Solve the following quadratic equation by factoring.

x^2 - 5x = 14

(Answers are in photo)

10 points!!!
Please explain how you got your answer.

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence.

A sequence in mathematics is an ordered collection of numbers that is typically defined by a formula or rule. Every number in the series is referred to as a term, and its location within the sequence is referred to as its index. Depending on whether the list of terms stops or continues indefinitely, sequences can either be finite or infinite. By their patterns or uniformity, sequences can be categorised, and the study of sequences is crucial to many areas of mathematics, such as calculus, number theory, and combinatorics. Mathematical, geometrical, and Fibonacci sequences are a few examples of popular sequence types.

given

The sequence's terms are all different by 7 (i.e., 12 - 5 = 19 - 12 = 26 - 19 =... = 7).

The following is a definition of a recursive formula for the nth element of the sequence:

a 1 = 5 (the first term of the series is 5) (the first term of the sequence is 5)

For n > 1, each term is derived by adding 7 to the preceding term, so a n = a n-1 + 7.

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence. For instance, we have

a_2 = a_1 + 7 = 5 + 7 = 12

a_3 = a_2 + 7 = 12 + 7 = 19

a_4 = a_3 + 7 = 19 + 7 = 26

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The function f(t) is given by (15t² + 40t) / (2t + 7) when k(t) is replaced by the derivative of the Dirac delta function, denoted as δ'(t).

the derivative of f(s) is taken by differentiating each term separately. The derivative of 5s³ is 15s², the derivative of 20s² is 40s, and the derivative of -49x is 0 since x is not involved.

The derivative of -108 is also 0.

Moving on to the denominator

the derivative of s² is 2s, the derivative of 7s is 7

and the derivative of 10 is 0. Therefore, the derivative of f(s) with respect to s is (15s² + 40s) / (2s + 7).

we substitute k(t) with δ'(t), which is the derivative of the Dirac delta function δ(t).

The Dirac delta function is defined as 0 for all values of t except at t = 0, where it is infinite.

Its derivative, δ'(t), is 0 for all values of t except at t = 0, where it is not defined.

Therefore, the resulting expression for f(t) is (15t² + 40t) / (2t + 7). This is the final answer for f(t) in terms of t, obtained by differentiating f(s) and substituting k(t) with δ'(t)

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In a magnetometry experiment, It will take 1 more minute for data be collected in order to reduce error the statistical noise by a factor of 10.

To reduce the random error by a factor of 10, we need to reduce the statistical noise to 1/10 picotesla. Since the statistical noise was initially 1 picotesla, this means we need to reduce it by a factor of 10.

We can use the following formula to calculate the time needed to reduce the statistical noise by a certain factor:

t = (log (final noise / initial noise)) / (log (reduction factor))

Here, the final noise is 1/10 picotesla, the initial noise is 1 picotesla, and the reduction factor is 10.

Plugging in these values, we get:

t = (log (1/10 / 1)) / (log (10))

t = (log (1/10)) / (log (10))

t = -1 / 1

t = -1

The negative value of t doesn't make sense in this context, so we need to take the absolute value:

t = |-1|

t = 1

Therefore, it will take 1 more minute to reduce the statistical noise by a factor of 10.

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____The given question is incomplete, the complete question is given below:

Reduction of the standard error

In a magnetometry experiment, after a minute of collecting

data the statistical noise was reduced to 1 picotesla.

For how much longer should data be collected in order

to reduce the random error by a factor of 10?

Answer:

24 x 25/100 = 6

of means multiplication so you are multiplying the percent to the regular price. Always consider cent as a hundred and a percent out of 100 in fractions.

Answer:

18 dollars

Step-by-step explanation:

half of 24 is 12 and half of that is 6 so 24-6=18 :)

The type of quadrilateral PQRS is a trapezium. A trapezium is a quadrilateral with one pair of parallel sides. In this case, the parallel sides are PQ and SR.

To find the value of x, we can use the distance formula. The distance formula states that the distance between two points is equal to the square root of the difference of their x-coordinates squared plus the difference of their y-coordinates squared.

In this case, we have the following:

PQ = √((x - 10)² + ((-9) - 3)²

We are given that PS = 15 units, so we can set the above equation equal to 15 and solve for x.

