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3 years ago

-7 a rational or irrational number

Mathematics

1 answer:

kogti [31]3 years ago

6 0

Irrational number
There is a chart on goggle

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Find the positive base $b$ in which the equation $5_b \cdot 23_b = 151_b$ is valid.

DanielleElmas [232]

Answer:

b=7

Step-by-step explanation:

We want to determine the positive base b in which:

$5_b \cdot 23_b = 151_b$

The easiest way to approach this is to convert all the numbers to base 10.

$5_b=5Xb^0=5\\23_b =(2Xb^1)+(3Xb^0)=2b+3\\151_b=(1Xb^2)+(5Xb^1)+(1Xb^0)=b^2+5b+1\\Therefore:\\5_b \cdot 23_b = 151_b\\5(2b+3)=b^2+5b+1\\10b+15=b^2+5b+1\\b^2+5b+1-10b-15=0$

$b^2-5b-14=0$

Next, we factorize the resulting expression.

$b^2-5b-14=b^2-7b+2b-14=0\\b(b-7)+2(b-7)=0\\(b-7)(b+2)=0\\b-7=0\: or \: b+2=0\\b=7\: or \: b=-2$

The positive value of b for which the equality hold is 7.

3 0

3 years ago

The difference between two numbers is 12. Four times the larger number decreased by 25 equals 48 increased by 3 times the smalle

Lostsunrise [7]

Step-by-step explanation:

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Math

The difference between two numbers is 12. Three times the larger number is seven times the smaller. What are the two numbers?

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Expert Answers info

JEEW-M | CERTIFIED EDUCATOR

Let us say the two numbers are x and y and x>y.

The data we have are;

Difference between the numbers are 12.

3 times larger number is equal to 7 times smaller number.

Then we can write;

----(1)

----(2)

From (1) we can say

Then substituting to (2) gives;

Then;

7 0

3 years ago

Type the correct answer in the box.

Akimi4 [234]

Answer:

$\huge\boxed{-8+8i}$

Step-by-step explanation:

$2(-36-3i)+(5+2i)(12-2i)\\\\\text{use the distributive property and FOIL}\\\\=(2)(-36)+(2)(-3i)+(5)(12)+(5)(-2i)+(2i)(12)+(2i)(-2i)\\\\=-72-6i+60-10i+24i-4i^2\\\\i=\sqrt{-1}\to i^2=-1\\\\=-72-6i+60-10i+24i-4(-1)=-72-6i+60-10i+24i+4\\\\=(-72+60+4)+(-6-10+24)=-8+8i$