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kakasveta [241]
3 years ago
11

A positive real number is 4 more than another. When -8 times the smaller is added to

Mathematics
1 answer:
Bumek [7]3 years ago
5 0

Answer:

Step-by-step explanation:

x = y+4

x > y

x² - 8y = 61

(y+4)² - 8y = 61

y² + 8y + 16 - 8y = 61

y² + 16 = 61

y² = 45

y = √45 = 3√5

x = y+4 = 4+3√5

3√5 and 4+3√5

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Tell whether the dilation is a reduction or an enlargement.
-BARSIC- [3]

Answer:

Step-by-step explanation:

can you explain

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3 years ago
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A number of squares are connected in a row to form a rectangle. The table shows the relationship between the number of squares,
svp [43]

Answer:

✅The table can be represented by the equation, y = 4x + 4

✅The relation is a function.

✅The graph of the function is linear.

Step-by-step explanation:

✍️The first statement: The table can be represented by the equation, y = 4x + 4.

To check if the first statement is correct let's find the equation that can represent the table by finding the slope (m) and y-intercept (b).

Using two pairs, (1, 8) and (2, 12),

Slope = \frac{y_2 - y_1}{x_2 - x_1} = \frac{12 - 8}{2 - 1} = \frac{4}{1} = 4.

Substitute, x = 1, y = 8, and m = 4 into y = mx + b to solve for b.

Thus:

8 = (4)(1) + b

8 = 4 + b

Subtract 4 from each side

8 - 4 = b

4 = b

Plug in the values of b and m into y = mx + b.

Thus, the equation that represents the table would be:

y = 4x + 4.

✅Therefore, the first statement is correct.

✍️The second statement: The graph of the function is non-linear.

This is NOT TRUE because the equation of the function, y = 4x + 4, represents the equation of a linear graph in the slope-intercept form. When graphed, it will give us a straight line.

✍️The Third statement: The relation is a function.

This is TRUE because each input value (x-value) has exactly one output value (y-value).

✍️The Fourth statement: The rate of change is NOT constant.

This standby is NOT TRUE.

The rate of change is the slope (m) that we have calculated above to be 4. Between any two pairs, the rate of change remains 4.

Therefore, this statement is not correct.

✍️The Fifth statement: The graph of the function is linear.

This is TRUE. As stated earlier, from the equation generated, it is safe to say that the equation represents graph of a linear function. The graph will be a straight line graph.

5 0
3 years ago
Mr Thompson please help with my new HW
sesenic [268]

Answers:

  1. C) x = plus/minus 11
  2. B) No real solutions
  3. C) Two solutions
  4. A) One solution
  5. The value <u>  18  </u> goes in the first blank. The value <u>  17  </u> goes in the second blank.

========================================================

Explanations:

  1. Note how (11)^2 = (11)*(11) = 121 and also (-11)^2 = (-11)*(-11) = 121. The two negatives multiply to a positive. So that's why the solution is x = plus/minus 11. The plus minus breaks down into the two equations x = 11 or x = -11.
  2. There are no real solutions here because the left hand side can never be negative, no matter what real number you pick for x. As mentioned in problem 1, squaring -11 leads to a positive number 121. The same idea applies here as well.
  3. The two solutions are x = 0 and x = -2. We set each factor equal to zero through the zero product property. Then we solve each equation for x. The x+2 = 0 leads to x = -2.
  4. We use the zero product property here as well. We have a repeated factor, so we're only solving one equation and that is x-3 = 0 which leads to x = 3. The only root is x = 3.
  5. Apply the FOIL rule on (x+1)(x+17) to end up with x^2+17x+1x+17 which simplifies fully to x^2+18x+17. The middle x coefficient is 18, while the constant term is 17.
3 0
3 years ago
[(8*9)] - (6*7)] -15
maks197457 [2]

Answer:

15

Step-by-step explanation:

Simplify the following:

8×9 - 6×7 - 15

8×9 = 72:

72 - 6×7 - 15

-6×7 = -42:

72 + -42 - 15

72 - 42 - 15 = 72 - (42 + 15):

72 - (42 + 15)

| 4 | 2

+ | 1 | 5

| 5 | 7:

72 - 57

| 6 | 12

| 7 | 2

- | 5 | 7

| 1 | 5:

Answer:  15

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Prime numbers are only divisible by 1 or itself; the first few are are 2, 3, 5, 7, and 11.
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