Pqrs is a rhombus . pq =12 cm , QS=16 cm . find the side of the rhombus

Your new flashlight uses a parabolic mirror which can be modeled by the equation (x – 2)² = 5(y + 1), where x and y are measured

Ksju [112]

The given equation is
(x - 2)² = 5(y + 1).

The given equation for the parabola is in the standard form
(x - h)² = 4p(y - k)
where
h = 2
4p = 5, so that p = 5/4
k = -1

The vertex is at
(h,k) or (2, -1)

The focus is located at
(h, k + p) or (2, -1 + 5/4) = (2, 1/4)

We should place the bulb at p = 5/4 from the vertex.

Answer: 1 1/4 or 1.25 cm

6 0

2 years ago

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The Venn diagram shows the results of two events resulting from rolling a number cube.

tankabanditka [31]

Answer:

$P(A|B)=\frac{2}{3}$

$P(A)*P(B)=\frac{1}{3}$

$P(A) =\frac{2}{3}$

$P(B) =\frac{1}{2}$ .

Step-by-step explanation:

We use the Venn diagram to calculate the desired probabilities.

Note that there are 6 possible results in the sample space

S = {1, 2, 3, 4, 5, 6}

Then note that in the region representing the intercept of A and B there are two possible values.

So

$P (A\ and\ B) = \frac{2}{6} = \frac{1}{3}$

In the region that represents event A there are 4 possible outcomes {4, 5, 1, 2}

So

$P(A) = \frac{4}{6} = \frac{2}{3}$

In the region that represents event B there are 3 possible outcomes {1, 2, 6}

So

$P(B) = \frac{3}{6} = \frac{1}{2}$ .

Now

$P(A | B)=\frac{P(A \ and\ B)}{P(B)}\\\\P(A | B)=\frac{\frac{1}{3}}{\frac{1}{2}}\\\\P(A|B)=\frac{2}{3}$

$P(A)*P(B)=\frac{2}{3}*\frac{1}{2}=\frac{1}{3}$

6 0

2 years ago

Carly tried to solve an equation step by step. 7a=28 Step 1: 7a/a = 28/7 Step 2: 7 = 4 Find Carly's mistake A: Step 1 B: Step 2

Murrr4er [49]

This are the right steps

Step 1: first you divide the both size by 7 because there is 7 a's

7a/7 = 28/7

Step 2: You solve the equation

7a/7= a. 28/7 = 4

So, the answer is a = 4

not 7 = 4

6 0

2 years ago

The following histogram presents the amounts of silver (in parts per million) found in a sample of rocks. One rectangle from the

gladu [14]

Answer:

The height of the missing rectangle is 0.15

Explanation:

The image attached has the mentioned histogram.

Such histogram presents the relative frequencies for the clases [0,1], [1,2],[2,3], [4,5], and [5,6] Silver in ppm.

Only the rectangle for the class [3,4] is missing.

The height of each rectangle is the relative frequency of the corresponding class.

The relative frequencies must add 1, because each relative frequency is calculated dividing the absolute class frequency by the total number in the sample; hence, the sum of all the relative frequencies is equal to the total absolute class frequencies divided by the same number, yielding 1.

In consequence, you can sum all the known relative frequencies and subtract from 1 to get the missing relative frequency, which is the height of the missing rectangle.

1. Sum of the known relative frequencies:

0.2 + 0.3 + 0.15 + 0.1 + 0.1 = 0.85

2. Missing frequency:

1 - 0.85 = 0.15

3. Conclusion:

The height of the missing rectangle is 0.15

4 0

2 years ago

A pool in the shape of a rectangle has a perimeter of 80feet. The pool is 8 feet less wide than it is long. Find the length and

Lyrx [107]

Answer:

The length and width of the pool = 24 ft and 16 ft

Step-by-step explanation:

Let length of pool be l and width of pool be w.

A pool in the shape of a rectangle has a perimeter of 80feet.

Perimeter of pool = 2 x ( l + w ) = 80 feet

That is

l + w = 40 ft -----------------------------------eqn 1.

The pool is 8 feet less wide than it is long.

l = 8 + w

l - w = 8 ft -----------------------------------eqn 2.

eqn 1 + eqn 2

2 l = 48

l = 24 ft

Substituting

24 + w = 40

w = 16 ft

The length and width of the pool = 24 ft and 16 ft

5 0

2 years ago

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