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3 years ago

A number b added to 10 is no more than -2

Mathematics

1 answer:

maksim [4K]3 years ago

7 0

Answer:

b + 10≤-2

b≤-12

Step-by-step explanation:

to get the inequality, just read the wording carefully. ex.: no more than = ≤

to get the answer, just leave the variable by itself

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Given f(x) and g(x) = f(k⋅x), use the graph to determine the value of k 2 -2 1/2 -1/2

Umnica [9.8K]

Answer:

Step-by-step explanation:

Using the graph we can notice something

let's take the abscissa -2 and -4

the ordinate that goes with -2 using g is 0
the ordinate that goes with -4 using f is 0

so we can say that :

f(-4)=g(-2)

wait we khow that g(x)=f(k*x)

so x= -2 then let's replace it in the expression : f(k*x)

we get f(-4)=g(-2)=f[k*(-2)]

let's solve the equation: -2k = -4

k = -4/-2

k=2

so finally we get k=2

let's check :

from the graph we get :

f(-2)=2
g(-1)=2

we have (-1)*2 = -2

so it is true

3 0

3 years ago

Y =9x+13 y =2x+48 Can you find the x and the y

Digiron [165]

9x+13=2x+48
-2x -2x
7x+13=48
-13 -13
7x=35
/7 /7
x=5

y=9(5)+13
y=45+13
y=58

4 0

2 years ago

What is 153 sixteenths as a mixed number

AURORKA [14]

To reduce a fraction divide the numerator and the denominator by their greatest common factor, GCF. ... The numerator and the denominator of the fraction are coprime numbers (no common prime factors, GCF = 1), the fraction cannot be reduced (simplified): irreducible fraction.

4 0

3 years ago

Use complete sentences to describe why √-1 ≠ -√1

tekilochka [14]

Well let's say that to compare these two numbers, we have to start with the definition first.

Definition

$\displaystyle \large{ {y}^{2} = x} \\ \displaystyle \large{ y = \pm \sqrt{x} }$

Looks like we can use any x-values right? Nope.

The value of x only applies to any positive real numbers for one reason.

As we know, any numbers time itself will result in positive. No matter the negative or positive.

Definition II

$\displaystyle \large{ {a}^{2} = a \times a = |b| }$

Where b is the result from a×a. Let's see an example.

Examples

$\displaystyle \large{ {2}^{2} = 2 \times 2 = 4} \\ \displaystyle \large{ {( - 2)}^{2} = ( - 2) \times ( - 2) = | - 4| = 4}$

So basically, their counterpart or opposite still gives same value.

Then you may have a question, where does √-1 come from?

It comes from this equation:

$\displaystyle \large{ {y}^{2} = - 1}$

When we solve the quadratic equation in this like form, we square both sides to get rid of the square.

$\displaystyle \large{ \sqrt{ {y}^{2} } = \sqrt{ - 1} }$

Then where does plus-minus come from? It comes from one of Absolute Value propety.

Absolute Value Property I

$\displaystyle \large{ \sqrt{ {x}^{2} } = |x| }$

Solving absolute value always gives the plus-minus. Therefore...

$\displaystyle \large{ y = \pm \sqrt{ - 1} }$

Then we have the square root of -1 in negative and positive. But something is not right.

As I said, any numbers time itself of numbers squared will only result in positive. So how does the equation of y^2 = -1 make sense? Simple, it doesn't.

Because why would any numbers squared result in negative? Therefore, √-1 does not exist in a real number system.

Then we have another number which is -√1. This one is simple.

It is one of the solution from the equation y^2 = 1.

$\displaystyle \large{ {y}^{2} = 1} \\ \displaystyle \large{ \sqrt{ {y}^{2} } = \sqrt{1} } \\ \displaystyle \large{ y = \pm \sqrt{1} }$

We ignore the +√1 but focus on -√1 instead. Of course, we know that numbers squared itself will result in positive. Since 1 is positive then we can say that these solutions exist in real number.

Conclusion

So what is the different? The different between two numbers is that √-1 does not exist in a real number system since any squared numbers only result in positive while -√1 is one of the solution from y^2 = 1 and exists in a real number system.

5 0

2 years ago

Read 2 more answers

What is the measure of each interior angle of the regular polygon pictured below? If necessary, round to the nearest tenth.

sammy [17]

Answer:

144

Step-by-step explanation:

Sum of interior angles:

180(n-2)

180(10-2)

1440

Measure of each interior angle:

1440/10=144

8 0

2 years ago