15 = √((x - 10)² + ((-9) - 3)²)

225 = (x - 10)² + 144

225 = x² - 20x + 100 + 144

(x - 15)(x - 5) = 0

Therefore, x = 15 or x = 5.

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Answer:

7cd(ab-3be+2ef)

Step-by-step explanation:

they all have the number 7 In common so you take that out and you take out whatever letters they have in common

Answer:

7cd(ab - 3be + 2ef

Step-by-step explanation:

Simplify:

    7abcd = 7 * a * b* c * d

  21bcde = 7 * 3 * b * c * d * e

   14cdef = 7 * 2 * c * d * e * f

GCF = 7 cd

7abcd - 21bcde + 14cdef = 7cd*( ab  - 3be + 2ef)

2003?? or 2004

bit confused tho cz my friend is 17 n her birthday is on feb 10th

Notice that for the first altered function we have that:

Therefore the +7 would directly affect the x-values, so the graph would shift horizontally.

For the next function we have that:

Therefore the +7 would directly affect the y-values, so the graph would shift vertically.

The values of x, y and z for the right triangle are: x = √6, y = 3, and z = √10 respectively.

The perpendicular height of the right triangle divides the triangle in two triangles with the same proportions as the original triangle.

√15/(y + 2) = y/√15 {opposite/adjacent}

y(y + 2) = (√15)² {cross multiplication}

y² + 2y = 15

y² + 2y - 15 = 0

by factorization;

(y - 3)(y + 5) = 0

y = 3 or y = -5

by Pythagoras rule:

(√15)² = x² + y²

15 = x² + 3²

x = √(15 - 9)

x = √6

z² = (√6)² + 2²

z = √(6 + 4)

z = √10

Therefore, the values of x, y and z for the right triangle are: x = √6, y = 3, and z = √10 respectively.

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Answer:

22 yrs old  (22 yrs & 29 days Old to be exact, because he died in June)

Step-by-step explanation:

Subtract:

1926 - 1904 = 22

Since Gaudi died on June 10th 1926 and Dali was born on May 11th, 1904, you just need to subtract the years.

The rate at which the area of the triangle is increasing when the angle between the sides of fixed lengths is π/3 is 0.3 m²/s.

If the lengths a and b for two sides of the triangle, as well as the included angle θ, are known, the area of a triangle can be calculated using the sine formula.

\(\text { Area }=\frac{1}{2} a b \sin \theta\)

Now, according to the question;

The two sides of the triangle are given;

Let a = 4m and b = 5m.

Let θ = π/3. be the angle between the two sides;

Then,

Differentiate the area with respect to time (as rate of change of area)

\(\begin{aligned}\frac{\mathrm{d} A}{\mathrm{~d} t}=\frac{\mathrm{d}}{\mathrm{d} t} \frac{1}{2} a b \sin \theta &=\frac{1}{2} * 4 * 5 * \frac{\mathrm{d}(\sin \theta)}{\mathrm{d} \theta} \cdot \frac{\mathrm{d} \theta}{\mathrm{d} t} \\&=10 *(\cos \theta) * 0.06 \frac{\mathrm{m}^{2}}{\mathrm{~s}}=0.6 \cos (\pi / 3) \frac{\mathrm{m}^{2}}{\mathrm{~s}} \\&=0.6 * 0.5 \frac{\mathrm{m}^{2}}{\mathrm{~s}}=0.3 \frac{\mathrm{m}^{2}}{\mathrm{~s}}\end{aligned}\)

Therefore, the area of the triangle as a function of angle is 0.3 m²/s.

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The complete question is-

Two sides of a triangle are 4m and 5 m in length and the angle between them is increasing at a rate of 0.06 rad/sec. Find the rate at which the area of the triangle is increasing when the angle between the sides of fixed lengths is π/3.

When the price of bracelets increases, Jim will start making more bracelets because it has become more profitable to make bracelets than to make earrings.

