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2 years ago

C is the midpoint of BD. If BC = x + 7 and CD = 8x, what is CD?

Mathematics

1 answer:

Anastaziya [24]2 years ago

8 0

Given :- 

C is the midpoint of BD .
BC = x + 7
CD = 8x

To Find :-

Value of BD ( correct )

Answer :- 

As C is the midpoint , we can say that the line is BCD . So that ,

BC + CD = BD

Substitute the values ,

( x+7 ) + 8x = BD
BD = x + 8x + 7
BD = 9x + 7 .

Hence the value of BD is 9x + 7 .

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Solve the inequality and graph the solution 4x-5>7

ohaa [14]

Answer:

x > 3

interval notation: (3, ∞)

Step-by-step explanation:

Given the inequality statement: 4x - 5 > 7,

The goal is to isolate x and find its solution.

Start by adding 5 to both sides:

4x - 5 + 5 > 7 + 5

4x > 12

Divide both sides by 4:

4x/4 > 12/4

x > 3

The solution can also be expressed in the following interval notation:

(3, ∞).

In terms of graphing, it involves an empty circle on the endpoint, x = 3, as it is not included as a solution. The solution to the given inequality statement must be greater than 3.

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2 years ago

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elixir [45]

Answer:

Min:3 Q:66-9 Med:9 Q3:10-14 Max19

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2 years ago

A large mixing tank currently contains 350 gallons of water, into which 10 pounds of sugar have been mixed. A tap will open, pou

Marysya12 [62]

Answer

Let t be number of minutes since tap is opened

water is increased by 20 gallons of water per minute.

sugar increase rate of 3 pounds per minute

water :- W(t) = 350 + 10 t

sugar :- S(t) = 10 + 3 t

concentration

C(t) = $\dfrac{S(t)}{W(t)}$

at t = 15 minutes

C(15) = $\dfrac{S(15)}{W(15)}$

C(15) = $\dfrac{10 + 3\times 15 }{350 + 10\times 15}$

C(15) = 0.11

at beginning t = 0 minutes

C(0) = $\dfrac{S(0)}{W(0)}$

C(0) = $\dfrac{10 + 3\times 0}{350 + 10\times 0}$

C(0) = 0.0286

C(15) > C(0)

hence, concentration is increasing as time is passing.

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3 years ago

A color printer prints 18 pages in 8 minutes. How many minutes does it take per page?

Sav [38]

Answer:

2.25 pages per minute

Step-by-step explanation:

Step 1:

18 ÷ 8

Step 2:

2.25

Answer:

2.25 pages per minute

Hope This Helps :)

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2 years ago

Which series of transformations will not map figure H onto itself

7nadin3 [17]

Answer:

Step-by-step explanation:

Given a square with vertices at points (2,1), (1,2), (2,3) and (3,2).

Consider option A.

1st transformation $(x+0,y-2)$ will map vertices of the square into points

$(2,1)\rightarrow (2,-1);$
$(1,2)\rightarrow (1,0);$
$(2,3)\rightarrow (2,1);$
$(3,2)\rightarrow (3,0).$

2nd transformation = reflection over y = 1 has the rule (x,2-y). So,

$(2,-1)\rightarrow (2,3);$
$(1,0)\rightarrow (1,2);$
$(2,1)\rightarrow (2,1);$
$(3,0)\rightarrow (3,2)$

These points are exactly the vertices of the initial square.

Consider option B.

1st transformation $(x+2,y-0)$ will map vertices of the square into points

$(2,1)\rightarrow (4,1);$
$(1,2)\rightarrow (3,2);$
$(2,3)\rightarrow (4,3);$
$(3,2)\rightarrow (5,2).$

2nd transformation = reflection over x = 3 has the rule (6-x,y). So,

$(4,1)\rightarrow (2,1);$
$(3,2)\rightarrow (3,2);$
$(4,3)\rightarrow (2,3);$
$(5,2)\rightarrow (1,2)$

These points are exactly the vertices of the initial square.

Consider option C.

1st transformation $(x+3,y+3)$ will map vertices of the square into points

$(2,1)\rightarrow (5,4);$
$(1,2)\rightarrow (4,5);$
$(2,3)\rightarrow (5,6);$
$(3,2)\rightarrow (6,5).$

2nd transformation = reflection over y = -x + 7 will map vertices into points

$(5,4)\rightarrow (3,2);$
$(4,5)\rightarrow (2,3);$
$(5,6)\rightarrow (1,2);$
$(6,5)\rightarrow (2,1)$

These points are exactly the vertices of the initial square.

Consider option D.

1st transformation $(x-3,y-3)$ will map vertices of the square into points

$(2,1)\rightarrow (-1,-2);$
$(1,2)\rightarrow (-2,-1);$
$(2,3)\rightarrow (-1,0);$
$(3,2)\rightarrow (0,-1).$

2nd transformation = reflection over y = -x + 2 will map vertices into points

$(-1,-2)\rightarrow (4,3);$
$(-2,-1)\rightarrow (3,4);$
$(-1,0)\rightarrow (2,3);$
$(0,-1)\rightarrow (3,2)$

These points are not the vertices of the initial square.

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3 years ago