A company has determined that the demand function for a certain couch is given by
= 2700 − 0.75, where p is the price per couch, and x is the number of couches sold. The fixed costs associated with producing a line of couches is $760,000, and each couch costs $360 to make. Determine how many couches should be manufactured and sold in order to maximize profit. Start by finding functions to represent the revenue and the total cost, then find a function for profit

Answers

Answer 1

The number of couches manufactured and sold in order to maximise the profit is 1560.

The demand function will be

p = 2700 - 0.75x

Here p = price per couch and x = number of couch

Total Fixed cost = $760000

Variable cost per couch = $360

Total cost = Fixed cost + variable cost

T(x) = 760000 + 360x

Revenue function will be

R(x) = Px

(2700 - 0.75x)x

2700x - 0.75x²

Since profit function = Pr(x)

Pr(x) = R(x) - T(x)

= 2700x - 0.75x² -760000 -360x

- 0.75x² + 2700x - 360x - 760000

For maximum profit

[tex]\frac{d}{dx}(Pr(x)) = 0[/tex]

[tex]\frac{d}{dx}[-0.75x^{2} + 2340x -760000 ] = 0[/tex]

-1.5x + 2340 = 0

x = 2340/1.5

x = 1560

The couches sold for maximum profit = 1560

Therefore, the number of couches manufactured and sold in order to maximise the profit is 1560.

To learn more about deman function refer here

https://brainly.com/question/15234429

#SPJ1


Related Questions

A cubic meter of water weighs 1 000 kg. What is
the weight of 2 meters by 3 meters by 20
centimetre of water?

Answers

Answer:

1200

Step-by-step explanation:

First , we need to calculate the new volume using the dimensions given.

V=L×W×H

L=3meters

W=2meters

H=20Centimeters

H=(20/100)meters=0.2 meters

V=3×2×0.2=1.2m³

using simple proportions

if 1m³=1000kg

then. 1.2m³=Y

Y=(1.2m³×1000kg)/1m3

Y=1200kg

Determine whether the graphs of the given equations are parallel, perpendicular, or neither. y=x+9 y = -x + 2​

Answers

Answer: Perpendicular

Step-by-step explanation:

Given are two equations as

We have to find whether these two are parallel or perpendicular or neither

For this first we have to find the slope of these two lines

I line slope = 1

II line slope =-1

Since slopes are not equal, the lines are not parallel.

Let us check product of these slopes.  IF product =-1 the lines are perpendicular

We find that product =

Hence two lines are perpendicular

4. Mrs. Santiago asked her fifth-grade students to fill out a survey at the end of the school year. 4/5 of the class filled out a survey, and 11/12 of them rated Mrs. Santiago as an excellent teacher. What Fraction of the class rated Mrs. Santiago an excellent teacher?

Answers

We just need to multiply the fractions

[tex]\frac{4}{5}\times\frac{11}{12}=\frac{4\times11}{4\times3\times5}=\frac{11}{15}[/tex]

Then, 11/15 of the class rated Mrs. Santiago as an excellent teacher

percents build on another in strange ways.it would seem that if you increased a number by 5% and then increased its result by 5%more , the overall increase would be 10% (a) increase 100 by 5%(b)increase your result form (a)by 5%(c)what was the overall percent increase of the number 100? why is not 10%

Answers

Answer:

Explanation:

a) increase 100 by 5%

[tex]\begin{gathered} 105\text{\% of 100 = 1.05}\times100 \\ =105 \end{gathered}[/tex]

b) increase your result form (a)by 5%

[tex]\begin{gathered} 105\text{\% of 105 = 1.05}\times105 \\ =110.25 \end{gathered}[/tex]

c) The overall percent increase of the number 100;

[tex]\begin{gathered} \text{ \%P = }\frac{110.25-100}{100}\times100\text{\%} \\ \text{ \%P= 10.25\%} \end{gathered}[/tex]

It is not 10% because the second 5% increase was not on the initial number 100.

increasing 105 by 5% is more than increasing 100 by 5%.