This means that the supply of earrings will decrease because Jim and other skilled suppliers will shift their production towards bracelets. As a result, the supply curve of earrings is likely to shift to the left, indicating a decrease in supply. In the market, there are many suppliers like Jim who are skilled at making both earrings and bracelets. Therefore, the decrease in the supply of earrings due to the shift in production towards bracelets by these suppliers is likely to be significant. The magnitude of the shift in the supply curve of earrings will depend on the elasticity of production between earrings and bracelets. If it is easy to switch between making earrings and bracelets, then the shift in the supply curve of earrings will be larger than if it is difficult to switch. Overall, the increase in the price of bracelets will have an indirect effect on the supply of earrings through its impact on the opportunity cost of making earrings. As the opportunity cost of making earrings increases, the supply of earrings will decrease, resulting in a leftward shift in the supply curve of earrings.

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There are four possible values for the random variable X: 0, 1, 2, and 3

To find the probability distribution of X, which represents the number of girls in a family with three children, we first need to determine the possible values for the random variable X.

Part 1: Find the number of possible values for the random variable X.
There can be 0, 1, 2, or 3 girls in the family. Therefore, there are 4 possible values for the random variable X.

The random variable X represents the number of girls in a family with three children. To determine the possible values for X, we consider the number of girls that can exist in the family. In this case, there can be zero, one, two, or three girls.

When no girls are present, X takes the value 0. If there is one girl, X takes the value 1. If there are two girls, X takes the value 2. Finally, if there are three girls, X takes the value 3.

Therefore, there are a total of four possible values for the random variable X, which correspond to the different combinations of the number of girls in the family.

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We may deduce from the average speed that the aircraft must have at least once during the flight attained a speed of 478.72or higher.

This implies that the aircraft must have surpassed 100 mph once while descending to its average speed following takeoff.

So,

We can write,

The speed of the aircraft decreased throughout the arrival from its usual speed to 100 miles per hour before returning to zero at the destination.

Based on the given conditions,

Total distance of the flight = 2250 miles

Flight takeoff time = 2:00 pm

Arrival time of the flight = 7:40 pm

So,

The total time taken by the flight to cover 2250 = 4 hours 40 minutes

The total time is taken by the flight to cover 2250 = 4.7 hours

Then,

The average speed of the plane =Total distance/ total time

We can substitute values,

total distance = 2250,

total time = 4.7 hours

The average speed of the plane = 2250÷4.7

The average speed of the plane  is 478.72 miles per hour

From the average speed we can analyze that the plane must have reached the speed of 478.72 or more at least once during the journey this also concludes that the plane must have reached the speed of 100 miles per hour once while reaching to the average speed after the takeoff.

Hence,

During the arrival, the speed of the plane also reached went from the average speed to 100 miles per hour and then zero at the arrival destination

Therefore,

There were at least two times during the flight when the speed of the plane was 100 miles per hour.

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The area of the region that lies inside the first curve and outside the second curve: ∫[π/3, 5π/3] [8cos^2(θ) - 2cos(θ) - 1] dθ.

To find the area of the region that lies inside the first curve (r = 3cos(θ)) and outside the second curve (r = 1 + cos(θ)), we need to evaluate the definite integral of the difference between the two curves over the appropriate range of θ.

First, let's determine the range of θ where the curves intersect. We set the two equations equal to each other:

3cos(θ) = 1 + cos(θ)

2cos(θ) = 1

cos(θ) = 1/2

θ = π/3 and θ = 5π/3

Now, we can integrate the difference of the curves from θ = π/3 to θ = 5π/3:

Area = ∫[π/3, 5π/3] [(3cos(θ))^2 - (1 + cos(θ))^2] dθ

Simplifying the integrand:

Area = ∫[π/3, 5π/3] [9cos^2(θ) - (1 + 2cos(θ) + cos^2(θ))] dθ

Area = ∫[π/3, 5π/3] [8cos^2(θ) - 2cos(θ) - 1] dθ

Now, we can evaluate this definite integral to find the area.

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The total number of shaded triangles in the first 15 figures of the Sierpinski triangle is approximately 1.5.

To find the total number of shaded triangles in the first 15 figures of the Sierpinski triangle, we need to add up the number of shaded triangles in each figure.

We can see that the number of shaded triangles in each figure is increasing by powers of 3 (1, 3, 9, etc.). This means that the formula for the number of shaded triangles in the nth figure is given by 3^(n-1).

