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Using Pythagoras theorem the hypothenuse of the figure is 32.5 feet

Pythagoras theorem is defined as “In a right-angled triangle,  the square of the hypotenuse must be equal to the sum of squares of the other two sides". The sides of this triangle  are legs and hypotenuse. The hypotenuse is the longest side, as it is opposite to the angle 90°.

The formula of Pythagoras theorem is given as

c² = a² + b²

Taking the two sides given, we can find the hypothenuse of the right angle triangle figure

c² = 26² + 19.5²

c² = 676 + 380.25

c = √1056.25

c = 32.5

The distance from the top of the pole to the stake is 32.5 feet

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The perimeter of the rhombus is 34.40 units. The length of diagonal is 7.21 units. The perimeter of the rectangle is 44.98 units. The perimeter of the square is 42.44 units

1.  Given: a rhombus with diagonals 10 and 14

Half-length of the diagonals are 10/2 = 5 and 14/2 =7

Length of side = √(5²+7²) = √74 = 8.6 units

Perimeter, P = 4 × length of side

P = 4 × 8.60 = 34.40 units

2. Given: m<ADC = 60⁰

Missing...

3. Given: a rectangle with side length of 6 and 4. The length of one of its diagonal can be found using Pythagoras' theorem:

length of diagonal = √(4²+6²) = √52 = 7.21 units

4. Given: a rectangle with a diagonal length of 16 and side length of 10

other side length = √(16²-10²) = √156 = 12.49 units

Perimeter, P = 2(L+W)

P = 2(10+12.49) = 44.98 units

5. Given: a square with diagonal length of 15

Let represent the side length of the square

x² + x² = 15²

2x² = 15²

x² = 225/2

x² = 112.5

x = √112.5 = 10.61 units

Perimeter, P = 4 × side length

P = 4×10.61 = 42.44 units

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The function ƒ(x) = e^(2x + 1) when graphed could be described as; an increasing exponential graph.

The graphs of exponential functions are nonlinear—because their slopes are always changing, they look like curves, not straight lines.

Now, we are given the exponential function as;  ƒ(x) = e^(2x + 1)

Now, as the exponent increases, the curves get steeper and the rate of growth increases respectively. Thus, we can see that the exponent we are given increases as seen in the exponent attached to it.

Thus, we can conclude that The function ƒ(x) = e^(2x + 1) when graphed could be described as; an increasing exponential graph.

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Answer:

B. False

Step-by-step explanation:

5x² - 6x + 4 | 5 × 4 = 20

Can't factor it normally

           √b² - 4ac

 -b  ±   ---------------

                2a

           √(-6)² - 4(5)(4)

 -(-6)  ±   ---------------

                   2(5)

           √36 - 80

 6  ±   ---------------

                 10

    6 ± √-44

  ---------------

         10

    6 ± √-4 × 11

  ---------------

         10

    6 ± 2i√11

  ---------------

         10

The answer is actually

    3 ± i√11

  ---------------

         5

I hope this helps!

Answer:

  B.  False

Step-by-step explanation:

You want to know if (x -2) is a factor of 5x² -6x +4.

There are a couple of ways you can determine whether (x -2) is a factor. One is to look at the polynomial value at x=2:

  5x² -6x +4 = (5x -6)x +4 = (5(2) -6)(2) +4 = 4(2) +4 = 12

The value is not 0, so (x -2) is not a factor.

Another way to tell is to determine what the other factor would be.

The product of roots is the ratio c/a = 4/5 in the polynomial. If 2 is a root, then (4/5)/2 = 2/5 is the other root. That would mean the factorization of the polynomial is ...

  (5x -2)(x -2) = 5x² -12x +4 . . . . . . not the same polynomial

The polynomial 5x² -6x +4 does not have a factor (x -2).

The graph of the polynomial has no x-intercepts, so (x -2) cannot be a factor.

The expression 2 1/2 (x - 8) = 4 1/2 is solved to get the value of x to be

The expression, 2 1/2 (x - 8) = 4 1/2 is solved be converting to decimal

2 1/2 (x - 8) = 4 1/2

2.5 (x - 8) = 4.5

expanding to remove the parenthesis

2.5x - 20 = 4.5

collecting like terms, being mindful of change of negative to positive when crossing the equality sign

2.5x = 4.5 + 20

applying addition property

2.5x = 24.5

dividing through by coefficient of  x which is 2.5

x = 24.5 / 2.5

x = 9.8

x = 9 4/5 as a mixed number

Therefore the value of x = 9 4/5

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Answer:

$27

Step-by-step explanation:

We find 50% of $18 and add it to $18.

50% of $18 = 5/100 × $18 = 0.5 × $18 = $9

Today, it is worth $9 more.

$18 + $9 = $27

Answer:

y + 4 = 5(x + 8)

Step-by-step explanation:

Slope: 5 => m = 5

Point: (-8, -4) => x = -8 and y = -4

y - y1 = m(x - x1)

y - (-4) = 5(x - (-8))

y + 4 = 5(x +8)

Answer: 3

Step-by-step explanation:  (x-2)(2x+1)=2x^2-3x-2 = 3

please put brainiest, please.

