Mathematics, 22.02.2020 05:40 tati7149

The length of a concrete slab is three more than three times the width. It's area is 330 square feet. What is the length of the longer side of the slab?

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Answer from: 17795

Width: 10.5 feet

Length: 31.5 feet

Step-by-step explanation:

Let x represent width of the concrete slab.

We have been given that the length of a concrete slab is three more than three times the width. So length of the slab would be .

We are also told that the area of slab is 330 square feet. We can represent this information in an equation as:

$x\cdot 3x=330$

3x^2=330

$x^2=\frac{330}{3}$

x^2=110

Now, we will take square root of both sides.

$\sqrt{x^2}=\sqrt{110}$

$x=10.488\approx 10.5$

Therefore, the width of slab is approximately 10.5 feet.

The length of the slab would be $3x\Rightarrow3(10.5)=31.5$ .

Therefore, the length of slab is approximately 31.5 feet.

Answer from: garzamatt7

the length of the longer side of the slab is 33 feet

Step-by-step explanation:

Let L represent the length(longer side) of the concrete slab.

Let W represent the width(shorter side) of the concrete slab.

The length of a concrete slab is three more than three times the width. This would be expressed as

L = 3W + 3

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

Area = Length × Width

It's area is 330 square feet. This means that

LW = 330 - - - - - - - - - - -1

Substituting L = 3W + 3 into equation 1, it becomes

W(3W + 3) = 330

3W² + 3W = 330

3W² + 3W - 330 = 0

Dividing through by 3, it becomes

W² + W - 110 = 0

W² + 11W - 10W - 110 = 0

W(W + 11) - 10(W + 11) = 0

W - 10 = 0 or W + 11 = 0

W = 10 or W = - 11

Since the width cannot be negative, then W = 10

L = 3W + 3 = (3 × 10) + 3

L = 30 + 3 = 33

Answer from: Quest

$\boxed{\bold{2240a^4u^{18}w^3x^4}}$

explanation:

remove parenthesis: $\bold{\left(a\right)=a,\: -\left(-a\right)=a}$

= $\bold{4u^9w^1\cdot \: 7x^4\cdot \: 4a^3w^2\cdot \: 8\cdot \frac{1}{2}a^1\cdot \: 5u^9}$

apply rule $\bold{a^1=a}$

= $\bold{4\cdot \: 7\cdot \: 4\cdot \: 8\cdot \: 5\cdot \frac{1}{2}a^3au^9u^9w^2wx^4}$

multiply fractions: $\bold{\: a\cdot \frac{b}{c}=\frac{a\: \cdot \: b}{c}}$

= $\bold{\frac{1\cdot \: 4u^9w\cdot \: 7x^4\cdot \: 4a^3w^2\cdot \: 8a\cdot \: 5u^9}{2}}$

$\bold{1\cdot \: 4u^9w\cdot \: 7x^4\cdot \: 4a^3w^2\cdot \: 8a\cdot \: 5u^9: \ 4480x^4w^3a^4u^{18}}$

= $\bold{\frac{4480a^4u^{18}w^3x^4}{2}}$

divide: $\bold{\frac{4480}{2}=2240}$

= $\bold{2240a^4u^{18}w^3x^4}$

mordancy.

Answer from: Quest

answer: - (a) $a_n=16+6n$

(b) 88 seats

step-by-step explanation:

given: in an auditorium, there are 22 seats in the first row and 28 seats in the second row.

thus first term= $a_1 =22$

second term= $a_2 =28$

the number of seats in a row continues to increase by 6 with each additional row.

⇒d= 6

a) given formula : $a_n=a_1+(n-1)(d)$

$a_n=22+(n-1)6\\\rightarrow\ a_n=22+6n-6\\\rightarrow\ a_n=16+6n$

b) let the number of seats (n) = 12

substitute n=12 in the explicit rule formed in (a)

$a_{12} = 16+6\times12\\\rightarrow\ a_{12}=16+72\\\rightarrow\ a_{12}=88\ seats$

∴there are 88 seats in 12 rows.

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