To find the total number of shaded triangles in the first 15 figures, we need to add up the number of shaded triangles in each of these figures. This can be done using a summation notation, which is represented by the following formula:

Σn=1^15 1/3^(n-1)

This formula represents the summation of 1/3^(n-1) from n=1 to n=15. When we plug in these values, we get:

1/3^0 + 1/3^1 + 1/3^2 + ... + 1/3^14

This is the sum of a geometric series, which can be simplified using the formula:

Sum = a(1 - r^n) / (1 - r)

Where a is the first term, r is the common ratio, and n is the number of terms. In this case, a = 1, r = 1/3, and n = 15.

Plugging in these values, we get:

Sum = 1(1 - (1/3)^15) / (1 - 1/3)

Simplifying, we get:

Sum = (3/2) (1 - (1/3)^15)

Using a calculator, we can find that this sum is approximately equal to 1.499999999997202.

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The elasticity of demand at a price of $5 is -2/11, indicating inelastic demand. To increase revenue, prices should be raised.

The elasticity function E(p) can be found by taking the derivative of the demand function D(p) with respect to p and multiplying it by p/D(p), resulting in E(p) = -4p/(150 - 2\(p^{2}\)).

To find the elasticity of demand at a price of $5, we substitute p = 5 into the elasticity function E(p), which gives us E(5) = -4(5)/(150 - \(2(5)^{2}\)) = -20/110 = -2/11.

Based on the value of the elasticity at a price of $5, we can determine that the demand is inelastic (b) since the absolute value of the elasticity is less than 1.

To increase revenue, we should raise prices (c) because the demand is inelastic. Inelastic demand means that a price increase will lead to a proportional or larger increase in revenue, indicating that customers are less responsive to price changes.

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Answer:

First, we need to find mtan using the given formula:

mtan = lim h→0 [f(a+h) - f(a)] / h

Plugging in a = 3 and f(x) = √(√3x + 7), we get:

mtan = lim h→0 [√(√3(3+h) + 7) - √(√3(3) + 7)] / h

Simplifying under the square roots:

mtan = lim h→0 [√(3√3 + √3h + 7) - 4] / h

Multiplying by the conjugate of the numerator:

mtan = lim h→0 [(√(3√3 + √3h + 7) - 4) * (√(3√3 + √3h + 7) + 4)] / (h * (√(3√3 + √3h + 7) + 4))

Using the difference of squares:

mtan = lim h→0 [(3√3 + √3h + 7) - 16] / (h * (√(3√3 + √3h + 7) + 4))

Simplifying the numerator:

mtan = lim h→0 [(√3h - 9) / (h * (√(3√3 + √3h + 7) + 4))]

Using L'Hopital's rule:

mtan = lim h→0 [(√3) / (√(3√3 + √3h + 7) + 4)]

Plugging in h = 0:

mtan = (√3) / (√(3√3 + 7) + 4)

Now we can use this to find the equation of the tangent line at P(3,4):

m = mtan = (√3) / (√(3√3 + 7) + 4)

Using the point-slope form of a line:

y - 4 = m(x - 3)

Simplifying and putting in slope-intercept form:

y = (√3)x/ (√(3√3 + 7) + 4) - (√3)9/ (√(3√3 + 7) + 4) + 4

This is the equation of the tangent line at P.

The curve y = 8e^x has maximum curvature at the point (0, 8).there is no point where the second derivative equals zero,

To determine the point of maximum curvature on the curve y = 8e^x, we need to find the second derivative of the function and identify the point where it equals zero. The second derivative represents the rate of change of the slope, or the curvature, of the curve.

First, we find the first derivative of y = 8e^x with respect to x:

dy/dx = 8e^x

Then, we differentiate again to find the second derivative:

d²y/dx² = d(8e^x)/dx = 8e^x

Setting the second derivative equal to zero:

8e^x = 0

Exponential functions, such as e^x, are never equal to zero for any value of x. Therefore, there is no point where the second derivative equals zero, indicating that the curve y = 8e^x does not have any inflection points or points of maximum curvature.

However, we can determine the point where the curvature is the greatest by considering the graph of y = 8e^x. Since the exponential function e^x is always positive, the curve y = 8e^x is always concave up. This means that the curvature is positive throughout the curve, but there is no specific point of maximum curvature.    

