Answer:15 inches by 27 inches
Step-by-step explanation:
A rectangle has a width of 5 inches and a length of 9 inches. This means that the original length of the rectangle is 9 inches. The original width of the rectangle is 5 inches.
The rectangle was dlated by
a scale factor of 3. It means that the dimensions of the length of the rectangle and the width of the rectangle were increased 3 times.
The new length of the rectangle would be 3 × original length. It becomes 3×9 =27 inches
The new width of the rectangle would be 3 × original width. It becomes 3×5 =15 inches
Answer:
4 ssquare units
Step-by-step explanation:
The answer that I got was:
8y (y-3x)
because I divided everything by 8y and then just did simple math
hope this helps
<em><u>10 subtracted from the quotient of a number and -3 is at least -1 is:</u></em>
![\left(\frac{x}{-3}\right)-10\ge \:-1\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-27\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-27]\end{bmatrix}](https://tex.z-dn.net/?f=%5Cleft%28%5Cfrac%7Bx%7D%7B-3%7D%5Cright%29-10%5Cge%20%5C%3A-1%5Cquad%20%3A%5Cquad%20%5Cbegin%7Bbmatrix%7D%5Cmathrm%7BSolution%3A%7D%5C%3A%26%5C%3Ax%5Cle%20%5C%3A-27%5C%3A%5C%5C%20%5C%3A%5Cmathrm%7BInterval%5C%3ANotation%3A%7D%26%5C%3A%28-%5Cinfty%20%5C%3A%2C%5C%3A-27%5D%5Cend%7Bbmatrix%7D)
<em><u>Solution:</u></em>
<em><u>Given statement is:</u></em>
10 subtracted from the quotient of a number and -3 is at least -1
Quotient means reuslt of dividing two numbers
Let the number be "x"
quotient of a number and -3 = ![\frac{x}{-3}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B-3%7D)
Therefore,
10 subtracted from
is at least -1
at least means "less than or equal to"
<em><u>Which is translated into algebraic expression as:</u></em>
![(\frac{x}{-3}) - 10\geq -1](https://tex.z-dn.net/?f=%28%5Cfrac%7Bx%7D%7B-3%7D%29%20-%2010%5Cgeq%20-1)
<em><u>Solve the above inequality</u></em>
![\left(\frac{x}{-3}\right)-10\ge \:-1\\\\\mathrm{Add\:}10\mathrm{\:to\:both\:sides}\\\\\frac{x}{-3}-10+10\ge \:-1+10\\\\\mathrm{Simplify}\\\\\frac{x}{-3}\ge \:9\\\\Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)](https://tex.z-dn.net/?f=%5Cleft%28%5Cfrac%7Bx%7D%7B-3%7D%5Cright%29-10%5Cge%20%5C%3A-1%5C%5C%5C%5C%5Cmathrm%7BAdd%5C%3A%7D10%5Cmathrm%7B%5C%3Ato%5C%3Aboth%5C%3Asides%7D%5C%5C%5C%5C%5Cfrac%7Bx%7D%7B-3%7D-10%2B10%5Cge%20%5C%3A-1%2B10%5C%5C%5C%5C%5Cmathrm%7BSimplify%7D%5C%5C%5C%5C%5Cfrac%7Bx%7D%7B-3%7D%5Cge%20%5C%3A9%5C%5C%5C%5CMultiply%5C%3Aboth%5C%3Asides%5C%3Aby%5C%3A-1%5C%3A%5Cleft%28reverse%5C%3Athe%5C%3Ainequality%5Cright%29)
When we multiply or divide by negative number. we have to flip the inequality sign
![\frac{x\left(-1\right)}{-3}\le \:9\left(-1\right)\\\\\mathrm{Simplify}\\\\\frac{x}{3}\le \:-9\\\\\mathrm{Multiply\:both\:sides\:by\:}3\\\\\frac{3x}{3}\le \:3\left(-9\right)\\\\\mathrm{Simplify}\\\\x\le \:-27](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5Cleft%28-1%5Cright%29%7D%7B-3%7D%5Cle%20%5C%3A9%5Cleft%28-1%5Cright%29%5C%5C%5C%5C%5Cmathrm%7BSimplify%7D%5C%5C%5C%5C%5Cfrac%7Bx%7D%7B3%7D%5Cle%20%5C%3A-9%5C%5C%5C%5C%5Cmathrm%7BMultiply%5C%3Aboth%5C%3Asides%5C%3Aby%5C%3A%7D3%5C%5C%5C%5C%5Cfrac%7B3x%7D%7B3%7D%5Cle%20%5C%3A3%5Cleft%28-9%5Cright%29%5C%5C%5C%5C%5Cmathrm%7BSimplify%7D%5C%5C%5C%5Cx%5Cle%20%5C%3A-27)
Thus the solution of inequality is found
Answer:
Step-by-step explanation:
Simplifying
-14 + 1 = rt + -4n
Combine like terms: -14 + 1 = -13
-13 = rt + -4n
Reorder the terms:
-13 = -4n + rt
Solving
-13 = -4n + rt
Solving for variable 'n'.
Move all terms containing n to the left, all other terms to the right.
Add '4n' to each side of the equation.
-13 + 4n = -4n + 4n + rt
Combine like terms: -4n + 4n = 0
-13 + 4n = 0 + rt
-13 + 4n = rt
Add '13' to each side of the equation.
-13 + 13 + 4n = 13 + rt
Combine like terms: -13 + 13 = 0
0 + 4n = 13 + rt
4n = 13 + rt
Divide each side by '4'.
n = 3.25 + 0.25rt
Simplifying
n = 3.25 + 0.25rt