A flour moth trap has the shape of a triangular prism that is open on both ends. An environmentally safe chemical draws the moth inside the​ prism, which is lined with an adhesive. What is the surface area of the​ prism-shaped trap?

Part of the value of sin(u) is cut off; I suspect it should be either sin(u) = -5/13 or sin(u) = -12/13, since (5, 12, 13) is a Pythagorean triple. I'll assume -5/13.

Expand the tan expression using the angle sum identities for sin and cos :

tan(u + v) = sin(u + v) / cos(u + v)

tan(u + v) = [sin(u) cos(v) + cos(u) sin(v)] / [cos(u) cos(v) - sin(u) sin(v)]

Since both u and v are in Quadrant III, we know that each of sin(u), cos(u), sin(v), and cos(v) are negative.

Recall that for all x,

cos²(x) + sin²(x) = 1

and it follows that

cos(u) = - √(1 - sin²(u)) = -12/13

sin(v) = - √(1 - cos²(v)) = -3/5

Then putting everything together, we have

tan(u + v)

= [(-5/13) • (-4/5) + (-12/13) • (-3/5)] / [(-12/13) • (-4/5) - (-5/13) • (-3/5)]

= 56/33

(or, if sin(u) = -12/13, then tan(u + v) = -63/16)

Answer:

x = -1/7

Step-by-step explanation:

3/5x + 5 = 4/5

3/5x + 5/1 = 4/5

3 + 25x/5x = 4/5

4(5x) = 5(3 + 25x)

20x = 15 + 125x

-15 = 125x - 20x

-15 = 105x

-15/105 = x

-1/7 = x

Answer:

6

out of the total donuts (90), Ryan ate 12 cream filled donuts. 45 is half of that, therefore he should eat half the cream filled donuts

Answer:

0.21

Explanation:

210 hundredths is larger than 209 hundredths.

Answer:

0.21 because .210 is more than .209

First note that any solution must belong to all of the intervals

x + 2 > 0   ⇒   x > -2

x > 0

2x - 1 > 0   ⇒   x > 1/2

3x - 12 > 0   ⇒   x > 4

so x must be larger than 4.

Recall that log(a) - log(b) = log(a/b). So we can rewrite

log(x + 2) - log(x) = log(2x - 1) - log(3x - 12)

log((x + 2)/x) = log((2x - 1)/(3x - 12))

Take the antilogarithm/exponential of both sides (note that the base of the logarithm doesn't matter here):

exp[log((x + 2)/x)] = exp[log((2x - 1)/(3x - 12))]

(x + 2)/x = (2x - 1)/(3x - 12)

Eliminate the fractions:

x (3x - 12) • (x + 2)/x = x (3x - 12) • (2x - 1)/(3x - 12)

(3x - 12) (x + 2) = x (2x - 1)

Expand both sides, collect terms and factorize to solve for x :

3x² - 6x - 24 = 2x² - x

x² - 5x - 24 = 0

(x - 8) (x + 3) = 0

x - 8 = 0   or   x + 3 = 0

x = 8   or   x = -3

The rule for the height of the tree during the nth month will be an = 83 + 1.5(n – 1). The correct option is A.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that in the third month of the study, a sugar maple tree is 86 inches tall. In the seventh month, the tree is 92 inches tall.

For option A satisfy the equation for n = 3 and n = 7,

an = 83 + 1.5(n – 1)

a₃ = 83 + 1.5(3 – 1)

a₃ = 83 + 3

a₃ =86

a₇ = 83 + 1.5(7– 1)

a₃ = 83 + ( 1.5 x 6 )

a₃ = 83 + 9

a₃ = 92

Therefore, the rule for the height of the tree during the nth month will be an = 83 + 1.5(n – 1). The correct option is A.

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Given :   Eitan rolls a fair six-sided die and a fair four-sided die simultaneously. A be the event that the sum of the dice is 8 and B be the event that Eitan rolls doubles

To find : probability of event A  , event B  , Event A or B  , Event A & B

Solution:

Six  Sides  Dice has { 1 , 2 , 3 , 4 , 5 ,6  }

4 Sides Dice has  = {  1 , 2 , 3 ,  4 }

Total possible outcome = 6 * 4  = 24

n(S) = 24

A  = Sum of Dice  = 8

(4 , 4)  , ( 5 , 3) , ( 6 , 2)

n(A) = 3

B  =   Double  ( means same number on each Dice )

B = ( 1 , 1) , (  2, 2) , ( 3 , 3) , ( 4, 4)

n(B) = 4

A U B  = ( 1 , 1) , (  2, 2) , ( 3 , 3) , ( 4, 4) ( 5 , 3) , ( 6 , 2)

n (A U B )   =  { 6 }

A ∩ B = { 4 , 4}

n(A ∩ B)  = 1

Probability of Event A  =  3/24  = 1/8

probability of Event B = 4/24   = 1/6

Probability of Event A or B  = 6/24  = 1/4

Probability of Event  A and B = 1/24

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You are given one 6 sided dice and an 8 sided dice. The 8 sided die

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You roll a fair 666-sided die. What is ext{P(roll greater than 4})P(roll ...

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Answer:

What is the question You are just stateing facts?

Step-by-step explanation:

Answer:f θ =2sin θ + square root of 3.

