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2 years ago

Is this a quadratic function 2x+13=13

Mathematics

1 answer:

lys-0071 [83]2 years ago

7 0

Answer:

Step-by-step explanation:

Simplifying

2x + 13 = 0

Reorder the terms:

13 + 2x = 0

Solving

13 + 2x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-13' to each side of the equation.

13 + -13 + 2x = 0 + -13

Combine like terms: 13 + -13 = 0

0 + 2x = 0 + -13

2x = 0 + -13

Combine like terms: 0 + -13 = -13

2x = -13

Divide each side by '2'.

x = -6.5

Simplifying

x = -6.5

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What is the average rate of change of the function on the interval from x = 1 to x = 2?

neonofarm [45]

x=1 f = 10(5.5)(1) = 55

x=2, f = 10(5.5)(2) = 110

110-55 = 55

2-1 =1

55/1 = 55

average rate of change = 55

6 0

3 years ago

Kate is a wage earner. One year she earned $72 000. She works 36 hours/week.

Lemur [1.5K]

Answer:

Kate's possible hourly rate of pay: $34.75

Hours of overtime: 100

Step-by-step explanation:

In order to find Kate's hourly wage, we can set up an equation based on the number of hours she works per week and the estimated number of overtime hours to equal her total pay for the year. If Kate works 36 hours/week and there are 52 weeks in a year, her total hours for one year are: 36 x 52 = 1872. Setting up an equation based on her total earnings of $72,000:

1872x + 100(2x) = 72000, where 'x' is the hourly rate and '2x' is her overtime rate which is double time.

Combine like terms: 1872x + 200x = 72000 or 2072x = 72000

Divide both sides by 2072: 2072x/2072 = 72000/2072

Solve for x: x = $34.75

Kate's hourly rate is estimated at $34.75. We can check to see if this is correct by putting this value back into our original equation:

1872(34.75) + 100(2)(34.75) = 65052 + 6950 = 72002

The answer of $72,002 is very close to $72,000 and the best estimate of Kate's hourly wage and overtime hours.

8 0

3 years ago

Which number has the smallest value

tester [92]

Answer:

c would be the correct answer

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

The graphs of the polar curves r = 4 and r = 3 + 2cosθ are shown in the figure above. The curves intersect at θ = π/3 and θ = 5π

Gennadij [26K]

(a)

$\displaystyle \frac{1}{2} \cdot \int_{\frac{\pi}{3}}^{\frac{5\pi}{3}} \left(4^2 - (3 + 2\cos\theta)^2 \right) \, d\theta$

or, via symmetry

$\displaystyle\frac{1}{2} \cdot 2 \int_{\frac{\pi}{3}}^{\pi} \left(4^2 - (3 + 2\cos\theta)^2 \right) \, d\theta$

____________

(b)

By the chain rule:

$\displaystyle \frac{dy}{dx} = \frac{ dy/ d\theta}{ dx/ d\theta}$

For polar coordinates, x = rcosθ and y = rsinθ. Since
r = 3 + 2cosθ, it follows that

$x = (3 + 2\cos\theta) \cos \theta \\ 
y = (3 + 2\cos\theta) \sin \theta$

Differentiating with respect to theta

$\begin{aligned}
\displaystyle \frac{dy}{dx} &= \frac{ dy/ d\theta}{ dx/ d\theta} \\
&= \frac{(3 + 2\cos\theta)(\cos\theta) + (-2\sin\theta)(\sin\theta)}{(3 + 2\cos\theta)(-\sin\theta) + (-2\sin\theta)(\cos\theta)} \\ \\
\left.\frac{dy}{dx}\right_{\theta = \frac{\pi}{2}}
&= 2/3
\end{aligned}$

2/3 is the slope

____________

(c)

"distance between the particle and the origin increases at a constant rate of 3 units per second" implies dr/dt = 3

Angle θ and r are related via r = 3 + 2cosθ, so implicitly differentiating with respect to time

 $\displaystyle\frac{dr}{dt} = -2\sin\theta \frac{d\theta}{dt} \quad \stackrel{\theta = \pi/3}{\implies} \quad 3 = -2\left( \frac{\sqrt{3}}{2}}\right) \frac{d\theta}{dt} \implies \\ \\ \frac{d\theta}{dt} = -\sqrt{3} \text{ radians per second}$

5 0

3 years ago

Find the prime factorization of 120.

artcher [175]

Answer:

(7/8 - 4/5)^2 = 9/

1600

= 0.005625

Step-by-step explanation:

Subtract: 7/

- 4/

= 7 · 5/

8 · 5

- 4 · 8/

5 · 8

= 35/

- 32/

= 35 - 32/

= 3/

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(8, 5) = 40. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 5 = 40. In the next intermediate step, the fraction result cannot be further simplified by canceling.

In words - seven eighths minus four-fifths = three fortieths.

Exponentiation: the result of step No. 1 ^ 2 = 3/

^ 2 = 32/

402

= 9/

1600

In words - three-fortieths squared = nine one-thousand six-hundredths.

7 0

3 years ago