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exis [7]
2 years ago
9

Rational Numbers-

Mathematics
1 answer:
ioda2 years ago
5 0

Answer:

1.

-9 11/15

2. 11/24

3.

34/45

4. -5.05

5. -0.622

Step-by-step explanation:

1. -2 4/5 - 6 2/15

convert them to a common denominator and an improper fraction:

-2 4/5= 18/5=- 54/15 -6 2/15= 92/ 15

*15 is the other denominator, so you keep the numbers in the second number the same*

subtract: -54/15- 92/15

since you are subtracting a negative number it goes farther away from zero

-146/15 or -9 11/15

2. -5/12 + 7/8

convert them to a common denominator

-5/12=- 20/48 7/8= 35/40

add: -20/48+35/40

11/24

since you are adding a negative number it goes closer to zero or past zero:

3. 3 3/5 x 2/9

convert 3 3/5 to an improper fraction: 18/5

mulitply the two denominators and the two numerators

17/5 x 2/9= 34/45

This is also the simplest form.

4. Convert to a decimal. -5 1/20

keep the -5 beacuse that is a whole number

divide 1/20 to turn it to a decimal to get 0.05

5. Which number is the largest? -0.65, -0.622, -5/8

to find this you would have to convert all numbers to either a decimal or a fraction.

5/8 is 0.625

the one closest to zero is the largest which is -0.622

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NNADVOKAT [17]
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4 0
4 years ago
Prove the identity.
Delvig [45]

Answer:

D. Pythagorean

Step-by-step explanation:

Given the identity

cos²x - sin²x = 2 cos²x - 1.

To show that the identity is true, we need to show that the left hand side is equal to right hand side or vice versa.

Starting from the left hand side

cos²x - sin²x ... 1

According to Pythagoras theorem, we know that x²+y² = r² in a right angled triangle. Coverting this to polar form, we have:

x = rcostheta

y = rsintheta

Substituting into the Pythagoras firnuka we have

(rcostheta)²+(rsintheta)² = r²

r²cos²theta+r²sin²theta = r²

r²(cos²theta+sin²theta) = r²

(cos²theta+sin²theta) = 1

sin²theta = 1 - cos²theta

sin²x = 1-cos²x ... 2

Substituting equation 2 into 1 we have;

= cos²x-(1-cos²x)

= cos²x-1+cos²x

= 2cos²x-1 (RHS)

This shows that cos²x -sin²x = 2cos²x-1 with the aid of PYTHAGORAS THEOREM

5 0
4 years ago
16y=14+9y please answer 23 points
NeTakaya

Answer:

<h2>y = 2</h2>

Step-by-step explanation:

16y=14+9y\qquad\text{subtract}\ 9y\ \text{from both sides}\\\\16y-9y=14+9y-9y\\\\7y=14\qquad\text{divide both sides by 7}\\\\\dfrac{7y}{7}=\dfrac{14}{7}\\\\y=2

4 0
3 years ago
How do you solve the system of equations for y=2x-4 y=4x-10?
SVEN [57.7K]
Set the equal to each other

2x-4=4x-10
6=2x
x=3
y=2(3)-4
  =6-4
y =2
8 0
4 years ago
a city doubles its size every 64 years. if the population is currently 225,000 what will the population be in 128 years
ale4655 [162]

Answer:

450,000

Step-by-step explanation:

128/64:2

225,000 X 2: 450,000

4 0
3 years ago
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