(b) Sketch the graph of f.​

Answer:

6 & 21

Step-by-step explanation:

Let x be the smaller number. Let y be the larger number.

We have:
x + y = 5x - 3

However, we also know the larger number is 2x + 9 (nine more than twice the smaller). So, we can plug in 2x + 9 for y:

x + (2x + 9) = 5x - 3

x + 2x + 9 = 5x - 3

3x + 9 = 5x - 3

9 = 2x - 3

12 = 2x

x = 6

Now solver for the larger:

2x + 9 = 6*2 + 9 = 12 + 9 = 21

Therefore, the numbers are 6 and 21.

I hope this helps :D

Answer: 56

Step-by-step explanation:

There are 8 runners competing in the 400-meter race, and the fastest 3 runners win a ribbon. This means that there are 3 places that the runners can finish in: first, second, and third.

Since the order in which the runners finish matters, we need to use permutations to find the number of ways that the runners can finish in first, second, and third place.

The number of permutations of a set of n objects taken r at a time is given by the formula:

n! / (n - r)!

In this case, there are 8 runners, so n = 8, and we are selecting 3 runners at a time, so r = 3. Plugging these values into the formula gives us:

8! / (8 - 3)! = 8! / 5! = 8 * 7 * 6 / 5 * 4 * 3 = 56

Therefore, there are 56 ways that the runners can finish in first, second, and third place.

The reflection of  f(x)=6(x–7)2+2 is g(x) = -1 * (6(x–7)^2 + 2) = -6(x–7)^2 - 2.

What is the reflection of a function?

A reflection is a transformation of the graph of a function over the x-axis or the y-axis (or both). The function retains its basic shape; however, by including a negative sign in the appropriate place in the equation, the graph of the function will flip over one or the other of the axes.

To find the reflection of a function across the x-axis, we can simply multiply the function's y-coordinate by -1.

For f(x) = 6(x–7)^2 + 2,

the reflection across the x-axis is

g(x) = -1 * (6(x–7)^2 + 2) = -6(x–7)^2 - 2.

Hence, the reflection of  f(x)=6(x–7)2+2 is g(x) = -1 * (6(x–7)^2 + 2) = -6(x–7)^2 - 2.

To learn more about the reflection visit,

https://brainly.com/question/22688709

#SPJ1

Part (i)

[tex]a^6 \times a^3=a^{6+3}=\boxed{a^9}[/tex]

Part (ii)

[tex]\frac{24}{6} \times \frac{b^{16}}{b^4}=4b^{16-4}=\boxed{4b^{12}}[/tex]

The total would be 25 + (0.06 x 350) = $51. So my friend's charge for last month will be $51.

My friend's charge for last month will be calculated by adding the monthly customer fee of $25 and the minutes spent price of 0.06 for the 350 minutes spent. The total would be 25 + (0.06 x 350) = $51. So my friend's charge for last month will be $51.

Monthly customer fee = $25

Price per minute = $0.06

Total minutes spent = 350

Total cost = $25 + (0.06 x 350)

Total cost = $25 + 21

Total cost = $51

Learn more about total cost here:

https://brainly.com/question/28652728

#SPJ4

Answer:

x = - 12 , x = 13

Step-by-step explanation:

x² - x = 156 ( subtract 156 from both sides )

x² - x - 156 = 0 ← in standard form

(x - 13)(x + 12) = 0 ← in factored form

equate each factor to zero and solve for x

x + 12 = 0 ⇒ x = - 12

x - 13 = 0 ⇒ x = 13

The correct option is option a) The critical value depends on the number of categories, not the sample size.

The critical value for a chi-square test is determined by the level of significance (alpha) and the degrees of freedom (df). The degree of freedom is a function of the number of categories in the test, not the sample size. Therefore, increasing the sample size does not affect the critical value for a chi-square test.

The chi-square test is a statistical test used to determine whether there is a significant difference between the expected frequencies and the observed frequencies in one or more categories. It is used to test the independence of two categorical variables.

Therefore, The correct option is option a) critical value depends on the number of categories, not the sample size.

To know more about  the chi-square test refer to:

brainly.com/question/14082240

#SPJ4

The equation y = 3/5 x is graphed on a coordinate plane and attached

The equation is graphed using some points for the input which is x values and solving to get the y values

This is called the table of values used to plot on the coordinate plane

The table of values for y = 3/5 x is formed as follows

For x = -10, y = 3/5 * -10 = -6

For x = -5, y = 3/5 * -5 = -3

For x = 0, y = 3/5 * 0 = 0

For x = 5, y = 3/5 * 5 = 3

For x = 10, y = 3/5 * 10 = 6

table of values

x     y

-10  -6

-5   -3

0     0

5     3

6     6

Learn more about linear graphs at:

brainly.com/question/14323743

#SPJ1

Answer: Not linear

Step-by-step explanation:

Use the slope-intercept form

y

=

m

x

+

b

to find the slope

m

.

