Write the quadratic equation in standard form:
-12x + x² + 14 = -5x

The vector in component form whose tail is the point (−1,5), and whose head is the point (8,−6) is (-9, 11)

A vector is a physical quabntity thet has both magnitude and direction.

To find  the component form of the vector whose tail is the point (−1,5), and whose head is the point (8,−6), we proceed as folows

Since we have the points (-1, 5) and (8, -6) and we want the head to be at (8, -6),

Let A = (8, -6) and B = (-1, 5)

So, AB = B - A

= (-1, 5) - (8, -6)

= (-1 - 8), (5 - (-6))

= (-9, 5 + 6)

= (-9, 11)

So, the vector in component form is (-9, 11)

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The required two column proof is explained below.

A midpoint is a point which divides a line segment into two equal parts. Thus it can be referred to as the middle point of the line segment.

The two column proof for the information is given as:

M is the midpoint of CD    (Given)

CD = CM + MD   (addition property of a line segment)

CM = MD  (definition of a midpoint)

So that;

5x – 2 = 3x + 2    (Definition of midpoint)#

Then,

5x - 3x = 2 + 2 (collecting like terms)

2x = 4

x = 2

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Adding the number 6 to the given dataset did not affect the mode, as the number 19 still appeared the most frequently in the new dataset. (option c).

Now, if we add the number 6 to this dataset, we need to determine how this will affect the mode. We can start by looking at the number 19, which was the original mode. If the number 19 still appears the most frequently in the dataset after the addition of the number 6, then the mode will remain 19. However, if another number appears more frequently than 19 after the addition of 6, then the mode will change.

In this case, the number 6 does not appear anywhere in the original dataset, so it cannot be the mode. Therefore, the mode can either remain as 19 or change to a new number, depending on whether any other number appears more frequently than 19 after the addition of 6.

To determine if the mode changes, we need to calculate the frequency of each number in the new dataset. After adding 6, the dataset becomes:

18 24 19

19 18 20

26 25 19

6

From this dataset, we can see that the number 19 still appears twice, while all other numbers appear only once. Therefore, the mode of the new dataset is still 19, and the answer to your question is (C) "The mode will change to one number."

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Complete Question:

What happens to the mode of the data set shown below if the number 6 is added?

18 24 19

19 18 20

26 25 19

A The mode will change to two numbers.

B The mode will increase by 4.

C The mode will change to one number.

D The mode will increase by 2.

Sides AB = 3√2 and BC = 6.

The given triangle ABC is a right-angled triangle, as ∠BAC = 90°.

In the given right triangle ABC,

Hypotenuse of the triangle = BC

Base and height = AC and AB.

Also, we see from the diagram that ∠ACB and ∠ABC are equal.

∴ Triangle ABC is isosceles, with sides AC = AB = 3√2.

Now, by Pythagoras' theorem,

Hypotenuse² = Base² + Height²

Or, BC² = AC² + AB²

Or, BC² = (3√2)² + (3√2)²

⇒ BC² = 36

Or, BC = 6

Hence, sides AB = 3√2 and BC = 6.

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Answer:

Do whatever you want, but paying attention would really help you.

Step-by-step explanation:

If you find yourself bored in class, consider the following options to make the most of your time and stay engaged:

1. Actively participate: Ask questions, contribute to discussions, and try to engage with the material. Active participation can make the class more interesting and help you retain the information better.

2. Take notes: Focus on taking detailed notes, even if you think you understand the material. This will help you stay engaged and make it easier to review the content later.

3. Find connections: Try to relate the class material to your interests or real-world applications. This can make the content more engaging and relevant.

4. Set learning goals: Set specific learning objectives for each class, and try to achieve them during the session. This can help you stay focused and motivated.

5. Practice active listening: Pay attention to the teacher and try to understand the main points they are making. This can help you stay focused and better comprehend the material.

6. Break down the material: Divide the content into smaller chunks and focus on understanding each part. This can make the material more manageable and engaging.

7. Speak with your teacher: If you're consistently bored in class, consider discussing your concerns with your teacher. They may be able to offer suggestions or modify their teaching approach to better suit your learning style.