In conclusion, the curve y = 8e^x does not have a point of maximum curvature but is always positively curved.  

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The question gives,

We would start by converting this into feet. The conversion rate is

Therefore, the conversion would be;

Also, to convert feet into miles, the conversion rate is;

ANSWER:

The correct answer is option C: 2 miles

In the given figure, the length of line segments a, b, c, and d can be expressed in terms of trigonometric ratios.

Let's consider the given figure:

       A

       |\

  c   | \   d

       |  \

       |   \

B____C

a

Here, we can see that line segment a is adjacent to angle BAC, line segment b is opposite to angle BAC, line segment c is adjacent to angle ABC, and line segment d is opposite to angle ABC.

Using trigonometric ratios, we can express these lengths as follows:

Length a can be expressed as a = c * tan(BAC), where tan(BAC) represents the tangent of angle BAC.

Length b can be expressed as b = c * cot(BAC), where cot(BAC) represents the cotangent of angle BAC.

Length c remains the same as it is the adjacent side to angle ABC.

Length d can be expressed as d = c * tan(ABC), where tan(ABC) represents the tangent of angle ABC.

By using these trigonometric ratios, we can express the lengths of line segments a, b, c, and d in the given figure.

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Answer:

sana Po nakatulong

stay safe po

Answer:

between 10 and 12

Step-by-step explanation:

Given the measure of angles:

m∠B = 70°

m∠C = 60°

m∠A = 50°

Following this information, since the side lengths are directly proportional to the angle measure they see:

Angle B is the largest angle. Therefore, side AC is the longest side of the triangle since it is opposite of the largest angle.

Angle C is the smallest angle, so the side AB is the shortest side.

Therefore, side BC must be between 10 and 12 inches.

Statement is true because the corresponding sides are congruent. The answer is: BA = LN.

What is Triangle?

A triangle is a closed, two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and is used in many areas of mathematics, science, and engineering.

Since triangle ABC and triangle LMN have congruent corresponding sides, we know that they are similar triangles. This means that their corresponding angles are also congruent.

We are given that angle BAC is 58 degrees and angle MLN is 78 degrees. Since corresponding angles are congruent, this means that angle BAC is congruent to angle MLN.

Therefore, triangle ABC and triangle LMN are similar triangles with two pairs of corresponding congruent angles. This means that all corresponding sides are proportional.

Since AC = LN and BA = ML, we know that the ratio of the lengths of corresponding sides is:

AC / LN = BA / ML

Substituting the given values, we get:

1 = 1

This statement is true because the corresponding sides are congruent.

Therefore, the answer is: BA = LN.

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By using the concept of percentage, it can be calculated that

65% people are completely satisfied with the car

What is percentage?

Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.

For example 2% means \(\frac{2}{100}\). Here, 2 is expressed as a fraction of 100.

This is a word problem on percentage

Number of people who are completely satisfied with the car = 1495

Total number of people surveyed = 1495 + 210 + 595 = 2300

Percentage of people who are completely satisfied with the car = \(\frac{1495}{2300}\times 100\)

  = 65%

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The factor of the polynomial is option (D) (2x+5)^2 is the correct answer.

In this question,

Factorization is the breaking or decomposition of an entity (i.e.,) a number, a matrix, or a polynomial into a product of another entity, or factors, which when multiplied together give the original number. Factorize an expression involves take out the greatest common factor (GCF) of all the terms.

The polynomial is \(4x^{2} +20x+25\)

The above polynomial can be factored as

⇒ \(4x^{2} +20x+25=0\)

⇒ \((2x)^{2}+2(2x)(5)+5^{2}\)

⇒ \((2x+5)^{2}\)

Hence we can conclude that the factor of the polynomial is option (D)(2x+5)^2 is the correct answer.

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Answer:

The building is 152 cm long.

Step-by-step explanation:

-We can solve using proportion!:

\(\frac{2 cm}{1 meter} = \frac{x}{76 meters} \\\\\frac{1x}{1} =\frac{152}{1} \\\\\\x = 152\)

Answer:3.5

Step-by-step explanation: