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2 years ago

A Mater Exam

Mathematics

1 answer:

astraxan [27]2 years ago

3 0

Answer:

The slope of the perpendicular line to the line is

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

Step-by-step explanation:

Step(i):-

Given that the line y =f(x) = 2x +6

⇒ y = 2x +6

comparing y =mx +c

The slope of the given line m =2

Step(ii):-

The slope of the perpendicular line = $\frac{-1}{m}$

The slope of the perpendicular line = $\frac{-1}{2}$

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Simplify by combining like terms: 3x - 10 + 2 + 6x

olya-2409 [2.1K]

Answer:

9x-8 is the simplified form

7 0

2 years ago

Can someone help me this is really confusing????? What is the solution set for the open sentence with the given replacement set?

IgorLugansk [536]

The answer is:

w^2 - 1 = w + 5

3^2 - 1 = w + 5

3^2 = 3(3) = 9

9-1 = 8

8 = 3 + 5

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6 0

3 years ago

A carpenter is assigned the job of expanding a rectangular deck where the width is one-fourth the length. the length of the deck

anzhelika [568]

Alright, lets get started.

Suppose the original deck size: width = x feet

the width is one-fourth the length given in question means length = 4 x feet

Means the originally area = $x * 4 x = 4 x^{2}$

Now the dimensions are changed.

New dimensions, width = (x + 6)

new length = (4x+10)

So, new area will be = $(x+6) * (4x+10) = 4x^{2} + 10 x + 24 x + 60 = 4x^{2} + 34 x + 60$

the area of the new rectangular deck is 128 ft2 larger than the area of the original deck, means

$4x^{2} + 128= 4x^{2} + 34 x + 60$

Subtracting $4x^{2}$ from both sides

$128 = 34 x + 60$

Subtracting 60 from both sides

$128 - 60 = 34 x + 60 - 60$

$68 = 34 x$

Dividing 34 in both sides

$\frac{68}{34} = \frac{34 x }{34}$

$x = 2$

Means width = 2 feet

Length would be = 4 time width = 4 * 2 = 8 feet

Means dimension of original deck would be = 2 feet and 8 feet :Answer

Hope it will help :)

8 0

3 years ago

5=1/3(2x+12) Solve for X in simplest form

garik1379 [7]

9514 1404 393

Answer:

x = 3/2

Step-by-step explanation:

Multiply by 3 and solve the resulting 2-step equation.

5 = (1/3)(2x +12)

15 = 2x +12 . . . . . . multiply by 3

3 = 2x . . . . . . . . . . subtract 12

3/2 = x . . . . . . . . . . divide by 2

4 0

2 years ago

The edge length of cube A is two times the edge length of cube B. How many times greater isthe volume of the cube A than the vol

allsm [11]

Answer:

<h2>8 times greater</h2>

Step-by-step explanation:

The formula of a volume of a cube:

$V=a^3$

a - edge length

-----------------------------------

The edge length of cube B is a.

The edge length of cube A is 2a.

Calculate the volumes:

$V_A=(2a)^3=2^3a^3=8a^3\\\\V_B=a^3$

How many times greater is the volume of the cube A than the volume of cube B?

Make the quotient:

$\dfrac{V_A}{V_B}=\dfrac{8a^3}{a^3}=8$

4 0

2 years ago