Find and prove algebraically the solutions (coordinate points) to the system of equations?
fx=x²+2x-1 and g x=x+1

Answer: 5

Step-by-step explanation:

tan(32) = x/8

8 x tan(32) = x

x = 4.998 ≈ 5

I remember doing this but I don’t seem to remember sorry

Answer:

Gary bought 5 notebooks

Step-by-step explanation:

the equation used for this would be 3n = 15

meaning you divide both sides by 3 which gets you n = 5

The list that gives the sample space for pulling two slips of paper out of the bucket with replacement is List 4.

The sample space for pulling two slips of paper out of the bucket with replacement means that after drawing the first slip of paper, it is returned to the bucket before drawing the second slip.

This means that each draw is independent of the previous draw, and the possible outcomes of each draw remain the same for all subsequent draws.

The possible outcomes for each draw are {Red, Blue, Yellow}, and there are three possible outcomes for each draw.

Since we are drawing with replacement, each draw has the same possible outcomes and the same number of outcomes. So, the total number of possible outcomes for two draws is simply the number of outcomes for a single draw raised to the power of 2:

3 x 3 = 9

Therefore, the list that gives the sample space for pulling two slips of paper out of the bucket with replacement is List 4.

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The equation is a linear combination of three angles that add up to 180°, he might consider using systems of linear equations or other algebraic methods to solve for the variables.

given that za + 2d + g = 180°, some observations that could potentially be useful to Jason include:

Identifying any relationships or constraints between the variables za, d, and g that might help him simplify or solve the equation. For example, if he knows that za and g are complementary angles (i.e., they add up to 90°), he could substitute 90 - za for g in the equation to get a new expression in terms of za and d.

Using additional information about the angles or the situation to derive new equations or constraints that could help him solve for one or more variables. For example, if he knows that za and d are equal (i.e., za = d), he could substitute za for d in the equation to get a new expression in terms of za and g.

Identifying any patterns or structures in the equation that might suggest a particular approach or technique for solving it. For example, if he notices that the equation is a linear combination of three angles that add up to 180°, he might consider using systems of linear equations or other algebraic methods to solve for the variables.

Ultimately, the most effective observations for completing the proof will depend on the specific details of the problem and the approach that Jason is taking.

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The complete question:Jason knows that za + 2d + g = 180°. Which of the following observations, if true, would allow him to prove a statement or theorem related to the angles za, d, and g?

The triangles are necessarily congruent by the ASA congruence rule.

The ASA, which is an acronym for Angle-Side-Angle, congruence rule states that if two angles and an included side of one triangle are congruent to two angles and an included side of another triangle, then the two triangles are congruent.

The angle markings on the triangles ΔJLK and ΔZXY indicates;

∠J ≅ ∠Z, ∠K ≅ ∠Y

The side markings on the triangles indicates

Side JK in triangle ΔJLK is congruent to side ZY in triangle ΔZXY

Therefore, two angles and an included side in triangle ΔJLK are congruent to two angles and an included side in triangle ΔZXY, therefore, triangle ΔJLK is congruent to triangle ΔZXY by Angle-Side-Angle, ASA congruence rule.

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The slope of the graph would give us the speed of the motion and that is  40 m/min.

We can use this principle to show that the slopes of two lines are equal if they are parallel and intersected by a transversal line. Here's how:

Draw two parallel lines, labeled as line A and line B.

Draw a transversal line that intersects both lines A and B at two points.

Draw a perpendicular line segment from one of the intersection points on line A to the transversal line, and label it as segment 1.

Draw a perpendicular line segment from the corresponding intersection point on line B to the transversal line, and label it as segment 2.

The triangles formed by segment 1, the transversal line, and a segment on line A, and by segment 2, the transversal line, and a segment on line B, are similar triangles.

Since the corresponding sides of similar triangles are proportional, we can set up the following proportion: segment 1 / segment on line A = segment 2 / segment on line B.

Simplifying the proportion, we get segment 1 / segment 2 = segment on line A / segment on line B.

Since segment 1 and segment 2 are both perpendicular to the transversal line, they represent the rise of the lines A and B, respectively. The segments on lines A and B represent the run of the lines A and B, respectively. Therefore, we can rewrite the proportion as rise of line A / run of line A = rise of line B / run of line B.

This shows that the slopes of the two parallel lines, line A and line B, are equal.

The slope of the graph is;

m = 140 - 60/2 - 0

m = 40 m/min

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Binomial distributions and hypergeometric distributions are similar in that they both have two possible outcomes (success or failure) and the probability of success is constant in each trial. They also both assume that each trial is independent of each other.

