MATHEMATICS HIGH SCHOOL

1) Find the simple interest on GH¢400.00 at a rate of 5% per annum for 2 years.2) Find the simple interest on GH¢6,000.00 at a rate of 12% per annum for 2 years.
3) Find the simple interest on GH¢500.00 at a rate of 3% per annum for 5 years.
4) Find the simple interest on GH$2,000.00 at a rate of 5% per annum for 4 years.
5) Find the simple interest on GH¢ 1,200.00 at a rate of 2%
dqper annum for 5 years.

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

1. 5/100*400*2=40

2. 12/100*6000*2=1440

3. 3/100*500*5=75

4. 5/100*2000*4=400

5. 2/100*1200*5=120

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Expand and simplify. (x+4)squared

Answers

The quadratic expression (x+4)² = x² + 8x + 16.

The given expression is,

(x+4)²

The expression (x+4)² represents a mathematical operation called "squaring."

To expand it, we need to multiply the expression by itself.

So, (x+4)² becomes (x+4) * (x+4).

When we multiply these terms, we apply the distributive property and combine like terms.

After simplifying, we get x² + 8x + 16.

Or we can directly use the identity,

(a+b)² = a² + b² + 2ab

Here a = x and b = 4

(x+4)² = x² + 4² + 8x

Hence,

(x+4)² = x² + 8x + 16

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(x+4)²= (x+4)×(x+4)

Use the FOIL method to simplify

F=First (multiply the first number of each expression)
O=Outside (multiply the outside edges of each expression)
I= Inside (multiply the inside edges of each expression)
L= Last (multiply the last number of each expression)

x times x= x²
x times 4= 4x
4 times x= 4x
4 times 4= 16

Add them together, we have: x²+4x+4x+16
We can simplify this by adding like terms
4x+4x=8x

Final expression= x² + 8x + 16

The value of y varies directly with x and y = 4.5 when x = 0.5. find y when x = 10

Answers

So what you asked this is what I got

x(y) = 4.5

If x= 0.5 then

0.5(y) = 4.5
y=9

x(y) = 4.5

10(y) = 4.5
y= 0.45

hope this helps :)

What mathematical operation applies (addition, subtraction, multiplication or division) and write your equation in the box below.

Answers

Equation. This word may fit your definition of a set of values or numbers –intergers- coupled with basic operations. Equation is mathematical form of body where there are two adjacent corners which aims as the word says, equation. Take for instance in illustration 2x + 5x = 7x.

Bob was thinking of a number between 5 and 15 that when squared and added to 23 equals the next number's square. What is the number?

Answers

The value of number will be;

⇒ 11

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Bob was thinking of a number between 5 and 15 that when squared and added to 23 equals the next number's square.

Now,

Let the value of number = x

Hence, We can formulate;

⇒ x² + 23 = (x + 1)²

Solve for x as;

⇒ x² + 23 = x² + 1 + 2x

⇒ x² - x² + 23 - 1 = 2x

⇒ 22 = 2x

⇒ x = 22/2

⇒ x = 11

Thus, The value of number will be;

⇒ 11

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Answer:

Step-by-step explanation:

(11)² = 121

121+23 = 144

(12)² = 144

In a right triangle, angle C measures 40. the hypotenuse of the triangle is 10 inches long. what is the approximate length of the side adjacent to angle C

Answers

In a right triangle, we know that we have one angle that is 90 degrees. In order to calculate the length of the adjacent side we have to use the cosine function of angle C which will give us the adjacent side length. The cosine function is: adjacent/hypotenuse = cos (40). We know the hypotenuse length is 10, so the equation is now adjacent/10 = cos (40). Solving for adjacent length we get 7.66 inches.

The approximate length of the side adjacent to angle $C$ is $\boxed{{\mathbf{7}}{\mathbf{.66 inches}}}$ .

Further explanation:

The cosine ratio can be expressed as,

$\cos\theta=\frac{{{\text{base}}}}{{{\text{hypotenuse}}}}$

Here, base is the length of the side adjacent to angle $\theta$ and hypotenuse id the longest side of the right angle triangle.

The length of side opposite to angle $\theta$ is perpendicular that is used for the sine ratio.

Step by step explanation:

Step 1:

The observed right angle from the given information is attached.

First determine the hypotenuse and the base of the triangle.

The side $BC$ is adjacent to angle $C$ and the side $AC$ is the hypotenuse of $\Delta ABC$ .

Therefore, the ${\text{base}}=BC$ and ${\text{hypotenuse}}=10$ .

Step 2:

Since, the cosine ratio is $\cos\theta=\frac{{{\text{base}}}}{{{\text{hypotenuse}}}}$ .

Now substitute the value ${\text{base}}=BC$ and ${\text{hypotenuse}}=10$ in the cosine ratio.

$\begin{aligned}\cos C&=\frac{{BC}}{{10}}\n{\text{co}}s40&=\frac{{BC}}{{10}}\n0.766&=\frac{{BC}}{{10}}\nBC&=7.66\n\end{aligned}$

Therefore, the approximate length of the side adjacent to angle $C$ is $7.66{\text{ inches}}$ .

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Answer details:

Grade: High school

Subject: Mathematics

Chapter: Trigonometry

Keywords: Distance, Pythagoras theorem, base, perpendicular, hypotenuse, right angle triangle, units, squares, sum, cosine ratio, adjacent side to angle, opposite side to angle.

The circular ring of the fountain has a radius of 9 feet. what is the area of the ring?a. 4.5 square feet

b. 28.26 square feet

c. 63.61 square feet

d. 254.34 square feet

Answers

The area of the circular ring of the fountain with a radius of 9 feet is approximately 254.34 square feet.

To find the area of the ring, we need to subtract the area of the smaller circle from the area of the larger circle. The area of a circle is given by the formula A = πr^2, where r is the radius of the circle. Therefore, the area of the larger circle is π(9^2) = 81π square feet, and the area of the smaller circle is π((9/2)^2) = 20.25π square feet.

Subtracting the area of the smaller circle from the area of the larger circle, we get:

81π - 20.25π = 60.75π

Using the approximation π ≈ 3.14, we get:

60.75π ≈ 60.75(3.14) ≈ 190.845

Therefore, the area of the ring is approximately 190.845 square feet, which is closest to option (d) 254.34 square feet.

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