Therefore, increasing 100 by 5% followed by increasing the result by 5% is greater than increasing 100 by 10%.

How is 3:1 interpreted?

A. 3 in 1
B. 3 out of 1
C. 3 to 1
D. 3 vs 1
E. None of these

Answers

Answer:

3 to 1.

Step-by-step explanation:

3:1 is a ratio, which is comparing 2 different things.

2.1.9 An initial investment amount P, an annual interest rate r, and a time t are given. Find the future value of the monthly, (c) daily, and (d) continuously. Then find (e) the doubling time I for the given interest rate. P = $2500, r=3.95%, t = 8 yr a) The future value of the investment when interest is compounded annually is $ 3408.29 (Type an integer or a decimal. Round to the nearest cent as needed.) b) The future value of the investment when interest is compounded monthly is $ (Type an integer or a decimal. Round to the nearest cent as needed.)

Answers

When the interest is compounded monthly, we have to do two things:

- Calculate the number of periods: in this case we have 8*12=96 months.

[tex]8\text{years}\cdot12\text{ months/year}=96\text{ months}[/tex]

- The monthly interest rate: we have to divide the annual nominal rate by 12 (the number of periods in the year).

[tex]\begin{gathered} r=3.95\text{ \%} \\ r_m=\frac{3.95}{12}=0.32917\text{ \%} \end{gathered}[/tex]

Then, we can calculate the future value as:

[tex]\begin{gathered} FV=C(1+r_m)^m \\ FV=2,500\cdot(1+0.0032917)^{96}=2,500\cdot1.37091864=3,427.30 \end{gathered}[/tex]

The future value when compounded monthly is $3,427.30.

General formula:

[tex]FV=PV\cdot(1+\frac{r}{m})^{m\cdot n}[/tex]

m: number of subperiods (monthly --> m=12)

Evaluate both the upper and lower limit of f(x) = 2x over [0,2] for n = 10,100,1000

Answers

We can solve both limits by using Riemann sums, which is represented by the following:

[tex]\lim _{n\to a}\sum ^n_{i=1}f(x_{i-1})\Delta x,\text{ where }\Delta x=\frac{b-a}{n}[/tex]

Then, for our function:

[tex]undefined[/tex]

IAn Individual Retirement Account (IRA) has $22,000 in it, and the owner decides not to add any more money to the account other than interest earned at 8%compounded daily. How much will be in the account 29 years from now when the owner reaches retirement age?There will be in the account.(Round to the nearest cent. Use a 365 day year.)

Answers

Given:

[tex]\begin{gathered} \text{Principal (P)= \$22000} \\ \text{Rate of interest= 8\%} \\ n=29\text{ years} \end{gathered}[/tex][tex]\begin{gathered} \text{Amount in the account after 9 years=}P(1+\frac{r}{365})^{365\times n} \\ =22000(1+\frac{8}{100\times365})^{365\times29} \\ =22000(1+0.0002)^{10585} \\ =22000(8.3044) \\ =\text{ \$182696}.80 \end{gathered}[/tex]

Amount in the account after 29 years is $182696.80

Solve 2 + by = 32 3x + 4 for y y.

Answers

2 + (1/6) y = 3x + 4

Take the 2 from left to right side: (1/6)y = 3x + 4 - 2 = 3x + 2

y/6 = 3x + 2

Take the 6 dividing on the left to the righ side multiplying:

y = 6 (3x + 2) = 18x + 12

Answer:

y = 18x + 12

2. Complete the table below by stating the number of solutions and explaining orsolving to show your reasoning.a) x2 - 25 = 0b) (x - 2)2 = 0c) (x - 3) ? = 81Number of solutions: Number of solutions: Number of solutions:0101201N2Type Here:Type Here:Type Here:Explain or show yourreasoning on how yousolved the aboveproblem.Explain or show yourreasoning on how yousolved the aboveproblem.Explain or show yourreasoning on how yousolved the aboveproblem.Type Here:Type Here:Type Here:I

