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3 years ago

Write a function rule for the values in the table

Mathematics

1 answer:

Alex777 [14]3 years ago

6 0

Answer:

y = 5x - 40

Step-by-step explanation:

The function rule can be written in slope-intercept form, y = mx + b.

Let's find slope (m) and y-intercept (b) of the function, using the values given in the table.

✔️Slope (m) = change in y / change in x

Using two pair of values from the table, (10, 10) and (12, 20),

Slope (m) = (20 - 10) / (12 - 10) = 10/2 = 5

Slope (m) = 5

✔️ y-intercept (b):

Substitute (x, y) = (10, 10) and m = 5 into y = mx + b.

Thus:

10 = 5(10) + b

10 = 50 + b

10 - 50 = b

b = -40

✔️Write the function by substituting m = 5 and b = -40 into y = mx + b

Thus:

y = 5x + (-40)

y = 5x - 40

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Step-by-step explanation:

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2 years ago

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In physics, it is important to use mathematical approximations. for instance, in a small angle approximation, tanα ∼ sin α . fin

siniylev [52]

Note that x is measured in radians.
The percent difference or error between sin(x) and tan(x) is calculated as
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We want this percent difference to be less than 10.4%.
Because tan(x) > sin(x) for small values of x, define
$f(x) = \frac{tan(x)-sin(x)}{sin(x)}= 0.104 \\ or \\ sec(x) - 1 = 0.104 \\ sec(x) = 1.104$

From the calculator, obtain
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3 years ago

An isosceles triangle has an angle that measures 38degrees. What measures are possible for the other two angles? Choose all that

Sphinxa [80]

Answer:

71° and 71°.

⠀

Step-by-step explanation:

The triangle having two sides equal along with one different side is called an isosceles triangle.

⠀

So, Let us assume the other sides (two equal sides) of the isosceles triangle as x. As the different side is already given in the question.

⠀

We know that,

The sum of all angles of a triangle is 180°

⠀

So, According to the question :

⠀

${\longrightarrow \it\qquad { \ { { 38 \: }^{ \circ} + x + x = 180{}^{ \circ} }}}$

⠀

${\longrightarrow \it\qquad { \ { { 38 \: }^{ \circ} + 2x = 180{}^{ \circ} }}}$

⠀

${\longrightarrow \it\qquad { \ { 2x = 180{}^{ \circ} - { 38 \: }^{ \circ}}}}$

⠀

${\longrightarrow \it\qquad { \ { 2x = 142{}^{ \circ} }}}$

⠀

${\longrightarrow \it\qquad { \ { x = \dfrac{142{}^{ \circ}}{2} }}}$

⠀

${\longrightarrow \it\qquad { \pmb { x = 71^{ \circ} }}}$

⠀

Therefore,

The measure of the two other angles of the isosceles triangle are 71° and 71°.

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2 years ago

Which expression is equivalent to x8 - 256?

lyudmila [28]

We have that
case A)
(x – 2)(x + 2)(x² + 8)(x4 + 8)
(x²-4)(x² + 8)(x4 + 8)

case B)
(x – 2)(x – 2)(x² + 4)(x4 + 16)
(x-2)²(x² + 4)(x4 + 16)

case C)
(x – 2)(x + 2)(x² + 4)(x4 + 16)
(x²-4)(x² + 4)(x4 + 16)
(x4 -16)(x4 + 16)
(x8-256)

case D)
(x + 2)(x + 2)(x² + 4)(x4 + 16)
(x+2)²(x² + 4)(x4 + 16)

the answer is
the option
C) (x – 2)(x + 2)(x2 + 4)(x4 + 16)

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4 years ago