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3 years ago

14

create a sketch of the graph of a function whose gradient is linear and that gradient has an x-intercept at x=4

1 answer:

valentina_108 [34]3 years ago

7 0

Here is one that meets your requirements.

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A person on tour has dollar 360 for his daily expenses. If he extends his tour for 4 days, he has to cut down his daily expenses

mash [69]

Answer:

The original duration of the tour = 20 days

Step-by-step explanation:

Solution:

Total expenses for the tour = $360

Let the original tour duration be for $x$ days.

So, for $x$ days the total expense = $360

<em>Thus the daily expense in dollars can be given by</em> = $\frac{360}{x}$

Tour extension and effect on daily expenses.

The tour is extended by 4 days.

<em>Tour duration now</em> = $(x+4)$ days

On extension, his daily expense is cut by $3

<em>New daily expense in dollars </em>= $(\frac{360}{x}-3)$

Total expense in dollars can now be given as: $(x+4)(\frac{360}{x}-3)$

Simplifying by using distribution (FOIL).

$(x.\frac{360}{x})+(x(-3)+(4.\frac{360}{x})+(4(-3))$

$360-3x+\frac{1440}{x}-12$

$348-3x+\frac{1440}{x}$

We know total expense remains the same which is = $360.

So, we have the equation as:

$348-3x+\frac{1440}{x}=360$

Multiplying each term with $x$ to remove fractions.

$348x-3x^2+1440=360x$

Subtracting $348x$ both sides

$348x-348x-3x^2+1440=360x-348x$

$-3x^2+1440=12x$

Dividing each term with -3.

$\frac{-3x^2}{-3}+\frac{1440}{-3}=\frac{12x}{-3}$

$x^2-480=-4x$

Adding $4x$ both sides.

$x^2+4x-480=-4x+4x$

$x^2+4x-480=0$

Solving using quadratic formula.

For a quadratic equation: $ax^2+bx+c=0$

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Plugging in values from the equation we got.

$x=\frac{-4\pm\sqrt{(4)^2-4(1)(-480)}}{2(1)}$

$x=\frac{-4\pm\sqrt{16+1920}}{2}$

$x=\frac{-4\pm\sqrt{1936}}{2}$

$x=\frac{-4\pm44}{2}$

So, we have

$x=\frac{-4+44}{2}$ and $x=\frac{-4-44}{2}$

$x=\frac{40}{2}$ and $x=\frac{-48}{2}$

∴ $x=20$ and $x=-24$

Since number of days cannot be negative, so we take $x=20$ as the solution for the equation.

Thus, the original duration of the tour = 20 days

6 0

3 years ago

Complete the identity

spin [16.1K]

Answer: $cos(\pi-x)=-cos(x)$

Step-by-step explanation:

We need to apply the following identity:

$cos(A - B) = cos A*cos B + sinA*sin B$

Then, applying this, you know that for $cos(\pi-x)$ :

$cos(\pi-x)=cos(\pi)*cos(x)+sin(\pi)*sin(x)$

We need to remember that:

$cos(\pi)=-1$ and $sin(\pi)=0$

Therefore, we need to substitute these values into $cos(\pi-x)=cos(\pi)*cos(x)+sin(\pi)*sin(x)$ .

Then, you get:

$cos(\pi-x)=(-1)*cos(x)+0*sin(x)$

$cos(\pi-x)=-1cos(x)+0$

$cos(\pi-x)=-cos(x)$

8 0

3 years ago

The areas of two similar rectangles are 180 ft.² and 320 ft.². What scale factor applied to the smaller rectangle will give the

grigory [225]

The ratio of areas is the square of the scale factor, so that factor is
√(320/180) = 4/3

8 0

2 years ago

Evaluate AB for A = 5, B =-2, C = 4 and D = -6.<br> 5/12<br> -5/12<br> -3/2<br> 3/2

Nezavi [6.7K]

Answer:

AB = -10

Im confused is this what you wanted?

5 0

2 years ago

Select all the statements that are correct rational approximation of irrational numbers?

eimsori [14]

The answers would most likely be A,C,and B from my calculations

6 0

3 years ago