Which of the three triangles below can be proven congruent by SSS or SAS

The number of kilograms that the crane is lifting, based on the maximum it can lift and the proportion being lifted is 160 kilos

The number of kilos that the crane is lifting can be found by the formula :

= Maximum kilogram capacity x Proportion of maximum being lifted

Maximum kilogram capacity = 224 kg

Proportion of maximum being lifted = 5 / 7

The kilos being lifted by the crane is therefore :

= 224 x 5/7

= 1, 120 / 7

= 160 kilos

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The length of the second rectangle is 8 in

Since we have painting with an area of 48 in.² and a length of 6 inches, since it is a rectangle, its area is A = LW where

So, making Wsubject of the formula, we have

W = A/L

Since

Substituting these into the equation, we have

W = A/L

W = 48 in²/6 in

W = 8 in

Now, since the  second painting with an area of 64 in.² it has the same width as the first painting, since it is also a rectangle, its area is A = LW where

So, making L subject of the formula, we have

L = A/W

Since

Substituting these into the equation, we have

L = A/W

L = 64 in²/8 in

L = 8 in

So, the length of the second rectangle is 8 in

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Answer:

x = 11

Step-by-step explanation:

(7x - 4) and 73 are alternate exterior angles and are congruent , then

7x - 4 = 73 ( add 4 to both sides )

7x = 77 ( divide both sides by 7 )

x = 11

Answer:

[tex]x = 11[/tex]

Step-by-step explanation:

two angles are congruent for the parallelism of the two horizontal lines (external alternates). thus

[tex]7x - 4 = 73 \\ 7x = 77 \rightarrow x = 11[/tex]

Answer:

IT IS A FUNCTION

It is specifically a Surjective/ onto Mapping/function

Step-by-step explanation:

surjective or onto function is when y has an image in x

Answer:

The graph is a function

Step-by-step explanation:

-For every input (x) there is only one output value (y)

Since the function does not have two of the same x values for several inputs, its considered a function. If the x values do not repeat values, or if you graph the function and it does not cross on more than one point, it is also considered a function.

Ex.

X: 2, 4, 7 , 2, 5         This is not a function. More than one input for each output.

Y: 1, 2, 4, -3, 7

Ex.

X: 5, 6, -5, 8  this is a function. Exactly one input for every output.

Y: 1, 4, 5, 9

Answer:

20

Step-by-step explanation:

Absolute value is the distance from zero. Absolute value is always positive.

| -20 | is positive. It is 20 units from 0. So it is 20.

| -20 | = 20

(Be careful, absolute value doesn't just flip the sign to the opposite.

| 20 | = 20 also because the distance from 0 to 20 is also 20.)

Answer:5/6

Step-by-step explanation:

Answer:

  (e)  b h a k

Step-by-step explanation:

You want the order of operations involved in the transformation ...

  g(x) = a(bx -h) +k

The Order of Operations tells you that multiplication takes precedence over addition, and expressions inside parentheses are evaluated first.

We note there is an expression in parentheses here: (bx -h). In that expression is a multiplication operation (bx) and an addition operation (_-h).

The multiplication is done first, so evaluating this expression in parentheses, we ...

Once the parenthetical expression is evaluated, we proceed to the main event. Again, multiplication and addition are required. That means the next two steps are ...

In summary, the operations we perform during evaluation of the transformation successively apply the parameters ...

  b h a k

The multiplication of the given function is  (fg)(x) = 12[tex]x^3[/tex]

What is operations of the function ?

   Similar to how a function's constituent terms can be added, subtracted, multiplied, and divided, so can functions. These are to be noted as follows:

Addition f( x ) + g ( x ) means to combine two functions, and it may alternatively be expressed as ( f + g ) ( x )

It is possible to write ( f g ) ( x ) to represent the operation of subtracting the g(x) function from the f(x) function.

The two functions are multiplied together when you multiply f (x ) g (x), which can also be represented as (f g ) (x).

Division f (x)/g (x) means to split the two functions in half, and it can alternatively be expressed as (f/g)(x).

Here the given function ,

=> f(x) = 4[tex]x^2[/tex]

=> g(x)= 3x

Now (fg)(x) = f(x)*g(x)

=> (fg)(x)=  4[tex]x^2[/tex]*3x

=>  (fg)(x) = 12[tex]x^3[/tex]

Hence the  (fg)(x) = 12[tex]x^3[/tex].

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The probability that the sum is 5/9.The additive dice roll has 36 different results, as explained. A sum of 9 is rolled using the numbers 6 (and vice versa) and 3 or 5 and 4. (and vice versa).

