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3 years ago

7

One case of books weighs 35 pounds. One case of magazines weighs 21 pounds. A book store wants to ship 72 cases of books and 94

cases of magazines to another store. What is the total weight of shipment?

1 answer:

gizmo_the_mogwai [7]3 years ago

4 0

The total weight would be 4,494 pounds

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Dentify on which quadratic function is positive.

Olin [163]

Answer:

$\textsf{$y = 2x^2 - 17x + 30$: \quad $\left(-\infty, \dfrac{5}{2}\right) \cup (6, \infty)$}$

$\textsf{$y = - x^2 - 6x - 8$: \quad $\left(-\infty, -4\right) \cup (-2, \infty)$}$

Step-by-step explanation:

A function is positive when it is <u>above the x-axis</u>, and negative when it is <u>below the x-axis</u>.

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

<u>Given quadratic equation</u>:

$y = 2x^2 - 17x + 30$

Factor the equation:

$\implies y = 2x^2 - 17x + 30$

$\implies y = 2x^2 - 5x-12x + 30$

$\implies y=x(2x-5)-6(2x-5)$

$\implies y=(x-6)(2x-5)$

The x-intercepts of the parabola are when y = 0.

To find the <u>x-intercepts</u>, set each factor equal to zero and solve for x:

$\implies x-6=0 \implies x=6$

$\implies 2x-5=0 \implies x=\dfrac{5}{2}$

Therefore, the x-intercepts are x = ⁵/₂ and x = 6.

The leading coefficient of the given function is positive, so the <u>parabola opens upwards</u>.

The function is positive when it is <u>above the x-axis</u>.

Therefore, the function is positive for the values of x less than the smallest x-intercept and more than the largest x-intercept:

$\textsf{Solution: \quad $x < \dfrac{5}{2}$ \;and \;$x > 6$}$

$\textsf{Interval notation: \quad $\left(-\infty, \dfrac{5}{2}\right) \cup (6, \infty)$}$

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

<u>Given quadratic equation</u>:

$y = - x^2 - 6x - 8$

Factor the equation:

$\implies y = - x^2 - 6x - 8$

$\implies y = -(x^2 +6x +8)$

$\implies y = -(x^2 +4x +2x+8)$

$\implies y = -((x(x+4)+2(x+4))$

$\implies y = -(x+4)(x+2)$

The x-intercepts of the parabola are when y = 0.

To find the <u>x-intercepts</u>, set each factor equal to zero and solve for x:

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

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

Therefore, the x-intercepts are x = -4 and x = -2.

The leading coefficient of the given function is negative, so the <u>parabola opens downwards</u>.

The function is negative when it is <u>below the x-axis</u>.

Therefore, the function is negative for the values of x less than the smallest x-intercept and more than the largest x-intercept:

$\textsf{Solution: \quad $x < -4$ \;and \;$x > -2$}$

$\textsf{Interval notation: \quad $\left(-\infty, -4\right) \cup (-2, \infty)$}$

4 0

1 year ago

Read 2 more answers

Y=-3x-6<br> y=-4x-9<br><br> Solve using substitution please

Black_prince [1.1K]

-3x-6=-4x-9

x - 6 = -9

x = -3

y = -3(-3)-6= 9 - 6 = 3

3 0

3 years ago

Kamila [148]

Answer:

x = 2

Step-by-step explanation:

Since the triangles are similar then corresponding sides are in proportion, that is

$\frac{AB}{DE}$ = $\frac{BC}{EF}$ , substitute values

$\frac{7x}{7}$ = $\frac{4}{x}$ ( cross- multiply )

7x² = 28 ( divide both sides by 7 )

x² = 4 ( take square root of both sides )

x = $\sqrt{4}$ = 2

7 0

3 years ago

9. Which one of the following dealt with

Elden [556K]

Answer:

lskwmzkmsmqmqmqkzkzzlosmz

3 0

3 years ago

How do you find 2/3 of a number?.

JulijaS [17]

The fraction 2/3 of a number is calculated by multiplying the number by 2 and then dividing the number by 3 .

Let us consider a number a.

To find 2/3 of the number a ,

we have to multiply the number by 2 = 2a

Then we have to divide the product by 3 .

Therefore 2/3 of a number will look like 2a/3 .

A number that represents a fraction of a whole is used to express fractions. Any number, amount, or portion of an object can all be regarded as a fraction.

The fractional bar is a horizontal bar that divides each fraction's numerator and denominator in half.

The numerator gives the number of selected or visible portions of the fraction. Above the fractional bar, in the upper portion of the fraction, is where it is located.

To learn more about fraction number visit:

brainly.com/question/343341

#SPJ4

3 0

1 year ago