George wants to buy a new television that is on sale for 1/4 off the regular price of $599.96. The sales tax is 7%. What is the final price of the television including tax? ​

Answer:

The answer is:

8x-29y

Step-by-step explanation:

4(2x-8y)+3y

8x-32y+3y

8x-29y

Answer:

b = 5

Step-by-step explanation:

  10(b+2) + 3 = 73

10b + 20 + 3 = 73

              10b = 50

               ∴ b = 5

Step-by-step explanation:

I never thought about this before, but yes, they can.

linear functions :

explicit :

y = ax + b

recursive :

xn+1 = xn + a

because

a(x + 1) + b = ax + b + a

ax + a + b = ax + a + b

exponential functions :

explicit :

y = a^x

recursive :

xn+1 = xn × a

because

a^(x + 1) = a^x × a = a^(x + 1)

remember,

a^x = a×a×a×a×a×...×a×a×a

x times a multiplied by itself.

On solving the provided question we can say that value equation is y = mx => -7 = m * 4 => m = -7/4 and x² + y² = 13 => x² + (-7)² = 13 => x

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence.

Squaring both sides and simplifying we get:

3m² + 56m + 36 = 0

The coordinates of the points A and B are (-12,103) and (-3,-89) respectively.

y = mx => -7 = m * 4 => m = -7/4

x² + y² = 13 => x² + (-7)² = 13 => x

So the equation of the tangent line is y = m(x - 0) + 0, where m = -(x+4)/(y-7)

Now we can substitute the coordinates of the center of the circle into the equation of the tangent line to get y = -(x+4)/(y-7) * x

Squaring both sides and simplifying we get:

3m² + 56m + 36 = 0

b) To find the coordinates of the points A and B, we can use the equation of the tangent line and the equation of the circle.

We know that the equation of the tangent line is y = -(x+4)/(y-7) * x and the equation of the circle is (x+4)² + (y-7)² = 13.

We can substitute y = -(x+4)/(y-7) * x into the equation of the circle and solve for x.

This equation simplifies to 3x² + 56x + 36 = 0, which factors to (x+12)(x+3) = 0

y = -(-12+4)/(y-7) * -12 = 8/(y-7) * 12 = 96/(y-7)

y = 96 + 7 = 103 and y = -96 + 7 = -89

The coordinates of the points A and B are (-12,103) and (-3,-89) respectively.

We know that the equation of the tangent line is y = mx and the equation of the circle is x² + y² = 13.

We can substitute the point (4, -7) for x and y in the equation of the tangent line and the equation of the circle and solve for m and x,y respectively.

y = mx => -7 = m * 4 => m = -7/4

x² + y² = 13 => x² + (-7)² = 13 => x

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The Least Common Factor of 4 and 15 is 1. The factors of 4 are 1, 2 and 4, and the factors of 15 are 1, 3, 5 and 15. Hence, 1 is the Least Common Factor of 4 and 15.

A factor is a number that fully divides another number.

To put it another way, if adding two whole figures results in a product, also the figures we're adding are factors of the product because the product is separable by them.

Factor simply translates to" doer" in Latin. therefore, a" factor" in English is a" actor,"" element," or" element" in a situation or number.

Success can depend on charm, and having a terrible constitution can affect from inadequate exercise.

Variable factors are those whose employment varies in proportion to affair; further are employed when product rises and smaller when product falls.

Labor, energy, and raw accoutrements employed directly in product are exemplifications of typical variable rudiments.

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Using the Pythagoras theorem, the height of the tree from the reflection pond is obtained as 27.3 m.

We know that the height of the tree can be obtained from the formula for the Pythagoras's theorem and looking at the theorem, we are going to have that;

C^2 = A^2 + B^2

Where A is the  height, in meters, of the tree.

Then we have that;

30.24^ = A^2 + 12.96^2

A^2 = 30.24^2 - 12.96^2

A =27.3 m

This is the length of the tree that have been measured from the ground to the given height as we have bene shown in the question above.

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a) Tunnel A is a circle with center (-14, 0) and radius 12, meaning that both the width and the height are of 12.

b) Tunnel B is a parabola that has a width of 32 feet and a height of 16 feet.

c) The maximum height of Tunnel A is of 12 feet and of Tunnel B is of 16 feet, hence, since the height of the truck is of 13.5 feet, it can pass through Tunnel B without damage, as it's height is greater than 13.5 feet.

The equation of a circle of center  and radius r is given by:

(x-x₀) +(y-y₀) = r²

For Tunnel A, the equation is given by:

x² + y² + 28x + 52 = 0

Completing the squares:

(x + 14)² + y² = -52 + 14²

(x + 14)² + y² = 144.

Tunnel A is a circle with center (-14, 0) and radius 12, meaning that both the width and the height are of 12.

