What is 5/8 as a decimal?

2. Between which two numbers will “the square root of 10” lie on the number line?

inessss [21]

Pi and 4, because the square root of ten is 3.1622...

8 0

2 years ago

Find the angles of a triangle whose two base angles are equal and whose third angle is 10° less than three times the base angle.

Illusion [34]

Answer:

well if the bottom two are 30 then that leaves you with 70

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Two horses are ready to return to their barn after a long workout session at the track. the horses are at coordinates H(1,10) an

ss7ja [257]

The given information are the coordinates of points H, Z and B. So, the first step to do is to plot these points on a Cartesian plane as shown in the attached picture. We can deduce visually that horse Z is closer to the barns than horse H. But, to further justify the answer, we have to provide the magnitude of the distance of horses H and Z to barn B. In this approach, we use the distance formula:

d = √(x₂ - x₁)² + (y₂ - y₁)²

Use the coordinates of the two points to know their linear distances. These are represented by the red and green lines for each of the horses.

Distance between H and B = √(⁻3 - 1)² + (⁻9-10)²
Distance between H and B = √(⁻3 - 1)² + (⁻9-10)²
Distance between H and B = 19.4165

Since the scale is 1 unit = 100 meters, the actual distance between horse H and barn B is 19.416*100 = 1,941.65 meters

Distance between Z and B = √(⁻3 - 10)² + (⁻9-1)²
Distance between Z and B = √(⁻3 - 10)² + (⁻9-1)²
Distance between Z and B = 16.4012

Since the scale is 1 unit = 100 meters, the actual distance between horse Z and barn B is 16.4012*100 = 1,640.12 meters

Comparing the distances: 1,941.65 meters > 1,640.12 meters. Therefore, it justifies that horse Z is nearer to the barn.

4 0

2 years ago

Let G denote the centroid of triangle ABC. If triangle ABG is equilateral with side length 2, then determine the perimeter of tr

zhannawk [14.2K]

We know from Euclidean Geometry and the properties of a centroid that GC=2GM. Now GM=sin60*GA= $\sqrt{3}$ . Hence CM=GC+GM=3* $\sqrt{3} /$ . Now, since GM is normal to AB, we have by the pythagoeran theorem that:
$AC^2=AM^2+GM^2=BM^2+GM^2=BC^2$
Hence, we calculate from this that AC^2= 28, hence AC=2* $\sqrt{7}$ =BC. Thus, the perimeter of the triangle is 2+4* $\sqrt{7}$ .

3 0

2 years ago

1. Let f(x) = x + 3 and g(x) = 3x + 5. Find f(g(4)) - g(f(4)) 2. Let f(x) = 5x^2 - 5. What is f(f(x))? 3. Let f(g(x)) = 3x + 3 a

ludmilkaskok [199]

Answer:

1. f(g(4)) - g(f(4)) = -6

2. f(f(x)) = 125x^4 - 250x^2 + 120

3. a + b = 0

4. g(4) = -9

Step-by-step explanation:

1.

First we need to find f(4) and g(4):

f(4) = 4 + 3 = 7

g(4) = 3*4 + 5 = 17

Then, we find g(f(4)) = g(7):

g(7) = 3*7 + 5 = 26

And we find f(g(4)) = f(17):

f(17) = 17 + 3 = 20

so f(g(4)) - g(f(4)) = 20 - 26 = -6

2.

To find f(f(x)), we use the value of f(x) for every x in f(x):

f(f(x)) = 5*(f(x))^2 - 5 = 5*(5x^2 - 5)^2 - 5 = 5*(25x^4 - 50x^2 + 25) - 5

f(f(x)) = 125x^4 - 250x^2 + 120

3.

To find f(g(x)), we use the value of g(x) for every x in f(x):

f(g(x)) = g(x) + 6 = ax + b + 6 = 3x + 3

ax + (b+6) = 3x + 3 -> a = 3 and b = -3

a + b = 3 - 3 = 0

4.

If we assume g(x) = ax + b, we have:

g(f(x)) = a*(2x - 3) + b = 2ax - 3a + b = 5 - 4x

2a = -4 -> a = -2

-3a + b = 5

6 + b = 5 -> b = -1

g(x) = -2x - 1

g(4) = -2*4 - 1 = -9

7 0

2 years ago