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3 years ago

7x-2y=16 11x+6y=32.3how to solve this math problem

Mathematics

1 answer:

Aneli [31]3 years ago

6 0

Answer:

Step-by-step explanation:

These types of equations are called simultaneous equations and the method we can use to solve these type of equations is either Substitution, Elimination and Graphing.

We use substitution here because it is easier.

Equation 1

$7x-2y=16$

Equation 2

$11x+6y=32.3$

Lets take equation 1

$7x-2y=16\\7x=16+2y\\x=\frac{16+2y}{7}$

This is our equation 3 , now put it inside equation 2.

$11x+6y=32.3\\11(\frac{16+2y}{7} )+6y=32.3\\\frac{176+22y}{7} +6y=32.3\\\frac{176+22y+42y}{7}=32.3\\176+22y+42y=226.1 \\\\42y+22y=226.1-176\\64y=50.1\\y=\frac{50.1}{64} \\y=0.783\\$

We found the value of y , now to find the value of x insert the value of y in equation 3

$x=\frac{16+2y}{7}\\x=\frac{16+2(0.783)}{7} \\x=\frac{16+1.566}{7}\\x=\frac{17.566}{7}\\x=2.509$

Solved ! See the attached image on both the straight line graphs i have attached for better understanding. Where both the lines intersect each other is our value of (x , y) respectively.

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Find the inverse when f(x)=3x^2-3x-2

Vikentia [17]

Answer:

The inverse of f(x) is $f^{-1}$ (x) = ± $\sqrt{\frac{x+\frac{11}{4}}{3}}$ + $\frac{1}{2}$

Step-by-step explanation:

To find the inverse of the quadratic function f(x) = ax² + bx + c, you should put it in the vertex form f(x) = a(x - h)² + k, where

h = $\frac{-b}{2a}$

k is the vlue f at x = h

∵ f(x) = 3x² - 3x - 2

→ Compare it with the 1st form above to find a and b

∴ a = 3 and b = -3

→ Use the rule of h to find it

∵ h = $\frac{-(-3)}{2(3)}$ = $\frac{3}{6}$ = $\frac{1}{2}$

∴ h = $\frac{1}{2}$

→ Substitute x by the value of h in f to find k

∵ k = 3( $\frac{1}{2}$ )² - 3( $\frac{1}{2}$ ) - 2

∴ k = $-\frac{11}{4}$

→ Substitute the values of a, h, and k in the vertex form above

∵ f(x) = 3(x - $\frac{1}{2}$ )² + $-\frac{11}{4}$

∴ f(x) = 3(x - $\frac{1}{2}$ )² - $\frac{11}{4}$

Now let us find the inverse of f(x)

∵ f(x) = y

∴ y = 3(x - $\frac{1}{2}$ )² - $\frac{11}{4}$

→ Switch x and y

∵ x = 3(y - $\frac{1}{2}$ )² - $\frac{11}{4}$

→ Add $\frac{11}{4}$ to both sides

∴ x + $\frac{11}{4}$ = 3(y - $\frac{1}{2}$ )²

→ Divide both sides by 3

∵ $\frac{x+\frac{11}{4}}{3}$ = (y - $\frac{1}{2}$ )²

→ Take √ for both sides

∴ ± $\sqrt{\frac{x+\frac{11}{4}}{3}}$ = y - $\frac{1}{2}$

→ Add $\frac{1}{2}$ to both sides

∴ ± $\sqrt{\frac{x+\frac{11}{4}}{3}}$ + $\frac{1}{2}$ = y

→ Replace y by $f^{-1}$ (x)

∴ $f^{-1}$ (x) = ± $\sqrt{\frac{x+\frac{11}{4}}{3}}$ + $\frac{1}{2}$

∴ The inverse of f(x) is $f^{-1}$ (x) = ± $\sqrt{\frac{x+\frac{11}{4}}{3}}$ + $\frac{1}{2}$

4 0

3 years ago

A group of 8 people are sharing gummy bears each person wants 5 gummy bears each bag has 9 gummy bears

ANEK [815]

At least 5 bags of gummy bear bags are needed for each person to get 5 gummy bears.

The given parameters;

total number of people sharing the gummy bears, n = 8 people
number of gummy bears in each bag, = 9 gummy bears
number of gummy bears needed by each person = 5 gummy bears

The number of gummy bear bags needed to share 5 gummy bears to each person is calculated as follows;

let the number of gummy bears bag = x

$\frac{9x}{8} = 5\\\\9x = 40\\\\x = \frac{40}{9} \\\\x = 4.4$

Thus, at least 5 bags of gummy bear bags are needed for each person to get 5 gummy bears.

Learn more about sharing and divisions here: brainly.com/question/112003

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3 years ago

the price of jet fuel in north america during the last week of 2012 was recorded as $3,062 for 1,000 gallons. What was the unit

Andrews [41]

$3,062 for 1,000 gallons

3062 ÷ 1000 = 3.062

Unit rate:- $3.062 per gallon

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4 years ago

the average rainfall in Clearview is 38 inches . this year 29.777 inches fell . How much less rain fell this year than falls in

dexar [7]

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4 years ago

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Step-by-step explanation:

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3 years ago

7x-2y=16 11x+6y=32.3how to solve this math problem​

7x-2y=16 11x+6y=32.3how to solve this math problem