using algebra prove that given any 3 consecutive whole numbers, the sum of the square of the smallest number and the largest number is always 2 more that twice the square of the middle number

Let's call the height of the second building "x". We can use trigonometry to solve for x.

First, let's draw a diagram to help visualize the problem:

A        B

\      /

 \    /

  \  / x

   \/

   C

Where:

A is the top of the 200 meters high building

B is the bottom of the second building

C is the point from which the angles of depression and elevation are measured

x is the height of the second building

From the diagram, we can see that:

angle BCA = 20 degrees (angle of depression)

angle BAC = 10 degrees (angle of elevation)

AB = 200 meters

Using the tangent function, we can write:

tan(20) = x / AB (tangent of angle BCA)

tan(10) = x / (AB + x) (tangent of angle BAC)

We can solve these equations for x:

x = AB * tan(20) (multiply both sides by AB)

x = (AB * tan(10)) / (1 - tan(10)) (multiply both sides by 1 - tan(10), then simplify)

Plugging in the values we know:

x = 200 * tan(20)

x = (200 * tan(10)) / (1 - tan(10))

Using a calculator:

x ≈ 67.35 meters

Therefore, the height of the second building is approximately 67 meters (to the nearest hundred meters).

Answer:

If 2:3 = x:12, then:

2/3 = x/12

Multiplying both sides by 12, we get:

x = 2/3 x 12 = 8

Therefore, the value of x is 8.

Answer: 54

Step-by-step explanation:

Start from the middle of the equation and work your way out.

First find g(3) :

g(3) = 3+7 = 10

Then plug g(3) into the f equation:

f(g(3)) = 5(10) + 4 = 54

Answer:

Step-by-step explanation:

9 * 9 = 81

4 * 4 = 16

81 + 16 = 97

Answer:

see explanation

Step-by-step explanation:

given a parabola in standard form

f(x) = ax² + bx + c ( a ≠ 0 )

then the equation of the axis of symmetry is

x = - [tex]\frac{b}{2a}[/tex]

f(x) = 2x² + 8x - 4 ← is in standard form

with a = 2, b = 8 , then equation of axis of symmetry is

x = - [tex]\frac{8}{2(2)}[/tex] = - [tex]\frac{8}{4}[/tex] = - 2

that is equation of axis of symmetry is x = - 2

the axis of symmetry passes through the vertex of the parabola

substitute x = - 2 into f(x) for corresponding y- coordinate

f(- 2) = 2(- 2)² + 8(- 2) - 4 = 2(4) - 16 - 4 = 8 - 20 = - 12

vertex = (- 2, - 12 )

the y- intercept is on the y- axis, where the x- coordinate is zero

substitute x = 0 into f(x)

f(0) = 2(0)² + 8(0) - 4 = 0 + 0 - 4 = - 4

y- intercept = - 4

Answer:

  569 square units

Step-by-step explanation:

You want the surface area of the 8-sided shape that has a square "base" 7 units on a side, and a "height" of 20 units.

The slant height of each triangular face is the hypotenuse of a right triangle with legs 7/2 units and 20 units. That height is ...

  h = √(3.5² +20²) = √412.25 ≈ 20.304 units

The area of one triangular face is ...

  A = 1/2bh

  A = 1/2(7)(20.304) . . . one face

There area 8 congruent triangular faces, so the total area is ...

  A = 8(1/2)(7)(20.304) = 8(7)√412.25 ≈ 568.51 ≈ 569

The total surface area is about 569 square units.

