Find the value of x that makes triangle ABC congruent to triangle DEF

The representation and comparison of a function f(x) and f(x - 4) are illustrated below with the attached graph.

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over y-axis, (-x, y).

-f(x) = Reflection over x-axis, (x, -y).

Let, The function f(x) = x², It is a quadratic function and the graph of this function is a parabola that opens upwards.

And, Let g(x) = f(x - 4) = (x - 4)²,

Now, The graph of this function is also a parabola that opens upwards but it is shifted 4 units to the right along the x-axis to the parent function

f(x) = x².

The table for f(x) and g(x) would be,

At x = 1,

f(x) = 1 and g(x) = 9.

At, x = 3,

f(x) = 9 and g(x) = 1.

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The minimum size of a cut where size is number of edges in the cut, for a graph that has more than one connected component is 1.

In graph theory, a bridge, also known as a cut-edge, is a fundamental concept that refers to an edge in a graph that has the property of disconnecting the graph when it is removed. This means that when an edge is considered a bridge, the removal of that edge would result in an increase in the number of connected components in the graph. The importance of bridges in graph theory lies in the fact that they provide a way to break down a complex graph into smaller, simpler components that can be analyzed and understood individually. Bridges can be found in many different types of graphs, including undirected graphs, directed graphs, and weighted graphs. It is also important to note that in a graph with more than one connected component, there must exist at least one bridge, meaning that the minimum size of a cut in a graph is 1. This is because a bridge is the edge that separates the graph into two or more separate components.

The minimum size of a cut in a graph is 1. This occurs in the case of a "bridge", where removing a single edge from the graph would result in two separate connected components. In any graph with more than one connected component, there must exist at least one bridge, meaning that the minimum size of a cut is 1.

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The amount that Cameron is paid per hour, given the number of hours he worked, is $ 17 per hour

To find the payment that Cameron got per hour, you first need to find the number of hours that he worked.

This number of hours is:

= 4 pm  - 8 am

= 1500 hours - 0800 hours

= 7 hours

The payment per hour is therefore:

= Amount Cameron paid / Number of hours worked

= 120 / 7

= $ 17 per hour

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Answer:

Probability of an even number product as requested = 7/10 = .7 = 70%

Step-by-step explanation:

Combinations of 2 digits from among 5 = 5!/(3!)(2!) = 10. Those combinations of 2 digits resulting in an even number product are even*even and even*odd. There are 2 even digits, (2,4) and 3 odd digits, (1,3,5).

Combinations of 2 even digits and 3 odd digits = 3*2 = 6. Combinations of 2 exact digits = 1*1 = 1. Thus, 6+1 = 7 different 2-digit products result in even numbers from among 10 possible 2-digit products.

Probability of an even number product as requested = 7/10 = .7 = 70%

The equation 5 + 4 - 2 = 9 - 2 represents a situation in which the scientist is measuring the mass of an object using a pan balance.

The equation shows that 5 units of mass are added to one pan, 4 units of mass are added to the other pan, and then 2 units of mass are removed from each pan. The equation shows that the total mass in both pans remains unchanged, which indicates that the pans are still in balance. The fact that the equation is balanced, with the same amount of mass on each side, suggests that the pans are in balance because the mass has been distributed evenly between them. The balance operates on the principle of equal weights, where equal weights on opposite sides will cancel each other out, resulting in a balanced state.

Therefore, by removing 2 units of mass from each pan, the scientist is maintaining the balance between the two pans. As long as the pans remain balanced, the scientist can accurately determine the mass of the object being measured. The equation 5 + 4 - 2 = 9 - 2 represents the scientist's assurance that the pans are still in balance and that the measurement of mass can be considered accurate.

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The proof that the angles are similar have been done below

To prove that two triangles are similar, we need to show that they have congruent angles.

We can use the Angle-Angle (AA) Similarity theorem, which states that if two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar.

In triangle ABC, angles A and B are equal to angles A and D in triangle ADE. So, according to the AA Similarity Theorem, triangles ABC and ADE are similar.

