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3 years ago

Why are expressions 3(y-2)+2(y-2) and 5(y-2) equivalent

Mathematics

1 answer:

AlladinOne [14]3 years ago

6 0

3(y-2) + 2(y-2) = 5(y-2)

Both terms have the base (y-2), so they can be added together.
3 + 2 = 5

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Which algebraic expression could NOT represent the phrase below?

skad [1K]

Answer:

Step-by-step explanation:

because 4 and 3 are grouped together you would add them first. this would change the outcome of the problem.

6 0

3 years ago

Read 2 more answers

The length of a rectangle is 7 more than the width. The area is 744 sqaure yards, find the length and width of the rectangle

AVprozaik [17]

Answer:

Length of rectangle is 31 yards and Width is 24 yards.

Given:

The length of a rectangle is 7 more than the width.
The area is 744 sqaure yards

Solution:

Let's assume Width of rectangle be x and Length of rectangle be x + 7 respectively.

Using formula

$\\ \: \: \: \: \pink{ \dashrightarrow \: \: \: \: \sf { \underbrace{Area_{(Rectangle)} = Length × Width }}} \\ \\$

On Substituting the required values, we get;

$\\ \: \: \: \: \dashrightarrow \: \: \: \: \sf (x)(x + 7) = 744 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf {x}^{2} + 7x = 744 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf {x}^{2} + 7x - 744 = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf {x}^{2} + 31x - 24x - 744 = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf x(x + 31) - 24 (x + 31) = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf (x + 31)(x - 24) = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf x = 24 \: or \: - 31 \\ \\$

As we know that width of the rectangle can't be negative. So x = 24

<u>Hence</u>,

Width of rectangle = x = 24 yards
Length of the rectangle = x + 7 = 31 yards

$\therefore$ Length of rectangle is 31 yards<u> </u>and Width is 24 yards.

8 0

1 year ago

[30 POINTS] Please help!!!

Len [333]

Answer:

Part 1) $y=1.5x+5$

Part 2) $y=-(2/3)x-(11/3)$

Part 3) $y=0.25x+2.75$

Part 4) $y=-2x+5$

Part 5) $y=0.5x-1$

Part 6) The graph in the attached figure

Step-by-step explanation:

Part 1) we have

$m=3/2=1.5$

$point(-2,2)$

The equation of the line into point slope form is equal to

$y-y1=m(x-x1)$

substitute

$y-2=1.5(x+2)$

$y=1.5x+3+2$

$y=1.5x+5$

Part 2) we know that

If two lines are perpendicular

then

the product of their slopes is equal to minus one

$m1*m2=-1$

the slope of the line 1 is equal to

$m1=1.5$

Find the slope m2

$1.5*m2=-1$

$m2=-2/3$

Find the equation of the line 2

we have

$m2=-2/3$

$point(-7,1)$

The equation of the line into point slope form is equal to

$y-y1=m(x-x1)$

substitute

$y-1=(-2/3)(x+7)$

$y=-(2/3)x-(14/3)+1$

$y=-(2/3)x-(11/3)$

Part 3) we have

$m=1/4=0.25$

$point(1,3)$

The equation of the line into point slope form is equal to

$y-y1=m(x-x1)$

substitute

$y-3=0.25(x-1)$

$y=0.25x-0.25+3$

$y=0.25x+2.75$

Part 4) we have

$m=-2$

$b=5$ -----> y-intercept

we know that

The equation of the line into slope intercept form is equal to

$y=mx+b$

substitute the values

$y=-2x+5$

Part 5) we have that

The slope of the line 4 is equal to $-2$

the slope of the line perpendicular to the line 4 is equal to

$-2*m=-1\\m=(1/2)=0.5$

therefore

in this problem we have

$m=0.5$

$point(-2,-2)$

The equation of the line into point slope form is equal to

$y-y1=m(x-x1)$

substitute

$y+2=0.5(x+2)$

$y=0.5x+1-2$

$y=0.5x-1$

Part 6)

using a graphing tool

see the attached figure

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2 years ago

Need answer quick. No need for big explanantion

Leona [35]

Answer:

Step-by-step explanation:

4.30/40=$0.1075

Hope this helps :)

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3 years ago

It's the same possible answers for both questions

Anettt [7]

Answer:

q10, vertically opp angles

q11, corresponding angles

Step-by-step explanation:

Topic: angle properties

If you like to venture further, feel free to check out my insta (learntionary). It would be best if you could give it a follow. I'll be constantly posting math tips and notes! Thanks!

5 0

2 years ago