Directions: The Johnson family is redesigning their backyard this spring. They want to include a sandbox area,
a swing set area, a patio area, a pool area and a grill area. Their plans for the yard layout in feet is shown in the
figure below. Use the figure and your knowledge of polynomials, perimeter, and area to solve the following:

Answer: = [tex]6x^{2}[/tex] − xy − [tex]40y^{2}[/tex]

Step-by-step explanation:

{Apply\:FOIL\:method}:\quad

\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd

a=2x,\:b=5y,\:c=3x,\:d=-8y

{Apply\:minus-plus\:rules}

+\left(-a\right)=-a

=2\cdot \:3xx-2\cdot \:8xy+5\cdot \:3xy-5\cdot \:8yy

Simplify 2 · 3xx − 2 · 8xy + 5 · 3xy − 5 · 8yy: 6x − xy − 40y

2 2

= [tex]6x^{2}[/tex] − xy − [tex]40y^{2}[/tex]

Hope This Helps!

According to the solving by  using substitution method the  x and y are x = 6/5 and y = -8/5 respectively.

The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable through one equation is substituted in the second equation in this procedure, as the name implies.

given equations are 2x+4y = 4 and -2x+ y = -4

Now, simplifying -2x+y = -4

-2x+y = -4

∴ y = -4 + 2x

i.e. y = 2x - 4

By substitution method,

y = 2x - 4 in other given equation 2x+4y = 4,

 2x+4y = 4

 2x+4(2x - 4) = 4

∴ 2x + 8x - 8 = 4

∴ 10x = 4 + 8

∴10x = 12

∴ x = 12/10

∴ x = 6/5

Now ,

substituting x = 6/5 in y = 2x - 4,

 y = 2(6/5) - 4

∴ y = - 8/5

∴ x = 6/5  &  y = - 8/5.

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If his growth spurt continued at the same rate Andrew will grow 26/7 inches per month during that growth spurt.

To calculate someone's age, you would subtract their birth year from the current year. For example, if someone was born in 1995 and it is now 2020, their age would be calculated as 2020 - 1995 = 25 years old.

If you have a birthdate, you can use a date calculator to find the exact age in years, months and days.

It's also important to note that, if the person's birthday hasn't occurred yet in the current year, you would subtract the birth year from the current year minus one.

We can start by converting the mixed number 4 1/3 to an improper fraction by multiplying the whole number by the denominator and adding the numerator: 4 x 3 + 1 / 3 = 13/3

To find out how much Andrew grew per month, we need to divide the total growth by the number of months.

13/3 inches / 3 1/2 months = (13/3) / (7/2) = (13/3) x (2/7) = 26/7 inches/month.

So, Andrew grew 26/7 inches per month during that growth spurt.

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178 students taking a music class and 82 students taking an art class

There was no clear question, but I'm assuming you want to know how many students are enrolled in music and painting classes.

Let x= the number of children enrolled in art classes.

number of children enrolled in music classes: 2x + 14

The overall number of children will be 260, including all of these children.

x+2x+14 = 260

3x=246 x=82 pupils attend an art lesson.

To find people taking music classes, enter x to 2x+14.

2(82)+14 = 178

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The complete question would be;

There are 260 eighth-grade students at South Whitemarsh Middle School. All eighth-grade students are required to enroll in either a music class or an art class. No students take both art and music classes. The number of students taking music classes is 14 more than twice the number taking art classes.

The system of equations .5(5x + 4) = 17.5x + 14 have Infinite solutions.

We know two simultaneous equations have a unique solution when they intersect at a point,

when they are parallel they have no solution and when they are coinciding they have an infinite no. of solutions.

Given, A system of equation 3.5(5x + 4) = 17.5x + 14.

17.5x + 14 = 17.5x + 14.

As the LSH and RHS are equal the equation of the two lines is the same and hence they coincide and have an infinite number of solutions.

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Answer:

x = 20

Step-by-step explanation:

180 - 135 = 45

115 + 45 + x = 180

160 + x = 180

180 - 160 = x

x = 20

Have a nice day!

Answer:

30 people

Step-by-step explanation:

First, calculate what number 75% is of 250. You then should get a total of 30.

