What is the value of x in the equation below?

For isosceles triangle we have proved a) ∆AHB = AHC b) AH is the median of ∆ABC c) BC = 2AD

a) To prove that ∆AHB = AHC, we need to show that the two triangles have equal sides and angles. Since ABC is an isosceles triangle at A, we know that AB = AC. Also, since AH is the altitude of the triangle, we know that it is perpendicular to BC. Therefore, angle AHB and angle AHC are both right angles.

Now, to prove that the triangles have equal sides, we need to show that HB = HC. Since AB = AC, we have:

[tex]AB^{2} = AC^2\\AB^2 - AH^2 = AC^2 - AH^2\\BH^2 = CH^2[/tex]

Therefore, HB = HC, and we have proved that ∆AHB = AHC.

From this, we can deduce that angle BHA = angle CHA, as they are opposite angles in congruent triangles. Also, we know that angle ABC = angle ACB, as it is an isosceles triangle. Therefore, angle ABH = angle ACH, and we have proved that ∆ABH = ∆ACH.

b) To prove that A, G, and H are collinear, we need to show that AH is the median of ∆ABC. Since ∆AHB = AHC, we know that HB = HC. Therefore, BG and CG are medians of the triangle, and they intersect at G.

Now, to prove that ∆GBC is equal, we can use the fact that medians of a triangle divide it into six equal triangles. Therefore, we have:

Area(∆GBC) = 2/3 * Area(∆BGC)

Area(∆GBC) = 2/3 * Area(∆ACG)

Area(∆GBC) = 2/3 * Area(∆ABG)

Since ∆ABH = ∆ACH, we know that the altitude from A to BC passes through H, which is the midpoint of BC. Therefore, AH is also the median of ∆ABC.

c) Let E be the midpoint of BC. Since AE is the median of the triangle, we know that it divides BC into two equal parts, so EC = EB. Let X be the midpoint of AD. Since M is the midpoint of HD, so:

HX = (1/2) * HD

HX = (1/2) * (2AD)

HX = AD

AX is parallel to DE so:

AB/AD = AE/AX

2 = AE/AX

Since EC = EB and HX = AD, so:

AE = EC + HX

AE = EB + HX

AE = 2HX

Therefore, substitute, simplify:

2 = 2HX/AX

2AX = 2HX

AX = HX

Since AX = HX, DX is also equal to HX, so:

AD = DX

Also, since AE = 2HX, so:

BC = 2AE

Substitute in HX = AD and AE = 2HX, so:

BC = 2AE

BC = 2(2HX)

BC = 4HX

BC = 4AD

Therefore, we have proved that BC = 2AD.

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The probability that a particular serving contains fewer than 300 calories is 0.71, more than 250 calories is -2.86, between 275 and 310 calories is  0.7186.

To solve this problem, we need to use the normal distribution and the corresponding z-scores. We can find the z-score for a particular value of x (number of calories) using the following formula:

z = (x - μ) / σ

where μ is the mean, σ is the standard deviation, and x is the specific value we are interested in.

Probability of serving containing fewer than 300 calories:

z = (300 - 290) / 14 = 0.71

Using a standard normal distribution table or calculator, we find that the probability of a z-score being less than 0.71 is 0.7611. Therefore, the probability of a serving containing fewer than 300 calories is 0.7611.

Probability of serving containing more than 250 calories:

z = (250 - 290) / 14 = -2.86

Using a standard normal distribution table or calculator, we find that the probability of a z-score being greater than -2.86 is 0.9977. Therefore, the probability of a serving containing more than 250 calories is 0.9977.

For 275 calories:

z = (275 - 290) / 14 = -1.07

For 310 calories:

z = (310 - 290) / 14 = 1.43

Next, we use a standard normal distribution table or calculator to find the probability of z falling between -1.07 and 1.43. For example, using a standard normal distribution table, we can find that the probability of z falling between -1.07 and 1.43 is approximately 0.7186.

Therefore, the probability that a particular serving of McDonald's Egg McMuffin contains between 275 and 310 calories is approximately 0.7186, or 71.86%.

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The value for the given expression is 60.

The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function, the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.

