NEED HELP ASAP!! can someone please explain this to me!

Answer: A $4000

Step-by-step explanation:

Let x represent the amount which he invested at 3% interest.

Let y represent the amount which he invested at 3.25% interest.

Walt made an extra $7000 last year from a part-time job. He invested part of the money at 3% and the rest at 3.25%. This means that

x + y = 7000

The formula for determining simple interest is expressed as

I = PRT/100

Considering the account paying 3% interest,

P = $x

T = 1 year

R = 3℅

I = (x × 3 × 1)/100 = 0.03x

Considering the account paying 3.25% interest,

P = $y

T = 1 year

R = 3.25℅

I = (y × 3.25 × 1)/100 = 0.0325y

He made a total of $220.00 in interest., it means that

0.03x + 0.0325y = 220 - - - - - - - -- -1

Substituting x = 7000 - y into equation 1, it becomes

0.03(7000- y) + 0.0325y = 220

210 - 0.03y + 0.0325y = 220

- 0.03y + 0.0325y = 220 - 210

0.0025y = 10

y = 10/0.0025

y = 4000

Answer:

Number of ways to select 3 cars and 4 trucks = 18,480

Step-by-step explanation:

Let x be the number of ways to select 3 cars and 4 truck.

Given:

Total number of cars = 8

Total number of Trucks = 11

We need to find out how many ways can the inspector select 3 cars and 4 truck.

Solution:

Using combination formula.

[tex]nCr = \frac{n!}{r!(n-r)!}[/tex]

Where, n = Total number of object.

m = Number of selected object.

We need to find out how many ways can the inspector select 3 cars and 4 truck from 8 cars and 11 trucks.

So, we write the the combination as given below.

[tex]8C_{3}\times 11C_{4} = Number\ of\ ways\ to\ selection[/tex]

[tex]\frac{8!}{3!(8-3)!} \times \frac{11!}{4!(11-4)!}= x[/tex]

[tex]x = \frac{8\times 7\times 6\times 5!}{3!\times 5!} \times \frac{11\times 10\times 9\times 8\times 7!}{4!\times 7!}[/tex]

Factorial 5 and 7 is cancelled.

[tex]x = \frac{8\times 7\times 6}{6} \times \frac{11\times 10\times 9\times 8}{24}[/tex]                     ([tex]3! = 6\ and\ 4! = 24[/tex])

[tex]x = (8\times 7) \times (11\times 10\times 3)[/tex]                ([tex]\frac{9\times 8}{24}=\frac{72}{24}=3[/tex])

[tex]x=56\times 330[/tex]

x = 18480

Therefore, the Inspector can select 3 cars and 4 trucks in 18,480 ways,

To determine how many ways the state inspector can select 3 cars from 8 and 4 trucks from 11, we need to calculate the combinations separately for each type of vehicle and then multiply them together to find the total number of ways to make both selections simultaneously.
### Selection of Cars:
The number of ways to choose 3 cars from 8 is a combination problem, because the order in which we select the cars does not matter. The formula for combinations, denoted as C(n, k), where n is the total number of items to choose from, and k is the number of items to be chosen, is given by:
C(n, k) = n! / (k! * (n - k)!)
Let's apply this formula to select 3 cars from 8:
C(8, 3) = 8! / (3! * (8 - 3)!) = 8! / (3! * 5!) = (8 × 7 × 6) / (3 × 2 × 1)
Simplify the factorials by canceling out common terms:
C(8, 3) = (8 × 7 × 6) / (3 × 2 × 1) = (8/2) × (7/1) × (6/3) = 4 × 7 × 2 = 56
So, there are 56 ways to choose 3 cars out of 8.
### Selection of Trucks:
Similarly, to choose 4 trucks out of 11 we use the combination formula again:
C(11, 4) = 11! / (4! * (11 - 4)!) = 11! / (4! * 7!) = (11 × 10 × 9 × 8) / (4 × 3 × 2 × 1)
Simplify the factorials:
C(11, 4) = (11 × 10 × 9 × 8) / (4 × 3 × 2 × 1) = (11/1) × (10/2) × (9/3) × (8/4) = 11 × 5 × 3 × 2 = 330
So, there are 330 ways to choose 4 trucks out of 11.
### Total Ways:
To find the total number of ways to select both the cars and trucks for inspection, we multiply the number of ways to choose the cars by the number of ways to choose the trucks:
Total number of ways = number of ways to choose cars × number of ways to choose trucks
Total number of ways = 56 (from choosing cars) × 330 (from choosing trucks)
Total number of ways = 56 × 330 = 18480
Therefore, the state inspector can select 3 cars out of 8 and 4 trucks out of 11 in 18,480 different ways.

