A train track through a mountain is 1600 feet long and makes an angle of 1.6 with the horizontal. What is the change in elevation from one end of the tunnel to the other.

Answer:

8

Step-by-step explanation:

For the smallest possible length, this has to be one of the shorter sides. Let the length of this side be x.

So, by the triangle inequality theorem, 1+x>8, which means x>7.

So, the smallest possible whole number length is 8.

Answer:

-3.86

Step-by-step explanation:

Answer:

9x^2 - 24x + 16 is area in terms of x alternativly (3x-4)^2 is also true

Step-by-step explanation:

L * W =  area  length = width on a sqare so L * L = area too

(3x - 4) * (3x - 4)

use foil method

9x^2 - 24x + 16

Answer:

9x^2 − 24x + 16

Step-by-step explanation:

To find the area of a square, you use the formula

A = x^2

So we plug in 3x-4 for x

A = (3x-4)^2

A = 9x^2 − 24x + 16

Answer:

1,040kg/m³

Step-by-step explanation:

1g/cm³ =1,000kg/m³

1.04g/cm³=?

= 1.04×1000

Density =1,040kg/m³

Answer:

7

Step-by-step explanation:

1. Solve for x in [tex]x^2 = 3x - 1[/tex].

[tex]x=\frac{3+ \sqrt{5}}{2} ,\frac{3- \sqrt{5}}{2}[/tex]

2. Substitute [tex]x=\frac{3+ \sqrt{5}}{2} ,\frac{3- \sqrt{5}}{2}[/tex] into [tex]x^2 + \frac{1}{x^2} = y[/tex].

[tex]\frac{(3+\sqrt{5})^2}{(2,2(3-\sqrt{5}))^2} + \frac{(2,2(3-\sqrt{5}))^2}{(3 + \sqrt{5})^2} = y[/tex]

3. Solve for y in [tex]\frac{(3+\sqrt{5})^2}{(2,2(3-\sqrt{5}))^2} + \frac{(2,2(3-\sqrt{5}))^2}{(3 + \sqrt{5})^2} = y[/tex]

[tex]y=\frac{(3+\sqrt{5})^2}{(2,2(3-\sqrt{5}))^2} + \frac{(2,2(3-\sqrt{5}))^2}{(3 + \sqrt{5})^2}[/tex]

4. Therefore,

[tex]x=\frac{3 + \sqrt{5} }{2}, \frac{3-\sqrt{5}}{2}\\y=\frac{(3+\sqrt{5})^2}{(2,2(3-\sqrt{5}))^2} + \frac{(2,2(3-\sqrt{5}))^2}{(3 + \sqrt{5})^2}[/tex]

............

[tex]x= \frac{3-\sqrt{5}}{2}[/tex]≈[tex]0.381966011, y=7[/tex]

[tex]x= \frac{\sqrt{5}+3}{2}[/tex]≈[tex]2.618033989, y=7[/tex]

Hope this helps! Please let me know if you need more help, or if you think my answer is incorrect. Please rate and click the Thanks button if it helped you out. Brainliest would be MUCH appreciated. Have a great day!

Stay Brainy!

−Kallmekrish

The best way to predict the future is to create it.

- Abraham Lincoln, Past U.S. President

Answer:

7

Step-by-step explanation:

Given equation:  [tex]x^2=3x-1[/tex]

Rearrange so that it is equal to zero:

[tex]\implies x^2-3x+1=0[/tex]

Quadratic formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0[/tex]

Using the quadratic formula to solve the given equation:

[tex]\implies x=\dfrac{-(-3) \pm \sqrt{(-3)^2-4(1)(1)} }{2(1)}[/tex]

[tex]\implies x=\dfrac{3 \pm \sqrt{5}}{2}[/tex]

[tex]\implies x^2=\dfrac{7 \pm 3\sqrt{5}}{2}[/tex]

Substituting this into [tex]x^2+\dfrac{1}{x^2}[/tex]

[tex]\implies \dfrac{7\pm3\sqrt{5}}{2}+\dfrac{1}{\dfrac{7\pm3\sqrt{5}}{2}}[/tex]

[tex]\implies \dfrac{7\pm3\sqrt{5}}{2}+\dfrac{2}{7\pm3\sqrt{5}}[/tex]

[tex]\implies \dfrac{(7\pm3\sqrt{5})(7\pm3\sqrt{5})}{2(7\pm3\sqrt{5})}+\dfrac{4}{2(7\pm3\sqrt{5})}[/tex]

