Rewrite in simplest terms: (3x+7)-(-4x+7)

Suppose the dimensions of a rectangle with a perimeter of 18 inches are quadrupled. Find the perimeter of the new rectangle in i

oee [108]

The new perimeter of the rectangle if the dimensions are quadrupled would be 72 inches.

<h3>What are the side lengths of the first triangle?</h3>

The perimeter is always obtained by adding all the sides. This means the possible side lengths of the original rectangle are:

5 inches + 5 inches + 4 inches + 4 inches

<h3>What are the side lengths of the new triangle?</h3>

5 inches x 4 = 20 inches

4 iches x 4 = 16 inches

<h3>What is the new perimeter?</h3>

20 + 20 + 16 +16= =72 inches

Learn more about perimeter in: brainly.com/question/6465134

6 0

2 years ago

Find the obtuse angle between the following pair of straight lines.

ioda

Given:

$y=-2$

$y=\sqrt{3}x-1$

To find:

The obtuse angle between the given pair of straight lines.

Solution:

The slope intercept form of a line is

$y=mx+b$ ...(i)

where, m is slope and b is y-intercept.

The given equations are

$y=0x-2$

$y=\sqrt{3}x-1$

On comparing these equations with (i), we get

$m_1=0$

$m_2=\sqrt{3}$

Angle between two lines whose slopes are $m_1\text{ and }m_2$ is

$\tan \theta=\left|\dfrac{m_2-m_1}{1+m_1m_2}\right|$

Putting $m_1=0$ and $m_2=\sqrt{3}$ , we get

$\tan \theta=\left|\dfrac{\sqrt{3}-0}{1+(0)(\sqrt{3})}\right|$

$\tan \theta=\left|\dfrac{\sqrt{3}}{1+0}\right|$

$\tan \theta=\pm \sqrt{3}$

Now,

$\tan \theta= \sqrt{3}$ and $\tan \theta=-\sqrt{3}$

$\tan \theta= \tan 60^\circ$ and $\tan \theta=\tan (180^\circ-60^\circ)$

$\theta= 60^\circ$ and $\theta=120^\circ$

$120>90$ , so it is an obtuse angle and $60$ , so it is an acute angle.

Therefore, the obtuse angle between the given pair of straight lines is 120°.

6 0

3 years ago

Mariyah bought 5 yards of fabric and a spool of thread for $22.75. If the spool of thread cost

Tems11 [23]

Answer:

$4.25

Step-by-step explanation:

Subtract the cost of the spool of thread from the total price:

22.75 - 1.50

= 21.25

Then, divide this by 5 to find the cost of fabric per yard:

= 4.25

So, the cost of the fabric per yard is $4.25

7 0

3 years ago

Read 2 more answers

1. There are 78 sophomores at a school. Each is required to take at least one year of either chemistry or physics, but they may

SVETLANKA909090 [29]

We are given that there are a total of 78 students. If we set the following variables:

$\begin{gathered} C=\text{students only in chemestry} \\ P=\text{students only in physics} \\ PC=\text{students in physics and chemistry} \end{gathered}$

Then, the sum of all of these must be 78, that is:

$C+P+PC=78$

Since there are 15 in chemistry and physics and 47 in chemistry, we may replace that into the equation and we get:

$47+P+15=78$

Simplifying:

$62+P=78$

Now we solve for P by subtracting 62 on both sides:

$\begin{gathered} 62-62+P=78-62 \\ P=16 \end{gathered}$

Therefore, there are 16 students in physics

3 0

1 year ago

Mona solved an equation incorrectly, as shown below:

CaHeK987 [17]

Mona subtracted 5 where she should have divided 5. If the equasion was. x+5=30 then she would have subtracted 5.

3 0

3 years ago

Read 2 more answers