Complete the statements below that show y = 8x2 + 32x + 17 being converted to vertex form.

Factor out the leading coefficient.

y = 8(x2 + 4x) + 17

Form a perfect-square trinomial.

Answer: Add to eliminate x

Step-by-step explanation:

So if you add to 2 equations you can look at it this way. remove all variables right that leaves you with 10+4=48 and -10-3=-56 right and if you add 10 and -10 you get 0 or 0x so by adding these to equations x is eliminated by adding

A temperature change of 20°C corresponds to a Fahrenheit temperature change of 36°F. The Fahrenheit scale has a different conversion formula than the Celsius scale, resulting in a larger change in degrees for the same temperature difference.

To convert from Celsius to Fahrenheit, we use the formula: F = (C * 9/5) + 32, where F represents the temperature in Fahrenheit and C represents the temperature in Celsius.

In this case, the temperature change is given as 20°C. To find the corresponding Fahrenheit temperature change, we apply the conversion formula: F = (20 * 9/5) + 32 = 36 + 32 = 68°F.

Therefore, a temperature change of 20°C corresponds to a Fahrenheit temperature change of 68°F. Among the given answer choices, the closest option is 36°F.

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A total of 81 apples and 72 spears are there in total.

Ratio is a quantitative relation between two amounts showing the number of times one value contains or is contained within the other. A statement expressing the equality of two ratios A:B and C:D is called a proportion. We can express proportion as -

A : B ∷ C : D

AND

A x D = B x C

Product of extremes equal to product of means.

Given is in a Petri café they discovered that as many apples as pears are rotten, ⅔ of all apples are rotten and that ¾ of all pears are rotten.

Assume that there are [x] apples and [y] pears in total.

Then, rotten apples = 2x/3

rotten paears = 3y/4

Since, they are equal, we get -

2x/3 = 3y/4

2x (4) = 3y (3)

8x = 9y

The whole number coordinates satisfying the equation are - (81, 72). Refer to the graph attached.

Therefore, a total of 81 apples and 72 spears are there in total.

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Answer:

A. Scale z by a factor of 1/6, then rotate clockwise by pi/8 radians.

Step-by-step explanation:

EDGE 2020

The geometric transformation of z that describes the quotient z/w is A. Scale z by a factor of 1/6, then rotate clockwise by pi/8 radians.

It should be noted that transformation means change. Therefore, a geometric transformation means changes in a geometric shape.

From the complete information, the complex numbers z = 30 (cos(2pi/3) + sin(2pi/3)) and w = 6 (cos(pi/8) + sin(pi/8).

The geometric transformation of z on the complex plane that describes the quotient z/w will be to scale z by a factor of 1/6, then rotate clockwise by pi/8 radians.

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The probability of getting at least one tails on the last two flips is 8/25.

The probability of getting a tails on a single toss of the coin is 3/5. Therefore the probability of getting tails on the last two flips is (3/5)^2. This is because the coin tosses are independent of one another.

Therefore the probability of getting at least one tails on the last two flips is 1 - (3/5)^2 = 8/25.

This is because the probability of getting two tails is (3/5)^2, and the probability of getting at least one tails is the complement of that. Therefore the probability of getting at least one tails on the last two flips is 8/25.

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The first five terms of the sequence are {-9, 54, -324, 1944, -11664}.Hence, the first five terms of the sequence are {-9, 54, -324, 1944, -11664}.

Given that a1 = -9 and an = -6an-1 to find the first five terms of an: {a1, a2, a3, a4, a5}

We have to use the formula an = -6 an-1 to find the next terms.

The first term a1 is given to us. So, a1 = -9

We can use the formula an = -6an-1 to find the next term using a1= -9 an1 = -6 * a1 = -6 * (-9) = 54

Thus the first two terms of the sequence are {-9, 54}.

We can use the formula an = -6an-1 to find the third term an2 = -6 * an1= -6 * 54 = -324

Thus the first three terms of the sequence are {-9, 54, -324}.

We can use the formula an = -6an-1 to find the fourth term an3 = -6 * an2= -6 * (-324) = 1944

Thus the first four terms of the sequence are {-9, 54, -324, 1944}.

We can use the formula an = -6an-1 to find the fifth term an4 = -6 * an3= -6 * (1944) = -11664

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The diameter of a wire significantly impacts its strength, range, and stiffness.

