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3 years ago

Solve the equation 5(x + 2) = 6x + 3x − 14, and show your work.

Mathematics

2 answers:

amm18123 years ago

8 0

Answer:

X=6

Step-by-step explanation:

5(x+2)=6x+3x−1

Step 1: Simplify both sides of the equation.

5(x+2)=6x+3x−14

(5)(x)+(5)(2)=6x+3x+−14(Distribute)

5x+10=6x+3x+−14

5x+10=(6x+3x)+(−14)(Combine Like Terms)

5x+10=9x+−14

5x+10=9x−14

Step 2: Subtract 9x from both sides.

5x+10−9x=9x−14−9x

−4x+10=−14

Step 3: Subtract 10 from both sides.

−4x+10−10=−14−10

−4x=−24

Step 4: Divide both sides by -4.

−4x / -4= −24 / −4

x=6

jarptica [38.1K]3 years ago

6 0

Answer:

$x=6$

Step-by-step explanation:-

$5\left(x+2\right)=6x+3x-14$

First, we will Add smiler elements: $6x+3x=9x$

⇢ $5\left(x+2\right)=9x-14$

Expand $5(x+2)$ by applying Distributive law: $a(b+c)=ab+ac$

⇢ $5x+5\times \:2$

⇢ $5x+10$

$5x+10=9x-14$

Now, Subtract 10 from both sides :

⇢ $5x+10-10=9x-14-10$

⇢ $-4x=-24$

Divide both sides by - 4:

⇢ $\frac{-4x}{-4}=\frac{-24}{-4}$

⇢ $x=6$

OAmalOHopeO

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Which is the graph of f (x) = 4 (1/2) Superscript x?

miss Akunina [59]

Answer:

Option (2) is correct graph.

Step-by-step explanation:

Given:

The function to graph is given as:

$f(x)=4(\frac{1}{2})^x$

Now, the above function is an exponential function of the form $f(x)=ka^x$

Where, 'k' and 'a' are constants.

The range of an exponential function is always greater than 0.

The domain is all real numbers.

Now, for graphing it, we need to find some points on it and its end behaviour.

Now, for x = 0, the function value is given as:

$f(0)=4(\frac{1}{2})^0=4$

So, (0, 4) is a point on the graph.

Now, for x = 1, the function value is given as:

$f(1)=4(\frac{1}{2})^1=4\times\frac{1}{2}=2$

So, (1, 2) is another point on the graph.

Now, for x = 2, the function value is given as:

$f(2)=4(\frac{1}{2})^2=4\times\frac{1}{4}=1$

So, (2, 1) is another point on the graph.

Now, as 'x' tends to ∞, the function value tends to:

$f(x\to\infty)=4\cdot\frac{1}{2}^{\infty}=\frac{4}{\infty}=0$

So, as

$x\to\infty,f(x)\to0\\\\x\to-\infty,f(x)\to\infty$

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4 years ago

Convert 48°36'12" to the nearest thousandth of a degree

uranmaximum [27]

48 degrees remains

divide minutes by 60

36/60 = 0.6

then divide seconds by 3600

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now add them all up

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4 years ago

The probability a household in a community uses gas for cooking is 0.18. If a shopper from the community is from a household tha

Lyrx [107]

Answer:

The probability of a person from the community not shopping at Prime Foods given that he uses gas for cooking at his household is 0.092

Step-by-step explanation:

Hello!

Given the information:

A: "The household uses gas for cooking" ⇒ P(A)= 0.18

B: "The person from the comunity shops at Prime Foods"

The person shops at Prime Foods given that he uses gas for cooking:

P(B/A)= 0.7

The person shops at Prime Foods given that he doesn't use gas for cooking:

P(B/Ac)= 0.35

If the person doesn't shop at Prime Foods, what is the probability that he uses gas for cooking?

Symbolically:

P(A/Bc) = P(A∩Bc)

P(Bc)

The event Bc is the complement of event B, so it's probability is P(Bc)= 1 - P(B)

You can calculate the probability of B as:

P(B)= P(A∩B)+ P(Ac∩B)

Using the information of P(B/A)= 0.7 and P(B/Ac)= 0.35 you can reach the values of both intersections.

P(B/A)= P(A∩B)

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P(B/A)*P(A)= P(A∩B)

P(A∩B)= 0.7*0.18= 0.126

and

P(B/Ac)= P(Ac∩B)

P(Ac)

If A and Ac are complementary events, then P(Ac)= 1 - P(A)= 1 - 0.18= 0.82

Then:

P(B/Ac)*P(Ac)= P(Ac∩B)

P(Ac∩B)= 0.35*0.82= 0.287

The probability of B is:

P(B)= P(A∩B)+ P(Ac∩B)= 0.126+0.287= 0.413

P(Bc)= 1 - P(B)= 1 - 0.413= 0.587

And

P(A)= P(A∩B)+P(A∩Bc)

P(A∩Bc)=P(A)=-(A∩B)= 0.18-0.126= 0.054

Finally:

P(A/Bc) = P(A∩Bc) =0.054 = 0.0919≅ 0.092

P(Bc) 0.587

I hope it helps!

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