<95141404393>

Answer:

The answer to this question is --> f(x) = -4x^2-8x+32

Hope this helps

The velocity of the two cars are 50km/hr and 60km/h

Velocity is the rate of change of distance with time. it is measured in meter per second and it is a vector quantity.

let the faster car be A and slower car be B

V(A) = V(B) +10

S( A) = v × t

S(B) = v(b) × t

S( A) = 5( v(b) +10)

S(A) +S(B) = 550

5v(b) +50+5vb = 550

10v(b) = 550-50

v(b) = 500/10

v(b) = 50km/h

v(a) = 50 +10

v(a) = 60km/h

Therefore the velocity of the two cars are 50km/h and 60 km/h

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Answer:

28+36+y=180

64+y=180

y=180-64

y=116°

Answer:θ≈2.15

θ≈4.13 are correct

Step-by-step explanation:We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):

3u^2 - 2u - 2 = 0

We can use the quadratic formula to solve for u:

u = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 3, b = -2, and c = -2. Substituting these values, we get:

u = (2 ± sqrt(4 + 24)) / 6

u = (2 ± 2sqrt(7)) / 6

Simplifying this expression, we get:

u = (1 ± sqrt(7)) / 3

Therefore, either:

Answer: 0.15

I don't really know how to show you work on here but you can think about it like this. if 5 x 3 is 15, and if there is a decimal like 0.3 x 0.5 it would result in the answer getting smaller as you're multiplying decimals if that makes sense... so it would result in the answer being 0.15. Sorry if it wasn't a good explanation.

The triangles are not similar. Triangle EFG and Triangle QRS are not similar. ΔEFG not ~ ΔQRS

From the question, we are to determine if the given triangles are similar

From one of Triangle similarity theorems, AA (or AAA) or Angle-Angle Similarity theorem.

The Angle-Angle similarity theorem states that If any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other

In the given diagram,

In triangle EFG

m ∠E = 104°

m ∠F = 45°

m ∠G = 180° - (104° + 45°) = 31°

In triangle QRS

m ∠R = 100°

m ∠Q = 45°

m ∠S = 180° - (100° + 45°) = 35°

Since no two angles of one of the triangles are equal to any two angles of other triangle, the triangles are not similar

Hence,

ΔEFG not ~ ΔQRS

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Answer: 200

Step-by-step explanation: 20% of 200 is 40

Answer:

200

Step-by-step explanation:

Since 20% of the movie is equal to 40 minutes of the entire movie, simply just keep adding 40 repeatedly until you hit 100%.

40+40+40+40+40=200

^      ^     ^     ^     ^

20+20+20+20+20=100

Answer:To solve this problem, we need to use the formulas for the area and perimeter of a triangle.

Let's start by using the formula for the area of a triangle:

Area = (base x height) / 2

where base and height are the length and height of the triangle's base, respectively.

Let's assume that the base of the triangle is x meters, and the height is y meters. Then we have:

Area = (x*y)/2 = 0.45 m²

Solving for y, we get:

y = (2*0.45)/x

y = 0.9/x

Now, let's use the formula for the perimeter of a triangle:

Perimeter = a + b + c

where a, b, and c are the lengths of the three sides of the triangle.

Since we know that the perimeter is about 325 cm, we can assume that the three sides are close to each other in length. Let's assume that each side has a length of 325/3 = 108.33 cm.

Converting to meters, we get:

a = b = c = 108.33/100 = 1.0833 m

Now, we can use the formula for the area of a triangle again to solve for x:

Area = (base x height) / 2

0.45 = (x * 0.9/x) / 2

0.9 = x²

x = √0.9 = 0.9487 m

Therefore, the base of the triangle is approximately 0.9487 meters, and the height is approximately 0.9/0.9487 = 0.9487 meters.

So the triangle has sides of length 1.0833 meters and a base of length 0.9487 meters, which gives us a perimeter of approximately 3.215 meters (rounded to three decimal places).

Step-by-step explanation:

Answer: it’s C, cubic

Step-by-step explanation:

Answer:

[C] Cubic

Step-by-step explanation:

Let find define all the answer choices:

Linear- Straight Line

Quadratic -  shape of a U or an upside down U

Cubic - trivalent graphs, are graphs all of whose nodes have degree 3

Exponential- curve that has a horizontal asymptote and it either has an increasing slope or a decreasing

As a result, the graph given is a Cubic graph.

RevyBreeze

From a stem-and-leaf plot,

1. The minimum value = 13

2. The maximum value = 62

3. The number of data with values greater than 25 = 16

4. The number of data with values of at least 40 = 4

5. The percentage of the data with value less than 15 = 6.25%

We know that on a stem and leaf plot, the minimum is the first value and the maximum is the last value.

