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3 years ago

Write using exponents. Rewrite the expression below in the same sequence: 4·4·4·a·b·a·b

Mathematics

2 answers:

spayn [35]3 years ago

5 0

4^3 ab^2

Four would be cubed (to the third power) and ab would be squared (to the second power)

ValentinkaMS [17]3 years ago

5 0

The answer your looking for is 4^3 a^2 b^2 and in that exact order

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Which statement best describes the function h(t) = 210 – 15t?

jonny [76]

Answer:

The answer is b.

h is the function name; t is the input and h(t) is the output.

The function name is the one outside the parentheses, the input is inside and the output is the whole function.

Step-by-step explanation:

8 0

3 years ago

The point P(7, −2) lies on the curve y = 2/(6 − x). (a) If Q is the point (x, 2/(6 − x)), use your calculator to find the slope

NARA [144]

Answer:

a) (i) $m = 2.22$ , (ii) $m = 2$ , (iii) $m = 2$ , (iv) $m = 2$ , (v) $m = 1.82$ , (vi) $m = 2$ , (vii) $m = 2$ , (viii) $m = 2$ ; b) $m \approx 2$ ; c) The equation of the tangent line to curve at P (7, -2) is $y = 2\cdot x + 12$ .

Step-by-step explanation:

a) The slope of the secant line PQ is represented by the following definition of slope:

$m = \frac{\Delta y}{\Delta x} = \frac{y_{Q}-y_{P}}{x_{Q}-x_{P}}$

(i) $x_{Q} = 6.9$ :

$y_{Q} =\frac{2}{6-6.9}$

$y_{Q} = -2.222$

$m = \frac{-2.222 + 2}{6.9-7}$

$m = 2.22$

(ii) $x_{Q} = 6.99$

$y_{Q} =\frac{2}{6-6.99}$

$y_{Q} = -2.020$

$m = \frac{-2.020 + 2}{6.99-7}$

$m = 2$

(iii) $x_{Q} = 6.999$

$y_{Q} =\frac{2}{6-6.999}$

$y_{Q} = -2.002$

$m = \frac{-2.002 + 2}{6.999-7}$

$m = 2$

(iv) $x_{Q} = 6.9999$

$y_{Q} =\frac{2}{6-6.9999}$

$y_{Q} = -2.0002$

$m = \frac{-2.0002 + 2}{6.9999-7}$

$m = 2$

(v) $x_{Q} = 7.1$

$y_{Q} =\frac{2}{6-7.1}$

$y_{Q} = -1.818$

$m = \frac{-1.818 + 2}{7.1-7}$

$m = 1.82$

(vi) $x_{Q} = 7.01$

$y_{Q} =\frac{2}{6-7.01}$

$y_{Q} = -1.980$

$m = \frac{-1.980 + 2}{7.01-7}$

$m = 2$

(vii) $x_{Q} = 7.001$

$y_{Q} =\frac{2}{6-7.001}$

$y_{Q} = -1.998$

$m = \frac{-1.998 + 2}{7.001-7}$

$m = 2$

(viii) $x_{Q} = 7.0001$

$y_{Q} =\frac{2}{6-7.0001}$

$y_{Q} = -1.9998$

$m = \frac{-1.9998 + 2}{7.0001-7}$

$m = 2$

b) The slope at P (7,-2) can be estimated by using the following average:

$m \approx \frac{f(6.9999)+f(7.0001)}{2}$

$m \approx \frac{2+2}{2}$

$m \approx 2$

The slope of the tangent line to the curve at P(7, -2) is 2.

c) The equation of the tangent line is a first-order polynomial with the following characteristics:

$y = m\cdot x + b$

Where:

$x$ - Independent variable.

$y$ - Depedent variable.

$m$ - Slope.

$b$ - x-Intercept.

The slope was found in point (b) (m = 2). Besides, the point of tangency (7,-2) is known and value of x-Intercept can be obtained after clearing the respective variable:

$-2 = 2 \cdot 7 + b$

$b = -2 + 14$

$b = 12$

The equation of the tangent line to curve at P (7, -2) is $y = 2\cdot x + 12$ .

7 0

3 years ago

How do you find the median?

Basile [38]

#1) Arrange the numbers from least to greatest.

#2) If there is a odd amount of numbers the middle number is your answer.

but if there is a even amount of numbers, take those two middle numbers, add them, then divide them by two. Then you got your answer.

5 0

3 years ago

Read 2 more answers

There are 30 boys in a sporting club. 20 of them play hockey and 15 play volleyball. Each boys plays at least one of the two gam

SVETLANKA909090 [29]

Answer:

5 boys play all the two games

25 boys play only one game

Step-by-step explanation:

Sets

There are two sets defined in the question: one for the boys who play hockey (H) and the other for the boys who play volleyball (V).

All the boys play at least one of the two games, so no elements are outside both sets.

There are 30 boys in total. 20 of them play hockey and 15 play volleyball. Since the sum of both numbers is greater than the total of boys, the difference corresponds to the boys who play both games.

Thus 20 + 15 - 30 = 5 boys play both games

Given that 5 boys are shared by both sets, from the 20 playing hockey, 15 play ONLY hockey. From the 15 boys playing volleyball, 10 play ONLY volleyball.

Thus 15 + 10 = 25 boys play only one game.

The Venn diagram is shown in the image.

7 0

3 years ago

What is true about triangle ABC. Select three options

liubo4ka [24]

Answer: The answer is sin A = cos C

Step-by-step explanation: sin A = cos C

6 0

3 years ago