Find the roots of the parabola given by the following equation.

2x2+ 5x - 9 = 2x

Answer:

A = 27π cm² or A ≈ 84.823... cm²

Step-by-step explanation:

From being shown that the missing area is 90 out of 360°, we know that we need to find 75% of the area of the given circle.

Our equation is altered to: A = 0.75πr²

Plug in: A = 0.75π(6)²

Multiply: A = 27π cm²

If you were instructed to multiply pi and round (which is not as probable given that this is RSM), then the answer would be A ≈ 84.823... cm²

Answer:

Exact answer: [tex]27\pi[/tex]

Answer rounded to nearest hundredths: 84.82 using the pi button and not 3.14.

Step-by-step explanation:

Let's pretend for a second the whole circle is there.

The area of the circle would be [tex]A=\pi r^2[/tex] where [tex]r=6[/tex] since 6 cm is the length of the radius.

So the area of the full circle would have been [tex]A=\pi \cdot 6^2[/tex].

[tex]A=\pi \cdot 6^2[/tex]

Simplifying the 6^2 part gives us:

[tex]A=\pi \cdot 36[/tex]

or

[tex]A=36 \pi[/tex]

Now you actually have one-fourth (because of the 90 degree angle located at the central angle) of the circle missing so our answer is three-fourths of what we got from finding the area of the full circle.

So finding three-fourths of our answer means taking the [tex]36\pi[/tex] we got earlier and multiplying it by 3/4.

This means the answer is [tex]\frac{3}{4} \cdot 36\pi[/tex].

3/4 (36)=3(9)=27

So the answer is [tex]27\pi[/tex]

Answer:

Step-by-step explanation:

We can prove it through different facts but we will use the fact of  alternate interior angles formed by a transversal with two parallel lines are congruent.

Look at the figure for brief understanding.

Construct a line through B parallel to AC. Angle DBA is equal to CAB because they are a pair of alternate interior angle(alternate interior angles are two interior angles which lie on different parallel lines and on opposite sides of a transversal) The same reasoning goes with the alternate interior angles EBC and ACB....

The sum of the interior angles of a triangle is 180 degrees, which can be demonstrated using properties of parallel lines, alternate interior angles, and Euclidean geometry axioms. By drawing a parallel line and using congruent angles, we show that the sum of angles in a triangle aligns with the angle sum on a straight line.

One classic proof that the sum of the interior angles of a triangle is 180 degrees involves drawing a parallel line to one side of the triangle through the opposite vertex. Let's name the vertices of our triangle A, B, and C. Extend a line from vertex C that is parallel to the line AB. This forms alternate interior angles with the angles at vertices A and B, which we know are equal because of the properties of parallel lines.

Call the angles at A and B in the triangle, angle A and angle B, respectively. Outside of the triangle, we have angles formed between the extended line and the lines AC and BC, let's call these angles A' and B'. By the property of parallel lines and angles, angle A is congruent to angle A' and angle B to angle B'. The line through C forms a straight line, so angle A' plus angle C plus angle B' must equal 180 degrees. Since angle A is congruent to angle A' and angle B to angle B', we can then say that angle A plus angle B plus angle C equals 180 degrees. This is because the sum of the interior angles at A and B and the newly defined angle C is equal to the sum along the straight line, which is always 180 degrees.

Moreover, considering the Euclidean geometry axioms, we know that the sum of angles in a triangle is inherently 180 degrees, and this can be seen in the equilateral triangle example where if we take the large triangle and divide it into four smaller congruent triangles, each of these smaller triangles also has the property that the sum of its angles equals 180 degrees. When we add up the angles from the four small triangles and subtract the sum of the straight angles formed at the large triangle's sides, the result confirms the sum for the large triangle is equivalent to four times the sum for one small one, reinforcing the 180-degree sum rule for each triangle.