After the dilation, the new volume of the cube is 125 times the original volume of the cube.

Remember that for a cube of sidelength S, the volume is written as:

V = S^3

If we apply a dilation of scale factor 5 to the cube, then the new sidelength of the cube is 5*S

Replacing that in the volume formula we will get the volume of the dilated cube, it is:

V' = (5*S)^3

V' = 5^3*S^3

V' = 125*S^3

Where S^3 is the original volume, so we can write:

V' = 125*V

So the new volume is 125 times the original volume.

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The reflection of the quadrilateral across the y-axis is shown in the graph below.

A point, line, or mathematical figure can be converted in one of four ways, and each has an effect on the object's structure and/or position.

The reflection does not change the shape and size of the geometry. But flipped the image.

The quadrilateral has four sides and four angles. And the sum of the internal angles of the quadrilateral is 360 degrees.

The quadrilateral is given in the figure.

The reflection of the quadrilateral across the y-axis is shown in the graph below.

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Answer in image

Step-by-step explanation:

Simplify both sides of the inequality.

Add 60 to both sides.

Divide both sides by 14.

r = 67/14 or 4.78571...

The amount of sugar that both companies would charge the same is 20 tons.

The cost when the two companies would charge the same is $9010.

The linear equation that represents the total charge of the companies : cost to rent truck + (ton of sugar x cost per ton)

The linear equation that represents the total charge of the first company : $5500 + ($175 x s)

$5500 + $175s

The linear equation that represents the total charge of the second company : $4995 + ($200.75 x s)

$4995 + $200.75s

When the two companies charge the same, the two linear functions above would be equal.

$4995 + $200.75s  = $5500 + $175s

In order to determine the value of s, take the following steps:

200.75s - 175.50s = $5500 - $4995

25.25s = 505

s = 505 / 27.25

s = 20

In order to determine when the cost of the two companies would be the same, substitute for s in either of the above linear functions.

$5500 + $175.50(20)

$5,500 + 3510 = $9010

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23.4 is  8.125 percentage of 288.

Percentage is defined as "out of 100." Similar to fractions and decimals, percentages are used in mathematics to represent subsets of a whole. When expressing a sum as a percentage, 100 equal components are regarded to make up the whole. A percentage can be shown by the symbol % or, less frequently, by the abbreviation 'pct'.

1. Since 288 is the output value of the task, we assume that it is 100%.

2. We make the assumption that the value we are looking for is x.

3. If 100% = 288 then we can express that as 100% = 288.

4. Since we already know that the output result of x% equals 23.4, we can write it down as x%=23.4.

5. We now have two straightforward equations:

1) 100%=288

2) x%=23.4 where both of their right sides and left sides have the same units, allowing us to write something like this: 100%/x%=288/23.4

6. All that is left for us to do is solve the straightforward equation, and we will have our answer.

7. Calculate 23.4 as a percentage of 288.

100%/x%=288/23.4

We multiply both sides of the equation by x 100=12.307692307692 to get *x=(288/23.4)*x.

*x - we get x 100/12.307692307692=x 8.125=x by dividing both sides of the equation by (12.307692307692) to get x=8.125.

23.4 is  8.125 percentage of 288.

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The complete table of function is,

   x        h(x)

  -4        -11

   0         -3

   2          1

   4          5

   5          7

What is function?

A function from a set X to a set Y in mathematics assigns each element of X exactly one element of Y. The set X is known as the function's domain, and the set Y is known as the function's codomain.

Let, the function h is defined by the rule,

h(x) = 2x - 3

We have to complete the function table.

x = -4  ⇒  h(-4) = 2(-4) - 3 = -8 - 3 = -11

x = 0  ⇒  h(0) = 2(0) - 3 = -3

x = 2  ⇒  h(2) = 2(2) - 3 = 4 - 3 = 1

x = 4  ⇒  h(4) = 2(4) - 3 = 8 - 3 = 5

x = 5  ⇒  h(5) = 2(5) - 3 = 10 - 3 = 7

Hence, the table becomes,

   x        h(x)

  -4        -11

   0         -3

   2          1

   4          5

   5          7

This is the complete table of function.

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The graph of your equation: [See in attachment]

What is graph?

A graph is a structure that resembles a set of items in discrete mathematics, more especially in graph theory, in which certain pairs of the objects are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

A graph is a structure that resembles a set of items in discrete mathematics, more especially in graph theory, in which certain pairs of the objects are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

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The equations, y=5x, b = 1/2 a, m=5n are direct variations.

A sort of proportionality known as "direct variation" occurs when one quantity directly changes in response to a change in another quantity. This suggests that if one quantity increases, the other quantity will also increase proportionately. Similar to the last example, if one quantity declines, the other amount also declines. The link between direct variation and the graph will be linear, resulting in a straight line.

