All categories

3 years ago

Leo reads 14 pages in 1/2 hour. What is the unit rate for pages per hour? For hours per page?

Mathematics

1 answer:

SVEN [57.7K]3 years ago

6 0

Answer:

1:28 | 1:1/28

Step-by-step explanation:

We can show the first two numbers as a ratio:

14:1/2

But we want that second number to be 1 so we can multiply by 1:

28:1 <------ Pages per hour

But now we need the left to be 1, so we divide by 28:

1/28:1

Then flip:

1:1/28

You might be interested in

Angles U and V are supplementary angles. The ratio of their measures is 7:13 Find the measure of each angle

GREYUIT [131]

If $u$ and $v$ are <span>supplementary angles, then

$u+v=180^{\circ}~~~~~\mathbf{(i)}$

The ratio of $u$ and $v$ is $\dfrac{7}{13}:$ <span>

$\dfrac{u}{v}=\dfrac{7}{13}\\\\\\ u=\dfrac{7v}{13}~~~~\mathbf{(ii)}$

Substitute $\mathbf{(ii)}$ into $\mathbf{(i)}:$

$\dfrac{7v}{13}+v=180^{\circ}\\\\\\ \left(\dfrac{7}{13}+1 \right )\cdot v=180^{\circ}\\\\\\ \left(\dfrac{7}{13}+\dfrac{13}{13} \right )\cdot v=180^{\circ}\\\\\\ \dfrac{20}{13}\cdot v=180^{\circ}\\\\\\ v=180^{\circ}\cdot \dfrac{13}{20}\\\\\\ \boxed{\begin{array}{c} v=117^{\circ} \end{array}}$

From $\mathbf{(i)},$ we find the measure of $u:$

$u=180^{\circ}-v\\\\ u=180^{\circ}-117^{\circ}\\\\ \boxed{\begin{array}{c} u=63^{\circ} \end{array}}$

</span></span>

7 0

3 years ago

Who knows how to sketch this kind of graph

Fofino [41]

The graph of f(x) = 0.5sin(4x) is sketched below

<h3>Graph of trigonometric functions </h3>

From the question, we are to sketch the graph of the given trigonometric function.

The given trigonometric function is

f(x) = 0.5sin(4x)

The graph of f(x) = 0.5sin(4x) is sketched below

Learn more on Graph of trigonometric functions here: brainly.com/question/4987799

#SPJ1

8 0

2 years ago

A 13foot lader i upagenst a tree the bottom of the ladder is 5 feet away form the tree how high is the ladder on the tree

SCORPION-xisa [38]

Think of the 13-ft length of the ladder as the hypotenuse of a right triangle. Represent the horiz. distance from foot of ladder to base of tree by x, or 5 ft.

Represent the vert. dist. from base of tree to top of ladder by y, which is unknown.

Then (13 ft)^2 = (5 ft)^2 + y^2, or

169 ft^2 = 25 ft^2 + y^2. This simplifies to y^2 = 144. Thus y = + 12 feeet.

Note: Please pay attention to your spelling: "lader i up agenst a tree" should be "the top of a 13-ft ladder is placed against a tree."

7 0

3 years ago

Find the exact value of sin2 theta given sin theta =5/13, 90°<theta <180°

Zepler [3.9K]

Now, we know that 90°< θ <180°, that simply means the angle θ is in the II quadrant, where sine is positive and cosine is negative.

$\bf sin(\theta )=\cfrac{\stackrel{opposite}{5}}{\stackrel{hypotenuse}{13}}\impliedby \textit{now let's find the \underline{adjacent side}}
\\\\\\
\textit{using the pythagorean theorem}\\\\
c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a\qquad 
\begin{cases}
c=hypotenuse\\
a=adjacent\\
b=opposite\\
\end{cases}$

$\bf \pm\sqrt{13^2-5^2}=a\implies \pm\sqrt{144}=a\implies \pm 12 =a \implies \stackrel{II~quadrant}{-12=a}
\\\\\\
therefore \qquad cos(\theta )=\cfrac{\stackrel{adjacent}{-12}}{\stackrel{hypotenuse}{13}}
\\\\
-------------------------------\\\\
sin(2\theta )\implies 2sin(\theta )cos(\theta )\implies 2\left(\frac{5}{13} \right)\left( \frac{-12}{13} \right)\implies -\cfrac{120}{169}$

3 0

3 years ago

Amy rode her bike 180 miles in 6 days, how many miles did she ride in a DAY?

Ipatiy [6.2K]

30. You’d do 180 divided by 6 :)

8 0

3 years ago

Read 2 more answers