Find the common ratio of the geometric sequence -7, -42, -252,. −7,−42,−252,

Check the picture below.

[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ S = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ n=4 \end{cases}\implies S=180(4-2)\implies S=360 \\\\[-0.35em] ~\dotfill\\\\ (40)+(2x)+( ~~ 360-(x+100) ~~ )+(x)~~ = ~~360 \\\\\\ (40)+(2x)+( ~~ 360-x-100 ~~ )+(x)~~ = ~~360\implies 2x+300=360 \\\\\\ 2x=60\implies x=\cfrac{60}{2}\implies \boxed{x=30}[/tex]

Answer:

Step-by-step explanation:

You want to know the parts of the composition of transformations that will map triangle A to A', then to A''. You also want to know what single transformation accomplishes the same thing.

The long side of triangle A points "south". In triangle A', it points "east". To transform a segment pointing south to one pointing east requires a rotation of +90°, or 90° CCW.

The long side of triangle A' lies along the line y=1. In triangle A'', it lies on the line y=-1. The line of reflection is halfway between these values, at ...

  y = (1 +(-1))/2 = 0/2 = 0

The line of reflection is y=0, the x-axis.

We know the transformation involves a reflection. The line of reflection can be found by finding the midpoints of the original and final vertices of the triangle.

The midpoint of the largest acute angle's vertex is ...

  ((2, -3) +(2, -3))/2 = (2, -3)

The midpoint of the right angle vertex is ...

  ((0, -3) +(2, -1))/2 = (1, -2)

The line through these two points is ...

  x +y = -1

The transformation of A to A'' is a reflection in the line x+y=-1.

Answer: Bonato

Step-by-step explanation:

The domain of function f is (-∞, 10) U (10, ∞) or {x|x ≠ 10}.

The range of function f is (-∞, -3) U (-3, ∞) or {y|y ≠ 3}.

The inverse of this function is f⁻¹ = (10x - 4)/(3 + x).

The domain of function f⁻¹ is (-∞, -3) U (-3, ∞) or {x|x ≠ 3}.

The range of function f⁻¹ is (-∞, 10) U (10, ∞) or {y|y ≠ 10}.

In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).

In order to determine the inverse of any function, you should swap both the input value (x-value) and output value (y-value) as follows;

f(x) = y = (3x + 4)/(10 - x)

x = (3y + 4)/(10 - y)

10x - yx = 3y + 4

3y + yx = 10x - 4

y(3 + x) = 10x - 4

f⁻¹ = (10x - 4)/(3 + x)

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This function has zeros at x = -2, x = -5, and x = 7, since when any of these values are plugged into the function, the corresponding factor becomes zero, making the entire expression zero.

An expression is a combination of numbers, variables, and operators that represents a mathematical quantity or relationship. It can consist of a single number or variable, or it can be a more complex combination of terms.Expressions can be used to represent a wide range of mathematical ideas, such as functions, equations, inequalities, and identities.

In the given question,

A possible function that has zeros at -2, -5, and 7 is:

f(x) = a(x+2)(x+5)(x-7)

where a is a constant that determines the scale of the function.

Expanding the expression, we get:

f(x) = a(x³ + 5x² - 14x - 70)

This function has zeros at x = -2, x = -5, and x = 7, since when any of these values are plugged into the function, the corresponding factor becomes zero, making the entire expression zero.

Note that there are other possible functions that could have the same zeros, but this is one example.

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The required expression represents the value in dollars of the coin n years after Hector found is [tex]$c(n) = 190 \times (1.1)^n$[/tex].

