Gerald purchased a rectangular plot of land. the length of the plot is 20 feet more than the width. the cost of the land was $12 per square foot. gerald also had a fence put around the entire perimeter of the plot, at a cost of s8 per linear foot. the total amount he spent on both the land and the fence was $10,560. part a write an equation in two variables for the perimeter, p, and an equation in two variables for the area, a, of the plot of land where x is the width of the plot in feet. provide evidence to support your equations

Answers

Answer 1

Answer:

P =2(x+ y) [tex]ft[/tex].

A =xy [tex]ft^{2}[/tex]

Step-by-step explanation:

perimeter of rectangle (P)= 2(L+B

Area of rectangle (A)        =    L×B

Given,

width = 'x'

length = y = x+20

therefore using above formula

P = 2(x+20 + x) = 2(2x+20)

A = (x+20)(x)

cost of land per square foot = $12

cost of land per linear foot   = $8

total cost of land                   = $10560

now,

P×8 + A×12   = 10560

2(2x+20)×8 +  (x+20)(x)×12 = 10560

32x + 320 + 12x²+ 240x     = 10560

12x² + 272x                         = 10240

12x² + 272x - 10240           = 0

solving this quadratic equation using Discriminant method

x = [-b ±√(b² - 4ac)]/2

where b is the coefficient of x

a is the coefficient of x²

and c is the constant term

by replacing values in the above formula

x = 19.5  , x = -42.24

as the area cannot be negative therefore -42.24 is neglected

hence x = 19.5ft

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Related Questions

may I have some assistance please
What method can be used to write the equation of a line in slope-intercept form given two points? Find the slope using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept. Find the slope using the formula m = StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept. Find the y-intercept using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the y-intercept into the equation y = m x + b to find the slope. Find the y-intercept using the formula m = StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction, and then substitute one point and the y-intercept into the equation y = m x + b to find the slope.

Answers

The method that can be used to write the equation of a line in slope-intercept form given two points is option A.

Calculations and Parameters

When a person wants to write the equation of a line in slope-intercept form given two points, he would have to:

Know the two pointsUse them to find the slopeYou would get the value of mUse it to solve the equation y= mx + bFind the y-intercept

Therefore, the answer is option A.

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can someone please do this for me ​

Answers

The range is from the maximum point into infinity that is [4, infty) and the vertex is at (0, 4)

Vertex, domain and range of a function

The given graph is a parabola. It represents the graph of a quadratic equation.

From the shown graph, the parabola has a maximum point at (0, 4). This is also the vertex of the graph

The domain area values along the x-axis while the range lies on the y-axis. From the graph shown, the domain is [-2, 2] (x lies between -2 and 2)

The range is from the maximum point into infinity that is [4, infty)

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What is 2 1/2 x 1 3/4 x 3/4

Answers

Answer:

45/32 or 1.40

Step-by-step explanation:

Answer:

3 9/32 or 105/32

Step-by-step explanation:

2 1/2 = 5/2, 1 3/4 = 7/4

5/2 * 7/4 = 35/8

35/8 * 3/4 = 105/32

105/32 = 3 9/32

Brainliest, please :)

What is the inverse of this function?
f(x) = -√x +3₁ x ≥ −3
f-¹(x) =
2-
-
for x ≤

Answers

Answer:

f(x)^-1=x^2-3

Step-by-step explanation:

So I'm assuming you meant to include the 3 in the radical as well which would make sense given the domain restriction. To find the inverse you simply swap the x and y since the inverse function is when the domain and range are swapped.