Answer:

  3 1/3

Step-by-step explanation:

Right side segments are proportional to left side segments:

  5/6 = x/4

  x = 4·5/6 = 3 1/3 . . . . . multiply by 4

Answer:

  2√13

Step-by-step explanation:

The distance formula is useful for this. One end of the vector is (0, 0), so the measure of its length is ...

  d = √((x2 -x1)² +(y2 -y1)²) = √((6 -0)² +(-4-0)²)

  = √(36 +16) = √52 = √(4·13)

  d = 2√13 = |(6, -4)|

Answer:

x = 18.

Step-by-step explanation:

As they are congruent, BC = DC  so

x + 12 = 2x - 6

12 + 6 = 2x - x

x = 18.

Answer:

x=18

Step-by-step explanation:

Because of the SSS criterion, The congruent sides are equal to each other. Meaning, Side AB is congruent to side AD. With this, you can set side BC and side DC equal to each other to solve for x.

x+12=2x-6

You subtract x to both sides;

12=x-6

You then add 6 to both sides to get x alone.

18=x or x=18.

Answer:

  126

Step-by-step explanation:

The number of numbers divisible by 9 is ...

  j = floor(500/9) = 55

The number of numbers divisible by 7 is ...

  k = floor(500/7) = 71

Then the total (j+k) is ...

  j +k = 55 +71 = 126

Answer: y int: (0,9)    x int: (3,0)

Step-by-step explanation:

In slope intercept form, the equation is y=-3x+9. In the formula y=mx+b, we know b is the y intercept, so our y int. is 9. To find our x intercept, we set y=0. So, 0=-3x+9=>3x=9=>x=3

Answer:

more the z-score more will be the extreme. therefore tallest man has high extreme

Step-by-step explanation:

Formula for z-score: [tex]\frac{X-\mu }{\sigma}[/tex]

where

X is height of tallest man

μ mean height

σ is standard deviation

z score for tallest is

z-score = [tex]\frac{ 262 - 175.32}{8.17} = 10.60[/tex]

similarly for shortest man

z-score = [tex]\frac{68.6 - 175.32}{8.17} = - 13.06[/tex]

more the z-score more will be the extreme. therefore tallest man has high extreme

Answer:

The shortest living man's height was more extreme.

Step-by-step explanation:

We have been given that the the tallest living man at one time had a height of 262 cm. The shortest living man at that time had a height of 68.6 cm. Heights of men at that time had a mean of 175.32 cm and a standard deviation of 8.17 cm.

First of all, we will find z-scores for both heights suing z-score formula.

[tex]z=\frac{x-\mu}{\sigma}[/tex]

[tex]z=\frac{68.6-175.32}{8.17}[/tex]

[tex]z=\frac{-106.72}{8.17}[/tex]

[tex]z=-13.06[/tex]

[tex]z=\frac{x-\mu}{\sigma}[/tex]

[tex]z=\frac{262-175.32}{8.17}[/tex]

[tex]z=\frac{86.68}{8.17}[/tex]

[tex]z=10.61[/tex]

Since the data point with a z-score [tex]-13.06[/tex] is more away from the mean than data point with a z-score [tex]10.61[/tex], therefore, the shortest living man's height was more extreme.

Answer:

Renting a vehicle when there are 5 cars, 3 vans, and 10 sports utility vehicles available

Step-by-step explanation:

Creating a stuffed animal when there are 6 animals, 3 fur colors, and 12 clothing themes available

This condition requires multiplication or factorials to determine outcomes

Renting a vehicle when there are 5 cars, 3 vans, and 10 sports utility vehicles available

This situation requires the addition counting principle to determine the number of possible outcomes as there is only one car to be picked so all the numbers 10+5+3 = 18 will be added to get the possible outcomes ..