1. Strength: As the diameter of a wire increases, its overall strength improves. A larger cross-sectional area allows the wire to withstand greater forces before breaking. This is because the increased material can distribute force more effectively, resulting in enhanced tensile strength.

2. Range: The diameter of a wire also influences its range or length. Thicker wires tend to have shorter range capabilities compared to thinner wires. As the diameter increases, the weight and stiffness of the wire rise as well, making it harder to extend or coil over long distances. Conversely, thinner wires are more flexible and lightweight, enabling them to cover greater lengths.

3. Stiffness: Lastly, the diameter of a wire impacts its stiffness, which is the resistance of the wire to bending or deformation. With a larger diameter, the stiffness of the wire increases due to the higher amount of material present. This means that it requires more force to bend or change the shape of the wire, resulting in greater rigidity. On the other hand, wires with smaller diameters are more pliable and can easily be bent or manipulated.

In summary, the diameter of a wire plays a crucial role in determining its strength, range, and stiffness. Thicker wires exhibit enhanced strength and stiffness but may have limited range capabilities, while thinner wires are more flexible and suitable for longer distances but may not be as strong or rigid.

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The length of BC rounded to 3 significant figures is 6.98.

Since ∠cab = 90°, we can use the Pythagorean Theorem to find the length of AB.

Let's call BC = x, then we have:

sin(65°) = AB/BC

AB = sin(65°) * BC

In right triangle ABC, we have:

AB^2 + BC^2 = AC^2

(sin(65°) * BC)^2 + BC^2 = 8.9^2

Solving for BC, we get:

BC = 8.9 / sqrt(sin^2(65°) + 1)

BC ≈ 6.98

Therefore, the length of BC rounded to 3 significant figures is 6.98.

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Answer:

2 - 6 = -4

Step-by-step explanation:

First, take the 2, and find how many it takes to get to 0, which is 2. So, with the number we are subtracting, which is 6, minus 2 from that to be left with 4.

Now we are at 0 with -4 left.

0 - 4 = -4

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Answer:

0.4

Step-by-step explanation:

Using the proportional method,

We take "x" as cups of red paint needed to make a shade of pink

Using cross multiplication

7x=3

x = \(\frac{3}{7}\)

x = 0.4

Answer:

115

Step-by-step explanation:

So you've already driven 124, so you would just subtract taht from 239

Answer:

0.1422 %

Step-by-step explanation:

$93.18 - $78.96 = $14.22

Move the decimal in 14.22 two spaces to the right and put a zero after the decimal point.

0.1422 %

I hope this helps u! :D

Answer:

The measures of the acute angles are 38 and 52 degrees.

Step-by-step explanation:

In a right triangle, there are three angles, a right angle and two acute angles. In every traingle, the sum of the measures of the angles is 180 degrees. Let's call the acute angles \(a\) and \(b\).

\(a + b +90 = 180\)

The problem also says that one angle is twice the difference of the other angle and 12. That would look like this:

\(a = 2(b-12)\)

Now we have two equations. If we simplify them, we get these:

\(\left \{ {{a=90-b} \atop {a=2b-24}} \right.\)

Now you can substitute \(a\) in the first equation for \(a\) in the second equation

\(90-b=2b-24\)

Add \(b\) to both sides of the equation

\(90 = 3b-24\)

Add \(24\) to both sides

\(114 = 3b\)

Divide both sides by 3

\(38 = b\)

Now, you can substitute \(38\) for \(b\) in the first equation and simplify.

\(a = 90-38\)

\(a=52\)

Therefore,

\(a=52\), and \(b=38\)

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The value of the angles are 38° and 52° respectively

Let the acute angles be represented by a and b.

Based in the information given,

a = 2(b - 12)

a = 2b - 24.

Note that the angle in an acute angle equals to 90°.

Therefore,

a = 90 - b.

a = 2b - 24

Equate the equations together

90 - b = 2b - 24

2b + b = 90 + 24

3b = 114

b = 114/3

b = 38

Therefore, a will be:

= 90° - 38° = 52°

The value of the angles are 38° and 52° respectively.

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Answer:

The fourth option is the answer.

Step-by-step explanation:

This parabola is in vertex form, the vertex is (5,4)

Since a is negative, the parabola will facing and opening downwards, so this means our vertex is the highest possible y value. So our range will be (- infinity, 4).

A domain of a Parabola accept in real number so the domain there is all reals or negative ♾ to positive ♾.

