Type the correct answer in the box. Round your answer to two decimal places.

A rectangle and a triangle have the same area.

Ivanshal [37]

Area of a rectangle is length times width. Area of a triangle is one-half base times height. Now just plug in everything we know and set the equations equal to each other.

(6)(8) = 0.5(8)(h)

Solve for height

48 = 4h

h = 12 m

7 0

2 years ago

The width of a rectangle is the length minus 2 units. The area of the rectangle is 35 units. What is the width, in units, of the

Andrews [41]

Answer: width = 5 units

Step-by-step explanation:

Let L represent the length of the rectangle.

The width of a rectangle is the length minus 2 units. It means that the width of the rectangle is (L - 2) units.

The formula for determining the area of a rectangle is expressed as

Area = length × width

The area of the rectangle is 35 units. It means that

L(L - 2) = 35

L² - 2L = 35

L² - 2L - 35 = 0

L² + 5L - 7L - 35 = 0

L(L + 5) - 7(L + 5) = 0

L - 7 = 0 or L + 5 = 0

L = 7 or L = - 5

Since the length cannot be negative, then

L = 7 units

Width = 7 - 2 = 5 units

6 0

2 years ago

Jed deposited $400 into a bank that offers 3.9% interest rate, compounded daily. In how many years will his balance be $800?

Klio2033 [76]

17.7 years----------->Apex correct answer

8 0

2 years ago

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A piecewise function f(x) is defined as shown. f(x) = StartLayout enlarged left-brace 1st Row 1st column negative five-fourths x

SVEN [57.7K]

Answer:

A 2-column table has 3 rows. The first column is labeled x with entries 40, 160, 200. The second column is labeled y with entries 60, 15, 0.

Step-by-step explanation:

All of the tables have x=40 in the first column. The function value there is ...

f(x) = (-3/8)(40) +75 = -15 +75 = 60

Only the last table has y = 60 for x = 40.

__

A check of the other points in that table shows they are all on the same (second) piece of the graph, as required by the problem statement. Those points are marked with a purple x in the attachment.

8 0

2 years ago

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What is the probability of drawing yellow marble followed by a red marble from a bag containing 12 yellow marbles, 16 red marble

boyakko [2]

Option B

Probability of drawing yellow marble followed by a red marble is $\frac{32}{301}$

Solution:

Given that a bag containing 12 yellow marbles, 16 red marbles, and 15 green marbles

So total number of marbles = 12 + 16 + 15 = 43

To find: probability of drawing yellow marble followed by a red marble if the first marble is not replaced

The probability of an event is given as:

$probability =\frac{\text { number of favorable outcomes }}{\text { total number of possible outcomes }}$$

probability of drawing yellow marble followed by a red marble if the first marble is not replaced:

First we pick up yellow marble.

Number of favorable outcomes = 12 yellow marbles

Total number of possible outcomes = 43 marbles

$\text{ probability} = \frac{12}{43}$

Now we have to pick red marble

But first marble is not replaced

So we have 43 - 1 = 42 number of possible outcomes

Favorable outcomes = 16 red marbles

$\text{ probability} = \frac{16}{42}$

So probability of drawing yellow marble followed by a red marble is:

$\text[ probability } = \frac{12}{43} \times \frac{16}{42} = \frac{32}{301}$

Thus probability of drawing yellow marble followed by a red marble is $\frac{32}{301}$

7 0

2 years ago