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3 years ago

A carpenter makes legs for 3-legged stools and 4-legged tables. He makes a total of 57 legs.

Mathematics

2 answers:

Nataly [62]3 years ago

8 0

19 legs for 3-legged stools

Viefleur [7K]3 years ago

6 0

4 legged tables : x 3 legged stools : y x + y = 20 y= 20 - x 4x + 3y = 68 Replace y by 20 - x so we only have one letter 4x + 3(20 - x) =68 4x + 60 - 3x =68 x + 60 = 68 x = 8 To find y replace x by 8 y = 20 - 8 y = 12 So you have 8 four legged chairs and 12 three legged stools. Hope I helped!

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If limx→3f(x)=7, which of the following must be true? I. f is continuous at x = 3 II. f is differentiable at x = 3

Viktor [21]

Without knowing anything else about $f(x)$ , neither of these need be true.

Suppose

$f(x)=|x-3|+7=\begin{cases}10-x&\text{for }x3\\0&\text{for }x=3\end{cases}$

Then (I) isn't true because, while the limit exists as $x\to3$ and is equal to 7, we have $f(3)=0\neq7$ , so $f(x)$ is not continuous there.

(II) also true because $f(x)$ is not differentiable at $x=3$ ; that is,

$\displaystyle\lim_{x\to3^-}f'(x)=\lim_{x\to3}(10-x)'=\lim_{x\to3}(-1)=-1$

but

$\displaystyle\lim_{x\to3^+}f'(x)=\lim_{x\to3}(x+4)'=\lim_{x\to3}1=1$

which means the derivative does not exist at $x=3$ .

3 0

3 years ago

If a rectangle has a area of 36x^3+24x^2-18x and the width is 6x what is the length

diamong [38]

Answer:

$lenght= 6 {x}^{2} + 4x - 3$

Step-by-step explanation:

$lenght = \frac{area}{width} \\ \\ = \frac{36 {x}^{3} + 24 {x}^{2} - 18x }{6x} \\ \\ = \frac{6x(6 {x}^{2} + 4x - 3) }{6x} \\ \\ lenght= 6 {x}^{2} + 4x - 3$

7 0

3 years ago

What's the number when the quotient of a number and -7 decreased by 2 is 10?

dsp73

Let's read through this and make an equation:
? ("number")
? / -7 ("quotient of a number and -7")
(? / -7) - 2 ("decreased by 2")
(? / -7) - 2 = 10 ("is 10")

Now we can solve:
(? / -7) - 2 = 10
? / -7 = 12
? = -84

The number is -84

3 0

4 years ago

What is the term for two fractions that are equal to each other?

ioda

Answer: Equivalent Fractions

For Example,
• 1/2 = 2/4
• 3/6 = 6/12
• 2/8 = 4/16

6 0

2 years ago

Someone plz help i need it in like 3 minutes

tamaranim1 [39]

Answer:

Step-by-step explanation:

A: -(3/-2)=-(-3/2)=3/2

B:3/-2=-3/2

C:-(-3/2)=3/2

D:-3/-2=3/2

8 0

3 years ago