Given an arithmetic sequence with the first term -6 and the common difference -7, the first five terms are: -6, -13, -20, -27, -34.

The formula for the n-th term of an arithmetic sequence is given by:

a(n) = a(1) + (n - 1) d

Where:

a(1): the first term

d = common difference

The consecutive terms of an arithmetic sequence can be obtained as:

a(n) = a(n - 1) + d

Information available in the problem:

first term = a(1) = -6

common difference = d = -7

Hence,

a(1) = -6

a(2) = -6 - 7 = -13

a(3) = -13 - 7 = -20

a(4) = -20 - 7 = -27

a(5) = -27 - 7 = -34

Therefore the first five terms are: -6, -13, -20, -27, -34

Learn more about arithmetic sequence here:

https://brainly.com/question/28354530

#SPJ4

By applying partial derivative rule, we can obtain the answer as follows:

A. 321312 pounds

B. [tex]f_{x}[/tex] = 13000 + 14xy - 39x²

C. [tex]f_{y}[/tex] = 3500 + 7x²

D. 15211 weekly pounds per skilled worker

E. 4347 weekly pounds per unskilled worker

Partial derivative is the derivative of a function that has several independent variables, to one of the independent variables by holding the other independent variables as constants.

Now we take a look at the given problem. The production function is:

z = f(x, y) = 13000x + 3500y + 7x²y - 13x³, where

z = the weekly number of pounds of acetate fiber

x = the number of skilled workers at the plant

y = the number of unskilled workers at the plant

Weekly fiber that can be produced with 11 skilled workers and 45 unskilled workers:

z = f(x, y) = 13000x + 3500y + 7x²y - 13x³

  f(11,45) = 13000*11 + 3500*45 + 7*11²*45 - 13*11³

              = 143000 + 157500 + 7*121*45 - 13*1331

              = 143000 + 157500 + 38115 - 17,303

              = 321312 pounds

Rate of change of output with respect to the number of skilled workers:

[tex]f_{x}[/tex] = dz / dx

   = d(13000x + 3500y + 7x²y - 13x³) / dx

   = 13000 + 7*2xy - 13*3x²

   = 13000 + 14xy - 39x²

Rate of change of output with respect to the number of unskilled workers

[tex]f_{y}[/tex] = dz / dy

  = d(13000x + 3500y + 7x²y - 13x³) / dy

  = 3500 + 7x²

Rate of change of output with respect to skilled workers when 11 skilled workers and 45 unskilled workers are employed:

[tex]f_{x}[/tex] = 13000 + 14xy - 39x²

   = 13000 + 14*11*45 - 39*11²

   = 13000 + 6930 - 4719

   = 15211 weekly pounds per skilled worker

Rate of change of output with respect to unskilled workers when 11 skilled workers and 45 unskilled workers are employed:

[tex]f_{y}[/tex] = 3500 + 7x²

   = 3500 + 7*11²

   = 3500 + 847

   = 4347 weekly pounds per unskilled worker

To learn more about partial derivatives, click here: https://brainly.com/question/2772503

#SPJ4

The probability that three points chosen uniformly and independently on a circle fall on a semicircle is 1/2 or 50%.

The probability of three points chosen randomly and independently on a circle falling on a semicircle is 1/2, or 50%. This is because the probability of a point landing on either side of the semicircle is equal. The points are chosen on a circle, so each point has an equal probability of being on either side of the semicircle. Therefore, the probability of three points randomly chosen on a circle landing on a semicircle is 1/2 or 50%.

Let A, B, and C be the three points chosen on a circle.

The probability that A, B, and C fall on the semicircle is:

P(A on semicircle) x P(B on semicircle) x P(C on semicircle)

= (1/2) x (1/2) x (1/2)

= (1/2)^3

= 1/8

Therefore, the probability that three points chosen randomly and independently on a circle fall on a semicircle is 1/8 or 12.5%.

Learn more about probability here

https://brainly.com/question/11234923

#SPJ4

The probability that three points chosen uniformly and independently on a circle fall on a semicircle is written as 1/8.

The term probability in math is defined as the chances of something materializing based upon the ratio of its number of outcomes to the number of outcomes of the whole sample space the event relies upon.

