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2 years ago

Which number is smaller, -5 or -17

Mathematics

2 answers:

irakobra [83]2 years ago

8 0

-17 because -5 is closer to 0 than -17

dalvyx [7]2 years ago

4 0

The answer is -17 because -5 is the closest to 0

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Arrange the pairs of points in increasing order of slopes of the lines joining them

sladkih [1.3K]

Answer:

(27,2) and (243,18)

(63,9) and (84,12)

(45,15) and (60,20)

(27,12) and (72,32)

(15,30) and (20,40)

(12,32) and (18,48)

(18,63) and (24,84)

Step-by-step explanation:

Formula for slope of a line is

$m=\dfrac{y_2-y_1}{x_2-x_1}$

a) (15,30) and (20,40).

$m_a=\dfrac{40-30}{20-15}=\dfrac{10}{5}=2$

Similarly find the slope of other lines.

b) (12,32) and (18,48).

$m_b=\dfrac{48-32}{18-12}=\dfrac{16}{6}=2.67$

c) (27,12) and (72,32).

$m_c=\dfrac{32-12}{72-27}=\dfrac{20}{45}=0.44$

d) (45,15) and (60,20).

$m_d=\dfrac{20-15}{60-45}=\dfrac{5}{15}=0.33$

e) (27,2) and (243,18).

$m_e=\dfrac{18-2}{243-27}=\dfrac{16}{216}=0.074$

f) (18,63) and (24,84).

$m_f=\dfrac{84-63}{24-18}=\dfrac{21}{6}=3.5$

g) (63,9) and (84,12).

$m_g=\dfrac{12-9}{84-63}=\dfrac{3}{21}=0.143$

After arranging the slopes in increasing order, we get

$m_e$

So, required arrangement of ordered pairs is

(27,2) and (243,18)

(63,9) and (84,12)

(45,15) and (60,20)

(27,12) and (72,32)

(15,30) and (20,40)

(12,32) and (18,48)

(18,63) and (24,84)

7 0

3 years ago

M∠ABD = 6x-1, m∠DBC = 11x+7, and m∠ABC = 148°, find x, m∠ABD and m∠DBC.

Bad White [126]

Answer:

JSKEJEISKJEJEJEJSJSJEJ

Step-by-step explanation:

7RHB3V BEJEJBEB 4

3 0

2 years ago

Consider the equation below. (If you need to use -[infinity] or [infinity], enter -INFINITY or INFINITY.)f(x) = 2x3 + 3x2 − 180x

soldier1979 [14.2K]

Answer:

(a) The function is increasing $\left(-\infty, -6\right) \cup \left(5, \infty\right)$ and decreasing $\left(-6, 5\right)$

(b) The local minimum is x = 5 and the maximum is x = -6

(c) The inflection point is $x = -\frac{1}{2}$

(d) The function is concave upward on $\left(- \frac{1}{2}, \infty\right)$ and concave downward on $\left(-\infty, - \frac{1}{2}\right)$

Step-by-step explanation:

(a) To find the intervals where $f(x) = 2x^3 + 3x^2 -180x$ is increasing or decreasing you must:

1. Differentiate the function

$\frac{d}{dx}f(x) =\frac{d}{dx}(2x^3 + 3x^2 -180x) \\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\f'(x)=\frac{d}{dx}\left(2x^3\right)+\frac{d}{dx}\left(3x^2\right)-\frac{d}{dx}\left(180x\right)\\\\f'(x) =6x^2+6x-180$

2. Now we want to find the intervals where f'(x) is positive or negative. This is done using critical points, which are the points where f'(x) is either 0 or undefined.

$f'(x) =6x^2+6x-180 =0\\\\6x^2+6x-180 = 6\left(x-5\right)\left(x+6\right)=0\\\\x=5,\:x=-6$

These points divide the number line into three intervals:

$(-\infty,-6)$ , $(-6,5)$ , and $(5, \infty)$

Evaluate f'(x) at each interval to see if it's positive or negative on that interval.

$\left\begin{array}{cccc}Interval&x-value&f'(x)&Verdict\\(-\infty,-6)&-7&72&Increasing\\(-6,5)&0&-180&Decreasing\\(5, \infty)&6&72&Increasing\end{array}\right$

Therefore f(x) is increasing $\left(-\infty, -6\right) \cup \left(5, \infty\right)$ and decreasing $\left(-6, 5\right)$

(b) Now that we know the intervals where f(x) increases or decreases, we can find its extremum points. An extremum point would be a point where f(x) is defined and f'(x) changes signs.

We know that:

f(x) increases before x = -6, decreases after it, and is defined at x = -6. So f(x) has a relative maximum point at x = -6.

f(x) decreases before x = 5, increases after it, and is defined at x = 5. So f(x) has a relative minimum point at x = 5.

(c)-(d) An Inflection Point is where a curve changes from Concave upward to Concave downward (or vice versa).

Concave upward is when the slope increases and concave downward is when the slope decreases.

To find the inflection points of f(x), we need to use the f''(x)

$f''(x)=\frac{d}{dx}\left(6x^2+6x-180\right)\\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\f''(x)=\frac{d}{dx}\left(6x^2\right)+\frac{d}{dx}\left(6x\right)-\frac{d}{dx}\left(180\right)\\\\f''(x) =12x+6$

We set f''(x) = 0

$f''(x) =12x+6 =0\\\\x=-\frac{1}{2}$

Analyzing concavity, we get

$\left\begin{array}{cccc}Interval&x-value&f''(x)\\(-\infty,-1/2)&-2&-18\\(-1/2,\infty)&0&6\\\end{array}\right$

The function is concave upward on $(-1/2,\infty)$ because the f''(x) > 0 and concave downward on $(-\infty,-1/2)$ because the f''(x) < 0.

f(x) is concave down before $x = -\frac{1}{2}$ , concave up after it. So f(x) has an inflection point at $x = -\frac{1}{2}$ .

7 0

3 years ago

Find the solution of the system of equations. 15x -4y = -50 3x - 2y = -16

Fittoniya [83]

Answer:

15x - 4y =-50 -----(i)

3x - 2y=-16 --------(ii)

Using Substitution

From (i)

15x=4y-50

x=4y-50/15

Substitute x=4y-50/[15] into eqn (ii)

3x - 2y= -16

3[4y-50]/15 - 2y =-16

Multiply through by 15 to clear the fraction

3(4y - 50) - 30y=-240

12y - 150 -30y=-240

12y-30y=-240+150

-18y = -90

y=90/18

y=5.

Substitute into any eqn of choice to get x

3x - 2y=-16

3x - 2(5)=-16

3x - 10=-16

3x=-16+10

3x=-6

x=-6/3

x=-2.

x= -2

y=5

5 0

2 years ago

Mark all the statements that are true.

Artyom0805 [142]

Answer:

Option A

Option C

Step-by-step explanation:

A relationship is defined as a function if and only if each element of the "domain" set is assigned only one element of the "range" set. That is, there is only one output value y assigned to each input value x.

The relation x = 3 is not a function because there are infinite output values y, assigned to the same input element x.

(3, 2), (3, 5) (3, 9) (3,10000)

Then the option A is true

Option C is also true, the equation of the line shown is

$x = 3$

The rest of the options are false because x = 3 is not a function

3 0

2 years ago