Remember, it's essential to stay engaged in class to maximize your learning experience and make the most of your education.

Answer:

watch RUN BTS EPISODE simple

Answer:A,D

Step-by-step explanation:

y = [5.3, 27]

x= [-1,3]

What does not make the context given as such is since PPI measures the change of the price the producer receives for their product and the CPI measure the change of the price the consumer pays for the product, one should rise while the other will fall. The Option D is correct.

This is because two indexes measure different things. The PPI measures change in prices of goods and services at the producer level while CPI measures the change in prices of goods and services at the consumer level.

That tells us PPI assess prices producers receive for their goods while CPI assess prices consumers pay for those same goods. So, while we have overlap between them, they are measuring different aspects of the economy and their trends may not always move in lockstep with each other.

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To perform this and any other construction in math, you need to use the right tools which include a compass, your drawing board or paper, and a clear understanding of the instruction.

A key to getting the shape and angles of any construction includes knowing what is required of you and implementing these in your construction. In the second slide, you are told to use the segment tool to create segment AB. This tool will be a scale and the measurement will be that of a  line AB.

Next, identify the radius of the circle. This is the point from the center of the circle to any line on the circle. Understanding the instructions is key to bisecting the segment and completing the other activities.

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Answer:

SA = 48 cm²

Step-by-step explanation:

the surface area (SA) is the sum of the areas of the 5 faces.

1 square and 4 congruent triangles form the pyramid

area of square = 4 × 4 = 16 cm²

area of triangle = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = 4 and h = 4

area = [tex]\frac{1}{2}[/tex] × 4 × 4 = 2 × 4 = 8 cm²

area of 4 triangles = 4 × 8 = 32 cm²

SA = 16 + 32 = 48 cm²

Answer:

x ≈ 6.5

Step-by-step explanation:

using the tangent ratio in the right triangle

tan25° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{14}[/tex] ( multiply both sides by 14 )

14 × tan25° = x , then

x ≈ 6.5 ( to the nearest tenth )

Answer:

[tex]a(1) = 144[/tex]

[tex]a(n) = 144{( - \frac{1}{6} )}^{n - 1} [/tex]

[tex]a(n) = - \frac{1}{6} a(n - 1)[/tex]

It looks like there are five data points in the box plot, representing Juan's total sales during each shift. The third data point is $200, which is the median value. Since there are an odd number of data points, we know that the median is exactly in the middle of the data set. This means that two of the data points are less than $200, and two of the data points are greater than $200.

The last data point is $300, which is the maximum value. So we know that only one of the data points is between $200 and $300. Therefore, the fraction of Juan's shifts that had total sales of $225 or more is 1/5, or 20%.

Answer:

Step-by-step explanation:

Answer:

<ABC + <CBD =180⁰

<ABC =180⁰ - <CBD

<ABC =180⁰ - 47⁰

<ABC =133⁰

The correct inequality to represent the normal temperature range of a dog is |t − 101.8| ≤ 0.7. So, correct option is B.

Here, |t - 101.8| represents the absolute value of the difference between the body temperature of the dog (t) and the average temperature of dogs (101.8° F). The inequality states that this absolute value must be less than or equal to 0.7° F, which is the maximum amount that the temperature of a dog can vary from the average.

If the temperature of a dog is within this range, it is considered to have a normal body temperature. If the temperature is outside this range, it may indicate an underlying health issue or illness.

The other answer choices are incorrect because they do not accurately represent the relationship between the body temperature of a dog and the normal temperature range. For example, |t - 0.7| ≥ 101.8 makes no sense in the context of the problem, as there is no logical reason to subtract 0.7 from the body temperature.

So, correct option is B.

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(a) The lesson time in 2007 is 11.1% more than the lesson time in 2006.

(b) The lesson lasted 40 minutes in 2005.

(c) James will take 180 seconds to swim 100 meters in a year's time.

(d)  Robert will also take 180 seconds to swim 100 meters in a year's time.

(e) James and Robert will swim equally which means that their speed will be same and they will be complete at same time.