While we looking into the given question, here let us consider that A, B, and C be the three points chosen on a circle.

Then the probability that A, B, and C fall on the semicircle is calculated as,

=> P(A on semicircle) x P(B on semicircle) x P(C on semicircle)

Now, we have to apply the value of each probability, then we get

=> (1/2) x (1/2) x (1/2)

Therefore, the resulting value is

=> (1/2)³ = 1/8

To know more about Probability here

https://brainly.com/question/11234923

#SPJ4

Answer:

The answer is D

Step-by-step explanation:

Trust me on this, its hard to explain but Im 100% sure.

Rounded to the nearest ten-thousandth, the solution is x of the logarithmic equation is 2.000.

To solve this equation, we can begin by isolating the logarithmic expression on one side of the equation. To do this, we can divide both sides of the equation by 3:

3 log 2x / 3 = 4 / 3

This simplifies to:

log 2x = 4/3

Now, we can use the property of logarithms that states that "log [tex]a^b[/tex] = b × log a" to rewrite the logarithmic expression on the left side of the equation:

log 2x = 4/3

log [tex]2^{(4/3)}[/tex] = 4/3

4/3 × log 2 = 4/3

This simplifies to:

log 2 = 1

Since "log [tex]a^1[/tex] = 1" for any value of "a," this means that [tex]2^1[/tex] = 2. Therefore, the solution to the equation is x = 2.

Learn more about logarithmic equations at

https://brainly.com/question/29197804?referrer=searchResults

#SPJ4

The radius of convergence,R, of the series [tex]\[ \sum_{n=1}^{\infty} ~9(-1)^n~ nx^n \][/tex] is (1, ∞)

We know that for a power series ∑an (x - p)^n

if |x - p| < R then the series converges,

and if |x - p| > R then the series diverges.

Here, the number R is called the radius of convergence.

We have been given a series [tex]\[ \sum_{n=1}^{\infty} ~9(-1)^n~ nx^n \][/tex]

We need find the radius of convergence.

We use ratio test.

We know for [tex]$\lim_{x\to\infty}~ | \frac{a_{n+1}}{a_n}|=L[/tex]

if L < 1, then the series converges

and If [tex]$\lim_{x\to\infty}~a_n \neq 0[/tex] then [tex]\sum a_n[/tex] diverges.

Using ratio test for given series,

[tex]$\lim_{x\to\infty}~ | \frac{9(-1)^{n+1}~ (n+1)x^{n+1}}{9(-1)^n~ nx^n}|\\\\\\[/tex]

= [tex]$\lim_{x\to\infty}~ | \frac{(n+1)x^{n+1}}{nx^n}|[/tex]

= [tex]$\lim_{x\to\infty}~ | \frac{(n+1)x}{n}|[/tex]

[tex]=|x| $\lim_{x\to\infty}~ | \frac{n+1}{n}|[/tex]

= |x|

This means, the series is convergent for |x| < 1.

Learn more about the radius of convergence here:

https://brainly.com/question/18763238

#SPJ4

Difference in miles travelled by Bus X and Y is  12.8 miles in distance

Velocity is the pace and direction of an item's movement, whereas speed is the time rate at which an object is travelling along a route. In other words, velocity is a vector, whereas speed is a scalar number.

The direction of a body or object's movement is defined by its velocity. In its basic form, speed is a scalar number. In essence, velocity is a vector quantity. It is the speed at which distance changes. It is the displacement change rate.

The size or extent of the displacement between two points is referred to as distance. Keep in mind that the distance between two points and the distance traveled between them are not the same. The length of the entire journey taken to go from one point to another is the distance traveled. Travel distance is not a vector.

Bus X travels 40 miles in 1 hour

Distance travelled in 2 hrs = 40*2 = 80 miles

Bus Y travels 60 miles per hour

Distance travelled in 1.12 hrs = 60*1.12 = 67.2 miles

Difference in miles travelled by Bus X and Y is = 80 - 67.2 = 12.8 miles

To learn more about Speed and Distance refer to :

https://brainly.com/question/29013239

#SPJ1

Answer:

13 square centimeters.

Step-by-step explanation:

There are 13 squares making up the shape

The quantity of fencing that the gardener would need to purchase would be = 1 5/12.

The total quantity of fencing the gardener needs to fence the the square garden = 4⅔

The length of one side of the garden = 3¼

The quantity of fencing the gardener needs to purchase would be = x

4⅔ = 3¼ + X

14/3 = 13/4 + X

X = 14/3 -13/4

X =56-39 /12

X= 17/12

X = 1 5/12ft.

