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3 years ago

The scale of a map is 4 cm: 15 km. If the distance on the map between two cities is 7 cm, what is the actual distance?

Mathematics

1 answer:

djverab [1.8K]3 years ago

3 0

Answer:

26.25 km

Step-by-step explanation:

Step up a portion. Here, 4 cm is to 7 cm as 15km is to x km

4/7 = 15/x

Now solve for x by cross multiplying

4x = 105

x = 105/4 (divide by 4 on both sides)

x = 26.25 km (simplify)

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Which of the following would best be solved using factoring the difference of squares? 2² + 3x - 10 = 0 O 3r² + 12x = 8 2³ +52²

IgorC [24]

Given: Different equations

To Determine: Which would be best solved using difference of two squares

Solution

The factorization of a difference of two squares is given below

$a^2-b^2=(a-b)(a+b)$

Let us examine each of the given equation

$\begin{gathered} x^2+3x-10=0 \\ x^2-2x+5x-10=0 \\ x(x-2)+5(x-2)=0 \\ (x-2)(x+5)=0 \end{gathered}$ $\begin{gathered} 3x^2+12x=8 \\ 3x^2+12x-8=0 \end{gathered}$ $\begin{gathered} x^3+5x^2-9x-45=0 \\ x^2(x+5)-9(x+5)=0 \\ (x+5)(x^2-9)=0 \\ x^2-9=x^2-3^2=(x+3)(x-3) \\ Therefore \\ (x+5)(x+3)(x-3)=0 \end{gathered}$ $\begin{gathered} x^2-25=0 \\ x^2-5^2=0 \\ (x+5)(x-5)=0 \end{gathered}$

From the above,

$\begin{gathered} x^3+5x^2-9x-45=0 \\ AND \\ x^2-25=0 \end{gathered}$

The two equation above can be solved by difference of two square, but the equation below is the easiest solved using differnce of two square

x² - 25 = 0

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1 year ago

WILL GIVE BRAINLIEST AND 30 POINTS! Multiply the matrix representing the vertices of the rectangle to transform the figure. What

alina1380 [7]

Answer:

What are the coordinates of the resulting figure?

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Step-by-step explanation:

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4 years ago

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3 years ago

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bagirrra123 [75]

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3 years ago

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The area of a compact disc is 78.53 square centimeters. What is the radius of the disc? Use pi = 3.14

Tom [10]

Answer:

r = 5 cm

Step-by-step explanation:

A = πr²

78.53 = (3.14)r²

divide by 3.14

25 = r²

r = ±5

r = 5

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3 years ago