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4 years ago

What is the solution to the system of equations?

Mathematics

1 answer:

MatroZZZ [7]4 years ago

5 0

x is -4 and y is 15

$3x + y = 3 \\ 2x + y = 7 \\ \\ 3x + y = 3 \\ - 2x - y = - 7$

$x = - 4 \\ \\ y = 12 + 3 \\ y =15$

good luck

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Angelica uses the point (4,3) to represent the location of her house and uses the point (10,8) to represent the location of a ga

Allushta [10]

Answer:

Distance between Gas Station and House = 7.81 miles.

Step-by-step explanation:

Given: House location ( 4, 3 ) and Gas station location ( 10, 8)

On graph 1 unit = 1 mile.

To find: Distance between Gas Station and House

We use the Distance formula to find the distance between two points $(x_1,y_1)\:and\:(x_2,y_2)$

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

From given points and formula,

$Distance\:between\:house\:and\:gas\:station=\sqrt{(10-4)^2+(8-3)^2}$

= $\sqrt{(6)^2+(5)^2}$

= $\sqrt{36+25}$

= $\sqrt{61}$ units

Since, 1 unit = 1 mile

⇒ $\sqrt{61}\:unit=\sqrt{61}miles=7.81 miles$

Therefore, Distance between Gas Station and House = 7.81 miles.

5 0

3 years ago

Read 2 more answers

Use any method to solve the equation. If necessary, round to the nearest hundredth. PLEASE HELP SOON!!!

masha68 [24]

We have that
x² + x − 30 = 0

using a graph tool
see the attached figure

the solution is
x=-6
x=5

the answer is the option
b. 5, –6

8 0

3 years ago

The perimeter of a particular square and the circumference of a particular circle are equal. What is the ratio of the area of th

Tasya [4]

Ratio of the area of the square to the area of the circle is $\frac{\pi}{4} : 1$

In terms of fraction $\frac{\pi}{4}$

Solution:

Given that perimeter of a particular square and the circumference of a particular circle are equal

To find: ratio of the area of the square to the area of the circle

Let the side of square be "a" and radius of circle be "r"

The perimeter of square is given as:

Perimeter of square = 4a

The circumference of circle is given as:

Circumference of circle = 2πr

From given,

perimeter of a particular square and the circumference of a particular circle are equal

perimeter of a particular square = circumference of a particular circle

$4a = 2 \pi r\\\\a = \frac{\pi r}{2}$

We need to find the ratio of the area of the square to the area of the circle.

We know that,

$\text{ Area of the square }= a^2\\\\\text{ Area of the circle }= \pi r^2$

Ratio of area of square to area of circle = $a^2 : \pi r^2$

Substituting the value of $a = \frac{\pi r}{2}$ in above ratio,

Ratio of area of square to area of circle = $(\frac{\pi r}{2})^2 : \pi r^2$

On reducing to lowest terms we get,

⇒ $\frac{\pi^2 r^2}{4} : \pi r^2 = \frac{\pi}{4} : 1$

In terms of fraction we get,

$\frac{\pi}{4} : 1 = \frac{\frac{\pi}{4}}{1} = \frac{\pi}{4}$

Thus ratio of the area of the square to the area of the circle is $\frac{\pi}{4} : 1$

3 0

4 years ago

Percent change Original amount: 165 End amount: 222.75

Rzqust [24]

Answer:

35%

Step-by-step explanation:

The percent change is calculated as

$\frac{change}{original}$ × 100%

change = 222.75 - 165 = 57.75, thus

% change = $\frac{57.75}{165}$ × 100% = 0.35 × 100% = 35%

4 0

3 years ago

What is the solution to the linear equation 6k+10.5=3k+12

satela [25.4K]

Answer:

k = 0.5

Step-by-step explanation:

3 0

3 years ago