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3 years ago

Let f(x) = 4x + 3

Mathematics

1 answer:

docker41 [41]3 years ago

7 0

Answer: f(x) = 4x + 3

g(x) = -2x + 5

(f · g)(5) = (4(5) + 3)(-2(5) + 5)

(f · g)(5) = (20 + 3)(-10 + 5)

(f · g)(5) = (23)(-5)

(f · g)(5) = -115

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Simplify: 3x2 - 27 Helppppp

oksian1 [2.3K]

3x^2- 27 … you divide the whole thing by 3 to get x^2- 9 and that’s the furthest you can simplify

6 0

3 years ago

Green thumb landscaping want to build a $124000.00 greenhouse in 2 years. The company sets up a sinking fund with payments made

DENIUS [597]

Answer:

$150,858.5

Step-by-step explanation:

The formula for calculating compound interest is expressed as;

A = P(1+r/n)^nt

P is the Principal = $124000.00

r is the rate = 12% = 0.12

t is the total time = 2 years

n is the time of compounding = 1/4 = 0.25(quarterly)

Substitute into the formula;

A= 124000(1+0.12/(0.25))^(0.25)(2)

A = 124000(1+0.48)^0.5

A = 124000(1.48)^0.5

A = 124000(1.2166)

A = 150,858.5

The amount after 2 years if compounded quarterly is 150,858.5

8 0

3 years ago

The human body has a normal temperature of 98.6°F. Doctors will get worried if a sick patient has a temperature that varies from

makvit [3.9K]

Answer:

$|T- 98.6| \geq 3$

And in order to solve this we have two possibilities:

Solution 1

$T -98.6 \leq -3$

And solving for T we got:

$T \leq 98.6- 3$

$T\leq 95.6$

Solution 2

And the other options would be:

$T -98.6 \geq 3$

$T \geq 101.6$

Step-by-step explanation:

For this case we can define the variable os interest T as the real temperature and we know that if we are 3 F more than the value of 98.6 we will be unhealthy so we can set up the following equation:

$|T- 98.6| \geq 3$

And in order to solve this we have two possibilities:

Solution 1

$T -98.6 \leq -3$

And solving for T we got:

$T \leq 98.6- 3$

$T\leq 95.6$

Solution 2

And the other options would be:

$T -98.6 \geq 3$

$T \geq 101.6$

6 0

3 years ago

A group of 3 adults and 5 children pay a total of $52 for movie tickets. A group of 2 adults and 4 children pay a total of $38 f

Ksivusya [100]

x = child ticket price
y = adult ticket price
5x+3y=52 the cost accounting for the first group.
3x+2y=38 the cost accounting for the second group.

Child price: 5$
Adult price: 9$

3 0

3 years ago

Let f(x)=x^3-x-1

alexira [117]

$f(x) = x^3 - x - 1$

To find the gradient of the tangent, we must first differentiate the function.

$f'(x) = \frac{d}{dx}(x^3 - x - 1) = 3x^2 - 1$

The gradient at x = 0 is given by evaluating f'(0).

$f'(0) = 3(0)^2 - 1 = -1$

The derivative of the function at this point is negative, which tells us the function is decreasing at that point.

The tangent to the line is a straight line, so we will have a linear equation of the form y = mx + c. We know the gradient, m, is equal to -1, so

$y = -x + c$

Now we need to substitute a point on the tangent into this equation to find c. We know a point when x = 0 lies on here. To find the y-coordinate of this point we need to evaluate f(0).

$f(0) = (0)^3 - (0) - 1 = -1$

So the point (0, -1) lies on the tangent. Substituting into the tangent equation:

$y = -x + c \\\\ -1 = -(0) + c \\\\ -1 = c \\\\ \text{Equation of tangent is } \boxed{y = -x - 1}$

6 0

3 years ago