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3 years ago

When two distinct circles lie in the same plane, what is the largest number of points at which they can intersect?

Mathematics

1 answer:

Rama09 [41]3 years ago

6 0

All the points if they lay on top of eachother

if they arent on top of eachother, they can intersect at 2 points

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What is the perimeter of a right triangle whose hypotenuse is the line segment A(-7, 5) B(1,0)

Svetradugi [14.3K]

Answer:

it depends

Step-by-step explanation:

The endpoints of the hypotenuse are insufficient to specify a right triangle. The perimeter can range from twice the distance between these points, about 18.868 units, to 1+√2 times the distance between these points, about 22.776 units.

___

In the attached figure, the colored numbers are the total length of the two legs of that color. The hypotenuse and its length are in black.

_____

The distance between two points is given by the formula ...

d = √((x2-x1)^2 +(y2 -y1)^2)

The perimeter will be the sum of the distances between pairs of points that define the vertices of the triangle. We need to know the third vertex to answer the question precisely.

5 0

3 years ago

Determine the coordinates of the vertices of the triangle to compute the area of the triangle using the distance formula (round

Karo-lina-s [1.5K]

Answer:

1. D. $50\text{ units}^2$

2. D. 45 units.

Step-by-step explanation:

We have been two graphs.

1. To find the area of our given triangle we will use distance formula.

$\text{Distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Upon substituting coordinates of base line of our triangle we will get,

$\text{Base length of triangle}=\sqrt{(15-5)^2+(5-15)^2}$

$\text{Base length of triangle}=\sqrt{(10)^2+(-10)^2}$

$\text{Base length of triangle}=\sqrt{100+100}$

$\text{Base length of triangle}=\sqrt{200}$

$\text{Base length of triangle}=10\sqrt{2}$

Now let us find the height of triangle similarly.

$\text{Height of triangle}=\sqrt{(20-15)^2+(10-5)^2}$

$\text{Height of triangle}=\sqrt{(5)^2+(5)^2}$

$\text{Height of triangle}=\sqrt{25+25}$

$\text{Height of triangle}=\sqrt{50}$

$\text{Height of triangle}=5\sqrt{2}$

$\text{Area of triangle}=\frac{\text{Base*Height}}{2}$

$\text{Area of triangle}=\frac{10\sqrt{2}*5\sqrt{2}}{2}$

$\text{Area of triangle}=\frac{50*2}{2}$

$\text{Area of triangle}=50$

Therefore, area of our given triangle is 50 square units and option D is the correct choice.

2. Using distance formula we will find the length of large side of triangle as:

$\text{Large side of rectangle}=\sqrt{(14-1)^2+(21-8)^2}$

$\text{Large side of rectangle}=\sqrt{(13)^2+(13)^2}$

$\text{Large side of rectangle}=\sqrt{169+169}$

$\text{Large side of rectangle}=\sqrt{338}$

$\text{Large side of rectangle}=13\sqrt{2}$

$\text{Small side of rectangle}=\sqrt{(4-1)^2+(5-8)^2}$

$\text{Small side of rectangle}=\sqrt{(3)^2+(-3)^2}$

$\text{Small side of rectangle}=\sqrt{9+9}$

$\text{Small side of rectangle}=\sqrt{18}$

$\text{Small side of rectangle}=3\sqrt{2}$

$\text{Perimeter of rectangle}=2(\text{Length + Width)}$

$\text{Perimeter of rectangle}=2(13\sqrt{2}+3\sqrt{2}}$

$\text{Perimeter of rectangle}=2(16\sqrt{2}}$

$\text{Perimeter of rectangle}=32\sqrt{2}$

$\text{Perimeter of rectangle}=45.2548339959390416\approx 45$

Therefore, the perimeter of our given rectangle is 45 units and option D is the correct choice.

8 0

4 years ago

Read 2 more answers

shirley owns a diner. she decides to charge $1.50 for 2 egga and one piece of toast a $.90 for one egg and one piece of toast. w

charle [14.2K]

Answer:

1 toast costs $0.30 and 1 egg cost $0.60

Step-by-step explanation:

Let price of 1 egg be $e$ and price of 1 toast be $t$

<u>"$1.50 for 2 eggs and one piece of toast":</u>

We can write $2e+t=1.50$

<u>"$.90 for one egg and one piece of toast":</u>

We can write $e+t=0.90$

Now, we can solve the first equation for t and substitute that into 2nd equation and solve for e:

$t=1.50-2e\\Also\\e+t=0.90\\Substituting:\\e+(1.50-2e)=0.90\\e+1.50-2e=0.90\\-e=0.90-1.50\\-e=-0.6\\e=0.6$

Now using the value of e (0.6) and putting it back in the first equation, we will get t:

$2e+t=1.50\\2(0.6)+t=1.50\\1.2+t=1.50\\t=1.50-1.20\\t=0.30$

Hence, 1 toast costs $0.30 and 1 egg cost $0.60

8 0

3 years ago

Apples costs $1.98 per pound, how much does 1.5 pounds of apples cost

4vir4ik [10]

Answer:

$2.97

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Look at the picture, pls help!!!

tangare [24]

Answer:

$c > 0\\t>0\\c+t\geq 60$

$6c+4t\leq300$

Step-by-step explanation:

Given that:

$c$ represents the number of cucumber plants

$t$ represents the number of tomato plants

Now, as per the question statement, we can write the inequalities.

The students need to plant some of each plants and at least 60 plants.

i.e.

$c > 0\\t>0\\c+t\geq 60$

Area required to plant each cucumber plant = 6 sq ft

Area required to plant each tomato plant = 4 sq ft

Area required to plant $c$ cucumber plants = 6 $c$ sq ft

Area required to plant $t$ tomato plants = 4 $t$ sq ft

Total area is at the maximum 300 square feet

$6c+4t\leq300$

Therefore, the inequalities to represent the situation are:

$c > 0\\t>0\\c+t\geq 60$

$6c+4t\leq300$

3 0

3 years ago