30 POINTS!!!

If the measurements for a living room were 5 1/2 by 3 ft. If the scale is 1/2 ft = 2 1/2 meters. If carpet cost 1.50 per square foot, how much will it cost to cover the living room floor?

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!

Answer:

15

Step-by-step explanation:

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:

the answer is A

[tex]x + 7 > 3[/tex]

Answer:The Surface Area of Pyramid is 105 cm².

Step-by-step explanation:

What is Surface Area of Pyramid?

If “P” is the base perimeter, “l” is the slant height, and “B” is the base area, then the total surface area of the regular pyramid formula is given by (½)Pl + B Square units.

Given:

slant height, l= 8 cm

So, the base Perimeter = 4 x 5

                                     = 20 cm

Now, area of the base = 5 cm x 5 cm

                                    = 25 cm²

Then,  surface area of a square pyramid

= 1/2 x slant height x base perimeter + area of base

= 1/2 x 8 x 20 + 25

= 80 + 25

= 105 cm²

The required statement is RS/VU = ST/UT and angle S is congruent-to angle U. Option A is correct.

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

The figure of the triangle is not given the quesiton, An figure is attached after the solution regarding the solution,

From diagram,
Consider the triangle RST and triangle VUT

ST/UT = 2

∠S = ∠U both are of 90°
RS/VU = 2.

So, triangles are similar by the SAS similarity theorem.

Thus, the required statement is RS/VU = ST/UT and angle S is congruent-to angle U. Option A is correct.

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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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Answer:

For 5x + y = 27;  [tex]x=\frac{-1}{5}y+\frac{27}{5}[/tex]

For -10x + 7y = -36;   [tex]x=\frac{7}{10}y+\frac{18}{5}[/tex]

Step-by-step explanation:

None because it will be in the screenshots.

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9514 1404 393

Answer:

  x = 5

Step-by-step explanation:

The x-coordinate of the solution can be found by subtracting the second equation from 7 times the first.

  7(5x +7) -(-10x +7y) = 7(27) -(-36)

  45x = 225 . . . . . simplify

  x = 5 . . . . . . . . . . divide by 45

The x-coordinate of the solution is 5.

_____

The y-coordinate is 2.

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

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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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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On solving the provided question, we can say that w = 10 in; l = 2 in; volume of prism = WL = 10 X 2 = 20 in sq

The definition of a prism in geometry is a polyhedron with an n-sided polygonal base, a second base that is a shifted copy of the first base, and n additional faces (necessarily all parallelograms), with two Connect the corresponding sides of the base. Translations of the base are all cross sections that are parallel to it. A prism is a two-sided, solid, three-dimensional object. It consists of equal cross-sections, flat sides, and identical bases. A prism has faces that are parallelograms or rectangles without bases. A prism is a homogenous, solid, transparent, refracting object enclosed by two planes that are obliquely angled to one another. Two triangular faces and three parallel rectangular faces make up a typical prism. They are constructed of either glass.

here,

w = 10 in

l = 2 in

volume of prism = WL = 10 X 2 = 20 in sq

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Explanation:

The ASA indicates that the side (S) is between the two angles (A). The order is important. For the bottom triangle, the side between the red angles is segment ST. The upper triangle has the segment UX between the red angles. If we know that ST = UX, then we can use the ASA rule to prove the triangles are congruent.

Side note: ST = UX is the same as UX = ST. Furthermore, ST is the same as TS, and UX is the same as XU. So there are a few ways to fill in that blank.

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:

[tex]\text{Perimeter}=8x^2+14x-5[/tex]

Step-by-step explanation:

[tex]\text{Perimeter}=(7x-4)+(3x^2+7x-1)+(5x^2)\\\text{Perimeter}=7x-4+3x^2+7x-1+5x^2\\\text{Perimeter}=5x^2+3x^2+7x+7x-4-1\\\text{Perimeter}=8x^2+14x-5[/tex]

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:

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:

c

Step-by-step explanation:

/l/b/a×4÷6×0rrrt he 3rjdhdyeeyy3gfwgqrt

Answer:

  b)  250,000

Step-by-step explanation:

You want to estimate the product of 5,398 and 47 by rounding to the nearest thousand and ten.

Rounding 5,398 to the nearest thousand gives 5000.

Rounding 47 to the nearest ten gives 50.

The product of these is the estimate you want:

  5000·50 = 250,000

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}

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:

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

The required probability as calculated from the data given above is found to be as 1 / 9.

Given,

The spinner is having the letters as A, B and C.

The possibility of getting any of these letters when the spinner is rolled is same.

Therefore , the sample space will be as follows ,

6 + 3 = 9

This is due to the fact a die has 6 sides.

Then the probability of getting a B will be ,  1/9

Sample space is known as the collection of all values which are used in an experiments. The total number of favorable outcomes are taken from this sample space only.

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Answer: Sophie's

Step-by-step explanation:

Q1 is the second point.

The correct statement regarding the probabilities from the table is given as follows:

C The golf ball is 2 times as likely to be orange as it is to be pink.

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The total number of balls for this problem is given as follows:

4 + 11 + 8 + 18 = 41.

Hence the probability of selecting each ball is obtained as follows:

Hence statement C is correct, as:

2 x 4/41 = 8/41.

(which is the probability of orange, obtained multiplying the probability of pink by two).

The number of pink balls is of 4.

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Elizabeth has a box that can hold exactly 24 unit cubes. It could also be said that her box has 24 cubic units. So, option D. is correct.

A cubic unit is a unit of measurement for volume. It represents the amount of space an object occupies in three dimensions: Length, Width and Height. It is often used to measure the volume of three-dimensional shapes such as cubes, square prisms, cylinders, and spheres. Cubic units are most commonly measured in cubic meters or cubic feet, but they can also be expressed in smaller units such as cubic centimeters or cubic inches.

The total volume of the box is 24 cubic units. A side of the box may measure 2 units x 3 units x 4 units = 24 cubic units.

Choice A is incorrect. This is because the area of ​​a shape is a measure of the two-dimensional space it occupies, and the volume of a shape is a measure of the three-dimensional space it occupies.

Choice B is incorrect. This is because the area of ​​a shape is a measurement of the two-dimensional space it occupies, not its volume.

Option C is incorrect because it states that the box has a volume of 12 cubic units, but it is not because the volume he has is 24 cubic units.

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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:

2^x=1

x=0

32•x=0

32.0=0

maybe