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3 years ago

6

Verda used a sensor to measure the speed of a moving car at different times. At each time, the sensor measured the speed of the

car in both miles per hour and kilometers per hour. The table below shows her results

1 answer:

USPshnik [31]3 years ago

4 0

Answer:

Option A

Step-by-step explanation:

If the speed of a car in miles per hour (m) is proportional to the speed in kilometers per hour (k),

m ∝ k

m = ck

Here, c = Proportionality constant

Therefore, c = $\frac{m}{k}$ should be constant for each value given in the table.

For m = 11 and k = 17.699,

c = $\frac{11}{17.699}$

c = 0.6215

For m = 26 and k = 41.834,

c = $\frac{26}{41.834}$

c = 0.6215

For m = 34 and k = 54.706,

c = $\frac{34}{54.706}$

c = 0.6215

Therefore, c is constant for each value of m and k.

Option A will be the correct option.

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The most precise name for a quadrilateral ABCD is a parallelogram

Step-by-step explanation:

we have

A(2,3) B(7,2) C(6,-1) D(1,0)

Plot the quadrilateral'

using a graphing tool

The quadrilateral ABCD in the attached figure

Verify the length of the sides

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

step 1

Find distance AB

A(2,3) B(7,2)

substitute

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step 2

Find distance BC

B(7,2) C(6,-1)

substitute

$d=\sqrt{(-1-2)^{2}+(6-7)^{2}}$

$d=\sqrt{(-3)^{2}+(-1)^{2}}$

$d_B_C=\sqrt{10}\ units$

step 3

Find distance CD

C(6,-1) D(1,0)

substitute

$d=\sqrt{(0+1)^{2}+(1-6)^{2}}$

$d=\sqrt{(1)^{2}+(-5)^{2}}$

$d_C_D=\sqrt{26}\ units$

step 4

Find distance AD

A(2,3) D(1,0)

substitute

$d=\sqrt{(0-3)^{2}+(1-2)^{2}}$

$d=\sqrt{(-3)^{2}+(-1)^{2}}$

$d_A_D=\sqrt{10}\ units$

step 5

Compare the length sides

AB=CD

BC=AD

Opposite sides are congruent

<em>Verify the slope of the sides</em>

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

step 1

Find slope AB

A(2,3) B(7,2)

substitute

$m=\frac{2-3}{7-2}$

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step 2

Find slope BC

B(7,2) C(6,-1)

substitute

$m=\frac{-1-2}{6-7}$

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$m_B_C=3$

step 3

Find slope CD

C(6,-1) D(1,0)

substitute

$m=\frac{0+1}{1-6}$

$m=\frac{1}{-5}$

$m_C_D=-\frac{1}{5}$

step 4

Find slope AD

A(2,3) D(1,0)

substitute

$m=\frac{0-3}{1-2}$

$m=\frac{-3}{-1}$

$m_A_D=3$

step 5

Compare the slopes

$m_A_B=m_C_D$

$m_B_C=m_A_D$

The slope of the opposite sides are equal, that means, opposite sides are parallel

The slopes of consecutive sides are not opposite reciprocal, that means, consecutive sides are not perpendicular

therefore

The most precise name for a quadrilateral ABCD is a parallelogram

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3 years ago