Both binomial distributions and hypergeometric distributions are similar in the following ways: they are both discrete distributions, they both have two possible outcomes (success or failure), the probability of success is constant in each trial, and they both assume that each trial is independent of each other.

A binomial distribution is a probability distribution that models the number of successes in a given number of independent trials with the same probability of success for each trial. In a binomial distribution, the random variable X is the number of successes in the given number of trials.

The probability of a success for each trial remains constant. The mean and variance of the binomial distribution are given by the formula: μ = np and σ2 = npq, respectively.

A hypergeometric distribution is a probability distribution that models the probability of selecting a certain number of successes in a given number of draws from a finite population without replacement. In a hypergeometric distribution, the random variable X is the number of successes in the given number of draws.

The probability of a success for each draw remains constant.

The mean and variance of the hypergeometric distribution are given by the formula: μ = nx/N and σ2 = nx(N-n)(N-x)/N2(N-1), respectively.

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Standard deviation of the following data is 0.655.

The standard deviation is equal to the variance's positive square root. It is a fundamental statistical analysis method. The amount by which data values deviate from the mean is referred to as "standard deviation," or "SD."

Whereas a big standard deviation implies that the values are much outside the mean, a low standard deviation shows that the values are frequently only a few standard deviations from the mean.

Here in the question,

Total kids = 20.

Mean = 9+9.5+9.5+10+10+10+10+10.5+10.5+10.5+10.5+11+11+11+11+11+11+11.5+11.5+11.5/20

= 10.52

Now square of distance between mean and ages.

(9-10.52) ² = 2.31

(9.5-10.52) ² = 1.04

(10-10.52) ² = 0.27

(10.5-10.52) ² = 0.0004

(11-10.52) ² = 0.23

(11.5-10.52) ² = 0.96

Now sum of all the differences = 2.31 + 1.04 + 1.04 + 4×0.27 + 4× 0.0004 + 6× 0.23+ 3×0.96

= 8.73

Now standard deviation = √8.73/20

= √0.43

= 0.655

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Answer:

2,5,7,9,0.1,8

Step-by-step explanation:

Gareth had £4,199,999.94 in his account at the start of 2015 at rate 5%.

Compound interest is computed as a percentage of the principle plus the accrued interest, whereas simple interest is determined as a fixed percentage of the original amount. In other words, whereas compound interest is calculated on the principle amount plus any interest that has previously been earned, simple interest is computed on the initial principal amount. So, over time, compound interest often produces larger returns than simple interest, particularly for long-term investments.

The compound interest is given by:

[tex]A = P(1 + r/n)^{(n*t)}[/tex]

Substituting the given values, we get:

[tex]P = 4,862,025 / (1 + 0.05/1)^{(1*3)}\\P = 4,862,025 / 1.157625\\P = 4,199,999.94[/tex]

Gareth had £4,199,999.94 in his account at the start of 2015.

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Answer: 6(x+1)^2

Step-by-step explanation:

1. Find the GCF. Because you know the equation is 6x^2+12x+6, you can see that the coefficients, 6 and 12, are all factors of 6. To make factoring easier, factor out 6 from all the coefficients, which leaves you with 6(x^2+2x+1)

2. Factor the equation in the parentheses. If you have learned your perfect squares, then you know that x^2+2x+1 is (x+1)^2 because x^2+2x+1 = (x+1)(x+1) (you can foil that out if you want to check). Once finished with this, it leaves you with 6(x+1)^2

Using a calculator, we find that the bearing of A from B is approximately 165.95 degrees. Using a calculator, we find that the bearing of C from B is approximately 87.88 degrees.

Trigonometry is a branch of mathematics that deals with the study of the relationships between the angles and sides of triangles. It is based on the three primary trigonometric functions: sine, cosine, and tangent, which relate the ratios of the sides of a right triangle to the angles opposite those sides.

Here,

i.  Let x be the distance from B to A and y be the distance from B to C. Then, we have:

tan(50) = x / y

Rearranging this equation, we get:

x = y * tan(50)

Thus, the coordinates of A are (-4 sin(50), 4 cos(50) - 4 sin(130)). The bearing of A from B is then:

bearing of A from B = tan⁻¹((y * sin(50)) / (y * cos(50) - x))

Substituting x and y, we get:

bearing of A from B = tan⁻¹(sin(130) / (cos(50) - sin(50) tan(50)))

≈165.95 degrees

ii. To find the bearing of C from B, we can use the same method. Let's assume that the coordinates of B are (0, 0), and the distance from B to A is 3 units. Then, the coordinates of A are (-3 sin(50), 3 cos(50) - 3 sin(130)). The bearing of C from B is then:

bearing of C from B =  tan⁻¹((4 * sin(50)) / (4 * cos(50) - 3 * sin(50) / tan(50)))