Answer:

Step-by-step explanation:

PV =  $2500

r = 6%

Compounded semi annually for ten years => number of periods: 10*2 = 20

a.  the balance of account at end of peroid (FV)

FV = PV [tex](1+r)^{n}[/tex] = 2500[tex](1+0.06)^{20}[/tex] = 8017.8386

b. How much interest is earned; FV - PV = 8017.8386 - 2500 = 5517.8686

c. what is effective rate of interest :

Answer:

The answers to the question are

a) The balance of account at end of period $4515.278

b) The interest earned $2515.278

c) The effective rate of interest is 0.0609 or 6.09 %

Step-by-step explanation:

To solve the question

a) Here we have the compound interest formula given by

[tex]A = P(1+\frac{r}{n})^{nt}[/tex] Where,

P = Initial investment =  $2500

r = Annual interest rate = 6% =0.06

n = Number of compounding periods per year = 2

t = Number of years 10

From which we have

[tex]A = 2500*(1+\frac{0.06}{2})^{2*10}= 2500(1.03)^{20}[/tex] = $4515.278

The balance of account at end of period $4515.278

b) Interest earned = Balance -  initial investment = $4515.278 - $2500 = $2515.278

c)

The effective interest rate is the interest rate that accrues to an investment or loan as a result of the compounding the interest for a given time period of time. It is also known as the effective annual interest rate

The effective rate of interest is given by

Effective rate = [tex](1+\frac{r}{n} )^n -1[/tex]Where

r = Annual interest rate

n = Number of annual compounding periods

this gives [tex](1+\frac{0.06}{2} )^{2} -1[/tex] =  0.0609 = 6.09 %

Answer:

A = $822 + $4.49r

Step-by-step explanation:

The question asks to know the equation that describes how much spent in the first six months and also the cost of the home theater.

Firstly, the equation asks to represent the total amount spent by A. She spent $4.49 per rental and made a total of r rentals in the first six months, thus, the total amount of money she spent on rentals is thus 4.49 * r = $4.49r. Now, she also spends $12/month as membership charges. The total membership charges in the first 6 months is thus 6 * 12 = $72

Lastly, she bought the home theater itself $750. Thus, the total amount of money spent A is $750 + $72 + $4.49r

This translates to $822 + $4.49r

In equation form, A = $822 + $4.49r

Answer:

HOPE U UNDERSTOOD

MARK AS BRAINLIEST ONE

Any doubts? please COMMENT

Answer: There are 2 decorations that Eli makes.

Step-by-step explanation:

Since we have given that

Length of a meter of ribbon used = [tex]\dfrac{1}{10}=\dfrac{1}{10}\times 100=10[/tex]

Length of a meter cut into equal pieces = [tex]\dfrac{1}{5}=\dfrac{1}{5}\times 100=20[/tex]

So, Number of decorations that Eli make is given by

[tex]\dfrac{\text{Length of total ribbon}}{\text{Length of ribbon used}}\\\\=\dfrac{20}{10}\\\\=2[/tex]

Hence, there are 2 decorations that Eli makes.

Final answer:

Eli made 2 decorations from 1/5 meter of ribbon by using 1/10 meter of ribbon for each decoration.

