Use the given terms to generate a recursive rule. Sequence:13,15,23,55,183

Answer:

\(4.\\\text{E. }x=5, x=-6,\\\\5.\\\text{A. }x=7, x=-3\\\\\text{18.}\\\text{D. No mistakes.}\)

Step-by-step explanation:

For \(a=|b|\), there are two cases:

\(\begin{cases}a=b,\\a=-b\end{cases}\)

Question 4:

Given \(5|2x+1|=55\),

Divide both sides by 5:

\(|2x+1|=11\)

Divide into two cases and solve:

\(\begin{cases}2x+1=11,2x=10, x=\boxed{5}\\-(2x+1)=11,2x+1=-11, 2x=-12, x=\boxed{-6}\end{cases}\)

Therefore, the solutions to this equation are \(\boxed{\text{E. }x=5, x=-6}\).

Question 5:

Given \(\frac{1}{2}|4x-8|-7=3\),

Add 7 to both sides:

\(\frac{1}{2}|4x-8|=10\)

Multiply both sides by 2:

\(|4x-8|=20\)

Divide into two cases and solve:

\(\begin{cases}4x-8=20,4x=28, x=\boxed{7}\\-(4x-8)=20, 4x-8=-20, 4x=-12, x=\boxed{-3}\end{cases}\)

Therefore, the solutions to this equation are \(\boxed{\text{A. }x=7, x=-3}\)

Question 18:

There are no mistakes in the solution shown. The answer properly isolates the term with absolute value with no algebraic mistakes. Following that, the answer divides the equation into both absolute value cases and solves algebraically correctly. Therefore, the correct answer is \(\boxed{\text{D. No mistakes.}}\)

The measure of angle T is 122 degrees in the pentagon

The sum of the interior angles of a pentagon is 180(5-2) = 540 degrees.

We can use this fact to find the measure of angle T

angle ∠T = 540 - ∠P - ∠Q -∠R -∠S

∠T = 540 - 85 - 134 - 97 - 102

∠T = 122

Therefore, the measure of angle T is 122 degrees in the pentagon

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The number of miles in a day at which the rental costs for Company A and Company B are the same will be 200 miles.

We are given that:

For Company A:

Fixed cost = $ 110

Variable cost = $ 0.20 per mile

For Company B:

Fixed cost = $ 70

Variables cost = $ 0.40 per mile

Let the number of miles in a day be x.

So, the equation for rental cost for company A will be:

Rental cost = 110 + 0.20 x

The equation for rental cost for company B will be:

rental cost = 70 + 0.40 x

Now, put both rental cost equal.

110 + 0.20 x = 70 + 0.40 x

0.40 x - 0.20 x = 110 - 70

0.20 x = 40

x = 40 / 0.20

x = 200 miles.

Therefore, the number of miles in a day at which the rental costs for Company A and Company B are the same will be 200 miles.

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Step-by-step explanation:

hope it helps.

Answer:

Below

Step-by-step explanation:

√(18*49)

= √882

= 29.70 to nearest hundredth.

Answer:

Step-by-step explanation:

b)  The number of roots, doubled tripled etc, should add up to degree.  We know that the curve is even becuase both ends are facing downward..  So the roots/solutions/zeroes, should add up to an even amount.

Roots happen when the curve hits the x-axis

Root (-2,0) is a single root because it goes right through the x-axis

Root (1,0) is a triple.   It does not go right through like a single,  it does not bounce off (like a parabolic shape) that's a double.  This tripe goes through but squiggles through so it's a triple.

C)  We will use factored form and the roots. Each root goes in a parenthesis, opposite sign.   If doubled will be squared, tripled will be cubed.  Also there is a negative in the front because it is a negative curve.

y= -(x+2)(x-1)³

30ft high above the ground is the lamp.

What is an angle?

An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Here, we have

BC⊥AD and DE⊥AD

∠ABC = ∠ADE(=90°)

Also,∠A=∠A

ΔABC ΔADE (AA similarity)

AB/AD = BC/DE

40/(200 + 40) = 5ft/DE

DE = 5ft×6 = 30ft

Hence, 30ft high above the ground is the lamp.

