What are the two solutions of x^2-2x-4=-3x+9

\(\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ \theta =\frac{\pi }{2}\\[1em] r=\frac{8}{3} \end{cases}\implies A=\cfrac{1}{2}\cdot \cfrac{\pi }{2}\cdot\left( \cfrac{8}{3} \right)^2 \\\\\\ A=\cfrac{1}{2}\cdot \cfrac{\pi }{2}\cdot \cfrac{64}{9}\implies A=\cfrac{16\pi }{9}\implies A\approx 5.59\)

Answer:

B 2^x+2 +3

Step-by-step explanation:

hope this helps :)

The function that matches the graph and the given points (7, 0) and (-8, 5) is: y = 2X + 2 + 3. (option b)

This function seems to have a typo, as it simplifies to y = 23, which is a constant value and does not depend on the variable x. This means the graph would be a horizontal line at y = 23 and would not pass through the points (7, 0) and (-8, 5).

y = 2X + 2 + 3

This function can be simplified to y = 2X + 5. Evaluating the points (7, 0) and (-8, 5) in this function:

For (7, 0):

y = 2 * 7 + 5

y = 14 + 5

y = 19

For (-8, 5):

y = 2 * (-8) + 5

y = -16 + 5

y = -11

y = 2X - 3 + 2 Y = 2ˣ + 3 + 2:

It seems there is a typo in this option with "Y" being capitalized. Assuming it is meant to be y, we have two separate functions:

a. y = 2X - 3 + 2

b. y = 2ˣ + 3 + 2

a. For y = 2X - 3 + 2:

Evaluating the points (7, 0) and (-8, 5):

For (7, 0):

y = 2 * 7 - 3 + 2

y = 14 - 3 + 2

y = 13

For (-8, 5):

y = 2 * (-8) - 3 + 2

y = -16 - 3 + 2

y = -17

b. For y = 2ˣ + 3 + 2:

Evaluating the points (7, 0) and (-8, 5):

For (7, 0):

y = 2⁷ + 3 + 2

y = 128 + 3 + 2

y = 133

For (-8, 5):

y = 2⁻⁸ + 3 + 2

y ≈ 0.004 + 3 + 2

y ≈ 5.004

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Answer:

Approximately 3.81 seconds

Step-by-step explanation:

d = 3t + 5t²

d = 84

84 = 3t + 5t²

3t + 5t² - 84 = 0

5t² + 3t - 84 = 0

5(t² + 3/5t - 84/5) = 0

5(((t + 3/10)² - 9/100) - 84/5) = 0

5((t + 3/10)² - 9/100 - 84/5) = 0

5((t + 3/10)² - 9/100 - 1680/100) = 0

5((t + 3/10)² - 1689/100) = 0

5(t + 3/10)² - 1689/20 = 0

5(t + 3/10)² = 1689/20

(t + 3/10)² = 1689/100

t + 3/10 = ±√(1689)/10

t = -3/10 ± √(1689)/10

t = -3/10 ± ≈41.1/10

t = -3/10 ± ≈4.11

t ≈ -0.3 ± 4.11

t [can only be positive] ≈ 4.11 - 0.3

t ≈ 3.81

Answer:

Step-by-step explanation:

Year 1: $850 * 0.91 = $773.50

Year 2: $773.50 * 0.91 = $704.69

Year 3: $704.69 * 0.91 = $641.95

...

Year 34: (continue the pattern)

We can continue this calculation for each year, but to save time, we can use an exponential decay formula:

Remaining Amount = Initial Amount * (1 - rate)^years

Substituting the values:

Remaining Amount = $850 * (1 - 0.09)^34

Calculating this expression:

Remaining Amount ≈ $850 * (0.91)^34 ≈ $255.88

After 34 years, approximately $255.88 will be left with Sally.

Considering the definition of parallel line, the correct answer is the second option: if the slope of line a is -4, then the slope of a line parallel to it is -4.

A linear equation o line can be expressed in the form y = mx + b

where

Parallel lines are two lines that are always at the same distance from each other and that prolonged towards infinity never touch.