≈87.88 degrees

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[tex]a = 7[/tex]

[tex]d = 12 - 7 = 5[/tex]

[tex]L = 102[/tex]

[tex]\implies a + (n-1)d = 102[/tex]

[tex]\implies 7 + (n-1)(5) = 102[/tex]

[tex]\implies (n-1)(5) = 95[/tex]

[tex]\implies n - 1 = 19[/tex]

[tex]\implies n = 20[/tex]

[tex]\text{Required sum = n/2} \ (a + L)[/tex]

[tex]= 20 \div2 \ ( 7 + 102)[/tex]

[tex]= 10 \times 109[/tex]

[tex]\bold{= 1090}[/tex]

Answer:

The sum is 1090

Step-by-step explanation:

S=7+12+17+22+...+102 ---> reason=5

We define the values, before starting:

Ratio = r , Term n = Tn , Term number = n , Term one = T1

To do this we first find the term number of 102, with the following formula:

Tn = t1 + (n - 1) r

102 = 7 + (n - 1) 5

102 = 7 + 5n - 5

102 = 5n + 2

100 = 5n

20 = n

Then we realize that 102 is the term N°20, now what we have to do is find the sum of the arithmetic series, with the following values and the following formula:

t1 = 7   ,   tn = 102   ,   n = 20

S = ( [tex]\frac{t1+tn}{2}[/tex]) . n

S = ( [tex]\frac{7+102}{2}[/tex]) . 20

S = 109 . 10

S = 1090

Answer:

Step-by-step explanation:

i think i is -1

Observation would be the most appropriate data collection method for studying how kids engage in play at a Montessori elementary school.

Therefore the answer is A) Observation.

This method involves observing and recording the behaviors and interactions of the children during playtime, which can provide valuable insights into their play patterns, preferences, and social dynamics.

Observation is particularly well-suited for studying young children because it allows researchers to capture their behavior in a naturalistic setting, without relying on self-report or other potentially unreliable sources of data. By watching how children interact with their peers and the materials available to them, researchers can gain a deeper understanding of their social, cognitive, and emotional development.

Observation can be conducted in a variety of ways, such as through structured or unstructured observation, video or audio recording, or field notes. Researchers may also choose to use multiple methods of observation to gain a more comprehensive understanding of children's play behavior.

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--The question is incomplete, answering to the question below--

"Answer in a very short answer of 1-3 sentence and an explanation of more than 100 words

For a study exploring how kids engage in play at Montessori elementary school, which would be the most appropriate data collection method?

A) observation

B) interviews

C) documents

D) audiovisual

E) audio materials"

Answer:Exact Form:

g=10/3

Decimal Form:

g=3. ¯3

Mixed Number Form:

g=3 1/3

Step-by-step explanation:

Answer:

Proved that tan45° × sec40° + tan60° × cosec40° =4 by using the trigonometric ratio formulas.

Given that,

We have to prove that tan45° × sec40° + tan60° × cosec40° =4

We know that,

What is trigonometry ratio?

Trigonometric ratios are ratios of triangle side lengths. These ratios in trigonometry demonstrate the relationship between the sides and angles of a right triangle. The three basic ratios in trigonometry are sine, cosine, and tangent.

Take the left hand side

tan45° × sec40° + tan60° × cosec40°

We know that tan45°=1 and tan60°=√3

1×sec40°+√3×cosec40°

sec40°+√3cosec40°

We know that from formula,

sec40° = \frac{1}{cos40\textdegree}

cos40\textdegree

1

and cosec40° = \frac{1}{sin40\textdegree}

sin40\textdegree

1

\frac{1}{cos40\textdegree}

cos40\textdegree

1

+√3× \frac{1}{sin40\textdegree}

sin40\textdegree

1

1+3

4 (Approximately)

Therefore, Proved that tan45° × sec40° + tan60° × cosec40° =4 by using the trigonometric ratio formulas.

Answer:

x=7

Step-by-step explanation:

Check the attachment below:  

This table is an example of exponential growth.

The equation that represents this exponential growth is y = 2ˣ.

Exponential growth is characterized by an equation of the form y = bˣ, where b is a positive constant.

This table is an example of exponential growth.

This is because the y-values are increasing exponentially as the x-values increase.

The equation that represents this exponential growth is y = 2ˣ.

This can be seen by the fact that the y-values are equal to 2ˣ, where x is the corresponding x-value.

When x = 0, y = 2⁰ = 2.

When x = 1, y = 2¹ = 6.

When x = 2, y = 2² = 18.

When x = 3, y = 2³ = 54.

And finally, when x = 4, y = 2⁴ = 162.

Here, b = 2.

