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3 years ago

Four cousins were born at two-year intervals. The sum of their ages is 36. How old are they?

2 answers:

7 0

They are 6, 8, 10, 12 years old.

all of those added is 36 and two-year intervals translates to 2 years apart per cousin.

Free_Kalibri [48]3 years ago

3 0

Answer:

6, 8, 10, 12

Step-by-step explanation:

x + (x + 2) + (x + 4) + (x + 6) = 4x + 12.

4x + 12 = 36

24 = 4x

x = 6

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Two ropes, AD and BD, are tied to a peg on the ground at point D. The other ends of the ropes are tied to points A and B on a fl

BigorU [14]

You have two 30-60-90 triangles, ADC and BDC.

The ratio of the lengths of the sides of a 30-60-90 triangle is

short leg : long leg : hypotenuse
1 : sqrt(3) : 2

Using triangle ADC, we can find length AC.
Using triangle BDC, we can find length BC.
Then AB = AC - BC

First, we find length AC.
Look at triangle ACD.
DC is the short leg opposite the 30-deg angle.
DC = 10sqrt(3)
AC = sqrt(3) * 10sqrt(3) = 3 * 10 = 30

Now, we find length BC.
Look at triangle BCD.
For triangle BCD, the long leg is DC and the short leg is BC.
BC = 10sqrt(3)/sqrt(3) = 10

AB = AC - BC = 30 - 10 = 20

6 0

3 years ago

Read 2 more answers

Which of the following are solutions to the equation below? check all that apply x^2+4x-9=x+1

Aleks04 [339]

The answer is C and D only

6 0

3 years ago

Can you answer number 3, 4, and 5?<br> (Whoever is right gets brainliest)

valkas [14]

Answer:

3: 200, 200

4:800

5:400

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

After getting 5 new rocks, George gave half of his rock collection to Susan. If George gave Susan 36 rocks, which equation could

White raven [17]

Answer:

1/2 (x+5) = 36 should be the equation that is used to determine how many rocks George started with.

Step-by-step explanation:

Let 'x' be the number of rocks George had.

As George gave, after getting 5 new rocks, half of his rock collection to Susan which is = 36 rocks

It means after getting 5 new rocks George's total rocks = 72

Given that he gave half collection to Susan = 36

Thus, before inducting 5 new rocks Georg's total rocks were = 67

Thus,

1/2 (x+5) = 36 should be the correct equation.

solving

1/2 (x+5) = 36

Multiplying both sides by 2

1/2 (x+5) × 2 = 36 × 2

x+5 = 72

x = 72 - 5

x = 67

Thus, before getting 5 new rocks, the number of rocks George had = 67

Therefore,

1/2 (x+5) = 36 should be the equation that is used to determine how many rocks George started with.

7 0

2 years ago

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EXAMPLE 5 Find the maximum value of the function f(x, y, z) = x + 2y + 9z on the curve of intersection of the plane x − y + z =

geniusboy [140]

The Lagrangian,

$L(x,y,z,\lambda,\mu)=x+2y+9z-\lambda(x-y+z-1)-\mu(x^2+y^2-1)$

has critical points where its partial derivatives vanish:

$L_x=1-\lambda-2\mu x=0$

$L_y=2+\lambda-2\mu y=0$

$L_z=9-\lambda=0$

$L_\lambda=x-y+z-1=0$

$L_\mu=x^2+y^2-1=0$

$L_z=0$ tells us $\lambda=9$ , so that

$L_x=0\implies-8-2\mu x=0\implies x=-\dfrac4\mu$

$L_y=0\implies11-2\mu y=0\implies y=\dfrac{11}{2\mu}$

Then with $L_\mu=0$ , we get

$x^2+y^2=\dfrac{16}{\mu^2}+\dfrac{121}{4\mu^2}=1\implies\mu=\pm\dfrac{\sqrt{185}}2$

and $L_\lambda=0$ tells us

$x-y+z=-\dfrac4\mu-\dfrac{11}{2\mu}+z=1\implies z=1+\dfrac{19}{2\mu}$

Then there are two critical points, $\left(\pm\frac8{\sqrt{185}},\mp\frac{11}{\sqrt{185}},1\pm\frac{19}{\sqrt{185}}\right)$ . The critical point with the negative $x$ -coordinates gives the maximum value, $9+\sqrt{185}$ .

8 0

3 years ago