Find the values of x
and y that make these triangles congruent by the HL theorem quiz: congruence in right triangles

Answer:

C $540

Step-by-step explanation:

Food: .30 × $1,200 = $360

Drinks: .15 × $1,200 = $180

-------

$540

The 50th partial sum of the given arithmetic sequence is 4600

From the question, we are to calculate the 50th partial sum of the given arithmetic sequence

The given arithmetic sequence is

-6, -2, 2, 6, ...

To find the 50th partial sum of the sequence, we will find the sum of the first 50 terms in the sequence.

The sum of n terms of a sequence is given by the formula,

S = n/2(a + l)

Where a is the first term

and l is the last term

l is given by

l = a + (n - 1)d

Where d is the common difference

In the given series

a = -6

d = -6 -(-2) = -6 + 2 = 4

Thus,

l = -6 + (50 - 1)4

l = -6 + 49×4

l = -6 + 196

l = 190

Then,

S = 50/2(-6 + 190)

S = 25(184)

S = 4600

Hence,

The sum is 4600

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The equation that represent the graph is C) y=3x.

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here let us take the two points [tex](x_1,y_1)=(1,3) , (x_2,y_2)=(3,9)[/tex].

Now using slope formula then,

=> slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> m = [tex]\frac{9-3}{3-1}=\frac{6}{2}=3[/tex].

Now using equation formula then,

=> [tex]y-y_1=m(x-x_1)[/tex]

=> y-3=3(x-1)

=> y-3 = 3x-3

=> y=3x.

Hence the equation that represent the graph is C) y=3x.

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The perimeter of the paperboard that remains after the semicircle is removed is 93.12 inches

Information given in the problem includes:

A rectangular paperboard measuring 26in long and 16in wide

information for the semicircle are

Width = 16 inches

Radius = 16 / 2 = 8 inches

Length = 26 inches

Circumference of the semi circle is calculated using the formula

= π * radius

Where the radius is 8 inches and π = 3.14.

Substituting in to the formula and solving for the circumference of the semicircle which same as perimeter of the semicircle gives:

= 8 x 3.14

= 25.12

The perimeter would be

26 inches + 26 inches + 25.12 inches + 16 inches

= 93.12 inches

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Answer:

-4z

Step-by-step explanation:

Simply add the z, which is a variable together.

Answer:

-4z

Step-by-step explanation:

The calculated value of the area of the rhombus is 35 sq units

From the question, we have the following parameters that can be used in our computation:

The rhombus

Also, we have

x = 3, y = 5 and h = 4

Using shape decomposition, we have the following

Shapes = Rectangle and 2 triangles

So, the area is

Area = Rectangle + 2 triangles

Using the area formulas, we have

Area = 1/2 * xy + 1/2 * xy + hy

substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * 3 * 5 + 1/2 * 3 * 5 + 4 * 5

Evaluate

Area = 35

Hence, the area is 35 sq units

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The average rate of change of the given function between the two given values is: 0.82

The Average Rate of Change of a function is one that is defined as the average rate at which one quantity is changing with respect to another thing changing. Thus, an average rate of change function is basically a process that helps to calculate the amount of change in one item divided by the corresponding amount of change in another.

It is given by the formula:

f'(x) = [f(b) - f(a)]/(b - a)

We are given the function:

f(x) = √(3x - 11)

Thus from x1 = 4 to x2 = 6, we will have:

f(4) = √(3*4 - 11) = 1

f(6) = √(3*6 - 11) = √7

Thus:

f'(x) = ((√7) - 1)/(6 - 4)

f'(x) = 0.82

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The values of x , y and z in the parallelogram are 12, -20 and -33 respectively

A parallelogram is a quadrilateral with opposite side equal to each other and opposite sides parallel to each other.

The opposite angles of parallelogram are equal . Consecutive angles in a parallelogram are supplementary .

Therefore,

-4y + 5 = 85

-4y = 85 - 5

-4y = 80

divide both sides by -4

y = 80 / -4

y = - 20

Therefore, let's find x and z as follows:

8x - 1 + 85 = 180

8x = 180 - 84

8x = 96

divide both sides by 8

x = 96 / 8

x = 12

Let's find z

- 3z - 4 + 85 = 180

-3z = 180 - 81

-3z = 99

divide both sides by -3

z = 99 / -3

z = -33

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The perimeter of the quadrilateral PQRS is calculated as:

= 180 units.

Recall that if two tangents meet outside a circle, their length will be the same based on the tangents theorem.

Therefore, note that every line segments that appear tangent and intersect each other outside the circle have the same length.

Thus, we have:

Perimeter of the quadrilateral PQRS = 52.5 + 37.5 + 23 + (37.5 - 23) + 27.1 + (52.5 - 27.1)

Perimeter of the quadrilateral PQRS = 180 units.

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The diameter of the lead in a pencil p must be within 0.01 millimetre of 1 millimeter. In the form of inequality, this can be expressed as 0.01<p<1.

