Write the quadratic equation in standard form that corresponds to the graph shown below.. Please help.

The quadratic equation that has the roots 3 + i and 3 - i is x² - 6x + 10 = 0.

The general form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants.

The roots of the quadratic equation are the values of x that make the equation equal to zero.

Therefore, if a quadratic equation has the roots 3 + i and 3 - i, it can be written in the factored form as (x - (3 + i))(x - (3 - i)) = 0. Expanding this product yields x² - (3 + i + 3 - i)x + (3 + i)(3 - i) = 0.

Simplifying this expression further results in the quadratic equation x² - 6x + 10 = 0.

The quadratic equation that has the roots 3 + i and 3 - i is x² - 6x + 10 = 0.

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Answer: The length of the rectangle is given as "2 feet more than 3 times its width."

Let's break it down step by step:

The formula for the area of a rectangle is length multiplied by width. So, in terms of n, the area of the rectangle would be:

Area = Length × Width

= (3n + 2) × n

= 3n^2 + 2n

Therefore, the area of the rectangle, in terms of n, is 3n^2 + 2n.

The ballroom dance couple can arrange their performance in 28 different ways by selecting 6 routines out of the 8 they have learned.

The idea of combinations can be used.

The number of ways to select k items from a set of n items is given by the formula for combinations:

C(n, k) = n! / (k! * (n - k)!)

In this case, n = 8 (the total number of routines they have learned) and k = 6 (the number of routines they will perform).

Using the formula, we can calculate:

C(8, 6) = 8! / (6! * (8 - 6)!)

= 8! / (6! * 2!)

The factorial function is represented in this case by the exclamation symbol (!).

The sum of all positive integers from 1 to n is the factorial of the number n.

Calculating the factorials involved:

8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320

6! = 6 * 5 * 4 * 3 * 2 * 1 = 720

2! = 2 * 1 = 2

Plugging in these values:

C(8, 6) = 40,320 / (720 * 2)

= 40,320 / 1,440

= 28

Therefore, the ballroom dance couple can arrange their performance in 28 different ways by selecting 6 routines out of the 8 they have learned.

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The expression -2(5 + 7x) + 5(x + 5) is equivalent to the expression -9x + 15. So, the answer is option B: 15 - 9x.

To simplify the expression -2(5 + 7x) + 5(x + 5), we can distribute the coefficients and simplify further.

Starting with the expression -2(5 + 7x):

-2(5 + 7x) = -2 × 5 - 2 × 7x

= -10 - 14x

= -14x - 10

Now let's simplify the expression 5(x + 5):

5(x + 5) = 5 × x + 5× 5

= 5x + 25

Finally, combining the two simplified expressions:

-14x - 10 + 5x + 25

Combining like terms:

(-14x + 5x) + (-10 + 25)

-9x + 15

Therefore, the expression -2(5 + 7x) + 5(x + 5) is equivalent to the expression -9x + 15.

So, the answer is option B: 15 - 9x.

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The greatest common factor of -x^2 + 6x - 19 is 1.

To find the greatest common factor (GCF) of the polynomial [tex]-x^2 + 6x - 19,[/tex] we need to factorize the polynomial and identify the common factors among its terms.

First, let's examine the polynomial and see if we can factor it further:

[tex]-x^2 + 6x - 19[/tex]

The polynomial does not appear to have any common factors among its terms.

It cannot be factored using simple integer factors.

In this case, we can say that the GCF of the given polynomial is 1.

It is important to note that the GCF represents the highest degree of common factors that can be factored out from all terms of a polynomial. In this particular case, the polynomial does not possess any common factors that can be factored out.

It's worth mentioning that this polynomial is already in its simplest form and cannot be factored further.

However, if the polynomial had common factors that could be factored out, such as common binomial factors or other mathematical patterns, the GCF would differ from 1.

But in this case, the polynomial does not exhibit any common factors beyond 1.

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The statement "Since the y-values decrease as the x-values increase, the scatter plot shows a negative association" correctly explains the association of the scatter plot.

From the plot, we see that:

A scatter pIot is a type of graph that shows the reIationship between two variables. The variabIes are plotted on the x-axis and y-axis, and each data point is represented by a dot. The pattern of the dots can be used to infer the reIationship between the variables.

