What two numbers multiply to 80 and add to 28

Final answer:

To solve the system of equations using elimination, multiply one equation by a constant so that the coefficients of one variable will be the same in both equations. Then add or subtract the equations to eliminate that variable. Finally, solve for the remaining variable and substitute back to find the complete solution.

Explanation:

To solve the system of equations using elimination, we need to eliminate one variable by adding or subtracting the two equations. In this case, we can eliminate the variable y by multiplying the first equation by 3 and the second equation by 4. This will give us:

15x + 12y = 36

12x - 12y = 72

Next, we can add the two equations together to eliminate y:

27x = 108

Dividing both sides by 27, we find that x = 4.

Substituting this value of x back into one of the original equations, we can solve for y:

5x + 4y = 12

5(4) + 4y = 12

20 + 4y = 12

Subtracting 20 from both sides, we get 4y = -8.

Dividing both sides by 4, we find that y = -2.

Therefore, the solution to the system of equations is x = 4 and y = -2.

Answer:

The correct option is C. 0.213

Step-by-step explanation:

Percentage of students at high school who takes chemistry = 40%

So, probability of students who take chemistry = 0.4

So, probability of students who do not take chemistry = 1 - 0.4

                                                                                          = 0.6

Total number of students taken for survey = 12

Now, we need to find the probability that exactly 4 students have taken chemistry among the 12 surveyed students.

By using binomial distribution :

n = 12 , p = 0.4 , q = 0.6 , k = 4

[tex]\text{Required Probability = }_{k}^{n}\textrm{C}\cdot(p)^k\cdot(q)^{n-k}\\\\\implies\text{Required Probability = }_{4}^{12}\textrm{C} \cdot(0.4)^4 \cdot(0.6)^8 \\\\\implies \text{Required Probability = }0.2128\approx 0.213[/tex]

Therefore, The correct option is C. 0.213

The person's body temperature will approach 98.6ºF as time lapses. Option A is correct.

A horizontal asymptote for a function is an imaginary line that is not part of the graph and lies along the x-axis of the graph either to the left or right.

The horizontal asymptote of the given function can be described as the nature of the function T(f) as t approaches infinity.

This is the point where the line y=0 which means that the person's body temperature will approach 0ºF above 98.6ºF as t goes to infinity.

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Answer:

$77.72

Step-by-step explanation:

This is the total cost of the book with tax.

Answer:

It's A. translation

Step-by-step explanation:

The number of hamburgers will be 348.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that On Saturday, a local hamburger shop sold a combined total of 464 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold.

The number of hamburgers will be calculated as below:-

Cheeseburgers= x

Hamburgers= 3x

3x+x=464

4x=464

x=116

Substitute the value of x in expression.

Hamburgers= 3x

Hamburgers= 3 x 116 = 348

Therefore, the number of hamburgers will be 348.

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The local hamburger shop sold 116 hamburgers on Saturday. We determined this by setting up an equation where the number of hamburgers (H) plus three times the hamburgers (3H) equaled the total sales of 464 burgers, and then solving for H.

The question asks us to solve a basic algebra problem involving hamburgers and cheeseburgers. Let's define the number of hamburgers sold as H. Since the number of cheeseburgers sold was three times the number of hamburgers sold, we can represent the number of cheeseburgers as 3H. The total number of burgers sold was 464. Now, we can write down the equation:

H + 3H = 464

This simplifies to:

4H = 464

Now, we divide both sides by 4 to find the value of H:

H = 464 / 4

H = 116

So, the local hamburger shop sold 116 hamburgers on Saturday.

To determine the price of each cupcake, subtract the price of the pie from the total bill and then divide the result by the number of cupcakes. Each cupcake costs $1.62.

To determine the price of each cupcake, Rich can subtract the price of the pie from the total bill and then divide the result by the number of cupcakes:

Therefore, each cupcake costs $1.62.

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Answer:

Yes. Ratios of miles to minutes for Samuel and Beverly are proportional

Step-by-step explanation:

Samuel's speed can be calculated as following:

[tex]28/32=0,875[/tex]

0,875 miles per minute.

On the other hand Beverly's speed can be calculated as following:

[tex]42/48=0,875[/tex]

0,875 miles per minute

If we convert the speed to mile per hour:

[tex]0,875*60=52,5[/tex]

It can be easily seen that both Samuel and Beverly drove at the same speed at 52,5 miles per hour.

Answer:

d the answer is d

Answer:

The domain is all real integers 0 through 9.

I've done the test, hope this helps

Answer:

12(pi)

Step-by-step explanation:

To integrate 1 / sqrt(25 - 16x^2) dx, we use trigonometric substitution with x = (5/4)sinθ. After substitution, integration, and back-substitution, the result is arcsin(4x/5) + C, where C is the constant of integration.

