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4 years ago

(05.03 LC)

2 answers:

6 0

$f(x)=3x-23,\ g(x)=-4.5x+7\\\\f(x)=g(x)\iff3x-23=-4.5x+7\qquad\text{add 23 to both sides}\\\\3x=-4.5x+30\qquad\text{add 4.5x to both sides}\\\\7.5x=30\qquad\text{divide both sides by 7.5}\\\\\boxed{x=4}$

scoundrel [369]4 years ago

4 0

Hello there,

(05.03 LC)

Determine the solution to f(x) = g(x) using the following system of equations:

f(x) = 3x − 23

g(x) = −4.5x + 7

Answer: x = 4

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What is the solution for x in the given equation? The square root of 9x +7 + the square root of 2x = 7

cestrela7 [59]

Answer:

The solution is x =2 for the given equation $\sqrt{9x+7} +\sqrt{2x}=7$

Step-by-step explanation:

We need to find the solution for x in the given equation.

$\sqrt{9x+7} +\sqrt{2x}=7$

Solving:

Subtract $\sqrt{2x}$ from both sides

$\sqrt{9x+7} =7-\sqrt{2x}$

Taking square on both sides

$(\sqrt{9x+7})^2 =(7-\sqrt{2x})^2\\Using\,\, (a-b)^2 = a^2-2ab-b^2\\9x+7=(7)^2-2(7)(\sqrt{2x})+(\sqrt{2x})^2\\9x+7=49-14\sqrt{2x}+2x\\9x-2x+7-49=-14\sqrt{2x}\\7x-42=-14\sqrt{2x}\\Taking\,\,square\,\,on\,\,both\,\,sides\\(7x-42)^2=(-14\sqrt{2x})^2\\49x^2-2(7x)(42)+(42)^2= 196(2x)\\49x^2-588x+1764=392x\\49x^2-588x+1764-392x=0\\49x^2-980x+1764=0\\Using \,\,quadratic \,\, equation \,\,to \,\, find \,\, value \,\, of \,\, x \\x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\a= 49, \, b= -980 \,\,and\,\, c = 1764$

Putting values and solving

$x=\frac{-(-980)\pm\sqrt{(-980)^2-4(49)(1760)}}{2(49)}\\x=\frac{980\pm\sqrt{614656}}{98}\\Solving\\x=18 \,\, and x =2$

Verifying the solution by putting values of x in given equation

Putting x=18

$\sqrt{9x+7} +\sqrt{2x}=7\\\sqrt{9(18)+7} +\sqrt{2(18)}=7\\\sqrt{169} +\sqrt{36}=7\\13+6=7\\19\neq 7$

So, x=18 is not solution o given equation.

Putting x = 2

$\sqrt{9x+7} +\sqrt{2x}=7\\\sqrt{9(2)+7} +\sqrt{2(2)}=7\\\sqrt{25} +\sqrt{4}=7\\5+2=7\\7=7$

So, x=2 satisfies the equation

The solution is x =2 for the given equation $\sqrt{9x+7} +\sqrt{2x}=7$

7 0

3 years ago

An electrician charges $60 per hour. How much does he charge for 6 hours?

aliya0001 [1]

60 times 6 equals 360.

So the answer is $360

4 0

4 years ago

Read 2 more answers

Is every isosceles triangle equilateral? Is every equilateral triangle isosceles? Explain

Len [333]

Every equilateral triangle is also anisosceles triangle, so any two sides that are equal have equal opposite angles. Therefore, since all three sides of an equilateral triangle are equal, all three angles are equal, too.

4 0

3 years ago

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Find the nth term for the following sequences: Q2)3, 9, 15, 21

elixir [45]

Answer:

$a_{n}$ = 6n - 3

Step-by-step explanation:

There is a common difference d between consecutive terms, that is

d = 9 - 3 = 15 - 9 = 21 - 15 = 6

This indicates the sequence is arithmetic with n th term

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 3 and d = 6, then

$a_{n}$ = 3 + 6(n - 1) = 3 + 6n - 6 = 6n - 3

6 0

3 years ago

I need help!! please, you don’t even have to do it all just explain to me how to do the first one I’ll catch on

lisov135 [29]

Hi there!

What we need to know:

The three main trigonometric ratios are sine, cosine and tangent:

$\displaystyle sin\theta=\frac{opposite}{hypotenuse}$ $\displaystyle cos\theta=\frac{adjacent}{hypotenuse}$ $\displaystyle tan\theta=\frac{opposite}{adjacent}$

"Opposite" refers to the side opposite the angle that is not the hypotenuse.

"Hypotenuse" refers to the side opposite the right angle of a right triangle.

"Adjacent" refers to the side next to the angle that is not the hypotenuse.

"θ" is read as "theta". It just represents the angle.

Keep in mind that these three ratios only apply to right triangles.

You can use the mnemonic "soh-cah-toa" to help you remember these ratios.

First question

For the first question, we're given the angle with a measure of 56 degrees and the length of the hypotenuse. We must calculate a, which represents the side adjacent to the given angle.

Given the hypotenuse and the adjacent side, we know that we must use the cosine ratio:

$\displaystyle cos\theta=\frac{adjacent}{hypotenuse}$

Plug in the given information:

$\displaystyle cos56=\frac{a}{13}$