Answer: 0.0902

Step-by-step explanation:

Given : The average number of phone inquiries per day at the poison control center : [tex]\lambda=2[/tex]

The Poisson distribution function is given by :-

[tex]\dfrac{e^{-\lambda}\lambda^x}{x!}[/tex]

Then ,  the probability that it will receive exactly 4 calls on a given day is  given by (Put [tex]x=4[/tex] and [tex]\lambda=2[/tex]) :-

[tex]\dfrac{e^{-2}2^4}{4!}=0.09022352215\approx0.0902[/tex]

Hence, the required probability : 0.0902

Answer:

Step-by-step explanation:

It can be easier to see the answer if you subtract the right side of the equation from both sides, then simplify.

1. 2(x + 2) + 2 = 2(x + 3) + 1

  2(x + 2) + 2 - (2(x + 3) + 1) = 0

  2x +4 +2 -2x -6 -1 = 0

  -1 = 0 . . . . no solution

__

2. 2x + 3(x + 5) = 5(x – 3)

  2x + 3(x + 5) - 5(x – 3) = 0

  2x +3x +15 -5x +15 = 0

  30 = 0 . . . . no solution

__

3. 4(x + 3) = x + 12

  4(x + 3) - (x + 12) = 0

  4x +12 -x -12 = 0

  3x = 0 . . . . one solution, x=0

__

4. 4 – (2x + 5) = (–4x – 2)

  4 – (2x + 5) - (–4x – 2) = 0

  4 -2x -5 +4x +2 = 0

  2x +1 = 0 . . . . one solution, x=-1/2

__

5. 5(x + 4) – x = 4(x + 5) – 1

  5(x + 4) – x - (4(x + 5) – 1) = 0

  5x +20 -x -4x -20 +1 = 0

  1 = 0 . . . . no solution

Answer:

The answer is a,b and e.

Step-by-step explanation:

a. 2(x + 2) + 2 = 2(x + 3) + 1

b. 2x + 3(x + 5) = 5(x – 3)

e. 5(x + 4) – x = 4(x + 5) – 1

i just did this question on my test hope that helps ;) !

Answer:

The inter-quartile range is 13.

Step-by-step explanation:

   1. Order the data from least to greatest

   2. Find the median  of the data.

   3. Calculate the median of both the lower and upper half of the data.

   4. The inter-quartile range is the difference between the upper and lower medians.

Lower Median: 17

Media: 25.5

Upper Median: 30

Answer:

32 degrees fahrenheit =

0 degrees celsius

Step-by-step explanation:

Formula

(32°F − 32) × 5/9 = 0°C

Answer:

  82.4 °F

Step-by-step explanation:

The appropriate conversion formula is ...

  F = 9/5C +32

For C = 28, this is ...

  F = (9/5)(28) +32 = 50.4 +32 = 82.4

The equivalent temperature in degrees Fahrenheit is 82.4.

Answer:

0.07

Step-by-step explanation:

it is given odds in favor of a win is 7 to 93

we have to find the degree of likelihood as a probability

total sample space =7+93=100

so the degree of likelihood as a probability = [tex]\frac{7}{100} =0.07[/tex]

so we can conclude that the probability will be 0.07 which is very less so the chances of win in the casino is very less

The odds 7 to 93, when converted to a probability, gives a value of 0.07. This means there is a 7% chance of winning in this slot machine game.

The question asks to express the odds in favor of winning a casino slot machine game as a probability value between 0 and 1. In this case, the odds given are 7 to 93. This means that for every 100 games, we expect 7 wins and 93 losses.

To convert these odds into a probability, we divide the number of win outcomes by the total number of outcomes. In this case, the probability of winning is 7/(93+7) = 7/100 = 0.07.

So the probability value of winning on this slot machine is 0.07, which is a number between 0 and 1 inclusive.

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Answer:

  (x, y, z) = (3, 1, 2)

Step-by-step explanation:

Solving using a calculator, I would enter the coefficients of 1/x, 1/y, 1/z as they are given. The augmented matrix in that case looks like ...

[tex]\left[\begin{array}{ccc|c}\frac{1}{2}&\frac{1}{4}&-\frac{1}{3}&\frac{1}{4}\\1&-\frac{1}{3}&0&0\\1&-\frac{1}{5}&4&\frac{32}{15}\end{array}\right][/tex]

My calculator shows the solution to this set of equations to be ...