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Answer:

189 minutes or 3 hours and 9 minutes

Step-by-step explanation:

Answer:

189 minutes or 3 hours and 9 minutes

Step-by-step explanation: N/A

The mean driving distance of the cricket balls is greater than 200 yards. Therefore, the ball manufacturing process should continue operating.

To perform a hypothesis test, we need to set up the null and alternative hypotheses:

Null hypothesis: The population mean driving distance of the cricket balls is 200 yards (µ = 200).

Alternative hypothesis: The population mean driving distance of the cricket balls is greater than 200 yards (µ > 200).

We can use a one-sample t-test to test the hypothesis since the sample size is less than 30 and the population standard deviation is unknown. The test statistic is given by:

t = (sample mean - hypothesized mean) / (sample standard error)

t = (203 - 200) / (12 / sqrt(30))

t = 1.8371

The degrees of freedom for the test is n - 1 = 29.

Using a t-distribution table or a calculator, the p-value for a one-tailed test with 29 degrees of freedom and a t-value of 1.8371 is approximately 0.0406.

Since the p-value (0.0406) is less than the significance level of 0.05, we reject the null hypothesis.

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Answer:

a. To find the volume when the width is 5 inches, we plug in w=5 into the equation:

V = 2w³ - 7w² + 3w

V = 2(5)³ - 7(5)² + 3(5)

V = 250 - 175 + 15

V = 90

Therefore, the volume is 90 cubic inches.

b. To factor the polynomial, we can first factor out a w:

V = w(2w² - 7w + 3)

Then we can factor the quadratic expression in parentheses:

V = w(2w - 1)(w - 3)

Each factor represents a dimension of the rectangular prism:

w is the width

2w - 1 is the length

w - 3 is the height

c. If the width is 5 inches, we can use the factorization from part b to find the other dimensions:

length = 2w - 1 = 2(5) - 1 = 9 inches

height = w - 3 = 5 - 3 = 2 inches

This means that the rectangular prism has dimensions 5 inches by 9 inches by 2 inches. We can also use the dimensions to calculate the volume:

V = 5 × 9 × 2 = 90 cubic inches

This is the same as the answer from part a.

d. The graph of the polynomial is:

Graph of the polynomial

The x-intercepts are approximately 0.5 and 3. These correspond to the widths at which the volume is 0, which means the rectangular prism has zero volume. In other words, the x-intercepts represent the points where the rectangular prism collapses into a flat shape.

e. The domain of the function is all real numbers, since we can plug in any width w and get a corresponding volume. The range of the function is also all real numbers, since the volume can be any positive or negative value depending on the width. Specifically, the range is (-∞, ∞).

A person's cycling rate can be expressed mathematically in the equation that describes their cycling motion. Specifically, the cycling rate can be represented by the frequency or number of revolutions per unit time (usually in seconds) that the person completes while cycling.

The equation that describes a person's cycling motion is typically a kinematic equation that relates the person's position, velocity, and acceleration as a function of time. One commonly used equation is:

d = vit + 1/2at^2

where d is the distance traveled by the person, vi is the initial velocity (usually zero), a is the acceleration, and t is the time elapsed.

The cycling rate can be incorporated into this equation by expressing the velocity as a function of the frequency of revolutions (f) and the radius of the wheel (r). This gives:

v = 2πrf

where v is the velocity of the cyclist, r is the radius of the wheel, and π is the mathematical constant pi (approximately 3.14).

Substituting this expression for v into the kinematic equation gives:

d = (2πrf)t + 1/2at^2

This equation shows how the person's cycling rate, represented by the frequency f, affects their distance traveled as a function of time. If the person increases their cycling rate, their velocity increases, and they will travel a greater distance in the same amount of time.

Answer: 32,000 meters

Step-by-step explanation:

By definition, 1 km = 1,000 m.

