if my bill is 25.00 and I get a 10% discount what is my new bill

The value of the indicated trigonometric ratio cosβ is equal to 11/12.

From the image attached above, we can logically deduce that the triangle is a right-angled triangle with the following side lengths:

In order to determine the magnitude of cosβ, we would apply the law of cosine because the given side lengths represent the adjacent side and hypotenuse of a right-angled triangle.

cos(θ) = Adj/Hyp

Where:

Therefore, we have the following cosine trigonometric function:

cosβ = 22/24

cosβ = 11/12

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Answer:

When using the number line, you represent subtraction of a negative number with an arrow going to the right. The direction of the arrow indicates the movement of the number line towards the positive side, which is the opposite of the direction of a negative number. Subtraction of a negative number is equivalent to addition of a positive number, so the arrow going to the right represents the addition of the absolute value of the negative number. For example, if you are subtracting -5 from 10, you can represent this on a number line by starting at 10 and drawing an arrow to the right that goes 5 units, ending at 15.

Answer:

When using the number line to represent subtraction of a negative number, you would represent it with an arrow going to the right (or in the positive direction).

For example, let's say you want to represent the following subtraction on a number line:

5 - (-3)

You can start at 5 on the number line and then move to the left by 3 units, since you are subtracting a negative number. However, instead of leaving the arrow pointing to the left to represent the subtraction, you can turn it around and point it to the right, which is the positive direction. This means that you end up at a point that is 8 units to the right of 0 on the number line, which represents the answer of 8.

So, the arrow would go to the right to show the subtraction of a negative number on the number line.

If the bars of a histogram roughly follow a symmetrical bell or hill shape, then the distribution is approximately normally distributed.

Histogram a diagram consisting of rectangles whose area is proportional to the frequency of a variable and whose width is equal to the class interval.

Given is relative frequency histogram.

Therefore, if the bars of a histogram roughly follow a symmetrical bell or hill shape, then the distribution is approximately normally distributed.

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The given sequence is

[tex]z_n = log(1 + (θ/(α + {i*cos(π/2) - i*sin(π/2)}))^n)[/tex]

First, we need to simplify the expression inside the log. The term [tex]{i*cos(π/2) - i*sin(π/2)}[/tex] can be simplified to 0, since cos(π/2) = 0 and sin(π/2) = 1.

Therefore, the expression inside the log becomes [tex](1 + (\theta/\alpha)^n)[/tex].

Now, we need to find the limit of this sequence as n approaches ∞.

If θ/α is less than 1, then (θ/α)^n will approach 0 as n approaches infinity, and the limit of the sequence will be log(1) = 0.

If θ/α is greater than 1, then (θ/α)^n will approach infinity as n approaches infinity, and the limit of the sequence will be log(infinity) = infinity.

If θ/α is equal to 1, then (θ/α)^n will always be 1, and the limit of the sequence will be log(2).

Therefore, the limit of the sequence depends on the values of θ and α. If θ/α < 1, the limit is 0. If θ/α > 1, the limit is infinity. If θ/α = 1, the limit is log(2).

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The area of the triangle is equal to half the product of the two base lengths (6) multiplied by the height (6), or 18.

Area is a quantity that measures the size of a two-dimensional surface or shape. It is expressed in square units such as square centimetres (cm2), square metres (m2) or square kilometres (km2). Area is used to describe the size of a garden, a house, a room, a city and much more. It can also be used to calculate the amount of material required for a project, such as paint, carpet or tiles. Knowing the area of a shape can help to calculate costs, and to make sure that enough materials are ordered.

The area of the triangle can be determined by using the midpoint formula, which states that the area of an isosceles triangle is equal to half the product of the two base lengths multiplied by the height.

In this case, the midpoint of the triangle is (3,0). This means that the triangle's base lengths are equal to 6 (the difference between the x coordinates of the midpoint and the two endpoints, 3-(-3)) and the height is equal to 6 (the difference between the y coordinates of the midpoint and the two endpoints, 3-(-3)).