(a) The increase in lesson time from 2006 to 2007 is:

Increase = 50 - 45 = 5 minutes

The percentage increase is:

Percentage increase = (5 / 45) x 100% = 11.1%

Therefore, the lesson time in 2007 is 11.1% more than the lesson time in 2006.

(b) Let x be the lesson time in 2005. The lesson time in 2007 is 25% more than it was in 2005, so:

1.25x = 50

Solving for x, we get:

x = 40

Therefore, the lesson lasted 40 minutes in 2005.

(c) James currently takes 240 seconds to swim 100 meters. If he improves his time by 25%, his new time will be:

New time = 240 - (0.25 x 240) = 180 seconds

Therefore, he will take 180 seconds to swim 100 meters in a year's time.

(d) Robert currently takes 240 seconds to swim 100 meters. If he increases his speed by 25%, his new time will be:

New time = 240 - (0.25 x 240) = 180 seconds

Therefore, he will also take 180 seconds to swim 100 meters in a year's time.

(e) Both James and Robert will take the same time to swim 100 meters in a year's time, so they will be equally fast.

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$9,664.47

After 15 years the account will have $9,664.47

If Cole brought 21 cans and his sister brought 7 cans less, then the total number of cans brought by them is 35 cans.

The number of cans which Cole brought = 21 cans of food.

His sister brought in 7 fewer cans than he did, which means she brought in:

⇒ 21 - 7 = 14 cans of food,

Let the total number of food-cans be = "f",

So, the equation to find the number of cans is written as :

⇒ x = 21 + 14,

On adding the number of cans,

We get,

⇒x =  21 + 14 = 35,

Therefore, together they brought in 35 cans of food.

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The resulting z-test statistic is 0.44, indicating that the evidence is not significant enough to reject the null hypothesis that the probability of heads is equal to 0.5.

The problem we are trying to solve is to determine if the sample proportion of heads obtained from spinning a penny 300 times (134 heads) is significant evidence against equal probabilities of heads and tails. To do this, we will be testing the null hypothesis H0: p = 0.5, which states that the probability of getting heads is equal to 0.5.

We can calculate the z-test statistic using the formula z = (sample proportion - hypothesized proportion) / (standard error). In this case, the z-test statistic is z = (0.444 - 0.5) / (√(0.5 * 0.5 / 300)) = -0.86. This means that the sample proportion of heads is 0.86 standard errors away from the hypothesized proportion of 0.5.

Therefore, the resulting z-test statistic is 0.44, indicating that the evidence is not significant enough to reject the null hypothesis that the probability of heads is equal to 0.5.

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Answer: The correct answer is B

Step-by-step explanation:

Remember that the coordinates (4,π3) tell us the radius r=4 and the angle θ=π3. So the point should be on the circle labeled 4 and form an angle of π3 with the positive x-axis. Point B is the correct point

Answer:

2013 - $880,000

2019 - $640,000

Step-by-step explanation:

The office building is being depreciated linearly over 25 years, which means the annual depreciation rate is:

Depreciation rate = (Cost - Scrap value) / Useful life = ($1,000,000 - $0) / 25 = $40,000 per year

To find the book value of the building in 2013, we need to determine how many years have elapsed since 2010. Since 2013 is three years after 2010, the building has been depreciated for three years. Therefore, the book value in 2013 is:

Book value in 2013 = Cost - Depreciation = $1,000,000 - ($40,000/year x 3 years) = $880,000

To find the book value of the building in 2019, we need to determine how many years have elapsed since 2010. Since 2019 is nine years after 2010, the building has been depreciated for nine years. Therefore, the book value in 2019 is:

Book value in 2019 = Cost - Depreciation = $1,000,000 - ($40,000/year x 9 years) = $640,000

Therefore, the book value of the building was $880,000 in 2013 and will be $640,000 in 2019.

Answer:

3/5

Step-by-step explanation:

opposite/hypotenuse

21/35

Simplify by dividing by 7 on the numerator and denominator

3/5

The total length of the nylon rope that Jamie will use would be 15.3 feet of nylon rope.