A quadratic equation is modeled by:

y = ax^2 + bx + c

For Tunnel B, the equation is given as follows:

x² - 36x + 16y + 68 = 0.

16y = -x² + 36x - 68.

Simplifying by 16:

y = -0.0625x² + 2.25x - 4.25.

Hence the coefficients are a = -0.0625, b = 2.25, c = -4.25, and the maximum height is:

y₀=(2.25)²-49-0.0625)(-1.25)/4(-0.0625) = 16

The width is the difference between the roots, which, using a calculator, are: 2 and 34, hence the width is of 32 feet.

This implies that the tunnel B is a parabola that has a width of 32 feet and a height of 16 feet.

For item c, we have that:

The maximum height of Tunnel A is of 12 feet and of Tunnel B is of 16 feet, hence, since the height of the truck is of 13.5 feet, it can pass through Tunnel B without damage, as it's height is greater than 13.5 feet.  

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Correct question:

An architect has designed two tunnels. Tunnel A is modeled by x2 + y2 + 28x + 52 = 0, and tunnel B is modeled by x2 – 36x + 16y + 68 = 0, where all measurements are in feet. The architect wants to verify whether a truck that is 8 feet wide and 13.5 feet high can pass through the tunnels.

Part A: Write the equation for Tunnel A in standard form and determine the conic section. Show your work. (4 points)

Part B: Write the equation for Tunnel B in standard form and determine the conic section. Show your work. (4 points)

Part C: Determine the maximum height of each tunnel. Is the truck able to pass through either tunnel without damage? If so, which tunnel(s) and why? Show your work. (7 points)

On solving the provided question we cans say that quadratic equation - x^2-5x-4 = 0 and x = 1 , 3

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

here, we have

quadratic equation -

x^2-5x-4 = 0

x(x-1) -3(x-3) =

(x-1)(x-3) = 0

x = 1 , 3

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The measure of the missing angle in a given pentagon is 115°. Therefore, option A is the correct answer.

The formula for calculating the sum of interior angles is (n-2)×180° where is the number of sides. All the interior angles in a regular polygon are equal. The formula for calculating the size of an interior angle is: interior angle of a polygon = sum of interior angles ÷ number of sides.

2) The sum of the interior angles of a nonagon

Here, n=9

(9-2)×180°

= 1,260°

3) Here, ∠3+∠4=180°

∠3=101°

101°+∠4=180°

∠4=79°

So, option A is the correct answer.

4) Given that, a regular polygon with 12 sides.

Now, sum of the interior angles = (12-2)×180°

= 1800°

Measure of each angle = 1800/12

= 150°

5) Four of the angles of a pentagon measure 85°, 110°, 135°, and 95°.

Let the measure of fifth angle be x°

85°+110°+135°+95°+x°=540°

425°+x°=540°

x°=115°

So, option A is the correct answer.

The measure of the missing angle in a given pentagon is 115°. Therefore, option A is the correct answer.

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The test that we have here is the one tailed test.

From the direction of change of the parameter, we would be able to tell if the test is a one tailed test or not. That is, if the parameter is increasing or decreasing.

This test is looking to determine if the bags are underfilled (decreased)  or if they are overfilled (increased).

The test's alternative hypothesis is written in a way that it predicts the direction of the difference between two groups. The test is one-tailed if the alternative hypothesis predicts a direction of change

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The value of x in the given equation is 17.5

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this article, let's learn more about math equations.

There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.

In the given equation:-

2x+20-55=0

x=35/2

x=17.5

Hence the value of x is 17.5

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Answer: Angle C for AAS, Side AC for SAS

Step-by-step explanation:

Your instructions were confusing since in the text it asks for SAS and in the image it asks for AAS so I just gave both.

Answer:

Step-by-step explanation:

The proposed rule would prohibit motor vehicle dealers from ... Used vehicles sold by new-vehicle dealerships cost $24,542 on average. Sorry I don't know the rest.

On solving the provided question, we can say that equation 6+6=4+1 has 1 solution that is x= -1.

In mathematics, an equation is a formula that uses the equals sign to connect two expressions and express their equivalence. We can solve equations to find the value of unknown variable given in the equation and the number of values that variable takes is called the solution of equation.

We have to find the no. of solution of 6+6=4+4.

To solve this, we bring all the variables to one side of equality and al the numbers on the other side. So we get,

6-4=4-6

2= -2

Dividing both sides by 2,

x= -1.

Hence, the equation 6+6=4+4 has only 1 solution. Correct option is D.

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Yes , 0 can have exponent of 2 , it is represented as 0² , and the value of 0 to exponent of 2 is 0 .

What is Exponent ?

The Exponent form form of numbers represents ,  how many times a number multiplied by itself .