Let's call the percentage increase in value each year "r". We know that after one year, the coin was worth $209, which is 209/190 = 1.1 times what it was worth when Hector found it. So we can set up an equation:

[tex]$190 \times (1 + r)^1 = 209$[/tex]

Simplifying this equation,

[tex]$1 + r = \sqrt[1]{\frac{209}{190}}$[/tex]

1 + r = 1.1

r = 0.1

So the percentage increase in value each year is 10%. To find the value of the coin "n" years after Hector found it, we can use the formula:

[tex]$c(n) = 190 \times (1 + r)^n$[/tex]

Substituting the value we found for "r", we get:

[tex]$c(n) = 190 \times (1.1)^n$[/tex]

So the expression for the value of the coin "n" years after Hector found it is:

[tex]$c(n) = 190 \times (1.1)^n$[/tex]

Thus, required expression represents the value in dollars of the coin n years after Hector found is [tex]$c(n) = 190 \times (1.1)^n$[/tex].

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Answer:

  80°

Step-by-step explanation:

You want the larger of two acute angles in a right triangle if their relationship is cos(8x°) = sin(2x-10°).

The cosine of an acute angle is equal to the sine of its complement. The given relation between the angles means ...

  (8x) +(2x -10) = 90 . . . . . the angles are complementary

  10x = 100 . . . . . . . . . . . add 10

  x = 10 . . . . . . . . . . . . . divide by 10

The two angles are 8·10° = 80° and (2·10 -10)° = 10°.

The larger of the two acute angles is 80°.

[tex]\tan^2(\theta )+3\tan(\theta )=0\implies \tan(\theta )[\tan(\theta )+3]=0 \\\\[-0.35em] ~\dotfill\\\\ \tan(\theta )=0\implies \theta =\tan^{-1}(0)\implies \theta = \begin{cases} 90^o\\ 270^o \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \tan(\theta )+3\implies \tan(\theta )=-3\implies \theta =\tan^{-1}(-3)\implies \theta \approx \begin{cases} \stackrel{ II~Quadrant }{108.43^o}\\ \stackrel{ IV~Quadrant }{288.43^o} \end{cases}[/tex]

The expression [tex]\sqrt{\sqrt{x1\⁰} }\sqrt{\sqrt{x\³ }}[/tex] is equivalent to 10 for  [tex]x = 10^{(8/15)}[/tex].

In mathematics, an expοnent (alsο called pοwer οr index) is a shοrthand nοtatiοn used tο represent the repeated multiplicatiοn οf a number by itself.

We can simplify the given expressiοn using the prοperties οf expοnents and rοοts.

First, we can simplify the expression inside the first square root as:

√√x1⁰ = [tex]\rm \sqrt{(x^{10})^{(1/4)} }= (x^{10})^{(1/8)} = x^{(10/8)} = x^{(5/4)}[/tex]

Next, we can simplify the expression inside the second square root as:

[tex]\sqrt{(\sqrt{x\³})} = \sqrt{(x^3)^{(1/4) }}= (x^3)^{(1/8)} = x^{(3/8)[/tex]

Therefore, the entire expression becomes:

[tex]\sqrt{(\sqrt{x1\⁰)}} (\sqrt{(\sqrt{x\³})} = x^{(5/4)} * x^{(3/8) }= x^{(15/8)}[/tex]

Now, we need to find the value of x that makes this expression equal to 10.

[tex]x^{(15/8) }= 10[/tex]

Taking the eighth power of both sides:

[tex]x^{15} = 10^8[/tex]

Taking the 15th root of both sides:

[tex]x = (10^8)^{(1/15)}[/tex]

[tex]x = 10^{(8/15)}[/tex]

the equivalent expression is:

[tex]\sqrt{\sqrt{x1\⁰} }\sqrt{\sqrt{x\³ }}= x^{(5/4) }* x^{(3/8)} = x^{(15/8)} = (10^{(8/15)})^{(15/8)} = 10[/tex]

Therefore, the expression [tex]\sqrt{\sqrt{x1\⁰} }\sqrt{\sqrt{x\³ }}[/tex] is equivalent to 10 for [tex]x = 10^{(8/15)}[/tex].

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a.sin(3θ)cos(θ) - cos(3θ)sin(θ) = sin(4θ) - sin(2θ) = sin(4θ - 2θ) = sin(2θ)

b.2θ = 0, π, 2π, 3π,...