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Answer:

  4

Step-by-step explanation:

You want the product of terms (n+1)/n for integers n from 1 to 3.

When there are only 3 terms, we can write out the product:

  (1 +1)/1 × (2 +1)/2 × (3 +1)/3 = 2 × 3/2 × 4/3 = 4

The product is 4.

__

Additional comment

You will notice the first term has a denominator of 1. In each pair of terms, the numerator of a term cancels the denominator of the next term. This means the product of k terms will always be (k+1). For 3 terms, the product is 3+1 = 4.

Apparently, the answer in each case is the hour number.

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A truck is being filled with cube-shaped packages that have side lengths of foot, the volume of the part of the truck that is being filled is 34,808 cubic feet.

To discover the finest range of applications that may in shape in the truck, we want to calculate the volume of the truck and divide it by using the quantity of every cube-formed bundle.

The quantity of the truck is given with the aid of the method:

Volume = Length x Width x Height

Volume = 8 ft x 61 ft x 71 ft

Volume = 34,808 cubic toes

The volume of every cube-shaped bundle is given with the aid of the method:

Volume = Side [tex]Length^3[/tex]

Volume = 1 [tex]ft^3[/tex]

Number of packages = Volume of truck / Volume of each package

Number of packages = 34,808 ft^3 / 1 ft^3

Number of packages = 34,808

Thus, the greatest number of packages that can fit in the truck is 34,808.

Volume of the part of the truck being filled = Number of packages x Volume of each package

Volume of the part of the truck being filled = 34,808 x 1 ft^3

Volume of the part of the truck being filled = 34,808 ft^3

Thus, the volume of the part of the truck that is being filled is 34,808 cubic feet.

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We cannot conclude that whether a subject lies or does not lie is independent of the polygraph test indication.

The test statistic needed to test the claim that whether a subject lies or does not lie is independent of the polygraph test indication is the chi-square statistic.

In this case, the grand total is 90. The row totals are 57 and 33, and the column totals are 42 and 48. The expected frequencies are as follows:

The chi-square statistic is calculated as 0.177. The p-value for the chi-square statistic is calculated using a chi-square table. The degrees of freedom for the chi-square table are the number of rows minus 1, multiplied by the number of columns minus 1.

Since the p-value is greater than 0.05, we fail to reject the null hypothesis. We cannot conclude that whether a subject lies or does not lie is independent of the polygraph test indication.

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A true statement based on the given information is that ΔCAT and ΔDOG are similar triangles, meaning their corresponding angles are congruent and their corresponding sides are in proportion.

If all pairs of corresponding angles and sides in triangles ΔCAT and ΔDOG are congruent, it implies that the two triangles are similar. In similar triangles, the corresponding angles are congruent, and the corresponding sides are in proportion.

Based on this information, the following true statement can be made:

The ratio of the lengths of the corresponding sides in ΔCAT and ΔDOG is equal.

For example, if the corresponding sides are CA and DO, the ratio CA/DO will be equal to the ratio of the lengths of the other corresponding sides.

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Answer:

Assuming the spinner has 6 equal sectors of different colors, and yellow is only one of those colors, we can say that the probability of the spinner not landing on yellow is 5/6 or approximately 0.8333.

To predict the number of times the spinner will not land on yellow out of 90 spins, we can multiply the probability by the total number of spins:

0.8333 x 90 = 74.997 or approximately 75

Therefore, the best prediction possible for the number of times the spinner will not land on yellow out of 90 spins is 75 times.

The depreciation schedule (in dollars) using MACRS for the metal-working lathe is as follows:

Year 1: $1,429.00

Year 2: $2,449.00

Year 3: $1,749.00

Year 4: $1,249.00

Year 5: $893.00

Year 6: $892.00

Year 7: $893.00

The depreciation schedule using the Modified Accelerated Cost Recovery System (MACRS) is prepared as follows:

Given data:

Purchase cost of the metal-working lathe: $38,000

Business use percentage: 90%

Section 179 deduction: $18,000

Special depreciation allowance: 50%

Depreciable basis = Purchase cost - Section 179 deduction

Depreciable basis = $38,000 - $18,000 = $20,000

Special depreciation allowance = $20,000 * 50%

Special depreciation allowance  = $10,000

Adjusted depreciable basis = $20,000 - $10,000

Adjusted depreciable basis  = $10,000

The recovery period for a metal-working lathe is 7 years.