Learn more about square here:

https://brainly.com/question/25092270

#SPJ1

The area of the parallelogram is 500 in squared

A parallelogram is a four sided polygon that has opposite sides parallel to each other.

The formula for the area of a parallelogram is base times height, just like the formula for the area of a rectangle.

A= bh

From the figure, b = 20 in, h= 25 in

Area = 20*25 = 500 in square

Conclusively, taking into consideration the height of the parallelogram as 25 in and the base as 20 in, the area is given as 500 in square

Learn more about parallelogram https://brainly.com/question/29147156

#SPJ1

The given expression [tex]x^{2} +8x+15[/tex] , can be expressed in completely factored form as [tex](x+5)(x+3)[/tex] .

The expression that is to be written in factored form is [tex]x^{2} +8x+15[/tex] ;

we will use the split the middle term method to express it in factored form , in this method we split the middle term and then write down the common factors .

the middle term [tex]8x[/tex] can be written as [tex]3x+5x[/tex] ;

we get ; [tex]x^{2} +3x+5x+15[/tex] ;

taking "x" common from first 2 terms and "5" common from the next two terms ,

we get ;

⇒ [tex]x(x +3)+5(x+3)[/tex] ;

⇒ [tex](x +3)(x+5)[/tex] ;

So , we get that the expression [tex]x^{2} +8x+15[/tex] is equivalent to [tex](x +3)(x+5)[/tex] .

Therefore , the completely factored form is [tex](x +3)(x+5)[/tex] .

The given question is incomplete , the complete question is

What is the completely factored form of the expression [tex]x^{2} +8x+15[/tex] ?

Learn more about Factored Form here

https://brainly.com/question/43919

#SPJ4

WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 9 mm.

A quadrilateral is defined as a two-dimensional shape with four sides, four vertices, and four angles. There are two main types: concave and convex. There are also various subcategories of convex quadrilaterals, such as trapezoids, parallelograms, rectangles, rhombi, and squares.

If quadrilateral WXYZ is a parallelogram, the opposite sides will be equal, in length from which the value of x will satisfy the two equations.

Given,

WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 9 mm.

The length of the opposite sides of a parallelogram are equal, which gives;

2x - 5 = x + 2

2x - x = 2 + 5

x = 7

Similarly, we have;

x + 8 = 15

x = 15 - 8 = 7

The lengths of the opposite sides are therefore;

2·x - 5 = 2 × 7 - 5 = 9 and x + 8 = 15

The option that indicates if WXYZ is a parallelogram is therefore;

WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 9 mm.

To learn more about parallelogram:brainly.com/question/21474928

#SPJ4

WXYZ cannot be a parallelogram because the value of x that makes one pair of sides congruent does not make the other pair of sides congruent best explains that WXYZ is not a parallelogram.

Therefore the answer is d) WXYZ cannot be a parallelogram because the value of x that makes one pair of sides congruent does not make the other pair of sides congruent.

A parallelogram is a quadrilateral with two pairs of parallel sides. This means that the sides of the quadrilateral are arranged such that opposite sides are parallel and have the same length. In other words, if you draw a line through one pair of opposite sides, the other pair of opposite sides will also be parallel to that line and have the same length.

So, to determine if a quadrilateral can be a parallelogram, we need to check if it has two pairs of parallel and congruent sides. It does not matter what the lengths of the sides are.

In this case, option (d) is the correct answer because it states that one pair of sides can be congruent, but the other pair of sides is not congruent, which means that the quadrilateral cannot be a parallelogram

--The question is incomplete, complete question is given below--

"Which best explains if quadrilateral WXYZ can be a parallelogram?

a) WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 9 mm.

b) WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 7 mm.

c) WXYZ cannot be a parallelogram because there are three different values for x when each expression is set equal to 15.

d) WXYZ cannot be a parallelogram because the value of x that makes one pair of sides congruent does not make the other pair of sides congruent."

To know more on parallelogram

https://brainly.com/question/888539

#SPJ4

The proper answer from each drop-down menu in the system depicted by the graph. Reset In the Next'system of Inequalities, the graph stands for 4x-y.

The system of inequality is depicted in the graph. 1. 4x-y less than or equal to 4 and 2x-2y less than or equal to 3, 2. 4x-y greater than or equal to 4 and 2x-2y less than or equal to 3, 3. 4x-y less than or equal to 4 and 2x-2y larger than or equal to 3, 4. 4x-y greater than or equal to 4 and 2x-2y greater than or equal to 3. In the graph-representation of the system, the test point fulfils both of the inequalities.

