Center of Triangles I please help

Answer:

x:5,x:7

x^2-12x+35

x^2-12x=-35

x^2-12x+6^2=-35+36

(x+6)^2=1

insert a radical anywhere

x+6=1

x=1-6

x=-5. x=5

x=-1-6

x=-7. x=7

The average rate of change of f(x) from x = -3 to x = 6 is 7.

What is meant by average?

The term "average" is used to describe a number that represents the central or typical value in a set of data. There are several different types of averages, including the mean, median, and mode.

To find the average rate of change of a function, we need to compute the difference between the function values at the two given points, and then divide by the difference in the input values.

For the function [tex]f(x) = x^2 + 4x - 15[/tex], the value of the function at [tex]x = -3[/tex] is:

[tex]f(-3) = (-3)^2 + 4(-3) -15 = 9 - 12 - 15 = -18[/tex]

The value of the function at [tex]x = 6[/tex] is:

[tex]f(6) = 6^2 + 4(6) - 15 = 36 + 24 - 15 = 45[/tex]

The difference in the function values is:

[tex]f(6) - f(-3) = 45 - (-18) = 63[/tex]

The difference in the input values is:

6 - (-3) = 9

Therefore, the average rate of change of f(x) from x = -3 to x = 6 is:

average rate of change = [tex](f(6) - f(-3)) / (6 - (-3)) = 63 / 9 = 7[/tex]

So, the average rate of change of f(x) from x = -3 to x = 6 is 7.

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Answer:

[tex]2 \sqrt{61} \: in[/tex]

Step-by-step explanation:

Use the Pythagorean theorem (assume, that the length of hypotenuse is x):

[tex] {x}^{2} = {10}^{2} + {12}^{2} = 100 + 144 = 244[/tex]

[tex]x > 0[/tex]

[tex]x = \sqrt{244} = 2 \sqrt{61} [/tex]

The Polynomials that are listed in the question are the options labelled;

B, C, E

A polynomial is a mathematical expression that consists of variables, coefficients, and exponents.

The variables represent unknown values, while the coefficients are constants that multiply the variables or their exponents. The exponents indicate the power to which the variables are raised.

Polynomials can be added, subtracted, multiplied, and divided to create more complex expressions, and they are used in a wide range of mathematical applications, including algebra, calculus, and geometry.

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Lisa would need to serve 12 customers to attain the projected income if Daisy calls in sick that day

What is linear function ?

A linear function is a mathematical function that can be represented by a straight line on a graph. It has the form of:

y = mx + b

where m is the slope of the line, which determines how steeply the line rises or falls, and b is the y-intercept, which is the point where the line crosses the y-axis.

According to the question:
If Daisy calls in sick, then Lisa will be the only stylist at the salon, and all customers will go to her. Let's use x to represent the number of Lisa's customers. Then the income generated by Lisa's customers can be represented by the equation:

18x = projected income

We can solve for x by dividing both sides of the equation by 18:

x = projected income / 18

Substituting the given projected income of $216, we get:

x = 216 / 18 = 12

Therefore, Lisa would need to serve 12 customers to attain the projected income if Daisy calls in sick that day.

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Answer:

10 + 2x

also,

2x + 10

Step-by-step explanation:

"a number value" is the unknown, so use a variable (letter) I used x, but could be almost any letter (avoid e and i, they have other math meanings)

"10 more than" means to add on 10. You can do that up front or at the end. Order is way more important for subtracting, so no worries here.

"product" means multiplying. So the "product of 2 and a number" is 2x.

So to translate this word phrase into an algebraic expression, you get:

10 + 2x

but also 2x + 10 is the same thing.

The given angles and measures is given below:

In mathematics and geometry, an angle is a measure of the space between two intersecting lines, rays, or line segments, usually expressed in degrees, radians, or grads. It is the measure of the opening between two lines that intersect at a common point, called the vertex of the angle.

5) tan x = 153 / 41

x = tan^-1 ( 153 / 41 )

75 degrees

6) tan y = 25/25

y = tan^-1 ( 25/25 )

45 degrees

7) sin z = 10/28

z= sin^-1 ( 10/28 )

21 degrees

8) cos a = 47/50

a = cos^-1( 47/50)

20 degrees

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Answer:

153

Step-by-step explanation:

The relationship in the row is below

4³ +2³ +1³ =64 + 8 +1 = 72

1³ + 2³ +6³= 1 + 8 + 216

3³ + 1³ + 5³ = 27 +1 +125 = 153

All numbers below the first level are raised to power 3 and added together

To check if the line drawn is diameter it should be intersected at centre and it must be equidistant from the centre of the circle.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.