Explanation:

Eli made fancy blue costume decorations for each dancer in his year-end dance performance.

Eli used 1/10 of a meter of ribbon for each decoration and initially cut a 1/5 meter ribbon into equal pieces.

To calculate the number of decorations Eli made, we need to divide the length of ribbon he cut (1/5 meter) by the length of ribbon used for each decoration (1/10 meter).

To solve this, we simply perform the division:

= 1/5 meter / 1/10 meter

= 2.
Therefore, Eli made 2 decorations from 1/5 meter of ribbon.

From the Death Valley to Black Mountain, it rises 1032 feet because Death Valley is 1032 ft lower than Black Mountain in elevation.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

It is given that:

Death Valley CA is 282 feet below sea level.

Black Mountain, KY is 750 feet above sea level.

Death Valley (282ft) + 282ft = sea level (0).

0 + 750ft = Black Mountain (750ft).

282ft + 750ft = 1032ft.

From Death Valley to Black Mountain, it rises 1032 feet. Death Valley is 1032 ft lower than Black Mountain in elevation.

Thus, from the Death Valley to Black Mountain, it rises 1032 feet because Death Valley is 1032 ft lower than Black Mountain in elevation.

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Answer:

c=f(x)−ax^2−bx

Step-by-step explanation:

Answer:

C=1

Step-by-step explanation:

Put the first point in the equation y=ax^2+bx+c where x=0 and y=1 you get

1=a*0+b*0+c

1=c

Answer:

12.9

Step-by-step explanation:

AB = [tex]\sqrt{2^{2}+3^{2} }[/tex] = [tex]\sqrt{13}[/tex]

BC = [tex]\sqrt{2^{2}+2^{2} }[/tex] = [tex]2\sqrt{2}[/tex]

CD = [tex]\sqrt{1^{2}+2^{2} }[/tex] = [tex]\sqrt{5}[/tex]

DE = 3

EA = [tex]\sqrt{1^{2} + 2^{2} }[/tex] = [tex]\sqrt{5}[/tex]

The sum of all of these (in decimal form) is (approx.) 12.9

Answer:

13.9 units

Step-by-step explanation:

AB = sqrt(2² + 3²) = sqrt(13)

BC = sqrt(2² + 2² = sqrt(8)

CD = sqrt(1² + 2²) = sqrt(5)

DE = 3

EA = sqrt(1² + 2²) = sqrt(5)

Add all these:

13.9 units

Answer:

The answer to the question is

The kinds of polygons that could be Diedre's quadrilateral are rectangle and square

Step-by-step explanation:

We  note the conditions of the polygon as thus

Number of sides = 4, Which include trapezoid, square, rectangle

Size of angles = 90 ° which eliminates trapezoid

Sizes of opposite sides = Equal opposite sides, includes square and rectangle

With the above we conclude that the possible polygons in Diedre's quadrilateral are rectangle and square

Solution set for given inequality  [tex]-18 < 5x - 3[/tex]  is  [tex]-3 < x[/tex].

" Solution set is defined as the such set of values which satisfies the given equation or any inequality."

According to the question,

Given inequality,

 [tex]-18 < 5x - 3[/tex]

Add 3 both the side of inequality we get,

[tex]-18 +3 < 5x - 3 +3[/tex]

[tex]= -15 < 5x[/tex]

Divide both the side by 5 to get the solution set ,

  [tex]-3 < x[/tex]

Hence, solution set for given inequality  [tex]-18 < 5x - 3[/tex]  is  [tex]-3 < x[/tex].

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Final answer:

The solution set for the inequality -18 < 5x - 3 is -3 < x, after adding 3 to both sides and then dividing by 5.

Explanation:

The student has asked to find the solution set for the inequality -18 < 5x - 3. To solve this, we first isolate the variable x by adding 3 to both sides of the inequality:

-18 + 3 < 5x - 3 + 3

-15 < 5x

Then, we divide both sides by 5 to solve for x:

-15 / 5 < 5x / 5

-3 < x

This simplifies to the inequality x > -3, which means that the correct answer is: -3 < x.