Make this into a conversion factor:  [(1,000 m)/(1 km)]

Then convert 32 km to meters by multiplying, in order to cancel the km and leave just meters:

  (32 km)*(1,000 m)/(1 km) = 32,000 meters  

[Note that km cancel and we are left with meters]

The order of the schools from the closest to farthest away from summer snow cones is South Elementary < West Side Elementary < North Junior High  .

In the question ,

it is given that

the Summer is planning to build a small snow cone shed .

the distance from north junior high = 7/8 miles = 0.875 miles

the distance from South elementary = 0.680 miles

the distance from West Side elementary = 5/6 miles = 0.833 miles

From , above result we see that

the farthest from summer snow cone is north junior high which is 0.875 miles .

the nearest from summer snow cone is South Elementary which is 0.680 miles .

So , the order from closest to farthest is

South Elementary < West Side Elementary < North Junior High

Therefore , The order of the schools from the closest to farthest away from summer snow cones is South Elementary < West Side Elementary < North Junior High  .

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Answer:

Step-by-step explanation:

To evaluate the given expression, we need to substitute the given values for x, y, and z. The expression becomes:

yz + x²

Substituting the given values, we get:

(6.1 * 0.2) + (3.2^2)

This simplifies to:

1.22 + 10.24

Therefore, the value of the expression is approximately 11.46.

11.46

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\(\frac{1187.25}{21.25}\) is equal to the maximum number of players the team can bring to the tournament, that is, \(x\).

In this context, we are to represent tape diagrams that could represent the situation where members of a baseball team raised $1187.25 to go to a tournament.

They rented a bus for $783.50 and budgeted $21.25 per player for meals. The tape diagram should be one that represents the context if x represents the number players the team can bring to the tournament.

Tape diagrams, also known as bar models, are pictorial representations that are helpful in solving word problems. They represent numerical relationships between quantities using bars or boxes.

Tape diagrams are used to solve a wide range of word problems, including problems related to ratios, fractions, and percents.

According to the context given, a tape diagram that could represent the situation where x represents the number of players the team can bring to the tournament can be illustrated as follows:
Hence, the tape diagram above represents the given situation if x represents the number of players the team can bring to the tournament.

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Estimating a population mean involves using a sample of data to make inferences about the overall average of a larger group or population. This is done by calculating a confidence interval, which provides a range of values where the true population mean is likely to lie.

In order to estimate the population mean birth weight of all girls, we can use a sample mean and standard deviation to construct a confidence interval. Assuming that the population standard deviation (o) is 2.9 hg, the sample mean is 30.9 hg, and the sample size (n) is 15, we can use the formula:

Confidence interval = sample mean ± (z-value x standard error)

The z-value is determined by the desired level of confidence and can be found in a standard normal distribution table. For a 95% confidence level, the z-value is 1.96. The standard error can be calculated by dividing the population standard deviation by the square root of the sample size:

Standard error = o / sqrt(n) = 2.9 / sqrt(15) = 0.748

Substituting these values into the formula, we get:

Confidence interval = 30.9 ± (1.96 x 0.748) = (29.44, 32.36)

Therefore, we can say with 95% confidence that the true population mean birth weight of all girls lies within the range of 29.44 hg to 32.36 hg. This means that if we were to take many samples of size 15 from the population and construct 95% confidence intervals for each sample, about 95% of those intervals would contain the true population mean.

In other words, based on our sample data, we can be reasonably confident that the average birth weight of all girls falls within the calculated interval.

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Answer:

Supplementary Angles: AOC and COD

Complementary Angles: COB and COD

Vertical Angles: AOE and COD

Adjacent Angles not supplementary or complementary: AOB and BOC

Step-by-step explanation:

Answer:

Step-by-step explanation:

Supplementary angles       : AOC & COD  

Complementary angles     :   COB & COD

Vertically angles                :  AOE & COD

Adjacent angles   (neither complementary nor supplementary)             :   AOB & BOC

The number of necklaces at the break-even point will be 10.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Kurt is beginning a business selling high-quality neckbands. He has chosen to contribute an underlying measure of $20 for publicizing, and materials cost $7 for every accessory he makes. Kurt can sell his manifestations for $9 per piece of jewelry.

