determine if each liners function is a direct variation. If it is state the constant of variation.

The measurement of three angles in the triangle are 43°, 81°, 56°.

A triangle's interior angles always add up to 180°, whereas its exterior angles are equal to the sum of the two interior angles that are not adjacent to it.

Given three angles,

∠A = (5x - 17)°

∠B = (7x - 3)°

∠C = 56°

We know that in a triangle ∠A + ∠B + ∠C = 180°

By substituting values,

(5x - 17) + (7x - 3) + 56 = 180

12x -20 + 56 = 180

12 x + 36 = 180

12x = 180 - 36

12x = 144

x = 144/12

x = 12

By substituting values of x we get,

∠A = (5x - 17)°

     = 5 x 12 - 17

     = 60 - 17

     = 43

∠A = 43°

∠B = (7x - 3)°

     = 7 x 12 - 3

     = 84 - 3

     = 81

∠B = 81°

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Answer: Angle-Side-Angle Theorem

Step-by-step explanation:

The two triangles are shown to have congruent angles. By the Reflexive Property of Congruence, Side PM is shared and congruent between the two.

Because the angles are on either side (left and right) of the shared side, the triangles are congruent by the Angle-Side-Angle Theorem.

Answer:

Step-by-step explanation:

You want the lengths of the segments of the hypotenuse of a right triangle when an altitude of 6 m divides the hypotenuse into parts with the ratio 1:9.

The altitude to the hypotenuse of a right triangle is the geometric mean of the parts it divides the hypotenuse into. If the shorter part is x, then the longer part is 9x, and their geometric mean is ...

  6 = √(x(9x)) = 3√x² = 3x

  x = 2 . . . . . . . divide by 3

The length of the shorter segment is 2 m; the longer one, 18 m.

The amount of white paint used by Tamara to paint the bedroom walls is 2.125.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Total amount of paint = 8.5

Three fourths of this amount is blue paint.

Amount of blue paint = (3/4) × 8.5 = 6.375

Rest is white paint.

Amount of white paint = Total paint - Amount of blue paint

                                     = 8.5 - 6.375

                                     = 2.125

Hence the amount of white paint used to paint bedroom walls is 2.125.

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keeping in mind that a function does not have any X-Repeats, that is, the 1st coordinate in every pair never repeats, Check the picture below.

Answer:

It is best to solve a system of equations using substitution when one of the equations isolates one of the variables, or when the coefficient of one of the variables is 1 or -1.

Step-by-step explanation:

This makes it easier to substitute one variable for the other, allowing you to solve for the remaining variable. It is also a good idea to check the solution back in the original equations just to make sure it is a valid solution

Answer:

Answer Below

Step-by-step explanation:

It is best to use substitution if one of the variables is isolated or has a coefficient of 1 or -1.

Answer: There is no picture

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

12a - 3b²

12(9) - 3(4)²

108 - 3(16)

108 - 48

60

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{12a - 3b^2}\\\mathsf{= 12(9) - 3(4)^2}\\\mathsf{= 12(9) - 3(4\times4)}\\\mathsf{= 12(9) - 3(16)}\\\mathsf{108 - 3(16)}\\\mathsf{= 108 - 48}\\\mathsf{= 60}\\\\\huge\text{Therefore, your answer should be: }\\\huge\boxed{\mathsf{60}}\huge\chdckmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

b = -8

Step-by-step explanation:

To determine the value of b, we can use the factoring method. We can factor the expression

(5b + 16)(b + 32) as (b + 8)(5b + 16).

Setting each factor to 0, we get b + 8 = 0 and 5b + 16 = 0.

Solving for b in the first equation, we get b = -8.

Substituting this value into the second equation, we get 5(-8) + 16 = 0, which simplifies to -40 + 16 = 0.

This equation is true only when the value of b is -8. Therefore, the value of b is -8.

Answer:

$30 per sweater is how much profit the store will make

Step-by-step explanation:

The cost of 1 sweater (for the store) is $6.

The store sells the sweater for $36 (504/14).

The store is making $30 per sweater.

Here we need to find the domain of the given function.

We will see that the domain is the set of all real numbers.

For a given function f(x), we define the domain as the set of possible inputs that we can use on the function.

Usually, we start by defining the domain as the set of all real numbers and then remove from the domain the numbers that cause "a problem" with our function.

Where these "problems" are undefined operations, like the logarithm of a negative number or a zero in a denominator.

Particularly, in our function: f(x) = (1/2)^x

We do not have a denominator that can become zero nor a function that has problems with some given values of x (the exponent of a number can be any real number).

Concluding, because there is no problem with any real value,  we can see that the domain is the set of all real numbers

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Answer:

Step-by-step explanation:

Can u give more detail as to what the question is asking pease

Answer:

[tex]4x^2+4vx + v^2[/tex]

Step-by-step explanation:

[tex](2x+v)^2 \\(2x)^2+2(2x)(v)+(v)^2\\4x^2+4vx + v^2[/tex]

Answer:

10x10x10 or 10*3......

Answer: We can use the information given to find the number of stars in the universe by multiplying the number of galaxies by the number of stars per galaxy:

number of stars = (10 ^ 11 galaxies) x (10 ^ 11 stars per galaxy)

This is a simple arithmetic problem and we can find the solution by multiplying the numbers 10^11 and 10^11

10^11 * 10^11 = (10101010101010101010)(101010101010101010*10) = 10^(11+11) = 10^22

So, there are estimated to be 10 ^ 22 stars in the known universe.

