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kotegsom [21]
3 years ago
12

two automobiles leave a city at the same time and travel along straight highways that differ in direction by 84 degrees. if thei

r speeds are 60 mi/hr and 45 mi/hr, approximatly how far apart are the cars at the end of 20 minutes?

Mathematics
1 answer:
Gelneren [198K]3 years ago
7 0

Answer:

D = 23.7 miles

Step-by-step explanation:

Given data:

\theta=84 degrees

Time= 20 min = \frac{1}{3} hr

Distance of A = (60 mi/hr)\times \frac{1}{3} hr =20 mi

Distance of B =(45 mi/hr)\frac{1}{3} hr = 15 mi

Draw a triangle.

By using cosine formula we can determine the distance between them

D^2 = 20^2 + 15^2 - 2\times 20\times 15\times cos(84)

D^2 = 625 - 600 cos(84)

D^2 = 625 - 63.2

D^2 = 561.8

Thus D = 23.7 miles

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Figure M and it’s congruent image, figure N, are graphed on the coordinate plane below.
mixer [17]

The reflection over the line y = x - 3 will take figure M onto its congruent image, figure N.

<h3>What is geometric transformation?</h3>

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

As we can see in the graph there are two shapes are shown.

Figure M and Figure N

The sequence of transformations that will take figure M onto its congruent image, figure N is:

First, we need to draw a line that passes through (3, 0) and (0, -3)

The equation of the line is:

\rm y+3=\dfrac{\left(-3\right)}{-3}\left(x\right)

y + 3 = x

y = x - 3

The reflection over the above line will take figure M onto its congruent image, figure N.

Thus, the reflection over the line y = x - 3 will take figure M onto its congruent image, figure N.

Learn more about the geometric transformation here:

brainly.com/question/16156895

#SPJ1

7 0
2 years ago
Question 1- explain how Sheldon immediately knew howard was incorrect?
Dmitrij [34]

Answer:

Part 1) In the procedure

Part 2) In the procedure

Step-by-step explanation:

Part 1) Observing the graph

The roots are x=-1/2 and x=4

Remember that, the roots are the x-values when the value of y is equal to zero (the x-intercepts)

That's why Sheldon immediately realizes Howard's solution is incorrect

Part 2) we have

y=2x^{2}-7x-4

The formula to solve a quadratic equation of the form ax^{2} +bx+c=0 is equal to

x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}

in this problem we have

equate the equation to zero

2x^{2}-7x-4=0  

so

a=2\\b=-7\\c=-4

substitute

x=\frac{-(-7)(+/-)\sqrt{-7^{2}-4(2)(-4)}} {2(2)}

x=\frac{7(+/-)\sqrt{49+32}} {4}

Howard's error is in this step, is wrong with the sign of the number 7, is positive instead of negative

x=\frac{7(+/-)\sqrt{81}}{4}

x=\frac{7(+/-)9}{4}

x=\frac{7(+)9}{4}=4

x=\frac{7(-)9}{4}=-1/2

4 0
3 years ago
Anyone have any idea on how to solve this
Mkey [24]

Answer:

O y = (x + 5) (x + 3)

Step-by-step explanation:

y = (x + 4)² - 1

y = x² + 8x + 15

y = x² + 3x + 5x + 15

y = x(x + 3) + 5(x + 3)

y = (x + 5) (x + 3)

7 0
2 years ago
Read 2 more answers
Which expression is equivalent to (xy)z?<br><br>A (x+y)+z<br>B 2z(xy)<br>C x(yz)<br>D x(y+z)​
qwelly [4]

Answer:

c

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Y + 4x = 8 and 5x + 2y = 13
Ivanshal [37]
Y + 4x = 8
y = 8 - 4x
substitute 8 - 4x for y in the other equation.
5x + 2(8 - 4x) = 13
5x + 16 - 8x = 13
-3x = -3
x = 1
y = 8 - 4(1) = 4
4 0
3 years ago
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