Let 'x' be the number of necklaces. Then the equations are given as,

Cost = 7x + 20

Sell = 9x

The number of necklaces at the break-even point is calculated as,

Sell = Cost

9x = 7x + 20

2x = 20

x = 10

The number of necklaces at the break-even point will be 10.

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From the given ratio, the number of yellow flowers are; 40 flowers

We are given;

Total number of flowers in the garden = 56

Ratio of orange to yellow flowers is; 2:5

Thus;

Fraction of total gives;

Fraction that is orange flowers = 2/7

Fraction that is yellow flowers = 5/7

Thus;

Number of yellow flowers = (5/7) * 56

Number of yellow flowers = 40 yellow flowers

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The system of statements, in standard form, modeling the relationships between amount of yoys (x) and amount of quects (y) is x ≥ 17, x ≥ 7y, and x + 7y ≤ 28.

The system of statements, in standard form, modeling the relationships between amount of yoys (x) and amount of quects (y) is calculated as follows;

She expected to sell at least 17 yoys, the equation  becomes;

x ≥ 17

She expected to sell at least $7 per quect, the equation becomes;

x ≥ 7y

She expected to make no more than $28.

x + 7y ≤ 28

The statements combined in standard form becomes;

x ≥ 17, x ≥ 7y, and x + 7y ≤ 28

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Answer:

Midpoint is (0, -4)

Step-by-step explanation:

x-coordinate of midpoint = (-7 + 7)/2 = 0/2 = 0

y-coordinate of midpoint = (3 - 11)/2 = -8/2 = -4

Midpoint is (0, -4)

Answer:

(0,-4)

Step-by-step explanation:

(x1 + x2/2,  y1 + y2/2)

(-7 + 7/2 ,  3 + -11/2)

(0/2,  -8/2)

(0,-4)

Step-by-step explanation:

solution

let first part be 5x and second part be 9x

so ,

5x = 35

x = 35\5

x = 7

Now 9x = 9*7 = 63

this might help you thank you

From calculations, the given integral ∫c x sin(y)ds is equal to \(20\left(-\frac{1}{3}\cos \left(4\right)+\frac{1}{9}\sin \left(4\right)-\frac{1}{9}\sin \left(1\right)\right)=0.806\).

The integrals are the opposite of derivatives. They are used in several applications, like: calculations of areas, volumes and others.

For solving an integration, you should know its rules. For this question will be necessary to apply the following integration rules:

First, you should calculate the segment from the points (0, 1) and (4, 4).

segment=(4-0,4-1)=(4,3).

After that you should parametrize the segment:

r(t)=(0,1)+(4t,3t)= (4t,3t+1), where 0≤t≤1

Now, you can find dr/dt.

r'(t)=(4,3)

Consequently, the magnitude of |r'(t)| will be:

|r'(t)|  =\(\sqrt{4^2+3^2}=\sqrt{16+9}=\sqrt{25} =5\)

Finally you can evaluate the integral: ∫c x sin(y)ds. From r(t), you know that x=4t and y=3t+1.

\(\int _0^1\:xsin\left(y\right)\:ds=\int _0^1\:4t\cdot sin\left(3t+1\right)\:\cdot 5ds=\int _0^1\:20t\cdot sin\left(3t+1\right)\:\cdot ds\)

Applying the Rule Integration for a Constant.

\(\int _0^1\:20t\cdot sin\left(3t+1\right)\:\cdot dt\\ \\ 20\cdot \int _0^1t\sin \left(3t+1\right)dt\\ \\\)

Applying the Rule Integration by Parts.

∫u v dx = uv -∫v du

u=t

dv= sin(3t +1 )dt, then v=

\(=20\left[-\frac{1}{3}t\cos \left(3t+1\right)-\int \:-\frac{1}{3}\cos \left(3t+1\right)dt\right]^1_0\\ \\=20\left[-\frac{1}{3}t\cos \left(3t+1\right)+\frac{1}{9}\sin \left(3t+1\right)\right]^1_0\\ \\ =20\left(-\frac{1}{3}\cos \left(4\right)+\frac{1}{9}\sin \left(4\right)-\frac{1}{9}\sin \left(1\right)\right)\\ \\ =0.806\)

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The value of the integral  ∫c x sin(y)ds where c is the curve is 0.806 if the line segment is from (0,1) to (4,4).