From the stem-and-leaf plot,

a) the minimum value is 13

b) the maximum value is 62

c) the number of data with values greater than 25:

26, 27, 28, 28, 31, 31, 32, 34, 34, 35, 38, 39, 42, 43, 47, 62

So, the number of data with values greater than 25 = 16

d) the number of data with values of at least 40:

42, 43, 47, 62

So, the required number = 4

e) the percentage of the data with value less than 15:

the data with values less than 15 are: 13, 14

So, the number of  the data with values less than 15 are: 2

The total number of data values = 32

So, the required percentage would be,

P = (2/32) × 100

P = 6.25%

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Answer:

  15

Step-by-step explanation:

You want the remainder from division of f(x) = 2x³ +5x² -12x by x -(-1).

The table used for synthetic division is built by listing the zero of the divisor at upper left, and the coefficients of the polynomial across the top to the right of that. They are listed in order of decreasing degree, with any necessary zero coefficients put in the appropriate place(s).

The attachment shows the table and the instructions for filling it out. The value at the bottom in the rightmost column is the remainder from the division.

The remainder theorem tells you that is also the value of the function for x = k.

The remainder from f(x) ÷ (x +1) is 15.

<95141404393>

The solution is the two dimensions will be 2121.32 by 1414.2.

Here, we have,

let X and Y be the two dimensions.

Area will be X times Y.

XY = 3000000

Y = 3000000 / X

Perimeter = 2x + 3y

substituting the values:

Perimeter = 2x + 3*3000000 / x

         = 2x + 9000000 / x

so, we get,

2 = 9000000 / x^2

x^2 = 9000000 / 2 = 4500000

x = sqrt(4,500,000)

= 2121.32

 = 1000 sqrt (4.5)

y = 3000000 / 2121.32

 = 1414.2

 = 1000 sqrt(2)

so the dimensions will be 2121.32 by 1414.2 .

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complete question:

A rancher wants to fence in an area of 3000000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?

In the quadrilateral ABCD and LBNM the corresponding angles and line segments are as follow,

∠A = ∠L, ∠D =∠M , ∠C = ∠N , and

AB = LB , CD = NM ,  DA = ML.

Quadrilateral ABCD rotates 180 degrees around point B,

New quadrilateral formed named LBMN

The corresponding angle after rotation of 180 degrees around B is equals to,

B remain at same position.

A rotates and point L take the position of A.

D rotates and point M take the position of D.

C rotates and point N take the position of C.

Corresponding angle to A is angle L.

Corresponding angle to D is angle M.

Corresponding angle to C is angle N.

Similarly corresponding segments are of ABCD and LBNM are

Line segment AB corresponds to line segment LB.

Line segment CD corresponds to line segment NM

Line segment DA corresponds to line segment ML.

Therefore, in the quadrilateral the corresponding angles and line segments are ∠A = ∠L, ∠D =∠M , ∠C = ∠N , AB = LB , CD = NM , and DA = ML.

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The graph is a function: yes.

The domain of this function is: x ≥ -3.

The range of this function: all real numbers.

In Mathematics and Geometry, a range can be defined as the set of all real numbers that connects with the elements of a domain.

Furthermore, the horizontal extent of any graph of a function represents all domain values and they are always read and written from smaller to larger numerical values, and from the left-hand side of the graph to the right-hand side.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = {-3, ∞}, x ≥ -3, or -3 ≤ x ≤ ∞.

Range = {-∞, ∞} or all real numbers.

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Answer:

The answer is (0,2) (1,-1) (2,-4)

Step-by-step explanation:

The slope is -3.

Because of this, you go down 3 and to the side 1 (it's also called rise/run).

I REALLY HOPE THIS HELPS!!!!

The simplest form of the expression (2x-3)(3x²+2x-1) is 6x³ - 5x² - 8x + 3.