[tex]\implies \dfrac{(7\pm3\sqrt{5})(7\pm3\sqrt{5})+4}{2(7\pm3\sqrt{5})}[/tex]

[tex]\implies \dfrac{49\pm42\sqrt{5}+45+4}{2(7\pm3\sqrt{5})}[/tex]

[tex]\implies \dfrac{98\pm42\sqrt{5}}{2(7\pm3\sqrt{5})}[/tex]

[tex]\implies \dfrac{14(7\pm3\sqrt{5})}{2(7\pm3\sqrt{5})}[/tex]

[tex]\implies \dfrac{14}{2}[/tex]

[tex]\implies 7[/tex]

Answer:

The answers are C, D, and F

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

25°-27°= -2°

At noon, the temperature outside was 25 degrees. By 8:00pm, the temperature had dropped 27 degrees. What was the temperature outside at 8:00pm, in degrees?

= 25 - 27

= - 2°

Answer:

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes. (In grammar school, you probably called the domain the replacement set and the range the solution set.

Answer:

B. -∞ [tex]\leq[/tex] x [tex]\leq[/tex] ∞

Step-by-step explanation:

The domain of a graph is all the x-values it covers. Since this graph does not have any arrows at its end or beginning points, we can assume it goes on forever. Lines that go on forever always have an infinite domain.

Answer:

C

Step-by-step explanation:

It's 50 cm for sure

Answer:

C

Step-by-step explanation:

It's 50 cm for sure

Answer:

h=[tex]-\frac{1}{3}[/tex]

Step-by-step explanation:

[tex]6h-1=-3\\6h=-2\\h=-\frac{2}{6} \\h=-\frac{1}{3}[/tex]

Answer:

Step-by-step explanation:

Isolate by the h from one side of the equation.

6h-1=-3

First, add by 1 from both sides.

[tex]\sf{6h-1+1=-3+1}[/tex]

Solve.

-3+1=-2

Rewrite the problem down.

6h=-2

Then, you divide by 6 from both sides.

[tex]\sf{\dfrac{6h}{6}=\dfrac{-2}{6} }[/tex]

Solve.

-2/2=-1

6/2=3

Rewrite as a fraction.

[tex]\boxed{\sf{h=-\dfrac{1}{3}=0.33}}[/tex]

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

(1+b/60) minutes

Step-by-step explanation:

A minute = 1minute

b seconds = b/60minutes =b/60 minutes

sum of a minute and b seconds= (1+ b/60) minutes

[tex]3(x - 2) + 7x = \frac{1}{2} (6x - 2) [/tex]

[tex]3(x - 2) + 7x = \frac{1}{2} (6x - 2) \\ \\ \implies3x - 6 + 7x = ([\frac{1}{2} \times 6 \: x] - [\frac{1}{2} \times 2]) \\ \\ \implies10x - 6 = ([\frac{1}{ \cancel2} \times \cancel 6 \: x] - [\frac{1}{ \cancel2} \times \cancel2]) \\ \\ \implies 10x - 6 = 3x - 1 \\ \\ \fbox{Bringing (3x )to left side whereas( - 6 )in right side} \\ \\ \implies10x - 3x = - 1 + 6 \\ \\ \implies7x = 5 \\ \\ \therefore x = \frac{5}{7} [/tex]

The Solution is = [tex] \frac{5}{7}[/tex]

[tex]\text\red{One Solution set is possible.}[/tex]

Answer:

33.3333333333

Step-by-step explanation:

we see that there are 6 candies in total

we also see that there is a 50% chance that someone will take out 3 candies of the same color,

50/3 = 16.66666666666667

so the chance of getting 2 marbles of the same color is 16.66666666666667 + 16.66666666666667 which is 33.3333333333

I hope I could help

Answer:

3/9

Step-by-step explanation:

Okay, first let's list all the numbers between 1 and 9

1, 2, 3, 4, 5, 6, 7, 8, 9

Now let's list all of the even numbers from the previous list

2, 4, 6, 8

Now let's list all of the numbers from the previous list that are equal to, or greater than, 4

4, 6, 8

That's only three potential numbers, out of a total of nine numbers

So it's a 3/9 chance

Explanation:

There are many approaches you can take. Perhaps one of the easiest is to show the sides of the rhombus are all the same length. This can be done several ways. Here are a couple of them.

__

A square has degree 4 rotational symmetry, so will map to itself when rotated by any multiple of 90°. This means the midpoints of adjacent sides will map to themselves, and any segment joining the midpoints of adjacent sides will map to itself. When segments map to themselves, they are congruent, hence the four sides of EFGH are congruent, and the figure is a rhombus.

__

The sides of a square are the same length and all corner angles are right angles. Midpoints of the sides divide the sides into congruent parts, so all of the segments PF, FQ, QG, GR, and so on are congruent. This means all of the triangles PFE, QGF, RHG, and SEH are congruent by the LL postulate. Corresponding sides of congruent triangles are congruent, so the sides of EFGH are congruent, and the figure is a rhombus.

Answer:

Step-by-step explanation:

Step-by-step explanation:

a + 2 = 2

a = 2 - 2

a = 0

a² - b² = 8

0 - b² = 8

b² = -8

This question is impossible.

Answer: 21

Step-by-step explanation:

Step-by-step explanation:

=[tex] =(3x + 2)(x + 1) \\ = 3x(x + 1) + 2(x + 1) \\ = {3x}^{2} + 3x + 2x + 2 \\ = {3x}^{2} + 5x + 2[/tex]

Answer:

Bro really?? Anyway it's

[tex]anyway \: its \: 3x { }^{2} + 3x + 2x + 2[/tex]

Answer: 166 feet^2

Step-by-step explanation:

The equation for surface area is 2(wl+hl+hw). So that would be:
Surface Area = 2×(5×7 + 5×4 + 7×4) = 166 feet^2

Answer:16 square cm

Step-by-step explanation: Surface area = base, height (Side 1 + Side 2+ Side 3) H = Side 1 = 5 cm

Side 2 = 7cm

Side 3 = 4cm (add all these numbers ) = 16 Square cm

Step-by-step explanation:

the easiest way to answer this is to calculate the area of the large rectangle (white) and subtract the area of the small rectangular (black).

we know the dimensions of the small rectangle : 10×6

and because of the 2m thick "frame" we know the dimensions of the large rectangle by adding 2×2 m to every small dimension : 14×10

(2 m on the top and the bottom, and 2 m left and right, so 4 m added in every direction).

the area of the large rectangle is

14 m × 10 m = 140 m²

the area of the small rectangle is

10 m × 6 m = 60 m²

so the area of the path is

140 - 60 = 80 m²

Answer:

a= 50

b=50

c=110

d=20

Answer:

Step-by-step explanation:

This is a kite. So the two triangles formed by the longest diagonal being drawn in form 2 congruent triangles.

Therefore c = 110 degrees.

d = 20 degrees.

a and b are found by noting that every triangle has 180 degrees.

110 + 20 + a = 180           Combine the left.

130 + a = 180                   Subtract 130 from both sides

a = 180 - 130

a = 50 degrees

b also equals 50 degrees.  Congruent triangles

Answer

Answer: a third

Step-by-step explanation: im simply a genius

Answer:

Step-by-step explanation:

Answer:

$1920.00

Step-by-step explanation:

You want to calculate the interest on $6000 at 4% interest per year after 8

year(s).

The formula we'll use for this is the simple interest formula, or:

I= P * r * t

Where:

• P is the principal amount, $6000.00.

• r is the interest rate, 4% per year, or in decimal form, 4/100=0.04.

• t is the time involved, 8.…..year(s) time periods

So, t is 8...year time periods.

To find the simple interest, we multiply 6000 x 0.04 x 8 to get that:

The interest is: $1920.00

Answer:

D) 130

Step-by-step explanation:

So there are three arc sections in this problem,

The first one is given: 158

To find the arc between S and R, you can use the angle of point T and double it.

So:

36 * 2 = 72

The second arc is 72

Now for the one that they want you to find, you have to add the two arcs that you have and substract it from 360, which is the angle of a whole circle

Like so:

360 - (158 + 72) = 130

Answer:

130

Step-by-step explanation:

Answer:

[tex]9 \times 3 = 27 \\ 15 \times 6 = 90 \\ = 30.255 \\ 49 \times 3.14 = 153.86 \\ 153.86 + 30.255 + 27 = 211.115[/tex]

The expression that best represents the value of pi is 53/d.

Pi can be described as the ratio of the circumference of a circle to its diameter. The circumference of the patio is the distance round the patio. The formula that can be used to represent the circumference of the patio is πD

53 = πD

π = 53/d

To learn more about how to determine the circumference of a circle, please check: https://brainly.com/question/14351152