Classify each number as rational or irrational. 4.27 ,0.375 ,0.232342345... V62 ,13/1

A gardener measured the heights of two plants at the end of every week. The function y=3x+8.5 gives the hight of plant a in cent

MAVERICK [17]

Answer:

12 weeks

Step-by-step explanation:

Step one:

given data

let the heights of the plants be y

and the number of weeks be x

Plant A

y=3x+8.5--------------1

Plant B

y=2.5x+14.5----------2

Required

The number of weeks taken for both plants to have the same height

,equate the two expressions above

3x+8.5=2.5x+14.5

3x-2.5x=14.5-8.5

0.5x= 6

divide both sides by 0.5

x= 6/0.5

x= 12 weeks

6 0

2 years ago

Find the equation for parabola Focus(3,4) Directrix y=2

sveta [45]

Answer:

Step-by-step explanation:

we know that distance d from the focus to P should be the same to the distance from P to the directrix

(x-h)^2=4p(y-k)

we need to find the y coordinate,

x is the same from focus, 3

y=(3, (4+2)/2)=(3,3)

we find p now by subtracting the y from the focus from the y that we just found

p=4-3=1

again (x-h)^2=4p(y-k), p=1

(x-3)^2=4(1)(y-3)

(x-3)^2=4(y-3), (x-3)^2=4y-12

simplify

4y=(x-3)^2+12

y=((x-3)^2)/4 + 3

4 0

2 years ago

Read 2 more answers

When 5 times a number is added to 45 the answer is the sm of 85 and 140 what is the number

zimovet [89]

Hello.

First, let the number be r.

5 times r is written like this:

$\rm{5r}$

Now, add 45:

$\mathrm{5r+45}$

Now, the sum of 5r+45 is equal to the sum of 85 and 140:

$\mathrm{5r+45=85+140}$

In order to solve this equation, we need to add 85 and 140:

$\mathrm{5r+45=225}$

Now, subtract 45 from both sides:

$\mathrm{5r+45-45=225-45}$

$\mathrm{5r=225-45}$

$\mathrm{5r=180}$

The last step is to divide both sides by 5:

$\mathrm{r=36}$

Therefore, the answer is

$\rm{r=36}$

I hope it helps.

Have a nice day.

$\boxed{imperturbability}$

8 0

2 years ago

Given:

diamong [38]

Answer:

10-5 $\sqrt{2}$

Step-by-step explanation:

As per the attached figure, right angled $\triangle MDL$ has an inscribed circle whose center is $I$ .

We have joined the incenter $I$ to the vertices of the $\triangle MDL$ .

Sides MD and DL are equal because we are given that $\angle M = \angle L = 45 ^\circ.$

Formula for area of a $\triangle = \dfrac{1}{2} \times base \times height$

As per the figure attached, we are given that side a = 10.

Using pythagoras theorem, we can easily calculate that side ML = 10 $\sqrt{2}$

Points P,Q and R are at $90 ^\circ$ on the sides ML, MD and DL respectively so IQ, IR and IP are heights of $\triangle$ MIL, $\triangle$ MID and $\triangle$ DIL.

Also,

$\text {Area of } \triangle MDL = \text {Area of } \triangle MIL +\text {Area of } \triangle MID+ \text {Area of } \triangle DIL$

$\dfrac{1}{2} \times 10 \times 10 = \dfrac{1}{2} \times r \times 10 + \dfrac{1}{2} \times r \times 10 + \dfrac{1}{2} \times r \times 10\sqrt2\\\Rightarrow r = \dfrac {10}{2+\sqrt2} \\\Rightarrow r = \dfrac{5\sqrt2}{\sqrt2+1}\\\text{Multiplying and divinding by }(\sqrt2 +1)\\\Rightarrow r = 10-5\sqrt2$