So, (x, y, z) = (3, 1, 2).

___

Doing this by hand, I might eliminate numerical fractions. Then the augmented matrix for equations in 1/x, 1/y, and 1/z would be ...

[tex]\left[\begin{array}{ccc|c}6&3&-4&3\\3&-1&0&0\\15&-3&60&32\end{array}\right][/tex]

Adding 3 times the second row to the first, and adding the first row to the third gives ...

[tex]\left[\begin{array}{ccc|c}15&0&-4&3\\3&-1&0&0\\21&0&56&35\end{array}\right][/tex]

Then adding 14 times the first row to the third, and dividing that result by 77 yields equations that are easily solved in a couple of additional steps.

[tex]\left[\begin{array}{ccc|c}6&3&-4&3\\3&-1&0&0\\3&0&0&1\end{array}\right][/tex]

The third row tells you 3/x = 1, or x=3.

Then the second row tells you 3/3 -1/y = 0, or y=1.

Finally, the first row tells you 15/3 -4/z = 3, or z=2.

The two lines start at the same point outside the circle, using the intersecting Secants theorem, When you multiply the two dims for each line together, they are equal

For A:

5 * (5+x) = 6 * (6+4)

25 + 5x = 60

5x = 35

x = 35/5

x = 7

For B:

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

40 = 16 + 4x

4x = 24

x = 24/4

x = 6

Answer:

I'm not quite sure but I think it's either 21.6 miles or 22 (Mostly 21.6 though, is what i think at least).

Answer:

0.75

Step-by-step explanation:

Total number of people = 400

Number of people who say yes to gun laws being more stringent = 300

Number of people who say no to gun laws being more stringent = 100

The proportion of people who will say yes = Number of people who say yes to gun laws being more stringent / Total number of people

[tex]\text{The proportion of people who will say yes}=\frac{300}{400}\\\Rightarrow \text{The proportion of people who will say yes}=\frac{3}{4}=0.75[/tex]

∴ Proportion in the population who will respond "yes" is 0.75

Answer:

The mean of these statistic is 2.18.

Step-by-step explanation:

According to the chart, from 1986-1996, unintentional drug overdose deaths per 100,000 population began to rise.

The given data set is

2, 1, 2, 2, 1, 2, 2, 3, 3, 3, 3

Formula for mean:

[tex]Mean=\frac{\sum x}{n}[/tex]

Using this formula, the mean of the data is

[tex]Mean=\frac{2+1+2+2+1+2+2+3+3+3+3}{11}[/tex]

[tex]Mean=\frac{24}{11}[/tex]

[tex]Mean=2.181818[/tex]

[tex]Mean\approx 2.18[/tex]

Therefore the mean of these statistic is 2.18.

The mean of these statistics is [tex]\large{\boxed{\bold{2.18}}[/tex]

Statistics is a study of a collection, preparation, analysis,presentation/conclusions from some data

Data is a collection of information presented in the form of numbers

Data collection can be done through a sample that represents all data (can be called a population) that is used as research

Data information can be stated in tables, diagrams or graphs

The average value or mean is a measure to provide an overview of a set of data

Mean is the average of a number of data

To determine the mean: the sum of all data divided by the amount of data

General formula

[tex]\large{\boxed{\bold{mean=\frac{\sum_{xi}}{n} }}}[/tex]

xi = data

n = amount of data

The numbers for each year for unintentional drug overdose deaths per 100,000 population are: 2, 1, 2, 2, 1, 2, 2, 3, 3, 3, 3

Total amount of data:

[tex]\displaystyle 2+1+2+2+1+2+2+3+3+3+3=\large{\boxed{24}[/tex]

Amount of data: [tex]\large{\boxed{11}}[/tex]

So the mean value:

