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3 years ago

14

A dilation with a scale factor of 2 is applied to the three line segments shown. The resulting images are P′Q′¯¯¯¯¯¯¯, A′B′¯¯¯¯¯

¯¯, and M′N′¯¯¯¯¯¯¯¯¯.
What are the lengths of the images?
Drag the answer into the box to match each segment.

1 answer:

ivanzaharov [21]3 years ago

4 0

Answer:

Step-by-step explanation:

Formula to determine the scale factor,

Scale factor = $\frac{\text{Dimension of the image}}{\text{Dimension of the original}}$

2 = $\frac{P'Q'}{PQ}$

2 = $\frac{P'Q'}{2}$

P'Q' = 4 cm

Similarly, for the length of A'B',

2 = $\frac{A'B'}{AB}$

2 = $\frac{A'B'}{1.5}$

A'B' = 3 cm

For the length of M'N',

2 = $\frac{M'N'}{MN}$

2 = $\frac{M'N'}{3}$

M'N' = 6 cm

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Find the value of x and y

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3 years ago

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

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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 $a$ .

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

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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.

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

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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

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LUCKY_DIMON [66]

Ask your teachers if you can still turn them in

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3 years ago

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tia_tia [17]

Answer:

(a) Growth

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Given

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$r = 24\%$ --- rate

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The question says his followers increases each day by 24%.

Increment means growth.

<em />

<em>Hence, it is a growth problem</em>

Solving (b): Equation to represent the scenario.

Since the rate represents growth, the equation is:

$y = a(1 + r)^x$

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Kisachek [45]

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3 years ago