The additive dice roll has 36 different results, as explained. A sum of 9 is rolled using the numbers 6 (and vice versa) and 3 or 5 and 4. (and vice versa). Given that this is feasible 4 times out of 36, the probability calculated by adding the two dice is 4/36, or 1/9.

I am assuming that you are rolling two dice.

Probability of even: 18 "evens" out of 36 total outcomes = 18/36

→(1,1), (1,3), (1,5), (2,2), (2,4), (2,6), (3,1), (3,3), (3,5),(4,2), (4,4), (4,6), (5,1), (5,3), (5,5), (6,2), (6,4), (6,6)

Probability of greater than 9: 6 ">9s" out of 36 total outcomes = 6/36

→(4,6), (5,5), (5,6), (6,4), (6,5), (6,6)

Probability of both evens and >9s: 4 "both" out of 36 total outcomes = 4/36

→(4,6), (5,5), (6,4), (6,6)

evens   OR    >9s    NOT both

18/36 + 6/8 - 4/36 = 20/36 = 5/9.

The probability that the sum is 5/9.  

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Answer:

24/8 = 3/1

40/20 = 20/1

Step-by-step explanation:



I hope this helps!

The division that can match the model is that 6 ÷ 1/5 = 30.

Division is one of the four fundamental mathematical operations, along with addition, subtraction, and multiplication. It is defined as the splitting of a large group into smaller groups so that each group has an equal number of items. In mathematics, it is an operation used for equal grouping and equal sharing.

It is a process of repeated subtraction. It is the inverse operation of multiplication. It is defined as the formation of equal groups. When we divide numbers, we break them down into smaller numbers so that the multiplication of those smaller numbers equals the larger number taken.

In this case, the division will be:

= 6 ÷ 1/5

= 6 × 5

= 30

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For isosceles triangle RST  the measure of angle T is 34 degree

In this question, we have been given a isosceles triangle RST with RS = RT.

So, by isosceles triangle theorem,

angle S = angle T

So, angle T = (3x - 2)°

We know that the sum of all angles of triangle is 180°

∠R + ∠S + ∠T = 180°

9x + 4 + 3x - 2 + 3x - 2 = 180°

15x + 4 - 4 = 180°

15x = 180°

x = 12

So, 3x - 2 = 3(12) - 2

                = 34°

Therefore, for triangle RST  the measure of angle T is 34 degree

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Step-by-step explanation:

10 hours per week: $10.50 x 10 = $105.00

20 hours per week: $105.00 x 2 = $210.00

40 hours per week: $210.00 x 2 = $420.00

When P₁ >3P₂ she must consume only tomatoes.

What are indifference curves ?

An indifference curve is a graph that illustrates numerous pairings of two goods or commodities that leave the customer equally well off or satisfied—hence indifferent—when it comes to owning any pairing of the two items that is represented along the curve.

Mary do trading 3 tomatoes for 1 nectarine.

So, MRS=3

P₁ >3P₂

P₁/P₂ > 3

P₁/P₂ < -3

This satisfies  MRS=3

P₁ >3P₂ shows budget constraint

consumer specializes in tomatoes consumption.

if  P₂ > 4 P₁ , consumer specializes in nectarine consumption. option is not there.

So, When P₁ >3P₂ she must consume only tomatoes.

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Answer: y+7=-4(x-2)

Answer: y+7=-4(x-2)

Answer:

-3

Step-by-step explanation:

we sure y2-y1/x2-x1 to find slope

6+6/-4+0

12/-4

-3 is the slope

Hopes this helps please mark brainliest

Answer:

y=4x+14

Step-by-step explanation:

Step-by-step explanation:

a + b + c + d = 125

a + 4 = b - 4 = 4c = d/4

a + 8 = b

a = b - 8

16c = d

b = 4c + 4

4a + 16 = d

b - 8 + 4c + 4 + c + 16c = 125

4c + 4 - 8 + 4c + 4 + c + 16c = 125

25c = 125

c = 5

d = 16c = 80

4a + 16 = d = 80

4a = 64

a = 16

b = a + 8 = 16 + 8 = 24

so, the numbers are

16, 24, 5, 80

Answer:

x = -32/31

Step-by-step explanation:

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

(32 - 1)/8 x = -4

31/8 x = -4

x = -4 * 8/31

x = -32/31

Answer:

[tex]\frac{7}{4}[/tex] or 1 [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

I am not sure if you meant 6x or 6+x at the end of the equation. I went with what was written.

