Question 8 (Essay Worth 10 points)
(07.04 MC)
Given the functions f(x)=x²+x²-3x+4 and g(x)=2"-4, what type of functions are f(x) and g(x)? Justify your answer. What key feature(s) do f(x) and g(x) have in common?
(Consider domain, range, x-intercepts, and y-intercepts.)

The solution of the equation written by completing square is (x + 1/2)² = 289/4.

In algebra, the process of "completing the square" is used to transform a quadratic expression into a perfect square trinomial. Using this method, a constant term is either added or subtracted from the quadratic expression to produce a perfect square trinomial that may be factored as the square of a binomial. Solving quadratic equations, locating the vertex of a parabola, and simplifying formulas with square roots all involve the completion of the square.

The value of the equation x² + x = 72 can be written as a completer square by taking half of the coefficient of the x-term.

(1/2)² = 1/4

Add this to both sides of the equation:

x² + x + 1/4 = 72 + 1/4

Now, the LHS is:

(x + 1/2)² = 289/4

x = -1/2 ± (17/2)

Hence, the solution of the equation written by completing square is (x + 1/2)² = 289/4.

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To solve this problem, we can use the formula for simple interest:

I = P * r * t

where I is the interest earned, P is the principal amount (the initial deposit), r is the interest rate as a decimal, and t is the time in years.

We want to find how long it will take for the account balance to earn $1,500 in interest, so we can set up the equation:

$1,500 = $5,000 * 0.025 * t

where t is the time in years.

Simplifying this equation, we get:

t = $1,500 / ($5,000 * 0.025)

t = 12 years

Therefore, it will take 12 years for the balance of the account to earn $1,500 in interest

The three sizes of school pictures may feature the same subject, but they are not similar to each other in terms of size and aspect ratio.

The 8 in. by 10 in. size has an aspect ratio of 5:4, which is wider than the 5 in. by 7 in. size that has an aspect ratio of 7:5. The wallet size 2¼ in. by 3¼ in. has an aspect ratio of 9:13, making it even more elongated. This means that the relative proportions of the images are different.

Furthermore, the larger sizes such as 8 in. by 10 in. and 5 in. by 7 in. provide a lot more detail than the wallet size, which is smaller and often used as a miniature version of the larger sizes. The larger sizes also have a higher resolution, making them more suitable for framing and displaying.

Therefore, while the school pictures may depict the same subject, they are not similar in size, aspect ratio, and level of detail.

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The probabilities for this problem are given as follows:

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The number of cars with purchase prices less than $20,000 is given as follows:

86 + 67 + 35 = 188.

Of those 188 cars, 86 had repair costs less than $10,000, hence the probability is given as follows:

p = 86/188

p = 0.4574.

The number of cars with repair costs less than $10,000 is given as follows:

86 + 71 + 40 = 197.

Of those, 40 had a purchase price of more than $40,000, hence the probability is given as follows:

p = 40/197

p = 0.203.

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Answer:

No

Step-by-step explanation:

The angles of a triangle must add up to 180. 140+15+15 = 140 +30 = 170. This is not 170, so no. Hope this helps!

Answer:

It is not possible to draw a triangle with these angles because 140 + 15 + 15 = 170, triangle angles must add up to 180 and 180=170 is a false statement.

Step-by-step explanation:

The value of x is given as follows:

B. 6.

The value of x is obtained applying the two secant segment theorem, which means that the following equation will hold true:

4(x + 4) = 5(5 + 3)

(we add the two parts), with the outer part being the multipler.

Expanding the operations, the value of x is obtained as follows:

4x + 16 = 40

4x = 24

x = 6.

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Answer:

3e + 3y + 2tr

Step-by-step explanation:

2e + tr + 4y + e - y + tr

=> (2e + e) + (tr + tr) + (4y - y)

=> 3e + 2tr + 3y

=> 3e + 3y + 2tr

Answer:  The answer is 3e + 3y - 2tr

Step-by-step explanation:

          2e + tr + 4y + e - y + tr

         =(2e + e) + (tr + tr) + (4y- y)

         =3e + 2tr + 3y

         =3e + 3y +2tr

Answer:

125

Step-by-step explanation:

the statement " 5 symbols for a 3-symbols- long pass code" in mathematics simply means 5 has a power of 3 or 5^3 = 5×5×5= 125

Answer: False.

Step-by-step explanation:

Squares have to have the same shape and size to be congruent. Therefore, not all squares are congruent, since not all of them are the same size. ... This means that they have the same shape, although not necessarily the same size.

The probability that Ben will get the Donut Shop pod after Maddy or Charlie's selection is 3/17.

We know that, probability of an event = Number of favorable outcomes/Total number of outcomes

There are 5 Donut Shop pods and Maddy and Charlie each took 2, leaving 3 Donut Shop pods in the green basket.

There are 17 pods left in the basket after Maddy and Charlie's selection (5 Donut Shop, 6 Swiss Miss, and 6 Breakfast Blend), so the probability that Ben will get the Donut Shop pod is 3/17.

Therefore, the probability that Ben will get the Donut Shop pod after Maddy or Charlie's selection is 3/17.

