Which equation best describes the graph shown?

The system of equations has one solution.

To check this, we can graph the two equations of the system:

y = (-1/3)x + 7

y = -2x³ + 5x² + x - 2

On the same coordinate axis, and check how many times do the graphs intercept.

The graph can be seen in the image at the end, there you can see that there is only one intecept point. Thus, the system of equations has only one solution.

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Answer:

The answer would be D hope this helps

Let's call x the angle.

Remember that its complement refers to the difference 90 - x, since complementary angles sum 90°.

Having said that, we express the following expression.

Notice that we multiplied its complement by 3 to make it triple, then we subtracted 51 since the angle x is 51 less.

Let's solve for x now

Answer:

The identity is proved below.

Step-by-step explanation:

The tangent of an angle \(\theta\) is given by:

\(\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}\)

In this question, we are given the following trigonometric identity:

\(\frac{\sin{\theta}}{\sin{\theta}+\cos{\theta}} = \frac{\tan{\theta}}{1+\tan{\theta}}\)

Applying the tangent

\(\frac{\sin{\theta}}{\sin{\theta}+\cos{\theta}} = \frac{\frac{\sin{\theta}}{\cos{\theta}}}{1+\frac{\sin{\theta}}{\cos{\theta}}}\)

Now, we apply the least common multiple on the denominator. So

\(\frac{\sin{\theta}}{\sin{\theta}+\cos{\theta}} = \frac{\frac{\sin{\theta}}{\cos{\theta}}}{\frac{\cos{\theta}+\sin{\theta}}{\cos{\theta}}}\)

SImplifying the cosine:

\(\frac{\sin{\theta}}{\sin{\theta}+\cos{\theta}} = \frac{\sin{\theta}}{\sin{\theta}+\cos{\theta}}\)

Which means that the identity is proved.

Answer:

d) Asking questions to make sure they understand what's being said

Step-by-step explanation:

Asking questions is important for learning and clears up any confusion.

Answer:

The p-value of the test is 0.2262 > 0.02, which means that the decision is to fail to reject the null hypothesis.

Step-by-step explanation:

An automobile manufacturer has given its jeep a 51.3 miles/gallon (MPG) rating.

At the null hypothesis, we test if the mean is of 51.3, that is:

\(H_0: \mu = 51.3\)

An independent testing firm has been contracted to test the actual MPG for this jeep since it is believed that the jeep has an incorrect manufacturer's MPG rating.

This means that at the alternative hypothesis, we test if the mean is different of 51.3, that is:

\(H_0: \mu \neq 51.3\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.

51.3 is tested at the null hypothesis:

This means that \(\mu = 51.3\)

After testing 230 jeeps, they found a mean MPG of 51.1. Assume the population variance is known to be 6.25.

This means that \(n = 230, X = 51.1, \sigma = \sqrt{6.25} = 2.5\)

Value of the test statistic:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{51.1 - 51.3}{\frac{2.5}{\sqrt{230}}}\)

\(z = -1.21\)

P-value of the test and decision:

The p-value of the test is the probability of the sample mean differing from 51.1 by at least 0.2, which is P(|z| > 1.21), which is 2 multiplied by the p-value of z = -1.21.

Looking at the z-table, z = -1.21 has a p-value of 0.1131.

2*0.1131 = 0.2262

The p-value of the test is 0.2262 > 0.02, which means that the decision is to fail to reject the null hypothesis.

The value of the n is 1

In a direct variation, the relationship between two variables is of the form y = kx, where k is a constant of proportionality.

To find the constant of proportionality k in this problem, we can use the fact that the given points satisfy the equation for direct variation.

(2,18) is one of the given points, so we can substitute these values into the equation y = kx and solve for k:

18 = k(2)

k = 18/2

k = 9

Now that we have found the value of k, we can use it to find n when y = 9:

9 = 9n

n = 1

Therefore, the value of n is 1.

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Answer:

The correct answer would be: "Maximum height 9 feet; horizontal distance 9 feet".

Step-by-step explanation:

I know this not only because I already took the test, BUT by graphing the equation (you can use graphing apps) it'll give you the answer.

Her maximum height is 9 feet & she is horizontally 9 feet from the end of the ramp when she lands.

The path of the skateboarder can be modelled by the equation,

(x-3)² = -4(y-9)

Now, from the equation, solving y,

(x-3)² = -4(y-9)

⇒ y-9 = -\(\frac{1}{4}\)(x-3)²

⇒ y = -\(\frac{1}{4}\)(x-3)² + 9

∴ Maximum height is 9 feet.