Therefore, the area of the triangle is equal to half the product of the two base lengths (6) multiplied by the height (6), or 18.

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The length of the base of the given isosceles triangle is 18.

What is an isosceles triangle?

A triangle with two equal sides is known as an isosceles triangle in geometry. Both having exactly two sides of equal length and having at least two sides of equal length are acceptable specifications, with the latter version containing the equilateral triangle as an exception. The theorem that describes the isosceles triangle is, "if the two sides of a triangle are congruent, then the angle opposite to them is likewise congruent."

Given the sides of the triangle as 2x+4, x+8 and 5x-2

∠A and ∠B are given as same.

So this is an isosceles triangle.

One of the properties of an isosceles triangle is that the opposite angle of an isosceles triangle will also be equal if the sides are equal. As a result, if two sides are equal, so will the two angles that are across from them.

So 2x + 4 = x + 8

Solving, we get x as

x = 4

So now substituting this value in 5x -2, which is the base of the triangle.

5 * 4 -2 = 20 - 2 = 18

Therefore the length of the base of the given isosceles triangle is 18.

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Answer:

(2x-1)(3x-4)

Step-by-step explanation:

6x²-11x+4

Now we will split the middle term so when we add the digits it will give the original number back but when we multiply them, it will give the sum of the first and the last digit

6x²-11x+4

6x²-3x-8x+4

Now you can that if we add -3 and -8, we get -11 back but if we multiple them, we get the sum of 6 and 4 (the first and the last digits), which is 24

Now we will simplify the values

3x(2x-1) - 4(2x-1)

Simplifying further, we get

(2x-1) (3x-4) which is the answer

1) A(1,2),A'(-1,2) : a reflection across the y-axis

2) A(1,2), A'(-2,1): a rotation 270⁰ clockwise around the origin

3) A(1,2),  A'(-1,4):  a translation of 2 units left and 2 unit up

4) A(1,2),A'(-1,-2): a rotation 180⁰ around the origin

5) A(1,2),A'(-3,-7): a translation of 4 units left and 9 units down

What is the transformation of a point?

The transformation, or f: X →X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the image X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one direction or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point. Two-dimensional mathematical figures move about a coordinate plane according to transformations.

The given point is A(1,2).

The rule of a rotation 180⁰ around the origin is (x,y)→(−x,−y).

Therefore, A(1,2)→A'(-1,-2).

A rule of translation of 2 units left and 2 unit up is (x,y)→(x-2,y+2)

Therefore, A(1,2)→A'(1-2,2+2) = A'(-1,4).

The rule of a reflection across the y-axis is (x,y)→(−x,y).

Therefore, A(1,2)→A'(-1,2)

A rule of translation of 4 units left and 9 units down is (x,y)→(x-4,y-9)

Therefore, A(1,2)→A'(1-4,2-9) = A'(-3,-7).

The rule of a rotation 270⁰ clockwise around the origin is (x,y)→(-y,x)

Therefore, A(1,2)→A'(-2,1)

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Answer:

Step-by-step explanation:

All of the solutions of the given system of linear inequalities above include the following:

A. (0, 3).

C. (6, 2)

E. (0, -1)

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph of a system of linear inequalities.

In this scenario, we can reasonably infer and logically deduce that the solution to the given system of linear inequalities is the shaded region and it lies in both quadrant I and quadrant IV with the following ordered pairs:

Ordered pair = 0, 3).

Ordered pair = (6, 2)

Ordered pair = (0, -1)

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Answer: Obtuse Triangle

Step-by-step explanation:

63 + 22 = 85

180 - 85 = 95

Since the unknown angle is over 90 degrees, it is an obtuse triangle.

Answer:

Step-by-step explanation:

18% of $3200.80 = $576.144.

$576.144 is for one month. So, for a year is 12 * $576.144 = $6913.728.

