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kap26 [50]
3 years ago
9

A painter earns 15$ per hour. What is the minimum number of hours he must work to earn at least 200$. Write an inequality to rep

resent this station and solve.
Mathematics
1 answer:
nasty-shy [4]3 years ago
5 0

Answer:  13 hours 40 minutes

<u>Step-by-step explanation:</u>

15x ≥ 200

\frac{15x}{15} \geq \frac{200}{15}

 x \geq \frac{200}{15}

 x \geq 13\frac{2}{3}

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HELP 40 POINTS
Tom [10]
Answer: the function g(x) has the smallest minimum y-value.


Explanation:


1) The function f(x) = 3x² + 12x + 16 is a parabola.


The vertex of the parabola is the minimum or maximum on the parabola.


If the parabola open down then the vertex is a maximum, and if the parabola open upward the vertex is a minimum.


The sign of the coefficient of the quadratic term tells whether the parabola opens upward or downward.


When such coefficient is positive, the parabola opens upward (so it has a minimum); when the coefficient is negative the parabola opens downward (so it has a maximum).


Here the coefficient is positive (3), which tells that the vertex of the parabola is a miimum.


Then, finding the minimum value of the function is done by finding the vertex.

I will change the form of the function to the vertex form by completing squares:

Given: 3x² + 12x + 16

Group: (3x² + 12x) + 16
Common factor: 3 [x² + 4x ] + 16
Complete squares: 3[ ( x² + 4x + 4) - 4] + 16
Factor the trinomial: 3 [(x + 2)² - 4] + 16
Distributive property: 3 (x + 2)² - 12 + 16
Combine like terms: 3 (x + 2)² + 4

That is the vertex form: A(x - h)² + k, whch means that the vertex is (h,k) = (-2, 4).


Then the minimum value is 4 (when x = - 2).


2) The othe function is <span>g(x)= 2 *sin(x-pi)
</span>

The sine function goes from -1 to + 1, so the minimum value of sin(x - pi) is - 1.


When you multiply by 2, you just increased the amplitude of the function and obtain the new minimum value is 2 (-1) = - 2


Comparing the two minima, you have 4 vs - 2, and so the function g(x) has the smallest minimum y-value.

7 0
3 years ago
Victoria has $2.90 in quarters, dimes and nickels. The numbers of nickels is one more than six times the number of quarters, and
maria [59]

Answer:

Step-by-step explanation:

She has 290 cents.

Nickels: 6x+1

Quarters: x

Dimes: 4x

Now that we've converted it algebraically, we can add them

6x+1 + x + 4x = 11x+1 = 290

11x = 289

x = 289/11

let me know if incorrect, i will fix

8 0
2 years ago
I need the answer for part b​
Softa [21]

Answer:

4/4

Step-by-step explanation:

1/4 plus 1/4 plus 2/4 is 4/4

4 0
1 year ago
A parking lot covers 32,420 square feet .what id its area to the nearest thousand feet
Mademuasel [1]

Answer: 32,000

Step-by-step explanation:

the thousands place (1000) is the fourth number to the left of the decimal, so round that one either up or down based on the number just one spot closer to the decimal, in this case, the hundreds place (100).

so we have 32,420

we can ignore the numbers that are going to become zeros as a result of the rounding . .

32,400

let's round 32,XXX either up or down based on the value in the hundreds place. if that value is 5 or greater, than we round up. if it is less than 5, than we round down.

4 is in the hundreds place, so we round down

32,000 is the answer

Hope this helps!!! Good luck!!! ;)

6 0
3 years ago
5+3x write in verbal expression
Keith_Richards [23]

Answer:

Five plus free equals 7

Step-by-step explanation:

I added five plus three

5 0
2 years ago
Read 2 more answers
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