Monica has $4.75 on her

(1) 4p²q : 10pq²

tiny-mole [99]

Answer: (1) 2p: 5q.

(2) 3:10.

(3) 5:6.

Step-by-step explanation:

To find : Ratio

(1) 4p²q : 10pq²

$=\dfrac{4p^2q}{10pq^2}\\\\=\dfrac{2p^{2-1}}{5q^{2-1}}\\\\=\dfrac{2p}{5q}$

i.e. Simplified ratio of 4p²q : 10pq² is 2p: 5q.

(2) 9 months : 2½ years

1 year = 12 months

$2\dfrac{1}{2}\text{years}=\dfrac{5}{2}\text{years}\\\\=\dfrac{5}{2}\times12=30\text{ months}$

Now, 9 months : 2½ years = $\dfrac{9\text{ months}}{30\text{ months}}=\dfrac{3}{10}$

Hence, Simplified ratio of 9 months : 2½ years is 3:10.

(3) 5 m : 600 cm

1 m = 100 cm

So, 5m = 500 cm

Now, 5 m : 600 cm = $\dfrac{500\ cm}{600\ cm}=\dfrac{5}{6}$

Hence, Simplified ratio of 5 m : 600 cm is 5:6.

7 0

2 years ago

Which of the following are identities? A) sin^2x - cos^2x = 1 . B) sin^2x = 1 - cos^2x . C) tan^2x = 1 + sec^2x . D) cot^2x = cs

Aloiza [94]

B ) sin² x = 1 - cos² x
sin² x + cos² x = 1 ( correct )
D ) cot² x = csc² x - 1
cos²x / sin²x = 1/sin²x - 1 = (1-sin²x) / sin²x = cos²x/sin²x
Identities are B ) and D).

6 0

3 years ago

Ellis grew by 9 centimeters in the past year, and is now 1.4 meters tall.

horrorfan [7]

Answer:

1.31 meters

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

I need help please answer correct please

eduard

Answer:

I believe the answer is 8m.

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

What is the equation of the line that is parallel to the line 2x+3y=-8 and passes through the point (2,-2)?

Leya [2.2K]

Equation of line passing through (2, -2) and parallel to 2x+3y = -8 is $y=\frac{-2 x}{3}+\frac{-2}{3}$

<h3><u>Solution:</u></h3>

Need to write equation of line parallel to 2x+3y=-8 and passes through the point (2, -2)

Generic slope intercept form of a line is given by y = mx + c

where "m" = slope of the line and "c" is the y - intercept

Let’s first find slope intercept form of 2x+3y=-8 to get slope of line

$\begin{array}{l}{2 x+3 y=-8} \\\\ {=>y=\frac{-2 x-8}{3}} \\\\ {\Rightarrow y=-\frac{2}{3} x-\frac{8}{3}}\end{array}$

On comparing above slope intercept form of given equation with generic slope intercept form y = mx + c,

$\text {for line } 2 x+3 y=-8, \text { slope } m=-\frac{2}{3}$

We know that slopes of parallel lines are always equal

So the slope of line passing through (2, -2) is also $m=-\frac{2}{3}$

Equation of line passing through $(x_1 , y_1)$ and having slope of m is given by

$\left(y-y_{1}\right)=\mathrm{m}\left(x-x_{1}\right)$

$\text { In our case } x_{1}=2 \text { and } y_{1}=-2$

Substituting the values in equation of line we get

$(y-(-2))=-\frac{2}{3}(x-2)$

$\begin{array}{l}{\Rightarrow y+2=\frac{-2 x+4}{3}} \\\\ {=>3(y+2)=-2 x+4} \\\\ {=>3 y+6=-2 x+4} \\\\ {3 y=-2 x-2}\end{array}$

$y=\frac{-2 x}{3}+\frac{-2}{3}$

Hence equation of line passing through (2 , -2) and parallel to 2x + 3y = -8 is given as $y=\frac{-2 x}{3}+\frac{-2}{3}$

7 0

3 years ago