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juin [17]
2 years ago
12

Solve the following addition and subtraction problems. a. 3 km 9 hm 9 dam 19 m + 7 km 7 dam b. 5 sq.km 95 ha 8,994 sq.m + 11 sq.

km. 11 ha 9,010 sq. m. c. 44 m – 5 dm d. 73 km 47 hm 2 dam - 11 km 55 hm
Mathematics
1 answer:
kipiarov [429]2 years ago
5 0
As a general rule to solve the problem we are going to transform all values to the lower unit.  
a. 3 km 9 hm 9 dam 19 m + 7 km 7 dam
  3,000 m 900 m 90 m 19 m + 7,000 m 70 m = 4,009 + 7,070 = 11,079 m 
  b. 5 sq.km 95 ha 8,994 sq.m + 11 sq. km. 11 ha 9,010 sq. m.
  5,000,000 sq m 95,0000 sq m 8,994 sq m + 11,000,000 sq m 110,000 sq
9,010 sq m
  5,103,994 sq m + 11,119,010 sq m = 16,223,004 sq m 
 c. 44 m – 5 dm
  44 m - 0.5 m = 43.5 m 
 d. 73 km 47 hm 2 dam - 11 km 55 hm

  73,000 m 4,700 m 20 m - 11,000 m 5,500 m 
77,720 m - 16,500 m = 61,220 m
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ANSWER

\frac{x - 4}{2x - 2}

EXPLANATION

The given expression is;

\frac{2 {x}^{2}  + 5x + 3}{ {x}^{2}  - 3x - 4}  \div  \frac{4 {x}^{2}  + 2x - 6}{ {x}^{2}  - 8x + 16}

We factor to obtain;

\frac{(x + 1)(2x + 3)}{(x - 4)(x + 1)}  \div  \frac{2(x - 1)(2x + 3)}{(x - 4)(x - 4)}

Multiply by the reciprocal of the second fraction

\frac{(x + 1)(2x + 3)}{(x - 4)(x + 1)}  \times \frac{(x - 4)(x - 4)}{2(x - 1)(2x + 3)}

Cancel out common factors to get,

\frac{1}{1}  \times \frac{(x - 4)}{2(x - 1)}

\frac{x - 4}{2x - 2}

8 0
2 years ago
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Bonita is testing prototype model rocket engines. To be considered a successful launch, the rocket must reach a height of at lea
lbvjy [14]

Answer:

(0, 33)   : Yes

(4.8,  30.5)  : Yes


Step-by-step explanation:

height of at least 24 ft :  y >= 24

horizontal distance of no more than 10 ft. : 0 <= x <= 10

The vertical height must be at least three times as high as the horizontal distance. No rocket should go higher than 33 ft.:

y >=  3x and y <= 33

So Constraints:

24 <= y <= 33

y >= 3x

0 <= x <= 10

Now check to see if those coordinate points meet all the constraints

(0, 33)   : Yes

(4.8, 30.5)  : Yes

(9, 26)  : No (because 26 is less than (3 * 9) = 27)

(4, 36) : No (because 36 > 33,  must be 24 <= y <= 33)

(2, 22): No (because 22 <24,  must be 24 <= y <= 33)

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2 years ago
The graph of the function f(x) = (x + 2)(x + 6) is shown below.
iren [92.7K]

Answer:

Step-by-step explanation:

f(x) = (x + 2)(x +6)

1) The function is positive for all real values of x where   x > –4 :

COUNTER-EXAMPLE : x =  - 3   you have -3>-4 but   (-3+2)(-3+6) = -1 ×3 =-3 no positive .

2) The function is positive for all real values of x where

x < –6 or x > –3.

COUNTER-EXAMPLE : x =  - 2.5   you have -2.5>-3 but   (-2.5+2)(-2.5+6) = -0.5 ×3.5 =-1.75 no positive .

same method for the statement : "The function is negative for all real values of x where

x < –2."

conclusion : statement about the function is true: "The function is negative for all real values of x where

–6 < x < –2."

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2 years ago
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telo118 [61]

Answer:

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makkiz [27]

The output y is y=22

Explanation:

The expression is y=5 x-3

We need to determine the output y, when the value of input is x is 5.

That is, substituting x=5 in y=5 x-3, we get,

y=5(5)-3

Multiplying the value within the bracket, we have,

y=25-3

Subtracting the terms, we get,

y=22

Thus, the value of output y is y=22

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