Using MACRS, the depreciation rates for a 7-year recovery period are as follows:

Year 1: 14.29%

Year 2: 24.49%

Year 3: 17.49%

Year 4: 12.49%

Year 5: 8.93%

Year 6: 8.92%

Year 7: 8.93%

Year 1:

Depreciation expense = $10,000 * 14.29% = $1,429.00

Year 2:

Depreciation expense = $10,000 * 24.49% = $2,449.00

Year 3:

Depreciation expense = $10,000 * 17.49% = $1,749.00

Year 4:

Depreciation expense = $10,000 * 12.49% = $1,249.00

Year 5:

Depreciation expense = $10,000 * 8.93% = $893.00

Year 6:

Depreciation expense = $10,000 * 8.92% = $892.00

Year 7:

Depreciation expense = $10,000 * 8.93% = $893.00

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The graph that shows only a translation is (c)

From the question, we have the following parameters that can be used in our computation:

The list of options

The general rule of translation it that

Using the above as a guide, we have the following:

the graph that shows only a translation is (c)

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Answer:

[tex]\textsf{a)} \quad x = 17[/tex]

[tex]\textsf{b)} \quad T_n=3n^2-3n-1[/tex]

[tex]\textsf{a)} \quad x = 20[/tex]

[tex]\textsf{b)} \quad T_n=3n^2-4n+5[/tex]

Step-by-step explanation:

Given quadratic number pattern:

To find the equation for the nth term, we can use the general form of a quadratic equation:

[tex]\boxed{T_n=an^2 + bn + c}[/tex]

where n is the position of the term.

Let's substitute the values of T₁, T₂ and T₄ into the quadratic equation: to create three equations:

[tex]\begin{aligned}T_1=a(1)^2+b(1)+c&=-1\\a+b+c&=-1\end{aligned}[/tex]

[tex]\begin{aligned}T_2=a(2)^2+b(2)+c&=5\\4a+2b+c&=5\end{aligned}[/tex]

[tex]\begin{aligned}T_4=a(4)^2+b(4)+c&=35\\16a+4b+c&=35\end{aligned}[/tex]

Rearrange the first equation to isolate c:

[tex]c=-a-b-1[/tex]

Substitute this into the second and third equations:

[tex]\begin{aligned}4a+2b+(-a-b-1)&=5\\3a+b&=6\end{ailgned}[/tex]

[tex]\begin{aligned}16a+4b+(-a-b-1)&=35\\15a+3b&=36\end{ailgned}[/tex]

Solve the equations simultaneously by rearranged the first equation to isolate b and substituting this into the second equation and solving for a:

[tex]b=-3a+6[/tex]

[tex]\begin{aligned}15a+3(-3a+6)&=36 \\15a-9a+18&=36\\6a&=18\\a&=3 \end{aligned}[/tex]

Substitute the found value of a into the equation for b and solve for b:

[tex]\begin{aligned}b&=-3a+6\\&=-3(3)+6\\&=-9+6\\&=-3\end{aligned}[/tex]

Finally, substitute the found values of a and b into the equation for c and solve for c:

[tex]\begin{aligned}c&=-a-b-1\\&=-3-(-3)-1\\&=-3+3-1\\&=-1\end{aligned}[/tex]

Therefore, the equation for the nth term is:

[tex]\boxed{T_n=3n^2-3n-1}[/tex]

The value of x is the 3rd term. Therefore, to find the value of x, substitute n = 3 into the equation for the nth term:

[tex]\begin{aligned}T_3&=3(3)^2-3(3)-1\\&=3(9)-3(3)-1\\&=27-9-1\\&=18-1\\&=17\end{aligned}[/tex]

Therefore, the value of x is 17.

[tex]\hrulefill[/tex]

Given quadratic number pattern:

To find the equation for the nth term, we can use the general form of a quadratic equation:

[tex]\boxed{T_n=an^2 + bn + c}[/tex]

where n is the position of the term.

