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3 years ago

PLEASE HELP ME W/ MATH ASAP!!

Mathematics

2 answers:

larisa [96]3 years ago

8 0

Use similarity property:

14 / (14+6) = 21 / (21 + (x+4))

14/20 = 21/(x+25) cross multiplication property

14*(x+25) = 20*21

14x + 350 = 420

14x = 70

x = 70/14 = 5.

seraphim [82]3 years ago

5 0

due to similarity of triangles TVW and TSU:

TV/TS=TW/TU
14/20=21/(x+4)
from this equation we get x=26

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The base of an aquarium with given volume is made of slate and the sides are made of glass. If slate costs five times as much (p

crimeas [40]

Answer:

Base = Length = (2V/5)^⅓

Height = V^⅓/(2/5)^⅔

Step-by-step explanation:

Let the sides of the aquarium be l,b and h

Where l = length

b = base

h = height

Volume = lbh

V = lbh

The surface area of the box is

A = 2bh + 2lh + 2lb

We'll replace the 2lb with 5lb to get the cost of area because it's given the question that the slate (base) of the box cost 5 times as much per unit area as glass

C(l,b,h) = 2bh + 2lh + 5lb

Make h the subject of formula in (V = lbh)

h = V/lb

This will enable us to account for the lowest cost of materials by taking derivatives of the cost equation, and we need to solve for a l to put into the solution.

Substitute V/lb for h in the cost equation

C(l,b,V/lb) = 2b(V/lb) + 2l(V/lb) + 5lb ------ Simplify

C(l,b,V/lb) = 2V/l + 2V/b + 5lb

Take the derivatives of the above with respect to l and b

Cl = -2V/l² + 5b

Cb = -2V/b² + 5l

Equate Cb to Cl (this implies that b = l)

Cb = Cl =>

-2V/l² + 5b = -2V/b² + 5l

So, we have

C(b,b) = -2V/b² + 5b = 0

-2V/b² + 5b = 0 ---- Solve for b

-2V/b² = -5b ---- Multiply through by b²

-2V = -5b³ ---- Divide through by -5

2V/5 = b³ ---; Rearrange

b³ = 2V/5

b = (2V/5)^⅓

b = l

So, l = (2V/5)^⅓

h = V/lb ---- (b = l)

h = V/l² ---- Substitute (2V/5)^⅓ for l

h = V/((2V/5)^⅓)²

h = V/(2V/5)^⅔

h = V/((V^⅔)(2/5)^⅔)

h = V^⅓/(2/5)^⅔

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3 years ago

The model represents an equation. What is the solution for the equation?

ryzh [129]

Answer: A x = 3

Step-by-step explanation:

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3 years ago

Solve by multiplying digits of value and filling in zeros: 200 x 80 x 60

shusha [124]

Answer:

down below:)

Step-by-step explanation:

200 times 80 times 60 is:

200 times 80 is 16000

16000 times 60 is 960000

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3 years ago

Triangle ABC has vertices at A(−3, 4), B(4, −2), C(8, 3). The triangle translates 2 units up and 1 unit right. Which rule repres

Nataly [62]

Answer:

The translation statement is given by:

$(x,y)\rightarrow (x+1,y+2)$

After the translation, the coordinates of vertex A is (-2,6).

Step-by-step explanation:

Given :

Vertices of a triangle ABC are:

A(−3, 4), B(4, −2), C(8, 3)

The triangle is translated 2 units up and 1 unit right.

To find the co-ordinates of point A after translation.

Translation rules.

For shift of $c$ units up, the translation is given as:

$(x,y)\rightarrow (x,y+c)$

For shift of $k$ units right, the translation is given as:

$(x,y)\rightarrow (x+k,y)$

So, it says the triangles is translated 2 units up and 1 unit right.

The translation statement is given by:

$(x,y)\rightarrow (x+1,y+2)$

So, co-ordinates of point A after translation is given by :

$(-3,4)\rightarrow (-3+1,4+2)=(-2,6)$

After the translation, the coordinates of vertex A is (-2,6).

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4 years ago

The letters 's', 't', 'u', 'd', 'y', 'i', 's', 'l', 'a', 'n', 'd' are placed in a bag. one letter is randomly selected from the

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Answer:

7/11

Step-by-step explanation:

There are 11 letters in 'S', 'T', 'U', 'D', 'Y', 'I', 'S', 'L', 'A', 'N', 'D', so there are 11 letters in the bag.

There are 7 consonants in the bag.

So, the probability of selecting a consonant is 7 out of 11, or 7/11

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4 years ago