find the first term in geometric sequence if the 11th term is -160 and the ratio is -1/3​

Step-by-step explanation:

cross multiply

12-m(3m)= 1

12-3m²-1=0

multiply by -1

3m²+1-12=0

3m²= 11

m²= 11/3

m=√11/3.

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.

Answer:

Step-by-step explanation:

The terms are ordered from greatest to least degree.

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.

System of equations y = 5x + 11 and y = 5x has no solution,  y = 6x + 3 and y = 3x has one solution and x + 4y = 8 and y = -1/4x + 2 no solution.

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

The given system of equations are

a. y = 5x + 11 and y = 5x

Substitute the y value in first equation

5x=5x+11

So the system of equations y = 5x + 11 and y = 5x has no solution.

b. y = 6x + 3 and y = 3x

Substitute the y value in first equation

3x=6x+3

-3x=3

x=-1

y=-3

The system of equations has one solution

c. x + 4y = 8 and y = -1/4x + 2

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

x-x+2=8

The  system of equations has one solution has no solution

Hence, system of equations y = 5x + 11 and y = 5x has no solution,  y = 6x + 3 and y = 3x has one solution and x + 4y = 8 and y = -1/4x + 2 no solution.

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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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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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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: There is no picture

Step-by-step explanation:

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:

  y = 2x -3

Step-by-step explanation:

You want the equation of the line through the points (-1, -5) and (2, 1).

The slope of the line is given by ...

  m = (y2 -y1)/(x2 -x1)

  m = (1 -(-5))/(2 -(-1)) = 6/3 = 2

The y-intercept of the line can be found from ...

  b = y -mx

  y = -5 -2(-1) = -3

The slope-intercept form of the equation of a line is ...

  y = mx +b . . . . . . . line with slope m and y-intercept b

Using our found values, the equation is ...

  y = 2x -3 . . . . . . . . line with slope 2 and y-intercept -3

Answer:

- 4s - q + r

Step-by-step explanation:

that's right. You do not put the p since 3p and -3p cancel out to give zero. I'll solve the question for you:-

⇒3p-3p+2s-6s+2q-3q+8r-7r

add or subtract the like terms(terms having same variables), then out of the two like terms, put the sign of the greater number, for e.g. 2q-3q = -1q

⇒0 - 4s - 1q + 1r

⇒- 4s - q + r Answer

hope that helps...

Answer:

Step-by-step explanation:

Dolls:240 Teddy Bears:120

120:240

Please Describe the fraction If Possible.

To translate the point P(x,y) , a units left and b units down, use P'(x−a,y−b) .

y=|x-10|-3

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Answer:

It is in its simplest form

Step-by-step explanation:

Answer:

  False

Step-by-step explanation:

You want to know if it is true that 10, 8, 6, 4, ... is a geometric sequence.

A geometric sequence has a common ratio between adjacent terms. Here the ratios are ...

  8/10 = 0.8

  6/8 = 0.75

These numbers are different, so there is no common ratio. The sequence is not a geometric sequence. (False)

The measures of missing angles in trapezoids are listed below:

Case 5: m ∠ J = 75°, Case 7: m ∠ T = 118°

In this question we must determine the measures of missing angles in trapezoids. There are two hints to determine the values of the missing angles:

Now we proceed to determine the missing angles in every trapezoid:

Case 5

m ∠ K + m ∠ J = 180°

21 · x + 15 · x = 180°

36 · x = 180°

x = 5

m ∠ J = 15 · x

m ∠ J = 15 · 5

m ∠ J = 75°

Case 7

m ∠ U = m ∠ T

m ∠ T = m ∠ U

m ∠ T = 118°

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Answer:

no

Step-by-step explanation:

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:

54

Step-by-step explanation:

Multiply 9 (players per team) and 6 (teams in the league) to find the total players in the league.

9 times 6 = 54

The image of the point (3, 3) after a translation 4 units right and one unit down is (7, 2)

Transformation involves moving an object from its original position to a new position on the coordinate plane. This can be a translation, dilation.

Translation is the movement of a point either up, down, left or right in the coordinate plane. Translation is a rigid transformation that preserves the shape and size. Other types of rigid transformation are reflection, and rotation

The translation using the rule (x, y) ⇒ (x + 4, y -1) is a translation 4 units right and 1 unit down.