With Scale factor=4, the area of bigger square is 2304 and perimeter is 192 and for smaller square area=144 unit and perimeter=48.

What is the definition of scaling factor?

The Scale Factor is used to scale shapes of different sizes. Geometry teaches us about different geometrical shapes in two and three dimensions. The scale factor is a statistic that is used to compare statistics that appear comparable but have distinct scales or metrics. Consider two circles with the same shape but different radii.

The scale factor indicates how much bigger or smaller a figure is in comparison to the original figure. You may create an extended or reduced version of any original form by using a scale factor.

Now,

side of smaller square=12

area=12²=144

perimeter=12*4=48

For bigger square, as scaling factor=4

then side=12*4=48

area=48²=2304

perimeter=4*48=192

Hence,

            the area of bigger square is 2304 and perimeter is 192 and for smaller square area=144 unit and perimeter=48.

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The cost of gasoline if the truck uses 5 gallons to drive 60 miles is $18.70

To calculate the cost of gasoline for the old truck, we can use the following formula:

Cost of gasoline = Price per gallon × Number of gallons used

Given that

Price per gallon = 3.74

Number of gallons used = 5 gallons

We have

Cost of gasoline = $3.74/gallon × 5 gallons

Evaluate

Cost = $18.70

Hence, the cost is $18.70

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Complete question

An old truck has a fuel efficiency of 12 mpg. What is the cost of gasoline if the truck uses 5 gallons to drive 60 miles if the gasoline costs $3.74 per gallon

Answer:

The value of ƒ (6) is the value of y.

Step-by-step explanation:

Given: y = f(x)

Step 1: Substitute x = 6 into the equation.

y = f(6)

Step 2: Solve for y.

y = f(6)

Answer:

f = 648

Step-by-step explanation:

[tex]\frac{f}{24} =27[/tex]

Multiply both sides by 24

[tex]f=648[/tex]

The table that is used to graph g(x) is given by table 3 and 4.

A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another. The reflected picture should have the same size and shape as the original, but it faces the opposite way. Changes in position during contemplation may also result in translation.

Given that, the function is:

f(x) = 1/3(6x) = 2x

f(x) = 2x

g(x) is the reflection of f(x) across the x-axis.

According to the rule of reflection, the reflection on x-axis is given as:

(x, y) → (x, -y)

Here, the y coordinated of the graph of g(x) has the same value but the opposite sign.

This is satisfied by the table 3 and 4.

Hence, the table that is used to graph g(x) is given by table 3 and 4.

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Step-by-step explanation:

8/8 in decimal form is equal to 1. To simplify 8/8 to a decimal, you divide the numerator (8) by the denominator (8). This is equal to 1. Therefore, 8/8 simplified into a decimal is 1.

Therefore, the rational function whose graph has an x-intercept at x=2.

In mathematics, a function is a rule that assigns to each input value from a set (called the domain) exactly one output value from another set (called the range). In other words, a function is a relationship between two sets of numbers, such that for each input value there is a unique output value. Functions are commonly denoted by an equation that defines the relationship between the input and output variables. For example, the equation y = f(x) defines a function f, where x is the input variable and y is the output variable.

Here,

To identify the rational function whose graph is given below, we need to determine its equation. We know that the graph has an x-intercept at x=2 and a y-intercept at y=−2/3.

We also know that the function is a rational function, which means it can be written as a ratio of two polynomials. The general form of a rational function is:

f(x) = p(x)/q(x)

where p(x) and q(x) are polynomials, and q(x) cannot be zero.

To find the specific equation of the function whose graph is shown, we can use the information about the intercepts to write down two points that are on the graph. We can use these points to set up a system of equations that we can solve for the coefficients of the polynomials p(x) and q(x).

