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3 years ago

Write and solve an inequality to find the values of x for which the perimeter of the rectangle is less than 140.

Mathematics

1 answer:

Mashcka [7]3 years ago

3 0

Given:

Length of the rectangle = $x+4$

Width of the rectangle = $x$

The perimeter of the rectangle is less than 140.

To find:

The inequality for the given situation and solve it.

Solution:

We have,

$l=x+4$

$w=x$

We know that, the perimeter of a rectangle is

$P=2(l+w)$

$P=2(x+4+x)$

$P=2(2x+4)$

$P=4x+8$

It is given that the perimeter of the rectangle is less than 140.

$P$

$4x+8$

$4x$

Divide both sides by 4.

$x$

Therefore, the correct option is A because the sign of inequality is < and the solution of inequality is $x$ .

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The junior senator can do a labyrinth in 50 minutes. The senior senator can do a labyrinth in 30 minutes. Working together, how

vladimir2022 [97]

Answer:

$225\:\text{minutes}$

Step-by-step explanation:

To navigate through this problem, start by finding how much each senator can complete in a fixed amount of time. I'll choose 10 as it's the greatest common factor of 30 and 50.

In 10 minutes, the junior senator can complete $\frac{10}{50}=\frac{1}{5}$ of the labyrinth.

In 10 minutes, the senior senator can complete $\frac{10}{30}=\frac{1}{3}$ of the labyrinth.

Therefore, working together, they can complete $\frac{1}{5}+\frac{1}{3}=\frac{8}{15}$ of the labyrinth in 10 minutes. Thus, it will take them $\frac{15}{8}\cdot 10 \text{ minutes}=18.75\:\text{minutes}$ to complete one labyrinth.

The amount of time it take them to complete 12 labyrinths is then $18.75\cdot 12 =\boxed{225\:\text{minutes}}$

5 0

2 years ago

Solve for n. 39 = n − –12 n =

Cloud [144]

Answer:

Two negative make a positive so this equation is basically 39 = n + 12 so you need to subtract 12 from each side. This makes it n = 27

Hope this helps!

6 0

2 years ago

Nth term sequences, please may I get some help. 15 p.

Dovator [93]

Answer:

$(n+2)^2+6$

Step-by-step explanation:

Pattern 1 consists of

$3+3\times 3+3$ small squares (here n = 1 and $3\times 3=(1+2)\times (1+2)$ ).

Pattern 2 consists of

$3+4\times 4+3$ small squares (here n = 2 and $4\times 4=(2+2)\times (2+2)$ ).

Pattern 3 consists of

$3+5\times 5+3$ small squares (here n = 3 and $5\times 5=(3+2)\times (3+2)$ ).

Thus, pattern n consists of

$3+(n+2)\times (n+2)+3=6+(n+2)^2$ small squares.

3 0

3 years ago

The playing time X of jazz CDs has the normal distribution with mean 52 and standard deviation 7; N(52, 7).

natita [175]

Answer:

68% of jazz CDs play between 45 and 59 minutes.

Step-by-step explanation:

The correct question is: The playing time X of jazz CDs has the normal distribution with mean 52 and standard deviation 7; N(52, 7).

According to the 68-95-99.7 rule, what percentage of jazz CDs play between 45 and 59 minutes?

Let X = playing time of jazz CDs

SO, X ~ Normal( $\mu=52, \sigma^{2} =7$ )

The z-score probability distribution for the normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

Now, according to the 68-95-99.7 rule, it is stated that;

68% of the data values lie within one standard deviation points from the mean.

95% of the data values lie within two standard deviation points from the mean.

99.7% of the data values lie within three standard deviation points from the mean.

Here, we have to find the percentage of jazz CDs play between 45 and 59 minutes;

For 45 minutes, z-score is = $\frac{45-52}{7}$ = -1

For 59 minutes, z-score is = $\frac{59-52}{7}$ = 1

This means that our data values lie within 1 standard deviation points, so it is stated that 68% of jazz CDs play between 45 and 59 minutes.

6 0

3 years ago

Where would we find the point (–10,0)? A). y-axis B).quadrant ll C).x-axis D).quadrant lll

madreJ [45]

C because its not in any quadrant because the Y isn't stated so the point -10,0 is located on the X-axis

4 0

3 years ago

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