[tex]y=-\sqrt{x+3}\\x=-\sqrt{y+3}\\-x=\sqrt{y+3}\\(-x)^2=y+3\\x^2-3=y\\f(x)^{-1}=x^2-3[/tex]

Solve the following simultaneous equations. x + y = 3
x -y = 1

Answers

Answer:

x = 2, y = 1 or (2, 1)

Step-by-step explanation:

Solving by elimination method :

x + y + (x - y) = 3 + 12x = 4x = 2

2 - y = 1y = 1

The solution is : x = 2, y = 1 or (2, 1)

Answer: x = 2, y = 1

Step-by-Step Solution:

=> x + y = 3 (Eq. 1)
=> x - y = 1 (Eq. 2)

Adding Eq. 1 and Eq. 2, we get :-

2x = 3 + 1
2x = 4
x = 4/2
=> x = 2

Therefore, x = 2

Substitute value of ‘x’ in Eq. 1 :-

x + y = 3
(2) + y = 3
2 + y = 3
y = 3 - 2
=> y = 1

Therefore, y = 1

Hence, x = 2 and y = 1.

HELPPP PLEASE!!!!!!!!!!!

Answers

Answer:

C

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (4, 0) ← 2 points on the line

m = [tex]\frac{0-2}{4-0}[/tex] = [tex]\frac{-2}{4}[/tex] = - [tex]\frac{1}{2}[/tex]

the y- intercept is the value of y where the line crosses the y- axis , then

y- intercept = 2

can someone please help me?

Answers

A slope of a line.

We have the equation of a line:

[tex]y=-\dfrac{5}{4}x-1[/tex]

The formula of a slope of a line passes through points A, B:

[tex]A(x_A,\ y_A),\ B(x_B,\ y_B)\\\\m=\dfrac{y_B-y_A}{x_B-x_A}[/tex]

Complete the table:

Put the values of x to the equation of a line and calculate the value of y:

[tex]x=0\\\\y=-\dfrac{5}{4}\cdot0-1\\\\y=-1\\\\\\x=4\\\\y=-\dfrac{5}{4}\cdot4-1\\\\y=-6[/tex]

Substitute to the formula of a slope:

[tex]m=\dfrac{-6-(-1)}{4-0}\\\\m=\dfrac{-6+1}{4}\\\\\huge\boxed{m=-\dfrac{5}{4}}[/tex]

Which of the following is a like radical to 3/7x?
4 (3√√7x)
O
O √Tx
0 x(³√7)
0 7√√√x

Answers

Answer:

Like radicals are those terms that are similar, just like like terms. From this concept we find that option A is correct. 4[∛(7x)] and ∛(7x) are like radicals.

Step-by-step explanation:

Mathematically, like radicals are just like like terms. For example,

x, 2x, -10x, , 7.3x are like terms because the power of x in each case is 1.

xy², -9xy², 13y²x are like terms because the total power of each expression is 3.

Similarly, like radicals are:

√2, -5√2, 1.1√2, etc.

Hence, from the given options, like radical to ∛(7x) is: 4[(7x)].

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Hi pls help
1) -15+4r=-9
2) 5-y/3=-1
3) 42=-5x-8

Answers

1) -15+4r=-9

-15+4r=-9

We move all terms to the left:

-15+4r-(-9)=0

We add all the numbers together, and all the variables

4r-6=0

We move all terms containing r to the left, all other terms to the right

4r=6

r=6/4

r=1+1/2

2) 5-y/3=-1

5-y/3=-1

We move all terms to the left:

5-y/3-(-1)=0

We add all the numbers together, and all the variables

-y/3+6=0

We multiply all the terms by the denominator

-y+6*3=0

We add all the numbers together, and all the variables

-1y+18=0

We move all terms containing y to the left, all other terms to the right

-y=-18

y=-18/-1

y=+18

3) 42=-5x-8

42=-5x-8

We move all terms to the left:

42-(-5x-8)=0

We get rid of parentheses

5x+8+42=0

We add all the numbers together, and all the variables

5x+50=0

We move all terms containing x to the left, all other terms to the right

5x=-50

x=-50/5

x=-10

Find the total surface area of a regular pyramid with a square base if each edge of the base is 16 inches, the slant height of one side is 17 inches, and the altitude is 15 inches.

