What's the area of the room in this diagram?A. 156 square feet
B. 84 square feet
C. 166 square feet
D. 25 square feet

Answers

Answer 1

Answer: Clearly its a rectangle. So, area of a rectangle = length * breadth = 12 feet *13 feet = 156 square feet

Answer 2

Answer: This is the Diagram. Right?
Answer is A. 156 square feet

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Function form
5x-7y=14

Answers

function form is when you put x in, you get y so the correct equaiton should be y=so and so

so

5x-7y=14
subtrac 5x form both ssides
-7y=14-5x
divide both sides by 7
-y=2-5/7x
multiply by -1
y=5/7x-2
that is it

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

Please help me with this!!
Thank u

Answers

Answer:

Step-by-step explanation:

Left

When a square = a linear, always expand the squared expression.

x^2 - 2x + 1 = 3x - 5 Subtract 3x from both sides

x^2 - 2x - 3x + 1 = -5

x^2 - 5x +1 = - 5 Add 5 to both sides

x^2 - 5x + 1 + 5 = -5 + 5

x^2 - 5x + 6 = 0

This factors

(x - 2)(x - 3)

So one solution is x = 2 and the other is x = 3

Second from the Left

i = sqrt(-1)

i^2 = - 1

i^4 = (i^2)(i^2)

i^4 = - 1 * -1

i^4 = 1

16(i^4) - 8(i^2) + 4

16(1) - 8(-1) + 4

16 + 8 + 4

Second from the Right

This one is rather long. I'll get you the equations, you can solve for a and b. Maybe not as long as I think.

12 = 8a + b

17 = 12a + b Subtract

-5 = - 4a

a = - 5/-4 = 1.25

12 = 8*1.25 + b

12 = 10 + b

b = 12 - 10

b = 2

Now they want a + b

a + b = 1.25 + 2 = 3.25

Right

One of the ways to do this is to take out the common factor. You could also expand the square and remove the brackets of (2x - 2). Both will give you the same answer. I think expansion might be easier for you to understand, but the common factor method is shorter.

(2x - 2)^2 = 4x^2 - 8x + 4

4x^2 - 8x + 4 - 2x + 2

4x^2 - 10x + 6 The problem is factoring since neither of the first two equations work.

(2x - 2)(2x - 3) This is correct.

So the answer is D

The price of an item increased by 25%. If the price of the item after the increase is $2, find the original price.a) $1.50, b) $1.60, c) $1.75, d) $2.50, e) $3.20

Answers

25 % = 25/100 = 0.25

x ⇒ original price

$x + 0.25x = 2 \n 1.25x = 2 \n x = 2/1.25 \n x = 1.6$

The original price was $1.6

$x+0.25x=2\n 1.25x=2\n x=\$1.6\Rightarrow B$

A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 16 ft, express the area A of the window as a function of the width x of the window.

Answers

This answer uses NMF for which, if needed, the syntax can be found in my profile. Please ignore the LaTeX (the image), I cannot remove it/change it, and it is incorrect. The answer is: f(x)={π{{x}^{2}}/{4}+x(16-{πx}/{2}-x)}/{2}

Final answer:

The area A of a Norman window in terms of its width x can be expressed as the function A(x) = 8x - x²/2 - πx²/8, deriving this equation involves isolating variables from the given perimeter equation.

Explanation:

A Norman window has the shape of a rectangle topped with a semicircle. If we take x as the width of the window and y as the height of the rectangle, then the perimeter of the window is given by P = 2y + x + πx/2 = 16 (since the perimeter is the sum of the rectangle's two sides, the width, and half the circumference of a circle with diameter x).

From this equation, we can express y as a function of x: y = 8 - x/2 - πx/4.

Then, the area A of the window is the sum of the area of the rectangle and the area of the semicircle, which equals A = xy + πx²/8 = x(8 - x/2 - πx/4) + πx²/8 = 8x - x²/2 - πx²/4 + πx²/8.

Therefore, the area A of the window as a function of the width x of the window is A(x) = 8x - x²/2 - πx²/8.

Learn more about Function of Window Area here:

brainly.com/question/32386293

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Kimberley wants to plot a graph to show the price of different numbers of skateboards. She has to plot the following points:(1, 49.99), (2, 99.98), (3, 149.97), (4, 199.96)

Which of the following best describes how the x-axis should be labeled?

From 0 to 6 at intervals of 3

From 0 to 8 at intervals of 4

From 0 to 3 at intervals of 1

From 0 to 5 at intervals of 1

Answers

Based on the given above, the values of the x's are 1, 2, 3, 4. It is best to draw the x-axis and label them from 0 to 5 with an interval of 1 to allow the better plotting of the points. In addition, all the values of the x may be found in the labels of the x-axis.

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