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Answer:

5w² + 4

Step-by-step explanation:

there's no like terms, so just write the expression again

Answer:

The correct frequency table is table c.

The height of point A is 0 feet. However, this is not the actual height of point A, as it is at the highest point on the Ferris Wheel, which is 185 feet as calculated previously.

The height of point A on the Ferris Wheel can be calculated using the sine function, as it is the vertical component of the point's position. The center of the Ferris Wheel is 100 feet off the ground, and its radius is 85 feet.

Let's denote the height of point A as h_A, which is the vertical distance from the center of the Ferris Wheel to point A.

Since point A is at the 0 radian position, it is at the highest point on the Ferris Wheel. At this point, the height of point A is equal to the sum of the radius and the center's height:

h_A = radius + center's height

h_A = 85 + 100

h_A = 185 feet

So, the height of point A off the ground is 185 feet.

To estimate the value of h_A using the sine function, we can use the fact that at any given angle θ on the unit circle, the height of the point on the circle is given by the sine of that angle multiplied by the radius. In this case, since point A is at the highest point on the Ferris Wheel, we can use the sine of 0 radians (which is 0) to estimate the height of point A:

h_A = radius * sin(0)

h_A = 85 * 0

h_A = 0

So, using the sine function, we estimate that the height of point A is 0 feet. However, this is not the actual height of point A, as it is at the highest point on the Ferris Wheel, which is 185 feet as calculated previously.

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The value of x in the given chords is determined as 9.

The measure of length x is calculated by applying the following formula.

Based on the angle of intersecting chord theorem, we will have the following equation.

3 (3 + x ) = 4 ( 4 + 5 )

9 + 3x = 36

collect similar terms ang solve for x;

3x = 36 - 9

3x = 27

divide both sides of the equation by 3;

3x/3 = 27/3

x = 9

Thus, the value of x in the given chords is determined by applying chord theorem.

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Answer:

MN and ML are on the same straight line.

Answer:

416

Step-by-step explanation:

The front and back are triangles

a = 1/2 bh

a = 1/2(12)(8)

a = 48

We times this by 2 to find the front and the back.

96

Bottom

a = lw

a = 10 x 12

a = 12

120

Right and left sides

a = lw

a = 10 x10 = 100

Multiply this by 2 to find the right and the left sides.

200

Add the numbers together:

96 + 120 + 200 = 416

Helping in the name of Jesus.

To find the surface area of a three-dimensional object, you need to add up the area of all its faces.

This can be done using formulas specific to the shape of the object. For example, the surface area of a rectangular prism (a box) can be found using the formula SA = 2lw + 2lh + 2wh, where l, w, and h represent the length, width, and height of the box, respectively. Other common three-dimensional shapes include spheres, cones, and cylinders, each with their own unique formulas for finding surface area. So, to answer your question, I would need to know what specific object you are referring to in order to provide an accurate answer about its surface area.

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Answer:

Account balance = $6,834.01

Interest accrued = $1,834.01

Step-by-step explanation:

To find the account balance of an initial investment of $5,000 at 6.25% compounded daily for 5 years, use the Compound Interest Formula.

[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]

where:

As the interest is compounded daily, n = 365.

Therefore, the values to substitute into the formula are:

Substitute the values into the formula and solve for A:

[tex]\implies A=5000\left(1+\dfrac{0.0625}{365}\right)^{365 \cdot 5}[/tex]

[tex]\implies A=5000\left(1.000171232...\right)^{1825}[/tex]

[tex]\implies A=5000\left(1.3668013759...\right)[/tex]

[tex]\implies A=6834.0068795...[/tex]

[tex]\implies A=6834.01\; \sf (2\;d.p.)[/tex]

Therefore, the account balance after 5 years is $6,834.01, and the total amount of interest earned is $1,834.01.

The percentages of people taking the test who scores between 421 and 645 is: 68 %

The empirical rule, also referred to as the three-sigma rule or the 68-95-99.7 rule, is defined as a statistical rule which states that almost all observed data for a normal distribution will fall within three standard deviations (denoted by σ) of the mean or average (denoted by µ).

We are given:

Sample mean: x' = 553

standard deviation; s = 112

Thus:

x' - ns = 421

x' + ns = 645

Where n is the number of standard deviations from the mean. Thus:

553 - 112s = 421

112s = 553 - 421

112s = 132

s = 132/112

s ≈ 1

So 1 standard deviation from the means indicates a percentage of 68%

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The total number of kilometers that the friends hiked in all would be 2. 02 km.

The total distance that Jordan, Jessica, Eloise, and James hiked in the Austrian Alps, can be found to be :

= Distance on Monday + Distance on Tuesday

= 1. 08 + 0. 94

= 2. 02 km

Using grids, you can represent a single box as 0. 1 km so that for 1. 08 km you will have a grid of 108 cubes. Do the same for Tuesday to get 94 cubes.

Add them up and you will get 202 cubes which would be 2.02 km.

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Answer:

Step-by-step explanation:

i start with y, add 5 and then, double the result​

y                      add 5

y + 5                double the result​

(y + 5) × 2         solve        

2y + 10

or

(y + 5) × 2 =

2y + 10

The side  GJ  in the big one corresponds to the side  WT  in the small one.

