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1 year ago

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Mathematics

1 answer:

sammy [17]1 year ago

5 0

Answer:

Explanation:

7. f(x) = x^4 + 3x^3 - 6x^2 - 10x + 8
f(2) = 2^4 + 2^3 - 6^2 - 10(2) + 8
f(2) = 16 + 8 - 12 - 20 + 8
f(2) = 0

8. x^2 - 9 = (x - 3)(x + 3)
x ^2 + x - 6 = (x + 3)(x -2)

Thus, the common factor is x + 3

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One of the tables shows a proportional relationship.

beks73 [17]

Answer:

See attached

Step-by-step explanation:

The graph of a proportional linear relationship is a line that passes through the origin (0, 0).

From inspection of the given tables, the linear equations for each table of points is:

Table 1: y = x + 1
Table 2: y = x/2
Table 3: y = x + 2
Table 4: y = 2x + 1

The only equation for which y = 0 when x = 0 is y = x/2 → Table 2.

Given points from Table 2:

(2, 1)
(4, 2)
(6, 3)
(8, 4)

To graph the line, plot the given points and draw a line through them (see attached).

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1 year ago

The average heights of x number of girls and 15 boys is 123. if the average heights of boys is 125 and that of girls is 120.find

mamaluj [8]

Answer:

$x = 10$ . In other words, there number of girls is $10$ .

Step-by-step explanation:

The average of a number of measurements is equal to the sum of these measurements over the number of measurements.

$\displaystyle \text{Average} = \frac{\text{Sum of measurements}}{\text{Number of measurements}}$ .

Rewrite to obtain:

$\begin{aligned}& \text{Sum of measurements}= (\text{Number of measurements}) \times (\text{Average}) \end{aligned}$ .

For this question:

$\begin{aligned}& \text{Sum of heights of boys} \\ &= (\text{Number of boys}) \times (\text{Average height of boys}) \\ &= 15 \times 125 = 1875\end{aligned}$ .

$\begin{aligned}& \text{Sum of heights of girls} \\ &= (\text{Number of girls}) \times (\text{Average height of girls}) \\ &= x \times 120 = 120\, x\end{aligned}$ .

Therefore:

$\begin{aligned}& \text{Sum of boys and girls} \\ &= \text{Sum of heights of boys} + \text{Sum of heights of girls}\\ &= 1875 + 120\, x\end{aligned}$ .

On the other hand, there are $(15 + x)$ boys and girls in total. Using the formula for average:

$\begin{aligned}& \text{Average height of boys and girls} \\ &= \frac{\text{Sum of heights of boys and girls}}{\text{Number of boys and girls}} \\ &= \frac{1875 + 120\, x}{15 + x}\end{aligned}$ .

From the question, this average should be equal to $123$ . In other words:

$\displaystyle \frac{1875 + 120\, x}{15 + x} = 123$ .

Solve this equation for $x$ to obtain:

$1875 + 120\, x= 123\, (15 + x)$ .

$(123 - 120)\, x = 1875 - 123 \times 15$ .

$x = 10$ .

In other words, the number of girls here is $10$ .

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vekshin1

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3 years ago

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Over [174]

Answer:

Its -1.9 for where point D is

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2 years ago

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jeka94

D. -48
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2 years ago