The exercise asks the value of the given expression a²-4a, for a=10. Thus, you should replace the variable a with the number 10. See below.

a²-4a

10²-4*10

100-40=60

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Answer: 30 mil

Step-by-step explanation:

Answer:

she would have to go 30 miles per hour or less to make this possible

Step-by-step explanation:

if it went over 35 31 miles per hour they would run out of gas before they got there

The number of people in the stadium whose favorite stadium food is nachos is 10000.

What is random sample space?

The set of all potential outcomes for an experiment is referred to as the sample space S in a random experiment. The results of a random experiment, also known as sample points, are incompatible (i.e., they cannot occur simultaneously).

Here, we have

Given: You ask 120 randomly chosen people at a stadium to name their favorite stadium food. There are about 50,000 people in the stadium.

We have to estimate the number of people in the stadium whose favorite stadium food is nachos.

24/120 = x/50,00

x = 1200000/120

x = 10000

Hence, the number of people in the stadium whose favorite stadium food is nachos is 10000.

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3600/p is an algebraic expression that represents the Share of each partner.

What is the algebraic expression?

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

Here, we have

Given: Suppose that p partners equally share the profits from a sale of $3,600.

Number of Partners  = p

Total Profit  = $ 3600

Profit of Each Partner  = Total Profit/number of Partners

=> Profit of Each Partner  = 3600 / p

Hence,  3600/p is an algebraic expression that represents the Share of each partner.

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The expression [tex]x^4y^4+x^5y^2[/tex] can be factored to [tex](x^4y^2 + x^3y^2)(x + y^2).[/tex]

To factor [tex]x^4y^4+x^5y^2[/tex], we start by taking out the highest common factor, which is [tex]x^4y^2[/tex]. We then divide the expression by [tex]x^4y^2[/tex] to get [tex]x+y^2[/tex].

We can then rewrite the expression as ([tex]x^4y^2 + x^3y^2)(x + y^2).[/tex]

To verify this solution, we can multiply it out to get [tex](x^4y^2 + x^3y^2)(x + y^2) = x^5y^2 + x^4y^4[/tex], which is equal to the original expression. Therefore, the expression [tex]x^4y^4+x^5y^2[/tex] can be factored to [tex](x^4y^2 + x^3y^2)(x + y^2[/tex]).

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Using the concept of the ratio of similar triangles, we can say that the length of LM is: 12 units

Similar triangles are defined as triangles that have the same shape, but then their sizes may very well vary. This means that we can say that, if two triangles are said to be similar triangles, then it means that their corresponding angles are congruent and corresponding sides are in equal proportion.

Looking at the given image, we can see that:

LM is similar to PN and LM is similar to QP

Thus:

LN/PN = LM/QP

(x + 3)/(x - 1) = 18/12

2(x + 3) = 3(x - 1)

2x + 6 = 3x - 3

3x - 2x = 6 + 3

x = 9

LM = 9 + 3

LM = 12

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The weight of the compact car, which is approximately 1,354 kilograms, can be converted to 1,354,000 grams.

In the metric system, "kilo" means thousand, so 1 kilogram is equal to 1000 grams. To convert from kilograms to grams, we simply multiply the weight in kilograms by 1000.

In this case, the weight of the compact car is given in kilograms as 1,354. To convert to grams, we multiply by 1000 to get:

1,354 kg x 1000 g/kg = 1,354,000 g

Therefore, the weight of the compact car in grams is approximately 1,354,000 grams.

The weight of an object is a measure of the force with which gravity pulls on the object. The unit of weight in the metric system is the newton (N), but kilograms (kg) are commonly used as a unit of mass and weight in everyday life. The conversion between mass and weight depends on the local acceleration due to gravity, which is approximately 9.81 m/s^2 at the Earth's surface.

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Answer:

6 pieces of the original pizza remain.

Step-by-step explanation:

Initially, the pizza was divided into 16 equal pieces. Violet and Sophie each ate 1/8 of the pizza on Friday, so a total of 1/8 + 1/8 = 1/4 of the pizza was eaten on Friday.

This means that 3/4 of the pizza remained after Friday.

The next day, Sophie ate 1/2 of the remaining pizza. So she ate 1/2 * 3/4 = 3/8 of the original pizza.

Therefore, the amount of pizza that remains is 3/4 - 3/8 = 3/8 of the original pizza.

