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3 years ago

The diagram shows a row of four identical tiles, each in the shape of an isosceles trapezoid. What is the area of one tile?

Mathematics

1 answer:

VMariaS [17]3 years ago

8 0

I saw the image that accompanied this problem.

4 identical isosceles trapezoid forming 2 parallelogram.
1 parallelogram has a base of 16 inches and its height is 10 inches.

We need to get the area of the parallelogram and multiply it by 2 before dividing it into 4 to get the area of each isosceles trapezoid.

Area of a parallelogram = base * height
A = 16 in x 10 in = 160 in²

160 in² x 2 parallelogram = 320 in²
320 in² / 4 tiles = 80 in²

The area of one tile is 80 square inches.

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Alma invests $300 in an account that compounds interest annually. After 2 years, the balance of the account is $329.49. To the n

-Dominant- [34]

Invested amount (P) = $300.

Time in years (t) = 2 years.

Balance after 2 years (A) = $329.49.

Let us assume rate of interest = r % compounds annually.

We know, formula for compound interest

$A=P(1+r)^t$

Plugging values in formula, we get

$329.49=300(1+r)^2$

$\mathrm{Divide\:both\:sides\:by\:}300$

$\frac{300\left(1+r\right)^2}{300}=\frac{329.49}{300}$

$\left(1+r\right)^2=1.0983$

Taking square root on both sides, we get

$1+r=\sqrt{1.0983}$

$\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}$

$1+r-1=\sqrt{1.0983}-1$

$r=\sqrt{1.0983}-1$

$r=1.048-1$

r=0.048.

Converting it into percentage by multiplying by 100.

r=0.048 × 100

r = 4.8 %

Therefore, the rate of interest on the account is 4.8% compounds annually.

5 0

3 years ago

50 POINTS !! PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.

maks197457 [2]

Answer:

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Trigonometry

[Right Triangles Only] Pythagorean Theorem: a² + b² = c²

a is a leg
b is another leg
c is the hypotenuse

Step-by-step explanation:

Step 1: Define

Identify variables

Leg a = a

Leg b = 12

Hypotenuse c = 20

Step 2: Solve for a

Substitute in variables [Pythagorean Theorem]: a² + 12² = 20²
Evaluate exponents: a² + 144 = 400
[Subtraction Property of Equality] Isolate a term: a² = 256
[Equality Property] Square root both sides: a = 16

3 0

3 years ago

Read 2 more answers

10. Determine the open interval(s) on which the function f(x) = 12x - x^3 is increasing.

Gre4nikov [31]

Answer:

$\large\boxed{x\in(-2,\ 2)}$

Step-by-step explanation:

$f(x)=12x-x^3$

Calculate the derivative of the function:

$f'(x)=\left(12x-x^3\right)'=(12x)'-\left(x^3\right)'=12-3x^2$

Calculate the zeros of the derivative:

$f'(x)=0\Rightarrow12-3x^2=0\qquad\text{add}\ 3x^2\ \text{to both sides}\\\\3x^2=12\qquad\text{divide both sides by 3}\\\\x^2=4\to x=\pm\sqrt4\\\\x=\pm2$

Let's check the derivative sign:

$f'(x)>0\iff12-3x^2>0\qquad\text{use the distributive property}\\\\-3(x^2-4)>0\\\\-3(x^2-2^2)>0\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\-3(x-2)(x+2)>0\\^{\qquad x=2\qquad x=-2$

Sketch a parabola open down

(before the brackets there is the number -3 < 0)

Look at the picture.

Where the derivative is negative, the function decreases.

Where the derivative is positive, the function increases.

Therefore your answer is:

$x\in(-2,\ 2)$

3 0

3 years ago

Janet took out a loan of $50,000 from Bank of America at 8% on March 19, 2015, which is due on July 8, 2015. Using exact interes

Paladinen [302]

The formula for this is I = PRT
I = Interest
P = Principal (starting amount) = $50,000
R = Rate (percentage) = 8% = .08
T = Time in years = days/years = 111/365

I = 50000(.08)(111/365)
I = $1216.438
I = $1216.44 (rounded)

5 0

3 years ago

The circumference of C is 72 cm. what is the length of arc AB (the minor arc)? The center angle is 45

Nat2105 [25]

The arc length is given by:
2πr(theta)/360
given the circumference is 72 cm, the arc length will be:
AB=45/360*C
AB=45/360*72
AB=9 cm
the answer is 9 cm

7 0

3 years ago

Read 2 more answers