Simplify the expression.

4(5x + 2) + 7x + 6 =
12x + 8
27x + 14
27x + 8
27 + 14x

RS and QR are -8 and -5, respectively, in the rectangle P Q R S. Consequently, v is equal to 23.

here, QR is 3 v - 77, RS is 4 v - 97, and PS is v-23.As a result,                   PS = v - 23 ⇒ v = 23. As a result, v has a value of 23. So,                           RS = 4 × 23 - 97 = -5 is used to calculate its value.So,                               QR = 3 × 23 - 77 = -8 is used to determine its value. A All of the internal angles of a rectangle's four sides are equal to 90 degrees.

Every corner or vertex has a right angle where the two sides meet. It differs from a square in that the length of the opposing sides of the rectangle are equal. First, determine the width w using the area of rectangle formula, which is "w = A/l," to determine the length and width of a rectangle.

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Therefore , the solution of the given problem of linear equation comes out to be x = 4 and y =4.

A model of linear regression is one that applies the formula y=mx+b. B is the slope, and m is the y-intercept. Ignoring the fact that while both y and y are distinct components, the previous sentence is frequently referred as a "mathematical formula with two variables." Bivariate linear equations only have two variables. The application domains of linear equations have zero solutions in all cases. The equation for a single system of equations is Y=mx+b, where m stands for the gradient & b for the y-intercept. Y=mx+b, where m stands for slopes and b for the y-intercept, is how the equation is expressed.

Here,

Given :

=>  y = 2x -4

=> x + 2y = 12

and

=> x + 2(2x -4) = 12

=>  x + 4x - 8  =12

=>  5x = 20

=> x = 4

=> y = 2(4) - 4

=>  y = 8 -4

=> y =4

Therefore , the solution of the given problem of equation comes out to be x = 4 and y =4.

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The given statement "The LCM of 2 numbers is the product of the two numbers" is false because the LCM of 2 numbers does not have to be product of the numbers involved.

The smallest positive integer that is divisible by both a and b is known as the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b in mathematics and number theory.

The statement is "never" true. The LCM (Least Common Multiple) of two numbers is the smallest multiple that is common to both numbers, whereas the product of two numbers is simply the result of multiplying the two numbers together.

For example, the LCM of 2 and 3 is 6, whereas the product of 2 and 3 is 6. But the LCM of 2 and 4 is 4 , whereas the product of 2 and 4 is 8.

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Answer: No it doesnt

Step-by-step explanation:

12+9 = 21 which is greater than 15 meaning it cannot create a triangle

It will cost Aurelia $631.80 to have her new computer shipped.

To calculate the shipping cost, we need to multiply the purchase price of the computer by the percentage of shipping cost, which is 8%.

To do this, we can use the following formula:

Shipping cost = Purchase price x (Shipping percentage/100)

In this case, the purchase price is $585 and the shipping percentage is 8, so we can plug in these values into the formula:

Shipping cost = $585 x (8/100)

Now we can solve the shipping cost:

Shipping cost = $46.80

So the total cost for Aurelia to have her new computer shipped would be

$585 + $46.80 = $631.80.

Thus, it will cost $631.80 for Aurelia to have her new computer shipped.

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A polynomial function v (x) in standard form for the volume of the piece of marble is v(x) = 18a^3.

What is volume?

Volume is a term used in mathematics to describe the volume of three-dimensional space occupied by an object or a closed surface. The measurement of volume is done in cubic units, like m^3, cm^3, in^3, etc. Volume is also referred to as capacity on occasion.

Given:

A rectangular piece of marble is cut such that the width is triple the length and the height is double the width.

We have to write a polynomial function v (x) in standard form for the volume of the piece of marble.

Let 'a' is the length of the marble.

⇒  Width of marble = 3a      (width is triple the length)

⇒ Height of marble = 2(3a) = 6a           (height is double the width)

⇒ Volume of marble = length x width x height

                                  = a x 3a x 6a

   Volume of marble = 18a^3

Hence, a polynomial function v (x) in standard form for the volume of the piece of marble is v(x) = 18a^3.

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A scale factor of 1/3 is not an enlargement. A scale factor of less than 1 is considered a reduction and not an enlargement.