The  the savings, expressed in percent if you order the combo is 18.75%, if the combo is bought at $6.50

What is the amount saved when combo is ordered?

The amount saved when ordering for combo instead of ordering hamburger and French fries is the difference between the total cost cost when for individual orders and the cost of the combo

total cost for individual orders=$5.00+$3.00

total cost for individual orders=$8.00

combo cost=$6.50

savings on combo=total cost for individual orders-combo cost

savings on combo=$8.00-$6.50

savings on combo=$1.50

% savings on combo=$1.50/$8.00

% savings on combo=18.75%

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Answer: all real numbers less than or equal to 3

Step-by-step explanation: third option

letter c

Answer:

all real numbers less than or equal to 3

Step-by-step explanation: Took the test

Answer:

it has a frequency of 5

Step-by-step explanation:

Answer:

its a  on edge 2022

Step-by-step explanation:

We need to check if 13 divides (20192018 - (1-1)") + 4H0. By performing the calculations, we find that 13 does not divide (20192018 - (1-1)") + 4H0. Hence, 20192018 is not divisible by 13.

To prove that 13 divides a number "a" if and only if 13 divides (an - (1-1)") + 4H0, we need to show that both conditions imply each other
First, let's assume that 13 divides "a". This means that "a" can be written as 13k, where k is an integer. We can express this in terms of base 10 as (13k - (1-1)") + 4H0. Simplifying further, we get (13k - 1) + 4H0. Since 13 divides 13k and 13 divides 4H0, it also divides their sum. Therefore, if 13 divides "a", it also divides (an - (1-1)") + 4H0.
Next, let's assume that 13 divides (an - (1-1)") + 4H0. This means that (an - (1-1)") + 4H0 can be written as 13k, where k is an integer. Simplifying the expression, we get an - (1-1)") + 4H0 = 13k. Rearranging, we have an = 13k + (1-1)") + 4H0. Since 13 divides 13k + (1-1)") + 4H0, it also divides their sum. Therefore, if 13 divides (an - (1-1)") + 4H0, it also divides "a".
In conclusion, we have proven that 13 divides "a" if and only if 13 divides (an - (1-1)") + 4H0.
To decide whether 20192018 is divisible by 13, we can apply the result from part (a). Let's express 20192018 as (an - (1-1)") + 4H0. Since 13 divides (an - (1-1)") + 4H0, if 13 divides 20192018, it will also divide (an - (1-1)") + 4H0. Therefore, we need to check if 13 divides (20192018 - (1-1)") + 4H0. By performing the calculations, we find that 13 does not divide (20192018 - (1-1)") + 4H0. Hence, 20192018 is not divisible by 13.

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Answer:

\(=\frac{4x+12}{7y-28}\)

Step-by-step explanation:

Four times a number (let's call this x) is added to twelve. In other words, this is:

\(4x+12\)

Now, this entire thing is divided by seven times a different number (let's use y) minus twenty-eight. So:

\((4x+12)\div (7y-28)\)

Let's put it into a fraction to simplify. Remember that dividing something by something else is the same as putting it over fraction. Thus:

\(=\frac{4x+12}{7y-28}\)

And we're done!

Answer:

12 + 4x

7y - 28

Step-by-step explanation:

Here we have 4 times a number is added to 12. So let's say that number is "x". Now we have 4x plus the 12 to get 4x + 12 And that is divided by 7 times a different number minus 8.

So 7 times a different number "y" is the same as 7y and put in that minus 28 to get 7y - 28 and don't forget the dividing!

It'll end up being;

12 + 4x

7y - 28

Hope this helps and have a great day!

Answer:  -3/5

Step-by-step explanation: If you compare these integers to their opposite, one will be 3/5, and the other will be -2, which is still negative. Let me know if this is right.

In "gas-mileage" experiment : (a) "gasoline-brand" is "categorical-variable" and weight is "quantitative-variable".

In this experiment, the brand of gasoline is a categorical variable because it represents different distinct categories or labels, namely Amoco, Marathon, and Speedway. Gasoline brands cannot be measured on a numerical scale, but rather they represent different brands.

The weight of the car is a quantitative variable because it can be measured on a numerical scale. The weight is given in pounds and represents a continuous range of values, such as 3,000, 3,500, or 4,000 pounds. It can be measured and compared using mathematical operations, such as addition or subtraction.

Therefore, the correct option is (a).