To determine if the line Neil drew is an actual diameter of the circle and not just a smaller chord, he can use the following method -

Extend the line on both sides to create two lines that intersect at a point outside the circle.

Use a compass to draw a circle with the same center as the original circle, and with a radius that is greater than half the length of the line Neil drew.

Check if the two lines intersect the circle at two points that are equidistant from the center of the circle.

If they do, then the line Neil drew is an actual diameter of the circle.

If they do not, then the line Neil drew is just a chord.

This method works because a diameter of a circle is the longest chord that passes through the center of the circle.

By extending the line Neil drew and creating two lines that intersect outside the circle, we can compare the distance from the center of the circle to each of the two intersection points with the radius of the circle we drew.

If the distances are equal, then the line Neil drew must be a diameter of the circle.

Therefore, the method to find the actual diameter is explained.

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Therefore , the solution of the given problem of graphs comes out to be a = [P² * G * Ms / [tex](4\pi ^2* Mp)]^(1/3)[/tex]

Graphs are used by theoretical coordinate points physicists to analytically and graphically present assertions rather than values. Typically, a graph point shows the relationship between several distinct objects. A graph is a particular kind of pas de container construction composed of groups and lines. The borders, also known as the channels, should be joined with glue.

Here,

According to Kepler's third law, one can determine the connection between a planet's orbital period and its separation from a star by:

=> P² = (4π² / GM) * a³

where P denotes the orbit's duration in years, a denotes the semi-major axis in astronomical units (AU), G denotes gravity's constant, and M denotes the star's mass in solar masses.

If we rewrite this equation, we obtain:

=> a = [P² * G * Ms / [tex](4\pi ^2* Mp)]^(1/3)[/tex]

We can rewrite this equation as follows since our goal is to estimate the distance from the sun in AU based on the mass of the planet in relation to the sun:

=> a = [P² * G * Ms / [tex](4\pi ^2* Mp)]^(1/3)[/tex]

where Mp is the mass of the planet in relation to the sun and Ms is the mass of the sun.

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The length of the reflected line segment is approximately 11.66 units.

The endpoints of the line segment mentioned in the question are (0,5) and (6,5). After the line segment is reflected across the x-axis, the endpoints of the reflected line segment are (0, -5) and (6, -5).To find the length of the reflected line segment, we will use the distance formula.

Using the distance formula:d = √[(x₂ - x₁)² + (y₂ - y₁)²]d = √[(6 - 0)² + (5 - 5)²]d = √[36 + 0]d = √36d = 6 units. So the length of the original line segment is 6 units.Now, let's find the length of the reflected line segment.Using the distance formula :d = √[(x₂ - x₁)² + (y₂ - y₁)²]d = √[(6 - 0)² + (-5 - 5)²]d = √[36 + 100]d = √136d = 11.66 (approx) units. So the length of the reflected line segment is approximately 11.66 units.

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The answer of the given question based on the supplementary angle is  the two angles are 58° degrees and 122° degrees.

An angle is a geometric figure that is formed by two rays or lines that share a common endpoint, called the vertex. The rays or lines are called  sides or arms of  angle. Angles are typically measured in the degrees or the radians.

The measure of an angle is determined by the amount of rotation needed to bring one of its sides into coincidence with the other side. A full rotation is 360° degrees, so an angle that is half of a full rotation is 180 degrees, an angle that is a quarter of a full rotation is 90° degrees, and so on.

Let's call the two angles "x" and "y". We know that they are supplementary, which means that their sum is 180° degrees:

x + y = 180

We also know that one angle (let's say "x") is two times the sum of the other angle (y) and 3:

x = 2(y + 3)

Now we can substitute the second equation into the first equation to eliminate "x":

(2(y + 3)) + y = 180

Simplifying the equation, we get:

3y + 6 = 180

Subtracting 6 from both sides, we get:

3y = 174

Dividing both sides by 3, we get:

y = 58

Now that we know "y", we can substitute it back into the equation for "x" to find its value:

x = 2(y + 3) = 2(58 + 3) = 122

Therefore, the two angles are 58° degrees and 122° degrees.

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The line-plot of the the given data 9 3/4, 10 1/2, 9 1/4, 10 1/4, 11, 10 1/4, 9 1/2 that displays the lengths of the books on the booom shelf is attached.

What is line plot?

