MATHEMATICS COLLEGE

Solve for c. a (c+b)=d

Answers

Answer 1

Answer:

Answer:

$c = (d)/(a) - b$

Step-by-step explanation:

a( c + b ) = d

Divide both sides by a

That's

$(a(c + b))/(a) = (d)/(a) \n c + b = (d)/(a)$

Move b to the right side of the equation to make c stand alone

We have the final answer as

$c = (d)/(a) - b$

Hope this helps you

Answer 2

Answer:

Answer:

c = $(d)/(a)$ - b.

Step-by-step explanation:

a(c + b) = d

(c + b) = d / a

c + b = $(d)/(a)$

c = $(d)/(a)$ - b.

Hope this helps!

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Share £360 in the ratio 2:7

Answers

Answer:

80:280

Step-by-step explanation:

Final answer:

To share £360 in the ratio 2:7, you first find the value of one part by dividing £360 by the total number of ratio parts (9). Then, multiply each part of the ratio by this amount, resulting in £80 and £280.

Explanation:

To share £360 in the ratio 2:7, you first need to understand that the sum of the parts of the ratio (2+7) equals to 9 parts. The amount of £360 should be distributed into these 9 parts.

First, you divide the total amount by the total number of parts:
£360 / 9 = £40.

This result £40 is the value of 1 part. To find the amounts for the ratio 2:7, you multiply each part of the ratio by the value of 1 part:

2 * £40 = £80 which is the amount for the first part of the ratio, and
7 * £40 = £280 which is the amount for the second part of the ratio.

Learn more about Ratios here:

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Perform each of the following computations using the measured quantities below. a. 917.2 + 45.63 = ___________
b. 3.423 x 10^-4 - 6.42 x 10^-3 =_________

Answers

Question

Perform each of the following computations using the measured quantities below.

Write your final answer with the correct number of significant figures in proper scientific notation (one non-zero number to the left of the decimal point).

a. 917.2 + 45.63 = ___________

b. 3.423 x 10^-4 - 6.42 x 10^-3 =_________

Answer:

(a) 9.6 x 10²

(b) -6.1 x 10⁻³

Step-by-step explanation:

(a) 917.2 + 45.63

First add the two numbers as follows (ensure that the decimal numbers are well aligned);

9 1 7 . 2

+ 4 5 . 6 3

9 6 2 . 8 3

To write the result in a proper scientific notation (one non-zero number to the left of the decimal point),

i. Express the number is standard form

962.83 = 9.6283 x 10²

Note that;

From the result in (i)

9.6283 = mantissa

10 = base

² = power or exponent.

ii. Express the mantissa of the number in 1 decimal place.

9.6 x 10²

Therefore, the result in the proper scientific notation is 9.6 x 10².

(b) 3.423 x 10⁻⁴ - 6.42 x 10⁻³

Find the difference between the two numbers as follows;

i. Re-write the numbers so that they both have the same exponents:

0.3423 x 10⁻³ - 6.42 x 10⁻³

ii. Factor out 10⁻³

10⁻³(0.3423 - 6.42)

iii. Solve the bracket

10⁻³(-6.0777)

iv. Rewrite the result in (iii)

-6.0777 x 10⁻³

To write the result in a proper scientific notation (one non-zero number to the left of the decimal point),

i. Express the number is standard form

-6.0777 x 10⁻³ [already in standard form]

Note that;

From the result in (i)

-6.0777 = mantissa

10 = base

⁻³ = power or exponent.

ii. Express the mantissa of the number in 1 decimal place.

-6.1 x 10⁻³

Therefore, the result in the proper scientific notation is -6.1 x 10⁻³.

The perimeter of a rectangle is 52 feet. Describe the possible lengths of a side if the area of the rectangle is not to exceed 120 square feet. I need to find the solution set for this.

Answers

Answer:

2x+2y=52

x*y=120

Step-by-step explanation:

Final answer:

The possible lengths of a side of the rectangle are 22, 21, 20, 19, 18, 17, 16 feet.

Explanation:

To find the possible lengths of a side of the rectangle, let's use the formula for the perimeter of a rectangle, which is 2(length + width). We can set up an equation using the given information:

2(length + width) = 52

Dividing both sides by 2, we get:

length + width = 26

Now, to find the possible lengths, we need to consider the area. The formula for the area of a rectangle is length x width. We are given that the area is not to exceed 120 square feet, so we can set up the inequality:

length x width <= 120

Using the relationship length + width = 26, we can substitute length = 26 - width into the inequality:

(26 - width) x width <= 120

Simplifying the inequality, we get:

-width^2 + 26width - 120 <= 0

Now, we can solve this quadratic inequality to find the range of possible widths. Once we have the widths, we can substitute them back into the equation length + width = 26 to find the corresponding lengths.

By solving the quadratic inequality, we find that the possible widths are 4 <= width <= 10. Substituting these widths back into the equation length + width = 26, we get the corresponding lengths:

If width = 4, then length = 22

If width = 5, then length = 21

If width = 6, then length = 20

If width = 7, then length = 19

If width = 8, then length = 18

If width = 9, then length = 17

If width = 10, then length = 16

The possible lengths of a side of the rectangle are {22, 21, 20, 19, 18, 17, 16} feet.

Learn more about rectangle side lengths here:

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What is the maximum height of the basketball when the player passes the ball to someone? Initially, the ball moves at a speed of 12m/sec at an angle with respect to the horizontal of 45 degrees. Is it possible that other player standing 8m away is able to catch the ball without any bounces?

Answers

Answer with explanation:

Since the motion of the ball is projectile motion we shall use the equations for projectile motion.

The maximum height achieved by the projectile is given by

$h_(max)=(v_(o)^(2)sin^(2)(\theta ))/(2g)$

Applying the values we get

$h_(max)=(12^(2)* sin^(2)(45))/(2* 9.81)\n\nh_(max)=3.669m$

The range of the projectile is given by

$R=(v_(o)^(2)sin(2\theta ))/(2g)$

Applying values we get

$R=(12^(2)* sin(2* 45 ))/(2* 9.81)\n\nR=7.339m$

thus the maximum horizontal distance reached by the ball equals 7.339 meters after which it bounces thus a person standing 8 meters away will not be able to catch it.

(The height of the players is not taken into account since no info is given about their height.)

How do you write
25/4
as a percentage?