Let's substitute the values of T₁, T₂ and T₄ into the quadratic equation: to create three equations:

[tex]\begin{aligned}T_1=a(1)^2+b(1)+c&=4\\a+b+c&=4\end{aligned}[/tex]

[tex]\begin{aligned}T_2=a(2)^2+b(2)+c&=9\\4a+2b+c&=9\end{aligned}[/tex]

[tex]\begin{aligned}T_4=a(4)^2+b(4)+c&=37\\16a+4b+c&=37\end{aligned}[/tex]

Rearrange the first equation to isolate c:

[tex]c=-a-b+4[/tex]

Substitute this into the second and third equations:

[tex]\begin{aligned}4a+2b+(-a-b+4)&=9\\3a+b&=5\end{ailgned}[/tex]

[tex]\begin{aligned}16a+4b+(-a-b+4)&=37\\15a+3b&=33\end{ailgned}[/tex]

Solve the equations simultaneously by rearranged the first equation to isolate b and substituting this into the second equation and solving for a:

[tex]b=-3a+5[/tex]

[tex]\begin{aligned}15a+3(-3a+5)&=33 \\15a-9a+15&=33\\6a&=18\\a&=3 \end{aligned}[/tex]

Substitute the found value of a into the equation for b and solve for b:

[tex]\begin{aligned}b&=-3a+5\\&=-3(3)+5\\&=-9+5\\&=-4\end{aligned}[/tex]

Finally, substitute the found values of a and b into the equation for c and solve for c:

[tex]\begin{aligned}c&=-a-b+4\\&=-3-(-4)+4\\&=-3+4+4\\&=5\end{aligned}[/tex]

Therefore, the equation for the nth term is:

[tex]\boxed{T_n=3n^2-4n+5}[/tex]

The value of x is the 3rd term. Therefore, to find the value of x, substitute n = 3 into the equation for the nth term:

[tex]\begin{aligned}T_3&=3(3)^2-4(3)+5\\&=3(9)-4(3)+5\\&=27-12+5\\&=15+5\\&=20\end{aligned}[/tex]

Therefore, the value of x is 20.

Answer:

250πcm³

Step-by-step explanation:

Length of bigger = k X length of smaller (k is a constant)

Area of bigger = k² X area of smaller (k is a constant)

Volume of bigger = k³ X volume of smaller (k is a constant)

ratio of 3:5 means that there are 3 + 5 = 8 parts.

Length of bigger = k X length of smaller

5 = 3k

k = 5/3.

Volume of bigger = k³ X volume of smaller

= (5/3)³ 54π

= 250πcm³

Step-by-step explanation:

5(2x – 3) = x – 15 + 9x

10x - 15 = x - 15 + 9x

10x - 9x - x = -15 + 15

0 = 0

Answer = A) Infinity many solutions

Answer:

-3.8 > -4.5

Step-by-step explanation:

Convert the fraction to decimal and then compare.

[tex]\sf -4\dfrac{1}{2}=\dfrac{-9}{2}[/tex]

          = -4.5

Now compare (-3.8) & (-4.5)

-3.8 > -4.5

The value of x is equal to 10 degrees.

In Mathematics and Geometry, the Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent:

By applying the alternate interior angles theorem to parallel lines p and q, we have the following congruent angles:

(5x - 65) = (x - 25)

5x - x = 65 - 25

4x = 40

x = 40/4

x = 10 degrees.

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The rate of electricity usage for the oven is 1.8275 units per hour.

The electricity consumption represents the amount of electrical energy that has been consumed over a specific time in units of Wh (or kWh),

To get rate of electricity usage for the oven in units per hour, we will divide the total electricity used by the number of hours.

Data:

Electricity used: 7.31 units

Time: 4 hours

Rate of electricity usage = Electricity used / Time

Rate of electricity usage = 7.31 units / 4 hours

Rate of electricity usage = 1.8275 units per hour.

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The initial and final conclusion would be Fail to reject the null hypothesis; there is not sufficient evidence to warrant rejection of the claim that the gender of the respondent is independent of the choice for the cause of global warming. Option C

The initial hypothesis is that the gender of the respondent is independent of the choice for the cause of global warming.