Pick the appropriate response from each drop-down menu in the system shown by the graph. Reset The graph represents 4x-y in the Next'system of Inequalities.. Equations simultaneously, or a system of equations Multiple equations must be solved simultaneously in algebra. There must be an equal number of equations and unknowns for a system to have a singular solution.

To learn more about system of equation refer to :

https://brainly.com/question/25976025

#SPJ1

The value of x from the given quadrilateral is 3.

A rhombus is a closed two-dimensional plane figure. It is considered a special parallelogram, and because of its unique properties, it gets an individual identity as a quadrilateral. A rhombus is also called an equilateral quadrilateral since all of its sides are equal in length.

Given that, rhombus (6x + 32)º and (17x - 1)º for what value of x is the figure given the special parallelogram.

A rhombus has two diagonals that bisect each other at right angles and diagonal bisects angles.

Now, (6x + 32)º=(17x - 1)º

17x-6x=32+1

11x=33

x=3

Therefore, the value of x is 3.

To learn more about an expression visit;

https://brainly.com/question/28170201.

#SPJ1

By solving a system of equations we will see that she has 9 quarters and 15 dimes.

Let's define the variables.

We know that Moolah has 24 coins, then:

d + q = 24

And the total value is $3.75, then:

q*0.25 + d*0.10 = 3.75

Then we can write the system of equations:

d + q = 24

q*0.25 + d*0.10 = 3.75

We can isolate d on the first equation to get:

d = 24 - q

Replacing that in the other equation we will get:

q*0.25 + (24 - q)*0.10 = 3.75

q*0.15 + 2.4 = 3.75

q*0.15 = 3.75 - 2.4

q*0.15 = 1.35

q = 1.35/0.15 = 9

So Moolah has 9 quarters and 15 dimes.

Learn more about systems of equations:

https://brainly.com/question/13729904

#SPJ1

Answer:

Below

Step-by-step explanation:

To find the number of games g that the team could lose and still be eligible for the playoffs, we can write the inequality:

g / 18 ≤ 40%

g / 18 ≤ 0.4

g ≤ 7.2

We can round down to 7 to get the maximum number of games the team could lose and still be eligible for the playoffs.

If the baseball team loses 8 of its remaining games, they will not advance to the playoffs. This is because 8 is greater than the maximum number of games they could lose and still be eligible for the playoffs, which is 7.

Subscribe to EvilMrGui Remastered

If a researcher finds that the probability of a word recognition program correctly interpreting a hand-written word is 9/10 . The number of  words that  the researcher expect the program to interpret correctly out of 40 words is 36 words.

Using this formula to find the number of words

Number of words = Probability of correctly interpreting a hand-written word × Expected words

Let plug in  the formula

Number of words = 9/10 × 40

Number of words = 36 words

Therefore we can conclude that the number of words is 36 words.

Learn more about number of words here:https://brainly.com/question/25567167

#SPJ1

The value of the vertex(central) angle EJF formed by the given polygon is; 30°

To find the central angle of a polygon, we will simply divide 360 degrees by the number of sides of the polygon.

Now, we are told that the sum of the central vertex angles sums up to 180 degrees. Now, by careful observation, we can tell that the number of isosceles triangles that will be formed in the semi circle are 6. Thus;

Number of polygon sides of the semi circle = 6 sides

Thus;

Central angle = 180/6

Central angle = 30°

Now, we know that the base of isosceles triangles are equal. Since we know that the sum of angles in all triangles is 180 degrees, then we can say that;

∠E = ∠F = [180 - 30]/2

∠E = ∠F = 75°

Read more about Polygon Central Angle at; brainly.com/question/224658

#SPJ1

By grouping like terms and taking common factors, we will see that the addition of the polynomials gives:

(6x^2 - 3) + (8x^2 - 5x - 1) = 14x^2 - 5x - 4

Here we want to add two polynomials:

6x^2 - 3

And

8x^2 - 5x - 1

To make that addition, we just need to group like terms and take common factors.

We start with:

(6x^2 - 3) + (8x^2 - 5x - 1)

Grouping like terms we will get:

(6x^2 + 8x^2) + (-5x) + (-3 - 1)

Now we can simplify that, so we will get:

(6 + 8)*x^2 - 5x - 4

14x^2 - 5x - 4

That is the addition of the polynomials.

Learn more about polynomials by reading:

https://brainly.com/question/4142886

#SPJ1