The image of the point (3, 3) using the rule (x, y) ⇒ (x + 4, y -1) is (7, 2)

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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.

To find the cost of 10 pounds of tomatoes, multiply 10 by the unit cost of tomatoes.

What is the unit cost?

The cost a business incurs to create, store, and sell one unit of a specific product is known as the unit cost. All fixed and variable production expenses are included in unit costs. Cost units are a way to measure the quantity of a good or service.

Unitary method: The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

The unitary method is used to find the unit cost of an object.

To find the cost of a unit object, multiply a by unit cost.

Given that, the unit cost of a unit pound of tomatoes.

The cost of 10 pounds of tomatoes is 10 ×  unit price of tomatoes.

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The solution is Option A. , Option C.

The equations which are also proportional is y = 3x and x = 2y

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

Let the values of x = { 0 , 3 , 6 }

Let the values of y = { 3 , 6 , 9 }

Now , the proportional equation is y = 3x

So , the proportionality constant is k = 3

b)

Let the values of x = { 0 , 6 , 12 }

Let the values of y = { 0 , 3 , 6 }

Now , the proportional equation is x = 2y

So , the proportionality constant is k = 2

Hence , the equations are y = 3x and x = 2y

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Answer: The solution is Option A. , Option C.

Step-by-step explanation:

The equations which are also proportional is y = 3x and x = 2y

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

Let the values of x = { 0 , 3 , 6 }

Let the values of y = { 3 , 6 , 9 }

Now , the proportional equation is y = 3x

So , the proportionality constant is k = 3

b)

Let the values of x = { 0 , 6 , 12 }

Let the values of y = { 0 , 3 , 6 }

Now , the proportional equation is x = 2y

So , the proportionality constant is k = 2

Hence , the equations are y = 3x and x = 2y

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The coordinates of the inflection points are (3, 0) and it concave upwards

From the question, we have the following parameters that can be used in our computation:

g(t) = t^2 - 27/t

Express properly

So, we have

g(t) = t² - 27/t

Calculate the second derivative

So, we have

g''(t) = 2 - 54/t³

Set the differentiated equation to 0

2 - 54/t³ = 0

So, we have

2t³ = 54

Divide by 2

t³ = 27

Take the cube roots

t = 3

Substitute t = 3 in g(t) = t² - 27/t

g(3) = 3² - 27/3

g(3) = 0

This means that the inflection point occurs at t = 3 and the coordinates of the inflection point are (3, 0)

Recall that

g''(t) = 2 - 54/t³

Next, we check if the second derivative exist at t = 0,

g''(0) = 2 - 54/0³

g(0) = undefined

The undefined value implies that the graph has a vertical inflection point at t = 0

And as such, the graph of the function is concave upward

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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 inequality g(30) ≥ 20 us that: D. Mona found no more than 20 seashells in the first 30 minutes.

In Mathematics, an inequality simply refers to a mathematical relation that can be used to compare two (2) or more numerical values, numbers, and variables in an algebraic equation, especially based on any of the following inequality symbols:

Assuming the variable g represents the total number of seashells and the variable x represents the total number of time (minutes), an inequality which would model the situation is given by;

g(x) ≥ x

when x = 30, we have;

g(30) ≥ 20

Therefore, Mona found no more than (less than or equal to) 20 seashells in the first 30 minutes.

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Complete Question:

Mona loves the ocean, so she was thrilled to visit the beach and collect some seashells. The function g(x) gives the number of seashells Mona found after x minutes of searching.

What does g(30) ≥ 20 tell you?

It took at least 20 minutes for Mona to find 30 seashells.

Mona found at least 20 seashells in the first 30 minutes.

It took at least 30 minutes for Mona to find 20 seashells.

Mona found no more than 20 seashells in the first 30 minutes.

The best answer is to simplifying each of the identity separately to get the same expression on both sides. Option C

Trigonometric identities are described mathematically as equalities consisting of trigonometric functions that proves true for all the value of occurring variables for which both sides of equality are defined.

These involve certain functions of one, two or more angles.

They also are different from triangle identities, which involves angles and side lengths of a triangle.

To verify a trigonometric identity, we take the following steps;

Hence, the best option is C

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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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