The integral to solve is ∑ (1 / sqrt(25 - 16x^2)) dx, which resembles the inverse trigonometric function, specifically the arcsine function. To solve this integral, we can use a trigonometric substitution. Since the integral involves a square root of a difference of squares, we can substitute x with (5/4)sinθ, which simplifies the integral considerably.

After substitution, we can then use the derivative of sinθ, which is cosθ, in order to find the full differential dx to replace in our integral. The resulting integral in terms of θ can be integrated using standard techniques, yielding an arcsine function as the antiderivative. After integrating, we must then convert back from θ to x to express the solution to the original integral in the original variable.

The answer to the integral ∑ (1 / sqrt(25 - 16x^2)) dx is arcsin(4x/5) + C, where C is the constant of integration. The substitution step is crucial in solving this type of problem and is a commonly used method in calculus.

Final answer:

The mixed number of 158/4 simplified is 39 1/2. A proportion comparing the ratios 1/48 and w/16 is solved by cross-multiplication resulting in w = 1/3 as the solution.

Explanation:

To write 158/4 as a mixed number in simplest terms, we first divide 158 by 4. When we do this division, 4 goes into 158, 39 times completely, since 4 * 39 = 156, and we get a remainder of 2. Therefore, the mixed number form of 158/4 is 39 2/4. To simplify this fraction further, we divide the numerator and the denominator by their greatest common divisor, which in this case is 2. Simplifying 2/4 by dividing both the numerator and denominator by 2, we get 1/2. Hence, the mixed number in its simplest terms is 39 1/2.

To set up a proportion using the given ratios, we start with the ratio 1/48 and set it equal to w/16, which can be represented as:

1/48 = w/16

When solving for w, we cross-multiply to get:

1 * 16 = 48 * w

Which simplifies to:

16 = 48w

Finally, to find the value of w, we divide both sides of the equation by 48, which gives us w = 16/48. Simplifying by dividing both numerator and denominator by the greatest common divisor, 16, we get:

w = 1/3

Answer:

There are infinitely many solution.

Step-by-step explanation:

Given  : 16(x + 2) - 8 = 16x + 24.

To find : How many solutions are there to the equation below.

Solution : We have given

16(x + 2) - 8 = 16x + 24.

On distributing 16 over ( x +2) .

16 x + 32 - 8 = 16x + 24 .

16 x + 24 = 16x + 24.

We can see left hand side is equal to right hand sides .

Therefore, There are infinitely many solution.

Answer:

1. a, -3,-1,1,3

2. a, 3+i/2, 3-i/2, -4

3. d, 6- sqrt 6

4. a, x3-8x2-11x+148=0

5. d, there are either 2 or 0 positive roots and one negative

Step-by-step explanation:

I did the quick check.

Final answer:

The roots of the polynomial equation 2x³ + 2x² – 19x + 20 = 0 are complex.

Explanation:

To find the roots of the polynomial equation 2x³ + 2x² – 19x + 20 = 0, we can use the factoring method or the quadratic formula. Let's use the quadratic formula. The formula is x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation. In this case, a = 2, b = 2, and c = 20. Plugging the values into the quadratic formula, we get:

x = (-2 ± √(2² - 4(2)(20))) / (2(2))

x = (-2 ± √(4 - 160)) / 4

x = (-2 ± √(-156)) / 4

Since we cannot take the square root of a negative number in the real number system, the roots of the given equation are complex, which means there are no real solutions.

Answer:

3 1/6

Step-by-step explanation: it is because you would have to divide the  1 and the 6 well not really divide more of the multiplying then after that you switch 1 and 2 and the 2 is and the top and 1 at the bottom and you to butterfly some  of you should know then you get 3 1/6

To find the inverse of a function, switch x and y and solve for y. The inverse of f(x) = (x-1)/5 is f^-1(x) = 5x + 1. Verify that f(f^-1(x)) = x and f^-1(f(x)) = x.

To find the inverse of a function, we need to switch the roles of x and y and solve for y. In other words, we need to solve the equation y = (x-1)/5 for x. Let's do that:

Step 1: Replace y with x and x with y: x = (y-1)/5.

Step 2: Solve for y: Multiply both sides by 5: 5x = y - 1. Add 1 to both sides: 5x + 1 = y.

So, the inverse of f(x) = (x-1)/5 is f-1(x) = 5x + 1.

To verify that f(f-1(x)) = x, substitute f-1(x) into f(x) and simplify:

f(f-1(x)) = f(5x + 1) = ((5x + 1) - 1)/5 = 5x/5 = x.

Similarly, to verify that f-1(f(x)) = x, substitute f(x) into f-1(x) and simplify:

f-1(f(x)) = f-1((x-1)/5) = 5((x-1)/5) + 1 = x-1+1 = x.

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