A line plot is a type of graph that represents the kind of data representation. It is line plot or a line chart shows the data in a visual form or visual representation. The graph is plotted with help of straight lines and points or dots. The x-axis is represented by straight lines or the it is labelled about the data. The y-axis is represented by the dots or frequency of the data. It is generally used to represent the small data set. This graph uses symbols to show or represent the frequency of the observations.

The data represented here is 9 3/4, 10 1/2, 9 1/4, 10 1/4, 11, 10 1/4, 9 1/2

we can make the frequency table using the above values, after which it can be plotted on the line-plot graph.

1-9 1/4--1 dot

2-9 1/2--1 dot

3-9 1/2--1 dot

4-10 1/4-2 dots

5-10 1/2--1 dot

6-11--1 dot

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Attached is a line-plot of the given data showing the lengths of the books on the book shelf: 9 3/4, 10 1/2, 9 1/4, 10 1/4, 11, 10 1/4, and 9 1/2.

An example of a graph that shows this sort of data representation is a line plot. The data is presented visually in the form of a line plot or a line chart. With the aid of straight lines, points, or dots, the graph is drawn. Straight lines or labels that describe the data are used to depict the x-axis. The dots or frequency of the data are used to depict the y-axis. It often serves as a representation for a tiny group of data. The frequency of the observations is shown or represented by symbols on this graph.

9 3/4, 10 1/2, 9 1/4, 10 1/4, 11, 10 1/4, and 9 1/2 are the numbers shown.

Using the aforementioned variables, we can create the frequency table, which can then be plotted on the line-plot graph.

1-9 1/4--1 dot

2-9 1/2--1 dot

3-9 1/2--1 dot

4-10 1/4-2 dots

5-10 1/2--1 dot

6-11--1 dot

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Answer: 40

Step-by-step explanation:

25/100 x ? = 10

multiply both sides by 100/25

x= 10 x 100/25

x=10

In conclusion, the power series converges absolutely over an interval given by [tex]\left|x-7\right|>\frac{\left|a_n+1\right|}{\left|a_n\right|}\;\;\;\forall\;\;\;n\in\mathbb{N}\;\;\;\text{and}\;\;\;n>N, where N\in\mathbb{N}[/tex]is a natural number.

The interval over which the power series converges absolutely is given by [tex]\left|x-7\right|>\frac{\left|a_n+1\right|}{\left|a_n\right|}\;\;\;\forall\;\;\;n\in\mathbb{N}\;\;\;\text{and}\;\;\;n>N, where N\in\mathbb{N}[/tex] is a natural number.

In other words, for any given N, the series will converge absolutely over the interval \left|x-7\right|>\frac{\left|a_n+1\right|}{\left|a_n\right|}\;\;\;\forall\;\;\;n>N.

This means that the series will converge absolutely over a larger interval as N increases, since the terms \frac{\left|a_n+1\right|}{\left|a_n\right|} get closer to 1 for larger values of n.

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The value of angle x in the right triangle KJI is approximately 63.4 degrees.

What is trigonometric ratios ?

Trigonometric ratios are mathematical functions that relate the angles of a right triangle to the lengths of its sides. The three primary trigonometric ratios are sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively.

These ratios are defined as follows:

Sine (sin) of an angle is the ratio of the length of the side opposite to the angle to the length of the hypotenuse.

Cosine (cos) of an angle is the ratio of the length of the adjacent side to the angle to the length of the hypotenuse.

Tangent (tan) of an angle is the ratio of the length of the side opposite to the angle to the length of the adjacent side.

Finding the value of x :

We can use the trigonometric ratios to find the value of angle x in the right triangle KJI.

First, we can use the Pythagorean theorem to find the length of the hypotenuse KI:

[tex]KI^2 = KJ^2 + JI^2[/tex]

[tex]KI^2 = 27^2 + 48^2[/tex]

[tex]KI^2 = 729 + 2304[/tex]

[tex]KI^2 = 3033[/tex]

[tex]KI =\sqrt{3033}[/tex]

Next, we can use the sine function to find the value of angle I:

[tex]sin(I) = JI / KI[/tex]

[tex]sin(I) = 48 / \sqrt{3033}[/tex]

[tex]I = sin^-1(48 / \sqrt{3033})[/tex]

[tex]I = 63.4[/tex] degrees

Therefore, the value of angle x in the right triangle KJI is approximately 63.4 degrees.

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There are 100,947 ways to assign the tasks to the 7 people.