Two lines are parallel if they have the same slope "m" and different y-intercepts "b".

If the slope of line a is -4, then the slope of a line parallel to it is -4 because two lines are parallel have the same slope "m".

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Answer:

1/5x

Step-by-step explanation:

1/5x

Angle L's in the triangle LMN is,

⇒ L = 72.54°

We have to given that;

A triangle LMN is shown in figure.

And, The sides are,

Since, We know that;

A triangle is a three-sided polygon with three vertices, three angles that add up to 180 degrees, and three sides.

Since, We know that;

⇒ sin L = Opposite / Hypotenuse

And, cos L = Base / Hypotenuse

Two rays after combined into an angle have a single terminal. And, latter is known as the vertex of the angle, and the rays are known as its sides, occasionally as its legs, and occasionally as its arms.

Now, We can use trigonometry formula to find the value of angle l we get;

⇒ sin L = Opposite / Hypotenuse

⇒ sin L = LM / LN

⇒ sin L = 18/60

Taking arc sin both side, we get;

⇒ L = 72.54°

Therefore, The value of measure of angle L is triangle LMN is,

⇒ L = 72.54°

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Answer:

(a)Distance traveled by each explorer travel as Mars rotates by 1 radian

(b)Number of hours it takes Mars to rotate 1 radian=3.9152 hours

(c)Speed of each explorer around Mars.

Step-by-step explanation:

Part A

For any given parallel of latitude\(\text{Circumference}=2\pi R \cos \beta$ where \beta$ is the angle of latitude.\)

Opportunity landed at 2° south latitude, where Mars’ radius is about 2110 miles.

\(\text{Circumference at 2\°S latitude}=2\pi*2110* \cos 2^\circ\\=13249.44$ miles\)

Phoenix landed at 68° north latitude, where Mars’ radius is about 790 miles.

\(\text{Circumference at 68\°N latitude}=2\pi*790* \cos 68^\circ\\=1859.44$ miles\)

Part B

Next, we determine the distance (Length of arc) covered by each explorer as Mars rotates by 1 radian.

\(\text{Length of arc (in radian)}=\dfrac{\theta}{2\pi} \times $Circumference\)

Opportunity's Distance

\(=\dfrac{1}{2\pi} \times 13249.44\\\\ =2108.71$ miles\)

Phoenix's Distance

\(=\dfrac{1}{2\pi} \times 1859.44\\\\ =295.94$ miles\)

Part C

Mars rotates on its axis once every 24.6 Earth-hours.

Therefore:

\(\dfrac{24.6}{2\pi} \approx $ 3.9152 hour per radian\)

Part D:Speed of each explorer

\(\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}\)

\(\text{Speed of Opportunity = }\dfrac{2108.71}{3.9152}\\$=538.59 miles per hour\\\\Speed of Phoenix =\dfrac{295.94}{3.9154}\\=75.59$ miles per hour\)

Based on the given scale, if Houston and Dallas are 1.6 centimeters apart on the map, the estimated distance between the two cities is approximately 242.1 miles.

To determine the distance between Houston, TX and Dallas, TX using the given scale, we can set up a proportion using the distances on the map and the actual distances.

Let's denote the distance between Houston and Dallas as "x" (in miles).

According to the scale provided, 2.3 centimeters on the map represents a distance of 348 miles. This can be expressed as:

2.3 cm / 348 miles = 1.6 cm / x miles

To find the value of "x," we can cross-multiply and solve the equation:

(2.3 cm) * (x miles) = (1.6 cm) * (348 miles)

2.3x = 556.8

Divide both sides by 2.3 to isolate "x":

x = 556.8 / 2.3

x ≈ 242.0869565

Therefore, based on the given scale, if Houston and Dallas are 1.6 centimeters apart on the map, the estimated distance between the two cities is approximately 242.1 miles.

Please note that this is an approximation based on the given scale and the assumption that the scale is linear and consistent throughout the map. Actual distances may vary and should be verified using more accurate measurements or reliable sources.