Answers

For the first equation:

x^2 - 25 = 0...... x^2 = 25..... x = sqrt(25)..... x = 5 and x = -5.... so it has two solutions: 5 and -5

For the second euation:

(x - 2)^2 = 0.... the solution is x = 2 because when x = 2, (2 - 2)^2 = 0 ^ 2 = 0

So it only has one solution: 2

For the third equation:

(x - 3)^2 = 81.... x - 3 = sqrt(81) = -9 and +9

x - 3 = -9... x = -6

x - 3 = 9... x = 12

so it has two solutions: -6 and 12

The length and width of a rectangle are consecutive odd integers. The perimeter of the rectangle is 120 meters. Find the length and width of the rectangle.

Answers

The value of the length and the width of the rectangle are 29.5 and 30.5 meters respectively

How to determine the dimension of the rectangle?

From the question, the statement is given as

Length and width are consecutive odd integers

Where perimeter = 120 meters

Represent the dimensions with x and y

Where Length = x and Width = y

And also, we have

y = x + 1

The perimeter of a rectangle is

Perimeter = 2 x (Length + Width)

Mathematically, this can be represented as

Perimeter = 2 x (x + y)

So, we have

2 x (x + y) = 120

Substitute y = x + 1 in 2 x (x + y) = 120

2 x (x + x + 1) = 120

This gives

2 x (2x + 1) = 120

Divide by 2

2x + 1 = 60

So, we have

2x = 59

Divide by 2

x = 29.5

Substitute x = 29.5 in y = x + 1

So, we have

y = 29.5 + 1

Evaluate

y = 30.5

Hence, the length and the width are 29.5 and 30.5

Read more about rectangle at

https://brainly.com/question/28984854

#SPJ1

E Y2-yi X2-X1 Find the slope of the line that passes through these two points. Simplify completely. (2, -3) (5,6) m = [?] Enter

Answers

Given:

Two given points are,

[tex]\begin{gathered} (x_1,y_1)=(2,-3) \\ (x_2,y_2_{})=(5,6) \end{gathered}[/tex]

THe objective is to find the value of slope, (m).

The formula to find the slope is,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Now, substitute the given values in the above slope formula.

[tex]\begin{gathered} m=\frac{6-(-3)}{5-2} \\ m=\frac{6+3}{5-2} \\ m=\frac{9}{3} \\ m=3 \end{gathered}[/tex]

Hence, the slope of the line is 3.

el valor de 1 décimo es menor que el vamos de 3 décimas.?

Answers

Cuando expresas un valor decimal en fracciones lo haces utilizando al 10 como denominador de la misma, entonces

1 décimo en fracciones es:

[tex]\frac{1}{10}[/tex]

3 décimas corresponde entonces a

[tex]\frac{3}{10}[/tex]

Al expresar estos valores utilizando cifras, el denominador 10 de la fracción indica que el numerador se encuentra en el primer lugar detrás de la coma decimal, entonces

[tex]\frac{1}{10}=0.1[/tex]

y

[tex]\frac{3}{10}=0.3[/tex]

Al organizar estos valores tienes que tener en cuanta la posición decimal en la que se encuentran. Si ambos se encuentran en la misma posición, entonces no debes tomar ninguna consideración y puedes ordenarlos siguiendo la mísma lógica que cuando ordenas números enteros.

Es decir, si al ordenar los enteros obtienes que:

0, 1, 2, 3

Cuando los divides por diez, simplemente corres la coma un lugar a la izquierda pero no cambias el orden de los valores, entonces:

0.0, 0.1, 0.2, 0.3

Dónde puedes ver que 0.1 es más cercano a 0 que 0.3, en otras palabras, 0.1 (una décima) es menor que 0.3 (tres décimas)

Please help. Calculus

Answers

Answer:

  0.339 m/min

Step-by-step explanation:

You want to know the rate of change of the third side in a triangle with sides 10 m and 14 m and an angle between them of 60°. The angle is increasing at 2°/min.

