What is the decimal multiplier to increase by 2.5%

Manny wants to cover the windows in his home with either wood blinds or curtains. He has 35 windows that he would like to cover,

stepladder [879]

Answer:

$x + y \leq 35\\\\100x + 60y\leq2100\\\\x\geq 0\\\\y\geq 0$

Step-by-step explanation:

Call x the amount of blinds that Manny buys.

Let's call and the amount of curtains that Manny buys

There are only 35 windows, so the number of curtains and windows can not be greater than 35.

$x + y \leq 35\\x\geq 0\\y\geq 0$

Manny can only spend $ 2100

Then we can represent this by an inequality in the following way.

$100x \leq 2100$

and

$60y\leq 2100$

We can write this as a single inequality:

$100x +60y \leq2100$

Finally, the set of inequalities to model this problem is:

$x + y \leq 35\\\\100x + 60y\leq2100\\\\x\geq 0\\\\y\geq 0$

5 0

4 years ago

What is the slope of the line through (-9,6) and (-6,-9)?<br> Your answer must be exact.

iogann1982 [59]

The formula for slope is:

$m=\frac{y_{2}-y_{1}}{x_{2}-{x_{1}}$

So just plug in the values:

$m=\frac{-9-6}{-6+9}=\frac{-15}{3}=-5$

So $m=-5$ !

5 0

3 years ago

Why is it better to use the metric system, rather than the English system, in scientific measurement?

Fofino [41]

Answer: B!

Step-by-step explanation:

8 0

3 years ago

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If g(x) = -3x + 12, what is the solution set<br> if the domain of gis (-2, 0,2}?

disa [49]

Given:

The function is

$g(x)=-3x+12$

Consider the given domain of g is {-2,0,2}.

To find:

The solution set if the domain of g for the given domain.

Solution:

Domain is the set of input values and range is the set of output value.

We have,

$g(x)=-3x+12$

Domain of g is {-2,0,2}.

For x=-2,

$g(-2)=-3(-2)+12$

$g(-2)=6+12$

$g(-2)=18$

For x=0,

$g(0)=-3(0)+12$

$g(0)=0+12$

$g(0)=12$

For x=2,

$g(2)=-3(2)+12$

$g(2)=-6+12$

$g(2)=6$

Now, the solution set of the given domain of g is

$\{f(-2),f(0),f(2)\}=\{18,12,6\}$

Therefore, the solution set is {18,12,6}.

4 0

3 years ago

Tamara and Clyde got different answers when dividing 2x4 + 7x3 – 18x2 + 11x – 2 by 2x2 – 3x + 1. Analyze their individual work.

Umnica [9.8K]

The statements and their individual answers are not provided in the question. However, please check the explanation given below for the equation.

Step-by-step explanation:

The equation given is $\frac{2x^{4} + 7x^{3} + 18x^{2} + 11x -2}{2x^{2} - 3x + 1 }$

Divide the leading term of the dividend by the leading term of the divisor: $\frac{2x^{4} }{2x^{2} } = x^{2}$

Multiply it by the divisor: $x^{2} ({2x^{2} -3x +1) = 2x^{4} - 3x^{3} + x^{2}$

Subtract the dividend from the obtained result: $(2x^{4} + 7x^{3} + 18x^{2} + 11x - 2) - (2x^{4} - 3x^{3} + x^{2} ) = (10x^{3} + 17x^{2} + 11x -2)$

Divide the leading term of the obtained remainder by the leading term of the divisor: $\frac{10x^{3}}{2x^{2} } = 5x$

Multiply it by the divisor: $5x (2x^{2} - 3x + 1) = 10x^{3} - 15x^{2} + 5x$

Subtract the remainder from the obtained result: $(10x^{3} + 17x^{2} + 11x -2) - (10x^{3} - 15x^{2} + 5x) = (32x^{2} + 6x - 2)$

Divide the leading term of the obtained remainder by the leading term of the divisor: $\frac{32x^{2} }{2x^{2} } = 16$

Multiply it by the divisor: $16 (2x^{2} - 3x +1) = 32x^{2} - 48x +16$

Subtract the remainder from the obtained result: $(32x^{2} + 6x - 2) - (32x^{2} - 48x +16) = 54x - 18$

Since the degree of the remainder is less than the degree of the divisor, then we are done.

Therefore, $\frac{2x^{4} + 7x^{3} + 18x^{2} + 11x -2}{2x^{2} - 3x + 1 } = (x^{2} + 5x +16 + \frac{54x - 18}{2x^{2} - 3x +1})$

7 0

3 years ago

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