Which rate is equivalent to the unit rate of 13 miles per gallon?

Solve for x in the triangle. Round your answer to the nearest tenth.

hodyreva [135]

Answer:

x ≈ 11.7

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos26° = $\frac{adjacent}{hypotenuse}$ = $\frac{x}{13}$ ( multiply both sides by 13 )

13 × cos26° = x , then

x ≈ 11.7 ( to the nearest tenth )

4 0

2 years ago

To estimate the height of a house Katie stood a certain distance from the house and determined that the angle of elevation to th

Nata [24]

the height of the house is $408ft$ .

<u>Step-by-step explanation:</u>

Here we have , To estimate the height of a house Katie stood a certain distance from the house and determined that the angle of elevation to the top of the house was 32 degrees. Katie then moved 200 feet closer to the house along a level street and determined the angle of elevation was 42 degrees. We need to find What is the height of the house . Let's find out:

Let y is the unknown height of the house, and x is the unknown number of feet she is standing from the house.

Distance of house from point A( initial point ) = x ft

Distance of house from point B( when she traveled 200 ft towards street = x-200 ft

Now , According to question these scenarios are of right angle triangle as

At point A

⇒ $Tan32 =\frac{Perpendicular}{Base}= \frac{y}{x}$

⇒ $Tan32 = \frac{y}{x}$

⇒ $y=x(Tan32 )$ ..................(1)

Also , At point B

⇒ $Tan42 = \frac{y}{x-200}$

⇒ $y=(x-200)(Tan42)$ ..............(2)

Equating both equations:

⇒ $(x-200)(Tan42) = x(Tan32)$

⇒ $x(Tan42-Tan32)=Tan42(200)$

⇒ $x=\frac{Tan42(200)}{(Tan42-Tan32)}$

⇒ $x=653ft$

Putting $x=653ft$ in $y=x(Tan32 )$ we get:

⇒ $y=x(Tan32 )$

⇒ $y=653(Tan32 )$

⇒ $y=408ft$

Therefore , the height of the house is $408ft$ .

4 0

2 years ago

Louisa ran at an average speed of five miles per hour along an entire circular park path. Calvin ran along the same path in the

docker41 [41]

Answer:

15 miles

Step-by-step explanation:

Let $x$ be the miles in the circular park path, $t_{L}$ the time Louisa takes to finish and $t_{C}$ the time Calvin takes to finish both in hours.

Then $x$ , the longitude is equal to the velocity times the time used to finish. So

$x=5t_{L}$

$x=6t_{C}$

And the difference between Louisa's time and Calvin' time is 30 minutes, half an hour. So:

$t_{C}=t_{L}-0.5$

Three equations, three unknowns, the system can be solved.

Equalizing the equation with x :

$5t_{L}=6t_{C}$

In this last equation replace $t_{C}$ with the other equation and solve:

$5t_{L}=6(t_{L}-0.5)\\ 5t_{L}=6t_{L}-3\\ 3=6t_{L}-5t_{L}\\ 3=t_{L}\\ t_{L}=3$

With Louisa's time find x:

$x=5t_{L}\\ x=5(3)\\ x=15$

7 0

2 years ago

In circle A below, chord BC and diameter DAE intersect at F. If arc CD = 46° and arc BE = 78°, what is m_BFE? D B А

wel

Given:

Consider the below figure attached with this question.

In circle A below, chord BC and diameter DAE intersect at F.

The arc CD = 46° and arc BE = 78°.

To find:

The measure of angle BFE.

Solution:

According to intersecting chords theorem, if two chords intersect inside the circle then the angle on the intersection is the average of intercepted arcs.

Using intersecting chords theorem, we get

$m\angle BFE=\dfrac{1}{2}(m(arcCD)+m(arcBE))$