The alternative hypothesis is that the gender of the respondent is dependent on the choice for the cause of global warming.

The test statistic of 0.792 is less than the critical value of 5.991. Therefore, we do not reject the null hypothesis.

Looking at the statistic that has been provided, we do not have enough evidence to conclude that the gender of the respondent is related to the choice of the cause of global warming at the 0.05 significance level.

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Answer is in the file atttached.            

Answer:

The answer is D, the last one.

Answer: i dont know what this is but i  do believe its the second one

Step-by-step explanation:

The values of given x and y is,

x  = 6 and  y = 13/2

Since we know that,

Basic proportionality theorem,

The basic proportionality theory was developed by Thales, a great Greek mathematician; hence, it is also known as the Thales theorem. According to the great mathematician, the ratio of any two matching sides of any two equiangular triangles is always the same. The basic proportionality theorem (BPT) was suggested based on this premise.

Since we know that,

In the figure we that,

⇒ 2x + 1 = x +7

⇒        x  = 6

Similarly

⇒ 3y - 8 = y +5

⇒ y = 13/2

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Answer: is X = 5 within the diagram.

The correct statement about the two cells is:Cell Y has a large vacuole.

Cell X is described as having chloroplast, which is an organelle found in plant cells and is responsible for photosynthesis. This indicates that Cell X is a plant cell. Since the presence of chloroplast is mentioned specifically for Cell X and not for Cell Y, it implies that Cell Y is an animal cell, as animal cells do not contain chloroplasts.

Cell X having a cell membrane is not stated explicitly, and it is a characteristic shared by both plant and animal cells. Therefore, we cannot conclude whether Cell X has a cell membrane or not based on the given information.

The statement Cell X has a small vacuole is not mentioned in the provided characteristics, so we cannot determine the size of the vacuole in Cell X.

On the other hand, Cell Y not having a cell wall is mentioned, which is a characteristic specific to animal cells.Cell Y does not have a cell wall.

The correct statement based on the given information is that Cell Y has a large vacuole, while the other statements cannot be determined from the provided characteristics.

The correct statement about the two cells is: Cell Y has a large vacuole.

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Container #1 is the only one large enough to hold the contents of a one liter bottle of soft drink.

Container #1: The volume formula for a cylinder is V = πr²h, where r is the radius and h is the height.

Radius (r) = 8 cm / 2 = 4 cm

Height (h) = 19 cm

So, V1 = π(4 cm)²(19 cm)

≈ 3032.07 cm³

Container #2:

Radius (r) = 5 cm

Height (h) = 12 cm

Using the formula:

V2 = π(5 cm)²(12 cm)

≈ 942.48 cm³

Container #3:

Diameter (d) = 12 cm

Radius (r) = 12 cm / 2 = 6 cm

Height (h) = 10 cm

V3 = π(6 cm)²(10 cm)

≈ 1130.97 cm³

Now, Comparing the volumes:

V1 ≈ 3032 cm³

V2 ≈ 942 cm³

V3 ≈ 1131 cm³

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Area of shape 1:

Area of triangle = 1/2 × b × h

Area of triangle = 1/2 × 6 × 8

Area of triangle = 24 cm²

Area of shape 2:

Area of Semicircle = πr²/2

Radius of Semicircle = Diameter / 2

Radius of Semicircle = 3 cm

Then,

Area of semicircle = π(3)²

Area of semicircle = 9π cm²

Total Area = Area of semicircle + Area of triangle

Total Area  = (24 + 9π) cm²

Total Area = 52.27 cm² .

Hence Total area of the figure combining triangle and semicircle is 52.27 cm².

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You can determine the median of a triangle by looking out for the point that is 2/3 of the distance tht connects from the vertices, to midpoint and oposite sides.

The perpendicular bisector is determined by measuring the point that is equidistant from the segment.

The altitude of a triangle can be found by measiring the height of the triangle's extension that could be inside or outside the triangle. In obtsue triangles, this altitude is commonly found outside the triangle.

Also, the angle bisector of a triangle is the point that is equidistant from the angles sides. These descriptions can help in analyzing a trinagle.

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