MATHEMATICS HIGH SCHOOL

A rectangle’s length is 2 units more than twice its width. Its area is 40 square units. The equation w(2w + 2) = 40 can be used to find w, the width of the rectangle.

Answers

Answer 1

Answer:

Answer: Value of w is 4 units and the equation is correct.

Step-by-step explanation:

Let width of a rectangle be 'w'.

Let length of a rectangle be '2w+2'.

Since we have given that

Area of rectangle = 40 square units.

As we know the formula for "Area = Length × Breadth" :

So, it becomes,

$40=w(2w+2)\n\n40=2w^2+2w\n\n20=w^2+w\n\nw^2+w-20=0\n\nw^2+5w-4w-20=0\n\nw(w+5)-4(w+5)=0\n\n(w+5)(w-4)=0\n\neither\ w=-5\ or\ w=4$

But dimension can't be negative.

So, w must be 4 units.

Hence, Value of w is 4 units and the equation is correct.

Answer 2

Answer: i hope this helps you

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Where does the irrational number 1.8693… fall?

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Answers

Answer:

y=7x+4

Step-by-step explanation:

Values of x and y satisfy the equation y=7x+4

A person springs off a 12-foot high diving board with an initial velocity of 10 feet per second. How many seconds does it take the person to hit the water?

Answers

Answer:

1.2 seconds

Step-by-step explanation:

The height of the diving board above water is 12 feet.

The person dives with an initial velocity of 10 feet per second.

The time taken is gotten by dividing the height jumped by the velocity at which the person dived.

That is:

t = d / s

where d = height jumped = 12 ft

s = velocity = 10 ft/s

Therefore:

t = 12 / 10 = 1.2 seconds

It took the person 1.2 seconds to hit the water.

What is the simplified base for the function f(x) = 2(3√27(2x)?2
3
9
18

Answers

Answer:

option C is correct i.e. 9

Step-by-step explanation:

We have given that : $f(x)=2 \sqrt[3]{27^(2x)}$

To find : The simplified base of the function f(x)

Solution:

Now, we solve the equation

$f(x)=2 \sqrt[3]{27^(2x)}$

$f(x)=2(27^x)^{(2)/(3)}$

$f(x)=2(3^(2x))$

$f(x)=2((3^2)^(x))$

$f(x)=2(9^(x))$

Therefore, the simplified base of the function f(x) is 9

Answer:

Option C is correct

9 the simplified base for the given function f(x)

Step-by-step explanation:

Using exponent rules:

$(x^m)^n = x^(mn)$

$\sqrt[n]{x^b} = x^{(b)/(n)}$

Given the function:

$f(x) = 2\sqrt[3]{27^(2x)}$

We can write 27 as:

$27 = 3 \cdot 3 \cdot 3 = 3^3$

then;

$f(x) = 2\sqrt[3]{(3^3)^(2x)}$

Apply the exponent rules:

$f(x) = 2\sqrt[3]{3^(6x)}$

Apply the exponent rules:

$f(x) =2 \cdot (3^(6x))^{(1)/(3)} = 2 \cdot 3^(2x)$

⇒ $f(x) = 2 \cdot (3^2)^x = 2 \cdot 9^x$

⇒ $f(x) =2 \cdot 9^x$

On comparing with exponential function $f(x) = ab^x$ where, b is base of the exponent function, then

b = 9

Therefore, the simplified base for the given function is, 9

How much Interest is earned on $470 at 4% for seven years ?

Answers

Answer:

End Balance $618.49

Total Principal $470.00

Total Interest $148.49

Hope this helps! Please mark brainliest! Have a great day!

Answer:

Step-by-step explanation:

how do i do this

What does interior angle A of the polygon in the figure equal?

Answers

Based on the attached image, the interior angle A of the polygon in the figure equal 110 degrees. If you can see the image the angle A is equal to the angle on the other side. The angle A is an example of obtuse angle because has the size of more 90 degrees and less than 180 degrees. All the angles in the image are obtuse except the one angle in the top that measures 50 degrees.

I don’t understand at all