Answer:

The correct option is A. 18x - 6y = 20

Step-by-step explanation:

A system of two equations has no solution if the lines having these equations are parallel to each other.

Also, two lines [tex]a_1x+b_1y=c_1[/tex] and [tex]a_2x+b_2y=c_2[/tex] are parallel,

If [tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq \frac{c_1}{c_2}[/tex]

While,

They coincide ( infinitely many solution ) if [tex]\frac{a_1}{a_2}=\frac{ b_1}{b_2}=\frac{c_1}{c_2}[/tex],

They are non parallel ( a unique solution ) if [tex]\frac{a_1}{a_2}\neq \frac{ b_1}{b_2}\neq \frac{c_1}{c_2}[/tex],

Here, the given equation,

-9x + 3y = 12

Since in lines -9x + 3y = 12 and 18x - 6y = 20,

[tex]\frac{-9}{18}=\frac{3}{-6}\neq \frac{12}{20}[/tex]

Hence, system −9x + 3y = 12, 18x - 6y = 20 has no solution.

In lines -9x + 3y = 12 and 3x - y = -4,

[tex]\frac{-9}{3}=\frac{3}{-1}= \frac{12}{-4}[/tex]

Hence, system −9x + 3y = 12, 3x - y = -4 has infinitely many solutions.

In lines -9x + 3y = 12 and  -16x + 9y = 30 ,

[tex]\frac{-9}{-16}\neq \frac{3}{9}\neq \frac{12}{30}[/tex]

Hence, system −9x + 3y = 12,  -16x + 9y = 30  has a solution.

In lines -9x + 3y = 12 and 5x + 8y = -1,

[tex]\frac{-9}{5}\neq \frac{3}{8}\neq \frac{12}{-1}[/tex]

Hence, system −9x + 3y = 12, 5x + 8y = -1 has a solution.

Answer: The test statistic is t= -0.90.

Step-by-step explanation:

Since we have given that

n₁ = 50

n₂ = 25

[tex]\bar{x_1}=3.02\\\\\bar{x_2}=3.04\\\\\sigma_1=0.08\\\\\sigma_2=0.06[/tex]

So, s would be

[tex]s=\sqrt{\dfrac{n_1\sigma_1^2+n_2\sigma_2^2}{n_1+n_2-2}}\\\\s=\sqrt{\dfrac{50\times 0.08^2+25\times 0.06^2}{50+25-2}}\\\\s=0.075[/tex]

So, the value of test statistic would be

[tex]t=\dfrac{\bar{x_1}-\bar{x_2}}{s(\dfrac{1}{n_1}+\dfrac{1}{n_2})}\\t=\dfrac{3.02-3.04}{0.074(\dfrac{1}{50}+\dfrac{1}{25})}\\\\t=\dfrac{-0.04}{0.074(0.02+0.04)}\\\\t=\dfrac{-0.04}{0.044}\\\\t=-0.90[/tex]

Hence, the test statistic is t= -0.90.

Final answer:

The result of multiplying −3y by the polynomial (5y³+11y²−y+8) is −15y⁴ − 33y³ + 3y² − 24y when expressed in standard form.

Explanation:

To multiply the expression −3y(5y³+11y²−y+8), we will distribute the −3y across each term inside the parentheses. The process involves the use of the distributive property, often also known as the multiplication of polynomials. Here are the steps:

Multiply −3y by 5y³ to get −15y⁴.

Multiply −3y by 11y² to get −33y³.

Multiply −3y by −y to get 3y².

Multiply −3y by 8 to get −24y.