To convert this fraction to a number of pieces, we need to multiply it by the total number of pieces the pizza was divided into:

3/8 * 16 = 6 pieces

The most accurate estimate of the distance on the ground between the wall and the bottom of the ladder is 2 meters.

One approach to tackle this problem is to apply trigonometry to establish the connection between the angle, height, and distance. Specifically, we can utilize the cosine function, which relates the adjacent side and the hypotenuse of a right triangle. In this case, the adjacent side represents the distance between the wall and the ladder, and the hypotenuse corresponds to the ladder's length. The given angle is 72 degrees.

By employing the formula cos(angle) = adjacent/hypotenuse, we can input the known values and determine the unknown distance:

cos(72) = distance/6

distance = 6 * cos(72)

distance is approximately 1.9 m

Thus, the most accurate estimation for the ground distance from the ladder's bottom to the wall is 2 m.

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Answer:2m

Step-by-step explanation:

i took the test

Answer:

Step-by-step explanation:trisha is running a marathon race  she runs th erace at a steady pace she makes a graph to show how far from the finsh line she will be as she runs the race

=2

Therefore, the length of the x is 24.04.

A triangle is a geometric shape that consists of three sides and three angles. It is a closed shape with three straight sides that connect at three vertices (corners). Triangles can be classified based on the lengths of their sides or the measures of their angles. For example, a triangle with three sides of equal length is called an equilateral triangle, while a triangle with two equal sides is called an isosceles triangle. Triangles can also be classified based on their angles, such as acute, obtuse, or right triangles. Triangles have a variety of properties and applications in mathematics, physics, and engineering.

by the question.

So, in this case, we have:

[tex]21 > x+7[/tex]

Where x is the length of the third side.

Simplifying the expression, we get:

[tex]21 > x+7[/tex]

Therefore, the length of the third side must be less than 28.

We can also use the Pythagorean theorem to determine if this triangle is a right triangle.

If a triangle is a right triangle, then the sum of the squares of the two shorter sides is equal to the square of the longest side (the hypotenuse).

In this case, we have:

[tex]21^2 - 7^2 = x^2[/tex]

Simplifying, we get:

[tex]441 - 49 = x^2[/tex]

[tex]392 = x^2[/tex]

Taking the square root of both sides, we get:

x ≈ 19.79

Again, If a triangle is a right triangle, then the sum of the squares of the two shorter sides is equal to the square of the longest side.

[tex](x+3)^2 = (19.79)^2-(4)^2\\(x+3)^2= 391.64-16\\(x+3)^2= 225.64\\(x+3)= \sqrt225.64\\(x+3)= 15.021\\x = 15.021-3\\x = 12.021[/tex]

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Answer:

1.49m

Step-by-step explanation:

Trigonometry:

cosθ = adjacent/hypotenuse

cos(74) = adjacent/(5.39)

adjacent = 5.39 × cos(74)

adjacent = 2.3125974152

1.49 (to 2 d.p.)

Answer:

36

Angle LON is a right angle so it equals 90 degrees.

Answer:

1 4/6 as an improper fraction is 5/3

Step-by-step explanation:

What is an improper fraction?

An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

How do you convert a mixed number to an improper fraction?

To convert a mixed number to an improper fraction, you multiply the whole number by the denominator and add the numerator. Then, you put that sum over the denominator.

For example, 1 4/6 can be converted to an improper fraction as follows:

1 x 6 + 4 = 10

10/6 = 5/3

So, 1 4/6 as an improper fraction is 5/3.

The answer is in the picture below

It is equal to (x-4)² - (x- 4) ⁶ = 0 to solve the quadratic equation u² - u - 6 = 0 where u = (x -4).

A numerical assertion known as a situation comprises of two mathematical articulations isolated by equivalent signs (=) on one or the other side.

It demonstrates that the printed statements on the left and right are in equal relationship.

In all formulas, the left side equals the right side. Equations can be solved to determine the values of unknown variables, which represent unknown quantities.

Without the equals sign, a statement is not an equation. A mathematical statement known as an equation will include the symbol "equal to" between two expressions that have the same value.

According to our question-

(x-4)² – (x − 4) − 6 = 0

Let (x - 4) = u

u² - u - 6 = 0

Hence, It is equal to (x-4)² - (x- 4) ⁶ = 0 to solve the quadratic equation u² - u - 6 = 0 where u = (x -4).