Using the x-intercept, we know that the point (2,0) is on the graph. Using the y-intercept, we know that the point (0,-2/3) is on the graph. So we can set up the following system of equations:

p(2)/q(2) = 0

p(0)/q(0) = -2/3

Since the denominator of a rational function cannot be zero, we know that q(2) and q(0) cannot be zero. This allows us to set up a third equation:

q(x) ≠ 0

Now we can use algebra to solve for the coefficients of p(x) and q(x). We can start by writing the rational function in general form:

f(x) = p(x)/q(x)

and then multiplying both sides by q(x):

f(x)q(x) = p(x)

We can now substitute x=2 and x=0 to get two equations:

f(2)q(2) = p(2) = 0

f(0)q(0) = p(0) = -2/3

We also have the equation q(x) ≠ 0. This means that the denominator cannot have any factors that would make it equal to zero, so we can assume that q(x) has a linear factor of (x - 2), since we know that the graph has an x-intercept at x=2. We can then write:

q(x) = a(x - 2)

where a is some constant.

Now we can substitute this expression for q(x) into the equation f(x)q(x) = p(x) and simplify:

f(x)q(x) = p(x)

f(x)a(x - 2) = p(x)

We can now substitute x=0 and use the equation we found for p(0):

f(0)a(-2) = -2/3

f(0) = 1/3a

Next, we can substitute x=2 and use the equation we found for p(2):

f(2)a(0) = 0

f(2) = 0

Finally, we can substitute these values for f(0) and f(2) into the general form of the rational function and simplify:

f(x) = p(x)/q(x)

f(x) = p(x)/(a(x - 2))

We know that p(x) = f(x)q(x) from the equation we derived earlier, so we can substitute this into the equation above:

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

We can now cancel the f(x) terms from both sides and simplify:

1 = (x - 2)/a

a = x - 2

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The discounted price per yard for ribbons and for fabrics is A. Ribbon costs $ 1. 50 per yard and fabric costs $ 5. 75 per yard.

You can find the discounted price by using the options and then multiplying the prices given, by the purchases of Gwen and Penelope to find out which price is right.

If the discounted price of ribbons were $ 1.50 per yard and the fabric was $ 5. 75 per yard, then the cost to Gwen would be:

= ( 1. 50 x 6 ) + ( 10 x 5. 75 )

= $ 66. 50

For Penelope :

= ( 1. 50 x 5 ) + ( 8 x 5. 75 )

= $ 53. 50

These are the amounts spent so these are the discounted prices.

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Answer:

-$32

Step-by-step explanation:

Credited = Positive Change

Debited = Negative Change

48-80 = -32

-$32

The value of A n (B U C) = {q, s, w, y} for the given sets.

A set is a clearly defined group of things in mathematics. We may define several operations on sets and look at their attributes, unlike numbers. An operation in set theory is a task that involves combining different sets in order to create a new set with unique attributes.

The set containing all elements shared by sets A and B is the intersection of the two sets.

The given sets are:

U= {q,r,s,t,u,v,w,x,y,z}, A={q,s,u,w,y}, B={q,s,y,z}, and C= {v,w,x,y,z}

The value of (B U C) depicts all the terms in B and C:

(B U C) = {q, s, y, z, v, w, x}

The value of A n (B U C) depicts all the common terms in set A and B U C:

A n (B U C) = {q, s, w, y}

Hence, the value of A n (B U C) = {q, s, w, y} for the given sets.

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Let's call the position of the plane "P", and the positions of clearing A and clearing B "A" and "B", respectively. We want to find the distance from the plane to clearing A.

First, draw a diagram. The angle of depression to clearing A means that the line from the plane to clearing A makes a 32 degree angle with the horizontal. Similarly, the angle of depression to clearing B means that the line from the plane to clearing B makes a 56 degree angle with the horizontal. We know that the distance between clearings A and B is 5.7 km.