Hope this helped ! :D

( apologies if I got it wrong)

Answer:

80mm

Step-by-step explanation:

According to Pythagorean theorem :

a² + b² = c²

=> a² + (60)² = (100)²

=> a² + 3600 = 10000

=> a² = 10000 - 3600

=> a² = 6400

=> a = √(6400)

=> a = 80

Answer:x=20

Step-by-step explanation:5x+9 and 3x+11 must add to 180, so you can set these equal to 180 and get  8x+20 = 180, this can be simplified to 8x=160 or x = 20

Answer:

x = 20°

Step-by-step explanation:

Given angles,

→ 5x + 9

→ 3x + 11

Forming the equation,

→ (5x + 9) + (3x + 11) = 180°

{Because, sum of two angles in a straight line leads to 180°}

Now the value of x will be,

→ (5x + 9) + (3x + 11) = 180°

→ 5x + 3x + 9 + 11 = 180°

→ 8x + 20 = 180°

→ 8x = 180° - 20

→ x = 160/8

→ [ x = 20° ]

Hence, the value of x is 20°.

Answer: Sophie's

Step-by-step explanation:

Q1 is the second point.

Answer:

Part A: 48in^2

Part B: 4in by 12in, 8in by 6in, and 3in by 16in

Step-by-step explanation:

Volume/height is the area of the base:

480/10 = 48in^2

Any two numbers that multiply to 48 are possible dimensions of the block:

4*12, 8*6, 3*16

Answer:

Option 3

Step-by-step explanation:

From the graph attached,

Coordinates of point A → (6, -2)

Coordinates of point A' → (4, 7)

Let the point A' is shifted by 'h' units horizontally and 'k' units vertically,

Rule that defines the translation,

A'(x, y) → A(x + h, y + k)

By this rule,

A'(4, 7) → A(4 + h, y + 7)

Since, coordinates of point A are (6, -2),

Therefore, (4 + h) = 6

h = 2

And y + 7 = -2

y = -9

Therefore, Rule of the translation will be,

[tex]T_{(2, -9)}[/tex]

Option 3 will be the answer.

Answer:

300 feet squared i think

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The width and height of the rectangle for which the perimeter of the window will be as small as possible are (3sqrt(2), 2sqrt(2)).

What is the Lagrange multiplier?

The Lagrange multiplier, λ, measures the increase in the objective function (f(x, y) that is obtained through a marginal relaxation in the constraint (an increase in k). For this reason, the Lagrange multiplier is often termed a shadow price.

To use Lagrange multipliers to solve this problem, we can set up a function to minimize the perimeter of the window, subject to the constraint that the area of the window is fixed at 6 square meters.

Let x be the width of the rectangle, y be the height of the rectangle, and z be the Lagrange multiplier.

The function to minimize is the perimeter of the window, which is P = 2x + 2y + (2 * sqrt(x^2 + y^2))

The constraint is the area of the window, which is A = xy + (x * sqrt(x^2 + y^2))/2 = 6

The Lagrange equation is

L(x,y,z) = P + z(A-6) = 2x + 2y + (2 * sqrt(x^2 + y^2)) + z(xy + (x * sqrt(x^2 + y^2))/2 - 6)

To find the critical points, we will take the partial derivatives of L(x,y,z) with respect to x, y, and z, and set them equal to zero:

∂L/∂x = 2 + zy + zx * (x/sqrt(x^2 + y^2)) = 0

∂L/∂y = 2 + zx + zy * (y/sqrt(x^2 + y^2)) = 0

∂L/∂z = xy + (x * sqrt(x^2 + y^2))/2 - 6 = 0

Solving these equations simultaneously will give us the critical points of the function.

We will get two critical points (x,y) = (3sqrt(2), 2sqrt(2)), (0,2sqrt(2))

We should eliminate the point where x=0 as it does not fulfill the condition of the problem ( the width should be greater than 0)

Hence, the width and height of the rectangle for which the perimeter of the window will be as small as possible are (3sqrt(2), 2sqrt(2)).

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Answer:

Yes

Step-by-step explanation:

If there was 200 hundred dollars just subtract 50 dollars if there is still money then yes.

Answer: yes

Step-by-step explanation:

200-50=159

Answer:

The tower is 113 meters.

Step-by-step explanation:

We are given a pole and a tower that both create a shadow.

Hence, the figures made are triangles.

If you draw the figure (attached to this response), you can see the two triangles are similar triangles.

⭐What are similar triangles?

The length of the height of the pole (3.2) corresponds to the length of the height of the tower (x).

The length of the shadow of the pole (1.32) corresponds to the length of the shadow of the tower (46.75).

Therefore, our two ratios are:

[tex]\frac{3.2}{x}[/tex] and [tex]\frac{1.32}{46.75}[/tex]

A proportion is when you set two ratios equal to each other:

[tex]\frac{3.2}{x} = \frac{1.32}{46.75}[/tex]

To solve for x, cross multiply by multiplying the opposite parts of the fraction together.

[tex]\frac{3.2}{x} = \frac{1.32}{46.75}\\46.75(3.2) = 1.32x\\149.6 = 1.32x\\\\113 = x[/tex]

∴ The tower is 113 meters tall!

