One number is 30% more than another number. Their sum is 23. What are the 2 numbers?

9514 1404 393

Answer:

  (x, y) = (3, 12)

Step-by-step explanation:

Using the given variable definitions, we can write the equations ...

  y = x + 9

  2(x +y) = 30

__

Solving the second equation for y, we have ...

  y = 15 -x

Substituting this into the first equation gives ...

  15 -x = x +9

  6 = 2x . . . . . . . . . add x-9

  3 = x . . . . . . . . . . divide by 2

  y = 3+9 = 12 . . . . substitute into the first equation

The numbers are (x, y) = (3, 12).

Answer:

Cost for each pound of jelly beans:  $2.75

Cost for each pound of almonds:  $3.75

Step-by-step explanation:

Let J be the cost of one pound of jelly beans.

Let A be the cost of one pound of almonds.

Using the given information, we can create a system of equations.

Given 3 pounds of jelly beans and 5 pounds of almonds cost $27:

\(\implies 3J + 5A = 27\)

Given 9 pounds of jelly beans and 7 pounds of almonds cost $51:

\(\implies 9J + 7A = 51\)

Therefore, the system of equations is:

\(\begin{cases}3J+5A=27\\9J+7A=51\end{cases}\)

To solve the system of equations, multiply the first equation by 3 to create a third equation:

\(3J \cdot 3+5A \cdot 3=27 \cdot 3\)

\(9J+15A=81\)

Subtract the second equation from the third equation to eliminate the J term.

\(\begin{array}{crcrcl}&9J & + & 15A & = & 81\\\vphantom{\dfrac12}- & (9J & + & 7A & = & 51)\\\cline{2-6}\vphantom{\dfrac12} &&&8A&=&30\end{array}\)

Solve the equation for A by dividing both sides by 8:

\(\dfrac{8A}{8}=\dfrac{30}{8}\)

\(A=3.75\)

Therefore, the cost of one pound of almonds is $3.75.

Now that we know the cost of one pound of almonds, we can substitute this value into one of the original equations to solve for J.

Using the first equation:

\(3J+5(3.75)=27\)

\(3J+18.75=27\)

\(3J+18.75-18/75=27-18.75\)

\(3J=8.25\)

\(\dfrac{3J}{3}=\dfrac{8.25}{3}\)

\(J=2.75\)

Therefore, the cost of one pound of jelly beans is $2.75.

Answer:

a) 9 beats

b) 9 beats per minute

c) y=9x

d) 180 times

Answer:area is 12

Step-by-step explanation:

Therefore , the solution to the given problem of function comes out to be slant asymptotes are y = x -4.

Numbers and their variants, equations & related structures, and geometry and their regions and potential applications are all mathematical topics. The link between a group of input, each of which generates a related output, is referred to as a "function." A function is a relationship between outputs and inputs where each input results in a single, distinct output. Each procedure has a domain and a city / municipality, which are frequently referred to as a scope. Functions are usually represented by the letter f. (x). The input is X. On activity, one-to-one activities, many-to-one activities, throughout operations, as well as on functions are the four main categories of supplied functions.

Here,

There are no limitations on the type of rational function, therefore it is feasible to construct one with each of the three asymptotes.

This is depicted in the attached graph, along with the graph of the rational function it represents. These are the asymptotes of the function.

Vertical asymptotes are x = -4,

horizontal asymptotes are y = 0 and

slant asymptotes are y = x -4.

Additional remarks

We employ an exponential function in our example function. Although it can be expressed as a polynomial of infinite degree, that is not often regarded as a polynomial. The proportion of polynomials is how most authors describe a rational function.

Therefore , the solution to the given problem of function comes out to be slant asymptotes are y = x -4.

To learn more about the function, visit:

https://brainly.com/question/28193995

#SPJ1

Answer:

x = 9 , y = 12

Step-by-step explanation:

Solve the following system:

{4 y - 5 x = 3

x = 2 y - 15

Hint: | Perform a substitution.

Substitute x = 2 y - 15 into the first equation:

{4 y - 5 (2 y - 15) = 3

x = 2 y - 15

Hint: | Expand the left-hand side of the equation 4 y - 5 (2 y - 15) = 3.

4 y - 5 (2 y - 15) = 4 y + (75 - 10 y) = 75 - 6 y:

{75 - 6 y = 3

x = 2 y - 15

Hint: | Choose an equation and a variable to solve for.

In the first equation, look to solve for y:

{75 - 6 y = 3

x = 2 y - 15

Hint: | Isolate terms with y to the left-hand side.

Subtract 75 from both sides:

{-6 y = -72

x = 2 y - 15

Hint: | Solve for y.

Divide both sides by -6:

{y = 12

x = 2 y - 15

Hint: | Perform a back substitution.

Substitute y = 12 into the second equation:

{y = 12

x = 9

Hint: | Sort results.

Collect results in alphabetical order:

Answer: {x = 9 , y = 12

Answer:

9 and 11

Step-by-step explanation:

thats all you need to know

Answer:

Step-by-step explanation:

The amplitude is the multiplier of the sine function: 3.

The period is 2π divided by the coefficient of x: 2π/2 = π.

The equation of the axis is any added constant: y = 0.

The range is the axis value ± the amplitude value: from -3 to +3.

Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:

10x + 5y ≥ 500 (minimum 500 units of vitamins)

5x + 10y ≥ 600 (minimum 600 units of minerals)

15x + 15y ≥ 1200 (minimum 1200 calories)

We want to minimize the cost, which is given by:

0.5x + 0.4y

This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:

10x + 5y = 500

5x + 10y = 600

15x + 15y = 1200

Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.

