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2 years ago

The graph of the function f(x) = (x + 2)(x + 6) is shown below.

Mathematics

2 answers:

iren [92.7K]2 years ago

4 0

Answer:

Step-by-step explanation:

f(x) = (x + 2)(x +6)

1) The function is positive for all real values of x where x > –4 :

COUNTER-EXAMPLE : x = - 3 you have -3>-4 but (-3+2)(-3+6) = -1 ×3 =-3 no positive .

2) The function is positive for all real values of x where

x < –6 or x > –3.

COUNTER-EXAMPLE : x = - 2.5 you have -2.5>-3 but (-2.5+2)(-2.5+6) = -0.5 ×3.5 =-1.75 no positive .

same method for the statement : "The function is negative for all real values of x where

x < –2."

conclusion : statement about the function is true: "The function is negative for all real values of x where

–6 < x < –2."

Ne4ueva [31]2 years ago

4 0

Answer:

The function is negative for all real values of x where

–6 < x < –2

Step-by-step explanation:

the function f(x) = (x + 2)(x + 6)

LEts find the x intercept of the given function

0 = (x+2)(x+6)

x+2=0 so x=-2

x+6 = , so x=-6

x intercepts are -6 and -2

Lets draw a number line and use x intercepts and make 3 intervals

- infinity to -6 , -6 to -2 and -2 to infinity

LEts pick a number from each interval and check with f(x)

x<-6, pick -7

f(x) = (x + 2)(x + 6)

f(-7)=(-7 + 2)(-7 + 6) =5 , which is positive

–6 < x < –2, pick 4

f(-4)=(-4 + 2)(-4 + 6) =-4 , which is negative

x>-2, pick 0

f(0)=(-0+ 2)(0 + 6) =12 , which is positive

The function is negative for all real values of x where

–6 < x < –2

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Remember, rise/run is the easiest way to determine slope

y=mx+b is form

mx is slope, whilst b is y int

so, answer? y=-3x-2

Or A.

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2 years ago

The earth has a mass of approximately 6\cdot 10^{24}6⋅10 24 6, dot, 10, start superscript, 24, end superscript kilograms (\text{

Alex_Xolod [135]

Answer:

0.02

Step-by-step explanation:

The volume of the earth's oceans is approximately 1.34\cdot 10^{9}1.34⋅10

1, point, 34, dot, 10, start superscript, 9, end superscript cubic kilometers (\text{km}^3)(km

)left parenthesis, start text, k, m, end text, cubed, right parenthesis, and ocean water has a mass of about 1.03 \cdot 10^{12}\,\dfrac{\text{kg}}{\text{km}^3}1.03⋅10

1, point, 03, dot, 10, start superscript, 12, end superscript, start fraction, start text, k, g, end text, divided by, start text, k, m, end text, cubed, end fraction .

To simplify, we will use the product of powers property of exponents that says that x^a\cdot x^b = x^{a+b}x

⋅x

a+b

x, start superscript, a, end superscript, dot, x, start superscript, b, end superscript, equals, x, start superscript, a, plus, b, end superscript.

\qquad 1.34\cdot 10^{9}\,\cancel{\text{km}^3} \cdot 1.03 \cdot 10^{12}\,\dfrac{\text{kg}}{\cancel{\text{km}^3}} = 1.3802 \cdot 10^{21}\,\text{kg}1.34⋅10

⋅1.03⋅10

=1.3802⋅10

kg1, point, 34, dot, 10, start superscript, 9, end superscript, start cancel, start text, k, m, end text, cubed, end cancel, dot, 1, point, 03, dot, 10, start superscript, 12, end superscript, start fraction, start text, k, g, end text, divided by, start cancel, start text, k, m, end text, cubed, end cancel, end fraction, equals, 1, point, 3802, dot, 10, start superscript, 21, end superscript, start text, k, g, end text

Hint #2

Next we want to know what portion of the earth's mass this represents. We have:

\qquad \begin{aligned} \dfrac{\text{mass of the oceans}}{\text{total mass of the earth}} &= \dfrac{1.3802 \cdot 10^{21}\,\text{kg}}{6\cdot 10^{24}\,\text{kg}} \\\\ &= \dfrac{1.3802}{6\cdot 10^{3}} \\\\ &= \dfrac{1.3802}{6000} \\\\ &= 0.0002300\overline{3} \end{aligned}

total mass of the earth

mass of the oceans

6⋅10

1.3802⋅10

6⋅10

1.3802

6000

1.3802

=0.0002300

To convert this to a percent, we multiply by 100100100, so the oceans represent 0.02300\overline{3}\%0.02300

%0, point, 02300, start overline, 3, end overline, percent of the earth's total mass, according to these figures.

Hint #3

To the nearest hundredth of a percent, 0.020.020, point, 02 percent of the earth's mass is from oceans.

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1 year ago

Jesus wants to start saving for college. His parents started an account for him that currently holds $325. Jesus adds $50 each m

erma4kov [3.2K]

Answer:

y-intercept, c = 325

Slope, m = 50

The x-axis represents the number of months and y-axis represents the total amount in saving accounts.

Step-by-step explanation:

We are given the following in the question:

A saving account currently holds $325. Jesus adds $50 each month.

Let x be the number of months and y be the total money n the saving account.

Then, we can use a linear function to represent the money in the account.

$y(x) = 325 + 50x$

Comparing to general linear function,

$y = mx + c$

where m is the slope and tells the rate of change and c is the y-intercept that is the value when x is zero.

Comparing we get:

m = 50

c = 325

y-intercept = c = 325

Slope, m = 50

The x-axis represents the number of months and y-axis represents the total amount in saving accounts.

The attached image shows a graph for the same.

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2 years ago

If f(x) = (xm + 9)2, which statement about f(x) is true?

Marina CMI [18]

Answer:

The correct statement for the given function is:

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Step-by-step explanation:

The correct statement for the given function is:

f(x) is an even function for all even values of m.

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2 years ago

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Elodia [21]

Answer:

29 minutes

Step-by-step explanation:

Given

$Total = \$43.25$