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3 years ago

Simplify using appropriate identity 0.85 × 0.85 +2 × 0.85 ×0.15 × 0.15

Mathematics

2 answers:

spayn [35]3 years ago

7 0

The answer is 0.76075!

Hope this helps!

guapka [62]3 years ago

4 0

Remember that multiplication is to be done before addition or subtraction. We see that both terms have the factor 0.85:

0.85 × 0.85 +2 × 0.85 ×0.15 × 0.15 =

0.85 * ( 0.85 + 2*0.15*0.15).

This is equivalent to 0.85 ( 0.85 + 2*0.0225 ) = 0.85 ( 0.895 ).

This last result could be left as is, or evaluated with a calculator:

0.76075

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How many bucketloads would it take to bucket out the world’s oceans? Write your answer in scientific notation.

kodGreya [7K]

Answer: $7\times10^{19} buckets$

Step-by-step explanation:

Given: A cubic kilometer= $10^{15}$ cubic centimeters

The volume of world’s oceans= $1.4\times10^{9}$ cubic kilometers of water.

⇒ The volume of world’s oceans= $1.4\times10^{9}\times10^{15}$ cubic centimeters of water.

Volume of a bucket = 20,000 cubic centimeters of water.

The number of bucket-loads would it take to bucket out the world’s oceans

$n=\frac{\text{volume of ocean}}{\text{volume of bucket}}=\frac{1.4\times10^{9}\times10^{15}}{20000}$

$\Rightarrow\ n=\frac{1.4\times10^{9+15}}{0.2\times10^5}......[a^n\times a^m=a^{m+n}]\\\Rightarrow\ n=7\times10^{24-5}.....[\frac{a^m}{a^n}=a^{m-n}]\\\Rightyarrow\ n=7\times10^{19}$

hence, $7\times10^{19}$ bucketloads would it take to bucket out the world’s oceans.

5 0

3 years ago

. Three types of shirts sold at a store cost $9.00, $11.00, and $12.50. One day, the store sells a total of 23 shirts and makes

lbvjy [14]

Answer:

X + 3y = 23

9x + 36y = 243

11 shirts sold at $9.0 per shirt, 4 shirts sold at $11 per shirt and 8 shirts sold at $12.5 per shirt

Step-by-step explanation:

-----Since we are told to assume that the number of shirts sold for $9.00 each is x, that of $11.00 is y and also that of $12.50 is z.

9x + 11y + 12.5z = 243

9x + 11y + 12.5(2y) = 243

9x + 36y = 243_______ equation 1

----- The statement also read that One day, the store sells a total of 23 shirts and makes $243 on the sales. TWICE AS MANY SHIRTS WERE SOLD FOR $12.50 THAN WERE SOLD FOR $11.00

Z = 2y

x + y + z = 23

X + y + 2y = 23

X + 3y = 23_____ equation 2

Now multiply the above by 9 to have this equation's "x" sharing the same coefficient with that of equation 1

9x + 27 = 207 will be the new one___equation 3

-----Subtract equation 3 from 1 and we have

9x + 36y = 243____ equation 1

9x + 27y = 207____ equation 3

9y = 36

Y = 4

-----Substitute y = 4 in equation 2

X + 3y = 23

X + 4(3) = 23

X + 12 = 23

X = 23 - 12

X = 11

-----Remember that x + y + z = 23

11 + 4 + z = 23

15 + z = 23

Z = 23 - 15

Z = 8.

So therefore, x =11 shirts, y = 4 shirts and z = 8 shirts

4 0

3 years ago

Find the equation of the straight line through (–2, 3) perpendicular to 2x + y =8

Thepotemich [5.8K]

Answer:

$y = \dfrac{1}{2}x + 4$

Step-by-step explanation:

The equation of a line in slope-intercept form is

y = mx + b

We need to find the slope, m, and the y-intercept, b.

The line we need is perpendicular to the line 2x + y = 8.

The slopes of perpendicular lines are negative reciprocals.

We solve the given equation for y to find the slope of the given line.

2x + y = 8

y = -2x + 8

The given line has slope -2.

The negative reciprocal of -2 is 1/2.

Our line has slope, m = 1/2.

Now we have

y = 1/2 x + b

Now we use the given point, (-2, 3), for x and y, using x = -2, and y = 3, and we solve for b.

y = 1/2 x + b

3 = 1/2 * (-2) + b

3 = -1 + b

4 = b

b = 4

Now we have

y = 1/2 x + 4

Answer: $y = \dfrac{1}{2}x + 4$

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3 years ago

45.15 ÷ 21 pleases solve it for me

sergiy2304 [10]

Answer:

2.15

Step-by-step explanation:

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3 years ago

A 26-foot long ladder is leaning against a building at a 60 degree angle with the ground. Which of the following equations can y

Sati [7]

Answer:

22.5 feet (to the nearest tenth).

Step-by-step explanation:

The equations have not been given but still the question can be solved. The ladder lying with a building makes a right angled triangle, in which the ladder is the hypotenuse, the building is the perpendicular, and the ground is the base. The length of the ladder (hypotenuse) is 26 feet and the angle with the ground is 60 degrees. The required length to be found is the length of the building (perpendicular). So the following formula will be used:

sin θ = Perpendicular/Hypotenuse.

Substituting in the equation gives:

sin60 = p/26.

p = 26*sin60.

p = 22.5 (to the nearest tenth).

The approximate height of the building is 22.5 feet!!!

4 0

3 years ago

Read 2 more answers