TRANSLATIONS ON THE COORDINATE PLANE

. A retailer sold 10 packs of pens in 3 days. There were 48 pens in each pack. He sold twice as many pens on Sunday than on Mond

Marizza181 [45]

Answer:

The number of pens sold on Monday is 107 pens

Step-by-step explanation:

total pack of pen sold by the retailer in 3 days = 10 packs

total number of pens in the 10 packs = 48 x 10 = 480 pens

let the number of pens sold on Monday = x

let the number of pens sold on Sunday = y

let the number of pens sold on Tuesday = z

He sold twice as many pens on Sunday than on Monday

y = 2x ------equation (1)

He sold 55 pens fewer on Tuesday than on Sunday

y = z + 55 ------equation (2)

total number of pens sold in the three days

y + z + x = 480 ------equation (3)

from equation (1) make x the subject of the formula

x = y/2

from equation (2) make z the subject of the formula

z = y - 55

substitute the value of x, and z into equation (3)

y + y/2 + y - 55 = 480

2y + y/2 = 480 + 55

5y/2 = 535

5y = 535 x 2

5y = 1070

y = 1070 / 5

y = 214

The number of pens sold on Monday is:

x = y / 2

x = 214 / 2

x = 107 pens

Thus, the number of pens sold on Monday is 107 pens

5 0

3 years ago

Each polygon pair is similar. Find the missing side length

ohaa [14]

I'll do problem 1 to get you started.

The vertical sides are 3 and x for the left and right figures.

The horizontal sides are 15 and 60 for the left and right figures.

The corresponding sides form fractions which are equal (due to the nature of the similar polygons)

3/x = 15/60

3*60 = x*15 ... cross multiply

180 = 15x

15x = 180

x = 180/15 .... divide both sides by 15

x = 12

----------

Another way you can see this is note how the jump from 15 to 60 is "times 4", so the jump from 3 to x must also be "times 4" to keep the same proportion

3 ---> x = 3*4 = 12

Or you could set up the proportion

60/15 = x/3

4 = x/3

x/3 = 4

x = 3*4

x = 12

-----------

<h3>Final Answer: 12</h3>

3 0

3 years ago

between 1995 and 2006, the population of samburg, usa(in thousands) can be modeled by f(x) = 0.35x(squared) - 2.1x+15.8 where x=

Juli2301 [7.4K]

$\bf f(x)=0.35x^2-2.1x+15.8\qquad 
\begin{cases}
x=\textit{year since 1995}\\
f(x)=\textit{population amount}
\end{cases}$

the equation is a quadratic one, and it has a positive coefficient on the leading term, meaning, is opening upwards, so it has a "burrow" for the vertex.

the minimum or lowest point for a quadratic opening upwards is, well, the vertex point :), the "x" value is the year, the "y" or f(x) value is the population, we're asked for the year, or the x-coordinate of the vertex

well $\bf \begin{array}{llll}
f(x)=&0.35x^2&-2.1x&+15.8\\
&\quad \uparrow &\quad \uparrow&\uparrow \\
&\quad a&\quad b &c
\end{array}
\\\\

\\\\
\qquad \textit{vertex of a parabola}\\ \quad \\
\qquad 

\left(\boxed{-\cfrac{{{ b}}}{2{{ a}}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)$

5 0

3 years ago

Now that the party is over, it’s time to help your friend write the thank you notes. You have $24 to purchase and mail 32 thank

Tasya [4]

0.75 Jordan went to the pond and died soon

6 0

3 years ago

Convert the rectangular coordinates (-9, 3V3) into polar form. Express the angle

Whitepunk [10]

Answer:

$(6\sqrt{3},\,\frac{5\pi}{6})$

Step-by-step explanation:

The radius r can be found from the relationship

$r^2=x^2+y^2\\r^2=(-9)^2+(3\sqrt{3})^2\\r^2=81+27=108\\r=\sqrt{108}\\r=6\sqrt{3}$

The point is in Quadrant II (-, +), so use the inverse cosine function to find the angle.

$\cos{\theta}=\frac{x}{r}=\frac{-9}{6\sqrt{3}}\\\cos{\theta}=-\frac{9}{6\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}\\\cos{\theta}=-\frac{9\sqrt{3}}{6\cdot3}\\\cos{\theta}=-\frac{\sqrt{3}}{2}\\\\\cos^{-1}\frac{-\sqrt{3}}{2}}=\frac{5\pi}{6}$

See the attached image.

7 0

3 years ago