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Stels [109]
3 years ago
5

The Patel family looks at a map to plan their family vacation. They plan to travel from Smithville to Jonesville, which are 334

3 3 4 inches apart on the map. Then they plan to travel from Jonesville to Clarksville, which are 514 5 1 4 inches apart on the map. The scale on the map is 12 1 2 inch equals 4 miles. What is the actual distance the Patel family will travel by the time they reach Clarksville?
Mathematics
1 answer:
katovenus [111]3 years ago
6 0

Answer:

282.63 miles

Step-by-step explanation:

A scale drawing is a reduced form in terms of dimensions of an original image / building / object

the scale drawing is usually reduced at a constant dimension

scale of the drawing = original dimensions / dimensions of the scale drawing

Distance from Smithsville to Clarksville = distance from  Smithville to Jonesville + distance from Jonesville to Clarksville

distance from  Smithville to Jonesville = (334 x 4) / 12 = 111. 3 miles

distance from Jonesville to Clarksville =  (514 x 4) / 12 = 171.33

111.3 + 171.33 = 282.63

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Find the equation of the line between the points (10, – 5) and ( - 2,0).
Natali5045456 [20]

Answer <u>(assuming it can be in slope-intercept form)</u>:

y = -\frac{5}{12} x-\frac{5}{6}  

Step-by-step explanation:

1) First, find the slope of the line between the two points by using the slope formula, m  = \frac{y_2-y_1}{x_2-x_1}. Substitute the x and y values of the given points into the formula and solve:

m = \frac{(0)-(-5)}{(-2)-(10)} \\m = \frac{0+5}{-2-10} \\m=\frac{5}{-12}

Thus, the slope of the line is -\frac{5}{12}.

2) Next, use the point-slope formula y-y_1 = m (x-x_1) to write the equation of the line in point-slope form. Substitute values for m, x_1, and y_1 in the formula.

Since m represents the slope, substitute -\frac{5}{12} in its place. Since x_1 and y_1 represent the x and y values of one point the line intersects, choose any of the given points (it doesn't matter which one, it will equal the same thing) and substitute its x and y values into the formula as well. (I chose (-2,0), as seen below.) Then, isolate y and expand the right side in the resulting equation to find the equation of the line in slope-intercept form:

y-(0)=-\frac{5}{12} (x-(-2))\\y-0 = -\frac{5}{12} (x+2)\\y = -\frac{5}{12} x-\frac{5}{6}

3 0
3 years ago
If the blue radius below is perpendicular to the green chord and the segment BC is 7.6 units long, what is the length of the cho
galina1969 [7]

Answer:

The correct answer is A. 15.2 units

Step-by-step explanation:

The segment AB is congruent to the segment BC  eg AB≅BC Why?

We can prove it with the triangle congruent theorem, postulate side-side-angle

We are watching triangle ΔABO and triangle ΔCBO, they are congruent

first element side OB=OB - common side

second element side OA=OC=r - radius of the circle

third element angle ∡ABO≅∡CBO=90°

According to the postulate side-side-angle we can conclude that triangles

ΔABO≅ΔCBO (triangles are congruent)

If they are congruent all of their elements are also congruent and therefore also

side AB=BC  => AB+BC=AC,  which is chord  => 7.6+7.6=15.2 units

AC= 15.2 units ( chord )

Good luck!!!


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