Law of Cosines

The law of cosines tells you the third side (c) satisfies the relation ...

  c² = a² +b² -2ab·cos(C)

Filling in the given values, we have ...

  c² = 10² +14² -2(10)(14)cos(C) = 296 -280cos(C)

Rate of change

Taking the square root and differentiating with respect to time, we have ...

  c = √(296 -280cos(C))

  c' = 280sin(C)·C'/(2√(296 -280cos(C)))

We want the value of this when C=60°, and C' = 2°/min = π/90 rad/min.

  c' = 280(sin(60°))·(π/90)/(2√(296 -280cos(60°))) = (14π√3/9)/(2√156)

  c' ≈ 0.339 . . . . m/min

The third side is increasing at a rate of about 0.339 meters per minute.

Help mee pleasee!!




thank you <3

Answers

The linear equation y = -500x + 5000 that models the price-sales.

What is an equation?

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Two points for $6, 2000 sales/day and $8, 1000 sales/day which is given in the question.

The slope varies in y as x changes.

m = (2000-1000 )/(6-8) = -500

The equation of a line with slope m is:

⇒ y = -500x+ b

Solve for b using one of the points (y-intercept)

2000 = -500(6)+b

5000 = b

The other point will provide the same result. To find b, you simply need one point (either one).

The linear relationship is:

y = -500x + 5000

Learn more about the equation here:

brainly.com/question/10413253

#SPJ1

A restaurant sells pizzas according to the formula y=8.50+0.45(x-3), where x represents the total number of toppings. You can spend no more than $10 on a pizza. What is the range of the this situation?

Answers

the formula is

[tex]y=8.50+0.45\left(x-3\right)[/tex]

For $10,

[tex]\begin{gathered} 10=8.5+0.45(x-3) \\ 10-8.5=0.45x-1.35 \\ 1.5+1.35=.45x \\ \frac{2.85}{0.45}=x \\ x=6.3 \end{gathered}[/tex]

So when, x=6.3, y=$10,

A bakery can make 33 cheesecakes for every 3 blocks of cream cheese. Which table
represents the relationship between the number of cheesecakes the bakery makes and
the number of blocks of cream cheese the bakery uses?

Answers

Answer:

it would be A.

Step-by-step explanation:

Why? well, if you divide 33/the total number of cream cheese blocks (3) you get 11. so for every 11 cheesecakes made, one cream cheese block is used. :)

please help I feel like I get it buy I don't know the answer

Answers

To find the area of the figure you can find the area of the figures that make it up and then add these areas, in other words

[tex]A_f=A_r+A_R[/tex]

Where

The formula to find the area of a rectangle is

[tex]\begin{gathered} A=l\cdot w \\ \text{ Where A is the area,} \\ \text{l is the length and} \\ w\text{ is the width of the rectangle } \end{gathered}[/tex]

So, you have

[tex]\begin{gathered} l_r=3\text{ mm} \\ w_r=1\text{ mm} \\ A_r=l_r\cdot w_r \\ A_r=3\operatorname{mm}\cdot1\operatorname{mm} \\ A_r=3\operatorname{mm}^2 \end{gathered}[/tex]

[tex]\begin{gathered} l_R=6\text{ mm} \\ w_R=2\text{ mm} \\ A_R=l_R\cdot w_R \\ A_R=6\operatorname{mm}\cdot2\operatorname{mm} \\ A_R=12\operatorname{mm}^2 \end{gathered}[/tex]

Finally, adding the areas you have

[tex]\begin{gathered} A_f=A_r+A_R \\ A_f=3\operatorname{mm}^2+12\operatorname{mm}^2 \\ A_f=15\operatorname{mm}^2 \end{gathered}[/tex]

Therefore, the area of the figure is 15 square milimeters.