We know that any equation, which can be expressed in the form of y=kx, can be called a direct variation.

y = 5x is in the form of y = kx, where k =5, hence this is a direct variation

y = 2x + 1 is not in the form of y = kx, hence this is not a direct variation

xy = 3 is not in the form of y = kx, hence this is not a direct variation

b = 1/2 a is in the form of y = kx, where k =1/2, hence this is a direct variation

y = 2/x is not in the form of y = kx, hence this is not a direct variation

m = 5n is in the form of y = kx, where k =5, hence this is a direct variation

Thus, y=5x, b = 1/2 a, m=5n are direct variation

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Answer:

[tex]\dfrac{17}{8}[/tex]

Step-by-step explanation:

Given statement:

[tex]\implies \dfrac{\frac{8}{5}}{\frac{8}{10}}+\left(\dfrac{8}{14} \times \dfrac{7}{12} \times \dfrac{3}{8}\right)[/tex]

To divide two fractions, flip the second fraction (make the numerator the denominator, and the denominator the numerator) then multiply it by the first fraction:

[tex]\implies \left(\dfrac{8}{5} \times \dfrac{10}{8}\right)+\left(\dfrac{8}{14} \times \dfrac{7}{12} \times \dfrac{3}{8}\right)[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}\times\dfrac{b}{d}=\dfrac{ab}{cd}:[/tex]

[tex]\implies \left(\dfrac{8 \times 10}{5\times 8}\right)+\left(\dfrac{8 \times 7 \times 3}{14 \times 12 \times 8}\right)[/tex]

Carry out the multiplications:

[tex]\implies \dfrac{80}{40}+\dfrac{168}{1344}[/tex]

Simplify the fractions by dividing the numerator and denominator by the GCF:

[tex]\implies \dfrac{80 \div 40}{40\div 40}+\dfrac{168 \div 168}{1344 \div 168}[/tex]

[tex]\implies \dfrac{2}{1}+\dfrac{1}{8}[/tex]

Make the denominators of both fractions the same:

[tex]\implies \dfrac{2 \times 8}{1\times 8}+\dfrac{1}{8}[/tex]

[tex]\implies \dfrac{16}{8}+\dfrac{1}{8}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]

[tex]\implies \dfrac{16+1}{8}[/tex]

[tex]\implies \dfrac{17}{8}[/tex]

Answer:

The answer is Bottom Left

Answer:

a worker can plant 2/5 acres in 7/8 days

or a worker can plant 2/5 acres in 7/8 hrs=21hrs

in one hrs he can plant 2/5×21 acres

in 24 hrs he can plant 2/105 ×24 acres

Therefore in one day he can plant 16/35 Acres

Answer:

[tex] {x + 2x}^{2} [/tex]

Answer:

biology = 255 ; sociology = 192

Step-by-step explanation:

b + s = 447

s = b - 63

b + b - 63 = 447

2b = 447 + 63

2b = 510

2/2 b = 510/2

b = 255

s = 255 - 63

s = 192

Answer: 192 sociology textbooks,  255 biology textbooks

Step-by-step explanation:

Let the number of biology be x, and the number of sociology be x

The number of the sociology textbook is x+63

So the equation is

x + x + 63 = 447

2x = 384

x= 192 sociology textbooks

To find the number of biology textbooks, just take 447- 192 = 255 biology textbooks

5(x2 + 4x + 4) = 7 + 20 quadratic equation by completing the square The correct statement  is 5(x2 + 4x + 4) = 7 + 20.

A quadratic function has the formula f(x) = ax2 + bx + c, with a, b, and c being integers and a not equal to zero. A parabola is a curve that represents the graph of a quadratic function. Parabolas can have openings that are upward or downward, different "widths" or "steepnesses," but they all share the same fundamental "U" shape.

Quadratic equations are the degree two, one-variable polynomial equations of the form f(x) = ax2 + bx + c = 0, where a, b, c, and an are all divisible by R and an is equal to zero. It is the quadratic equation's general form, with 'a' standing for the leading coefficient and 'c' standing for the absolute term of f. (x).

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Answer: 261 cm²

Step-by-step explanation: 87 x 3 = 261

Answer:

------------------------------

The area is the function of two dimensions.

The scale factor is 3. It means each dimension is 3 times greater.

Therefore the surface area is 3*3 = 9 times greater:

Answer: It's in the picture

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

-2x + 10  Means that the line crosses the y axis at 10.  The slope is -2 that means that as the y changes by -2, the x changes by 1.  

The second equations means that we have a horizontal line with no slope that goes through -28 1/2

The cube has a side that is 6 cm long.

Volume of cuboid:-

Height × width × depth

⇒9 cm × 6 cm × 4 cm

⇒ 216 cm³

when the cuboid is melted and a cube is made using just metal.

So, the cube's volume is 216 cm³.

side³ = volume of cube

⇒ Side³ = 216

⇒ Side = ∛216

⇒ Side = ∛6×6×6

⇒Side = 6 cm

As a result, the cube's side measures 6 cm.

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Answer:

68266==874624./4

Step-by-step explanation:

77353877473=287365-2874662kkh=2875