Answers

Answer:

the answer you're looking for is 60 inches

The perimeter of the base is 4 s since it is a square.

p = 4(16) = 64 inches

The area of the base is s².

B = 16² = 256 inches ²

[tex]\boldsymbol{CST=\dfrac{1}{2}(64)(17)+256=544+256=800 \ inches^{2} }[/tex]

[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]

What is the difference between the answers when numbers are switched in a subtraction?

Answers

The other one is usually negative or smaller than the first or viceversa

Determine the equation of a cubic polynomial function with roots at (3,0), (2,0) and (-4,0) that also passes through the point (1,30).

Answers

Step-by-step explanation:

Step 1: Setting Up the Factors

Our roots are 3, 2, and -4 so

our factors are

[tex](x - 3)(x - 2)(x + 4)[/tex]

Step 2: Initial Test to see if the result equal 30

Let a be a constant, such we have

[tex]a(x - 3)(x - 2)(x + 4) = 30[/tex]

Plug in. 1 for x.

[tex]a(1 - 3)(1 - 2)(1 + 4) = 30[/tex]

[tex]a( - 2)( - 1)(5) = 30[/tex]

[tex]a(10) = 30[/tex]

[tex]a = 3[/tex]

So our equation is

[tex]3(x - 3)(x - 2)(x + 4)[/tex]

Or if you want it simplifed

[tex]3( {x}^{2} - 5x + 6)(x + 4) = 3( {x}^{3} + - {x}^{2} - 14x + 24) = 3 {x}^{3} - 3 {x}^{2} - 42x + 72[/tex]

Answer:

[tex]f(x)=3(x-3)(x-2)(x+4)[/tex]

Step-by-step explanation:

General form of a cubic polynomial function with 3 roots:

[tex]f(x)=a(x-b)(x-c)(x-d)[/tex]

where:

a is some constant to be foundb, c and d are the roots of the function

Given roots:

(3, 0)(2, 0)(-4, 0)

Substitute the given roots into the general form of the function:

[tex]\implies f(x)=a(x-3)(x-2)(x-(-4))[/tex]

[tex]\implies f(x)=a(x-3)(x-2)(x+4)[/tex]

To find the value of a, substitute the given point (1, 30) into the equation:

[tex]\begin{aligned} f(1) & = 30\\\implies a(1-3)(1-2)(1+4) & =30\\a(-2)(-1)(5) & = 30 \\10a & = 30\\\implies a & = 3 \end{aligned}[/tex]

Therefore, the equation of the cubic polynomial function is:

[tex]f(x)=3(x-3)(x-2)(x+4)[/tex]

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PLEASE HELP (not good at math)

Answers

Answer:

-7,-6,-5 are the values when x=0,1,2

Step-by-step explanation:

please mark me as brainlest

Answer:

Step-by-step explanation:

y =x - 7

Substitute x = 0 and find the y-value

       y = 0 - 7

      y = -7

(0,-7)

Substitute x = 1,

    y = 1 - 7

    y = - 6

(1,-6)

Substitute x = 2,

        y = 2 - 7

       y = -5

(2,-5)

Need help to understand how to do this.

Answers

Answer: -1(x+2)^2+10

Step-by-step explanation:


1. The coefficient of -x^2 is just the number in front, which in this case would be a = -1 So now the function is -1(x^2+4x)+6 since negative one has been factored out of the first two terms.

2. Half of the coefficient of x would be 2 since x has a coefficient of 4, and half pf 4 is 2. Squared, it is 4. That will be added inside the bracket. Subtracted on the outside is the same equation but multiplied by a, which we found out was -1 in the beginning. So, the function becomes -1(x^2+4x+4)+6-(-4).

3. Factor the inside equation to find that it’ll become (x+2)^2, and simplify the outside to get 10. The function will now be;


f(x)=-1(x+2)^2+10


Hope that made sense and make sure to check just in case I did the math wrong :]

If f(x) = 2x² + 3x and g(x)= x - 2, what is (f+ g)(2)?