To solve this equation, first use addition or subtraction to simplify. In this case, it is best to add the two terms together and use the trigonometric identity sin(A)cos(B) + cos(A)sin(B) = sin(A+B). Applying this, we can rewrite the equation as:

sin(3θ)cos(θ) - cos(3θ)sin(θ) = sin(4θ) - sin(2θ) = sin(4θ - 2θ) = sin(2θ)

Now, to find all solutions of the simplified equation, use the fact that sin(2θ) = 0 when 2θ = 0, π, 2π, 3π,... Using this, the solutions of the equation are:

2θ = 0, π, 2π, 3π,...

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Simple Interest = (Principal x Rate x Time)

where:

Principal = R500 (the amount invested)

Rate = 12% per annum = 0.12 (expressed as a decimal)

Time = 4 years

So, the simple interest earned by John over 4 years is:

Simple Interest = (500 x 0.12 x 4) = R240

To find the total amount of money John will have at the end of 4 years, we need to add the simple interest to the principal:

Total amount = Principal + Simple Interest = 500 + 240 = R740

Therefore, John will have R740 at the end of 4 years.

Answer:

The total amount he has at the end is ₹740.

Step-by-step explanation:

Simple Interest = [tex]\frac{PRT}{100}[/tex]

                          =  [tex]\frac{500 * 12 * 4}{100}[/tex] = ₹240

Total amount he has at the end of 4 years = Principal + Interest
                                                                       = ₹500 + ₹240

                                                                       = ₹740

Answer: Its 12 the answer.

Step-by-step explanation:

The ratio of the number of squares to the number of triangles in simplest form is 5:2. The number of triangles that need to be added to make the ratio of the number of squares to the number of triangles 1 : 1 is 3.

What is the ratio?

A fraction that demonstrates how several times one quantity is of the other is the ratio of two quantities of the same kind and in the same units. Ratio is represented by the symbol ":". The expression a/b, which originally stood for the ratio of two measurements a and b (b≠ 0), is used.

Given that the number of squares are 5 and the number of triangles are 2.

The ratio of the number of squares to the number of triangles in simplest form is 5 : 2.

Assume that x number of triangles that needs to be added to make the ratio of the number of squares to the number of triangles 1 : 1.

The equation is:

5:(2+x) = 1:1

5/(2+x) = 1/1

Cross multiply both sides:

5 = 2 + x

x = 5 - 2

x = 3

3 triangles need to be added to make the ratio of the number of squares to the number of triangles 1 : 1

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The exponential function of the line that goes through points (0, 20) and (2, 180) is y = 20 × 3ˣ.

To find the exponential function of a line that goes through two points, we need to use the general form of the exponential function:

y = a × bˣ

where a is the initial value, b is the base, and x is the independent variable (usually time).

We can use the two points given to find the values of a and b.

Let's start with the point (0, 20):

y = a × bˣ

Plug in x = 0 and y = 20

20 = a ×  b⁰

20 = a ×  1

a = 20

Next, let's use the point (2, 180):

y = a × bˣ

Plug in x = 2 and y = 180

180 = 20 × b²

b² = 180/20

b² = 9

b = 3

Now, plug these values into y = a × bˣ

Therefore, the exponential function y = 20 × 3ˣ

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The cup will hold more ice cream than cone since volume of cup is 169.6 cubic inches which is greater than volume of 25.1 cubic inches.

The volume of a cone is given by the formula:

V= 1/3.π[tex]r^{2}[/tex]h

where r is the radius of the circular base and h is the height.

The volume of a cylinder is given by the formula:

V= π[tex]r^{2}[/tex]h

where r is the radius of the circular base and h is the height.

Assuming that the height of both the cone and the cup is the same, we can compare their volumes by comparing their radii.

For the cone, the radius r is equal to half the diameter of the circular base, which is equal to w/2 = 2 in.

The height of the cone is equal to y, which is 6 in.

V= 1/3.π[tex]r^{2}[/tex]h= 1/3.π[tex]2^{2}[/tex]6

For the cup, the radius r is equal to x/2 = 3

The height of the cup is equal to y, which is also 6 in.

