If the dimensions of an equilateral triangle are trebled, how is the area affected?

On a map 1/4 inch = 50 miles. If two cities appear 3 inches apart, how many

Mumz [18]

Answer:

Step-by-step explanation:

3⅛ inches × (50 miles)/(¼ inch) = 625 miles

4 0

2 years ago

Determine whether the point (2, 2) is a solution to the system of equations. Explain your reasoning in complete sentences. Prove

goblinko [34]

Answer:

(0,2) is the solution of the given functions.

Step-by-step explanation:

We have been given two functions f(x)=|x-1|+1 and g(x)=3x+2

To find the solution of the two functions mathematically, we will equate the given functions:

3x+2=|x-1|+1

3x+1=|x-1|

When we will open the modulus function we will have two values +, -

In positive case:

3x+1 =x-1

2x=-2

x=-1

Now, substitute x=-1 in g(x)=3x+2 we get

g(-1)=3(-1)+2=-1

Hence, (-1,-1) is the solution of the given functions.

In negative case:

Now, 3x+1=-(x-1)

3x+1=-x+1

4x=0

x=0

Now, put x=0 in g(x)=3x+2 we get

g(0)=3(0)+2=2

We have another solution: (0,2)

The point (2,2) is not the solution.

And graphically, the solution of two functions is their intersection point which is (0,2)

Hence, (0,2) is the solution of the function.

6 0

2 years ago

The ratio of the measure of the sides of the triangle is 1/6: 1/3: 1/4 if the perimeter of the triangle is 13.5 inches find the

marissa [1.9K]

Answer:

The shortest side of the triangle is 3 inches.

Step-by-step explanation:

Given:

The ratio of the measure of the sides of the triangle is 1/6: 1/3: 1/4.

The perimeter = 13.5 inches.

Now, to find the shortest side.

Let the one side be $\frac{1}{6}x$

And the second side be $\frac{1}{3}x$ .

And the third side be $\frac{1}{4}x$ .

According to question:

$\frac{1}{6}x+\frac{1}{3}x+\frac{1}{4}x=13.5$

⇒ $\frac{x}{6}+\frac{x}{3}+\frac{x}{4}=13.5$

Adding all the variables by taking common denominator we get:

⇒ $\frac{9x}{12}=13.5$

Multiplying both sides by 12 we get:

⇒ $9x=162$

Dividing both sides by 9 we get:

⇒ $x=18$

Thus, the sides of the triangle are:

1/6×18=3 inches.

1/3×18=6 inches.

1/4×18=9/2=4.5 inches.

Therefore, the shortest side of the triangle is 3 inches.

4 0

2 years ago

Sam and Amelia make bean bags for a tossing game. Amelia makes a line plot to show the weight, in pounds, of the bean bags.

frosja888 [35]

Answer:

amelia

Step-by-step explanation.

Amelia is correct because she has the heviest bag

4 0

1 year ago

247 is 38 percent of what amount? ❓

prisoha [69]

The question is asking that X times 38% will equal to 247. So we set up the equation:

$x * \frac{38}{100} = 247$

Then, we multiply both sides by $\frac{100}{38}$

and we get the answer is 650

7 0

2 years ago

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