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3 years ago

-x2 - 4x + 21 Factorise

Mathematics

2 answers:

Gwar [14]3 years ago

8 0

The answer is
= -6x +21

wlad13 [49]3 years ago

5 0

9514 1404 393

Answer:

-(x -3)(x +7)

Step-by-step explanation:

Apparently, you're supposed to match the given expression with the parts of the identity ...

(x + a)(x + b) = x² +(a +b) +ab

First of all, we notice that the sign of x² in our given expression is negative. So, we factor -1 out of the expression first.

-x² -4x +21 = -(x² +4x -21)

Now, matching the coefficients of x, and the constant to those in our identity, we see ...

a + b = 4 . . . . . coefficients of x

ab = -21 . . . . . . constants

It is relatively easy to find the factors of -21. We are interested in those factor pairs such that the sum is positive:

-21 = -1(21) = -3(7) = -7(3) . . . . at this point the sum -7+3 becomes negative

The factor pair a=-3, b=7 will satisfy ...

a + b = -3 + 7 = 4

ab = (-3)(7) = -21

So, our factorization is ...

-x² -4x +21 = -(x² +4x -21) = -(x -3)(x +7)

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3. Simplify. * 5m3 + 2m– 7m3 – 8m

Oksanka [162]

Step-by-step explanation:

5m³ + 2m - 7m³ - 8m

= -2m³ -6m

= -2m(m² + 3)

4 0

3 years ago

The varsity basketball team started selling T-shirts online in 1994. The number of T-shirts sold online, s, is modeled by the gr

-Dominant- [34]

(PART-A): s-intercept in this case represents the y-intercept of the graph, whereas the t-intercept in this case represents the x-intercept of the graph.

Always remember that y-intercept represents the value of y where the curve (or line) crosses the y-axis, and x-intercept represents the value of x where the curve (or line) crosses the x-axis.

In the graph attached with the question, at point (0,6) the curve crosses the y-axis. Therefore, the y-intercept (s-intercept) in this case is 6. It means that in year 2000 (t=0), 6 hundred shirts were sold.

However, there is no point on the graph where the curve crosses the x-axis, meaning there is no x-intercept (t-intercept). It means that there is not a single year when the number of shirts sold is 0.

(PART B): As you can see in the graph (attached with the question) that the f(t) is increasing (exponentially) with the increase in t. Therefore, we can safely say that as t increases without bound, the f(t) increases (also). In this context, it means that the sale of shirts increases as the years go by. Hence, the correct blank is "increases."

(PART C): The average rate of change is actually the slope. To find the slope, we can use the following formula:

slope = $\frac{y_2 - y_1}{x_2 - x_1}$ --- (X)

Given points: (5, 12.5) and (7, 22). Plug the values in equation (X),

slope = $\frac{22-12.5}{7-5} = 4.75$

Hence, the average rate of change for the function between t=5 and t=7 is 4.75 (answer).

(PART D): This part is bit tricky. Therefore, read the explanation carefully!

You can see in the graph that number of Shirts sold is in hundreds. It means that 1 unit (of y-axis in a graph) represents 100 shirts. Therefore, as in the question it is mentioned that there are 1000 T-shirts sold, it will become 10 units (since 10*100 = 1000). So, the function g(t) will become the following:

$g(t) = f(t) + 10$ --- (Y)

Why did I add f(t)? Because in the question, the word "and" is underlined. It means that g(t) represents not only 1000 T-shirts (10*100 = 1000) sold at the basketball games each year, but it also has the number of T-shirts sold ONLINE, which is f(t).

Now insert f(t) in (Y) and solve:

$g(t) = f(t) + 10\\g(t) = (1.5)^t + 5+ 10\\g(t) = (1.5)^t + 15$