An enlargement is a transformation that increases the size of a figure, it is characterized by a scale factor greater than 1. A dilation with a scale factor greater than 1 will increase the size of a figure and thus is considered an enlargement.

A dilation with a scale factor of 1/3 will decrease the size of a figure, as each point on the figure will be moved one-third as far from the origin as it was before the dilation. This means that the dilated figure will be smaller than the original figure and will have a scale factor of 1/3.

It's important to note that if the scale factor is less than 1, the dilation will reduce the size of the figure and if the scale factor is greater than 1, the dilation will increase the size of the figure.

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(a) The sum of the interior angles of the nonagon is 1260°.

(b) The sum of the interior angles of the dodecagon is 1800°.

(c) The sum of the interior angles of the 23-gon is 3780°.

What is a convex polygon?

A convex polygon is a closed figure with all of its interior angles less than 180° and all of its vertices pointing outward. The term convex refers to a shape with a curve or a projecting surface. To put it another way, all of the lines across the outline are straight and point outwards.

The formula for the sum of the interior angle is (n -2)180°.

The number of sides of the nonagon is 9.

Putting n = 9 in (n -2)180°, to find the sum of interior angle of nonagon:

The sum of the interior angle is (9 -2)180° = 1260°.

The number of sides of dodecagon is 12.

Putting n = 12 in (n -2)180°, to find the sum of interior angle of dodecagon:

The sum of the interior angle is (12 -2)180° = 1800°

Putting n = 23 in (n -2)180°, to find the sum of interior angle of 23-gon:

The sum of the interior angle is (23 -2)180° = 3780°.

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The additive inverse of 14 /- 15 is -14 /+ 15.

The antithesis of a number is the additive inverse. It is found by changing the sign of the number. To find the additive inverse of 14 /- 15, start by changing the sign of the number from a negative sign to a positive sign. The result is 14 /+ 15. This is the additive inverse of 14 /- 15. The additive inverse of any number is the same number, but with the opposite sign. For example, the additive inverse of -14 is 14, and the additive inverse of 14 is -14. The additive inverse of any number always adds up to zero when added together, which is why it is called the "additive inverse".

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The point represents the number of small gloves is 16 and the number of large gloves is 2.

According to the mathematical definition of inequality, neither side is equal. When a relationship leads to a non-equal comparison between two expressions or numbers, it is known as an inequality in mathematics. The equal sign "=" in this statement can be replaced with any of the inequality symbols, such as greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), or not equal to (≠).

Given  Wanda sews small and large gloves,

time for small gloves = 45 minutes

time for large gloves = 120 minutes

total time = 16 hours = 960 minutes

let x be the number of small gloves and y be the number of large gloves,

inequality equation is 45x + 90y ≤ 960

and the cost of small gloves = $2

cost of large  gloves = $4

total amount = $40

equation 2x + 4y ≤ 40

let us assume the system of inequality in form of a linear equation,

45x + 90y = 960

2x + 4y = 40

by solving the equations

the equation is written as

x = 20 - y

45(20 -y) + 90y = 960

y = 2

and x = 16

so the minimum values for x and y are 16 and 2 to maximize the profit Wanda should not decrease the production of small gloves from 16 and large gloves to 2.

Hence the point of maximization is (16, 2).

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the complete question is in image.

Answer: 45 min

Step-by-step explanation:

The polynomial expression would be 30G + 15S.

What is the polynomial expression?

A polynomial expression is an algebraic expression that is made up of one or more terms, where each term is the product of a constant coefficient and one or more variables raised to a non-negative integer power.

Elizabeth earns a $30 bonus for each gold membership she sells, and a $15 bonus for each silver membership she sells. Let G be the number of gold memberships she sells and S be the number of silver memberships she sells.

We can express Elizabeth's total bonus as:

$30G + $15S

This is a polynomial expression because it is a sum of two or more terms, each term being the product of a constant coefficient and a non-negative power of a variable.

It is also a linear polynomial expression because the highest power of the variable is 1.

Hence, the polynomial expression would be 30G + 15S.

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The function rule for the line is,

f(x) = -2/3x -2.

The correct option is B.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

From the diagram,

the function has y-intercept at -2 and x-intercept at -3.

To find the slope:

First, we interpreted two points (-3, 0) and (0, -2).