We have to take y = 0,

Now, -\(\frac{1}{4}\)(x-3)² + 9 = 0

        ⇒ -(x²-6x+9)+36 = 0

        ⇒ -x²+6x-9+36 = 0

        ⇒  x²-6x-27 = 0

        ⇒ x²-9x+3x-27 = 0

        ⇒ (x-9)(x+3) = 0

        ⇒ x = 9 or x = -3

Neglecting the negative value we get, x = 9

So, Her horizontal distance from end of the ramp is 9 feet.

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The hypotenuse = √2 · legs

x = √2 · 5

x = 5√2

The given function is continuous at  x = 3,  RHL = LHL = F(2)

In mathematics, The function is called as continuous at the particular value of x,  if right hand limit, left hand limit and the value of function at x all are equal.

RHL   = LHL  = F(x)

Limit exist and continuous

Given that,

F(x)  =  (x²-9)/(x² - x -6)(x² + 6x +9)

To check whether it is continuous at x = 2

First taking LHL,

\(\lim_{h \to \ 0}\)  ((2-h)²-9)/((2-h)² - (2-h) -6)((2-h)² + 6(2-h) +9)

⇒  -5/(-4x25)

⇒   1/20

Now, taking RHL

\(\lim_{h \to \ 0}\)  ((2+h)²-9)/((2+h)² - (2+h) -6)((2+h)² + 6(2+h) +9)

⇒  -5/(-4x25)

⇒   1/20

The value at x = 3

F(3)  =   ((2)²-9)/((2)² - (2) -6)((2)² + 6(2) +9)

       =  -5/(-4x25)

       =   1/20

Hence Proved,   RHL = LHL = F(2)

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Answer:

0.0083 = 0.83% probability that the boys will stand in alphabetical order from left to right in the picture

Step-by-step explanation:

Probability:

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Arrangments of x elements:

The total number of arrangments of x elements is given by:

\(A_{x} = x!\)

Desired outcomes:

Standing in alphabetical order, so only 1 possible outcome, which means that \(D = 1\)

Total outcomes:

Arrangments of 5 people, so

\(T = A_{5} = 5! = 120\)

Probability:

\(p = \frac{D}{T} = \frac{1}{120} = 0.0083\)

0.0083 = 0.83% probability that the boys will stand in alphabetical order from left to right in the picture

The situation Veronica receives $21 for babysitting, and then spends the same amount, $21, on a new shirt quantities combine to make 0.The correct answer is option C.

When we add +21 (the money she receives) and subtract -21 (the money she spends), the result is 0. This means that the net change in Veronica's money is zero, indicating that the quantities combine to make 0.

In situations A, B, and D, the quantities do not combine to make 0. In situation A, the player earns 4 points for getting an answer right and then earns an additional 4 points for making it around the board.

The total points earned in this situation would be 8, which is not equal to 0.

In situation B, the car is initially filled with 10 gallons of gas, but then half of that, which is 5 gallons, is used on a day's drive. The remaining fuel in the car would be 5 gallons, which is also not equal to 0.

In situation D, the bird flies 25 feet up in the air and then 25 feet across to its nest. The total distance traveled by the bird would be 50 feet, which is not equal to 0.

Therefore, only in situation C, where Veronica receives and spends the same amount of money, do the quantities combine to make 0.

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The probable question may be:

In which of these situations do the quantities combine to make 0?

A. A player a game earns 4 points for getting an answer right. She then earns 4 points for making it around the board.

B. A car is filled with 10 gallons of gas. Half of the 10 gallons are then used on a day's drive.

C. Veronica receives $21 for babysitting. She then spends $21 on a new shirt.

D. A bird flies 25 feet up in the air. It then flies 25 feet across to its nest.

Answer:

  c.  71°

Step-by-step explanation:

You have isosceles triangle XYZ with a.pex angle Y = 38°. You want to know the measure of angle Z.

The base angles of the triangle are X and Z, which are congruent. The sum of all angles is 180°:

  X +Y +Z = 180°

  2Z +38° = 180° . . . . . . substitute for X and Y

  2Z = 142° . . . . . . . . . subtract 38°

  Z = 71° . . . . . . . . . . divide by 2

The measure of angle Z is 71°.

If principal is $2,658 and rate of interest 9% then the value of  the account balance is approximately $10,253 by using continuous compound interest formula.

Recurring interest is interest calculated on principal plus all interest and other interest. The idea is that lenders always receive interest, not individually at specific times.