This problem can be solved using combinations. We need to choose 17 tasks from a total of 17, which can be done in one way, and then assign each of these tasks to one of the 7 people. We can do this by considering all possible combinations of tasks that each person could be assigned.

Let's use the stars and bars method to count the number of ways to distribute the tasks. We can represent the tasks as stars and the people as bars, with each bar representing a separate person. For example, if person 1 is assigned 4 tasks, person 2 is assigned 2 tasks, and person 3 is assigned 1 task,

The number of ways to distribute the tasks is then the number of ways to arrange the 17 stars and 6 bars, which is

(17 + 6) choose 6 = 23 choose 6 = 100947

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The values of x is [tex]x < 39.5[/tex].

Given that the shopkeeper spends on rent and electricity is [tex]= 5x+14[/tex]

Spending of shopkeeper on rent [tex]= 3x-7[/tex]

So shopkeeper spends on electricity [tex]= (5x+14) - (3x-7) = 2x+21[/tex]

Given that amount the shopkeeper spends on electricity less than 100.

So suitable inequality,

[tex]2x+21 < 100[/tex]

[tex]2x < 100-21[/tex]

[tex]2x < 79[/tex]

[tex]x < 39.5[/tex]

All the values of [tex]x < 39.5[/tex].

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In the bridge, when the south has 13 points and 3 clubs and bids 1 club, the north responding with 3 clubs means that the North has a strong hand with six or more clubs.

In the game of bridge, bidding is a method of indicating the strength of a player's hand, which is the number of tricks that they believe they can win if they become the declarer. Every player has to declare their abilities based on the bid of the previous player when it is their turn to bid.

The bidding starts with the dealer and proceeds in a clockwise direction. The players can either make a bid or pass. The following are the four basic bids in Bridge:

When South has 13 points and 3 clubs, he makes a 1 Club bid. This bid can be interpreted as follows:

South has a strong hand with five or more clubs and 13 to 21 high card points. When South bids 1 Club, he implies that he has a balanced hand, which means that he has four cards in each suit, or an unbalanced hand, which means that he has a long suit, a singleton, or a void in some other suit.

When North responds with 3 Clubs, it means that he has a strong hand with six or more clubs. North has understood that South has five or more clubs and therefore responds with the number of clubs that he has in his hand to show that he is strong enough to support South's suit. Thus, North is trying to force South to become the declarer in clubs.

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The value of the given lengths are as follows:

a.) KL = 11.1ft

LO = 5.7ft

b.) m<OMN = 45°

For Side LO ;

7/11 = 7√2/7√2+LO

7(7√2+LO) = 11×7√3

69.3+7LO = 108.9

7LO = 108.9-69.3

LO = 39.6/7

LO = 5.7 ft

For KL ;

This can be solved using the Pythagorean theorem;

c²= b²+a²

C = 5.7+7√2 = 15.6

b = 11

a²= 15.6²-11²

= 243.36 - 121

= 122.36

a= √122.36

a= 11.1ft

For angle OMN;

This can be solved using SOHCAHTOA.

Sin∅ = opposite/hypotenuse

opposite = 7

hypotenuse = 7√2

sin∅ = 7/7√2

sin∅ = 0.707106781

∅= sin-1 0.707106781

∅ = 45°

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The expression or equation that correctly represents the situation given is y = 2x.

Based on the table, for each package of cashews 2 cans of peanuts are required. Here are some examples:

Based on this relationship and assuming y represents the cans of peanuts and x represents the packages of cashews a possible equation to represent this situation would be y = 2x.

Note: This question is incomplete; below I attach the missing information:

Write an equation to represent this relationship:

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Answer:

13 - The first option

11 - (x+1)

16 - first option

Step-by-step explanation:

The given equation 3x + 7y = 11 is equal to (1,-2).

The given equation is 3x + 7y = 11.

To find the solution of the equation, we need to consider the given options:

(6,-1)(1,-2)(0,4)

Now substitute each value of x and y in the given equation, we get,

If x = 6 and y = -13(3 × 6) + (7 × -1) = 18 - 7 = 11 ≠ 11

If x = 1 and y = -2(3 × 1) + (7 × -2) = 3 - 14 = -11 ≠ 11

If x = 0 and y = 4(3 × 0) + (7 × 4) = 0 + 28 = 28 ≠ 11

Therefore, the given equation 3x + 7y = 11 is equal to (1,-2).