A mathematical expression with values that on the left and right are not equal is referred to as having an inequality. In essence, an inequality examines any two values as well as demonstrates whether one is bigger than, less than, or neither greater nor less than the comparable quantity. Numbers are compared using inequalities to determine the range of quantities that fall inside the parameters of a variable. The diameter of the lead in a pencil p must be within 0.01 millimetre of 1 millimeter. This can be expressed as 0.01<p<1 inequality.

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Your question is incomplete but most probably your full question was,

The diameter of the lead in a pencil p must be within 0.01 millimetre of 1 millimeter. Express this statement of an inequality.

To find the ordered pair solutions for the system of equations y = -x² + 2 and y = x, we can set the two equations equal to each other:

-x² + 2 = x

Now we can rearrange this equation into standard quadratic form by moving everything to one side:

-x² + x + 2 = 0

We can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = -1, b = 1, and c = 2

Plugging these values into the formula, we get:

x = (-1 ± √(1 - 4(-1)(2))) / 2(-1)

x = (-1 ± √9) / (-2)

x = (-1 ± 3) / (-2)

So the solutions for x are x = -1 and x = -2.

To find the corresponding values of y, we can plug these values of x into either of the original equations. Let's use y = x:

When x = -1, y = -1

When x = -2, y = -2

Therefore, the ordered pair solutions for this system of equations are (-1, -1) and (-2, -2).

Answer: d) the amount of clay for each student. 8

Step-by-step explanation: For the sketch, draw 8 pieces of paper being divided evenly. For the expression write 2 divided by 1/4 = 8.

a) To find the total sales in units by product and customer type, we need to multiply the number of bags sold by the selling price per bag. The table below shows the calculations:

Town Product Consumers Retailers Wholesalers

Huye Maize 800 600 800

Potatoes 6,000 2,000 3,000

Carrots 3,500 500 2,500

Tomatoes 2,800 4,200 2,100

Muhanga Maize 800 1,000 0

Potatoes 5,000 8,000 4,000

Carrots 1,500 2,000 0

Tomatoes 4,200 2,800 700

b) To determine the difference between the two towns in sales (in Units) by product and customer type, we subtract the sales in Muhanga from the sales in Huye. The table below shows the calculations:

Town Product Consumers Retailers Wholesalers

Maize 0 -400 800

Huye Potatoes 0 -1,000 0

Carrots 2,000 0 2,500

Tomatoes -1,400 1,000 1,400

Total 600 -400 4,700

Product Consumers Retailers Wholesalers

Maize 0 400 0

Muhanga Potatoes 0 6,000 1,000

Carrots -2,000 -500 0

Tomatoes 1,400 -1,400 -700

Total -600 4,500 300

c) To calculate the total sales in Rwf by each town, we need to add up the sales in units for each town and product and then multiply by the selling price per bag. The table below shows the calculations:

Town Total sales in Rwf

Huye 24,400

Muhanga 23,700

d) To find the sales in Rwf by customer type for each town, we need to multiply the number of bags sold by the selling price per bag and then add up the sales for each customer type. The table below shows the calculations:

Town Customer Maize Potatoes Carrots Tomatoes

Huye Consumers 800 6,000 3,500 2,800

Retailers   600 2  

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The value of (f∘g)(x) is 3x² - 2.

What is a function?

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

Here, we have

Given: f(x) = √x²-4 and g(x) = 3x²

We have to find the value of (f∘g)(x).

(f∘g)(x) = f(g(x))

(f∘g)(x) = f(3x²)

f(3x²) = √9x⁴- 4

f(3x²) = 3x² - 2

Hence, the value of (f∘g)(x) is 3x² - 2.

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Answer:

lesser x = 9

greater x = 11

Step-by-step explanation:

(x-10)² - 1 = 0

(x-10)² = 1

(x-10) = +- root1 (positive and negative root1)

So (x-10) = +1 and (x-10) = -1

Firstly

X - 10 = 1

X = 11

Secondly

X - 10 = -1

X = 9

So you have x = 9, and x = 11

The smaller one is the lesser x (9)

The larger one is the greater x (11)

The 7th term of the binomial expression given can be found to be 8.136 × 10^7 × x^(-4)

To find the 7th term of (3x - 4/x²)¹⁴, we can use the binomial theorem, which states that for any positive integer n and any real numbers a and b:

(a + b)ⁿ = ∑(C(n, k) x a^(n-k) x b^k)

Using the binomial theorem formula, the 7th term can be calculated as follows:

Term_7 = C(14, 6) x (3x)^(14-6) x (-4/x²)^6

First, let's find C(14, 6):

C(14, 6) = 14! / (6! x (14-6)!)

C(14, 6) = 14! / (6! x 8!)

C(14, 6) = 3003

Now, we can put everything together:

Term 7 = 3003 x (3x)^8 x (4096 / x¹²)

Term 7 = 8.136 × 10^7 × x^(-4)

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The wildlife group can estimate that there are 100 wild hogs in the area. The answer is C.

The basic idea behind this method is that if we capture a random sample of animals from a population, tag them, and release them back into the population, then later capture another sample of animals, the ratio of tagged to untagged animals in the second sample can be used to estimate the total population size.