Write and solve an inequality for each of the word problems.A person does door to door sales and earns a salary of $1500 per month plus 6.5% of the sales. What must the sales be if the person has a monthly income of at least $3,350.

Answers

Explanation

Let the sales be represented by x

Since the person earns 6.5% of the sales, this becomes;

[tex]\frac{6.5}{100}\times x=0.065x[/tex]

Recall that at least implies greater than or equal to in inequality. Therefore, the equation becomes;

[tex]0.065x+1500\ge3350[/tex]

We will then solve for x

[tex]\begin{gathered} 0.065x\ge3350-1500 \\ 0.065x\ge1850 \\ x\ge\frac{1850}{0.065} \\ x\ge28461.5385 \end{gathered}[/tex]

Answer: $28461.5385

class A: 1,2,3,3,4,4,4,4,5,3find the interqwarta le range

Answers

Class: 1,2,3,3,4,4,4,4,5,3

First, order from lowest to highest

1,2,3,3,3,4,4,4,4,5

Median = (1,2,3,3) 3, 4,(,4,4,4,5) = (3+4)/2 = 3.5

Find the median of the first and last half:

Q1 = 1,2,3,3,3.5 = 3

Q3 = 3.5,4,4,4,5 = 4

Then for the interquartile: Q3- Q1 = 4 -3 = 1

the verticles of a triangle are located at (2,0), (5,0) and (5,5). which best describes the triangle?

Answers

Answer:

Right scalene


1. Noah placed an empty bowl on a scale. He added different amounts of a liquid to the
bowl, recording the amount of liquid added, in tablespoons, and the total weight of
the bowl and liquid, in grams, each time on a scatter plot. He fit the line
y = 14.75x+861.82 to the data in his scatter plot, where x represents the amount
of the liquid, in tablespoons, and y represents the total weight of the bowl and the
liquid, in grams.
a. Interpret the slope of the line based on the context.

b. Interpret the y-intercept of the line based on the context.

Answers

a)  slope of the line based on the context is 14.75

b)  y-intercept of the line based on the context is 861.82

what is slope?

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

Given equation:

y = 14.75x+861.82

Now, using the general form

y= mx+ c

Now, comparing it with the given equation

m=14.75

and c= 861.82

a)  slope of the line based on the context is 14.75

b) y-intercept of the line based on the context is 861.82

Learn more about slope here:

https://brainly.com/question/3605446

#SPJ1

A CD has a diameter of 12 cm. The hole in the middle of the CD has a diameter of 1.5 cm. Find the area of one side of the CD to the nearest tenth. Use 3.14 for π .

Answers

A CD has a diameter of 12 cm and the diameter of the hole in the middle is 1.5 cm. So the area of the CD excluding the area of the hole will be 111.27 cm².

What is the area?

The area is a mathematical concept that expresses the size of a region on a planar or curved surface. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, while the area of a plane region or plane area is the area of a form or planar lamina.

According to the question, the given values are :

Diameter of CD = 12 cm.

Radius of CD, r₁= D/2 = 6 cm

Diameter of hole = 1.5 cm.

Radius of hole, r₂ = D/2 = 0.75 cm.

Area of one side of CD, A = Area of CD - Area of hole

Area of circle = πr²

A =  π(6)² - π(0.75)²

A = 36π - 0.5625π

A = 35.437π cm².

The area of CD will be, A = 35.437 × 3.14 = 111.27 cm².

Hence, the area of one side of the CD will be 111.27 cm².

To get more information about the area :

https://brainly.com/question/27683633

#SPJ1

Polygon Exterior Angle Sum Theorem - The _____ of the ________ angle measures, one at each vortex, of a ________ polygon is_____.

Answers

The completed statement is:

Polygon Exterior Angle Sum Theorem - The sum of the exterior angle measures, one at each vortex, of a convex polygon is 360°.

What is a polygon?

A polygon is a planar figure characterized by a limited number of straight line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both. A polygonal circuit's segments are known as its edges or sides.