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Answer:

$302.40

Step-by-step explanation:

Answer:

284.90 or 285

Step-by-step explanation:

you would multiply the savings account by the ROR.

savings: $8,400

ROR: 3.4%

8,400 x 3.4% = 285 (which is 284.90 rounded)

Answer:

2/3 gallons

Step-by-step explanation:

Given data

We have the following data

1/2 gallons is the same as 0.5 gallons

hence 0.5 gallons will cover 3/4 of his deck

           x gallons will cover 1 of his deck

cross multiply we have

3/4*x = 0.5*1 gallons

3x/4= 0.5

3x= 2

divide both sides by 3

x= 2/3

Hence 2/3 gallons will cover the entire deck

Answer:

Step-by-step explanation:

The answer is, no!

Step-by-step explanation:

The reason to that answer is that some other shapes are also, having the same properties as shown. An example for that property would also mean a rectangle and not always a parallelogram.

So, here is the given information on what we need to classify a shape as a parallelogram:-

1) Parallel Sides

2)Opposite Sides are equal.

3) Adjacent sides are not equal.

4) Opposite angles are equal.

5)Adjacent angles are not equal.

Based on this, we can classify a shape as a parallelogram.

Hope, this answer helps!

Answer:

By flipping the second fraction (finding its reciprocal) we change the equation mathematically. In order to maintain the equation mathematically, we must turn the division question into a multiplication question.

Step-by-step explanation:

Answer:

75 ft

Step-by-step explanation:

Let 20/50 = 30/x

So,

20X = 30x50

20x = 1500

X = 1500/20

X = 75

#HopeItHelps

Answer:

x = 75 ft

Step-by-step explanation:

20/50 = 30/x

20 . x = 50 . 30

20x = 1,500

x = 1,500/20

x = 75 ft

Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$. Therefore $x=y=12\sqrt{3}$, which is our answer

In a 30-60-90 triangle, the sides have the ratio of $1: \sqrt{3}: 2$. Let's apply this to solve for the variables in the given problem.

Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form. x=y=Let's first find the ratio of the sides in a 30-60-90 triangle.

Since the hypotenuse is always twice as long as the shorter leg, we can let $x$ be the shorter leg and $2x$ be the hypotenuse.

Thus, we have: Shorter leg: $x$Opposite the $60^{\circ}$ angle: $x\sqrt{3}$ Hypotenuse: $2x$

Now, let's apply this ratio to solve for the variables in the given problem. We know that $x = y$ since they are equal in the problem.

Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$

Therefore, $x=y=12\sqrt{3}$, which is our answer.

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Answer:

Below

Step-by-step explanation:

32/2 x 100% = 1600 %

Answer:

\(x=7.8\)

Step-by-step explanation:

In any right triangle, the sine of an angle is equal to its opposite side divided by the hypotenuse.

The angle marked 33 degrees has its opposite side labelled with \(x\) and the hypotenuse of the triangle labelled with 12.

Thus, we can set up the following equation to solve for \(x\):

\(\tan 33^{\circ}=\frac{x}{12},\\x=12\tan 33^{\circ}=7.79289111837\approx \boxed{7.8}\)

Answer:

Step-by-step explanation:

tan(33°) = x/12

x = 12tan(33°) ≈ 7.79

Answer:

D. -4x(x - 2)(x+3)

Step-by-step explanation:

We are given the following trinomial:

\(-4x^3 - 4x^2 + 24x\)

-4x is the common term, so:

\(-4x(\frac{-4x^3}{-4x} - \frac{4x^2}{-4x^3} + \frac{24x}{-4x}) = -4x(x^2+x-6)\)

The second degree polynomial can also be factored, finding it's roots.

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

\(ax^{2} + bx + c, a\neq0\).