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The given question is incomplete, the complete question is

You are planning an experiment to determine the effect of the brand of gasoline and the weight of a car on gas mileage measured in miles per gallon. You will use a single test car, adding weights so that its total weight is 3,000, 3,500, or 4,000 pounds. The car will drive on a test track at each weight using each of Amoco, Marathon, and Speedway gasoline.

In the gas mileage experiment,

(a) gasoline brand is a categorical variable and weight is a quantitative variable.

(b) gasoline brand and weight are both categorical variables.

(c) gasoline brand and weight are both quantitative variables.

(d) gasoline brand is a quantitative variable and weight is a categorical variable.

Databases of variants are crucial in helping to identify disease gene candidates. Here's how they are used:

1. Collect and store genetic variants: Databases collect and store genetic variants from various individuals, including those with specific diseases and those without.

2. Compare variants between groups: By comparing the variants in affected individuals to those in unaffected individuals, researchers can identify variants that are more common in the disease group. This helps to narrow down the list of potential disease-causing genes.

3. Calculate probability: Databases can be used to calculate the probability of certain variants appearing in the general population. If a variant is rare in the general population but more common in individuals with a specific disease, it may be more likely to be a disease-causing variant.

4. Filter out common variants: As you mentioned, variants that are common in the general population or present in individuals without the disease are less likely to cause a rare genetic disease. By filtering out these common variants, researchers can focus on rare variants that may have a stronger association with the disease.

5. Identify disease gene candidates: Through this process of comparing and filtering genetic variants, researchers can identify potential disease gene candidates that warrant further investigation.

In summary, databases of variants help researchers identify disease gene candidates by storing genetic information, enabling comparison between affected and unaffected individuals, calculating variant probabilities, filtering out common variants, and ultimately pinpointing rare variants that may be associated with specific genetic diseases.

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Answer:

Vertex.

Step-by-step explanation:

There are 3 medians in a triangle.

Answer:

The answer is vertex

Step-by-step explanation:

The length of tangent CD is 2 unit.

Tangent of a circle is a straight line which touches the circle at only one point.

Therefore,

AB = AD = radius = 1.5

∠D = 90 degrees

Using Pythagoras theorem,

AC² = AD² + CD²

AC = 1.5 + 1 = 2.5

AD = 1.5

Therefore,

2.5² - 1.5² = CD²

CD² = 6.25 - 2.25

CD² = 4

CD = √4

CD = 2

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After plotting the inequalities, we see that the second set satisfies the graph provided.

How can we graph inequalities?

A linear or quadratic inequality can be graphed in a manner similar to that of an equation. The distinction is that an inequality displays a range of values greater than or less than, thus your graph will display more than just a dot on a number line or a line on a coordinate plane. You can figure out which numbers are part of an inequality solution by utilizing algebra and evaluating the inequality sign.

Let the first inequality be  \(3x+5y\leq 10\).

When we plot the equality, we see that it covers the portion including the origin.

Next inequality is \(-x+y > -5\).

When plotting this one, we again see that it covers the portion including the origin.

The last equality is \(y-6 > -5x\).

While plotting it, we see that this line overlaps the other 2 lines making a common space of the triangle that is shown in the figure.

Hence the second set of inequalities represent the graph.

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After plotting the inequalities, we see that the second set satisfies the graph provided.

How can we graph inequalities?

To graph inequalities, you can use a number line or a coordinate plane. Here's an example of how to graph an inequality on a number line:

First, determine the inequality symbol: >, <, ≥, or ≤.

Next, determine the value of the inequality.

Plot the value on the number line, using an open circle for > or <, and a closed circle for ≥ or ≤.

Shade in the region on one side of the plotted point, according to the inequality symbol. For example, if the inequality is x > 3, then you would shade in the region to the right of 3, since values greater than 3 satisfy the inequality.

Here's an example of how to graph an inequality on a coordinate plane:

First, determine the inequality symbol: >, <, ≥, or ≤.

Next, rewrite the inequality in the form "y > f(x)" or "y < f(x)" by isolating the y term on one side of the inequality.

Plot the function f(x) on the coordinate plane.

Shade in the region above or below the plotted function, depending on the inequality symbol. For example, if the inequality is y > f(x), then you would shade in the region above the plotted function, since values of y greater than f(x) satisfy the inequality.

Let the first inequality be \(3x+5y\leq 10\)

When we plot the equality, we see that it covers the portion including the origin.

Next equality is \(-x+y > -5\)

When plotting this one, we again see that it covers the portion including the origin.

