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3 years ago

7

Let (3x+24) represent the measure of an obtuse angle. what are the possible values of x?

1 answer:

Fofino [41]3 years ago

3 0

An obtuse angle is an angle with more than 90 degrees and less than 180. so, we can add < 180 and > 90 to the expression, making it the inequality 180 < 3x + 24 > 90. we then solve.

3x + 24 > 90 and 3x + 24 < 180
3x > 66 and 3x < 156
x > 22 and x < 52

so x can be anything more than 22 and less than 52 (it cannot be 52 or more or 22 or less)

hope this helps!

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$5604.41 will be worth after 20 years I think

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3 years ago

The mosquito population is a function of rainfall, and can be approximated by the formula N(x)=−x3+45x2+1000 where x is the numb

KiRa [710]

Answer:

Therefore the population will be maximum when x=30 inches.

Step-by-step explanation:

Given that, the mosquito population is a function of rainfall and can be approximated by the formula

$N(x)= -x^3+45x^2+1000$

where x is the number of inches of rainfall.

$N(x)= -x^3+45x^2+1000$

Differentiating with respect to x

$N'(x)= -3x^2+90x$

Again differentiating with respect to x

$N''(x)=-6x+90$

Now we set N'(x)=0

$-3x^2+90x=0$

$\Rightarrow -3x(x-30)=0$

$\Rightarrow x=0,30$

$N''(0)=-6.0+90=90>0$

$N''(30)=-6.30+90=-90$

Since at x=30, N''(x)<0, So at x=30, N(x) has maximum value.

Therefore the population will be maximum when x=30 inches.

5 0

3 years ago

Can someone please help me with this? thank u so much

MatroZZZ [7]

Step-by-step explanation:

The perimeter of a triangle is calculated by adding all three side lengths together

That means x + 3 + x + 4 + x + 1 = 17 add the like terms

3x + 8 = 17

3x = 9

x = 3

BC = x + 3 ➡ 6

CD = x + 4 ➡ 7

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6 0

4 years ago

Read 2 more answers

1. One rule of thumb for estimating crowds is that each person occupies 2.5 square feet. Use this value to

givi [52]

Answer:

216 people

Step-by-step explanation:

Given:

2.5 feet² is occupied by 1 person

Dimension of room = 216 in × 360 in

Required:

No. of people that would occupy the room

SOLUTION:

Step 1:

Convert the dimensions of the room from in to ft

Note: 1 foot = 12 inches

216 inches = $\frac{216}{12} = 18 ft$

360 inches = $\frac{360}{12} = 30 ft$

Step 2: calculate area of the room.

Area of the room = 30*18 = 540 ft²

Step 3: calculate the no. of people the room will contain.

2.5 ft² will contain one person

Therefore, 540 ft² will contain: $\frac{540}{2.5} = 216 people$

6 0

3 years ago

Use the distributive property to create an equivalent expression to the equation 9(2j + 5j).

frez [133]

Answer:

63 Hope this helps you and everyone else :)

Step-by-step explanation:

First, multiply 9x2 to get 18. Then, multiply 9x5 to get 45. Finally add both numbers to get 63.

3 0

3 years ago

Read 2 more answers