[tex]\displaystyle mean=\frac{\sum_{xi}}{n}=\frac{24}{11}=\large{\boxed{\bold{2.18}}}[/tex]

Statistics

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Answer:

[tex]\tt B. \ \ \ \cfrac{1+\frac{\sqrt{3}}{3}}{1-\frac{\sqrt{3}}{3}}[/tex]

Step-by-step explanation:

[tex]\displaystyle\tt \tan75^o=\tan(45^o+30^o)=\frac{\tan45^o+\tan30^o}{1-\tan45^o\cdot\tan30^o} =\frac{1+\frac{\sqrt{3}}{3}}{1-\frac{\sqrt{3}}{3}}[/tex]

For this case we have to define that:

[tex]tg (x + y) = \frac {tg (x) + tg (y)} {1-tg (x) * tg (y)}[/tex]

So, according to the problem we have:

[tex]tg (45 + 30) = \frac {tg (45) + tg (30)} {1-tg (45) * tg (30)}[/tex]

By definition we have to:

[tex]tg (45) = 1\\tg (30) = \frac {\sqrt {3}} {3}[/tex]

Substituting we have:

[tex]tg (45 + 30) = \frac {1+ \frac {\sqrt {3}} {3}} {1-1 * \frac {\sqrt {3}} {3}}\\tg (45 + 30) = \frac {1+ \frac {\sqrt {3}} {3}} {1- \frac {\sqrt {3}} {3}}[/tex]

Answer:

option B

Answer:

20%

Step-by-step explanation:

Population of white-tailed deer in 1991 = 25 deer per square mile

Population of white-tailed deer in 1992 = 30 deer per square mile

We have to find the percentage increase in the deer population. The formula for percentage change is:

[tex]\frac{\text{New Value - Original Value}}{\text{Original Value}} \times 100 \%[/tex]

Original value is the population in 1991 and the New value is the population in 1992.

Using the values, we get:

[tex]\frac{30-25}{25} \times 100 \%\\\\ = 20%[/tex]

Thus, the deer population increased by 20% from 1991 to 1992

Final answer:

The deer population in the state park in Indiana increased by 20% from 1991 to 1992.

Explanation:

The question asks by what percentage the deer population increased between 1991 and 1992 in a state park in Indiana. To calculate the percentage increase, we use the formula: Percentage Increase = ((New population - Original population) / Original population) × 100%. Applying this formula to the given numbers, we have:

Original population in 1991 = 25 deer per square mile

New population in 1992 = 30 deer per square mile

Percentage Increase = ((30 - 25) / 25) × 100% = (5 / 25) × 100% = 20%

Therefore, the deer population increased by 20% from 1991 to 1992.

Answer:

[tex]\frac{24}{65}[/tex]

Step-by-step explanation:

Total number of students in the class = 26

Number of boys in the class = 10

Number of girls in the class = 26 - 10 = 16

The formula for probability is :

[tex]\text{Probability}=\frac{\text{Favorable Outcomes}}{\text{Total Outcomes}}[/tex]

In this case the favorable outcomes would be the number of girls in the class and total outcomes would be the total number of students in the class.

Eduardo has to pull out two names from the hat. Since there are 16 girls in the class of 26, the probability that the first name will be of the girl will be = [tex]\frac{16}{26}[/tex]

After picking up the 1st name, there would be 25 names in the hat with 15 names of girls as one of the girl is already been chosen. So,

The probability that the second name would belong to a girl = [tex]\frac{15}{25}[/tex]

The probability that both the partners will be girls will be equal to the product of two individual probabilities as both the events are independent.

Therefore,

The probability that both of Eduardo's partners for the group project will be girls = [tex]\frac{16}{26} \times \frac{15}{25} = \frac{24}{65}[/tex]

ANSWER

C, D, and E

EXPLANATION

The given ellipse has been translated therefore the center is no longer at the origin.

Option A is not correct.

The major axis is the horizontal axis. Its length is 8 units.

Option B is also not correct.

