Use the drawing tool(s) to form the correct answer on the provided graph.

Serjik [45]

The triangle ADC and the triangle CDB are similar. Therefore:
$\dfrac{x}{6}=\dfrac{6}{8}\ \ \ \ |cross\ multiply\\\\8x=6\cdot6\\\\8x=36\ \ \ |:8\\\\x=4.5$
Answer: A 4.5

6 0

2 years ago

The area of a rectangle has decreased by 2%.

MissTica

Answer:

The other side was decreased to approximately .89 times its original size, meaning it was reduced by approximately 11%

Step-by-step explanation:

We can start with the basic equation for the area of a rectangle:

l × w = a

And now express the changes described above as an equation, using "p" as the amount that the width is changed:

(l × 1.1) × (w × p) = a × .98

Now let's rearrange both of those equations to solve for a / l. Starting with the first and easiest:

w = a/l

now the second one:

1.1l × wp = 0.98a

wp = 0.98a / 1.1l

1.1 wp / 0.98 = a/l

Now with both of those equalling a/l, we can equate them:

1.1 wp / 0.98 = w

We can then divide both sides by w, eliminating it

1.1wp / 0.98w = w/w

1.1p / 0.98 = 1

And solve for p

1.1p = 0.98

p = 0.98 / 1.1

p ≈ 0.89

So the width is scaled by approximately 89%

We can double check that too. Let's multiply that by the scaled length and see if we get the two percent decrease:

.89 × 1.1 = 0.979

That should be 0.98, and we're close enough. That difference of 1/1000 is due to rounding the 0.98 / 1.1 to .89. The actual result of that fraction is 0.89090909... if we multiply that by 1.1, we get exactly .98.

6 0

2 years ago

What is the quotient

mario62 [17]

Answer:

The quotient is 3x - 11 + 60/(x + 5) ⇒ 2nd answer

Step-by-step explanation:

* We will use the long division to solve the problem

- The dividend is 3x² + 4x + 5

- The divisor is x + 5

- The quotient is the answer of the division

- If the divisor not a factor of a dividend, the quotient has

a remainder

* Lets solve the problem

- At first divide the first term in the dividend by the first term in

the divisor

∵ 3x² ÷ x = 3x

- Multiply the divisor by 3x

∴ 3x (x + 5) = 3x² + 15x

-Subtract this expression from the dividend

∴ 3x² + 4x + 5 - (3x² + 15x) = 3x² + 4x + 5 - 3x² - 15x = -11x + 5

- Divide the first term -11x in the new dividend by the first

term x in the divisor

∴ -11x ÷ x = -11

- Multiply the divisor by -11

∴ -11(x + 5) = -11x - 55

-Subtract this expression from the new dividend

∴ -11x + 5 - (-11x - 55) = -11x + 5 + 11x + 55 = 60

∴ The quotient is 3x - 11 with remainder = 60

* The quotient is 3x - 11 + 60/(x + 5)

5 0

2 years ago

Solve s=2(lw+lh+wh) for w

Scilla [17]

   s = 2(lw + lh + wh)

Divide each side by 2 :    s/2 = lw + lh + wh

Subtract 'lh' from each side:       s/2 - lh = lw + wh

Combine the 'w' terms:      s/2 - lh = w(l + h)

Divide each side by (l + h): (s/2 - lh) / (l + h) = w

7 0

2 years ago

A square carpet of side length 9 feet is designed with one large shaded square and eight smaller, congruent shaded squares, as s

Pepsi [2]

Answer:

$3\sqrt{3} + 72$

Step-by-step explanation:

I attached an image to aid the understanding of the question.

Looking at the image, we see that the 8 shaded parts are congruent, as affirmed in the question as well. And we are told that T = 3, this implies that the area of the square with T as it's side is 9ft². Since all the 8 squares are congruenrt, it means each square has its area to be 9. Therefore, the total area of the 8 shaded squares will be:

$9 \times 8 = 72ft^{2}$

It remains the area of the shaded square with side S.

From the question, we have the following ratio:

$\frac{9}{S} = \frac{S}{T}[\tex]But[tex]\frac{9}{S} = \frac{S}{3}[\tex]Multiplying through by 3S we have27 = S² and this gives:[tex]S = \sqrt{27} = 3\sqrt{3}$

I did not add ± because length is always positive, so the case of negative is eliminated.

Now the areas of S is $3\sqrt{3}$

Therefore, the total area of the shaded squares is

$3\sqrt{3} + 72$

3 0

2 years ago