The last equality is \(y-6 > -5x\)

While plotting it, we see that this line overlaps the other 2 lines making a common space of the triangle that is shown in the figure.

Hence the second set of inequalities represent the graph.

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The value of the cylindrical coordinates of the region W with the given conditions 13 ≤ z ≤ 1 and x^2 + y^2 + z^2 ≤ 1 is given by (2π/3)(1 - (1/3)^3)^(3/2).

Let us consider cylindrical coordinates as ( ρ , θ, z )

ρ =Distance from origin to point present in xy-plane

θ =  Angle measured counterclockwise direction from the positive x-axis

z = Vertical distance from the xy-plane

Substitute cylindrical coordinates as

x = ρ cos θ

y = ρ sin θ

z = z

In the equation ,

(x²+ y² + z²)^(-1/2) dx dy dz

= (ρ² cos² θ + ρ² sin² θ + z² )^(-1/2) ρ dρ dθ dz

= (ρ² + z²)^(-1/2) ρ dρ dθ dz

According to the condition

(x²+ y² + z²) ≤ 1

⇒ ρ² + z² ≤ 1

And 13 ≤ z ≤ 1

⇒z ∈ [13, 1]

⇒Region W can be expressed in the form,

W = { (ρ, θ, z) : 0 ≤ ρ ≤ 1, 0 ≤ θ ≤ 2π, 13 ≤ z ≤ 1, ρ² + z² ≤ 1 }

Now taking integration in the region for the given condition we have,

∫∫∫W(x²+ y² + z²)^(-1/2) dx dy dz

= ∫∫∫W(ρ² + z²)^(-1/2) ρ dρ dθ dz

= \(\int_{0}^{1}\int_{0}^{2\pi }\int_{1}^{13}\)(ρ² + z²)^(-1/2) ρ dρ dθ dz

Using standard techniques of integration we have,

= (2π/3)(1 - (1/3)^3)^(3/2)

Therefore, the value of the cylindrical coordinates of the region as per conditions is equal to (2π/3)(1 - (1/3)^3)^(3/2).

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The above question is incomplete , the complete question is:

Evaluate the following by using cylindrical coordinates. W (x^2 + y^2 + z^2)^(−1/2) dx dy dz, where W is the region determined by the conditions 13 ≤ z ≤ 1 and x^2 + y^2 + z^2 ≤ 1

The total amount of water Carlos drank throughout the day is 2.65 liters.

In order to calculate the total amount of water Carlos drank throughout the day, we must add all the amounts that he drank. The total amount of water Carlos drank during the day is equal to:

1/5 liters + 3/4 liters + 7/20 liters

This can be expressed in fraction form as:

\(\frac{19}{20} + \frac{27}{20} + \frac{7}{20} = \frac{53}{20}\)

= 2.65 liters

Therefore, Carlos drank a total of 2.65 liters of water throughout the day.

To calculate this, we can use the addition of fractions formula. This formula states that to add two fractions, we must find the least common denominator of the two fractions, and then add the numerators of the two fractions.

In this case, the least common denominator of the three fractions is 20. This is because all three fractions have a denominator of 20, and 20 is the smallest number that can be divided by both 5 and 4.

Once we have the least common denominator, we can add the numerators of the fractions. For the first fraction, 1/5, the numerator would be 1, for the second fraction, 3/4, the numerator would be 3, and for the third fraction, 7/20, the numerator would be 7.

Therefore, the addition of fractions formula would look like this:

\(\frac{1 + 3 + 7}{20}\\\\ = \frac{11}{20}\\\\ = 2.65 liters\)

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Answer:

Our calculator limits your interest deduction to the interest payment that would be paid on a $1,000,000 mortgage. Interest rate: Annual interest rate for this

Step-by-step explanation:

Jeff's savings account, which earns simple interest, has a total amount of 10,405.2 today after 2 years.

Simple interest is given by the formula:

SI = PTR/100

Where SI = simple interest

P = principal

R = interest rate (in percentage)

T = time duration (in years)

If he deposited 8700 into the account 2 years ago and earns interest at a rate of 9.8%, then using the formula, the amount of interest earned can be determined.

SI = PTR/100

SI = 8700(2)(9.8)/100

SI = 1705.2

To get the total amount on his account, add the interest earned to the principal amount he deposited.

total amount = 8700 + 1705.2

total amount = 10,405.2

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