find the 8th term of the geometric sequence 3,9,27

Answer:

1. HK = 24

2. x = 13

3. x = -26

4. ∠ABC = 120°

Step-by-step explanation:

(1) In all parallelograms, the diagonals bisect each other, or split each other into two congruent (same) halves.

We are given parallelogram HJKL. Its diagonals are HK and JL, because they both are segments that connect two opposite vertexes.

This means that HK and JL are bisected.

Thus, HM is half of HK.

Let's make an equation to represent this situation and solve for HK.

[tex]HM = \frac{1}{2}HK[/tex]

⇒ [tex]12 = \frac{1}{2}HK[/tex] . . . . . . substitute known values

⇒ [tex]12(2) = \frac{1}{2}HK(2)[/tex] . . . . . . multiply the LHS and RHS by 2 to isolate HK

⇒ ∴ [tex]24 = HK[/tex] . . . . . . compute

(2) This problem is similar to #1, so we can use the same concepts as #1.

However, we are given an expression instead of integers.

The only thing that's different about this problem is that we need to solve for x, not a diagonal or part of a diagonal.

VX and UW are the diagonals of parallelogram UVWX.

Thus, VX and UW are bisected.

Thus, the VY and YX are the same length, because they are split in half.

Let's make an equation to represent this situation and solve for x.

[tex]VY = YX[/tex]

⇒ [tex]80 = 6x + 2[/tex] . . . . . . substitute the known values

⇒ [tex]78 = 6x[/tex] . . . . . . . . . subtract 2 from the LHS and RHS

⇒ ∴[tex]13 = x[/tex] . . . . . . . . . divide both sides by 6 to isolate x

(3) This problem uses the exact same concepts and steps as #2.

Thus, RS and SP are the same length.

Let's make an equation to represent this situation and solve for x.

[tex]RS = SP[/tex]

⇒ [tex]65 = -2x - 7[/tex] . . . . . . . . substitute the known values

⇒ [tex]72 = -2x[/tex] . . . . . . . . . . . add 7 to the LHS and RHS

⇒ ∴[tex]-36 = x[/tex] . . . . . . . . . . . divide both sides by -2 to isolate x

(4) In a parallelogram, the opposite angles are congruent (the same).

In parallelogram ABCD, we are given ∠CDA and asked to solve for ∠ABC.

∠ABC and ∠CDA are opposite angles.

∠CDA = 120°

∠ABC = ∠CDA

∴ ∠ABC = 120°

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The parallelogram HJKL is handed to us. The segments HK and JL, which both link two vertexes that are in opposition to one another, serve as its diagonals, triangle HK = 24;  x = 13;  x = -26; ∠ABC = 120°

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

All parallelograms have diagonals that cut them in half or divide them into two congruent (same) halves.

HK = 24, x = 13, x = -26, and ABC = 120 degrees.

The parallelogram HJKL is handed to us. The segments HK and JL, which both link two vertexes that are in opposition to one another, serve as its diagonals.

As a result, HK and JL are divided. HM therefore makes up half of HK.

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Answer:

i think it will be 16% percent increase in the value of the painting

Answer:

60% increase

Step-by-step explanation:

The painting increases from 120 000 to 192 000 <==== a 72 000 increase

72 000 is what percent of 120 000 ?

   72 000 / 120 000    x  100% =  60% increase

Jack worked 40 hours a week with fractions of something because he had been employed at the time.

To represent a whole, any number of equal parts or fractions can be utilized. In standard English, fractions show how many units there are of a particular size. 8, 3/4. Fractions are part of a whole. In mathematics, numbers are stated as a ratio of the numerator to the denominator. These can all be expressed as simple fractions as integers. A fraction appears in a complex fraction's numerator or denominator. The numerators of true fractions are smaller than the denominators. A sum that is a fraction of a total is called a fraction. You can analyze something by dissecting it into smaller pieces. For instance, the number 12 is used to symbolize half of a whole number or object.

given

40-hour work week

jack worked 40  hours in a week

Jack worked 40 hours a week with fractions of something because he had been employed at the time.