Combining all these products gives us the expression in standard form:

−15y⁴ − 33y³ + 3y² − 24y

Answer:

r=17.0

Step-by-step explanation:

In a circle with center (h,k) and any point (x,y) on the circle, the radius of the circle is given as:

[tex](x -h)^2 + (y - k)^2 =r^2[/tex]

Center (h,k)=(-6,1)

(x,y)=(7,12)

[tex]r^2=(x -h)^2 + (y - k)^2 \\r^2=(7 -(-6))^2 + (12 - 1)^2\\r^2=(7 +6)^2 + 11^2\\r^2=13^2 + 11^2=169+121=290\\r=\sqrt{290}=17.03[/tex]

radius, r=17.0 (to the nearest tenth)

The radius of the circle with center (-6,1) and passing through the point (7,12) can be found using the distance formula. The radius, or distance between these two points, calculates to approximately 17.0 units when rounded to the nearest tenth.

In Mathematics, you can determine the radius of a circle if you have the coordinates of the center and a point on the circle. Here, we have the center of the circle at (-6,1) and a point (7,12) lying on the circle. We will use the distance formula to find the radius, r, which is essentially the distance between these two points.

Distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

By substituting the given points into the distance formula, we get

Radius (r) = sqrt((7 - (-6))^2 + (12 - 1)^2)

Sample calculation: r = sqrt((7 - (-6))^2 + (12 - 1)^2) = sqrt(169 + 121) = sqrt(290). Therefore, the radius of the circle, rounded to the nearest tenth, is approximately 17.0 units.

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The system of equations is inconsistent, meaning there is no solution for [tex]\(x\)[/tex] and [tex]\(y\)[/tex] that satisfies both equations simultaneously.

The given information can be translated into equations:

1. "The difference of the product of 10 and (x) and the product of 6 and y is -8":

[tex]\[10x - 6y = -8\][/tex]

2. "The sum of the product of -5 and x and the product of 3 and y is -1":

[tex]\[-5x + 3y = -1\][/tex]

Now, we have a system of two equations with two variables:

[tex]\[ \begin{cases} 10x - 6y = -8 \\ -5x + 3y = -1 \end{cases} \][/tex]

Let's solve this system step by step:

Step 1: Eliminate one variable from one of the equations.

Multiply the second equation by 2 to make the coefficients of [tex]\(y\)[/tex] in both equations opposites:

[tex]\[ \begin{cases} 10x - 6y = -8 \\ -10x + 6y = -2 \end{cases} \][/tex]

Now, add the two equations to eliminate [tex]\(y\)[/tex]:

[tex]\[ 0 = -10 \][/tex]

The result is a contradiction, indicating that the system is inconsistent. This means there is no solution that satisfies both equations simultaneously.

Conclusion:

The system of equations is inconsistent, meaning there is no solution for [tex]\(x\)[/tex] and [tex]\(y\)[/tex] that satisfies both equations simultaneously. The given information might contain an error or contradiction. Please double-check the equations and conditions provided.

Answer:

The answer to your question is C and D are parallel  

                                                    B and C  and B and D are perpendiculars.

Step-by-step explanation:

Data

Line A         (-2, 3)    (2, 2)

Line B         (-3, 0)    (3, -2)

Line C         (2, 4)      (0, -2)

Line D         (0, 6)      (-2, 0)

Process

1.- Calculate the slope of each line

    m = (y2 - y1)/(x2 - x1)

Line A   m = (2 - 3) / (2 + 2)

             m = -1/4

Line B = (-2 - 0) / (3 + 3)

          = -2/6

          = -1/3

Line C = (-2 -4)/(0 - 2)

           = -6/-2

           = 3

Line D = (0 - 6) / (-2 - 0)

           = -6/-2

           = 3

2.- Conclusion

If the slopes are the same, the lines are parallel if are reciprocal, the lines are perpendicular

Line C ║ Line D

Line B ⊥ Line C    and Line B ⊥ Line D

Answer:

Step-by-step explanation:

given that Joan is building a sandbox in the shape of a regular pentagon.

The perimeter of the pentagon is

[tex]35y^4 - 65x^3[/tex]inches.

Since regular pentagon we know that all sides are equal and there are totally five sides.