Exponential growth is different from linear and quadratic growth in that the rate of increase is not constant; instead, it increases as the x-values increase.

This is because the exponent in the equation increases as the x-values increase. This is why the y-values increase exponentially as the x-values increase.

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As it is known that the temperature of hot coffee will cool to room temperature following an exponential mode, the option which would linearize the data for temperature and minutes is "Minutes, ln(Temperature)". The Option B is correct.

Using logarithmic transformation, we can convert the exponential relationship between temperature and time into a linear relationship. By taking the natural logarithm of the temperature, we can rewrite the exponential model as:

ln(Temperature) = -kt + ln(T0)

In this model, ln(Temperature) is the natural logarithm of the temperature, k is a constant representing the rate of cooling, t is the time elapsed, and T0 is the initial temperature of the coffee.

This equation is in the form of a linear equation, y = mx + b, where ln(Temperature) is the y variable, -k is the slope, t is the x variable, and ln(T0) is the y-intercept. Therefore, plotting Minutes versus In(Temperature) will give a linear relationship.

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The surface area of the triangular prism is 2160 square centimeters.

To calculate the surface area of a triangular prism, you need to find the area of each face and add them up.

In this case, the triangular prism has two identical triangular faces and three rectangular faces.

The area of one triangular face is:

0.5 x base x height = 0.5 x 30 cm x 24 cm = 360 cm²

Since there are two triangular faces, the total area of the triangular faces is:

2 x 360 cm² = 720 cm²

The area of each rectangular face can be calculated as:

length x height

Two of the rectangular faces have a length of 30 cm (the same as the base of the triangular face) and a height of 24 cm.

The area of each of these faces is:

30 cm x 24 cm = 720 cm²

The third rectangular face has a length of 30 cm (the same as the base of the triangular face) and a height of the height of the prism, which is also 24 cm.

The area of this face is:

30 cm x 24 cm = 720 cm²

Therefore, the total surface area of the triangular prism is:

720 cm² + 720 cm² + 720 cm² = 2160 cm²

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The length of AD is 23.5 cm.

The perimeter of a rectangle is the sum of the lengths of all four of its sides. So,

Perimeter = AD + AB + BC + CD

38 cm = AD + (x + 4) + (3x - 12) + (x + 4)

38 cm = 4x + 4

34 cm = 4x

x = 8.5 cm

Therefore, AD = 3x - 12 = 3(8.5) - 12 = 23.5 cm

The formula used to calculate the perimeter of a rectangle is P = 2(l + w) where P is the perimeter, l is the length and w is the width. The length of AD can be calculated by solving the equation 38 cm = 2(l + w). We know that AB = x + 4 and BC = 3x - 12, so l + w = x + 4 + 3x - 12 = 4x - 8. This means that 38 cm = 2(4x - 8), which can be rearranged to 34 cm = 4x. Therefore, x = 8.5 cm, so l = 8.5 cm + 4 cm = 12.5 cm and AD = 12.5 cm - 8.5 cm = 23.5 cm.

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Answer:

C=15.7cm

A=78.54cm^2

Step-by-step explanation:

C=πr = π(5cm) = 15.7cm

A=πr^2 =π (5cm)^2 =78.54cm^2

The total area of the given composite geometric figure is: 27 cm²

The formula for the area of a parallelogram is:

Area = base * height

The formula for the area of a square is:

Area = ¹/₂ * base * height

The area of the square is:

Area = 3 * 3

= 9 cm²

Area of parallelogram = 3 * 6

Area of parallelogram = 18 cm²

Total area of composite figure = 18 + 9

= 27 cm²

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Answer:

90.52

Step-by-step explanation:

The area of the final image is greater than 121 square centimeters, so the final image will not fit into a rectangular space that has an area of 121 square centimeters.

What is the scale factor?

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The original image has a length of 6 cm and a width of 9 cm, and when it's enlarged by a scale factor of 3, its new length becomes 6 cm x 3 = 18 cm, and its new width becomes 9 cm x 3 = 27 cm.

Then, the designer reduces the enlarged image by a scale factor of 0.5, which means the new length becomes 18 cm x 0.5 = 9 cm, and the new width becomes 27 cm x 0.5 = 13.5 cm.

So, the final image has a length of 9 cm and a width of 13.5 cm.

To check if the final image will fit into a rectangular space that has an area of 121 square centimeters, we need to calculate its area:

Area of the final image = length x width

Area of the final image = 9 cm x 13.5 cm

Area of the final image = 121.5 square centimeters

Therefore, the area of the final image is greater than 121 square centimeters, so the final image will not fit into a rectangular space that has an area of 121 square centimeters.

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Answer:

x=3

Step-by-step explanation: