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3 years ago

Let x = 0.147 and let y = 0.147.

Mathematics

1 answer:

Step2247 [10]3 years ago

5 0

Answer:

X is a rational number, y is not a rational number, and y is larger.

Step-by-step explanation:

The line above the 0.147 means that the number goes on forever and never stops. This is a characteristic of an irrational number. Rational numbers, however, do stop, so x is rational. Because y goes on forever, it has more values after the 0.147, making it larger.

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What is the general form of the equation of a circle with its center at (-2, 1) and passing through (-4, 1)?

AnnZ [28]

Answer:

$x^{2}+y^{2} +4x-2y+1=0$

Step-by-step explanation:

we know that

The general form of the equation of a circle is

$x^{2} +y^{2}+ Dx + Ey + F=0$

where D, E, F are constants

step 1

Find the radius of the circle

Remember that the distance from the center to any point on the circle is equal to the radius

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

$(-2,1)\\(-4,1)$

substitute the values

$r=\sqrt{(1-1)^{2}+(-4+2)^{2}}$

$r=\sqrt{(0)^{2}+(-2)^{2}}$

$r=2\ units$

step 2

Find the equation of the circle in standard form

$(x-h)^{2} +(y-k)^{2}=r^{2}$

In this problem we have

center ( -2,1)

radius r=2 units

substitute

$(x+2)^{2} +(y-1)^{2}=2^{2}$

$(x+2)^{2} +(y-1)^{2}=4$

Step 3

Convert to general form

$(x+2)^{2} +(y-1)^{2}=4\\ \\x^{2}+4x+4+y^{2}-2y+1=4\\ \\x^{2}+y^{2} +4x-2y+1=0$

7 0

4 years ago

10. I purchased a hair-dryer for 5,400 including 8% VAT. Find the price before VAT was added.

Semmy [17]

Answer:

4968

Step-by-step explanation:

432 is 8% of 5400 and after deducting 432 we get 4968.

8 0

3 years ago

The salaries Marc has earned in the past 4 years are shown.

Rina8888 [55]

Answer:

$28,348

Step-by-step explanation:

28,348 is the lowest number in the list.

8 0

4 years ago

A quadrilateral is a four sided polygon. True False

Viefleur [7K]

True

_____
"quad" is a prefix meaning 4.
"lateral" refers to sides.

"Quadrilateral" means "4-sided".

3 0

4 years ago

Read 2 more answers

Two car washes charge a basic fee plus a fee based on the number of extras that

mezya [45]

Answer:

a. The first car wash charges more for the basic fee

b. 6 extras must be chosen for the total cost to be the same

Explanation:

The complete question is shown in the attached diagram

The general form of the linear equation is:

y = mx + c where m is the slope and c is the y-intercept

The y-intercept represents the initial value which, in the given problem, is the basic fee

For the first car wash, we are given the equation:

y₁ = x + 9

Now, we will start by getting the equation for the second car wash:

1- getting the slope:

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{12-9}{4-2}=1.5$

The equation now is: y = 1.5x+c

2- getting the y-intercept:

To get the y-intercept, we will simply choose a point, substitute with it in the equation from 1 and solve for c. I will use point (2,9)

y = 1.5 x + c

9 = 1.5 (2) + c ............> c = 6

The equation for the second car wash is:

y₂ = 1.5x + 6

Part 1:

As mentioned above, the y-intercept represents the basic fee

For the first car wash:

y₁ = x + 9 ................> The basic fee is $9

For the second car wash:

y₂ = 1.5x + 6 ..............> The basic fee is $6

It is clear that the basic fee for the first car wash charges more for the basic fee

Part 2:

In both equations, x represents the number of extras. We want the total cost to be the same. So, we will simply equate y₁ and y₂ and solve for x

x + 9 = 1.5x + 6

1.5x - x = 9 - 6

0.5x = 3

x = 6

Let's verify:

For x = 6:

y₁ = x + 9 = 6 + 9 = $15

y₂ = 1.5x + 6 = 1.5(6) + 6 = $15

Total cost is the same. This means that 6 extras must be chosen for the total cost to be the same

Hope this helps :)

6 0

3 years ago