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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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Trisha packs x boxes with 12 bottles in each box. The total number of bottles she packs is 216. Which equation and solution repr

LiRa [457]

Answer:

Number of boxes Trisha pack = 18 boxes

Step-by-step explanation:

Given:

Number of boxes Trisha pack = X

Number of bottles in each box = 12

Total number of bottle = 216

Find:

Number of boxes Trisha pack

Computation:

Total number of bottle = Number of boxes Trisha pack x Number of bottles in each box

216 = X × 12

X = 216 / 12

X = 18

Number of boxes Trisha pack = 18 boxes

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3 years ago

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kkurt [141]

Answer:

AQ1: Divide what she owed by 4

AQ2: -18

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Solve the following problem.

Serggg [28]

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3 years ago

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Identify the interval on which the quadratic function is positive.

Alenkasestr [34]

Answer:

$\textsf{1. \quad Solution: $1 < x < 4$,\quad Interval notation: $(1, 4)$}$

$\textsf{2. \quad Solution: $-2 < x < 4$,\quad Interval notation: $(-2, 4)$}$

Step-by-step explanation:

<h3>Question 1</h3>

The intervals on which a quadratic function is positive are those intervals where the function is above the x-axis, i.e. where y > 0.

The zeros of the quadratic function are the points at which the parabola crosses the x-axis.

As the given quadratic function has a negative leading coefficient, the parabola opens downwards. Therefore, the interval on which y > 0 is between the zeros.

To find the zeros of the given quadratic function, substitute y = 0 and factor:

$\begin{aligned}y&= 0\\\implies -7x^2+35x-28& = 0\\-7(x^2-5x+4)& = 0\\x^2-5x+4& = 0\\x^2-x-4x+4& = 0\\x(x-1)-4(x-1)&= 0\\(x-1)(x-4)& = 0\end{aligned}$

Apply the zero-product property:

$\implies x-1=0 \implies x=1$

$\implies x-4=0 \implies x=4$

Therefore, the interval on which the function is positive is:

Solution: 1 < x < 4
Interval notation: (1, 4)

<h3>Question 2</h3>

The intervals on which a quadratic function is negative are those intervals where the function is below the x-axis, i.e. where y < 0.

The zeros of the quadratic function are the points at which the parabola crosses the x-axis.

As the given quadratic function has a positive leading coefficient, the parabola opens upwards. Therefore, the interval on which y < 0 is between the zeros.

To find the zeros of the given quadratic function, substitute y = 0 and factor:

$\begin{aligned}y&= 0\\\implies 2x^2-4x-16& = 0\\2(x^2-2x-8)& = 0\\x^2-2x-8& = 0\\x^2-4x+2-8& = 0\\x(x-4)+2(x-4)&= 0\\(x+2)(x-4)& = 0\end{aligned}$

Apply the zero-product property:

$\implies x+2=0 \implies x=-2$

$\implies x-4=0 \implies x=4$

Therefore, the interval on which the function is negative is:

Solution: -2 < x < 4
Interval notation: (-2, 4)

3 0

1 year ago

A figurine of a lighthouse is shown. if the actual lighthouse is 30feet wide, how tall is the lighthouse

r-ruslan [8.4K]

Answer:

30× 60 ( 3×2= 6 + tens= 60 )= minimum- 180 fery

6 0

3 years ago