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Does there seem to be a pattern in the population estimates of the bugs on this tree is the query or the question .

Variation is the difference in an individual's genetic make-up that causes a population's members to have different physical characteristics. Variation can be shown in an individual's physical characteristics, fertility, metabolism, and method of reproduction. A variation is a relationship between a set of values for one variable and another set of values. direct change. If m is a nonzero constant and b = 0, the function y = mx (commonly written y = kx) that results from the equation y = mx + b is known as a direct variation.

given

the population of the bugs

b is the no. of bugs = 50 . [tex]3^{t}[/tex]

t is the no. of weeks they first counted

so this question explains

the range of population estimates

Is there a trend in the variation of estimates

Does there seem to be a pattern in the population estimates of the bugs on this tree is the query or the question .

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The Angle-Angle-Angle (AAA) criterion for the similarity of triangles states that "If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or percentage) and consequently the two triangles are similar".

A triangle is a closed two-dimensional shape or polygon with the fewest sides in mathematics. A triangle is made up of three sides and three angles. The most significant attribute of a triangle is that the sum of its internal angles equals 180°.

Conditions for Triangle Similarity

If the corresponding angles of two triangles are identical, they are said to be comparable triangles.

If their respective sides have the same proportion/ratio.

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Answer:

BC =21.03540021

Step-by-step explanation:

We know the measure of angle B since the sum of the angles of a triangle add to 180

A + B+ C = 180

61+ B + 12 =180

B = 180 - 12 -61

B =107

Then we can use the law of sines to find BC

sin B           sin A

-------- = -------------

AC                BC

sin 107       sin 61

-------- = -------------

23                BC

Using cross products

BC  sin 107 = 23 sin 61

BC = 23 sin 61/ sin 107

BC =21.03540021

Answer:

20.12m

Step-by-step explanation:

180 - (12 + 61) = 107° = ∡B

[tex]\frac{23}{sin(107)} = \frac{a}{sin(61)}[/tex]                     *Cross Multiply*

[tex]a(sin(107)) = 23(sin(61))[/tex]      *Divide by sin(107)*

[tex]a = \frac{23(sin(61))}{sin(107)}[/tex]                         *Solve*

a = BC ≈ 20.12m

Answer:

2^x=1

x=0

32•x=0

32.0=0

maybe

Answer:

A∪B = {5, 10, 15, 20, 25, 30, 35, 40, 45}

Step-by-step explanation:

A = {5, 10, 15, 20, 25}

B = {25, 30, 35, 40, 45}

Find A∪B

There are 5 elements in set A

There are 5 elements in set B

A∪B is the combination of all the elements in set A and set B without repeating any

A∪B = {5, 10, 15, 20, 25, 30, 35, 40, 45}

A∪B has 9 elements in it

A ⋂ B = {25}

A (A) histogram is a useful tool for condensing qualitative data.

An effective tool for summarizing qualitative data is a histogram.

The distribution of numerical data is roughly depicted by a histogram.

Karl Pearson was the person who first coined the phrase.  

The first stage in creating a histogram is to "bin" (or "bucket") the range of values, divide it into a series of intervals, and then count the number of values that fall into each interval.

The bins are often defined as a series of discrete intervals that don't overlap.

The bins (intervals) must be close together and frequently, though not always, have the same size.

Therefore, a (A) histogram is a useful tool for condensing qualitative data.

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Answer:

i think its 70 percent maybe

Answer:

72 fraction if polygon are expectations but when you divide it it will sepetate to 70 and add the 2 angles so it would be (72)

Step-by-step explanation:

HOPE IT HELPS!!

Answer:

15

Step-by-step explanation:

Actual length is 5.5m and percentage error is 20%.We can find by using percentage error formula.

Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage. In other words the percent error is the relative error multiplied by 100.

Subtract the actual value from the estimated value.And then divide the results with the real value. Multiply the results by 100 to find the total percentage.The formula represent it as a percentage of the exact value.Percent error = |Approximate value – Exact Value|/Exact value * 100.

Now we find

wall is measured 5m to the nearest so

approximate value= 4.5

actual value     =5.5

putting value in the formula

Percentage error  = 5.5- 4.5/5 *100

                              = 20%

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Answer:

L' = (-1,2)

M' = (1,2)

L'M' = 2

The slope of the original segment and dilated segment are both zero

Step-by-step explanation: just did it on edge!

Answer:

Step 2 is wrong

Step-by-step explanation:

[tex](Sin Ф )^{2}[/tex]= [tex](1/4)^{2}[/tex] = 1/16