Using these values, we can calculate the volume of the cup as:

[tex]V_cup[/tex]= π[tex]r^{2}[/tex]h=π[tex]3^{2}[/tex]6

Therefore, the cup will hold more ice cream than the cone.

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Cost of materials for each boy's costume = 5 * 4 * 4 + 5 * 3 * $.50 = 80 + 7.5 = $87.50 Cost of materials for each girl's costume = 6 * 5 * 4 + 6 * 2 * $2 = 120 + 24 = $144

Let A = [5; 6], B = [4; 5], C = [3; 2], D = [4; 2], E = [$.50; $2].

Cost of materials for each costume = A * B * D + A * C * E

Cost of materials for each costume = [5; 6] * [4; 5] * [4; 2] + [5; 6] * [3; 2] * [$.50; $2]

Cost of materials for each costume = [80; 120] + [15; 24]

Cost of materials for each costume = [95; 144]

Total cost of materials for each costume = $239

Cost of materials for each boy's costume = 5 * 4 * 4 + 5 * 3 * $.50 = 80 + 7.5 = $87.50

Cost of materials for each girl's costume = 6 * 5 * 4 + 6 * 2 * $2 = 120 + 24 = $144

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If a painter mixed 56 ounces of blue and yellow paint. The ratio is 3 to 11, 12 ounces of blue paint were utilized by the painter.

To solve the problem, we can use the ratio of blue to the total amount of paint to determine how many ounces of blue paint were used. The ratio of blue to the total paint is 3 to 11. This means that for every 3 parts of blue paint, there are 11 parts of total paint. We can use this information to set up a proportion:

3/14 = x/56

Where x represents the number of ounces of blue paint used. To solve for x, we can cross-multiply and simplify:

356 = 14x

168 = 14 × x

x = 12

Therefore, the painter used 12 ounces of blue paint.

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Answer: We can solve this problem using trigonometry and basic geometry. Let's first draw a diagram:

               A (top of house)

              /|

             / | h

            /  |

           /   |

          /θ1  |

         /     |

        /      |

       /       |

      /        |

     /         |

    /          |

   /           |

  /            |

 /             |

B (top of column)  

 | d          

 |            

 |

 |

C (bottom of column)

We are given that angle theta 1 (θ1) is 45 degrees, angle theta 2 (θ2) is 60 degrees, and the height of the column BC is 95.62 meters. We want to find the height of the house AB, which we'll call "h".

First, we can use trigonometry to find the length of segment CD. Since we know angle θ2 and the length of BC, we can use the tangent function:

tan(θ2) = opposite / adjacent

tan(60°) = d / 95.62

d = 95.62 * tan(60°)

d ≈ 165.30 meters

Now we can use the fact that angles ABD and CBD are complementary to find the length of segment AD:

tan(θ1) = opposite / adjacent

tan(45°) = h / (d + 165.30)

h = (d + 165.30) * tan(45°)

h ≈ 165.30 meters

Therefore, the height of the house is approximately 165.30 meters.

Step-by-step explanation:

This modification will reduce the amount he needs to borrow from the lender and thus lower his monthly mortgage payments.

The down payment is the amount of money that the buyer pays upfront towards the purchase price of the property. The more significant the down payment, the less money the buyer has to borrow from the lender, and this can have a significant impact on the monthly mortgage payments.

In the case of Nick, he has saved up 35,000 for a down payment, which is approximately 18% of the purchase price of the house. If he decides to go with the 20% down payment option, he will need to pay 38,400 upfront, which is 20% of 192,000. The remaining 153,600 will be the amount he borrows from the lender.

Now, let's assume that Nick has taken a 30-year fixed-rate mortgage at 6.25% interest. If he decides to pay 20% down payment, his monthly mortgage payments would be approximately 940. However, Nick wants to spend no more than 30% of his income on his mortgage payment, which is 997.50 per month (30% of 3,325). Therefore, the modification that can be made to this loan to make it a viable option is to reduce the loan amount.