This polynomial has roots \(x_{1}, x_{2}\) such that \(ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})\), given by the following formulas:

\(x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}\)

\(x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}\)

\(\Delta = b^{2} - 4ac\)

x² + x - 6

Quadratic equation with \(a = 1, b = 1, c = -6\)

So

\(\Delta = 1^{2} - 4(1)(-6) = 25\)

\(x_{1} = \frac{-1 + \sqrt{25}}{2} = 2\)

\(x_{2} = \frac{-1 - \sqrt{25}}{2} = -3\)

So

\(x^2 + x - 6 = (x - 2)(x - (-3)) = (x - 2)(x + 3)\)

The complete factorization is:

\(-4x(x^2+x-6) = -4x(x - 2)(x + 3)\)

Thus the correct answer is given by option d.

Answer:Use the following statements and figure to write a compound statement for each conjunction or disjunction. Then find its truth value. Explain your reasoning. p ...

Step-by-step explanation:

The truth values of compound statements for each conjunction or

disjunction are as 1. p ^ r is false, 2. p ^ r is false, 3. q v r is false, 4. r v q is true, 5. ~ p ^ q is true, and 6. ~r v ~p is false.

In logic, a conjunction is true only when both p and q are true. A disjunction is true when at least one of the statements is true. The negation of a statement(~) is true when the statement is false and vice versa.

p:-3-2=-5

q: Vertical angles are congruent.

r: 2+8> 10

1. p and q is a conjunction statement, the compound statement is "p is true and q is true",

The statement is false because p is true but q is false.

2. p ^ r is a conjunction statement, the compound statement is "p is true and r is true".

The statement is false because p is true but r is false.

3. q v r is a disjunction statement, the compound statement is "q is true or r is true or both are true".

The statement is false because q is false and r is true.

4. r v q is a disjunction statement, the compound statement is "r is true or q is true or both are true".

The statement is true because r is true

5. ~ p ^ q is a conjunction statement, the compound statement is "not p is true and q is true".

The statement is true because p is false and q is false

6. ~r v ~p is a disjunction statement, the compound statement is "not r is true or not p is true or both are true"

The statement is true because r is false and p is false.

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Answer:

Answer is = 3

Will you my friend

Answer:

Part A: Which family paid more for their house? And at what cost.

The Miller family

Part B: Which family’s home value is increasing at a faster rate?

The Adams family

Step-by-step explanation:

Answer:

The answer is 526 1760

Step-by-step explanation: You first solve for all the parenthisis then once you do that you multiply the number you get from the parenthisis by 2 to get your answer hope this helps.

Answer:

$15.69

Step-by-step explanation:

multiply the retail price by 1.06 to get the price after taxes.

find the discounted price by multiplying the price after taxes(19.61) by 0.8 since it is 20% off to get the answer

The value of S4 for the given expression ♾️. n-1 Σ 1/4(-1/3) is -1/12.

The given expression ♾️. n-1 Σ 1/4(-1/3) represents a summation of the term 1/4(-1/3) over a range of values from 1 to n-1, where n is an unknown value. We need to find the value of S4, which represents the sum of this expression when n is equal to 4.

To find the value of S4, we substitute n = 4 into the expression and evaluate it.

♾️. n-1 Σ 1/4(-1/3) = ♾️. 4-1 Σ 1/4(-1/3)

Simplifying, we get:

♾️. 3 Σ 1/4(-1/3)

Since the term 1/4(-1/3) is constant, we can pull it out of the summation:

1/4(-1/3) ♾️. 3

Now, ♾️. 3 represents the sum of 3 terms. Multiplying 1/4(-1/3) by 3 gives:

1/4(-1/3) * 3 = -1/4 * 1/3 * 3 = -1/12

Therefore, the value of S4 for the given expression ♾️. n-1 Σ 1/4(-1/3) is -1/12.

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The probable question could be:

What is the value of s4 for expression ♾️. n-1 Σ 1/4(-1/3) ?

A) 1/9

B) 7/54

C) 5/27

D) 10/27

Based on the table, by adding all the expenses, Steven's net monthly income is $2250.

To get the percentage spent in each category, simply divide each amount in the category by $2250 and multiply it by 100.

See table below.

b. To identify which category Steven is underspending, overspending, and just spending right, let's take a look at the guidelines.

