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2 years ago

5. Carla babysits and tutors to make extra money. She babysits for $5 an hour and tutors for $10 an hour.

Mathematics

1 answer:

HACTEHA [7]2 years ago

5 0

Carla can babysit for 5 hours and tutor for 7 hours or babysit for 8 hours and tutor for 5.5 hours

<h3>How to graph the inequality?</h3>

Let x represents hours babysitting and y represents hours tutoring

So, we have:

Earnings = Rate of babysitting * x + Rate of tutoring* y

This gives

Earnings = 5x + 10y

He wants to earn at least $95.

This means that:

5x + 10y ≥ 95

See attachment for the graph of the inequality

From the attached graph, two possible solutions are: (5, 7) and (8, 5.5)

This means that Carla can babysit for 5 hours and tutor for 7 hours or babysit for 8 hours and tutor for 5.5 hours

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1. (a) Let A = 1, 3, 5, 7 and B = X : X is the first three multiple of 7 . Find (A−B).

ICE Princess25 [194]

Answer:

a) A-B = { 1 , 3, 5 }

b) The remainder is 50

c) f + g)(x) = x⁴+ 5x³

d) $\frac{dy}{dx} = \frac{2x- y^3(3x^2)) }{ 1- x^3 3y^2}$

Step-by-step explanation:

Step(I):-

1) a)

Let A = { 1, 3, 5, 7 } and B = { 7 , 14 , 21 }

A - B = {1,3,5,7} - { 7,14,21}

A - B = { 1 , 3, 5}

Given f (x)=3x³−11x−48

x-1 ) 3 x³ - 11x -48 (- 3x²-3x -2

-3<u>x³ +3x</u>²

3x²-11x-48

<u> </u> 2x -48

-2x +2

The remainder is 50

c) Given f(x) = x³ and g(x) = x + 5

(f. g)(x) = f(x) .g(x) = x³ . (x+5) = x³(x) + 5 x³ = x⁴+ 5x³

Given function y = 3 + x²+x³y³ ...(I)

By using derivative formulas

y = xⁿ

$\frac{dy}{dx} = n x^{n-1}$

Apply d/dx ( UV) = U V¹ + V U¹

Differentiating equation (I) with respective to 'x' , we get

$\frac{dy}{dx} = 0 + 2x + ( x^3 3y^2(\frac{dy}{dx} )+ y^3(3x^2))$

$\frac{dy}{dx} - ( x^3 3y^2(\frac{dy}{dx} )= 2x- y^3(3x^2))$

$\frac{dy}{dx} = \frac{2x- y^3(3x^2)) }{ 1- x^3 3y^2}$

7 0

2 years ago

Factor the cubic polynomial 6x3 – 11x2 – 12x 5. use the rational root theorem and synthetic division

pochemuha

The factorization of given cubic polynomial 6x³ - 11x² - 12x + 5 is:

6x³ - 11x² - 12x + 5 = (x + 1)(x - $\frac{5}{2}$ )(x - $\frac{1}{3}$ )

For given question,

We have been given the cubic polynomial 6x³ - 11x² - 12x + 5

We need to factorize given cubic polynomial.

By the rational roots theorem, any rational zero of f(x) is expressible in the form ± $\frac{p}{q}$ for integers p, q with p a divisor of the constant term 5 and q a divisor of the coefficient 6 of the leading term.

Factors of p = 5: 1, 5

Factors of q = 6: 1, 2, 3, 6

That means that the only possible rational zeros are:

±{ $\frac{1}{1} ,\frac{1}{2} ,\frac{1}{3} ,\frac{1}{6} ,\frac{5}{1} ,\frac{5}{2} ,\frac{5}{3} ,\frac{5}{6}$ }

= ±{ $1 ,\frac{1}{2} ,\frac{1}{3} ,\frac{1}{6} ,5 ,\frac{5}{2} ,\frac{5}{3} ,\frac{5}{6}$ }

We need to find the exact zeros of given cubic polynomial.

For x = 1,

6(1)³ - 11(1)² - 12(1) + 5 = -12

This means, x = 1 is not a zero of given cubic polynomial.

For x = -1,

6(-1)³ - 11(-1)² - 12(-1) + 5 = 0

This means, x = -1 is a zero of given cubic polynomial and (x + 1) is a factor.

To factorize given cubic polynomial we use synthetic division.

The synthetic division (6x³ - 11x² - 12x + 5) ÷ (x + 1) is as shown in following image.

⇒ 6x³ - 11x² - 12x + 5 = (x + 1)(6x² - 17x + 5)

The factors of above quadratic polynomial 6x² - 17x + 5 are:

⇒ 6x² - 17x + 5 = (x - $\frac{5}{2}$ )(x - $\frac{1}{3}$ )

So, the factors of given cubic polynomial are:

⇒ 6x³ - 11x² - 12x + 5 = (x + 1)(x - $\frac{5}{2}$ )(x - $\frac{1}{3}$ )

Therefore, the factorization of given cubic polynomial 6x³ - 11x² - 12x + 5 is: 6x³ - 11x² - 12x + 5 = (x + 1)(x - $\frac{5}{2}$ )(x - $\frac{1}{3}$ )

Learn more about the polynomial here:

brainly.com/question/16594008

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4 0

1 year ago

The base of a cone shaped glass is 12 inches and it is 18 inches tall. You

Damm [24]

Answer:

Step-by-step expla

To find the volume of a cone, use the equation: V = 1/3Bh.

In this equation, V is the volume, B is the base, and h is the height.

We are given that the base is 12 inches, and the height is 18 inches. With those necessary values, we can substitute those values, and calculate it.

V = 1/3(12)(18)

V = 4(18)

V = 72.0

Therefore, the volume of this glass is 72.0 cubic inches.

7 0

3 years ago

(X+2y)(x-2y) how do I solve this

Fudgin [204]

Step-by-step explanation:

(x+2y)(x-2y)

x^2-2xy+2xy-(2y)^2
x^2-4y^2

5 0

3 years ago

PROVE THESE TRIANGLES ARE CONGRUENT

jenyasd209 [6]

Answer:

These triangles cannot be proved congruent

Step-by-step explanation:

The theorems for congruence are SSS SAS ASA AAS. Here, there is only one common side and one common angle marked, therefore you cannot prove congruency.

8 0

1 year ago

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