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3 years ago

14

Terry is building a tool shed with a 90 square foot base and a length that is three more than twice the width. This can be model

ed by the equation (2w+15) (w-6)= 0. The length of Terry's tool shed is______ feet.

1 answer:

Lilit [14]3 years ago

8 0

Answer:

l = 15 feet

Step-by-step explanation:

l = 2w + 3

First you solve for the width(w)

(2w+15) (w-6) = 0

This means

2w+15=0 OR. w-6=0

First let’s solve 2w+15=0

2w = -15

w = -7.5

Width can’t be negative so that can’t be the answer. So we look at the second equation w-6=0

w= 6

Since we found the width now we can find the length by using the formula l = 2w + 3

= 2(6) + 3

= 12 + 3

= 15 feet

You can check this by using the given area which is 90.

A = lw = 15*6 = 90

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21. The expansion of the given expression is ...

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3 years ago

Can someone explain this step by step? I'm very confused on how to solve it. Thanks!

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Answer:

x = -8

Step-by-step explanation:

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3 0

2 years ago

Read 2 more answers

Let A be a set of numbers.

LUCKY_DIMON [66]

Answer:

a. closed under addition and multiplication

b. not closed under addition but closed under multiplication.

c. not closed under addition and multiplication

d. closed under addition and multiplication

e. not closed under addition but closed under multiplication

Step-by-step explanation:

a.

Let A be a set of all integers divisible by 5.

Let $x,y$ ∈A such that $x=5m\,,\,y=5n$

Find $x+y,xy$

$x+y=5m+5n=5(m+n)$

So, $x+y$ is divisible by 5.

$xy=(5m)(5n)=25mn=5(5mn)$

So,

$xy$ is divisible by 5.

Therefore, A is closed under addition and multiplication.

b.

Let A = { 2n +1 | n ∈ Z}

Let $x,y$ ∈A such that $x=2m+1\,,\,y=2n+1$ where m, n ∈ Z.

Find $x+y,xy$

$x+y=2m+1+2n+1=2m+2n+2=2(m+n+1)$

So,

$x+y$ ∉ A

$xy=(2m+1)(2n+1)=4mn+2m+2n+1=2(2mn+m+n)+1$

So,

$xy$ ∈ A

Therefore, A is not closed under addition but A is closed under multiplication.

c.

$Let A=\{2,5,8,11,14,...\}$

Let $x=2,y=5$ but $x+y=2+5=7$ ∉A

Also,

$xy=2(5)=10$ ∉A

Therefore, A is not closed under addition and multiplication.

d.

Let A = { 17n: n∈Z}

Let $x,y$ ∈ A such that $x=17n,y=17m$

Find x + y and xy

$x+y=17n+17m=17(n+m)$

$xy=(17m)(17n)=289mn=17(17mn)$

So,

$x+y,xy$ ∈ A

Therefore, A is closed under addition and multiplication.

e.

Let A be the set of nonzero real numbers.

Let $x,y$ ∈ A such that $x=-1,y=1$

Find x + y

$x+y=-1+1=0$

So,

$x+y$ ∈ A

Also, if x and y are two nonzero real numbers then xy is also a non-zero real number.

Therefore, A is not closed under addition but A is closed under multiplication.

4 0

3 years ago

4st^2-s^2 were s=5 and t=7

barxatty [35]

➣ Assignment: $\bold{Solve \ Equation: \ \left(4\left(5\cdot \:7^2\right)\right)-5^2}$

↔↔↔↔↔↔↔↔

➣ Answer: $\boxed{\bold{955}}$

↔↔↔↔↔↔↔↔

Explanation: ↓↓↓↓↓

↔↔↔↔↔↔↔↔

➤ [ Step One ] Follow PEMDAS Order Of Operations

$\bold{4\left(5\cdot \:7^2\right): \ 980}$

➤ [ Step Two ] Rewrite Equation

$\bold{4\left(5\cdot \:7^2\right)}$

➤ [ Step Three ] Calculate Within Parenthesis

$\bold{4\left(5\cdot \:7^2\right): \ 245}$

➤ [ Step Four ] Rewrite Equation

$\bold{4\cdot \:245}$

➤ [ Step Five ] Multiply

$\bold{4\cdot \:245: \ 980}$

➤ [ Step Six ] Rewrite Equation

$\bold{980-5^2}$

➤ [ Step Seven ] Calculate Exponents

$\bold{5^2: \ 25}$

➤ [ Step Eight ] Rewrite Equation

$\bold{980-25}$

➤ [ Step Nine ] Solve

$\bold{955}$

↔↔↔↔↔↔↔↔

$\bold{\rightarrow Mordancy \leftarrow}$

4 0

3 years ago

How much was your loan

leonid [27]

Answer:

Your loan was for $16,000.

Step-by-step explanation:

The formula for simple interest is i = prt, where p is the principal, r is the interest rate as a decimal fraction, and t is the time in years.

If i = prt, then p = i / (rt)

Here, p = ($1200) / 0.075 = $16,000

Your loan was for $16,000.

8 0

2 years ago