For Example : if the number 3 is multiplied by 5 times by itself , then in the exponent form it can be written as : 3⁵ .

we have to check whether can 0 have an exponent of 2 ;

So, the representation of 0 to exponent of 2 is ⇒ 0² ,

that means 0 is multiplied by itself 2 times , and we know that if a number is multiplied by 0 , then the value of that number is 0 .

Therefore , 0 can have an exponent of 2 and it's value is 0 .

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Answer: 300 tires < x < 450 tires

Step-by-step explanation:

The first store sells between 100-200 tires. This means that the number it sells is greater than 100, but less than 200. This can be represented in this inequality:

100 < x < 200

The second store sells between 200-250 tires. This means that the number it sells is greater than 200, but less than 250. This can be represented in this inequality:

200 < x < 250

The total number of tires sold can be found by adding these two inequalities:

100 < x < 200

200 < x < 250

The following inequality represents the total amount of tires sold:

300 < x < 450

The distance up the building that the ladder would reach, given the ladder height and the base of the building, is 13.4 ft.

To find out how far up the building the ladder reaches, we can use the Pythagorean theorem. The theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (the hypotenuse).

Assuming the height that the ladder reaches is x, the formula would be:

x ² + 4 ² = 14 ²

x ² = 14 ²  - 4 ²

x ² = 196 - 16

x = √ 180

x = 13. 4 ft

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Andrea's distance from the base of the cliff is given as follows:

233 feet.

The three trigonometric ratios are defined as follows:

For this problem, we have a right triangle in which:

Hence the distance is obtained as follows:

tan(42º) = 209.75/d

d = 209.75/tan(42º)

d = 233 feet.

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The equation which has been given is a linear equation, therefore in order to solve the equation, simply the basic mathematical operation is to be performed. The acquired value of x is not the same as the value. So, when 12=13.x+5, the value of x=21 is not true.

Given information:

The equation given in the question is: 12 = 3x + 5

The value of x=21

Perform the basic mathematical operations and find the value of a variable.

  13x + 5 =12

⇒13x = 12 -5

⇒ 13x = 7

⇒ x = 7/13

⇒ x = 0.538

The acquired value of x is not the alike as the given value.

Hence, when 12=13.x+5 the value of x=21 is not true.

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The equation relating the two variables is r + 2b = 20.

The equation with r as the dependent variable is r = 20 - 2b.

The equation with b as the dependent variable is b = (20 - r)/2.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2xx + 3 = 9 is an equation.

We have,

Number of rings = r

Number of bracelets = b

Cost of one ring = $1

Cost of one bracelets = $2

Total cost = $20

Now,

r + 2b = 20

The equation with r as the dependent variable.

r = 20 - 2b

The equation with b as the dependent variable.

2b = 20 - r

b = (20 - r)/2

Thus,

The equation with r as the dependent variable is r = 20 - 2b.

The equation with b as the dependent variable is b = (20 - r)/2.

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Answer:

1) The standard form of a circle's equation is (x - h)² + (y - k)² = r². (h,k) is the center and r is the radius.

2) The vertex is the midpoint of the directrix and the focus. It involves the parabola changing directions, and at any point the directrix and the focus will be equidistant from the parabola. The focus is a single point inside the curve of the parabola, and the directrix is a line outside the parabola.

3) The standard form of an equation of an ellipse is:

(x − h)2a 2 +( y − k) 2 b 2 = 1 ( x − h ) 2 a 2 + ( y − k ) 2 b 2 = 1. (h,k) is the center, a is the distance from the center to the horizontal vertices and b is the distance from the center to the vertical vertices.

4) The foci are (−c,0) and (c,0). The ellipse is the set of all points (x,y) which are the sum of the distances from (x,y) to the foci is constant.  (a,0) is a vertex of the ellipse. Finally, the endpoints of the minor axis is a co-vertex of the ellipse.

5) A hyperbola has two standard equations. These equations of a hyperbola are based on its transverse axis and conjugate axis. The standard equation of the hyperbola is [(x² / a²) – (y² / b²)] = 1, where the X-axis is the transverse axis and the Y-axis is the conjugate axis.

6) The foci are located on the line that where the transverse axis is. The conjugate axis is perpendicular to the transverse axis and has the co-vertices as its endpoints. The center of a hyperbola is the midpoint of both the transverse and conjugate axes, where they intersect.

Let me know if I didn't answer all of your questions, I hope this helps! :)

Step-by-step explanation:

Correlation Coefficient (r) o A model is deemed to be "excellent fit" if r is near to 1 (or -1). o The model is "not a good match" if r is close to 0. o The model has a "perfect fit" if r = 1, with all data points falling on the line. o The two variables do not have a linear connection if r = 0.

The strength of the linear link between two separate variables, x and y, is shown by correlation coefficients.

