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2 years ago

A triangle has one side measuring 16 inches and two sides measuring 13 inches. Is this triangle scalene?

Mathematics

2 answers:

Tema [17]2 years ago

4 0

Answer:

Step-by-step explanation:

A triangle is scalene when its sides have three different lengths. Your triangle has two sides with the same measure, so it is <em>isosceles</em>, not scalene.

nadya68 [22]2 years ago

3 0

No, because a scalene triangle has to have all sides that are different lengths. 2 sides being 13 inches would mean that the triangle has 2 sides that are equal, making it an isosceles triangle.

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A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 166 feet and a maximum height of 40 feet. Find

scoray [572]

Answer:

38.27775 feet

Step-by-step explanation:

The bridge has been shown in the figure.

Let the highest point of the parabolic bridge (i.e. vertex of the parabola) be at the origin, $O(0,0)$ in the cartesian coordinate system.

As the bridge have the shape of an inverted parabola, so the standard equation, which describes the shape of the bridge is

$x^2=4ay\;\cdots(i)$

where $a$ is an arbitrary constant (distance between focus and vertex of the parabola).

The span of the bridge = 166 feet and

Maximum height of the bridge= 40 feet.

The coordinate where the bridge meets the base is $A(83, -40)$ and $B(-83, -40).$

There is only one constant in the equation of the parabola, so, use either of one point to find the value of $a$ .

Putting $A(83,-40)$ in the equation (i) we have

$83^2=4a(-40)$

$\Rightarrow a=-43.05625$

So, on putting the value of $a$ in the equation (i), the equation of bridge is

$x^2=-172.225y$

From the figure, the distance from the center is measured along the x-axis, x coordinate at the distance of 10 feet is, $x=\pm 10$ feet, put this value in equation (i) to get the value of y.

$(\pm10)^2=-172.225y$

$\Rightarrow y=-1.72225$ feet.

The point $P_1(10,-1.72225)$ and $P_2(-10,-1.72225)$ represent the point on the bridge at a distance of 10 feet from its center.

The distance of these points from the x-axis is $d=1.72225$ feet and the distance of the base of the bridge from the x-axis is $h=40$ feet.

Hence, height from the base of the bridge at 10 feet from its center

$= h-d$

$=40-1.72225=38.27775$ feet.

8 0

2 years ago

Niu has decorated x cards. He started with 24 stickers, and he used 4 stickers per card. Which expressions can we use to describ

Kisachek [45]

Answer:

$24-4x$

Step-by-step explanation:

We have been given that Niu has decorated x cards. He started with 24 stickers and he used 4 stickers per card. So stickers used in x cards will be 4x.

As initial number of stickers was 24, so we can find number of stickers left after decorating x cards by subtracting number of stickers used in x cards from 24.

$\text{Number of stickers that Niu has left}=24-4x$