How do you find the perimeter of the window to the nearest tenth. Half the widows radius is 20.

The table shows the ratio of caramel corn to cheddar cornvin a bag. What is the constant propotionality?

zvonat [6]

Since we know is a proportionality, namely a multiplier on "x", we can simply use any of those points, say hmmm let's use 10, 15,

$\bf \qquad \qquad \textit{direct proportional variation}\\\\
\textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------\\\\
\textit{we know that }
\begin{cases}
x=10\\
y=15
\end{cases}\implies 15=k10\implies \cfrac{15}{10}=k\implies \cfrac{3}{2}=k$

8 0

3 years ago

Sandy has 27 roses, 9 daisies, and 18 tulips. She wants to arrange all the flowers in bouquets. Each bouquet has the same number

AlekseyPX

Answer:

The greatest number of flowers that could be in a bouquet is 9 flowers

Step-by-step explanation:

We solve the above question using Greatest Common Factor method. We find the factors of 27, 9 and 18. The greatest factor common to the 3 number is our answer.

The factors of 9 are: 1, 3, 9

The factors of 18 are: 1, 2, 3, 6, 9, 18

The factors of 27 are: 1, 3, 9, 27

Then the greatest common factor is 9.

The greatest number of flowers that could be in a bouquet is 9 flowers

5 0

3 years ago

How do you solve these equations? I don't want you to answer all of them, just tell me how to solve each type of equation on the

miss Akunina [59]

Answer:

8. Identify the common denominator; express each fraction using that denominator; combine the numerators of those rewritten fractions and express the result over the common denominator. Factor out any common factors from numerator and denominator in your result. (It's exactly the same set of instructions that apply for completely numerical fractions.)

9. As with numerical fractions, multiply the numerator by the inverse of the denominator; cancel common factors from numerator and denominator.

10. The method often recommended is to multiply the equation by a common denominator to eliminate the fractions. Then solve in the usual way. Check all answers. If one of the answers makes your multiplier (common denominator) be zero, it is extraneous. (10a cannot have extraneous solutions; 10b might)

Step-by-step explanation:

For a couple of these, it is helpful to remember that (a-b) = -(b-a).

$\dfrac{5}{x+2}+\dfrac{25-x}{x^2-3x-10}=\dfrac{5(x-5)}{(x+2)(x-5)}+\dfrac{25-x}{(x+2)(x-5)}\\\\=\dfrac{5x-25+25-x}{(x+2)(x-5)}=\dfrac{4x}{x^2-3x-10}$

___

$\displaystyle\frac{\left(\frac{x}{x-2}\right)}{\left(\frac{2x}{2-x}\right)}=\frac{x}{x-2}\cdot\frac{-(x-2)}{2x}=\frac{-x(x-2)}{2x(x-2)}=-\frac{1}{2}$

___

$\dfrac{3}{x-1}+\dfrac{6}{x^2-3x+2}=2\\\\\dfrac{3(x-2)}{(x-1)(x-2)}+\dfrac{6}{(x-1)(x-2)}=\dfrac{2(x-1)(x-2)}{(x-1)(x-2)}\\\\3x-6+6=2(x^2-3x+2) \qquad\text{multiply by the denominator}\\\\2x^2-9x+4=0 \qquad\text{subtract 3x}\\\\(2x-1)(x-4)=0 \qquad\text{factor; x=1/2, x=4}$