Perimeter of regular pentagon = 5*side

= 5a where a = length of side

Equate 5a to given perimeter to get

[tex]5a=35y^4 - 65x^3\\[/tex]

divide by 5

[tex]a=\frac{35y^4 - 65x^3}{5} \\=7y^4-13x^3[/tex]

Answer:

D. 7y^4 - 13x^3 inches

Answer:

1224 cm^3

Step-by-step explanation:

The shape of the box is a rectangular prism.

The volume of a rectangular prism is given by the formula below.

volume = length * width * height

volume = 10.2 cm * 15 cm * 8 cm

volume = 1224 cm^3

Final answer:

The volume of a shoebox with dimensions 10.2 cm x 15 cm x 8 cm is calculated by multiplying these three dimensions together, resulting in a volume of 1224 cm³.

Explanation:

To calculate the volume of a shoebox, you multiply its length by its width by its height. For a shoebox with dimensions of 10.2 cm, 15 cm, and 8 cm, the calculation would look like this:

Volume = Length × Width × Height

Volume = 10.2 cm × 15 cm × 8 cm

Volume = 1224 cm³

Therefore, the volume of the shoebox is 1224 cubic centimeters.

The solution is in the attachment

Answer:

0.0865

Step-by-step explanation:

Binomial Problem with n = 9 and p(triggered) = 0.99

And the photo below is the full answer,

I could not insert the fomula and hope it will find you well.

Answer:

Name the congruent triangles:

triangle RWS, triangle SWT, and triangle TSR

Answer:

b. Steve's Scratch and Dent.

Step-by-step explanation:

Tom should purchase his washing machine from Steve's Scratch and Dent.

Answer:

There are 48 girls at the banquet

Step-by-step explanation:

Let the number of boys =x

Let the number of girls=y

Ratio Of boys to girls=5:3

Therefore, x:y=5:3......(1)

If 20 boys leave, the ratio becomes 5:4

Sine number of boys=x

If 20 boys leave, new number = x-20

Therefore, x-20:y=5:4......(2)

From (1),

3x=5y

From Equation (2),

4(x-20)=5y

Therefore: 3x=4x-80

x=80

From (1),

3x=5y

5y=3X80

y=240/5=48

Therefore, there are 48 girls at the banquet

Answer:

8.899s

Solve: -5t^+40t+40

4-2√2 is the time taken by the ball to hit the ground.

Distance is the total movement of an object without any regard to direction

Given that Abraham throws a ball from a point 40 m above the ground. The height of the ball from the ground level after ‘t' seconds is defined by the function h(t) = 40t – 5t². then we need to find the time for ball to hit the ground.

The given function is

h(t)=40t-5t²

Let h(t)=40

We get,

40t-5t²=40

5t²-40t+40=0

t²-8t+8=0

(t-4)²=8

t-4=±√8

t=±√8+4

t=√8+4; t=4-√8

By considering the reality we know t>0

t=4-2√2

Hence  t=4-2√2 is the time taken by the ball to hit the ground.

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Answer:

niglgapopfart

Step-by-step explanation:

12(5)6$78$???98

Question:

Nick and Tasha are buying supplies for a camping trip. They need to buy chocolate bars to make s’mores, their favorite campfire dessert. Each of them has a different recipe for their perfect s’more. Nick likes to use 1/2 of a chocolate bar to make a s’more. Tasha will only eat a s’more that is made with exactly 2/5 of a chocolate bar.

Answer:

The fraction of a chocolate bar will Nick and Tasha will use in total if they each eat one s'more is [tex]\frac{9}{10}[/tex] bar.