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Step-by-step explanation:

[tex]volume = {x}^{3 \\} \\ so \: 1000000 = {x}^{3 \\} \\ x = \sqrt[3]{1000000} \\ x = 100[/tex]

Answer:

=(x+9)(x+5)

Step-by-step explanation:

Using the given values, the values of the expression and equations are:

25. -0.8

28. S ≈ 137.22

29. V ≈ 50.94

From the question, we are to evaluate each of the expressions for the given values

25.

[-b + √(b² -4ac)]/2a

a = 2, b = 8, c = 5

Substituting the values into the expression

[-b + √(b² -4ac)]/2a

= [-8 + √((8)² - 4(2)(5))]/2(2)

= [-8 + √(64 - 40)]/4

= [-8 + √(24)]/4

= [-8 + 2√6]/4

= -2 + 1/2(√6)

= -0.775

≈ -0.8

28.

S = 2πrh + 2πr²

r = 2.3, h = 7.1 (Take π = 3.14)

Thus,

S = 2(3.14)(2.3)(7.2) + 2(3.14)(2.3)²

S = 103.9968 + 33.2212

S = 137.218

S ≈ 137.22

29.

V = 4/3 πr³

r = 2.3(Take π = 3.14)

V = 4/3 × 3.14 × (2.3)³

V = 50.939

V ≈ 50.94

Hence, the value of V is 50.94

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Only the final option, which is typical of a longitudinal study, calls for retesting the same set of individuals over a lengthy period of time.

It is a numerical value that runs from 0 to 1, with 0 denoting the impossibility of an event and 1 denoting its certainty. The probability of an event A is expressed mathematically as P(A), where P(A) is the number of possible ways that event A could happen divided by the total number of outcomes.

given

The final choice is the long-term study: "An intelligence test is given to a class of kindergarteners. During 30 years, they are retested every other year."

In a longitudinal study, a group of individuals are followed over a lengthy period of time, frequently years or even decades. A longitudinal study's goal is to look at how people change or grow over time and to pinpoint any potential contributing elements.

Only the final option, which is typical of a longitudinal study, calls for retesting the same set of individuals over a lengthy period of time.

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b + 2p = 10 ,we have an equation that relates the number of bracelets to the number of purses and the total cost of the purchase. if Evelyn buys two purses, she also buys six bracelets.

Let's start by defining our variables. We'll let "b" represent the number of bracelets that Evelyn buys and "p" represent the number of purses she buys.

We know that each bracelet costs $6 and each purse costs $12. We also know that her total purchase is $60.

Using this information, we can create an equation:

6b + 12p = 60

Now we want to solve for "b", which represents the number of bracelets. To do this, we need to isolate "b" on one side of the equation. We can start by simplifying the equation by dividing both sides by 6:

b + 2p = 10

Now we have an equation that relates the number of bracelets to the number of purses and the total cost of the purchase. We can use this equation to find the value of "b" given any value of "p". For example, if Evelyn buys two purses, we can substitute "p = 2" into the equation and solve for "b":

b + 2(2) = 10

b + 4 = 10

b = 6    

So if Evelyn buys two purses, she also buys six bracelets.

In general, we can see that the equation tells us that for every two purses that Evelyn buys, she buys one less bracelet. This makes sense because purses are more expensive than bracelets, so as she buys more purses, she can afford fewer bracelets.

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Answer:

Let's denote the first term of the sequence as a, and the common difference between consecutive terms as d.

Then, we know that the fifth term is 5, so:

a + 4d = 5

Similarly, we know that the sixth term is 2.5, so:

a + 5d = 2.5

We can solve this system of equations by subtracting the first equation from the second:

(a + 5d) - (a + 4d) = 2.5 - 5

d = -2.5

Now, we can substitute this value of d into either equation to find the value of a:

a + 4d = 5

a + 4(-2.5) = 5

a - 10 = 5

a = 15

Therefore, the first term of the sequence is 15, and the common difference is -2.5. We can use this to find the value of the second term:

a + d = 15 + (-2.5) = 12.5

Therefore, the second term of the sequence is 12.5.

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The probability that Emme answers exactly 3 questions correctly is 0.1961.

Since each question has four answer choices and only one is correct, the probability of Emme randomly guessing the correct answer for each question is 1/4 = 0.25. Emme needs to answer exactly 3 out of the 9 questions correctly, so we use the binomial distribution with n = 9 and p = 0.25 to calculate the probability:

P(X = 3) = (9 choose 3) * (0.25)^3 * (0.75)^6

Using a calculator, we get:

P(X = 3) = 0.1961

Therefore, the probability that Emme answers exactly 3 questions correctly is 0.1961.

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