To estimate the total population of wild hogs in the area, we can use the capture-recapture method.

In this case, the wildlife group tagged and released 20 wild hogs, and later counted 8 wild hogs out of the 40 they saw. We can set up a proportion to estimate the total population size:

(Tagged hogs in first sample) / (Total population size) = (Tagged hogs in second sample) / (Number of hogs in second sample)

Putting the values,

⇒ 20 / x = 8 / 40

Simplifying and solving for x, we get:

⇒ x = (20 × 40) / 8 = 100

⇒ x = 100

Therefore, the wildlife group can estimate that there are 100 wild hogs in the area. The answer is C.

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The frequency table that summarizes the data by the biologist and the additional plants is c. third table.

From the data by the biologist and the additional plants, we see that there are 11 plants with flowers and 7 with caterpillars.

The number of flowering plants with caterpillars is 6 plants. Those without flowers would then be:

= 11 - 6

= 5 plants

This is shown by the second frequency table.

In conclusion, the correct frequency table showing the data by the biologist is the second frequency table.

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The value of quantity after 0.2 hours is, 960

Given that;

A quantity with an initial value of 480 grows exponentially at a rate such that the quantity doubles every 6 minutes.

We know that;

The exponential growth function is

A = A₀ (1 + r)ⁿ

Where, A= The number of quantity after t days

A₀ = initial number of quantity

r = rate of growth

n = time in minutes

A quantity with an initial value of 830 grows at a rate such that the quantity doubles in 0.2 hours = 12 minutes

And, A = 2 x 480 = 960

A₀ = 480

n = 12 minutes

r = ?

⇒ A = A₀ (1 + r)ⁿ

⇒ 960 = 480 (1 + r)¹²

⇒ 2 = (1 + r)¹²

⇒ [tex]r = \sqrt[12]{2} - 1[/tex]

Now, to find the quantity after 12 minutes, we plug A = 830, t = 12 minutes in exponential function;

⇒ A = A₀ (1 + r)ⁿ

⇒ [tex]A = 480 (1 + \sqrt[12]{2} - 1)^{12}[/tex]

⇒ A = 480 (2)

⇒ A = 960

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Answer:

S - S - P

Step-by-step explanation:

(S) Statistic - The opinion of just those employees who were there on time one morning about a new training program would be a statistic as it represents a sample of the entire population of employees in the company.

(S) Statistic - The range of employees' salaries in a study about a small company with 25 employees would be a statistic as it represents a characteristic of a sample of employees from the company.

(P) Parameter - The average decrease of all the homes sold in Gwinnett in a study about the value of American homes in 2012 would be a parameter as it represents a characteristic of the entire population of American homes in Gwinnett.

Answer:

Step-by-step explanation:

To find the total cost of interest, we first need to find the total payment over the life of the loan:

Total payment = Monthly payment x Number of payments

Total payment = $370.41 x (30 x 12)

Total payment = $133,347.60

Next, we need to subtract the principal (loan) amount to find the total interest paid:

Total interest = Total payment - Principal

Total interest = $133,347.60 - $69,000

Total interest = $64,347.60

Rounding to the nearest whole dollar, the total cost of interest is $64,348.

Answer:

 39 1/3 = 118/3 square units

Step-by-step explanation:

You want the area under the curve y = -x² +9x on the interval [3, 5].

The fundamental theorem of calculus tells us the integral of the function will be its anti-derivative. That is, for f(x) = -x² +9x, we want the function F(x) whose derivative is f(x). The reverse of the power rule for derivatives can be used:

  [tex]F(x)=-\dfrac{x^3}{3}+9\dfrac{x^2}{2}[/tex]

The area of interest is ...

  F(5) -F(3) = -1/3(5³ -3³) +9/2(5² -3²) = -98/3 +72

  F(5) -F(3) = 39 1/3

The area under the curve between x=3 and x=5 is 39 1/3 square units.

Step-by-step explanation:

See image

Answer: B

Step-by-step explanation:

Ex: Shortest to smallest.

In the first hour of their run, Jenna ran 1 mile more than George.

Given graph shows the data on Jenna's running status.

It shows that Jenna ran 12 miles in 2 hours of time.

Jenna's running status in the first one hour = 12/2 = 6 miles.

Given that George ran at a constant of 5 miles per hour.

To find out how many miles will Jenna ran more than George in the first one hour = 6 -5 = 1 mile.

From the above analysis, we can conclude that the Jenna will run 6 miles in the first one hour and George will run 5 miles in the first one hour. So, Jenna will run 1 mile more than George.

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Given question is not having enough information, the complete question is attached below,

(1. 5,0 ) , (1 , 0 ) are the values of x in linear equation.

What is a linear equation in mathematics?

A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.

                        Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.

2x² -5x + 5 = 3

2x² -5x + 5 - 3 = 0

2x² -5x + 3 = 0

2X² - (2+ 3)X + 3 = 0

 2X² -2X - 3X + 3 = 0

  2x(x - 1 )-3(x - 1 ) = 0

  (2x - 3) (x - 1 )

    x = 3/2 , 1

    x = 1. 5 , 1

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