A positive relationship is shown by a linear correlation coefficient greater than zero.

Indicating a negative association is a value less than zero. The two variables x and y do not have any relationship when their values are 0, to sum up.

The correlation coefficient (r2) is a statistic that expresses how closely two variables' movements are related to one another.

To determine the linear relationship between two variables, the Pearson product-moment correlation, the most popular correlation coefficient, is used.

However, this correlation value might not necessarily be a reliable indicator of reliance in a non-linear connection.

Hence, Correlation Coefficient (r) o A model is deemed to be "excellent fit" if r is near to 1 (or -1).

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So on solving the provided question, we can say that the triangle are similar, angles have a cosine that is equal to sin(L) are angle K and angle R

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.

the triangle are similar and angle K and angle R are congruent and is a right angled triangle

so,  angles have a cosine that is equal to sin(L) are angle K and angle R

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This square pyramid has a volume of 48 cm³.

The term "square pyramid" refers to a three-dimensional geometric form with a square base and four faces or sides that are triangular and meet at a single point (called the vertex). Its five faces give it the name "pentahedron."

The five faces of a square pyramid, four of which are triangles, are square in shape. An upright pyramid's base is also square-shaped.

Although the square pyramid and square prism both have a square base, the four lateral faces of the former are triangular and the latter are rectangular.

V=13s2h, where s is the length of the square base's sides, is a formula that may be used to calculate the volume of a pyramid whose base is square.

           v = 1/3 * b² *h

           v = 1/3 * 6² *4

           v = 1/3 *36 *4

           V = 48cm³

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The fraction which is recommended as value of iron in 1 cup of oatmeal as per the given relation is equal to 2/15.

As given in the question,

Daily recommended value of iron in the given cup of oatmeal

3 / 4 cup of oatmeal  gives  1/10 daily value of iron.

Fraction recommended as daily value of iron is given by :

⇒ 3 /4 cup of oatmeal = 1 /10 value of iron

⇒ 1 cup of oatmeal = ( 1 × 4 ) / ( 3 × 10 ) value of iron

⇒ 1 cup of oatmeal = ( 4 ) / ( 30 ) value of iron

⇒ 1 cup of oatmeal = ( 2 ) / ( 15 ) value of iron

Therefore, the fraction recommended as daily value of iron is equal to

( 2/15 ).

The above question is incomplete, the complete question is :

In 3/4 cup of oatmeal, there is 1/10 of the recommended daily value of iron. What fraction of the daily recommended value of iron is in 1 cup of oatmeal? ( multiplication and division equation)

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Answer:

69

Step-by-step explanation:

33 + (23)2 =

= 33 + 46

= 69

This is the correct answer to the problem you posted. If you meant something else, you should have written it differently.

Use / for fractions and ^ for exponents.

We can use some rules for exponents to simplify the expression, we will get:

7⁵/7¹  = 7⁴

Here we need to use two properties about exponents, these are:

The exponent of 1 bassically does nothing:

x¹ =x

The rule for divisions is:

xᵃ/xᵇ = x⁽ᵃ ⁻ ᵇ ⁾

Now we have the expression:

7⁵/7

We can rewrite that as:

7⁵/7¹

Now we can use the second property to get:

7⁵/7¹ = 7⁵ ⁻ ¹ = 7⁴

That is the simplified expression.

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Ariana is 20 years old, and Nora is 18 years old.

The word integers meaning a whole number but not fraction or decimal.

The positive whole number, zero and negative whole numbers are classified as integers.

Consecutive means following a specific sequence. Consecutive even integers mean the integers that follow a sequence and difference between each number is 2.

Ariana is older than Nora and their ages are consecutive even integers.

let Ariana is (x+2) years old and Nora is X years old.

The statement says the sum of Ariana's age and 2 times Nora's age is 56

the equation that expresses it can be written as

x+2+2x = 56

3x = 56 -2

3x = 54

x = 18

Nora is 18 years old.

Ariana is x+2 = 18+2 =20 years old.

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Answer:

Step-by-step explanation:

m/s =kph divided by  3.600000

m/s =13  divided by3.600000

m/s =3.611111

Answer: 216.67 meters/ min

Step-by-step explanation: Converting 13 km/h to meters per minute

First, we will convert 13 km to meters

So, we know 1 km = 1000 meters

Then 13 km/ h =  x

x = 1000 multiplied 13

x = 13,000 meters/ h

Now, we will convert to hours to minutes

We know 1 h = 60 min

Then 13,000 meters/ 60 min

That = 216.667 meters/ min

After approximating

Answer = 216.7 meters / min

Answer: 1 is 15 and 2 is 10.

Step-by-step explanation:

15/3=5

5+2 equals 7

10/2=5

5+6=11

m=15

x=10