Find the volume of the prism. 3 cm 37 cm 5 cm

1) A line with gradient 2 passes through (0, 4). Write down the equation of the line.

blondinia [14]

For the attached image, note that slope is the same thing as gradient.

1) y = 2x + 4

2) Substituting in x = 1 and y = 1,

1 = 4(1) + c

1 = 4 + c

c = -3

So, the equation is y = 4x - 3

7 0

2 years ago

What is the square root of 864

skelet666 [1.2K]

There are two ways to evaluate the square root of 864: using a calculator, and simplifying the root.

The first method is simplifying the root. While this doesn't give you an exact value, it reduces the number inside the root.

Find the prime factorization of 864:

$\sqrt{864} = \sqrt{2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3}$

Take any number that is repeated twice in the square root, and move it outside of the root:

$\sqrt{864} = \sqrt{(2 \cdot 2) \cdot (2 \cdot 2) \cdot 2 \cdot (3 \cdot 3) \cdot 3}$

$\sqrt{2 \cdot 2} = \sqrt{4} = 2$

$\sqrt{3 \cdot 3} = \sqrt{9} = 3$

$\sqrt{(2 \cdot 2) \cdot (2 \cdot 2) \cdot 2 \cdot (3 \cdot 3) \cdot 3} = \sqrt{(4) \cdot (4) \cdot 2 \cdot (9) \cdot 3}$

$\sqrt{(4) \cdot (4) \cdot 2 \cdot (9) \cdot 3} = (2 \cdot 2 \cdot 3) \sqrt{2 \cdot 3} = \boxed{12 \sqrt{6}}$

The simplified form of √864 will be 12√6.

The second method is evaluating the root. Using a calculator, we can find the exact value of √864.

Plugged into a calculator and rounded to the nearest hundredths value, √864 is equal to 29.39. Because square roots can be negative or positive when evaluated, this means that √864 is equal to ±29.39.

6 0

3 years ago

So yeah if someone can help me with

Law Incorporation [45]

Answer:

y = x - 5

Step-by-step explanation:

The equation of the line parallel to the line $ax + by + c_1 = 0$ is $ax + by + c_2 = 0$ .

That is, equations of parallel lines differ only by constant.

The given equation is $y = x + 4$

This is written as $x - y + 4 = 0$

Therefore, the equation of the line parallel to this line is given by $x - y + c = 0$

The value of c is determined using the point given.

Substituting the point (3,-2) we get:

$3 + 2 + c = 0$

$\implies c = -5$

Therefore, the equation of the line becomes y = x - 5.

6 0

3 years ago

For the given functions f and g, complete parts (a)-(h). For parts (a)-(d), also find the domain.

slamgirl [31]

The domain for (a) , (b) , (c) is all set of real numbers , for (d) (x ε R except x = 3/8.

The complete question is

a) (f + g)(x), (b) (f – g)(x), (c) (f × g)(x), (d) (f / g)(x), (e) (f + g)(7), (f) (f - g)(2), (g) (f.g)(3), (h) (f/g)(27)

<h3>What is a Function ?</h3>

A function is the law that defines the relation between independent and a dependent variable.

It is given that

f(x) = 3x+8

g(x) = 8x-3

(a) (f + g)(x) = 3x+8 +8x-3 = 11x+5

(b) (f – g)(x) = 3x+8 -8x+3 = -5x +11

(c) (f × g)(x) = (3x+8)(8x-3) = 24x²-9x+64x -24 = 24x² +55x-24

(d)(f / g)(x) = (3x+8)/(8x-3)

(e) (f + g)(7) = 11*7+5 = 77+5 = 82

(f) (f - g)(2)= -5*2 +11 = 1

(g) (f.g)(3) =24*9 +55*3 -24 = 357

(h) (f/g)(27) = (3x+8)/(8x-3) = (3 * 27 +8)/(8*27-3) = 89/213

The domain for (a) , (b) , (c) is all set of real numbers , for (d) (x ε R except x = 3/8)

To know more about Function

brainly.com/question/12431044

#SPJ1

3 0

2 years ago

Multiply and simplify

aleksandr82 [10.1K]

Answer and explanation:

1. 2 × 3/10 = 6/10 = 3/5

2. 8 × 4/8 = 32/8 = 4

3. 9 × 3/9 = 27/9 = 3

4. 12 × 2/11 = 24/11 = 2 2/11

5. 3 × 5/7 = 15/7 = 2 1/7

6. 2 × 3/5 = 6/5 = 1 1/5

7. 11 × 4/8 = 44/8 = 5 4/8 = 5 1/2

8. 10 × 1/4 = 10/4 = 2 2/4 = 2 1/2

9. 5 × 1/4 = 5/4 = 1 1/4

10. 11 × 2/7 = 22/7 = 3 1/7

Hope this helps!

4 0

3 years ago