A pile of sand has a weight of 90kg.The same is put into a small bag, a medium bag and a large bag in the ratio of 2:3:7.Work out the weight of sand in each bag
Answers
Remark
This requires some sort of constant that each of the ratio members is multiplied by.
Call the constant x
Equation
2x + 3x + 7x = 90 Add the left hand side
Solution
12x = 90 Divide by 13
x = 90 /12
x = 7,5
Answer
2x = 2 * 7.5
2x = 15
3x = 22.5
7x = 52.5
Sum = 90 as it should be
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Answers
To find the area of a rectangle, you must multiply the length by the width.
A= L*w, L= 3w
A=3w*w
48 = 3w*w
48=3w^2
48/3 = w^2
16= w^2
squareroot of 16 = w
w= 4
plug 4 back in the equation of L= 3w
3(4) = 12
If the Area is equal to 48, and the length is three times the width, then the length must be equal to 12 inches, while the width is equal to 4.
Hope this helps!
Answers
later snow depth = 1.6 feet
change
2 - 1.6
0.4 feet
percentage change
(0.4 / 2) * 100
20 %
The given values are the initial depth of snow which is 2 feet and the final depth which is 1.6 feet.
The solution of the problem is:
2 ft. - 1.6 ft. = 0.4 ft.
0.4 ft. / 2 ft. = 0.2
To calculate for the percentage,
0.2 x 100% = 20%
Answers
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A. Find the exact length of c in unsimplified radical form
B. Find the exact length of c in simplified radical form
C. Find c to the nearest hundredth
**I put the pic down below**
2. Consider the numbers 4/13 and 3/10 .
A. Compare the numbers.
B. Find a rational number between the two given numbers.
3. Use the Babylonian method to approximate √19 to the nearest hundredth.
Answers
so that will be 3^2+3^2=c^2
9+9=c^2
18=c2
then
and the nearest hundredth 4.24
The correct answers are:
#1: A) c = √18
B) c = 3√2
C) c = 4.24
#2: A) 4/13 > 3/10
B) 79/260
#3: 4.36
Explanation:
#1: A) We use the Pythagorean Theorem to solve this:
a² + b² = c²
3² + 3² = c²
9 + 9 = c²
18 = c²
Taking the square root of each side:
√18 = √c²
√18 = c
B) To simplify √18, we first find the prime factorization of 18:
18 = 9*2
9 = 3*3
This gives us
18 = 3*3*2
When we take the square root, we are looking for pairs. We have a pair of 3's; this means we take a 3 out:
3√2
C) In the calculator, we see that 3√2 = 4.24.
#2: A) First, we find a common denominator. The first thing that both 13 and 10 will divide into is 130:
(4*10)/130; (3*13)/130
40/130; 39/130
Since 40 > 39, this means that 4/13 > 3/10.
B) There is not enough space between the two fractions to use 130 as the denominator; we will double that to 260:
(40*2)/260; (39*2)/260
80/260; 78/260
The fraction between these two would be 79/260.
#3: Using the Babylonian method, we first make a guess. Since 9 is nearly half of 19, we will start there.
Next, we divide 19 by our guess:
19/9 = 2.111
We average this quotient with our guess:
(9 + 2.111)/2 = 11.111/2 = 5.5555
This is our new guess. Now divide 19 by this guess:
19/5.5555 = 3.4200342
Average this with our guess:
(5.5555+3.4200342)/2 = 4.4877671
This is our new guess. Divide 19 by this guess:
19/4.4877671 = 4.233731291
Average this with our new guess:
(4.4877671+4.233731291)/2 = 4.360749196
This is our new guess. Divide 19 by this guess:
19/4.360749196 = 4.357049476
Average this with our new guess:
(4.360749196+4.357049476)/2 = 4.358899
Make this our new guess. Divide 19 by this guess:
19/4.358899 = 4.3588988
Average this with our guess:
(4.358899+4.3588988)/2 = 4.3588989
Since the hundredths place has been the same the last few lines, we round to that: 4.36.
b) a = –3
c) a = 3
d) a = 5
Answers
Answers
2x + x = 180
3x = 180
x = 60
The x is 60°
2x° and 2 y on the straight angle is 180°
since you know 2x is 120°
180 - 120 = 60
There is 2 y, so you divide 60 by 2
60 ÷ 2 = 30
The y is 30°