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Therefore , the solution of the given problem of quadratic equation comes out to be  x =-2 and x = -7 .

A single variable equations regression model is the quadratic equation x = ax2 + bx + c=0. a 0. This polynomial has precisely one solution, as stated by the First Theorem in Algebra, due to its second order. Simple or sophisticated solutions are both possible. An equation with four variables is referred as a quadratic formula. This suggests that there must be at most one squared word in it. "ax2 + bx + c = 0" is a common formula for solving arithmetic problems, where the mathematical factors or constants a, b, and c stand for the unknown variable "X."

Here,

Given : x² + 9x + 14 = 0

=> x² + 7x + 2x + 14 = 0

=> x(x + 7) + 2(x+7)

=> (x+2)(x+7)

=> x =-2 and x = -7

Therefore , the solution of the given problem of quadratic equation comes out to be  x =-2 and x = -7 .

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A degree 6 polynomial results from multiplying a degree 2 polynomial by a degree 4 polynomial.

In algebra, a symbol (typically a letter) denotes an unknown numerical value in a formula or algebraic expression. A quantity that can be changed and is not fixed is known as a variable. Numeric and category variables are the two main types. Subcategories are then established for each category for categorical and numerical variables, respectively, using nominal or ordinal and discrete or continuous categories. A brief summary of various types is provided in this section. a metric that is open to a wide range of interpretations. a component of a scientific experiment that may be subject to change; the sign of a variable; something that is variable.

given

The first step is to multiply the first term inside the first parenthesis by each term inside the second parentheses.

The second term in the first parenthesis is now multiplied by every phrase in the second parentheses, and the results are then added to the first terms.

A degree 6 polynomial results from multiplying a degree 2 polynomial by a degree 4 polynomial.

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A constant speed to complete ride is 4 minutes

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Answer:

five thousand seven hundred and eighty-nine

Step-by-step explanation:

Answer:

$313.98

Step-by-step explanation:

[tex]Equation: A=P(1+\frac{r}{n} )^{nt} \\\\A=12000(1+\frac{0.0375}{12} )^{12(5.5)} \\\\A=12000(1+0.003125)^{66} \\\\A=12000(1.003125)^{66}\\\\A=12000(1.228665)\\\\A=14743.98\\[/tex]

So to see the difference of account balances we would subtract offer 1 balance from offer 2 balance.

14743.98-14430 = 313.98

So, therefore the difference in the account balances at the end of the loan terms is $313.98.

Note: the 5.5 comes from converting 66 months to years which is 5.5

Answer:

To find the mean (average) of a set of numbers, we add them together and divide by the number of items in the set.

The first step is to convert all the fractions into a common denominator. In this case, the least common multiple of 3, 3, and 4 is 12.

2 1/3 = 7/3

3 2/3 = 11/3

5 1/4 = 21/4

Now we can add these numbers together:

7/3 + 11/3 + 21/4 = (7 + 11 + 21) / 3 = 39/3 = 13

There are three numbers, so we divide by 3.

Mean = 13/3 = 4 1/3

So the mean of 2 1/3, 3 2/3 and 5 1/4 is 4 1/3.

Step-by-step explanation:

A number is -7 less than nine divided by 4, which results in a number of -19.

A number is an arithmetic value that is used to calculate and represent a quantity. Numerical symbols, such as "3," are written to represent numbers. A number system is a logical way of writing numbers that uses digits or symbols to represent them.

