State the theorem that proves the triangles are congruent. Then write a congruence statement.

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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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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0.05×0.04=0.002 is the product represented by the model

Two or more expressions with an Equal sign is called as Equation.

Given:

5 column (hundred grid) = 5/100 = 0.05

4 row (hundred grid) = 4/100 = 0.04

We need to find Area equation

Computation:

Area equation = 0.05 x 0.04

0.05 x 0.04 = 0.002

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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 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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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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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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Answer:

Step-by-step explanation:

From the ratio gotten, the total cost of the pepper will be $129.90.

How to solve a ratio

Since the students planted 8 tomato plants and 16 pepper plants in a school garden. The ratio will be:

= 8/16 = 1:2

This year, the students planted 15 tomato plants, the number of pepper will be:

= 15 × 2 = 30

Since pepper plants cost $4.33 each, the total cost will be:

= 30 × $4.33

= $129.90

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 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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Answer:

68266==874624./4

Step-by-step explanation:

77353877473=287365-2874662kkh=2875

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

Buy the land !all angles will be greater than 30 °

Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes. The cosecant, cosine, cotangent, secant, sine, and tangent are among the trigonometric functions (also known as the circular functions) that make up trigonometry.

A branch of mathematics called trigonometry examines connections between triangles' sides and angles. Due to the fact that every straight-sided shape can be decomposed into a group of triangles, trigonometry can be found throughout all of geometry.

cos x = 500²+800²-900²/-2(800)(900)

x = [tex]cos^{-1}[/tex](+1200000/+1440000)

=336°

Buy the land !all angles will be greater than 30 °

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Answer:

D. 6, 8, 10

Step-by-step explanation:

Apply the Pythagorean theorem equation to all set of number, and see which one works.

A.

3² + 11² ≠ 20²

9 + 121 ≠ 400

131 ≠ 400

B.

5² + 9² ≠ 17²

25 + 81 ≠ 289

106 ≠ 289

C.

6² + 7² ≠ 8²

36 + 49 ≠ 64

85 ≠ 64

D.

6² + 8² = 10²

36 + 64 = 100

100 = 100

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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Answer:

g(3) = - 6

Step-by-step explanation:

g(3) = 9 - 5(3)

g(3) = 9 - 15

g(3) = - 6

Answer: It's in the picture

Step-by-step explanation:

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

The function operation h(8) - f(-7) of the functions f(x) = -4x+1, and h(x) = 19-3x is -34.

A function is simply a relationship that maps one input to one output.

Given the data in the question;

First, solve for the output value of h(8) by replacing x with 8 and simplify.

h(x) = 19 - 3x

h(8) = 19 - 3(8)

h(8) = 19 - 24

h(8) = -5

Next, solve for the output value of f(-7) by replacing x with -7 and simplify.

f(x) = -4x + 1

f( -7 ) = -4( -7 ) + 1

f( -7 ) = 28 + 1

f( -7 ) = 29

Now, replace the function designators with the actual output values.

h(8) - f(-7) =  -5 - ( 29 )

h(8) - f(-7) =  -5 - 29

h(8) - f(-7) =  -34

Therefore, the output of the function operation h(8) - f(-7) is -34.

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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.

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...

Answer:

The answer is Bottom Left

Answer: 3

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

please put brainiest, please.

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:

x < 5

Step-by-step explanation:

the dot is empty so we don’t consider 5

The coloured arrow continues to the left so we use this symbol : < (minor)

x<5

The inequality for the number line show is x<5.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

We can see that the inequality starts from 5 moves towards 2.

As, the starting of number line have open dot which shows we cannot include 5.

So, the inequality will have sign '<'.

Now, the inequality of the number line is

x < 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:

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