Step-by-step explanation:

Here, we are meant to learn how to add fractions and to know about the essence of a common denominator

The portion of the chocolate that Nick makes an s'more with is 1/2

The portion of the chocolate that Tasha makes an s'more with is 2/5

Therefore the fraction of the chocolate bar Nick and Tasha use in total if they each eat one s'more is 1/2 + 2/5

Where [tex]\frac{1}{2}[/tex] + [tex]\frac{2}{5}[/tex]  multiplying the fraction [tex]\frac{1}{2}[/tex] by [tex]\frac{5}{5}[/tex] and  [tex]\frac{2}{5}[/tex]  by  [tex]\frac{2}{2}[/tex] wee have

[tex]\frac{5}{5}[/tex]× [tex]\frac{1}{2}[/tex] + [tex]\frac{2}{2}[/tex]× [tex]\frac{2}{5}[/tex]  =   [tex]\frac{5}{10}[/tex] +  [tex]\frac{4}{10}[/tex] =  [tex]\frac{9}{10}[/tex] bar

Therefore the fraction of the chocolate bar that would be left is

1 bar -  [tex]\frac{9}{10}[/tex] bar = [tex]\frac{1}{10}[/tex] bar.

Here is the complete question

Nick and Tasha are buying supplies for a camping trip. They need to buy chocolate bars to make s’mores, their favorite campfire dessert. Each of them has a different recipe for their perfect s’more. Nick likes to use 1/2 of a chocolate bar to make a s’more. Tasha will only eat a s’more that is made with exactly 2/5 of a chocolate bar.

Answer:

Both Nick and Tacha will use 9/10 of the chocolate bar

Step-by-step explanation:

Nicks share of the chocolate bar is 1/2(fraction of the chocolate bar need to make the s'more

And Tasha requires 2/5 to make her own s'more.

Then if both of them share a single chocolate bar,then it will be:

2/5(Tasha's share) + 1/2(Nick's share)

= 9/10 of a single chocolate bar will be used.

In case they were interested to know the amount remaining, it will be:

1 - 9/10 = 1 1/10

Answer: 14x² - 4x - 17

Step-by-step explanation:

The formula for determining the area of a rectangle is expressed as

Area = length × width

The rectangular back yard measures 5x + 4 by 3x - 2. This means that the area of the rectangular back yard would be

Area = (5x + 4)(3x - 2)

Area = 15x² - 10x + 12x - 8

= 15x² + 2x - 8

The formula for determining the area of a square is expressed as

Area = length²

Length of square patio = x + 3

Area of square patio = (x + 3)(x + 3)

= x² + 3x + 3x + 9

= x² + 6x + 9

The expression for the area of grass that will be left in the back yard after the patio is built is

15x² + 2x - 8 - (x² + 6x + 9)

= 15x² + 2x - 8 - x² - 6x - 9

= 15x² - x² + 2x - 6x - 8 - 9

= 14x² - 4x - 17

Answer:

The vectors r and  p = Aˆi + Bˆj + Ckˆ are perpendicular between them. Thus, the plane equation come from the fact that the dot product is equal to zero.

Step-by-step explanation:

The dot product of r and p

r*p = (xˆi + y ˆj + zk)*(Aˆi + Bˆj + Ckˆ) = Ax + By + Cz = 0

5  √ 3  c m

A t = √ 34  *  s 2  =  25  √ 3

this makes the sides 10cm

At= 1/2 b * h

25 √ 3  =  12  ⋅ 10  ⋅  h  = 5 √ 3 c m

Answer:

Height = 8.66 cm

Step-by-step explanation:

The formula for the area of an equilateral triangle is expressed as

A = S²√3/4,

where s represents the length of each side. The area of the given equilateral triangle is 25 √3 cm squared. Therefore

25 √3 = S²√3/4

Dividing both sides of the equation by √3, it becomes

25 √3/√3 = S²√3/4√3

25 = S²/4

Cross multiplying, it becomes

S² = 25 × 4 = 100

Taking square root of both sides of the equation, it becomes

√S² = √ 100

S = 10 cm

In an equilateral triangle, all the sides are equal. The height of the equilateral triangle divides it into two equal right angles triangle. The angles in each right angle triangle are 90, 60 and 30 degrees. To determine the height, h, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

10² = h² + 5²

100 = h² + 25

h² = 100 - 25 = 75

h = √75

h = 8.66 cm