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3 years ago

The table represents a linear function f(x) in the equation represents a function g(x):

1 answer:

4 0

A: Looking at the last two rows of the table of f(x), the slope is simply (3-0)/(1-0) = 3, while the slope of g(x) is the coefficient of the variable x, which is 7.

B. y-int is the y value when x = 0. f(x) has a y-int of 0, which g(x) is 2. The latter has a greater y-int.

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Please help simplify with steps

Leviafan [203]

Remember that you can always multiply or divide BOTH the numerator and denominator
of the fraction by anything you want to. You just have to do exactly the same to both of
them.

The way to simplify a fraction is to divide both the numerator and denominator by their
greatest common factor.

Do you see all of those 'x's on the top and bottom ? The top and bottom can
both be divided by x-cubed.

Numerator:
Divide (-4³) by x³, and you have (-4) left.

Denominator:
Divide (x³ - 2x⁴) by x³, and you have (1 - 2x) left.

So, the simplified fraction is [ -4 / (1 - 2x) ].

That's a perfectly good answer, but you could make it look a little prettier
if you multiply the top and bottom both by -1 . Then it would be

4 / (2x - 1) .

Either one is fine.

8 0

3 years ago

there are 12 boys and 16 girls in a classroom which represents the simplified ratio of girls to students in a classroom? 3 to 4,

Marat540 [252]

Answer:

Ratio of girls to students = 4 : 7

Step-by-step explanation:

Number of boys= 12

Number of girls= 16

Total number of students= 12+16= 28

Number of girls to number of students= $\frac{16}{28}$ = $\frac{4}{7}$

Ratio of girls to students = 4:7

Hope this helps.

4 0

2 years ago

Read 2 more answers

Solve the following pair of equations simultaneously.

Alchen [17]

Answer:

No solutions.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS
Equality Properties

Algebra I

Solving systems of equations using substitution/elimination
Solving systems of equations by graphing
Expanding
Finding roots of a quadratic
Standard Form: ax² + bx + c = 0
Quadratic Formula: $x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$

Step-by-step explanation:

Step 1: Define systems

2x - y = 9

4x² + 3y² - 2x + y = 16

Step 2: Rewrite systems

2x - y = 9

Subtract 2x on both sides: -y = 9 - 2x
Divide -1 on both sides: y = 2x - 9

Step 3: Redefine systems

y = 2x - 9

4x² + 3y² - 2x + y = 16

Step 4: Solve for x

Substitution

Substitute in y: 4x² + 3(2x - 9)² - 2x + (2x - 9) = 16
Expand: 4x² + 3(4x² - 36x + 81) - 2x + (2x - 9) = 16
Distribute 3: 4x² + 12x² - 108x + 243 - 2x + 2x - 9 = 16
Combine like terms: 16x² - 108x + 234 = 16
Factor GCF: 2(8x² - 54x + 117) = 16
Divide 2 on both sides: 8x² - 54x + 117 = 8
Subtract 8 on both sides: 8x² - 54x + 109 = 0
Define variables: a = 8, b = -54, c = 109
Resubstitute: $x=\frac{54\pm\sqrt{(-54)^2-4(8)(109)} }{2(8)}$
Exponents: $x=\frac{54\pm\sqrt{2916-4(8)(109)} }{2(8)}$
Multiply: $x=\frac{54\pm\sqrt{2916-3488} }{16}$
Subtract: $x=\frac{54\pm\sqrt{-572} }{16}$

Here we see that we start to delve into imaginary roots. Since on a real number plane, we do not have imaginary roots, there would be no solution to the systems of equations.

Step 5: Graph systems

We can verify our results.

8 0

2 years ago

Fractional Equations Help with steps

Sliva [168]

Answer:

see explanation

Step-by-step explanation:

(e)

$\frac{2x-1}{3}$ - $\frac{3x-1}{4}$ = 1

Multiply through by 12 to clear the fractions

4(2x - 1) - 3(3x - 1) = 12 ← distribute parenthesis and simplify

8x - 4 - 9x + 3 = 12

- x - 1 = 12 ( add 1 to both sides )

- x = 13 ( multiply both sides by - 1 )

x = - 13

---------------------------------------------------------------

(f)

$\frac{3m}{4}$ - 5 = 24 ( add 5 to both sides )

$\frac{3m}{4}$ = 29 ( multiply both sides by 4 )

3m = 116 ( divide both sides by 3 )

m = $\frac{116}{3}$

--------------------------------------------------------------

(g)

$\frac{5(y+2)}{2}$ - $\frac{4(y+1)}{3}$ = 3

Multiply through by 6 to clear the fractions

15(y + 2) - 8(y + 1) = 18 ← distribute parenthesis and simplify

15y + 30 - 8y - 8 = 18

7y + 22 = 18 ( subtract 22 from both sides )

7y = - 4 ( divide both sides by 7 )

y = - $\frac{4}{7}$

4 0

3 years ago

Please help with questions 3,4,and 5 See questions on sheet

e-lub [12.9K]

Answer:

For Question Number 3 :

Option 2 is correct as x is 6 units left means it has been subtracted by 6 units, it becomes x-6 and y is 6 units down it means it has also been subtracted by 6 units which becomes y-6.

For Question Number 4 : The correct answer is option 3.

Step-by-step explanation: As the reflection is along the line y=1, it simply means that x coordinate will remain constant which is 3. Now as the point is (3,10) which means it is 9 units up the line y=1 and so it will be down 9 units from the line y=1. As the law of reflection says that it has to be same on both the sides. hence 9 units down from the line y=1 means y=-8. So coordinate of the reflection of that point becomes (3,-8).

For Question Number 5 : The given vertices are P(4,1),Q(2,-8) and R(-8,1)

Now reflection along Y Axis , P' becomes (-4,1)

Q' becomes (-2,-8) and R' becomes (8,1). hence these are the new vertices of the triangle.Option 2 is the correct option.

8 0

3 years ago