The formula for continuous compound interest :

  A=    Peˣⁿ                          

Where,

A =Amount of money  after a certain amount of time

P= principal or the amount of money you start with

e =Napier's number, which is approximately 2.7183

x =Interest rate

n =Amount of time in years.

Use the continuous compound interest formula :

Given  P= 2658

x =9% =   = 0.09

n = 15

e = 2.7183

By using

A=    Peˣⁿ  

A= (2658)(2.7183)⁰°⁰⁹¹⁵

A =10,253 (approximately)

Hence, the value of account balance after 15 years is approximately $10,253

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Answer:

Yes.

Step-by-step explanation:

They are definitely the same. They have the same angles, they are just flipped around, to make it look different, when in reality they are the same thing.

:)

no they r not identical bez

for being identical they must have same length of sides with same angles

The required appropriate properties to fit the black space is given as,
(a) Congruent angles
(b) Addition of angles
(c) straight angles
(d) Subtraction of angles.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

It is given that m ∠ AOB = 42 ∘ and m ∠ EOF = 66 ∘ . By the definition of congruent angles, ∠ EOF ≅ ∠ BOC. Therefore, m ∠ BOC = 66 ∘ . In the addition, m ∠ AOC = 108 ∘ , and by definition of the straight angle, m ∠ AOC + m ∠ COD = 180 ∘ . After application of the subtraction of the angle, m ∠ COD = 72 ∘ .

Thus, the required appropriate properties to fit the black space is given as,
(a) Congruent angles
(b) Addition of angles
(c) straight angles
(d) Subtraction of angles.

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Answer:

It is given that m∠AOB = 42º and m∠EOF = 66º. By the vertical angles theorem, ∠EOF ≅ ∠BOC. By the angle addition postulate, m∠AOC = 108º, and by the linear pair theorem, m∠AOC + m∠COD = 108º. After the application of the subtraction property of equality, m∠ COD = 72º.

Step - by - step

first box: vertical angles theorem

second box: angle addition postulate

third box:  linear pair theorem

fourth box: subtraction property of equality

The correct statement that F: "I agree. The ratios of consecutive x-values are constant, and the y-values are increasing at a constant rate."

To determine whether the function shown in the table is exponential, we need to analyze the relationship between the x-values and y-values.

The table shows x-values that are increasing by a power of 2 (1, 2, 4, 8, 16, 32, 64) and y-values that are increasing by a constant rate of 1 (0, 1, 2, 3, 4, 5, 6).

The constant ratio between consecutive x-values indicates exponential growth or decay.

In this case, the function is growing exponentially because the y-values are increasing at a constant rate.

Based on this information, we can conclude that the function is exponential.

Therefore, we agree with statement F: "I agree. The ratios of consecutive x-values are constant, and the y-values are increasing at a constant rate."

The other statements are incorrect because they do not accurately describe the relationship between the x-values and y-values in an exponential function.

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1. The possible amounts of time for which the chemistry club could rent the meeting room are 1 to 5 hours.

2. Solving the inequality for t is 39 + 6.80t ≤ 73, where the maximum time is 5 hours.

Inequality is a mathematical statement that two or more mathematical expressions are unequal.

Inequalities are depicted using the following symbols:

The total budget of the chemistry club for renting a meeting room = $73.60

The reservation fee charged by the college = $39

The additional fee (variable cost) per hour = $6.80

The number of hours the club can rent the meeting room = t

The inequality representing the situation is:

39 + 6.80t ≤ 73.

39 + 6.80t ≤ 73

6.8t ≤ 73 - 39

6.8t ≤ 34

t ≤ 5 (34/6.8)

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Answer:

Based on the given data, there is no evidence to support the claim that the standard deviation of the heights of women aged 25 to 34 have a different standard deviation from men aged 25 to 34

Step-by-step explanation:

The standard deviation for the heights of men aged 25 to 34, σ₀ = 2.9

The population variance, σ₀ = 2.9² = 8.41

The significance level of the test = 0.05

The number of randomly selected women in the sample, n = 16

The given heights of the 16 randomly selected women are listed as follows;

62.13, 65.09, 64.18, 66.72, 61.15, 67.50, 64.65, 63.09, 63.80, 64.21, 60.17, 68.28, 66.49, 62.10, 65.73, 64.72

By using the Mean (Average) and standard deviation of a sample formula from Microsoft Excel, we have;

