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3 years ago

Which graph correctly shows the solution of the compound inequality 3x 2 -12 and 8x < 16?

Mathematics

1 answer:

Genrish500 [490]3 years ago

7 0

Answer:

8x < 16 it shows the solution of the compound inequality

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Multiple choice, need help with this ASAP; I'll give BRANIEST to whoever gets it right and no links

Sunny_sXe [5.5K]

Answer:

so it should be a,c,e, and b

Step-by-step explanation:

49s square root is 7 and 7 is an integer so check.

7 is a whole number check

7 is rational check

and 7 is a real number check.

6 0

2 years ago

Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand service to two nearby towns, Spr

NeX [460]

Answer:

20.2057 Units.

Step-by-step explanation:

First, we determine the length of the cable.

Distance between Centerville (8,0) and point (x,0) is given as:

$\sqrt{(8-x)}^2=8-x$

Distance between point (x,0) and Springfield(0,7) is:

$\sqrt{(7-0)^2+(0-x)^{2}}=\sqrt{(7)^2+(x)^{2}}$

Distance between point (x,0) and Shelvyfield(0,-7) is:

$\sqrt{(-7-0)^2+(0-x)^{2}}=\sqrt{(7)^2+(x)^{2}}$

Therefore the Length of the Cable L(x)

$L(x)=(8-x)+2\sqrt{(7)^2+(x)^{2}}$

To find the critical point, we set the derivative of L(x)=0

$L^{'}(x)=-1+\frac{2x}{\sqrt{\left( 49 - x^{2}\right) }}$

$\frac{-\sqrt{\left( 49 - x^{2}\right)}+2x}{\sqrt{\left( 49 - x^{2}\right)}}=0\\-\sqrt{\left( 49 - x^{2}\right)}+2x=0\\\sqrt{\left( 49 - x^{2}\right)}=2x\\(\sqrt{\left( 49 - x^{2}\right)})^2=(2x)^2\\49 - x^{2}=4x^2\\49=5x^2\\x^2=\frac{49}{5}\\x= 3.1305$

To verify that L(x) has a minimum at this critical number we compute the second derivative L″(x) and find its value at the critical number.

$L^{''}(x)=\frac{\left( 98\right) \,\sqrt{\left( 49 - x^{2}\right) }}{{\left( 7 - x\right) }^{2}\,{\left( 7+x\right) }^{2}}\\At \:x=3.1305, L^{''}=0.3993$

Since $L^{''}(x)$ is positive, the minimum point of L(x) exists.

Next, we find the minimum length by substituting z=3.1305 into L(x)

$L(3.1305)=(8-3.1305)+2\sqrt{(7)^2+(3.1305)^{2}}$

Minimum Length, L=20.2057

The minimum length of the cable is 20.2057 Units.

6 0

2 years ago

Use an exponent to write each expression 3/4 x 3/4 x 3/4 x 3/4 x 3/4

Advocard [28]

Answer:

${ \frac{3}{4} }^{5}$

6 0

3 years ago

Complete the remainder of the table for the given function rule: y = 2x + 4

Yanka [14]

Answer:

eight.

Step-by-step explanation:

2(6) ÷ 3

12÷3

4+4

8 0

3 years ago

Mario invested $6,000 in an account that pays 5% annual interest compounded annually. Using the formula A = P(1 + r)t, what is t

Rudiy27

Answer:

$6778.36

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Compounded Interest Rate Formula: $\displaystyle A = P(1 + \frac{r}{n})^{nt}$

P is principle amount
r is rate
n is compounded rate
t is time

Step-by-step explanation:

Step 1: Define

Identify variables

P = 6000

r = 5% = 0.05

n = 1

t = 2.5

Step 2: Find Interest

Substitute in variables [Compounded Interest Rate Formula]: $\displaystyle A = 6000(1 + \frac{0.05}{1})^{1 \cdot 2.5}$
Simplify: $\displaystyle A = 6000(1.05)^{2.5}$
Evaluate: $\displaystyle A = 6778.36$

8 0

3 years ago