If the percentage is lower than what is on the guidelines, Steven is underspending.

If the percentage is higher than what is on the guidelines, Steven is overspending.

If the percentage is within the provided interval on the guidelines, Steven is just spending right.

So, let's compare the percentage of Steven's expenses to the guidelines.

So, we can say that Steven is underspending on the following categories: Food and Clothing, Savings, and Miscellaneous.

Steven is overspending on the following categories: Housing and Utilities, Transportation, and Recreation and Education.

Lastly, Steven is spending within the guidelines for Health and Personal care.

The new arc length function for the curve after reparametrization is as follows

\(\\\\r(s) = ( 4 - \frac{s}{\sqrt{26}})i + (\frac{4s}{\sqrt{26} } + 4)j+(\frac{3s}{\sqrt{26} } + 3)k\)

What is meant by the arc length of a curve?

The distance between two places along a segment of a curve is known as the arc length.

The formula for arc length is used to determine how far something is along the curved line that makes up an arc. The arc length is, to put it simply, the distance that passes through the curved line of the circle that forms the arc.

Given,

Vector equation of curve  r(t) = (5 - t) i + (4t - 3) j + 3t k

    Given P = (4, 1, 3)

5 - t = 4

So, t = 1

Now differentiate r(t)

 r'(t) = -i + 4j + 3k

Magnitude of r'(t) = |r'(t)| = √[(-1)² + 4² + 3²] = √26

The arc length function for the curve

 \(s = \int\limits^t_1 { |r'(t)| } \, dt = \int\limits^t_1 { \sqrt{26} } \, dt = \sqrt{26} (t-1)\)

  \(t = \frac{s}{\sqrt{26} } + 1\)

Now to reparametrize the curve with respect to arc length, substitute t with (s/√26) + 1 in r(t).

\(r(s) = (5 - ( \frac{s}{\sqrt{26} } + 1)) i + (4( \frac{s}{\sqrt{26} } + 1) - 3) j + 3( \frac{s}{\sqrt{26} } + 1) k\\\\r(s) = ( 4 - \frac{s}{\sqrt{26}})i + (\frac{4s}{\sqrt{26} } + 4)j+(\frac{3s}{\sqrt{26} } + 3)k\)

Therefore the new arc length equation of the curve when  \(t = \frac{s}{\sqrt{26} } + 1\) is as follows

\(\\\\r(s) = ( 4 - \frac{s}{\sqrt{26}})i + (\frac{4s}{\sqrt{26} } + 4)j+(\frac{3s}{\sqrt{26} } + 3)k\).

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Answer:

1 adult ticket and 7 student tickets were purchased

Step-by-step explanation:

let a represent number of adult tickets purchased and s the number of student tickets purchased, then

a + s = 8 ( subtract s from both sides )

a = 8 - s → (1) ← based on total tickets purchased

10.5a + 7.25s = 61.25 → (2) ← based on cost of tickets

substitute a = 8 - s into (2)

10.5(8 - s) + 7.25s = 61.25

84 - 10.5s + 7.25s = 61.25

84 - 3.25s = 61.25 ( subtract 84 from both sides )

- 3.25s = - 22.75 ( divide both sides by - 3.25 )

s = 7

substitute s = 7 into (1)

a = 8 - 7 = 1

that is 1 adult ticket and 7 student tickets were purchased

Answer:

  76 units

Step-by-step explanation:

You want the length of AC in the given triangular pyramid.

The Pythagorean theorem can be used to find the lengths of AD and CD.

  AD² + 40² = 41²

  AD² = 41² -40² = 81 . . . . . = 9²

and

  CD² +40² = 85²

  CD² = 85² -40² = 5625 . . . . . = 75²

It can also be used to find AC:

  AD² + CD² = AC²

  81 + 5625 = AC²

  AC = √5706 = 3√634 ≈ 76

The length of side AC is about 76 units.

__

Additional comment

The Pythagorean theorem tells you the square of the hypotenuse is the sum of the squares of the legs of a right triangle.

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