Step-by-step explanation:

On solving the provided question, we can say that - here in equation 10x + =4 = 2

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

here,

the equation we have is  = 10x + =4 = 2

10x = -2

x = -1/5

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Answer: Lydia used 1/3 pound of peppers and 1/10 pound of cheese to make 3 pizzas, which means that she used 1/3 / 3 = 1/9 pound of peppers and 1/10 / 3 = 1/30 pound of cheese per pizza.

If Lydia uses the same recipe to make 1 pizza, she will need 1/9 pound of peppers and 1/30 pound of cheese. Therefore, the amount of cheese needed is 1/30 pound.

Step-by-step explanation:

According to the table, the Range of pools sold during this period is 8.

The range in statistics for a given data set is the difference between the highest and lowest values. For example, if the given data set is {2,5,8,10,3}, then the range will be 10 – 2 = 8.

Thus, the range could also be defined as the difference between the highest observation and lowest observation. The obtained result is called the range of observation. The range in statistics represents the spread of observations.

Range = Highest Value – Lowest Value

Range = 18 – 10

Range = 8

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Answer:

6 hours

Step-by-step explanation:

The swim team trains 4 days every week, with 1/2 hour in the gym and 1 1/4 hours in the pool on Monday, Tuesday and Thursday. On Saturday, there is no gym, but the swim time is doubled, so the total swim time is 2 1/2 hours.

Therefore, the total time spent training each week is 6 hours.

1/2 hour in the gym plus 5 1/2 hours in the pool.

Answer: The swim team trains for 7 hours and 45 minutes a week.

Step-by-step explanation:

Since the swim team trains in the gym and the pool (collectively) on Monday, Tuesday and Thursday, subsequently we will be multiplying GYM TIME + POOL TIME, 3 TIMES to get the time taken for training on the three days i.e. 3 ( ½ + 1 ¼ ) and add twice the time taken in pool for Saturday i.e. 2(1 ¼ )

                                                                   = 3( ½ + 5/4) + 2(5/4)

                                                                   =31/4

                                = 7 ¾

Multiply ¾ with 60 as 1 hour = 60 minutes to get the answer in time format.

Firstly, convert mixed fractions into improper ones and find the final answer. Then, convert the final answer into Time format i.e. hours and minutes.

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Answer:

The first 5 prime numbers are 2, 3, 5, 7 and 11. Their LCM is 2310

The dimensions of the box if it is to use the minimum possible amount of metal are,

⇒ 2.714 m, 2.714 m, 1.358 m

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A container with an open top is to have 10 m³ capacity.

Now,

Let the dimensions are x, y and z.

Since, Volume of box = 10 m³

Hence, We get;

⇒ xyz = 10

⇒ z = 10/xy

Since, A container is open in top.

Hence, The surface area = 2xz + 2yz + xy

Substitute z = 10/xy;

⇒ S.A = 2x (10/xy) + 2y (10/xy) + xy

          = 20/y + 20/x + xy

For minimum metal;

⇒ d (S.A)/ dx = 0

⇒ - 20/x² + y = 0

⇒ y = 20/x²  ..(i)

And, d (S.A) / dy = 0

⇒ - 20/y² + x = 0

⇒ x = 20/y²   ..(ii)

Divide equation (i) and ((ii);

⇒ x = y

Hence, We get;

⇒ xyz = 10

⇒ x³ = 10

⇒ x = 2.714

And, y = 2.714

So, The value of z is,

⇒ z = 10/xy

⇒ z = 10 / 2.714×2.714

⇒ z = 1.358 m

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Answer:

It is in its simplest form

Step-by-step explanation:

On solving the provided question, we can say that - the value of the given polynomials domain will be ( - infinity, 0)

The range of values a function may accept is referred to as its domain. These numbers represent the x-values of a function like f. (x). The range of values that a function may operate on is referred to as its domain. The value that the function returns following the insertion of the x value is this set. A function containing the independent variable x and the dependent variable y is said to be y = f(x). A value of x is said to be in the domain of a function f if it can be used to successfully create a single value y utilizing the value of x for that purpose.

domain will be ( - infinity, 0)

range = (-infinity, +infinity)

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Answer:

no

Step-by-step explanation:

The value of x is 20 and the value of y is 8 from the given quadrilaterals.

The definition of a congruent polygon is a polygon that is the same shape, has the same length of sides, and has the same interior angles as the polygon it is being compared to. Congruent shapes must all be the same type of shape in order to fulfill the requirement.

Given that, ABCD≅EFGH

We know that, corresponding parts of congruent polygon are equal.

Now, (4y-4)°=28°

4y=32

y=8

(10x-65)°=135°

10x=200

x=20

Therefore, the value of x is 20 and the value of y is 8 from the given quadrilaterals.

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Answer:

Step-by-step explanation:

Dolls:240 Teddy Bears:120

120:240

Please Describe the fraction If Possible.

Answer:

50/30

5/0

1.6%

Step-by-step explanation:

Answer:

Ann traveled 165 miles on 5 gallons of gas

Step-by-step explanation:

First we must know how many miles are in a gallon (in this situation). Last weekend Ann drove 132 miles with 4 gallons of gas, we can divide to find out how many miles she drove on 1 gallon. 132/4 = 33. This means Ann drove 33 miles on 1 gallon of gas. To get your answer, simply multiply 5 and 33. 5 times 33 = 165.

The value of side GH as shown in the parallelogram is 2 units

Parallelogram is a polygon that has four sides (quadrilateral) and opposite sides are always equal and parallel to each other

Two shapes are said to be similar if they have the same shape and the ratio of their corresponding sides are proportional. Also, their corresponding angles are equal to each other.

Parallelogram abcd is similar to parallelogram efgh, hence:

FG/BC = GH / CD

substituting:

7/21 = GH / 6

GH = 6 * 7/21 = 2

GH is 2 in

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