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The supplied data collection has a periodic period of 4 and an amplitude of 25.

Let's study data points with a 4-day gap;

Data point 2 is [tex](2, 76)[/tex]

Data point 6 is[tex](6, 74)[/tex]

Data point 10 is[tex](10, 75)[/tex]

Every four day intervals, the readings are within the typical range. The points[tex](3, 91), (7, 88),[/tex] and (114) all support this same 4-day timeframe [tex](11, 92).[/tex]

As the data points at intervals of 4 days follow a pattern, we may infer that the period is 4 and the amplitude is around 25.

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Answer:

periodic with a period of 4 and an amplitude of about 30

Step-by-step explanation:

The lake activity with a central angle of 46.8° is waterskiing, since it is the lake activity chosen by 13% of the campers.

what is central angle ?

A central angle is an angle formed by two radii of a circle that intersect at its center. The central angle is measured in degrees and is used in circle graphs or pie charts to represent the proportion or percentage of each category in the data.

In the given question,

To find out which lake activity has a central angle of 46.8°, we first need to calculate the total number of campers who participated in the survey:

Total number of campers = 15 + 11 + 7 + 13 + 54 = 100

Next, we need to find the percentage of campers who chose each lake activity:

Percentage of campers who chose kayaking = (15/100) x 100% = 15%

Percentage of campers who chose wakeboarding = (11/100) x 100% = 11%

Percentage of campers who chose windsurfing = (7/100) x 100% = 7%

Percentage of campers who chose waterskiing = (13/100) x 100% = 13%

Percentage of campers who chose paddleboarding = (54/100) x 100% = 54%

Now we can use the formula for calculating the central angle of a circle graph:

Central angle = (Percentage/100) x 360°

For the lake activity with a central angle of 46.8°, we can set up the following equation:

(Percentage/100) x 360° = 46.8°

Solving for Percentage, we get:

Percentage = (46.8°/360°) x 100% = 13%

Therefore, the lake activity with a central angle of 46.8° is waterskiing, since it is the lake activity chosen by 13% of the campers.

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Each of the expressions has been simplified by using properties of exponents as shown below.

In Mathematics, an exponent refers to a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

the variables b and n are numerical values (numbers) or an algebraic expression.

n is referred to as a superscript or power.

By applying the multiplication and division law of exponents for powers to each of the expressions, we have the following:

(1.25 × 10⁷) + 63,000,000 = (1.25 × 10⁷) + (6.3 × 10⁷) = (1.25 + 6.3) × 10⁷ = 7.55 × 10⁷

12,000 + 7 × 10⁴ = 1.2 × 10⁴ + 7 × 10⁴ = (1.2 + 7) × 10⁴ = 8.2 × 10⁴

5.88 × 10⁵ - 3.44 × 10⁵ = (5.88 - 3.44) × 10⁵ = 2.44 × 10⁵

6 × 10⁸ ÷ 120 = 6 × 10⁸ ÷ 1.2 × 10² = (6 ÷ 1.2) × 10⁸⁻² = 5 × 10⁶

9 × 10¹² ÷ 4.5 × 10⁴ = (9 ÷ 4.5) × 10¹²⁻⁴ = 2 × 10⁸

1.3 × 10³ · 2,200 = 1.3 × 10³ × 2.2 × 10³ = (1.3 × 2.2) × 10³⁺³ = 2.86 × 10⁶

(6.3 × 10⁴) + 1.3 × 10⁴ = (6.3 + 1.3) × 10⁴ = 7.6 × 10⁴

3,400 · 2 × 10⁴ = 3.4 × 10³ × 2 × 10⁴ = (3.4 × 2) × 10³⁺⁴ = 6.8 × 10⁷

9.78 × 10⁵ - 732,000 = (9.78 - 7.32) × 10⁵ = 2.46 × 10⁵

3.5 × 10² · 2 × 10⁴ = (3.5 × 2) × 10²⁺⁴ = 7 × 10⁶

1.1 × 10⁸ ÷ 22,000 = 1.1 × 10⁸ ÷ 2.2 × 10⁴ = (1.1 ÷ 2.2) × 10⁸⁻⁴ = 0.5 × 10⁴ = 5 × 10³.

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The insurance company expects the interest rate to be around 4.16%.