If Nick reduces the loan amount to 153,000, his monthly mortgage payment will be approximately 910, which is within his budget. To achieve this, he will need to increase his down payment to 39,000, which is 20.3% of the purchase price. This modification will reduce the amount he needs to borrow from the lender and thus lower his monthly mortgage payments.

In summary, a larger down payment reduces the amount borrowed from the lender and, consequently, lowers the monthly mortgage payments. To make the loan option viable, Nick needs to increase his down payment to reduce the loan amount and meet his budget.

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a) The probability that it will not rain on the homecoming parade in Amina's first year is 0.84. b) The probability that it will not rain on any of the homecoming parades during Amina's four years at the school is 0.49. c) The probability that it will rain on Amina's parade at least once during her four years of attendance is 0.51.

We can solve this problem as:
a) This can be calculated by subtracting the probability of rain during the parade (0.16) from 1.

So, the probability is,

1 - 0.16 = 0.84.

b) This can be calculated by taking the probability of no rain (0.84) and multiplying it by itself four times.

So, the probability is,

0.84^4 = 0.49.

c) This can be calculated by subtracting the probability of no rain (0.49) from 1.

So, the probability is,

1 - 0.49 = 0.51.

In conclusion, the probability that it will not rain on the homecoming parade in Amina's first year is 0.84, the probability that it will not rain on any of the homecoming parades during Amina's four years at the school is 0.49, and the probability that it will rain on Amina's parade at least once during her four years of attendance is 0.51.

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each person would have 2 feet and two inches of tape

Answer:

y > -5

Step-by-step explanation:

Answer:

Step-by-step explanation:The width would be 2 the same for the height

Answer:

Step-by-step explanation:u better not be him cause im him

In triangle ABC, AB + BC > AC is the correct option.

Three straight sides and three angles make up the two-dimensional geometric shape known as a triangle. they can be of many types .

I think that the question is related to the triangle,

Choose the correct option for ∆ABC,

a. AB + BC > AC

b. AB + BC < AC

c. AB + AC < BC

d. AC + BC < AB

Given, ABC is a triangle.

We are aware that the length of a triangle's third side is always greater than the sum of its other two sides.

Let the two sides of ∆ABC is AB and BC and the third side is AC.

So, AB + BC > AC

Therefore, option a is true.

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What are the possible orderings of the sides of triangle ABC, given the three sides are AB, BC, and AC?

a: BC, AB, AC

b: AB ,BC, AC

c: AC ,AB, BC

d: AB ,AC, BC

Monica is not correct. Monica will earn $13.50 in 1 year while Paul will earn $13.20 in 1 year.

Simple interest is a linear function of the amount deposited, the interest rate and the number of years.

Simple interest = amount deposited x interest rate x time

Interest earned by Monica = $400 x 0.033 x 1 = $13.20

Interest earned by Paul = $500 x 0.027 x 1 = $13.50

Difference in the interest = $13.50 - $13.20 = $0.30

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An effective indicator for assessing retail store efficiency, spotting market trends, and making strategic business decisions is annual earnings per employee for profits.

The retail sales industry's annual profits per employee are shown in the data. The data's mean or median is most likely about $4,000,000, according to the assumption. You may compare the productivity of several retail stores by looking at the annual profits per employee. Businesses that generate more annual earnings per employee are typically more productive than those that do not.

The information can also be utilized to spot patterns in the retail sector, such as which businesses are operating better than others. For instance, if a business has been steadily increasing its annual profit per employee, it can be a sign that it is growing or streamlining its operations. In contrast, a business with declining annual profits per employee might be having trouble or seeing a drop in the demand for its goods.

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Answer:

Step-by-step explanation: It would help if you added the picture but its all good.

The point which is a solution to the equation 2x - 7y = 7 as required to be determined is; (0, -1).

As evident from the task content; the point which is a solution to the given equation is to be determined.

For a given equation; the y-intercept represents a solution to the equation.

On this note, if x = 0; therefore, we have that;

2 (0) - 7y = 7

y = 7 / -7

y = -1.

Ultimately, the point which is a solution to the equation is; (0, -1).

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