Polygon examples include the following:

Concave PolygonsConvex PolygonsHexagon PolygonsIrregular PolygonsPentagon PolygonsQuadrilateral PolygonRegular Polygons.

Learn more about Polygon:
https://brainly.com/question/26583264
#SPJ1

congruent sides are marked on the figure to the right. Find the values of x and y.

Answers

You can identify that the triangle ACD is divided into two different triangles. These triangles are ABD and BCD.

Notice that the triangle BCD has two congruent sides. Therefore, it is an Isosceles triangle.

The triangle ABD has three congruent sides. This means that it is an Equilateral triangle. The measure of each interior angle of and Equilateral triangle is:

[tex]60\degree[/tex]

Therefore, you can determine that:

[tex]x=60\degree[/tex]

Let's assume that ABD is a Right triangle. Then:

[tex]ADC=90\degree[/tex]

Since the other triangle C has twol equal angles:

[tex]m\angle BDC=y=90\degree-60\degree[/tex]

Therefore:

[tex]y=30\degree[/tex]

The answer is:

[tex]\begin{gathered} x=60\degree \\ y=30\degree \end{gathered}[/tex]

Find x and y . Approximate your answer to one decimal place. I used comma for decimal separation. A random variable X has as a range of values the values 1, 2 and 3 with probabilities P (X = 1) = 0.2, P (X = 2) = x, and P (X = 3) = y. If Var (X) = 0.29, then x = and y =

Answers

We have a random discrete variable X, that takes values 1, 2 and 3.

As the probabilities of all the sample space is equal to 1.

So then we can define x in function of y:

[tex]\begin{gathered} P(x=1)+P(x=2)+P(x=3)=1 \\ 0.2+x+y=1 \\ y=1-0.2-x \\ y=0.8-x \end{gathered}[/tex]

We can start by calculating the mean of X as:

[tex]\begin{gathered} \mu=\sum ^3_{i\mathop=1}p_i\cdot x_i \\ \mu=0.2\cdot1+x\cdot2+y\cdot3 \\ \mu=0.2+2x+3(0.8-x) \\ \mu=0.2+2x+2.4-3x \\ \mu=2.6-x \end{gathered}[/tex]

We can write the variance of X as:

[tex]\begin{gathered} \sigma^2=\sum ^3_{i\mathop=1}p_i\cdot(x_i-\mu)^2 \\ \sigma^2=0.2\cdot(1-(2.6-x))^2+x\cdot(2-(2.6-x))^2+(0.8-x)\cdot(3-(2.6-x))^2 \\ \sigma^2=0.2\cdot(x-1.6)^2+x\cdot(x-0.6)^2+(0.8-x)\cdot(x+0.4)^2 \\ \sigma^2=0.2\cdot(x^2-3.2x+2.56)+x\cdot(x^2-1.2x+0.36)+(0.8-x)(x^2+0.8x+0.16) \\ \sigma^2=0.2x^2-0.64x+0.512+x^3-1.2x^2+0.36x+0.8x^2+0.64x+0.128-x^3-0.8x^2-0.16x \\ \sigma^2=(1-1)x^3+(0.2-1.2+0.8-0.8)x^2+(-0.64+0.36+0.64-0.16)x+(0.512+0.128) \\ \sigma^2=-x^2+0.2x+0.64 \end{gathered}[/tex]

As the variance, σ², is equal to 0.29, then we can find the possible values for x as:

[tex]\begin{gathered} \sigma^2=0.29 \\ -x^2+0.2x+0.64=0.29 \\ -x^2+0.2x+0.64-0.29=0 \\ -x^2+0.2x+0.35=0 \\ x^2-0.2x-0.35=0 \end{gathered}[/tex]

We can find the roots of this equation as:

[tex]\begin{gathered} x=\frac{-(-0.2)\pm\sqrt[]{(-0.2)^2-4\cdot1\cdot(-0.35)}}{2\cdot1} \\ x=\frac{0.2\pm\sqrt[]{0.04+1.4}}{2} \\ x=\frac{0.2\pm\sqrt[]{1.44}}{2} \\ x=\frac{0.2\pm1.2}{2} \\ x_1=\frac{0.2-1.2}{2}=-\frac{1}{2}=-0.5 \\ x_2=\frac{0.2+1.2}{2}=\frac{1.4}{2}=0.7 \end{gathered}[/tex]

The value of x = -0.5, as it is a probability, has to have a value of between 0 and 1, is not valid.