To find the expected interest rate, we can use the formula for present value of an annuity:

PV = PMT x (1 - (1 + r)^(-n)) / r

Where:

PV = present value of the annuity, which is the amount the insurance company needs to deposit

PMT = payment per period, which is $45,000

r = interest rate per period, which is what we need to find

n = total number of periods, which is unknown

We know that the insurance company needs to deposit $2,500,000 to make the payments, so we can set:

PV = $2,500,000:

$2,500,000 = $45,000 x (1 - (1 + r)^(-n)) / r

To solve for r, we can use trial and error or an iterative method. Here, we'll use trial and error.

Let's assume n = 20, which is a reasonable number of years for an insurance policy. Then we can solve for r:

$2,500,000 = $45,000 x (1 - (1 + r)^(-20)) / r

$2,500,000r = $45,000 x (1 - (1 + r)^(-20))

(1 + r)^(-20) = 1 - ($45,000 / $2,500,000) x r

1 + r = (1 - ($45,000 / $2,500,000) x r)^(-1/20)

r ≈ 0.0416 or 4.16%

Therefore, the insurance company expects the interest rate to be around 4.16%.

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The cost of one adult tickets would be $12.5 and the cost of one youth tickets would be $8.75 .Therefore the cost of six adult tickets and eight youth tickets would be 6(12.5) + 8(8.75) = $145.

Let the cost of adult tickets be x.

Let the cost of youth tickets be y.

So, from the given condition given in question the equations are :-

For The Jefferson family,

2x + 2y = 42.50

x + y = 21.25 —---------- equation(1)

and for The Mendoza family,

4x + 3y = 76.25 —------ equation(2)

To solve above equation 4 × equation(1) - equation(2).

y = 8.75

and x = 12.5

Hence the cost of one adult tickets would be $12.5 and the cost of one youth tickets would be $8.75 .

Therefore the cost of six adult tickets and eight youth tickets would be 6(12.5) + 8(8.75) = $145.

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—-------- Correct question format is given below —--------

(Q). Two families go to a movie on Saturday night. The Jefferson family purchases 2 adult tickets and 2 youth tickets for $42.50. The Mendoza family purchases 4 adult tickets and 3 youth tickets for $76.25. How much would it cost to purchase six adult tickets and eight youth tickets?

Answer:

Loss = Rs. 198

Step-by-step explanation:

[tex]{ \sf{\%loss = \frac{loss}{cost \: price} \times 100\%}} \\ \\ { \sf{10 = \frac{loss}{1980} \times 100}} \\ \\ { \sf{loss = \frac{10 \times 1980}{100} }} \\ \\ { \sf{loss = 198}}[/tex]

The difference between a sample statistic and the corresponding population parameter is known as the sampling error.

     Sampling error is the disparity between a statistic from a sample and a corresponding parameter from a population. Statistic and parameter are two crucial words in inferential statistics that are used to describe data. A statistic is used to calculate a parameter, which is a calculated value from the population, which is a large group of people or objects.

    The variance between the mean of the population and the sample's mean is known as sampling error. The sample statistic that is used to estimate the population parameter may not be the same as the population parameter.

    The discrepancy between these two values is referred to as sampling error. When a small sample is chosen from a larger population, a sampling error is created.

   Therefore, The sampling error is the discrepancy between a sample statistic and the equivalent population parameter.

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The number of students enrolled in the Spanish class who are also enrolled in the French class is 0.

Let the number of students enrolled in French class be F

Let the number of students enrolled in Spanish class be S

Let the number of students enrolled in German class be G

From the given information, we have

S + F + G = Total number of students...... (1)

Total number of students = 34S = 34 - F - G...... (2)

Now, we need to find out how many students are enrolled in both Spanish and French classes. So, let us assume that x students are enrolled in both Spanish and French classes.

So, the total number of students in Spanish and French classes will be S + F - x (as x students are enrolled in both the classes).

But we are given that there are 34 students enrolled in the Spanish class. Hence, the above expression will be equal to 34.

Therefore, S + F - x = 34

Now, substituting the value of S from equation (2) we get,

34 - F - G + F - x = 34 or, - G - x = 0 or, x = - G

But x represents the number of students enrolled in both Spanish and French classes, which cannot be negative.

Hence, there are no students enrolled in the Spanish class who are also enrolled in the French class.

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Answer:

Step-by-step explanation: