ABD = ABC + CBD
So 6x + 27 + 7x - 9 = 96
Now we need to isolate x
13x + 18 = 96
13x = 88
x = 6
And then apply x to the angle we need to find ( CBD )
CBD = 6x + 27
CBD = 6(6) + 27
CBD = 36 + 27 = 63
Angle CBD = 63°

6 0

4 years ago

If p is inversely proportional to the square of q, and p is 22 when q is 8, determine p when q is equal to 2. 9 w

Amiraneli [1.4K]

Answer:

167.42

Step-by-step explanation:

p = 1/q²

22 = k* 1/8² .........k is the constant which we re finding now

k = 1408

p = 1408/2.9²

= 167.42

7 0

3 years ago

A swimming pool is being filled at the rate of 54 pt/min (pints per minute). How many quarts per hour is this?

Rainbow [258]

Answer:

Approximately $1620\; \text{quart} / \text{hour}$ .

Step-by-step explanation:

The given quantity was in the unit $\displaystyle \frac{\text{pint}}{\text{minute}}$ while the required quantity should have the unit $\displaystyle \frac{\text{quart}}{\text{hour}}$ . It would thus be necessary to use conversion factors of the following forms:

$\begin{aligned}\frac{\text{pint}}{\text{minute}} \times \underbrace{\frac{\text{minute}}{\text{hour}} \times \frac{\text{quart}}{\text{pint}}}_{\text{conversion factors}} &= \frac{\text{quart}}{\text{hour}} \end{aligned}$ .

Make use of the fact that:

$1\; \text{pint} = 0.5\; \text{quart}$ , and
$60\; \text{minute} = 1\; \text{hour}$ .

Rearrange the equation $1\; \text{pint} = 0.5\; \text{quart}$ to obtain the conversion factor:

$\begin{aligned} 1 &= \frac{0.5\; \text{quart}}{1\; \text{pint}}\end{aligned}$ .

Similarly, rearrange the equation $60\; \text{minute} = 1\; \text{hour}$ to obtain the conversion factor:

$\begin{aligned} 1 &= \frac{1\; \text{hour}}{60\; \text{minute}}\end{aligned}$ .

Combine both conversion factors and evaluate:

$\begin{aligned} & 54\; \frac{\text{pint}}{\text{minute}} \\ =\; & 54\; \frac{\text{pint}}{\text{minute}} \times \frac{0.5\; \text{quart}}{1\; \text{pint}} \times \frac{60\; \text{minute}}{1\; \text{hour}} \\ =\; & (54 \times 0.5 \times 60) \; \frac{\text{pint} \times \text{quart} \times \text{minute}}{\text{minute} \times \text{pint} \times \text{hour}} \\=\; & 1620\; \frac{\text{quart}}{\text{hour}}\end{aligned}$ .

5 0

3 years ago

Read 2 more answers

Match the inequality to the graph of its solution.

Lana71 [14]

The graph shows a number line marking all numbers less that 10.

Choice a:
c + 7 ≤ 3
c ≤ 3-7
c ≤ -4
Choice a is a wrong choice

Choice b:
c - 3 > 1
c > 1+3
c > 4
Choice b is a wrong choice

Choice c:
c - 7 < 3
c < 3+7
c < 10
Choice c is the correct choice

6 0

3 years ago