The vertices are where the major horizontal axis intersected the ellipse. They are indeed 4 units to the right and left of the center.

Option C is correct.

The foci can be found using

[tex] {a}^{2} - {b}^{2} = {c}^{2} [/tex]

a=4 is the distance from the center to the vertex and b=2 is the distance from the center to the co-vertex.

[tex] {4}^{2} - {2}^{2} = {c}^{2} [/tex]

[tex]16 - 4 = {c}^{2} [/tex]

[tex]12 = {c}^{2} [/tex]

[tex]c = \pm \sqrt{12} [/tex]

[tex]c = \pm 2\sqrt{3} [/tex]

Option D is also correct.

The directrices are parallel to the semi-minor axis therefore they are vertical lines.

Option E is also correct.

Answer: 15 yards per mistake.

Step-by-step explanation:

Given : A football team had 4 big mistakes in a game.

i.e. the number of big mistakes done by the football team = 4

The total lost of yards because of the big mistakes done by football team = 60 yards

Now, the portion of  team's yardage change per mistake is given by :-

[tex]\dfrac{\text{Total lost of yards}}{\text{Number of big mistakes}}\\\\=\dfrac{60}{4}=15\text{ yards}[/tex]

Hence, the team's yardage changes by 15 yards per mistake.

Answer:

-15 yardage per mistake

Step-by-step explanation:

Answer:

(- 6, 6 )

Step-by-step explanation:

Assuming the centre of dilatation is the origin, then

The coordinates of the image points are 3 times the original points

B = (- 2, 2 ), then

B' = ( 3 × - 2, 3 × 2 ) = (- 6, 6 )

Check the picture below.

make sure your calculator is in Degree mode.

The length of the ladder is 30.83 ft

Trigonometric ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

various ratios are:-

The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as trigonometric.

CALCULATIONS:-

The angle of elevation is 70°

using the height and distance formula

    cos∅ = base/hypotenuse

cos 70°= 0.454  

   cos∅ = base/hypotenuse

     0.454  =14/hypotenuse

hypotenuse(length of ladder)= 14/0.454

       length of ladder= 30.83 ft

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Answer:

  (x +8)² +(y +6)² = 100

Step-by-step explanation:

The equation of a circle with center (h, k) and radius r can be written:

  (x -h)² +(y -k)² = r²

For your given values of h=-8, k=-6, r=10, the equation is ...

  (x +8)² +(y +6)² = 100

Answer:

[tex]\large\boxed{n\leq9\ or\ n>13\to n\in\left(-\infty;\ 9\right]\ \cup\ (13,\ \infty)\to\{x\ |\ x\leq9\ or\ x>13\}}[/tex]

Step-by-step explanation:

[tex]n-12\leq-3\ or\ 2n>26\\\\n-12\leq-3\qquad\text{add 12 to both sides}\\n\leq9\\\\2n>26\qquad\text{divide both sides by 2}\\n>13\\\\n\leq9\ or\ n>13\to n\in\left(-\infty;\ 9\right]\ \cup\ (13,\ \infty)\to\{x\ |\ x\leq9\ or\ x>13\}[/tex]

Answer: x > 5

Step-by-step explanation: You need to isolate x. First, distribute the 1/2 into the parentheses. You will get:

4x + x + 2 > 12

Combine like terms.

5x + 2 > 12

Subtract 2 from each side.

5x > 10

Divide by 5 on each side.

X > 2

Since x is by itself, that is the answer.

Answer:

x > 2

Step-by-step explanation:

Distribute 1/2

Distribute 1/2 inside the parentheses

1/2 * 2x = x

1/2 * 4 = 2

Simplify

4x + x + 2 > 12

Combine like terms

5x + 2 > 12

Subtract 2 in both sides

2 - 2 = 0

12 - 2 = 10

5x > 10

Divide 5 in both sides

5x/5 = x

10/5 = 2

Simplify

x > 2

Answer

x > 2

Answer:

only C

Step-by-step explanation: