What is the volume, in cubic ft, of a rectangular prism with a height of 17ft, a width of 11ft, and a length of 18ft?

d = 17.3 m

Step-by-step explanation:

We can extend Pythagorean theorem to 3 dimensions by writing

[tex] {d}^{2} = {x}^{2} + {y}^{2} + {z}^{2} [/tex]

or

[tex]d = \sqrt{ {x}^{2} + {y}^{2} + {z}^{2} } [/tex]

Since we are dealing with a cube of side 10 m, then

x = y = z = 10 m

so we get

[tex]d = \sqrt{ {10}^{2} + {10}^{2} + {10}^{2} } [/tex]

or

[tex]d = \sqrt{3 \times {10}^{2} } = 10 \sqrt{3} \: m[/tex]

This becomes

d = 17.3 m

Answer:

Theta

Step-by-step explanation:

Indeed all angles of a triangle have a opposite side. And in trigonometry, the side opposite to theta is opposite side

Answer:

This is the ans i think this is right

Answer:

its be without a doubt

Step-by-step explanation:

Answer

Ok i will help

Step-by-step explanation:

Yay!

Answer:

y = -3

Step-by-step explanation:

y = -0.5(6)

y = -3

Answer:

m = -8/5

Step-by-step explanation:

First determine how much x changes as we go from the first point to the second:  -1 to +4.  This change (the 'run') is 5 units.

Then find the change in y:  -4 - (4) = -8.  This change (the 'rise') is -8.

Thus the slope m = rise / run is m = -8/5

Answer:

-10

Step-by-step explanation:

i think this is the answer

Answer:

a. i. sinθ = +0.941

ii. cosθ = +0.339

b. i. sinθ = -0.842

ii.  cosθ = +0.540

Step-by-step explanation:

a. Given that tanθ almost equal to≈ 2.773 where 0<θ<π/2, find the values of sinθ and cosθ.

i. sinθ

Given that 1 + cot²θ = cosec²θ

cotθ = 1/tanθ

Since tanθ = 2.773, cotθ = 1/tanθ = 1/2.773 = 0.3606

So, 1 + cot²θ = cosec²θ

1 + (0.3606)² = cosec²θ

1 + 0.13 = cosec²θ

1.13 = cosec²θ

cosec²θ = 1.13

cosecθ = ±√1.13

cosecθ = ±1.063

1/sinθ = ±1.063

sinθ = ±1/1.063

sinθ = ±0.9407

sinθ ≅ ±0.941

Since we have 0<θ<π/2, sinθ is in the first quadrant, so we choose the positive value.

So, sinθ = +0.941 where 0<θ<π/2

ii. cosθ

Given that 1 + tan²θ = sec²θ

Since tanθ = 2.773,

So, 1 + tan²θ = sec²θ

1 + (2.773)² = sec²θ

1 + 7.6895 = sec²θ

8.6895 = sec²θ

sec²θ = 8.6895

secθ = ±√8.6895

secθ = ±2.9478

1/cosθ = ±2.9478

cosθ = ±1/2.9478

cosθ = ±0.3392

cosθ ≈ ±0.339

Since we have 0<θ<π/2, cosθ is in the first quadrant, so we choose the positive value.

So, cosθ = +0.339 where 0<θ<π/2

b. Given that tanθ ≈ -1.559 where 3π/2<θ<2π, find the values of sinθ and cosθ.

i. sinθ

Given that 1 + cot²θ = cosec²θ

cotθ = 1/tanθ

Since tanθ = -1.559, cotθ = 1/tanθ = 1/-1.559 = -0.6414

So, 1 + cot²θ = cosec²θ

1 + (-0.6414)² = cosec²θ

1 + 0.4114 = cosec²θ

1.4114 = cosec²θ

cosec²θ = 1.4114

cosecθ = ±√1.4114

cosecθ = ±1.1880

1/sinθ = ±1.1880

sinθ = ±1/1.1880

sinθ = ±0.8417

sinθ ≈ ±0.842

Since we have 3π/2<θ<2π, sinθ is in the fourth quadrant, so we choose the negative value.

So, sinθ = -0.842 where 3π/2<θ<2π

ii. cosθ

Given that 1 + tan²θ = sec²θ

Since tanθ = -1.559,

So, 1 + tan²θ = sec²θ

1 + (-1.559)² = sec²θ

1 + 2.4305 = sec²θ

3.4305 = sec²θ

sec²θ = 3.4305

secθ = ±√3.4305

secθ = ±1.8522

1/cosθ = ±1.8522

cosθ = ±1/1.8522

cosθ = ±0.5399

cosθ ≈ ±0.540

Since we have 3π/2<θ<2π, cosθ is in the fourth quadrant, so we choose the positive value.

So, cosθ = +0.540 where 3π/2<θ<2π

Answer:

x=46 degree

Step-by-step explanation:

32 +x=Angle ABC

32 + x =78 degree

x=78 - 32

x=46 degree

Answer:

[tex](x +10)^2 + (y+6)^2 = 121[/tex]

Step-by-step explanation:

Given equation :

                        [tex]x^2 + y^2 + 20x +12y + 15 = 0[/tex]

Standard equation of circle :

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

We will consider the x terms in the equation first to find a.

[tex](x-a)^2 = x^2 - 2ax + a^2[/tex]

-2ax = 20x

a = -20x/2x = -10

a = -10

Next consider the y terms to find b.

[tex](y - b)^2 = y^2 -2by + b^2[/tex]

-2by = 12y

b = -12y /2y = -6

b = -6

[tex](x+10)^2 + (y-6)^2 = x^2 +20x +100 + y^2 +12y + 36[/tex]

                             [tex]=x^2 + y^2 + 20x +12y + 136\\[/tex]

But the given equation constant is 15. So find the difference between 136 and 15 to find the radius : 136 - 15 = 121

Therefore, radius = √121 = 11

Equation in standard form :

                                         [tex](x +10)^2 + (y+6)^2 = 121[/tex]

Answer:

b = x - y

Step-by-step explanation:

Given the expression x - y = b

We are to rewrite the value of b;

We can simply do this by swapping both sides that are putting b at the Left hand side and x - y at the right as shown

b = x - y

Hence the correct expression will be b = x - y

Answer:

Two real distinct solutions

Step-by-step explanation:

Hi there!

Background of the Discriminant

The discriminant [tex]b^2-4ac[/tex] applies to quadratic equations when they are organised in standard form: [tex]ax^2+bx+c=0[/tex].

All quadratic equations can be solved with the quadratic formula: [tex]x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}}[/tex].

When [tex]b^2-4ac[/tex] is positive, it is possible to take its square root and end up with two real, distinct values of x.

When it is zero, we won't be taking the square root at all and we will end up with two real solutions that are equal, or just one solution.

When it is negative, it is impossible to take the square root and we will end up with two non-real solutions.

Solving the Problem

[tex]3x^2+5x=-1[/tex]

We're given the above equation. It hasn't been organised completely in [tex]ax^2+bx+c=0[/tex], but we can change that by adding 1 to both sides to make the right side equal to 0:

[tex]3x^2+5x+1=0[/tex]

Now that we can identify the values of a, b and c, we can plug them into the discriminant:

[tex]D=b^2-4ac\\D=(5)^2-4(3)(1)\\D=25-4(3)(1)\\D=25-12\\D=13[/tex]

Therefore, because the discriminant is positive, the equation has two real, distinct solutions.

I hope this helps!

Answer:

69.47%

Step-by-step explanation:

Calculation to determine Find the percent of markup

Using this formula

Percent of markup=New price-Old price/Old price

Let plug in the formula

Percent of markup=$15.95-$4.87/$15.95

Percent of markup=$11.08/$15.95

Percent of markup=0.6947*100

Percent of markup=69.47%

Therefore the percent of markup is 69.47%

Answer:

A. 52

Step-by-step explanation:

Find how many months are in 4 years, since there are 4 years between her 13th and 17th birthdays.

There are 12 months in a year, so multiply 12 by 4:

12(4)

= 48

So, there are 48 months in 4 years. Since she buys a new teacup every month, this means she will have bought 48 more teacups.

Add this to the 4 teacups she got on her 13th birthday:

48 + 4

= 52

So, on her 17th birthday, she will have A. 52 teacups

Answer:

3x - 4

Step-by-step explanation:

(6x^2 − 8x) ÷ (2x) =

(6x^2)/2x - 8x/2x =                 

3x - 4

Answer:

(C). 3x - 4

Step-by-step explanation:

It will be easily to break this down so,

6/2=3

x^2/x=x

therefore, 6x^2/2x = 3x

Minus stay minus

8/2 = 4

x/x=1

therefore, 8x/2x=4

If we put it all together,

3x - 4

if this helps you, please give brainliest!

Answer:

Surds. Note: a root we can't simplify further is called a Surd. So √3 is a surd.

Answer:

58cm2

Step-by-step explanation:

put it in section and them slove

so area of triangle = b×h÷2= 6×3/2=9cm2

area of terpizium = 5(4+6)/2=25cm2

area of triangle = 8×6÷2=20cm2

add all these together You get 58cm2

hope this helps :)

Answer:

Step-by-step explanation:

for y

take 30 degree as reference angle using sin rule

sin 30=opposite/hypotenuse

1/2=9/y (do cross multiplication)

2*9=y

18=y

for x

using pythagoras theorem

a^2+b^2=c^2

9^2+x^2=18^2

81+x^2=324

x^2=324-81

x^2=243

x=[tex]\sqrt{243[/tex]

x=9[tex]\sqrt{3[/tex]

Step-by-step explanation:

The formula for the lateral area of a right cone is :

LA = rs

Where

r is the radius of the base and s is the slant height of the cone

Equivalent expression,

[tex]r=\dfrac{LA}{s}[/tex]

or

[tex]s=\dfrac{LA}{r}[/tex]

Hence, this is the required solution.

Answer:

The answers are C & E

= 5-³ -³

= 5-⁶

= 1/5⁶

= 5⁷+³

= 5¹⁰

= 5⁶ - ⁴

= 5²

= 5-⁴ + ⁴ × 1

= 5⁰

Answer:

answser  in picturew

Step-by-step explanation:

Answer: 3rd

Answer: 3rd

25/15

Answer:

ummmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm   and i Oop

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

20/100 * j = 12

j = 12 * 100/20

j = 60

Answer: 160 chicken sandwiches were sold.

To convert a percentage into a decimal, move the decimal two places back.

40%=0.40, or 0.4

This means that 0.4 is still equivalent to 40%

Remember that "of" means multiplication.

So 0.4*400=160

160 chicken sandwiches were sold

Answer:

the first one

Step-by-step explanation:

Answer:

x=-14

Step-by-step explanation:

because -2(-14)=-26