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antiseptic1488 [7]

3 years ago

10

Jill’s front door is 42” wide and 84” tall. She purchased a circular table that is 96 inches in diameter. Will the table fit thr

ough the front door? Explain using approximations.

1 answer:

Butoxors [25]3 years ago

3 0

No, if the door is 42 inches wide(across), and the table is 96 inches in diameter(across), then it will not fit vertically or horizontally through the door because its diameter is greater than both the width and the height of the door.

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Pleasantburg has a population growth model of P(t)=at2+bt+P0 where P0 is the initial population. Suppose that the future populat

yulyashka [42]

Answer:

The population will reach 34,200 in February of 2146.

Step-by-step explanation:

Population in t years after 2012 is given by:

$P(t) = 0.8t^{2} + 6t + 19000$

In what month and year will the population reach 34,200?

We have to find t for which P(t) = 34200. So

$P(t) = 0.8t^{2} + 6t + 19000$

$0.8t^{2} + 6t + 19000 = 34200$

$0.8t^{2} + 6t - 15200 = 0$

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

In this question:

$0.8t^{2} + 6t - 15200 = 0$

So $a = 0.8, b = 6, c = -15200$

Then

$\bigtriangleup = 6^{2} - 4*0.8*(-15100) = 48356$

$t_{1} = \frac{-6 + \sqrt{48356}}{2*0.8} = 134.14$

$t_{2} = \frac{-6 - \sqrt{48356}}{2*0.8} = -141.64$

We only take the positive value.

134 years after 2012.

.14 of an year is 0.14*365 = 51.1. The 51st day of a year happens in February.

So the population will reach 34,200 in February of 2146.

6 0

2 years ago

Solve the system by substitution.<br> 4y =<br> 5x -10y =-50

Trava [24]

Answer:

$x = -20 ; y =-5$

Step-by-step explanation:

Eqn. 1 ----> 4y = x

Eqn. 2 ----> 5x-10y = -50

(Simplifying eqn.2 further)

$=>5(x-2y)=-50$

$=>x-2y=\frac{-50}{5} =-10$

(Substituting the value of x from eqn. 1)

$=>4y-2y=-10$

$=>2y=-10$

$=>y =\frac{-10}{2} =-5$

Now, substituting the value of y in eqn. 1 ,

$x = 4*(-5)=-20$

7 0

2 years ago

How the points are placed in graphing linear inequalities?

Yanka [14]

Answer:

Plot the line y = 2x - 3 and the portion above the line will satisfy the inequality.

5 0

3 years ago

a gardener has 322 tulip bulbs she wants to plant rows of 15 bulbs how many bulbs can be planted how many bulbs will she have le

Elden [556K]

Answer:315 bulbs planted and 7 left over

Step-by-step explanation:322/15 = 21.44

Roughly around 21 rows.

21 x 15 = 315 bulbs planted

322 - 315 = 7 bulbs left over

3 0

3 years ago

The vertices of quadrilateral MNPQ are M(−3,−2),N(−1,4),P(2,4), and Q(4,−2). Translate quadrilateral MNPQ using the vector ⟨3,−4

timofeeve [1]

Answer:

M'(0,-6),N'(2,0),P'(5,0) and Q'(7,-6)

Step-by-step explanation:

We are given that the vertices of quadrilateral MNPQ are M(-3,-2),N(-1,4),P(2,4) and Q(4,-2).

We have to translate the quadrilateral MNPQ using vector <3,-4>

The translate the coordinates of vertices (x,y) using the vector <a,b> is given by the rule

$(x,y)\rightarrow (x+a,y+b)$

Using the rule

The new coordinates of M

$(-3,-2)\rightarrow (-3+3,-4-2)$

$(-3,-2)\rightarrow (0,-6)$

The new coordinates of N

$(-1,4)\rightarrow (2,0)$

The new coordinates of P

$(2,4)\rightarrow (5,0)$

The new coordinates of Q

$(4,-2)\rightarrow (7,-6)$

Hence, after translation the new vertices of quadrilateral are

M'(0,-6),N'(2,0),P'(5,0) and Q'(7,-6)

5 0

3 years ago