5x -3(x-3) = -5 +4x +6x  Distribute the -3

5x -3x + 9 = -5 + 4x + 6x  Combine like terms

2x + 9 = -5 + 10x  Subtract 2x from both sides

9 = -5 + 8x  Add 5 to both sides

14 = 8x  Divide both sides by 5

[tex]\frac{14}{8}[/tex] = x

[tex]\frac{7}{4}[/tex] o r 1 [tex]\frac{3}{4}[/tex]

Answer:

  (2/3)√15 wide by 10/3 tall, approx 2.582 by 3.333

Step-by-step explanation:

You want the dimensions of the largest rectangle that fits under the graph of y = 5 -x² above the x-axis.

The graph of y=5-x² is symmetrical about the y-axis, so the width of it will be x -(-x) = 2x and the height will be 5-x².

The area will be the product of the width and height:

  A = WH

  A = (2x)(5 -x²) = 10x -2x³

The area will be a maximum where the derivative of the area function is zero.

  dA/dx = 10 -6x² = 0

  x² = 10/6

  x = (√15)/3

The corresponding rectangle dimensions are ...

  width = 2x = (2/3)√15

  height = 5 -x² = 5 -5/3 = 10/3

The rectangle with largest area is (2/3)√15 wide by 10/3 tall.

For the given polynomial the degree is 1, the leading coefficient is 1, and the constant term is 5.

A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.

The given polynomial is x+5.

(1) The degree is the highest power of the polynomial.

Degree = 1

(2) The leading coefficient is 1.

(3) The constant term is 5

Therefore, the given polynomial degree is 1, the leading coefficient is 1, and the constant term is 5.

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In the proportional relationship table, x would represent distance and y, weight.

The complete table is given in the explanation below.

If two variables that have quantities that vary proportionately are x and y, then the constant of proportionality that lies between both varies can be calculated as k = y/x. The equation for the proportional relationship would be expressed as y = kx.

x represents distance (cm)

y represents weight (newtons).

Using the pair of value that is given in the table, (20, 28), the constant of proportionality, k, would be:

k = y/x = 28/20

k = 1.4

The equation would be y = 1.4x.

Use the equation to complete the table by substituting the value of each missing variables:

Row 2, when x = 55:

y = 1.4(55)

y = 77

Row 3, when y = 140:

140 = 1.4x

140/1.4 = x

100 = x

x = 100

Row 4, when x = 1:

y = 1.4(1)

y = 1.4

The table would be:

           Distance (cm)     Weight (newtons)          

Row 1        20                     28

Row 2       55                     77

Row 3       100                    140

Row 4        1                        1.4              

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The 30 feet by 15 feet dimension of the old stage and the 1,000 square feet of the new stage generates equations that gives the depth of the new stage;

An equation states the relationships between two expressions as being of the same value.

The width and depth of the concert hall for the old stage are 30 feet and 15 feet respectively

Area of the new stage = 1000 ft.²

The dimensions of the new stage are;

Width = 30 + x

Depth = 15 + x

Which gives;

(30 + x) × (15 + x) = 1,000

(30 + x) × (15 + x) - 1,000 = 0

x² + 45·x - 550 = 0

(x + 55)·(x - 10) = 0

The distance added to the width and length of the old stage, x = 10

The width of the new stage = 30 feet + 10 feet  = 40 feet

The depth of the new stage = 15 feet + 10 feet = 25 feet

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Using the triangle rule, the length of the third side falls between 5 cm and 29 cm.

In the given question,

The measurements of two sides of a triangle are 12 cm and 17 cm.

We have to find which side length could be the measurement of the third side of the triangle.

We know that,

The sum of the length of any two sides is always greater than the third side.

The given sides of triangles are 12 cm and 17 cm.

Hence, the length of the third side should be shorter than the total of the other two sides,

12 + 17 = 29 cm.

Considering that the third side must be less than the difference between the first two sides,

17 – 12 = 5 cm

So, the length of the third side falls between 5 cm and 29 cm.

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The equation and solution representing the total interest, T, earned by Kalia when the principal amount is $100, the annual simple interest rate is 1%, and the number of years is 10, is D. T = 100 • 0.01 • 10; $10.

Simple interest is interest that does not compound.

Simple interest does not accumulate interest, unlike compound interest, which is added to the principal for subsequent interest.

Principal = $100

Simple interest rate = 1%

Period of savings = 10 years

The simple interest in dollars = T

T = 100 x 0.01 x 10

T = $10

Thus, Option D correctly represents the total interest earned by Kalia.

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