What is the slope of the line? 1 2 -2 1/2

£70 is divided between Natasha, Richard & Stephen so that Natasha gets twice as much as Richard, and Richard gets three time

Korvikt [17]

The share of Natasha is £ 42

Solution:

£70 is divided between Natasha, Richard & Stephen

Total amount = 70

Let the share of natasha be "x"

Let the share of richard be "y"

Let the share of stephen be "z"

Natasha gets twice as much as Richard

x = 2y ------ eqn 1

Richard gets three times as much as Stephen

y = 3z

$z = \frac{y}{3}$ ----- eqn 2

Total amount = 70

share of natasha + share of richard + share of stephen = 70

x + y + z = 70

Substitute eqn 1 and eqn 2

$2y + y + \frac{y}{3} = 70\\\\\frac{6y+3y+y}{3} = 70\\\\10y = 210\\\\y = 21$

Substitute y = 21 in eqn 1

x = 2y = 2(21) = 42

x = 42

Thus natasha gets £ 42

6 0

3 years ago

Multiply your answer should be in a monomial standard form (7h^3)(3h^7)

KonstantinChe [14]

Answer:

21 h^10

Step-by-step explanation:

(7h^3)(3h^7)

Lets multiply

7*3 h^3 h^7

When the bases are the same , we add the exponents (x^a * x^b) = x ^ (a+b)

21 h^(3+7)

21 h^10

5 0

3 years ago

Read 2 more answers

Write the quadratic function f(x) = x2 - 5x + 3 in vertex form. Complete the square to determine the maximum or minimum value of

enyata [817]

Answer:

a). Vertex form f the function f(x) = (x - 2.5)²+3.25

b). Maximum value of the function is (-3)

Step-by-step explanation:

a). f(x) = x² - 5x + 3

we have to write this function in the vertex form.

f(x) = x² - 2(2.5)x + 3

= [(1)²x²- 2(2.5)x + (2.5)²-(2.5)²] + 3

= (x - 2.5)²- 6.25 + 3

= (x - 2.5)² - 3.25

So the vertex for of the function is

f(x) = (x - 2.5)² - 3.25

b). Given quadratic function f(x) = -x² - 6x + 6 is in the standard form of f(x) = ax² + bx + c.

By comparing the coefficients of both the functions,

a = -1, b = 6 and c = 6

Here the value of a is negative, therefore, the given parabola is opening downwards.

And the maximum will occur at

$x=-\frac{b}{2a}$

When we plug in the values,

$x=-\frac{6}{2(-1)}$

x = 3

Now to get the value of maximum of the function we will get the value of f(3).

f(3) = -(3)²- 6(3) + 6

f(3) = 9 - 18 + 6

f(3) = -3

Therefore, maximum value of the quadratic function is (-3).

4 0

3 years ago

Can someone help me with this question?

charle [14.2K]

Finding the sol'n to f(x) - g(x) = 0 is the same as finding the solution of f(x)=g(x). You could do this analytically by setting the actual function f(x) = g(x) and solving for x (and then for y), or you could estimate the solution from the given graph. The two lines intersect at approx. x=-3.75, y=2.5.

6 0

3 years ago

Convert the equation (y + 2) = –1/3(x – 4) to the point-slope form. Then fill in the blanks below to describe how to graph the e

alisha [4.7K]

The point-slope form of the equation of the line is:

(y - y1) = m (x - x1)

So, (y + 2) = - 1/3 (x - 4) in the point-slope form is:

[y - (-2) ] = (-1/3) [ x - 4 ]

You must, then realize that the line passes through the point (4,-2) and its slope is - 1 /3.

That slope, -1 / 3, means that the function is decresing (because the slope is negative), and it decreases one unit when x increases 3 units.

Now you can fill in the blanks in this way:

Plot the point (4, -2), move 1 unit down, and 3 units over to find the next point on the line.

7 0

4 years ago