The sum of two numbers is 37. the greater number is 5 more than three times the lesser number. what is the lesser of the two numbers?

Answers

Answer 1

Answer: Hi there!

In order to solve this problem, we should first write this into expressions.

Let x = the bigger number
Let y = the smaller number

x + y = 37
x = 3y + 5

Now, we can use substitution of the system ofinequalities to solve.

We substitute the value of x into the equation.

3y + 5 + y = 37

Now, we simplify.

4y + 5 = 37
4y = 32
y = 8

So, 8 is the answer.

Hope this helps!

Answer 2

Answer: 3y+y+=37 that’s the answer to that

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If 9 men can do a job in 24 days, how many men are needed to do the same job in 18 days?a. 11
b. 12
c. 15
d. 18

Answers

Answer:

b 12

Step-by-step explanation:

1/(9*24)=1/(x*18)

9*24=18x

x=12

Answer:

b. 12 mens are needed to do that job

The number p is 20 more than the number q . using algebra write the relationship between p and q .

Answers

From what we know, p is 20 more than q. So, we can assume p = 20 + q. Q can also be found by subtracting 20 from both sides. So, q = p - 20.

Hope this helped!

Find all relative extrema of the function. use the second derivative test where applicable. (if an answer does not exist, enter dne.) f(x) = x3 − 9x2 + 2

Answers

First find the derivative of the function. The derivative is $f'(x)=3 x^(2) -18x$ . Now set it equal to 0 to find the critical numbers. $0=3 x^(2) -18x$ . Factor to solve for the zeros of the derivative. $0=3x(x-6)$ . So 3x = 0, and x = 0, or x - 6 = 0 and x = 6. We will make a table with values for -∞<x<0, 0<x<6, 6<x<∞. Pick a value within those boundaries for each interval and find the sign, positive or negative, that results from subbing that number into the derivative. If we choose -1 in the first interval f'(-1)=21, so the function is increasing from negative infinity to 0. If we choose 1 in the second interval, f'(1)=-15, so the function is decreasing from 0 to 6. If we choose 10 in the last interval, f'(10)=120, so the function is increasing from 6 to infinity. The points of extrema are found by subbing the critical x values into the original function. We know the function is increasing from negative infinity to 0, so f(0)=2, and our max point is (0, 2). We know the function is decreasing from 6 to infinity, so f(6)=-106, and our min point is (6, -106). I do this instead of the second derivative test, but they both work.

How many odd numbers greater than 60000 can be formed, using numbers 2,3,4,5 and 6 if each digit is used only once in each number?

Answers

Hello,

All the numbers must begin with 6.

There are still 2,3,4,5 digits : 4 possibilities.

4!=4*3*2*1=24

The first is 62345 and the last 65432.

Final answer:

To find the number of odd numbers greater than 60000 that can be formed using the given numbers with each digit used only once, you can determine the number of possibilities for each digit and multiply them together. The answer is 96.

Explanation:

To find the number of odd numbers greater than 60000 that can be formed using the numbers 2, 3, 4, 5, and 6 with each digit used only once, we need to consider the possible arrangements of these digits. First, we can determine the number of possibilities for the leftmost digit, which must be either 3, 4, 5, or 6. Next, we can determine the number of possibilities for the remaining four digits, which can be arranged in 4! (4 factorial) ways. Multiplying these two values gives us the total number of odd numbers greater than 60000 that can be formed using these digits with each digit used only once.

Thus, the number of odd numbers greater than 60000 that can be formed using the numbers 2, 3, 4, 5, and 6 with each digit used only once is 4 * 4! = 4 * 4 * 3 * 2 * 1 = 96.

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At how many points does the graph of the function below intersects the x-axis?y=3x^2-5x+1
A. 0
B. 1
c, 2

Answers

Answer: 2 points

Step-by-step explanation: the graph of y=3x^2-5x+1 intersect the x-axis at those real values of x where y=0

i.e. 3x^2-5x+1=0

ax²+bx+c=0 has real roots if b²-4ac≥0

if b²-4ac=0 implies real and equal roots

here a=3,b=-5 and c=1

b²-4ac=25-12>0

this implies that this equation has unequal real roots

so,this equation will intersect the x-axis at two distinct points

Unfortunately it doesn't factor nicely. You can try completing the square but it's really hard because A isn't 1. Because A is positive, you know that the parabola opens upwards. That means if you can find a negative function value then it definitely crosses the x axis twice because of symmetry. If you plug in 1 for x then y is -1. So the answer is C. 2.

The cost C, in dollars, for delivered pizza depends on the number p of pizzas ordered. The situation is represented by the function rule C equals 5 plus 9 p. Would the graph be continuous or discrete? Explain your answer.

Answers

Answer: discrete

Step-by-step explanation:

The graph would be discrete, because you can only order a whole number of pizzas. This means you cannot have 0.4 of a pizza or 3/5 of a pizza. Therefore, p can only be whole numbers, so you cannot draw a line through the points, since prices for non-whole pizzas are not possible.

Final answer:

The graph representing the cost of delivered pizzas depending on the number ordered is discrete because you can only order a whole number of pizzas, therefore the graph will show distinct points for each whole number of pizzas.

Explanation:

The graph representing the cost C, in dollars, for delivered pizza depending on the number p of pizzas ordered would be discrete. This is because you can only order a whole number of pizzas, not a fraction of a pizza. In this case, the number of pizzas p is a discrete variable, as is the cost C. A continuous graph has points that are connected, showing all possible values, while a discrete graph consists of isolated points representing specific values. In our pizza scenario, the graph would indicate specific costs for 1 pizza, 2 pizzas, 3 pizzas, and so on. Hence, the graph will be a series of distinct points, making it a discrete graph.

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