Positional notation was separately established by a number of civilizations, including the Aztecs, Chinese, and Babylonians. Indian mathematicians developed a decimal (or base ten) positional system in the seventh century that could express any number using just ten special symbols.
Suppose r is a number.
(r-9)/4 = - 7
r-9 = -28
r = -28+9
r = -19

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The number of points scored by Howie and Theo is 600 (Nearest Hundred)

Addition in mathematics is a process of combining two or more numbers. Addends are the numbers being added, and the result or the final answer we get after the process is called the sum.

from the table,

Howie scored 272 points

Theo scored 325 points

By adding their scores

=272 + 325

=597

Rounding off to the nearest Hundred, 597=600

Hence, Howie and Theo scored 600points

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The required solution of the simultaneous equation is given as x = 10 and y = -1.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

here,
Given equations,
x – y = 11  - - - - - (1)
2x + y = 19 - - - -- -(2)

Put x form equation 1 in equation 2
2 [11 + y] + y = 19
y = -1

Now,
x = 11 + y
x = 10

Thus, the required solution of the simultaneous equation is given as x = 10 and y = -1.

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Answer:The most efficient step to finding the solution to the given inequality is, to subtract 4 from both sides. Option D is correct.

Given that,

To determine which step is the most efficient way to find the solution of x + 4 > -8.

Step-by-step explanation:

The limit of lim t→0+ cos(t), cos(t), [tex]t^3[/tex] ln(t) as t approaches 0 from the right is not defined.

The limit of the function lim t→0+ cos(t), cos(t), [tex]t^3[/tex] ln(t) as t approaches 0 from the right is not defined.

The limit of cos(t) and [tex]t^3[/tex] ln(t) is zero as t approaches zero from the right. However, the limit of cos(t) as t approaches zero from the right is not defined. This is because the cosine function oscillates between -1 and 1 as t approaches zero, and therefore it does not approach a specific value. The limit of the entire function is undefined, as one of the components of the function is undefined.

It's important to note that if you have differentiability conditions, you can use L'Hopital's rule to find the limit, but in this case, L'Hopital's rule can't be applied since the function is not differentiable at t = 0.

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Therefore , the solution of the given problem of function comes out to be Option 2 is correct.

The study of numbers, their variations, mathematics and the regional tissue, structures, and both their actual and imagined locations, is known as mathematics. A function is a mathematical representation of the relationship between a set of inputs, each of which has an associated output. A function is a group of inputs that, when combined, result in a single, recognized output for each input. Each function is given a city, town, or scope, which is frequently referred to as a realm. Functions are typically denoted by the letter f. (x). The input contains an x.

Here,

=> f(x) = 3x³ + 2

=> g(x) = 3√ x-2 / 3

For ,

=> f(g(x)) =   3x³ + 2

=>  f(g(x)) = 3(3√ x-2 / 3)³ + 2

=>   f(g(x)) = (9/√x - 2/3)³ + 2

Thus ,

Option 2 is correct.

Therefore , the solution of the given problem of function comes out to be Option 2 is correct.

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Answer:

2

Step-by-step explanation:

x^2+6x+7

(-5)^2+6(-5)+7

(-5)(-5)-30+7

25-30+7

-5+7

2

===========================================

Work Shown:

A = final value = 38750

P = amount loaned = 25000

i = interest

i = A - P = 38750 - 25000 = 13750

Now apply the simple interest formula to solve for t.

i = P*r*t

13750 = 25000*0.055*t

13750 = 1375*t

t = 13750/1375

t = 10 years to pay off the loan

Side note: r = 0.055 is the decimal form of 5.5%

Answer:

Step-by-step explanation:

(8 + 24) ÷ (12 x 4) = 2/3

Value of C = 25 when d = 625

Square root is denoted by operator√. It is a factor which can be multiplied. When a square root of a particular number is multiplied by itself, we get the original number. As example, square root of 12 is √12 is multiplied by √12 and we get (√12) ² = 12.

What is the value of C when d = 625?

As per question, C varies directly as the square root of d.

C = 16 when d = 256

C = √d

√d = √256

√d = 16

when d = 625

the value of C will be,

C = √d

C =√625

C = 25

When, d = 625, the value of C =25

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The linear equation L, which is a translation of line M, can be written as:

y = (2/3)*x - 2

So the correct option is the last one.

First, we need to find the equation of line M.

Remember that the general linear equation is:

y = a*x + b

Where a is the slope and b is the y-intercept.

