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3 years ago

Bob the builder is making 480kg of concrete mix

Mathematics

1 answer:

vichka [17]3 years ago

5 0

To answer this item, we are first to determine the common factor between the amounts of the cement, sand, and gravel.

If we let x be this factor, the amount of the cement would be x. Similarly, the amount of sand is 3x, and lastly the amount of gravel is 4x. Then, we establish the equation that would let us relate the amounts.

x + 3x + 4x = 480

Simplifying,

8x = 480

x = 60

Hence, the amount of cement is 60 kg, that of sand is 180 kg. Lastly, the amount of gravel is 240 kg.

You might be interested in

3x - 4y =7 solve for y

pochemuha

Y= 3/4x - 7/4
Hope this helps

5 0

4 years ago

Read 2 more answers

The slope of a line that is parallel to each line whose equation is given

Kobotan [32]

Parallel lines, slope is the same so
1) 3x+8y = 12
8y = -3x + 12
y = -3/8(x) + 3/2, slope = -3/8

slope of a line that is parallel = -3/8

2)5x+4y = 5
4y = -5x + 5
y = -5/4(x) + 5/4; slope is -5/4

slope of a line that is parallel = -5/4
--------------------
perpendicular, slope is opposite and reciprocal

3)
3x+8y = 11
8y = -3x + 11
y = -3/8(x) + 11/8. slope = -3/8
slope of perpendicular line = 8/3

4)
x = -7, slope is undefined
so slope of perpendicular line is 0

5)
3x+2y = 12
2y = -3x + 12
y = -3/2(x) + 6 ; slope = -3/2

5x - 6y = 8
6y = 4x - 8
y = 2/3(x) - 4/3; slope is 2/3

slope is opposite and reciprocal, so the equals are perpendicular

6)
3x + y = 5
y = -3x + 5; slope = -3

6x + 2y = -15
2y = -6x - 15
y = -3x - 7.5; slope = -3

both have slope = -3 so equations are parallel

3 0

3 years ago

Given r(x) = 11/ (x - 42)

julsineya [31]

For a given function f(x) we define the domain restrictions as values of x that we can not use in our function. Also, for a function f(x) we define the inverse g(x) as a function such that:

g(f(x)) = x = f(g(x))

<u>The restriction is:</u>

x ≠ 4

<u>The inverse is:</u>

$y = 4 + \sqrt{\frac{11}{x} }$

Here our function is:

$f(x) = \frac{11}{(x - 4)^2}$

We know that we can not divide by zero, so the only restriction in this function will be the one that makes the denominator equal to zero.

(x - 4)^2 = 0

x - 4 = 0

x = 4

So the only value of x that we need to remove from the domain is x = 4.

To find the inverse we try with the general form:

$g(x) = a + \sqrt{\frac{b}{x} }$

Evaluating this in our function we get:

$g(f(x)) = a + \sqrt{\frac{b}{f(x)} } = a + \sqrt{\frac{b*(x - 4)^2}{11 }}\\\\g(f(x)) = a + \sqrt{\frac{b}{11 }}*(x - 4)$

Remember that the thing above must be equal to x, so we get:

$g(f(x)) = a + \sqrt{\frac{b}{11 }}*(x - 4) = x\\\\{\frac{b}{11 }} = 1\\{\frac{b}{11 }}*4 - a = 0$

From the two above equations we find:

b = 11

a = 4

Thus the inverse equation is:

$y = 4 + \sqrt{\frac{11}{x} }$

If you want to learn more, you can read:

brainly.com/question/10300045

3 0

3 years ago

7) What is the slope-intercept form of this equation? Show all your work. 6x + 2y = 12

mariarad [96]

Answer:

Step-by-step explanation:

6x+2y=12

2y=6x-12

y=6x/2- 12/2

y=3x-6

7 0

2 years ago

PLASE ANSWER THIS QUESTION I GIVE YOU 18 POINTS

sukhopar [10]

Answer:

(a) 144

(b) 117

(d) 588

(e) 5472

Step-by-step explanation:

To find the LCM of two numbers, first find the prime factorization of each number. Then the LCM is the product of common and not common factors with the larger exponent.

(a)

$72 = 2^3 \times 3^2$