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r-ruslan [8.4K]
3 years ago
12

What is 10/9 closer to 1, 1/2

Mathematics
1 answer:
Serga [27]3 years ago
3 0

Answer:

It is closer to 1/2.

Step-by-step explanation:

First of all, 10/9 is the same thing as 1 1/9.

Draw a number line:

                                  1/2                               1

--|------|------|------|-----|---|---|------|------|------|-----|-----

0/9  1/9   2/9  3/9  4/9  5/9  6/9  7/9  8/9  9/9

Halfway between 4/9 and 5/9 is the same as 1/2 and 9/9 is the same as 1.

You can see that 1/9 is way closer to 1/2 than 1.

So, 10/9 is closer to 1/2.

(There are other ways to solve this, but this way is easiest for me!)

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Solve 3 -x = 243 -5 1/5 5
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Answer:

x=-243

Step-by-step explanation:

The equation is

-3^{-5}=\frac{1}{x}

Solve for x

we know that

-3^{-5}=-\frac{1}{3^{5}}=-\frac{1}{243}

substitute

-\frac{1}{243}=\frac{1}{x}

so

x=-243

3 0
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Find the area please and an explanation would be appreciated but its not demanded
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Step-by-step explanation:

just multiply 18x9

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If the volume of the pyramid shown is , what is the area of its base?
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John can jog twice as fast as he can walk. He was able to jog the first mile to his grandmas house but then he got tired and wal
statuscvo [17]

Answer:

  12 mph

Step-by-step explanation:

The relationship between jogging speed and walking speed means the time it takes to walk 4 miles is the same as the time it takes to jog 8 miles. Then the total travel time (0.75 h) is the time it would take to jog 1+8 = 9 miles. The jogging speed is ...

  (9 mi)(.75 h) = 12 mi/h . . . average jogging speed

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<em>Check</em>

1 mile will take (1 mi)/(12 mi/h) = 1/12 h to jog.

4 miles will take (4 mi)/(6 mi/h) = 4/6 = 8/12 h to walk.

The total travel time is (1/12 +8/12) h = 9/12 h = 3/4 h. (answer checks OK)

_____

<em>Comment on the problem</em>

Olympic race-walking speed is on the order of 7.7 mi/h, so John's walking speed of 6 mi/h should be considered quite a bit faster than normal. The fastest marathon ever run is on the order of a bit more than 12 mi/h, so John's jogging speed is also quite a bit faster than normal. No wonder he got tired.

7 0
3 years ago
Can you help me with my homework
goldfiish [28.3K]

Answer:

4. Option C (3a+2) inches

5. Extraneous solution x=-5/6 because we get for width and length negative values.

Solution: Value of x is 3

Length of the box: 5 ft

Width of the box: 4 ft

Step-by-step explanation:

4. Area of a rectangle: A=12a^2-a-6 square inches

Width: w=4a-3

Length: l=?

A=w l

Replacing A by 12a^2-a-6 and w by 4a-3

12a^2-a-6 = (4a-3) l

Solving for l: Dividing both sides of the equation by 4a-3:

(12a^2-a-6) / (4a-3) = (4a-3) l / (4a-3)

Simplifying:

(12a^2-a-6) / (4a-3) = l

l = (12a^2-a-6) / (4a-3)

Factoring the numerator:

12a^2-a-6 = (4a-3)(3a+2)

Let's check it:

(4a-3)(3a+2)=4a(3a)+4a(2)-3(3a)-3(2)=12a^2+8a-9a-6→(4a-3)(3a+2)=12a^2-a-6

Replacing the numerator:

l = (4a-3)(3a+2) / (4a-3)

Simplifying:

l = (3a+2) inches


5. Length: l=(3x-5) ft

Width: w=(2x-1) ft

Height: h=2 ft

Volumen of the box: V=40 ft^3

x=?

Length: l=?

Width: w=?

V = l w h

Replacing the given:

40 ft^3 = (3x-5) ft (2x-1) ft 2 ft

40 ft^3 = 2 (3x-5)(2x-1) ft^3

40=2(3x-5)(2x-1)

Dividing both sides of the equation by 2:

40/2=2(3x-5)(2x-1)/2

Simplifying:

20=(3x-5)(2x-1)

Eliminating the parentheses on the right side of the equation applying the distributive property:

20=3x(2x)+3x(-1)-5(2x)-5(-1)

20=6x^2-3x-10x+5

Adding like terms:

20=6x^2-13x+5

Equaling to zero: Subtracting 20 from both sides of the equation:

20-20=6x^2-13x+5-20

0=6x^2-13x-15

6x^2-13x-15=0

ax^2+bx+c=0; a=6, b=-13, c=-15

Using the quadratic formula:

x=[-b+-sqrt(b^2-4ac)]/(2a)

x=[-(-13)+-sqrt((-13)^2-4(6)(-15))]/(2(6))

x=[13+-sqrt(169+360)]/12

x=[13+-sqrt(529)]/12

x=[13+-23]/12

x1=(13-23)/12=(-10)/12=-10/12=-(10/2)/(12/2)→x1=-5/6

x2=(13+23)/12=36/12→x2=3


With x=-5/6

l=(3x-5) ft

l=(3(-5/6)-5) ft

l=(-5/2-5) ft

l=-(5/2+5) ft

l=-(5+2(5))/2 ft

l=-(5+10)/2 ft

l=-15/2 ft < 0. The length cannot be a negative number then x=-5/6 is a extraneous solution.

w=(2x-1) ft

w=(2(-5/6)-1) ft

w=(-5/3-1) ft

w=-(5/3+1) ft

w=-(5+3(1))/3 ft

w=-(5+3)/3 ft

w=-8/3 ft <0. The width cannot be a negative number then x=-5/6 is a extraneous solution.


With x=3

l=(3x-5) ft

l=(3(3)-5) ft

l=(9-5) ft

l=4 ft

w=(2x-1) ft

w=(2(3)-1) ft

w=(6-1) ft

w=5 ft

and h=2 ft

Let's check the volume

V= w l h

V=(5 ft)(4 ft)(2 ft)

V=40 ft^3 Correct

7 0
3 years ago
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