The rectangle has a perimeter P of 58 inches.The length l is one more than 3 times the width w.write and solve a system of linear equations to find the length and width of the rectangle?

Answer:

Length(L)=22 inches

Width(W) = 7 inches

Step-by-step explanation:

GIven:-

Perimeter (p)=58 inches,

Length(L)= one more than 3 times the width(W)

Let, W=x ---------------------------------(equation 1

$L=3x+1$ -----------------------(equation 2)

Here x is unknown and to find the Width(W) we have to find the value of x.

Now,

Perimeter of rectangle(p) = 2 times length(L) + 2 times width(W)

$p=2L+2W$

$p=2(3x+1)+2x$ ----------------(from equation 1)

$58=6x+2+2x$ ----------------(given p=58 inches)

$58=8x+2$

$8x=58-2$

$8x=56$

$x=\frac{56}{8}$

$x=7$ ----------------------(equation 3)

Now substituting the value of equation 3 in equation 2.

$L=3x+1$

$L=(3\times 7)+1$

$L=21+1$

$L=22$

$L=22 inches$

as, $W=x$ -----------------------(from equation 1)

$W=7$ inches -------------------(equation 3)

Therefore, Length(L) = 22 inches and Width(W) = 7 inches.

7 0

3 years ago

A spinner marked A, B, C is spun then a 6-sided die is rolled. What is the probability of getting a B and then a 6.

BigorU [14]

Given:

A spinner marked A, B, C is spun then a 6-sided die is rolled.

To find:

The probability of getting a B and then a 6.

Solution:

We know that,

$\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}$

Total possible values for a spinner are 3. So, the probability of getting B, we get

$P(B)=\dfrac{1}{3}$

Total possible values for a die are 6. So, the probability of getting 6, we get

$P(6)=\dfrac{1}{6}$

Now, the probability of getting a B and then a 6 is

$P(B,6)=\dfrac{1}{3}\times \dfrac{1}{6}$

$P(B,6)=\dfrac{1}{18}$

The required probability is $\dfrac{1}{18}$ .

Therefore, the correct option is D.

5 0

2 years ago