Can anyone answer question 15 and 16

Answers

Answer 1

Answer: 15) (6x²y³)(3xy²z⁵) = 18x³y⁵z⁵

16) area of square with side lengths (x-3) units

area of a square = a²
A = (x-3)²
A = (x-3)(x-3)
A = x(x-3) -3(x-3)
A = x² - 3x -3x + 9
A = x² - 6x + 9

Area of a rectangle with a length of x units and a width of (x-5)units

Area of a rectangle = length * width
A = x * (x-5)
A = x(x-5)
A = x² - 5x

Value of x for Area of square and Area of rectangle to be equal.

Area of square = Area of rectangle
x² - 6x + 9 = x² - 5x
x² - x² - 6x + 5x = -9
-x = -9
x = -9/-1
x = 9

x² - 6x + 9 = x² - 5x
9² - 6(9) + 9 = 9² - 5(9)
81 - 54 + 9 = 81 - 45
90 - 54 = 36
36 = 36

Related Questions

Please help! Fast−6(2x−4)≤30.
"What temperatures are included in the temperature danger zone? A) 0°F (-18°C) to 41°F (5°C) B) 32°F (0°C) to 100°F (38°C) C) 41°F (5°C) to 140°F (60°C) D) 141°F (61°C) to 240°F (116°C)."
What are the excluded values of the function? y = 5/6x-72A. x=0 B. x=12 C. x=72 D. x=11
a student skipped a step when she tried to convert 26 hours into seconds, and she got the following incorrect result. what conversion ratio did she skip in this multiple-step conversion?
Find x if f(x) = 2x + 7 and f(x) = -1.

Convert 0.27¯¯¯¯¯ to a rational number in simplest form.(1 point) responses 127 start fraction 1 over 27 end fraction 2799 start fraction 27 over 99 end fraction 27100 start fraction 27 over 100 end fraction 311

Answers

Answer:

.272727.... = .27/(1 - .01) = .27/.99 = 27/99 = 3/11

Final answer:

To convert a repeating decimal to a rational number in simplest form, multiply the decimal by a power of 10 to eliminate the repeating part. Then, divide the result by the appropriate power of 10. For 0.27¯¯¯¯¯, the simplest form is 27/100.

Explanation:

To convert a repeating decimal to a rational number in simplest form, we can use the algebraic technique. Let x be the repeating decimal. Multiply x by a power of 10 so that all the repeating digits are to the left of the decimal point. Subtract x from the result to eliminate the repeating part. Finally, divide the result by the appropriate power of 10 to get the rational number in simplest form.

In this case, 0.27¯¯¯¯¯ is equal to 27¯¯¯¯¯/100¯¯¯¯¯. Now, let's simplify it by dividing both the numerator and denominator by their greatest common divisor, which is 1. The simplified form of 27¯¯¯¯¯/100¯¯¯¯¯ is 27/100.

Learn more about Converting repeating decimals to rational numbers here:

brainly.com/question/20104287

#SPJ2

If the points show below are collinear, what can you conclude about the lengths AB, BC, and AC? SOMEONE PLEASE ANSWWR THIS WILL GIVE BRAINLIEST!!!!

Answers

Answer:

$\sf\nAB+BC=AC$

Explanation:

$\sf\n\textsf{This is because the lengths of line segments AB, BC and AC are the distances}\n\textsf{between the points A,B and C respectively. And since A, B and C are collinear,}\n\textsf{these distances must add up to the total distance between A and C.}$

$\textsf{Here is a simple explanation:}\n\rightarrow \textsf{Suppose you are standing at point A and you want to walk on point C. You }\n\textsf{\ \ \ \ can either walk directly to point C (along line segment AC), or you can}\n\textsf{\ \ \ \ first walk to point B and then from point B to point C (along line segments}\n\textsf{\ \ \ \ AB and BC).}$

$\rightarrow \textsf{The total distance you walk in either case is the same. So, AB+BC=AC.}$

In the parking lot at Central, there are 21 blue cars and 75 cars total. What is the ratio of blue cars to cars that are not blue in simplest form?

Answers

Answer: The ratio of blue cars to cars that are not blue in simplest form = 7:18

Step-by-step explanation:

Given: There are 21 blue cars and 75 cars total.

Then, number of cars that are not blue = 75 -21 = 54

Now, the ratio of blue cars to cars that are not blue = $(21)/(54)=(7)/(18)$ [Divide numerator and denominator by 3.]

Hence, the ratio of blue cars to cars that are not blue in simplest form = 7:18

How do I get (tan^2(x)-sin^2(x))/tan(x) equal to (sin^2(x))/cot(x)

Answers

$LHS\n \n =\frac { \tan ^( 2 ){ x-\sin ^( 2 ){ x } } }{ \tan { x } } \n \n =\frac { 1 }{ \tan { x } } \left( \tan ^( 2 ){ x-\sin ^( 2 ){ x } } \right)$

$\n \n =\frac { \cos { x } }{ \sin { x } } \left( \frac { \sin ^( 2 ){ x } }{ \cos ^( 2 ){ x } } -\frac { \sin ^( 2 ){ x\cos ^( 2 ){ x } } }{ \cos ^( 2 ){ x } } \right) \n \n =\frac { \cos { x } }{ \sin { x } } \left( \frac { \sin ^( 2 ){ x-\sin ^( 2 ){ x\cos ^( 2 ){ x } } } }{ \cos ^( 2 ){ x } } \right)$

$\n \n =\frac { \cos { x } }{ \sin { x } } \cdot \frac { \sin ^( 2 ){ x\left( 1-\cos ^( 2 ){ x } \right) } }{ \cos ^( 2 ){ x } } \n \n =\frac { \cos { x } }{ \sin { x } } \cdot \frac { \sin ^( 2 ){ x\cdot \sin ^( 2 ){ x } } }{ \cos ^( 2 ){ x } } \n \n =\frac { \cos { x } \sin ^( 4 ){ x } }{ \sin { x\cos ^( 2 ){ x } } } \n \n =\frac { \sin ^( 3 ){ x } }{ \cos { x } }$

$\n \n =\sin ^( 2 ){ x } \cdot \frac { \sin { x } }{ \cos { x } } \n \n =\sin ^( 2 ){ x } \cdot \frac { 1 }{ \frac { \cos { x } }{ \sin { x } } } \n \n =\sin ^( 2 ){ x } \cdot \frac { 1 }{ \cot { x } } \n \n =\frac { \sin ^( 2 ){ x } }{ \cot { x } } \n \n =RHS$

Solve for
a. 7a-2b = 5a+b