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3 years ago

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Mathematics

2 answers:

viva [34]3 years ago

6 0

Answer:

(x - 1) (x + 2) (x + 4)

Step-by-step explanation:

Factor the following:

x^3 + 5 x^2 + 2 x - 8

The possible rational roots of x^3 + 5 x^2 + 2 x - 8 are x = ± 1, x = ± 2, x = ± 4, x = ± 8. Of these, x = 1, x = -2 and x = -4 are roots. This gives x - 1, x + 2 and x + 4 as all factors:

Answer: (x - 1) (x + 2) (x + 4)

Dvinal [7]3 years ago

6 0

Answer:

x + 4

x – 1

x + 2

Step-by-step explanation:

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Anna11 [10]

V=hpir^2
c=2pir

assuming they havve same height

first one is
v=hpi5^2
v=25hpi

2nd one
c=2pir=20pi
2pir=20pi
2r=20
r=10
v=hpir^2
v=hpi10^2
v=100hpi

big/small=100hpi/25hpir=4

4 times greater

4 0

3 years ago

In an auditorium, a charity show is conducted in order to raise at least $3,750. The auditorium can accommodate up to 180 specta

Maksim231197 [3]

Answer:

See explanation

Step-by-step explanation:

Let $x,\ x\ge 0$ be the number of students and $y,\ y\ge 0$ be the number of adults on the show.

1. Tickets cost $15 for students, so x student tickets cost $15x.

Tickets cost $25 for adults, so y adult tickets cost $25y.

Total cost of all tickets is $(15x + 25y).

The charity show is conducted in order to raise at least $3,750, thus

$15x+25y\ge 3,750$

2. The auditorium can accommodate up to 180 spectators, hence

$x+y\le 180$

3. We get the system of inequalities:

$\left\{\begin{array}{l}x\ge 0\\y\ge 0\\x+y\le 180\\15x+25y\ge 3,750\end{array}\right.$

Plot all solutions sets to each inequality and the common region is the solution set to the system of inequalities. This region is not empty, so the charity will reach its goal. For example, if they sell 50 students tickets and 125 adult tickets, they will raise $\$(15\cdot 50+25\cdot 125)=\$3,875$

8 0

3 years ago

What is the lateral surface area of the square pyramid below?

den301095 [7]

Answer:

lateral surface area = 48 inches²

Step-by-step explanation:

The picture below is the square base pyramid you are referring. The lateral area is adding the area of the 4 triangles in the pyramid.

area of a triangle = 1/2 × b × h

The slant height of the triangle is gotten using Pythagoras theorem

lateral surface area = 4 × (1/2 × 3 × 8)

lateral surface area = 4 × 24/2

lateral surface area = 4 × 12

lateral surface area = 48 inches²

3 0

3 years ago

Read 2 more answers

Verify the identity: (1-sinx)/cosx = cosx/(1+sinx)

Tresset [83]

Cross multiply the expression so that we can get

(1+sinx)(1-sinx) = cos^2 x

1 - sin^2 x = cos^2 x

cos^2 x + sin^2 x = 1

since

cos^2 x + sin^2 x = 1

therefore

1 = 1

the two expressions are identical in a trigonometric sense

4 0

3 years ago

HELP A line passes through two points with coordinates (6,-8) and (-3,7).

FromTheMoon [43]

Answer:

Step-by-step explanation:

<u>Equation of the Line</u>

The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:

$\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$