Then, the only valid value for x is x = 0.7.

We then can calculate y as:

[tex]y=0.8-x=0.8-0.7=0.1[/tex]

Answer: x = 0.7 and y = 0.1

When graphing a sine curve model using the equation y = sine b x, the period (or wavelength) will be represented by StartFraction 2 pi Over b EndFraction, so b = StartFraction 2 pi Over period EndFraction.
Determine the equation for the sine curve that models the E wave if the
wavelength of E = 1.042 meters.
a.
y = sine (6.03 x)
b.
y = sine (1.042 x)
c.
y = sine (5.68 x)
d.
y = sine (7.59 x)

Answers

The answer is d because the start fraction is the equivalent and when u divide is is the dividend

1. question ❓given A(-3,4) B(0,1) and C(4,2), reflect as follow. Ry-axis (ABC). what is a B?2

Answers

[tex]\begin{gathered} A(-3,4) \\ B(0,1) \\ C(4,2) \\ \text{ reflection across the y ax}is\text{ } \\ B(0,1)\rightarrow B\text{'(0,1)} \end{gathered}[/tex]

The reflection across the y axis the x value changes sign but the y value remain the same.

The answer is C

Select all the equations that represent a line perpendicular to the line 3x - 2y = 10

Answers

All the equations of the family:

y = (-2/3)*x + c

Where c is a real number, are perpendicular to the linear equation 3x - 2y = 10

How we can find the perpendicular equations?

A general linear equation is of the form:

y = m*x + b

Where m is the slope and b is the y-intercept.

Now, two linear equations are only perpendicular if the slope of one is equal to the inverse of the opposite of the other line's slope.

So, a line perpendicular to y = m*x + b is of the form:

y = (-1/m)*x + c

In this case, the given line is:

3x - 2y = 10

Writing this in slope-intercept form we get:

-2y = 10 - 3x

y = (10 - 3x)/-2

y = (3/2)*x - 5

So the slope of a perpendicular line will be: (-2/3)

Then any line of the form:

y = (-2/3)*x + c

Is perpendicular to the given line.

Learn more about linear equations:

https://brainly.com/question/1884491

#SPJ1

tony wants to write large numbers as the product of as many whole numbers greater than 1 as possible. he writes 144 as 2 x 72 but he sees he can go further and writes it as 2 x 2 x 36. can he go further still? explain your reasoning.​

Answers

Tony can still go further go and write 144 as the product of whole numbers greater than one in the following way -

2 x 2 x 2 x 2 x 3 x 3

What are whole numbers?

Whole numbers include all natural numbers and 0. They are real numbers that do not include fractions, decimals, and negative integers.

Given is tony, who wants to write large numbers as the product of as many whole numbers greater than 1 as possible. So, he writes 144 as

2 x 72 but he sees he can go further and writes it as 2 x 2 x 36.

Yes we can still go further and write 144 as the product of whole numbers greater than 1. We have -

144 = 2 x 72 = 2 x 2 x 36 = 2 x 2 x 2 x 18 = 2 x 2 x 2 x 2 x 9 =  

2 x 2 x 2 x 2 x 3 x 3

Now, he cannot go on further to express 144 as the product of whole number greater than 1. The last digit 3 is a prime number and is divided by either 1 or itself. So, if the last digit in the product expansion is a prime number, than we cannot break it further into smaller whole numbers.

