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3 years ago

Solve the inequality 4(x – 3) – 7 < 2(x – 3).

Mathematics

2 answers:

enot [183]3 years ago

4 0

Answer:

x < 13/2

Step-by-step explanation:

4(x-3) -7: 4x - 19

4x - 19 < 2x-6

4x - 19 + 19 < 2x - 6 + 19

4x < 2x + 13

4x - 2x < 2x + 13 - 2x

2x < 13

2x/2 < 13/2

x < 13/2

natima [27]3 years ago

3 0

Answer:

{x}\lt\frac{{13}}{{2}}

Step-by-step explanation:

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We can get two different equations from this:

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Phoebe usually drives to work each day on a 12-mile road that is currently closed for construction. While the road is closed she

Mumz [18]

The total distance phoebe has to drive each day (round trip) while her usual route is closed is 42 miles

<h3>What is a Pythagoras theorem?</h3>

The square of the longest side is equal to the square of the sum of the othersides.

Before we can calculate the total distance, we will need to get the hypotenuse on both sides using the Pythagoras theorem as shown:

H^2= 12^2 + 9^2

H² = 144 + 81

H² = 225

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For the other hypotenuse

h² = 12² + 5²

h² = 144 + 25

h² = 169

h = 13 mils

The total distance = 5 + 15 + 9 + 13

The total distance = 42 miles

The total distance phoebe has to drive each day (round trip) while her usual route is closed is 42 miles

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2 years ago

If f(x)=3x-2 and g(x)=x^2+1, find f(g(-1)) and g(f(3))

julsineya [31]

Answer:

$f(g(-1))=4$

$g(f(3))=50$

Step-by-step explanation:

We know the definition of both functions: $f(x)=3x-2$ , and $g(x)=x^2+1$

A) In order to evaluate what $f(g(-1)) is$ , let's first investigate what g(-1) is using the definition for this function:

$g(x)=x^2+1\\g(-1)=(-1)^2+1\\g(-1)=1+1\\g(-1)=2$

Now let's find what f(2) is using f(x) definition: $f(x)=3x-2\\f(2)=3(2)-2\\f(2)=6-2\\f(2)=4$

B) In order to evaluate what $g(f(3)) is$ , let's first investigate what f(3) is using the definition for this function:

$f(x)=3x-2\\f(3)=3(3)-2\\f(3)=9-2\\f(3)=7$

Now let's find what g(7) is using the definition for this function:

$g(x)=x^2+1\\g(7)=(7)^2+1\\g(7)=49+1\\g(7)=50$

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3 years ago

Write an expression that represents the volume of a rectangular-shaped box with a length 3 inches less than its height and a wid

AfilCa [17]

The expression that represents the volume of a rectangular-shaped box is: A. x³ + x² - 12x.

<h3>What is the Volume of a Rectangular Prism?</h3>

A rectangular-shaped box is a rectangular prism. To find the volume of a rectangular-shaped box, we would apply the formula of the volume of a rectangular prism, which is expressed as: V = (length)(width)(height).

We are given the following dimensions of the rectangular-shaped box:

Let the height be represented as x

Height of the rectangular-shaped box = x in.

Length of the rectangular-shaped box = (x - 3) in.

Width of the rectangular-shaped box = (x + 4) in.

Plug in the values into the volume formula:

Volume of the rectangular-shaped box = (x - 3)(x)(x + 4)

Expand (x - 3)(x)(x + 4)

Volume of the rectangular-shaped box = x³ + x² - 12x.

Therefore, the expression that represents the volume of a rectangular-shaped box with the given dimensions is: A. x³ + x² - 12x.

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2 years ago