Now, we can use trigonometry to find the distance from the plane to clearing A. Let's call this distance "d". We can set up the following equation:

tan(32) = d/x

where x is the horizontal distance from the plane to clearing A. We can rearrange this equation to solve for d:

d = x tan(32)

Similarly, we can set up an equation for the distance from the plane to clearing B:

tan(56) = (x + 5.7) / d

We can rearrange this equation to solve for d:

d = (x + 5.7) / tan(56)

Now we can set the two expressions for d equal to each other and solve for x:

x tan(32) = (x + 5.7) / tan(56)

x tan(32) tan(56) = x + 5.7

x (0.6561) = x + 5.7

0.6561 x = x + 5.7

-0.3439 x = 5.7

x = -5.7 / 0.3439

x ≈ -16.57

Since the distance from the plane to clearing A is a positive distance, we can ignore the negative solution. Therefore, the distance from the plane to clearing A is approximately:

d = x tan(32) ≈ (-16.57) tan(32) ≈ 9.18 km

Rounding this to the nearest hundredth of a kilometer gives:

d ≈ 9.18 km

Therefore, the distance from the plane to clearing A is approximately 9.18 km.

:)?

The t-test statistic of the data is -1.23

To test the null hypothesis that the mean of the population is 3 against the alternative hypothesis, u <3 with a significance level of 0.05, we can use a one-tailed t-test since the sample size is small and the population standard deviation is unknown.

The formula for the t-test statistic is:

t = (x(bar) - μ) / (s / √n)

Where:

x(bar) = sample mean

μ = population mean (null hypothesis)

s = sample standard deviation

n = sample size

Given the sample of six measurements: 2, 3, -1.5, 1.2

First, we need to calculate the sample mean, sample standard deviation, and t-test statistic.

Sample mean (x(bar)) = (2 + 3 - 1.5 + 1.2) / 4 = 1.93

Sample standard deviation (s) = √[(∑(x - x(bar))^2) / (n - 1)]

= √[((2 - 1.93)^2 + (3 - 1.93)^2 + (-1.5 - 1.93)^2 + (1.2 - 1.93)^2 +  / (4 - 1)]

= 1.92

t-test statistic = (x(bar) - μ) / (s / √n)

= (1.93 - 3) / (1.92 / √5)

= -1.23 (rounded to two decimal places)

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The equation of rational function is f(x) = 3 - (5/2)(x - 5)(x + 1) / ((x + 2)(x + 6))

One possible equation for a rational function with the given properties is:

f(x) = 3 + (k(x + 5)(x - 5)) / ((x + 2)(x + 6))

Here, k is a constant that determines the vertical scale of the function. We choose the factor (x + 5)(x - 5) in the numerator to make the x-intercepts at x = 5 and x = -5. We choose the factors (x + 2) and (x + 6) in the denominator to make the vertical asymptotes at x = -2 and x = -6. We choose the constant term 3 in the equation to make the horizontal asymptote at y = 3.

To determine the value of k, we can use one of the x-intercepts, say x = 5. Substituting x = 5 into the equation and setting the result to 0 (since the function has an x-intercept at x = 5) gives:

0 = 3 + (k(5 + 5)(5 - 5)) / ((5 + 2)(5 + 6))

Simplifying the right-hand side, we get:

0 = 3 + 0 / (7 * 11)

0 = 3

This equation is not true, which means that we have made a mistake somewhere. The mistake is in assuming that the x-intercepts occur at x = 5 and x = -5. Instead, we should have x-intercepts at x = 5 and x = -1, which are the roots of the numerator (x - 5)(x + 1). So we need to adjust the numerator in the equation to (x - 5)(x + 1) in order to get the correct x-intercepts.