Answers

Answer:

14.

Step-by-step explanation:

If f(x) = 2x2 + 3x and g(x) = x - 2, (f + g)(2) is 14.

Answer:

14

Step-by-step explanation:

f(x) = 2x² + 3x

f(2) = 2 * 2^2 + 3(2) = 2*4 + 6 = 8+6 = 14

g(x)= x - 2

g(2) = 2-2 = 0

(f+ g)(2) = 14+0 = 14

How would i work this out?

Answers

You want to find the number of visits IN BETWEEN 12:30 PM and 6:45 PM

there some visits already recorded before 12:30. These visits are visits that you want to exclude but are included in the TOTAL visits

Before 12:30 the website has 1200 visits and at 6:45 the website has 14000.

You can do 14000-1200 to find the number of visits in the time frame between 12:30 and 6:45

ANSWER 12800 visits

Find the value of x

Answers

Answer:

3

Step-by-step explanation:

11(3)+2 = 6

also,

33-29 =

and

29 - 23 = 6

I take a guss, but I think its 3

Someone pls help I don’t really understand graphing

Answers

It’s very simple in every line you need slope and y-intercept so you use,

y=Mx+c (M is slope and c is y-intercept)

First find slope and use any two points on the line I prefer picking (-3,0) and (0,2)
= y2-y1/x2-x1 = 2-0/0-(-3) = 2/3

Y=2/3x+c (now last step we find c by replacing any of the giving points)

2=2/3(0)+c
C= 2

Final answer :

Y=2/3x+2

Which of the following inequalities matches the graph?

graph of an inequality with a solid line through the points 0, negative 2 and 2, 1 with shading above the line

3x − 2y ≥ 4
3x − 4y ≤ 2
3x − 2y ≤ 4
The correct inequality is not listed.

Answers

Answer:

The correct option is 3.

Step-by-step explanation:

It is given a graph of an inequality with a solid line through the points (0, −2) and (2, 1) with shading above the line.

The equation of a solid line is:

[tex]y-y_{1} = \frac{y_{2}- y_{1} }{x_{2}- x_{1} } (x-x_{1})\\ y+2= \frac{1+2}{2-0}(x-0)\\ y+2= \frac{3}{2} x[/tex]

The y-intercept of the line is -2 and the shaded region is shading above the line. So, (0,0) must be lies in the shaded region.

Check the related equation by point (0,0).

0+2 =[tex]\frac{3}{2}(0)[/tex]

2 = 0

The statement is true if and only if the sign is greater than or equal instead of equal.

The required inequality is

[tex]y+2 \geq \frac{3}{2}x[/tex]

Multiply both sides by 2.

[tex]2y + 4 \geq 3x\\4\geq 3x-2y\\3x-2y \leq 4[/tex]

Therefore option 3 is correct.

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Write down in terms of n, an expression for the nth term of the following sequences:
a) 12 10 8 6 4
b) 25 20 15 10 5​

Answers

Answer:

The formula for an arithmetic sequence is:

an = a1 + (n - 1)d

In which a1 is the first term and d is the common difference.

a) 12, 10, 8, 6, 4

an = 12 + (n - 1)-2

an = 12 -2n + 2

an = -2n + 14

b) 25, 20, 15, 10, 5

an = 25 + (n - 1)-5

an = 25 -5n + 5

an = -5n + 30


Suppose y varies inversely as x, and y = 16 when x = 1/2. Find y when x = 17.

Answers

Finding the proportionality constant :

y = k/x16 = k/(1/2)k = 8

Finding y when x = 17 :

y = 8/(17)y = 8/17

The value of y is 8/17 when x = 17.

A delivery of 5 large boxes and 3 small boxes has a total mass of 137 kilograms. A delivery of 2 large boxes and 6 small boxes has a total mass of 128 kilograms. What is the mass of each type of box?