Given the expression in the question:

( 2x - 3 )( 3x² + 2x - 1 )

To simplify the expression (2x-3)(3x²+2x-1), we need to use the distributive property of multiplication,

which states that: a(b+c) = ab + ac

Using this property, we can expand the expression as follows:

(2x-3)(3x²+2x-1)

2x(3x²+2x-1) - 3(3x²+2x-1)

6x³ + 4x² - 2x - 9x² - 6x + 3

Add like terms

= 6x³ - 5x² - 8x + 3

Therefore, the simplest form is 6x³ - 5x² - 8x + 3.

Option A) 6x³ - 5x² - 8x + 3 is the correct answer.

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Check the picture below.

so the maximum height will occur at its vertex y-coordinate.

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-4.9}t^2\stackrel{\stackrel{b}{\downarrow }}{+48}t\stackrel{\stackrel{c}{\downarrow }}{+6} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 48}{2(-4.9)}~~~~ ,~~~~ 6-\cfrac{ (48)^2}{4(-4.9)}\right) \implies \left( - \cfrac{ 48 }{ -9.8 }~~,~~6 - \cfrac{ 2304 }{ -19.6 } \right)[/tex]

[tex]\left( \cfrac{ 48 }{ 9.8 } ~~~~ ,~~~~ 6 +\cfrac{ 2304 }{ 19.6 } \right) ~~ \approx ~~ (4.89~~,~~\text{\LARGE 124})[/tex]

Answer: the inequalities for which 0 is a solution are x - 5 ≤ -3 and x/-2 ≥ 0.

Step-by-step explanation: x - 5 ≤ -3 (0 is less than or equal to 2)

x/-2 ≥ 0 (0 is greater than or equal to 0)

In mathematical form, this can be written as:

0 ≤ x - 5 ≤ -3 or x - 5 ≤ 0 and x ≤ -3

Answer:

C. complementary

Michel-Eugène Chevreul discovered that placing complementary colors next to each other can create the greatest contrast and vibrancy in color perception. This is because complementary colors are located opposite each other on the color wheel and, when placed side by side, they enhance each other and create a strong visual impact. For example, placing yellow next to violet or blue next to orange can create a dynamic and eye-catching effect. In contrast, placing tertiary colors (colors made by mixing primary and secondary colors) or arbitrary colors next to each other may not create as much contrast or visual interest. Overall, understanding color theory and the relationships between different colors can be helpful for creating visually appealing designs, artworks, or other color-based projects.

The value of the unknown perimeter is derived to be 96 cm using the ratio of the known side of the similar figures.

A ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. It can be used to express one quantity as a fraction of the other ones.

By comparison using the variable x to represent the unknown perimeter, and the ratio of the known side lengths;

24/32 = 72cm/x

x = (32 × 72cm)/24 {cross multiplication}

x = 2304cm/24

x = 96 cm

Therefore, the value of the unknown perimeter is derived to be 96 cm using the ratio of the known side of the similar figures.

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The value of x which I suppose is the angle M is calculated to be 32°

In a right-angled triangle KLM, it is a known fact that the sum of the three angles in any triangle is 180°.

Since angle L is a right angle and has a measure of 90°, we can find angle M by subtracting the sum of angles K and L from 180°.

Thus,

angle M = 180° - angle K - angle L

= 180° - 58° - 90°

= 32°

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The expressions that are equivalent to the expression 8x + 32y are:

4(4 ⁢x + 8y) − 2⁢(4x)

8(x + 4y)

Equivalent expressions are expressions that work the same even though they look different.

If two algebraic expressions are equivalent, then the two expressions have the same value when we substitute the same value(s) for the variable(s).

Let's simply the options to see if they are equivalent to the expression 8x + 32y:

4(4 ⁢x + 8y) − 2⁢(4x)   = 16x + 32y - 8x

                               = 8x + 32y

8(x + 4y)  = 8x  + 32y

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

                                   = 8x + 30y

Therefore, only 4(4 ⁢x + 8y) − 2⁢(4x) and 8(x + 4y)  are equivalent to the expression below.

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Complete Question

Which of the following expressions are equivalent to the expression below?

8x + 32y

4(4 ⁢x + 8y) − 2⁢(4x)

8(x + 4y)

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