Within this scenario specifically, one side of the right-angled triangle comprises the height of the tent (standing at 6.5-feet), and the other forms as the measure from the center of the tent to where Jaime stakes the ropes stretching outwards in another direction (with a calculated measure of 4-feet). Subsequently, we will refer to the extent of the nylon rope as R.

The Pythagorean theorem formula is:

R ² = 6.5 ² + 4 ²

R ² = 42. ²25 + 16

R ² = 58.25

R = 7. 63 ft

There are two ropes so the length would be :

= 7. 63 + 7. 63

= 15. 3 ft

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The surface area of the rectangular prism in this problem is given as follows:

A. 426 m².

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas. -> net method.

By the net method, the prism is divided as follows:

Hence the surface area of the prism is given as follows:

S = 2(5 x 12 + 5 x 9 + 12 x 9)

S = 426 m².

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Three ordered pairs that could represent the location of another vertex of the square are (7, 2), (-5, 2), (1, 8).

To find the possible locations of the other vertices of the square, we need to determine the distance from point K to any other vertex of the square. Since the perimeter of the square is 20 units, each side of the square has a length of 20/4 = 5 units.

One way to find the other vertices is to draw a circle with center at K and radius 5 units, and then look for points on the circle that have integer coordinates. Alternatively, we can use the distance formula to calculate the distance from K to another point (x, y), which must be 5 units, and then solve for y in terms of x.

Using the distance formula, we get:

[tex]\sqrt{(x-1)^{2} +(y-1)^{2} }[/tex] = 5

Simplifying and squaring both sides, we get:

(x-1)^2 + (y-2)^2 = 25

Expanding the left side and simplifying, we get:

[tex]x^{2}[/tex] - 2x + [tex]y^{2}[/tex] - 4y + 20 = 0

Completing the square for x and y, we get:

[tex](x-1)^{2}[/tex]  + [tex](y-1)^{2}[/tex]  = [tex]6^{2}[/tex]

This is the equation of a circle with center at (1, 2) and radius 6 units. Any point on this circle that has integer coordinates could be a vertex of the square, since it will be exactly 5 units away from K.

Using this method, we can find several possible locations of the other vertices of the square. Three of them are:

(7, 2), (-5, 2), (1, 8)

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Answer:

[tex]a_{n}[/tex] = 3[tex]a_{n-1}[/tex] : a₁ = 7

Step-by-step explanation:

a recursive formula allows a term in the sequence to be found from the preceding term.

the sequence here has a common ratio between consecutive terms

[tex]\frac{21}{7}[/tex] = [tex]\frac{63}{21}[/tex] = 3

thus to find a term in the sequence multiply the previous term by 3, that is

[tex]a_{n}[/tex] = 3[tex]a_{n-1}[/tex] : first term a₁ = 7

Answer:

Okay, let's break this down step-by-step:

   The initial point is P(-4, 5)

   The terminal point is Q(-2, 7)

To find the components of the vector V, we need to determine:

   The change in x-coordinate = -4 - (-2) = -2

   The change in y-coordinate = 5 - 7 = -2

So the vector components are:

<change in x-coordinate, change in y-coordinate>

= <-2, -2>

Therefore, the answer is choice (i): < -2,-2>

The other choices do not represent the correct changes between the given points P and Q.

Step-by-step explanation:

The equation (x+7)x^2 -(x-3)x^2 =(x+35)x^2 -(x+34)x^2 has no solution for x

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

(x+7)x^2 -(x-3)x^2 =(x+35)x^2 -(x+34)x^2

Divide through the equation by x^2

so, we have the following representation

(x+7) -(x-3) = (x+35) -(x+34)

When the brackets are removed and the like terms are evaluated, we have

2x + 10 = 2x - 1

Evaluate the like terms again

So, we have

10 = -1

The above equation is false

Hence, the equation has no solution for x

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Answer:

the corresponding sides are proportional

Answer: 358 miles

Step-by-step explanation:

Answer: 385

Step-by-step explanation: 77x5

Answer:

C. Points have no size and no dimensions.

Answer:

I think it is choice A and choice C