Answers

Answer:

Large boxes are 18.25 kg

Small boxes are 15.25 kg

Step-by-step explanation:

This is a system of equations. You need to set up each equation first.

I am assigning x to be big boxes and y to be small boxes.

5x + 3y = 137

2x + 6y = 128

To solve, you will need to eliminate a variable. That means you will have to multiply one of the equations by a number to make it so a variable will be eliminated. I will be multiplying the top equation by -2.

-2 ( 5x + 3y = 137)

    2x + 6y = 128

Distribute the -2 to everything in the parentheses in the first equation.

-10x - 6y = -274

2x + 6y = 128

Notice the 6y will go away because -6y + 6y = 0. Now add the equations together. The remaining equation is:

-8x = -146

Solve for x by dividing by -8.

x = 18.25

Now plug that into one of the original equations.

2(18.25) + 6y = 128.

36.5 + 6y = 128                Subtract 36.5 from each side

-36.5            -36.5

6y = 91.5                          Divide by 6 to solve

y = 15.25

use your calc to work this out

Answers

I think question a is 9.4419
A is 9.4419
B is 9.3361

Chris lost $8.59 playing poker in one week. If this continued, what would be his net
winnings or losses after five weeks?

Answers

Answer:

$42.95

Step-by-step explanation:

If Chris lost $8.59 playing poker in one week, in five weeks he would lose $42.95.

$8.59 lost per week.

5 weeks.

$8.59 x 5 = $42.95.

Hope this helps!

If not, I am sorry.

What else would need to be congruent to show that ABC = XYZ by ASA

Answers

Answer:

Option d

Step-by-step explanation:

BC = YZ

AC cannot be equal to XZ else it will be SAA congruency

f(x)=(2x−3)(x+6)(5x+6)f, left parenthesis, x, right parenthesis, equals, left parenthesis, 2, x, minus, 3, right parenthesis, left parenthesis, x, plus, 6, right parenthesis, left parenthesis, 5, x, plus, 6, right parenthesis has zeros at x=-6x=−6x, equals, minus, 6, x=-\dfrac{6}{5}x=− 5 6 ​ x, equals, minus, start fraction, 6, divided by, 5, end fraction, and x=\dfrac{3}{2}x= 2 3 ​ x, equals, start fraction, 3, divided by, 2, end fraction. What is the sign of fff on the interval -6

Answers

Answer:

566

Step-by-step explanation:

I got it right..................

Sahil chooses a number, divides it by 8 , adds 8 to the answer. Then multiples the answer with 8 . He obtains the result as 952 . The number he chooses in the beginning was


USER IS DEAD
TAKE POINTS ​

Answers

Answer:

888

Step-by-step explanation:

Sahil chooses a number, [We'll call it x]

divides it by 8 ,   [x/8]

adds 8 to the answer.  [(x/8) + 8]

Then multiples the answer with 8 .  [((x/8) + 8)*8]

He obtains the result as 952 .   [((x/8) + 8)*8 = 952]

The number he chooses in the beginning was

((x/8) + 8)*8 = 952

x + 64 = 952

x = 888

CHECK:

Does (888/8 + 8)*8 = 952?

(119)*8 = 952?   YES

The number is 888

Solve for x. Round to the nearest tenth, if necessary

Answers

The value of x in the triangle to the nearest tenth is calculated as; 1.1

How to use trigonometric ratios?

We have different trigonometric ratios such as;

sin θ = opp/hyp

cos θ = adj/hyp

tan θ = opp/adja

Thus, from the given triangle we can use the formula for cos θ to get the value of x. Thus;

cos 41° = 0.8/x

x = 0.8/cos 41

x = 1.06

To the nearest tenth, we have x = 1.1

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K'L'M'N' is a dilation image of KLMN. Which is the correct description of the dilation?

Answers

Answer:

d

Step-by-step explanation:

Write an equation in slope intercept form with the given information.
Slope = 4 and goes through point (3,0)

Answers

Answer:

y = 4x - 12

Step-by-step explanation:

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