given the function rule:

h(u) = -9u -3                               ......[1]

To find h(2y+6)

Substitute u = 2y + 6 in [1] we get;

h(2y+6) = -9(2y+6) - 3

Using distributive property: [tex]a\cdot (b+c) = a\cdot b + a\cdot c[/tex]

h(2y+6) = - 18y - 54 - 3 = -18y - 57

Therefore, the value of [tex]h(2y+6) = -18y - 57[/tex]

Answer:

Step-by-step explanation: by Saturday,, he would have read 25 + 32 +  39 +46 +53 +60 =255 pages. Note the number of pages read increases by 7 each day

Answer:

21.76 Centimeters

Step-by-step explanation:

Length - 3.2 Cm

Width - 6.8 Cm

Area = Width * Length (Or other way around)

Multiply:

3.2 * 6.8

= 21.76

- I.A -

Answer: C. [tex]\frac{7}{25}-\frac{24}{25}i[/tex]

Step-by-step explanation:

1. You have the following division:

[tex]\frac{4-3i}{4+3i}[/tex] (As you can see, to find the conjugate of  4-3i you must change the sign between the terms).

2. To solve this division, you must multiply the numerator and the denominator by the conjugate of the denominator, as following:

[tex]=\frac{(4-3i)}{(4+3i)}\frac{(4-3i)}{(4-3i)}=\frac{16-12i-12i+9i^{2}}{16-9i^{2}}[/tex]

3. Keeping on mind that [tex]i^{2}=-1[/tex], you have:

[tex]=\frac{16-12i-12i+9(-1)}{16-9(-1)}[/tex]

4. Simplifying:

[tex]=\frac{7-24i}{25}=\frac{7}{25}-\frac{24}{25}i[/tex]

5. The result is:

[tex]\frac{7}{25}-\frac{24}{25}i[/tex]

The quotient of the complex number 4 - 3i divided by its conjugate is  [tex]\dfrac{7}{25} -\dfrac{24}{25}i[/tex]. And option (C) is correct.

Given data:

The complex number is, 4 - 3i.

To find: The quotient when divided by conjugate of given complex number.

For a given complex number say, a + bi, the conjugate is given as,

a - bi

Then, the conjugate of the given complex number is, 4 + 3i.

Divide the given complex number with its conjugate as,

[tex]=\dfrac{ 4 - 3i}{4 + 3i}\\\\=\dfrac{ 4 - 3i}{4 + 3i} \times \dfrac{4-3i}{4-3i} \\\\=\dfrac{(4-3i)^{2}}{4^{2}-(3i)^{2}}[/tex]

Since, [tex]i^{2} =-1[/tex].

Solving further as,

[tex]=\dfrac{4^{2}+(3i)^{2}-2(4)(3i)}{16-9(-1)} \\\\=\dfrac{16+9(-1)-24)}{25}} \\\\=\dfrac{7}{25} -\dfrac{24}{25}i[/tex]

Thus, we can conclude that the quotient of the complex number 4 - 3i divided by its conjugate is  [tex]\dfrac{7}{25} -\dfrac{24}{25}i[/tex]. And option (C) is correct.

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Answer:

Mass of one penny = .005 pounds

10 pounds of pennies = 10 / .005 = 2,000 pennies

Step-by-step explanation:

Final answer:

To calculate the number of pennies, divide the total weight of the pennies in the jar (10 pounds) by the weight of one penny (0.005 pounds), resulting in approximately 2000 pennies.

Explanation:

To determine the number of pennies in Ian's jar, we need to use the weight of one penny and the total weight of pennies in the jar. The question states that one penny weighs about 5*10^-3 pounds, which can also be represented as 0.005 pounds.

Next, we divide the total weight of pennies in the jar, which is 10 pounds, by the weight of one penny:

Convert the weight of one penny to pounds: 5*10^-3 pounds.

Divide the total weight of the pennies by the weight of one penny: 10 pounds \/ 0.005 pounds per penny = 2000 pennies.

Hence, there are approximately 2000 pennies in Ian's jar.

Answer:

0.34

Step-by-step explanation:

I just used a calculator

Answer: C. (x+1) is a factor

Step-by-step explanation:

First we need to factor the polynomial x^2 - x - 2.

It is written in the form ax^2 + bx + c

a = 1

b = -1

c = -2

Since the coefficient in front of x^2 is 1 we can start with (x + _) (x + _).

Now we need to find a pair of numbers that when multiplied together equal -2 (c) and when added together equal -1  (b).

The only pairs of numbers that multiply to make -2 are: -2 and 1, -1 and 2

The pair must also equal -1 when added together.

-1 + 2 = 1

-2 + 1 = -1

Therefore, to fill in the blanks for (x+_)(x+_) we should use -2 and 1.

x^2 - x - 2 factored becomes: (x-2)(x+1)

As you can see, (x+1) is a factor of x^2 - x - 2, so you can select c.