Next, we can calculate the value of the cost function at each corner point of the feasible region:

Corner point A: (20, 40) -> Cost = 20

Corner point B: (40, 25) -> Cost = 25

Corner point C: (60, 0) -> Cost = 30

Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.

Answer:

Commission amount

0.70

$

Owner receives

34.30

$

The equation of line with slope as "-7" and passes through point (5,9) in function notation is f(x) = -7x - 26 .

We know that the equation of the line with slope "m = -7" passing through the point (-5, 9) can be found using the point-slope form of the equation of a line : which is ⇒ y - y₁ = m(x - x₁)

where (x₁, y₁) = (-5, 9) is the point and m = -7 is the slope.

On Substituting the values of point and slope , in the equation ,

⇒ y - 9 = -7(x - (-5)) ;

Simplifying the expression further ;

⇒ y - 9 = -7(x + 5)  ;

⇒ y - 9 = -7x - 35  ;

Adding 9 to both sides,

⇒ y = -7x - 26

In function notation is f(x) = -7x - 26  .

Therefore, the required equation of the line  is  f(x) = -7x - 26  .

Learn more about Equation Of Line here

https://brainly.com/question/29775305

#SPJ4

We are 95% confident that the true population proportion is between 71.6% and 80.4%

The 95% confidence interval for the proportion of all U.S. grown people who would include those  on their list of 10 historic events can be constructed using the formula:

Where:

\(pi\) = sample proportion (76%)

SE = standard error (square root of \(pi(1-pi)/n\))

z = the critical value for a 95% confidence level (1.96)

n = sample size (2025)

Plugging in the values, we get:

\(SE =\sqrt{(0.76(1-0.76)/2025)} = 0.0240\\CI = 0.76 ± (1.96)(0.0240) = (0.716, 0.804)\)

The 95% confidence interval can be interpreted as follows: If we repeated this study many times, 95% of the intervals constructed would contain the true population proportion of all U.S. grown persons who would include on their list of 10 historic events. Based on this sample, we are 95% confident that the true population proportion is between 71.6% and 80.4%.

Learn more about confidence intervals here:

https://brainly.com/question/17097944

#SPJ4

take I don't know it's right or wrong I just guessing and saying to u .

78

Answer:

C

Step-by-step explanation:

I have the same question and computer lol

3 1/2 = 7/2

7/2 ÷ 1/4

7/2 × 4/1

14/2

7 pieces

hope it helps...!!!

Answer:

16

Step-by-step explanation:

Answer: 24

Step-by-step explanation: LCM(8, 12) = 24

12 x 2 = 24

8 x 3 = 24

Answer:

Step-by-step explanation:

4.375

The sum of the inverse cosine and the inverse sine of the same ratio is; Choice B; 90°.

The sine and inverse sine functions can help find the missing angle in a right triangle; Choice C; both is correct.

Recall that; if angles A and B are complementary angles; i.e A + B = 90; then

sin A = cos B = x

On this note since sin A = x and cos B = x;

sin-¹ x = A and cos-¹ x = B

On this note, the sum of sin-¹ x and cos-¹ x = A + B = 90°.

Hence, Choice B is correct.

2. It follows from triangle geometry that the measure of acute angles of a right triangle can be determined by trigonometric ratios.

Hence, both sin and sin-¹ would allow one to find the missing angle in a right triangle. Hence, Choice C is correct.

Read more on trigonometry;

https://brainly.com/question/3418378

#SPJ1

Answer:

942 square millimeters.

Step-by-step explanation:

The formula for the surface area of a cylinder is:

S = 2πr^2 + 2πrh

where S is the surface area, r is the radius, and h is the height.

Substituting the given values, we get:

S = 2 x 3.14 x 10^2 + 2 x 3.14 x 10 x 5

S = 628 + 314

S = 942

Therefore, the surface area of the cylinder is 942 square millimeters.

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer:

2(7x-1)

Step-by-step explanation:

14 & 2 gcf 2 factor and wal lah!

If the least value of n is 4, then the inequality best shows all the possible values of n is, n ≥ 4. So Option B is correct

Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.

We use these symbols to represent inequalities, '>' , '<', '≥', '≤'

Given that,

The least value of n is 4,

Inequality representation = ?

It is known that,

Least value  of n is 4

So, Minimum possible value of n is 4

Maximum value of n should be more than 4,

In order to satisfy the condition,

So,

n  > 4

By combining both the things,

It can be written as,

n ≥ 4

Hence, the best inequality representation is n ≥ 4

To know more about inequalities check:

https://brainly.com/question/28823603

#SPJ1

Answer:

ray UV and ray UT

Step-by-step explanation:

The sides are the rays that make up the angle

ray UV and ray UT make up the angle VUT

Answer:

see explanation below

Step-by-step explanation:

4. ∠A = 35, a = 8.9, find c

since side a is opposite to m∠A and c is the hypotenuse, we can use sin(∠A) = opp/hypo equation

5. sin(35) = 8.9/c

=> c = 8.9/sin(35) = 8.9/0.5736 = 15.516

6. 15.5

Answer:

Slope

Step-by-step explanation:

Given

The above statement

Required

What compares the steep of linear functions

Literally, steepness means slope.

So, when the slope of the two linear functions are calculated, we can make comparison between the calculated slopes to determine which of the functions is steeper or less steep.

Also:

Higher slope means steeper line

e.g.

4 is steeper than 1