Therefore, tony can still go further go and write 144 as the product of whole numbers greater than one in the following way -

2 x 2 x 2 x 2 x 3 x 3

To solve more questions on whole numbers , visit the link below-

https://brainly.com/question/15342938

#SPJ1

Other Questions
Two candles start burning at the same time. one candle is 15 cm tall and burn and burns at a rate of 5 cm every 6 hours. The other candle is 25 cm tall at a rate of 2 1/2 cm every hourHow tall will the candles be when they first burn down to the same height? 5. A patient must receive an injection of 2.4 grams of medication. If 1 milliliter ofliquid contains 120 milligrams of medication, how many milliliters should be injectedinto the patient? What does Tom tell Jordan and Nick on their way to the city that reveals his opinion of Gatsby? How do his comments illustrate the divide between old-money and new-money millionaires 8. What major conflicts led England to gain or lose land? (2 points) The Nazi party was able to gain support as they spread messages about_________ and ________to Germany's problems.a. love and revealed secretsb. hope and solutionsc. hope and consequencesd. hatred and disgustHelp Please help.. :(The night came slowly, softly, as I lay out there under the maple tree. It came creeping, creeping stealthily out of the valley, thinking I did not notice. And the outlines of trees and foliage nearby blended in one black mass and the night came stealing out from them, too, and from the east and west, until the only light was in the sky, filtering through the maple leaves and a star looking down through every cranny. The night is solemn and it means mystery. Human shapes flitted by like intangible things. Some stole up like little mice to peep at me. I did not mind. My whole being was abandoned to the soothing and penetrating charm of the night. The katydids began their slumber song: they are at it yet. How wise they are. They do not chatter like people. They tell me only: "sleep, sleep, sleep." The wind rippled the maple leaves like little warm love thrills.How does the setting affect the character(s) and enhance the mood of the passage? Respond in a well-developed paragraph that:is at least 5 sentences in lengthincludes textual supportuses correct grammar, punctuation, and spelling PART B Wich detail from the text best supports the answer to part A how religion drive politics in pre modern Europe which colloid is expensive but rapidly expands plasma volume? continuous interaction means that we never stop refining our understanding because changes in one component means potential changes in the other components. this is known as what? Graph for y = -x 6. Alison had lost some puzzle pieces. She found 3/10 of them under the coffee table and another 4/10 of them under the couch. How much is she still missing? Of the following situations, which is best represented by the product5x-3AThe amount of money a snack bar earns for selling 333 sandwiches for $555 per sandwichBThe change in elevation of a submarine as it sinks 333 meters every second for 555 secondsCThe change in temperature as it decreases 555 degrees every hour for 333 hoursDThe height of a child who grew 333 inches each year for 555 yearsi need the answer fast pls A football team scored 3 touchdowns 3 extra points and 4 field goals write an expression to represent the total points the football team scored Which type of carbohydrates are used to produce energy This table shows a function.(-16, -41)(-15, -20)(-7, -2)(-5, 5)(2, 1)(13, 10)What is the average rate of change over the interval 2 x 137A. -11/9B. -9/11C. 9/11D. 11/9 F(x-3)=x^2-1. F(0)=? Evaluate each expression if r=1, s=3, 1=3, and u=10. tu-3r Write an equation that expresses the following relationship: x varies directly as a and inversely as the difference between y and z. Then solve the equation for yWrite an equation that expresses the given relationship. Use k as the constant of variation. Multiply.3c^6(9c+4c^3)Simplify your answer as much as possible Kaiya has been living in an assisted living facility after taking a fall in her house. She has actively participated in physical therapy and has shown an increase in her abilities to take care of herself. She really missed her freedom and being surrounded by people she knows and loves. She is extremely shy and does not like to be around strangers. So despite all her physical improvements, she remained very sad. Kaiyas doctor should most likelywait for six months and see if her attitude has changed.arrange a transfer to Kaiyas granddaughter, who is able to care for her.discharge Kaiya to allow her the chance to find her own facility.suggest to the nursing assistant, Dan, that he take her to more social events.