Then the slope,

m =  (y₂- y₁) / (x₂ - x₁)

m = (-2, 0)/(0 + 3)

m = -2/3

Now, the equation is,

f(x) = -2x/3 - 2

Therefore, the equation is,

f(x) = -2x/3 - 2

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Answer:

Well yeah its -18

Step-by-step explanation:

The amount of eric investment would be $ 6290.

Investors benefit from compound interest, although the term "investors" can indicate many different things. For instance, banks profit from compound interest when they make loans and then reinvest the interest they earn to make more loans. When holders of deposits receive interest on their bank accounts, bonds, or other investments, they also profit from compound interest.

The concept of compound interest applies outside of contexts where the phrase is normally employed, such as bank accounts and loans, despite the fact that the term compound interest includes the word interest.

Let the rate of interest be 2.16 % per year

Time n = 5 years

Amount A = $6999.31

A = P(1 + R/100)ⁿ

substitute the values in the above equation, we get

⇒ 6999.31 = P (1  + 2.16/100)⁵

simplifying the equation, we get

⇒ P = 6290

Therefore, the amount of investment would be $ 6290.

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Answer:

B.) An isosceles triangle has at least two sides with equal measures.

Step-by-step explanation:

There are two equal sides and two equal angles in an isosceles triangle. There should be at least 2 equal sides for an Isosceles triangle. This means, even an equilateral triangle is an Isosceles triangle. In this case, at least two equal sides are 8 inches each. This is why the correct answer is 'Yes; an isosceles triangle has at least two sides that have equal measures.'

Missing: 2x³ ‎+15x²- ‎10Linear

Step-by-step explanation:

Answer: 1. linear equation

2. non-linear equation

3. non-linear equation

4. non-linear equation

5. linear equation

Step-by-step explanation:

not sure

The domain of the piecewise function as described in the task content is; ( −∞ , ∞ ).

It follows from the task content that the domain of the piecewise function which is as described in the task content be determined.

The domain of a function is the set of all possible input values of that function.

For the first piece, since the curve increases from left ( -∞ ) through a point and ends at a closed point (-2, -2). Hence, the set of inputs for the first piece in interval notation is; ( -∞, -2 ].

Also, for the second piece which is linear with an open point at (-2, -1) and ends at an endpoint (2, 1). Hence, the domain of the second piece is; [-2, 2].

Finally, the third piece is curved with an endpoint at (2, 1) and continues to increase tonthe right. Hence, the domain of the third piece is; [2, ∞)

Ultimately, by combining all sets of input values as determined; ( -∞, -2 ], [-2, 2] and [2, ∞); the domain of the whole piecewise function is; (−∞,∞).

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The equation (t6)(t-14) is identical to tn when n = 8. A mathematical expression is composed of numbers .

You can multiply, divided, add, or take something away in mathematics. An expression is put together as follows: Expression, numeric value, and math operator A mathematical expression is composed of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) Contrasting phrases and emotions is possible. An algebraic expression is any mathematical statement that has elements, quantities, and an arithmetic operation. As an illustration, the phrase 4m + 5 consists of the terms 4m and 5, as well as the given equation's variable m, which are all split by the algebraic sign +.

given

(t^6) (t^-14) = t^n

= 6 -14 = n

n = 8

The equation (t6)(t-14) is identical to tn when n = 8.

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Based on the side-side-side rule, it is possible to construct the triangle.

Let the side a be 2.5 cm, side b be 3.0 cm and side c be 6.5 cm. Now, the sum of any two sides of triangle should be greater than the thrid side of triangle.

Side a + side b > side c

2.5 + 3 > 6.5

Performing addition on Left Hand Side of the equation

5.5 not greater than 6.5

Side b + side c > side a

3 + 6.5 > 2.5

Performing addition on Left Hand Side of the equation

9.5 > 2.5

side c + side a > side b

6.5 + 2.5 > 3

Performing addition on Left Hand Side of the equation

9 > 3

Thus, the right angled triangle can be constructed from sides 2.5 cm 3.0 cm and 6.5 cm.

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The result of simplifying the quadratic polynomial (9x2- 8x-3) + (2x+8) is 9x2 - 6x + 5.

