What is inequality to compare

The height of a rectangular prism is 3 feet. The length and width can be expressed as x-1 and x+4. If the volume of the prism is

SashulF [63]

Answer:

Step-by-step explanation:

Volume = 198 ft

length * width * height = 198

(x - 1) * (x + 4) * 3 = 198

(x - 1) * (x + 4) = 198/3

(x - 1) * (x + 4) = 66

x*x + x*4 -1*x - 1*4 = 66 {Use FOIL method to multiply}

x² + 4x - x - 4 = 66

x² + 3x - 4 =66

x² + 3x - 4 - 66 = 0

x² + 3x - 70 = 0

Now factorize.

x² + 10x - 7x - 7*10 = 0

x(x +10) - 7(x + 10 ) = 0

(x + 10)(x - 7) = 0

x - 7 = 0 {x + 10 is ignored because measurement cannot be in negative}

x = 7

length = x - 1 = 7 - 1 = 6ft

Width = x + 4 = 7 + 4 = 11 ft

4 0

3 years ago

Casey wants to buy a gym membership. Gym A has a $150 joining fee and costs $35 per month. Gym B has no joining fee and costs $6

MariettaO [177]

Answer:

Step-by-step explanation:

Gym A has a $150 joining fee and costs $35 per month.

Assuming that Casey wants to attend for x months, the cost of using gym A will be

150 + 35 times x months. It becomes

150 + 35x

Gym B has no joining fee and costs $60 per month.

Again, assuming that Casey wants to attend for x months, the cost of using gym B will be

60 × x months = 60x

A) To determine the number of months that it will both gym memberships to be the same, we will equate them.

150 + 35x = 60x

60x - 35x = 150

25x = 150

x = 150/25 = 6

It will take 6 months for both gym memberships to be the same.

B) If Casey plans to only go to the gym for 5 months,

Plan A will cost 150 + 35×5 = $325

Plan B will cost 60 × 5 = $300

Plan B will be cheaper

6 0

3 years ago

What is the equation of the line that passes through the point (5,3) and has a slope of -1/5 ?

deff fn [24]

Answer: y=-1/5x+4

Step-by-step explanation: use the equation y=mx+b (x,y)->(5,3) 5 is an x value and 3 is a y value so you want to plug in these values into the equation. 3=-1/5(5)+b. We already know our slope so just plug it into m. Now multiply -1/5 and 5 which is -1. 3=-1+b you want to isolate b so you can find the intercept. Add one to both sides so it cancels out. 4=b we found our y-intercept so we can write the equation now. y=-1/5x+4

6 0

1 year ago

The perimeter of equilateral triangle ABC is 81/3 centimeters, find the length of the radius and apothem.

MAXImum [283]

There is a typo error, the perimeter of equilateral triangle ABC is 81/√3 centimeters.

Answer:

Radius = OB= 27 cm

Apothem = 13.5 cm

A diagram is attached for reference.

Step-by-step explanation:

Given,

The perimeter of equilateral triangle ABC is 81/√3 centimeters.

Substituting this in the formula of perimeter of equilateral triangle = $3\times\ side$

$3\times\ side$ $=[tex]81\sqrt{3}$

$Side = \frac{81\sqrt{3} }{3} =27\sqrt{3} \ cm$

Thus from the diagram , Side $AB=BC=AC= 27\sqrt{3} \ cm$

We know each angle of an equilateral triangle is 60°.

From the diagram, OB is an angle bisector.

Thus $\angle OBC = 30$ °

Apothem is the line segment from the mid point of any side to the center the equilateral triangle.

Therefore considering ΔOBE, and applying tan function.

$tan\theta =\frac{perpendicular}{base} \\tan\theta=\frac{OE}{BE} \\tan\theta=\frac{OE}{\frac{27\sqrt{3}}{2} } \\tan30\times {\frac{27\sqrt{3} }{2} }= OE\\\frac{1}{\sqrt{3} } \times\frac{27\sqrt{3} }{2} =OE\\$

Thus ,apothem OE= 13.5 cm

Now for radius,

We consider ΔOBE

$cos\theta=\frac{base}{hypotenuse} \\cos30= \frac{BE}{OB} \\Cos30 = \frac{\frac{27\sqrt{3} }{2}}{OB} \\OB= \frac{\frac{27\sqrt{3} }{2}}{cos30} \\OB= \frac{\frac{27\sqrt{3} }{2}}{\frac{\sqrt{3} }{2} } \\OB =27 \ cm$