The mean height of the women, \(\overline x\) = 63.37563

The standard deviation of the variance, s₂ = 2.2 78511

The null hypothesis, H₀; σ = 2.9

The alternative hypothesis, H₀; σ ≠ 2.9

The chi-square test is given as follows;

T = (N - 1)(s/σ₀)²

Therefore, we have;

T = (16 - 1)(2.278511/2.9)² ≈ 9.2597

The critical value for the lower tail = 6.908

The critical value for the upper tail = 28.845

For the critical region, we have;

Reject H₀ if T <6.908 or T > 28.845

Therefore, given that the critical T is larger than 6.908 and less than 28.845, we fail to reject the null hypothesis, and there is not enough statistical evidence to prove that there is a difference in the standard deviation of the heights of men and women aged 25 to 34

The volume of the hexagonal prism is 212.4 unit square

Prism is three-dimensional solid which has identical faces at both ends. It is a polyhedron, which means all faces are flat.

How to determine this

When an hexagonal prism has a base area = 36 units

Height = 5.9 units

Volume of Prism = Base area * Height

Volume of prism = 36 units * 5.9 units

Volume = 212.4 units square

Therefore, the volume of the hexagonal prism is 212.4 units square

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The value of every variable in the parallelogram is: a = 9 HK = 27.0 GK = 46 G = 63.5°

A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.These shapes include squares, rectangles, rhombuses, and rhomboids. All of these shapes have four sides, four corners, and four angles

We know that sides of a parallelogram are parallel and congruent, as opposite angle

According to question  that GA equals HK, as:

46 is equal to 3a plus 19 When we subtract 19 from both sides, we get:

27 x 3a is the result of dividing both sides by 3:

we know that opposite angles in a parallelogram are congruent, we can use a = 9. Since angle H is 56 degrees, angle K must also be 56 degrees. The length of side HK can be determined using the Law of Cosines:

HK2 = GA2 + GK2 - 2(GA)(GK)cos(H) When we substitute the values we are familiar with, we obtain:

After solving the equation we obtain: HK2 = 462 + (3a + 19)2 - 2(46)(3a + 19)cos(56°).

HK2 = 2112 + 9a2 + 342a - 2764cos(56°) HK2 = 2112 + 9(9)2 + 342(9) - 2764cos(56°) HK2  732.4 By taking the square root of both sides, we obtain the following results:

∵ GA = 46, we can use the parallelogram's opposite sides being congruent to determine the length of side GK: HK  27.0

Then, we can use the Law of Cosines to determine the angle G's measurement:

cos(G) = (HK2 + GA2 - GK2) / (2(HK)(GA)) Using the values we are familiar with, we get,

cos(G) = (27.02 + 462 - 462) / (2(27.0)(46)) cos(G)  0.465 Using the inverse cosine, we get the following:

G ≈ 63.5°

Hence, the worth of every variable in the parallelogram is:

a = 9 HK = 27.0 GK = 46 G = 63.5°

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The required value of h, representing the height of the three-dimensional rectangle, is 12.

The diagonal of a three-dimensional rectangle is defined by the equation d² = x² + y² + h². To solve for h, we can rearrange the equation as follows:

h² = d² - x² - y²

Given the values d = 13, x = 3, and y = 4, we can substitute them into the equation:

h² = 13² - 3² - 4²

h² = 169 - 9 - 16

h² = 144

Taking the square root of both sides, we find:

h = 12

Therefore, the value of h, representing the height of the three-dimensional rectangle, is 12.

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Answer:

x=130°

y=50°

z=130°

Step-by-step explanation:

__________

Answer:

x = 130°

y = 50°

z = 130°

Step-by-step explanation:

From the diagram, you can see that the angle given, 50° is a vertical angle to y. This means they are equal, so y = 50°.

Next, angle x, and the given 50° angle are supplementary since they form a straight line. Because of this, you get that:

50° + x = 180°

- and -

x = 130°

You can see that angle z is a vertical angle to angle x, so they are equal, which gives you z = x = 130°. --> z = 130°

The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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Area of sector would be,

⇒ Area of sector = 102.6 feet squared

We have to given that,

Radius of circle = 14 ft

Angle θ = 60°

Now, We know that,

Area of sector = [θ/360]πr²

Where, r is radius of circle.

Hence, We can substitute all the values, we get;

Area of sector = [θ/360]πr²

Area of sector = [60/360](22/7)(14)²

Area of sector = [1/6][22/7][196]

Area of sector = 102.6 feet squared

Thus, Area of sector would be,

⇒ Area of sector = 102.6 feet squared

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