The correct equation for the rational function is:

f(x) = 3 + (k(x - 5)(x + 1)) / ((x + 2)(x + 6))

To determine the value of k, we can use the other x-intercept, x = -1. Substituting x = -1 into the equation and setting the result to 0 gives:

0 = 3 + (k(-1 - 5)(-1 + 1)) / ((-1 + 2)(-1 + 6))

Simplifying the right-hand side, we get:

0 = 3 + 6k / 5

Multiplying both sides by 5, we get:

0 = 15 + 6k

Solving for k, we get:

k = -15 / 6 = -5/2

So the final equation for the rational function is:

f(x) = 3 - (5/2)(x - 5)(x + 1) / ((x + 2)(x + 6))

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Answer:

3

Step-by-step explanation:

∠LMN = ∠BMN + ∠LMB (linear angles)

59x + 3 = 160 + (-1 + 7x)

59x - 7x = 160 - 1 - 3

52x = 156

x = 156/52 = 3

Answer:

No

Step-by-step explanation:

The y intercept is 7. For it to be proportional it has to go through (0,0).

Answer:

Yes

Step-by-step explanation:

Answer:

A.35°, 114°, 31°.

B.61°,119°,153°,27° and 92°

A. alternates angles are equal;

35°=35°

Vertically opposites angles are equal;

114°=114°

Sum of interior angles of a triangle is 180;

114+35+x=180

x=180-(114+35)

x=31

Picture B.

Corresponding angles are equal;

61°=61°

Sum of angles on a straight line is 180°

61+x=180

x=180-61

x=119°

Corresponding angles are equal;

153°=153°

Sum of angle on straight line is 180;

153+x=180

x=180-153

x=27

Sum of interior angle of a triangle is 180;

27+61+X=180

x=180-(27+61)

x=92

Answer:

Step-by-step explanation:

To find the equilibrium quantity and equilibrium price for the demand and supply functions, we need to find the point where the quantity demanded and the quantity supplied are equal. This point is known as the equilibrium point and is represented by the intersection of the demand and supply curves.

The demand function is given by p = -0.1q²-0.2q+9, and the supply function is given by p = 0.2q²+0.4q+1.8.

To find the equilibrium quantity, we need to set the quantity demanded equal to the quantity supplied:

-0.1q²-0.2q+9 = 0.2q²+0.4q+1.8

Simplifying and rearranging the terms, we get:

0.3q² + 0.6q - 7.2 = 0

Using the quadratic formula, we can solve for q:

q = (-0.6 ± √(0.6² - 4(0.3)(-7.2))) / (2(0.3))

q = (-0.6 ± √(0.6² + 8.64)) / 0.6

q = (-0.6 ± √9.36) / 0.6

q = (-0.6 ± 3.06) / 0.6

q = 4.6, -5.0

Since the quantity cannot be negative, the equilibrium quantity is q = 4.6.

To find the equilibrium price, we can substitute the equilibrium quantity into either the demand or supply function:

p = 0.2q²+0.4q+1.8

p = 0.2(4.6)²+0.4(4.6)+1.8

p = 7.82

Therefore, the equilibrium quantity is 4.6 units and the equilibrium price is $7.82.

Kevin's error is that he incorrectly identified the vertex of the parabola as (3, 2) instead of (2, 3), which resulted to the parabola opens downward. The correct vertex is at (2, 3) and the parabola opens upward.

You are correct that the vertex of the parabola can be determined using the equation f(x) = a(x - h)² + k, where the vertex is at (h, k). In this case, we have f(x) = -(x-2)² + 3, so the vertex can be found by setting x - 2 = 0, which gives x = 2. Plugging this value into the equation,

we get f(2) = -(2-2)² + 3 = 3, so the vertex is at (2, 3).

However, your reasoning for why h is positive is not correct. The expression x - h represents the horizontal distance from the vertex to any point on the parabola. So if x is greater than h, then the expression x - h will be positive, and if x is less than h, then the expression x - h will be negative. In this case, the vertex is at (2, 3), so we have h = 2. This means that any point to the right of the vertex will have a positive value of x - h, while any point to the left of the vertex will have a negative value of x - h.

Therefore, the correct explanation of Kevin's error is that he incorrectly identified the vertex as (3, 2) instead of (2, 3), and as a result, he also incorrectly concluded that the parabola opens downward. In fact, the parabola opens upward because the coefficient of the x² term, -1, is negative.

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