On the graph we can see that the y-intercept is y = -2, then we wll get:

y = a*x - 2

And we can also see that the line passes through (-3, -4)

Replacing these values we will get:

-4 = a*-3 - 2

-4 + 2 = -3a

-2/-3 = a

2/3 = a

So line M is:

y = (2/3)*x - 2

And line M is a translation of 3 units down and 2 units left of L, then L is a translation of 3 units up and 2 units to the right, then we can write line L as:

y = (2/3)*(x - 2) - 2 + 3

y = (2/3)*x + (2/3)*-2 - 2 + 3

y = (2/3)*x - 4/3 + 1

y = (2/3)*x - 1/3

So the correct option is the last one.

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Answer:

The cost of renting a car can be represented by the expression:

C = 30m + 0.25m

Where C is the total cost, 30 is the fixed cost per day, and 0.25 is the cost per mile.

Step-by-step explanation:

On the map distance between two cities is 19.2 inches.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

The actual distance between Danton and Crowley is 672 miles.

Here, the scale factor is 1 inch =35 miles

So, on map distance = 672/35

= 19.2 inches

Therefore, on the map distance between two cities is 19.2 inches.

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Answer:

5/54

Step-by-step explanation:

Substitute 8 for X, then solve

-5 / 8 (-8) + 10

-5 / -64 + 10

-5 / -54

5/54

The World Health Organization (WHO) sets standards for Oral Rehydration Salts (ORS) which are used to treat dehydration, particularly in children.

The old formula for ORS packets recommended by the WHO contained 75 mM (millimoles) of sodium chloride, which is equivalent to 3.5 grams of salt per liter of water. The new formula for ORS packets recommended by the WHO contains 65 mM (millimoles) of sodium chloride, which is equivalent to 3.0 grams of salt per liter of water.

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In naming a covalent compound, you can tell how many of each atom are present from the prefix in the name.

The process of identifying binary (two-element) covalent compounds is similar to that of naming simple ionic compounds. The first element in the formula is simply specified using its name. The second element is named by taking the element name's stem and appending the suffix -ide.

The subscript, which is where the x in Ax is located.

This indicates how many atoms of that particular element or group are present in the compound.

In H2O, for example, there are two hydrogen atoms. There are two NO3 ions in Be(NO3)2.

The number of neutral atom bonds equals the number of electrons in the complete valence shell (2 or 8 electrons) minus the number of valence electrons.

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Answer: 24.28

Step-by-step explanation:

24.275 can be rounded to 24.28

Answer:

1. Growth

2. Decay

3. Decay

Step-by-step explanation:

Growth means as x increases, y increases too. On the other hand, decay means as x increases, y decreases. There's the theory for exponential function regarding this growth and decay.

Growth

If the base is not a decimal or a fraction then it's growth.

Decay

If the base is a decimal or a fraction then it's decay.

From the problem, first function has base of 5. Hence, it's growth. On the other hand, second and third function both have decimal and fraction as the base. Hence, it's decay.

When considering growth or decay graph, we can ignore the coefficient since it doesn't determine the growth and decay. The only thing that determines if a function increases or decreases is the base under the exponent.

Answer:

[tex]56.7[/tex] degrees

Step-by-step explanation:

The distance of [tex]115[/tex] degrees from [tex]98.6[/tex] degrees is [tex]115 - 98.6 = 16.4[/tex] while the space of [tex]56.7[/tex] degrees from [tex]98.6[/tex] degrees is [tex]98.6-56.7 = 41.9[/tex], so the answer is [tex]56.7[/tex].

The value of the expression (x - 5y) at y = 5 and x = 47 will be 22.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ (x - 5y)

The value of the expression at y = 5 and x = 47 will be given as,

⇒ 47 - 5 (5)

⇒ 47 - 25

⇒ 22

The value of the expression (x - 5y) at y = 5 and x = 47 will be 22.

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The complete question is given below.

y = 5 and x = 47. Find the value of the expression (x - 5y).