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3 years ago

Find the distance between the two points rounding to the nearest tenth (if necessary).

Mathematics

2 answers:

jeka943 years ago

4 0

Answer:

Step-by-step explanation:

$(-3,-3) =(x_1,y_1)\\ (-6,1)=(x_2,y_2)\\\\d = \sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}\\ \\d = \sqrt{(-6-(-3))^2+(1-(-3))^2}\\ \\d = \sqrt{(-6+3)^2+(1+3)^2}\\ \\d = \sqrt{(-3)^2 +(4)^2}\\ \\d = \sqrt{9+16}\\ \\d = \sqrt{25}\\ \\d =5$

Law Incorporation [45]3 years ago

3 0

(9,4) ...........................

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Which represents the solution(s) of the graphed system of equations, y = x2 + x – 2 and y = 2x – 2? (–2, 0) and (0, 1) (0, –2) a

Luda [366]

ANSWER

$(0,-2), (1,0)$

EXPLANATION

The first equation is

$y = {x}^{2} + x - 2$

The second equation is

$y = 2x - 2$

We equate both equations to get,

${x}^{2} + x - 2 = 2x - 2$

${x}^{2} + x - 2x - 2 + 2 = 0$

Simplify

${x}^{2} - x = 0$

Factor

$x(x - 1) = 0$

Either

$x = 0$

$x - 1 = 0$

$x = 1$

Put x=0 or x=1 into the second equation to get,

$y = 2(0) - 2 = - 2$

$y = 2(1) - 2 = 0$

Therefore the solutions are;

$(0,-2), (1,0)$

3 0

2 years ago

Read 2 more answers

Round to 2 decimal places *

EleoNora [17]

Answer: The circumference of the dome is therefore 149.15 feet or 47.5π feet

Step-by-step explanation:

A scale is basically referred to as the ratio of the dimensions of an object as represented in a draft to the real or true dimensions of the object being drafted.

The figure(s) on the left of the ratio sign represents the size and dimensions of the model with respect to the actual size or dimensions of the object. On the other hand, the figure on the right hand size represents the actual dimensions and size of the real object.

So, if an object is being drawn with the ratio, 1cm : 5cm it means that the size of the object is being reduced because every 5cm of the actual object will always be represented by 1cm in the drawing. If the object is being drawn with a scale of 5cm : 1cm then the actual size of the object will be increased in the drawing. That is, for every 1cm in the actual dimensions of the object, there will be a 5cm representation in the drawing.

Now, the architect draws with a scale of 0.25 inches : 1 foot. If the diameter of the hemispherical dome is 23.75 inches in the scale model, then the actual diameter of the dome is:

0.25 inches ------- 1 foot

23.75 inches ------- ? feet

= 23.75/0.25 × 1

= 95 feet

Therefore, the actual diameter of the dome is 95 feet. We are now required to find the circumference of this dome.

The dome is a hemisphere which literally means half of a sphere. So, if the formula for finding the circumference of a sphere is πd, that of a hemisphere will then be πd/2. Since the diameter is already known to be 95 feet, the circumference of the hemisphere =

(π × 95)/2

=47.5π feet

If π = 3.14, then the circumference = (3.14 × 95)/2 = 149.15 feet

The circumference of the dome is 149.15 feet or 47.5π feet

5 0

3 years ago

Find a formula for the described function. A rectangle has perimeter 16 m. Express the area A of the rectangle as a function of

Alex17521 [72]

Part A:

Let the length of one of the sides of the rectangle be L, then the length of the other side is obtained as follow.

Let the length of the other side be x, then

$2(L+x)=16 \\ \\ \Rightarrow L+x=8 \\ \\ \Rightarrow x=8-L$

Thus, if the length of one of the side is x, the length of the other side is 8 - L.

Hence, the area of the rectangle in terms of L is given by

$L(8 - L) = 8L-L^2$

Part B:

To find the domain of A

Recall that the domain of a function is the set of values which can be assumed by the independent variable. In this case, the domain is the set of values that L can take.

Notice that the length of a side of a rectangle cannot be negative or 0, thus L cannot be 8 as 8 - 8 = 0 or any number greater than 8.

Hence the domain of the area are the set of values between 0 and 8 not inclusive.

Therefore,

$dom(Area)=0\ \textless \ L\ \textless \ 8 \ or \ (0, 8)$