In mathematics, the intersection point is the place on the y-axis where the slope of the line passes. a place where the y-axis crosses on a line or curve. Y = mx+c, where m stands for the slope and c for the y-intercept, is used as the equation for the straight line to show this. The slope (m) of the line and its y-intercept (b) are highlighted in the equation's intercept form. When an equation has the intercept form (y=mx+b), the slope is m and the y-intercept is b. Some equations can also be rewritten so that they appear to be slope intercepts. If y=x is rewritten as y=1x+0, for instance, the slope and y-intercept are both changed to 1.

given

(9x2- 8x-3) + (2x+8)

9x2 - 8x - 3 + 2x + 8

9x2 - 6x + 5

Thus, the result of simplifying (9x2- 8x-3) + (2x+8) is 9x2 - 6x + 5.

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Answer:

The height of the cylinder is 10 cm.

Step-by-step explanation:

1. The volume of a cylinder is given by

-V = pi r^2 h  where r is the radius and h is the height

- 90 pi = pi r^2 h

2. We know the radius is 3

-90 pi = pi (3)^2 h

-90 pi = 9 pi h

3. Divide each side by 9 pi

- 90 pi /9 pi = 9 pi h / 9pi

- 10 =h

The height of the cylinder is 10 cm.

Answer:

A = 1/2b^2 + 3b

Step-by-step explanation:

If the height of the triangle is 6 units longer than the base length, we can represent the height with the variable h and the base length with the variable b.

h = b + 6

We can substitute h with b+6 in the formula for the area of the triangle:

A = 1/2bh

A = 1/2b(b+6)

So, the area of the triangle can be represented in terms of b only, as

A = 1/2b^2 + 3b

The likelihood of the spinner to land on a consonant rather than a vowel is C. Less likely.

The likelihood of the spinner landing on a consonant rather than a vowel can be found by the formula :

= Number of consonants / Number of outcomes on the spinner

= 4 / 9

= 0. 44

This likelihood is less than 50 % which is what would have made the likelihood equally likely. However, it is not much lower than 50 % so the likelihood would be less likely.

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If G is the incenter of triangle ABC the values of the unknown sides are

a) GD = 12

b) BG = 13.42

c) FC = 35

d) BF = 6

Considering that G is the incenter of triangle ABC, we have that

Using the right triangle CDG and applying Pythagoras theorem given by  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

GC² = GD² + DC²

37² = GD² + 35²

GD² = 37² - 35²

GD² = 144

take square root of both sides

GD = √144

GD = 12

Using the right triangle BEG to solve for BG

BG² = EB² + GE²

BG² = 6² + 12²

BG² = 180

take square root of both sides

BG = √180

BG = 13.42

Using the right triangle CFG to solve for FC

GC² = GF² + FC²

rearranging the equation

FC² = GC² - GF²

FC² = 37² - 12²

FC² = 1225

take square root of both sides

FC = √1225

FC = 35

Using the right triangle BFG to solve for BF

BG² = GF² + BF²

rearranging the equation

BF² = BG² - GF²

BF² = 13.42² - 12²

BF² = 36.0964

take square root of both sides

BF = √36.0964

BF = 6

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The function g(x) = (2/3)ˣ is the graph of the function f(x) = (3/2)ˣ reflected over y-axis.

A function is a process or a relation that associates each element 'a' of a non-empty set A , at least to a single element 'b' of another non-empty set B. A relation f from a set A (the domain of the function) to another set B (the co-domain of the function) is called a function in math.

f = {(a, b)| for all a ∈ A, b ∈ B}.

Given, the function

f(x) = (3/2)ˣ

g(x) = (2/3)ˣ

We have to compare the graphs of the functions f(x) and g(x).

Exponential function is of the form: y = abˣ

Where a is the initial value and b is the growth factor.

a) If b > 1, then the function is an exponential growth function.

b) If 0 < b < 1, then the function is an exponential decay function.

f(x) = y = (3/2)ˣ

The function is an exponential growth function.

The rule of reflection over y-axis:

(x, y) → (-x, y)

Applying the rule, we get,

(3/2)ˣ = (3/2)⁻ˣ

= (2/3)ˣ

= g(x)

Therefore, g(x) is graph of f(x) reflected over y-axis

Hence, graph of the function f(x) = (3/2)ˣ  reflected over y-axis is function g(x) = (2/3)ˣ .

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