Step-by-step explanation: I think this is right

Answer:

Option D, [tex]121x^2 + 100x + 25[/tex]

Step-by-step explanation:

Step 1:  Determine the one that is not a perfect square

Factor Option A

[tex]64x^2 + 48 + 9[/tex]

[tex](8x + 3)(8x + 3)[/tex]

[tex](8x + 3)^2[/tex]

Factor Option B

[tex]25x^2 + 70x + 49[/tex]

[tex](5x + 7)(5x + 7)[/tex]

[tex](5x + 7)^2[/tex]

Factor Option C

[tex]100x^2 + 60x + 9[/tex]

[tex](10x + 3)(10x + 3)[/tex]

[tex](10x + 3)^2[/tex]

Factor Option D

[tex]121x^2 + 100x + 25[/tex]

Cannot factor this equation with rational number

Answer:  Option D, [tex]121x^2 + 100x + 25[/tex]

Answer:

A

Step-by-step explanation:

If 50 is the diameter that thr radius is 25 and the equation to find the area of a circle is pi(r^2). So you would do pi(25^2) and that is 1963

Answer:

[tex]\frac{27}{38}[/tex]

Step-by-step explanation:

P (Srawberry or Cherry)

= [tex]\frac{23 + 4}{38}[/tex]

= [tex]\frac{27}{38}[/tex]

I hope this help out.

Answer:

  [tex]\left[\begin{array}{ccc}-3&3&3\\3&6&3\end{array}\right][/tex]

Step-by-step explanation:

Reflection over the line y=x is described by the transformation ...

  (x, y) ⇒ (y, x)

The corresponding transformation matrix is ...

  [tex]\left[\begin{array}{cc}0&1\\1&0\end{array}\right][/tex]

When this left-multiplies the given coordinate matrix, the result is the one shown above.

Check the picture below.

[tex]\stackrel{\textit{\Large Areas}}{\stackrel{rectangle}{(160)(20)}~~ + ~~\stackrel{triangle}{\cfrac{1}{2}(90)(120)}}\implies 3200~~ + ~~5400\implies 8600[/tex]

Answer:

1,4,7 1,74. 4,7,1 ,4,1,7 ,7,4,1

Step-by-step explanation:

if width = 3 length = 5 hight = 10

Volume of rectangular prism = 3×5×10

= 150

Answer:

[tex] \hookrightarrow \sf \bold{ - \frac{1}{2} }[/tex]

Step-by-step explanation:

⇢ [tex] \bold{5x+5=3x+4} [/tex]

⇢ - 3x + 5x = 4 - 5

⇢ 2x = -1

⇢ 2x/2.= -1/2

⇢ x = -1/2

5x+5=3x+4

5x-3x=4-5

2x=-1

2x/2=-1/2

x=-1/2

Answer:

15.22

Step-by-step explanation:

You add the amount for lettuce on week 1 and week 3. then you subtract the total for lettuce from that number to get lettuce for week 2. After that just add the lettuce, apples, and chicken in the week two section and thats your answer

Problem 9

Reason:

The height of the cylinder is 2.5 ft. It's misleading because the cylinder is tipped onto its side, so it appears that 4 ft is the height. The height of any cylinder is always perpendicular to the circular base. It might help to rotate the paper so that the circular base is horizontal.

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

Problem 10

Reason:

The diameter of the base is 4 feet, which divides in half to 2 feet and it's the radius of the circle.

Area = pi*(radius)^2 = pi(2)^2 = 4pi

So the area expression should be either pi(2^2) or pi(4) or 4pi

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

Problem 11

Reason:

V = pi*r^2*h

V = 3.14*2^2*2.5

V = 31.4 cubic feet

This volume is approximate since pi = 3.14 is approximate.

Answer:

And great great the owner is 44

Step-by-step explanation:

or 36 because you have to add all sides

Answer:

can you post the question but more clear I didn't understand

Step-by-step explanation:

post it again I didn't understand

Answer:

The Perimeter of the trapezoid = 42.6 inches

Step-by-step explanation:

______

Formula:

let a , b , c , d be consecutively the lengths of the sides of the trapezoid

then

The Perimeter of the trapezoid  = a + b + c + d

___________________________________

Suppose a = 11 , b = 1.5 , c = 11 , d = 19.1

therefore,

The Perimeter of the trapezoid  = a + b + c + d

                                                     = 11 + 1.5 + 11 + 19.1

                                                     = 42.6

The function g(x) = x³ - x² - 4x + 4 has zeros at 1, 2 and -2. The y intercept is at 4.

An equation is an expression that shows the relationship between two or more numbers and variables.

The zeros of the function is at:

g(x) = 0, hence:

x³ - x² - 4x + 4 = 0

(x - 1)(x² - 4) = 0

(x - 1)(x + 2)(x - 2) = 0

x = 1, x = -2 and x = 2

The y intercept is at x = 0, hence:

g(0) = 0³ - 0² - 4(0) + 4 = 4

The function g(x) = x³ - x² - 4x + 4 has zeros at 1, 2 and -2. The y intercept is at 4.

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Answer:

33

Step-by-step explanation:

simply replace x with 7!

7^2 = 49

49-16=33

Answer:

Price before Taxes: $ 25.00

Sales Tax (8.5%): $ 2.13

Total Price with Tax: $ 27.1

Step-by-step explanation:

Answer:

answer attached

Step-by-step explanation:

just solve them out

The expressions to the correct function combination is (f. g)(x).

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given that;

f(x) = 12 - 61 – 27

g(t) = 1 - 9

Now,

To match the expressions to the correct function combinations, you can substitute the values of f(x) and g(t) into the expressions and simplify. For example:

( + 5)() = (f(x) + 5)(g(t))

( + 5)() = ((12 - 6x - 27) + 5)(1 - 9t)

( + 5)() = (17 - 6x)(1 - 9t)

( + 5)() = 17 - 153t - 6x + 54xt

Therefore, by the given equation the answer will be (f. g)(x).

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