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

First, we have to calculate line segment (0,1 ) to (4, 4)

= (4-0, 4-1) = (4, 3)

Parametric form of the segment:

P(t) = (0+4t, 3t)   where 0 ≤ t ≤ 1

Now differentiate the segment:

P'(t) = (4, 3)

The magnitude of the P'(t)

\(\rm P'(t) = \sqrt{4^2+3^2}\)

P'(t)  = 5

Now the integration can be evaluated from the P(t)

\(\rm \int\limits^1_0 {xsin(y)} \, ds = \int\limits^1_0 {4tsin(3t+1)} \, 5ds\)    ( x= 4t, y = 3t+1)

\(\rm \int\limits^1_0 {xsin(y)} \, ds = 20\int\limits^1_0 {tsin(3t+1)} \, ds\)

The value of the integration:

\(\rm \int \limits^1_0 {tsin(3t+1)} \, ds = 0.040\)

\(\rm \int\limits^1_0 {xsin(y)} \, ds = 20(0.04)\)

\(\rm \int\limits^1_0 {xsin(y)} \, ds =0.806\)

Thus, the value of the integral  ∫c x sin(y)ds where c is the curve is 0.806 if the line segment is from (0,1) to (4,4).

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The symbol for proportionality is "∝". It is read as "is proportional to" or "varies in proportion to".

Proportionality is a mathematical concept that describes the relationship between two quantities. When two quantities are proportional, it means that they have a constant ratio. For example, the distance traveled by a car is proportional to the time it takes to travel that distance. This means that if the time taken to travel doubles, then the distance traveled also doubles.

In mathematics, we use the symbol "∝" to represent proportionality. This symbol is read as "is proportional to" or "varies in proportion to". So, if we say that A ∝ B, it means that A is proportional to B. This implies that if B increases or decreases, then A also increases or decreases, but the ratio of A to B remains constant.

The concept of proportionality is used in various mathematical fields, such as algebra, geometry, and physics. It is a powerful tool for solving problems that involve relationships between quantities, and it is widely used in real-world applications, such as in engineering, economics, and statistics.

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Answer:

x>9

Step-by-step explanation:

\(\frac{1}{3}\)x-7 > -4

\(\frac{1}{3}\)x > -4+7

\(\frac{1}{3}\)x > 3 (multiply the whole equation by 3)

x>9

Answer:

7.5

Step-by-step explanation:

10 is to 8 as    x is to 6

10/8  = x/6

6 (10/8) = x = 7.5

Answer:

Step-by-step explanation:

The two triangles are similar because the corresponding angle in each is equal to the angle corresponding angles in the other.

Put in simpler language. ΔAEB ~ ΔADC by parallel lines properties. If that's the case 10/(10 + 8) = x/(x + 6)

Equation

AE/AD = AB/AC                  Substitute values

Solution

10/(10 + 8) = x/(x + 6)           Cross Multiply

10*(x + 6) = x* (10 + 8)          Combine

10*(x + 6) = 18x                     Remove the Brackets

10x + 60 = 18x                      Subtract 10x from both sides

8x = 60                                 Divide by 8.

x = 60/8

x = 7.5

Answer: A

The number is x. And the value of x after calculating the equation is -2.

Let x be the number

A number decreased by 10 is the same as 8 minus 2 times the number.

(Twice a number) (decreased by) (8) (is equal to) (the number) (decreased by) (10)

   2x - 8  =  x  - 10.

So, we have:

2x - 8 = x - 10

subtracting x from both sides

2x - 8 - x = x - 10 - x

x - 8 = -10

adding 8 on both sides we get

x - 8 + 8 = -10 + 8

x = -10 + 8

x = -2

the number x, = -2

The number is x. And the value of x after calculating the equation is -2.

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