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3 years ago

2. A coffee shop sign is in the shape of a circle. The sign measures 18 inches across

Mathematics

1 answer:

Katen [24]3 years ago

3 0

Answer:J

Step-by-step explanation:

Area= pi times radios squared

3.14 times 9 squared

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Operations with rational expressions

Scorpion4ik [409]

$$\frac{50-2 w^{2}}{3 w^{2}+9 w-30} \cdot \frac{w^{2}+5 w-14}{6 w-30}=-\frac{w+7}{9}$

Solution:

Given expression:

$$\frac{50-2 w^{2}}{3 w^{2}+9 w-30} \cdot \frac{w^{2}+5 w-14}{6 w-30}$

To solve the given expression:

First simplify: $\frac{50-2 w^{2}}{3 w^{2}+9 w-30}$

$$\frac{50-2 w^{2}}{3 w^{2}+9 w-30}=-\frac{2(w+5)(w-5)}{3(w-2)(w+5)}$

Cancel the common factor (w + 5).

$$=-\frac{2(w-5)}{3(w-2)}$

Now substitute this in the given expression.

$$\frac{50-2 w^{2}}{3 w^{2}+9 w-30} \cdot \frac{w^{2}+5 w-14}{6 w-30}=-\frac{2(w-5)}{3(w-2)} \cdot \frac{w^{2}+5 w-14}{6 w-30}$

Multiply the fractions $\frac{a}{b} \cdot \frac{c}{d}=\frac{a \cdot c}{b \cdot d}$

$$=-\frac{2(w-5)\left(w^{2}+5 w-14\right)}{3(w-2)(6 w-30)}$

Factor the denominator $3(w-2)(6 w-30) =18(w-2)(w-5)$

$$=-\frac{2(w-5)\left(w^{2}+5 w-14\right)}{18(w-2)(w-5)}$

Cancel the common factor 2(w – 5).

$$=-\frac{w^{2}+5 w-14}{9(w-2)}$

Factor the numerator $w^{2}+5 w-14=(w-2)(w+7)$

$$=-\frac{(w-2)(w+7)}{9(w-2)}$

Cancel the common factor (w – 2).

$$=-\frac{w+7}{9}$

$$\frac{50-2 w^{2}}{3 w^{2}+9 w-30} \cdot \frac{w^{2}+5 w-14}{6 w-30}=-\frac{w+7}{9}$

3 0

3 years ago

Solve this equation using an algebraic method: (x + 4)( x - 4) = 9<br> Help me out please

Artyom0805 [142]

You have to FOIL out the (x+4)(x-4) and then subrtract away the 9 in order to get a quadratic that you can solve for x. As it is, you can't do it.
$(x+4)(x-4)= x^{2} -4x+4x-16= x^{2} -16$
Now if you move the 9 over with it, you get this:
$x^{2} -16-9=0$
which simplifies to
$x^{2} -25=0$
Now you can either solve this by recognizing that is the difference of perfect squares, or you can move the 25 over to the other side and take the square root of both sides, like this:
$x^{2} =25$
$\sqrt{ x^{2} } = \sqrt{25}$
$x=+/-5$

5 0

4 years ago

The ANSWERS and how to get them

Nookie1986 [14]

Answer: The answers for question 3 are x = 5, y = 13, and z = 10.

Now for question #4. The answer for those are a = 6.40312, b = 6.70820, c = 9.43398, d = 5.29150, e = 4.89898, f = 7.54983.

You would solve all these problems by using this formula a^2 + b^2 = c^2 with a and b representing two of the legs and c representing the hypotenuse (the longest side.) Simply input the respective numbers for the appropriate variables and solve for the missing variable.

Now lastly question #5. We just need to solve for the diagonal length. The answers are as follows. 5.66, 7.07, and 9.9. You get these answers by using the formula for finding a diagonal in a square which is d= $\sqrt{}$ 2a

6 0

4 years ago

Christina is building a slide for her kids. The ladder is 4 feet tall and the slide is 9 feet long. What is the distance between

xxMikexx [17]

Answer: 8.1ft

Step-by-step explanation:

It may help to draw it out but for this question you would have to use pythagoras' theorem.

The formula for the shorter side is a²=c²-b²

The height of this triangle is 4ft (b) and the hypotenuse (the diagonal that stretches from the top to the bottom) is 9ft (c).

When we put the numbers in the formula you get a²=9²-4²

9²=81

4²=16

a²=81-16

a²=65

Then because we want to find a on it's own you would have to square root 65 which is 8.1 (to the nearest tenth)

7 0

3 years ago

estimate the number of cubic yards of gravel needed to fill a 26' x 20' garage with a layer of gravel that is 18 inches deep, ro

Gemiola [76]

$26 \times 20 + 18$

5 0

3 years ago