It's not possible to find the scale factor between the two drawings, because there's no numerical information given to show us the relationship between any pair of corresponding sides.  (This information is probably there in the book or on the homework sheet you copied the problem from, but for some strange reason, you didn't include it in what you decided to show us.)

The final counts are:

Given a survey of 240 students, 35% of students were interested in athletics, which is equal to 84 students.

3/5 of students were interested in academic clubs, which is equal to 144 students.

26 students were interested in both athletics and academic clubs.

Using this information, we can fill in the remaining cells of a table to show the number of students in each category.

The final counts are:

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The gain on sale of the laptop which Jack purchased in 2012 for $64,000 with a current book value of $18,000 but sold for $28,000 is $10,000.

The book value of an asset is the difference between the original value or purchase cost and the accumulated depreciation.

Accumulated depreciation represents the depreciation from the purchase date to the current period. It can be determined as the difference between the purchase price and the current value.

The purchase price of the laptop in 2012 = $64,000

Current book value = $18,000

Accumulated depreciation = $46,000 ($64,000 - $18,000)

Sales price = $28,000

Gain on sale = $10,000 ($28,000 - $18,000)

Thus, when the laptop is sold by Jack, he realized a gain of $10,000 because the sales price exceeded the current book value.

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Answer:

The probability of choosing a brown egg from the carton is 2/12 or 1/6. This is because there are two brown eggs in the carton and a total of twelve eggs, so the probability of choosing a brown egg is 2/12 or 1/6.

The perimeter of the right triangle is 30 units.

What is perimeter?

In geometry, perimeter refers to the total length of the boundary of a two-dimensional shape, such as a polygon or a circle. It is the sum of the lengths of all the sides of the shape.

To find the perimeter of the right triangle, we need to determine the lengths of its sides first.

Using the distance formula, we can find the lengths of the three sides of the triangle:

Side 1: From (-5, 3) to (-5, -2)

[tex]Length = \sqrt{[(3 - (-2))^2 + (-5 - (-5))^2]} = \sqrt{[5^2]} = 5[/tex]

Side 2: From (-5, -2) to (7, -2)

[tex]Length = \sqrt{[(7 - (-5))^2 + (-2 - (-2))^2]} = \sqrt{[12^2]} = 12[/tex]

Side 3: From (7, -2) to (-5, 3)

[tex]Length = \sqrt{[(-5 - 7)^2 + (3 - (-2))^2]} = \sqrt{[144 + 25]} = \sqrt{[169]} = 13[/tex]

We know that the triangle is a right triangle because two of its sides (Side 2 and Side 3) form a straight line along the x-axis, and the third side (Side 1) is perpendicular to this line.

Therefore, Side 1 is the hypotenuse, and Sides 2 and 3 are the legs of the right triangle.

To find the perimeter, we add up the lengths of all three sides:

Perimeter = Side 1 + Side 2 + Side 3 = 5 + 12 + 13 = 30

Therefore, the perimeter of the right triangle is 30 units.

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In the conversion of fractions to decimals, the fraction should be thought of as a division problem.

A fraction represents the division of the numerator (n) by the denominator (d). So, when you have a fraction like n/d, you can convert it to a decimal by dividing n by d.

The purchase price of the anitque dresser purchased by Danielle is $120 and the advertised price is $ 300 after which it was sold on profit of $255. Correct answer:optionA

What is profit?

The extra money is left after paying your business expenses is your profit. Gross profit, operating profit, and net profit are the three primary types of profit. The cost foundation for determining profit or loss when selling a product is the price the buyer pays at the time of purchase, known as the purchase price. The price of a product as advertised for marketing purposes is known as the marketed price.

Let us consider the purchase price of antique dresser with mirror= p

Given that the advertised price= 250% of her purchase price

                                                  =[tex]\frac{250}{100}[/tex] of p

                                                   =[tex]\frac{250}{100}[/tex] p

                                                   =[tex]\frac{250 p}{100}[/tex]

Also given that the selling price which was 15% less than advertised price= $255

advertised price - 15% of advertised price =$255

                                   [tex]\frac{250 p}{100}[/tex] - 15% of  [tex]\frac{250 p}{100}[/tex]       =$255

                                    [tex]\frac{250p}{100} - \frac{15}{100} of \frac{250p}{100}[/tex]       =$255

                                             [tex]\frac{250p}{100} - \frac{3750p}{10000}[/tex]      =$255

                                                 [tex]\frac{250p}{100} - \frac{375p}{1000}[/tex]    =$255

                                                  [tex]\frac{2500p - 375p}{1000}[/tex]     =$255

                                                      [tex]\frac{2125p}{1000}[/tex]         =$255

                                                                  p  = [tex]\frac{255 (1000)}{2125}[/tex]

                                                                  p  = $120

The purchasing price is $120

Advertised price =[tex]\frac{250 p}{100}[/tex]

                           = [tex]\frac{250(120)}{100}[/tex]

                           = 25 x 12

                            = $ 300

The Advertised price  is $ 300

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