All categories

3 years ago

The length of a rectangle is 2 cm less than it’s width.If the area of the rectangle is 35 cm^2,find the width

Mathematics

1 answer:

Elan Coil [88]3 years ago

5 0

Answer:

7cm

Step-by-step explanation:

Area = Length x width

A = 35

w= L - 2

L = w+ 2

Now it becomes

35 = ( w+2) x w

35 = w^2 + 2w

W^2 + 2w - 35 = 0

By Factorization we have

( w + 7)( w-5)

w = 5cm

Since L = w + 2, we have

L = 5 + 2

= 7cm

You might be interested in

A gift bag is shaped like a rectangular prism and has a volume of 1152 cubic inches. The width of the bag is w, the length is 2w

Dafna11 [192]

1. You must use the formula for calculate the volume of a rectangular prism, which is:

V=(h)(l)(w)

V: It is the volumen of the rectangular prism (V=1152 inches³).
h: It is the height of the rectangular prism (h=18-w).
l:It is the lenght of the rectangular prism (l=2w+4).

2. When you substitute these calues into the formula, you obtain:

V=(h)(l)(w)
1152=(18-w)(2w+4)(w)
(18-w)(2w+4)(w)-1152=0

3. Then, you should mutiply them:

36w²-2w³+72w-4w²-1152=0
32w²-2w³+72w-1152=0

4. When you factor, you obtain:

2(w-16)(w-6)(w+6)

w1=16
w2=6
w3=-6

5. The problem says that the height is greater than the width, therefore, the widht is:

w=6 inches

6. The length is:

l=2w+4
l=2(6)+4
l=16 inches

7. And the height is:

h=18-w
h=18-6
h=12 inches

What are the dimensions of the bag?

The dimensions of the bag are:

l=16 inches
h=12 inches
w=6 inches

8 0

3 years ago

use the explicit formula an = a1 + (n - 1) * d to find the 500th term of the sequence below. 24,30,36,42,48,... A. 3018 B. 3042

marishachu [46]

Answer:

Option A.

Step-by-step explanation:

The given sequence is

24, 30, 36, 42, 48, ...

It is an AP. Here,

First term = 24

Common difference = 30-24 = 6

The given explicit formula for nth term is

$a_n=a_1+(n-1)d$

where, $a_1$ is first term, d is common difference.

Substitute $a_1=24, d=6 \text{ and }n=500$ in the above formula.

$a_{500}=24+(500-1)(6)$

$a_{500}=24+(499)(6)$

$a_{500}=24+2994$

$a_{500}=3018$

The 500th term of the sequence is 3018.

Therefore, the correct option is A.

3 0

3 years ago

A driving exam consists of 29 multiple-choice questions. Each of the 29 answers is either right or wrong. Suppose the probabili

Sholpan [36]

Answer and explanation:

Given : A driving exam consists of 29 multiple-choice questions. Each of the 29 answers is either right or wrong. Suppose the probability that a student makes fewer than 6 mistakes on the exam is 0.26 and that the probability that a student makes from 6 to 20 (inclusive) mistakes is 0.53.

Let X be the number of mistake

$P(X$

$P(6\leq X\leq 20)=0.53$

To find : The probability of each of the following outcomes.

a) A student makes more than 20 mistakes

i.e. $P(X>20)$

$P(X>20)=1-P(X\leq 20)$

$P(X>20)=1-(P(X\leq 5)+P(6\leq X\leq 20))$

$P(X>20)=1-(0.26+0.53)$

$P(X>20)=1-(0.79)$

$P(X>20)=0.21$

b. A student makes 6 or more mistakes

i.e. $P(X\geq 6)=1-P(X$

$P(X\geq 6)=1-0.26$

$P(X\geq 6)=0.74$

c. A student makes at most 20 mistakes

i.e. $P(X\leq 20)=1-P(X>20)$

Using 'a' part $P(X>20)=0.21$

$P(X\leq 20)=1-0.21$

$P(X\leq 20)=0.79$

d. Which two of these three events are complementary?

The complement of an event happening is the exact opposite: the probability of it not happening.

According to definition,

Option a and c are complementary events.

6 0

3 years ago

Read 2 more answers

Amelia is going to buy some cards for her friends.Each card costs $3.She finds a coupon for $2 off the entire purchase.Write an

dalvyx [7]

y = ( 3 * x ) - 2.

This is because the card costs for 3 $ and should be multiplied by the number of total cards she buys in that particular day. So 3 * x.

Now as she has got a 2$ off coupon, whatever the total is she gets 2 dollars off on that price. So we will subtract 2 at that time. FInally all this summed up would be equal to y.

7 0

3 years ago

If two angles are complimentary and one angle measures 34 degrees, what is the measure of the other angle?

allochka39001 [22]

Answer: 90º

Step-by-step explanation: complimentary angles are either of the two angles whose sum is 90º

8 0

2 years ago