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enyata [817]
2 years ago
12

The sum of 2 numbers is 49. The second number is 15 less than the first number. The first number is

Mathematics
2 answers:
liubo4ka [24]2 years ago
5 0

Answer:

x + y = 49

y = x - 15

Step-by-step explanation:

The sum of 2 numbers is 49 means that x+y = 49. (The two numbers are x and y, and the sum of them are 49.)

The second number is 15 less than the first number, means that y = x - 15 (The second number is y, and it is 15 less than x, which is the first number.)

Therefore the equations will be

x + y = 49

y = x - 15

ruslelena [56]2 years ago
4 0

Answer:

Step-by-step explanation:

The sum of 2 numbers is 49

x  +  y = 49

The second number is 15 less than the first number.

y = x - 15

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Artyom0805 [142]

Answer:

r =2.9985yd

Step-by-step explanation:

Given that the circumference of a circle is 2\pir

where r is the radius and \pi = 3.1415926....

You have

2\pir = 18.84 yd

2(3.1415926)r = 18.84 yd

6.2831r = 18.84yd

divide through by 6.2831

r = 2.9985yd = aprox 3yds

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2 years ago
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Liono4ka [1.6K]

Answer:

Correct.

Step-by-step explanation:

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2 years ago
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Alexandra [31]

First, let's turn all the numbers into improper fractions so that we can find the answer easier.

-2 \frac{1}{4} = r - \frac{4}{5}

-\frac{9}{4} = r - \frac{4}{5}

Now we have to isolate 'r'.

First, we have to make sure that the variable is on one side and all the numbers are on the other side.

To do this, we have to add \frac{4}{5} to both sides.

In order to do this, we need to ensure that both fractions have a common denominator.

-\frac{9}{4} = r - \frac{4}{5}

Ensure that the denominators are the same:

\frac{45}{20} = r - \frac{16}{20}

\frac{45}{20} + \frac{16}{20} = r

\frac{61}{20} = r

Good luck!

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3 years ago
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2 years ago
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Kryger [21]

Step-by-step explanation:

distance AB is (using Pythagoras with the coordinate differences between both points as sides and the distance as Hypotenuse = baseline of the triangle, the side opposite of the 90 degree angle):

distance² = (5 - -10)² + (7-2)² = 15² + 5² = 225 + 25 = 250

distance = sqrt(250)

to split this distance into a 3/2 ratio, we need actually 3+2=5 equal parts. and then AM gets 3 off these parts, and MB gets 2 of these parts.

so,

distance/5 = sqrt(250)/5 = sqrt(250/25) = sqrt(10)

so,

AM = 3×sqrt(10) = sqrt(90),

and

MB = 2×sqrt(10) = sqrt(40)

now, we need to calculate back using the same Pythagoras approach (calling the coordinates of M xm and ym)

AM² = (xm - -10)² + (ym - 2)² = (xm+10)² + (ym-2)² = 90

90 = xm² + 20xm + 100 + ym² - 4ym + 4

MB² = (5 - xm)² + (7 - ym)² = 40

40 = 25 - 10xm + xm² + 49 - 14ym + ym²

as a first approach we calculate AM² - MB²

90 = xm² + 20xm + ym² - 4ym + 104

- 40 = xm² - 10xm + ym² - 14ym + 74

----------------------------------------------------

50 = 0 + 30xm + 0 + 10ym + 30

20 = 30xm + 10ym

2 = 3xm + ym

ym = 2 - 3xm

this we use now e.g. in the first equation for AM.

90 = xm² + 20xm + (2-3xm)² - 4×(2-3xm) + 104

-14 = xm² + 20xm + 4 - 12xm + 9xm² - 8 + 12xm

-10 = 10xm² + 20xm

-1 = xm² + 2xm

xm² + 2xm + 1 = 0

solving such a squared equation

xm = (-b ± sqrt(b² - 4ac))/(2a)

a = 1

b = 2

c = 1

xm = (-2 ± sqrt(4 - 4))/2 = -1

only one combined solution (as a squared equation usually has 2 solutions).

ym = 2 - 3xm = 2 - 3×-1 = 2 + 3 = 5

so, M = (-1, 5)

8 0
2 years ago
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