Thus, we can write:

ABC ~ ADE

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Answer:

D(t) = 20 * sin(B * t - B * 3 + k * 2π) + 45 = 20 * sin(B * (t - 3) + k * 2π) + 45

Step-by-step explanation:

The temperature over a day can be modeled by a sinusoidal function of the form:

D(t) = A * sin(Bt + C) + D

Where A is the amplitude (half the difference between the high and low temperatures), B is the angular frequency, C is the phase shift, and D is the vertical shift.

From the given information, we know:

The high temperature is 85 degrees.

The low temperature of 45 degrees occurs at 3 AM, or 3 hours after midnight.

So, the amplitude is (85 - 45)/2 = 20

The temperature at 3 AM can be found by setting t = 3:

D(3) = 20 * sin(B * 3 + C) + 45

So, the vertical shift is 45.

Finally, we can find the phase shift by using the fact that the low temperature occurs at 3 AM:

C = -B * 3 + k * 2π

Where k is an integer.

Putting it all together, we get:

D(t) = 20 * sin(B * t - B * 3 + k * 2π) + 45 = 20 * sin(B * (t - 3) + k * 2π) + 45

This is the equation for the temperature, D, in terms of t.

Answer:

2

Step-by-step explanation:

Answer:

Step-by-step explanation:

The volume of a cylinder with height "h" and radius "r" is given by the formula: V = πr^2h.

The volume of a cone with height "h" and radius "r" is given by the formula: V = (1/3)πr^2h.

To find the volume of a cone with the same height and radius as a cylinder with a volume of 234 cubic inches, we need to find the height and radius of the cylinder. We can use the volume formula for the cylinder to do this:

V = πr^2h

234 = πr^2h

Dividing both sides by πr^2:

h = 234 / (πr^2)

Now that we know the height, we can use it to find the radius using the volume formula for the cylinder:

234 = πr^2h

Taking the square root of both sides:

r = √(234 / πh)

Finally, we can use the height and radius to find the volume of the cone:

V = (1/3)πr^2h

This answer will give us the volume of a cone with the same height and radius as a cylinder with volume 234 cubic inches.

The 95% confidence interval estimate for the true proportion of women in Europe who use the internet is = (34.968%, 35.032%)  can be calculated using the following formula:

p ± z*(√(p(1-p))/n)

where pis the sample proportion (35% in this case), z is the z-score for a 95% confidence level (approximately 1.96), and n is the sample size (750 in this case).

Substituting the values, we get:

35% ± 1.96 * (√(35%(1-35%)/750))

= 35% ± 1.96 * (√(0.35 * 0.65/750))

= 35% ± 1.96 * (√(0.000936))

= 35% ± 0.0312

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The number listed below that are the solution of equation are option A 16 and option C 1.

The opposite of squaring an integer is finding its square root. The result of multiplying a number by itself yields its square value, while the square root of a number can be found by looking for a number that, when squared, yields the original value.

The given equation is:

√s² = s

The numbers that satisfy thus equation are 16 and 1.

Negative numbers do not satisfy the equation as the square root of a number is a positive number, and hence the two sides will not be equal.

Hence, the number listed below that are the solution of equation are option A 16 and option C 1.

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The height of the tree is solved to be x = 50 * tan(57°)

The description is modelled to a right triangle. The height, x, of the tree can be found using trigonometry.

Using the tangent function:

tan 57 = height of the tree, x / distance from the tree

tan 57 = x / 50

x = 50 * tan(57°)

The sin and cos will require the hypotenuse which is the slant distance and this is not given

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The number of the one-point shot is 17 and the number of the 2 point shot is 36.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that at a basketball​ game, a team made 53 successful shots. They were a combination of​ 1- and​ 2-point shots.

Let the one-point shot is x and the 2 point shot is y. The equations can be written as below:-

x + y = 53

-x - 2y = -89

_________

y = 36

The value of x will be calculated as:-

x + y = 53

x + 36 = 53

x = 53 - 36

x = 17

Hence, the one-point shot number is 17, and the two-point shot number is 36.

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Answer:

103.42

Step-by-step explanation:

use the big circle area - 2 little white circles' area

big r = 12.5/2 = 6.25 so big circe area = π r² =π * 6.25²

small r = 3.5/2 = 1.75 so small circe area = π r² =π * 1.75²

2 of them = 2π * 1.75²

so π 6.25² - 2π * 1.75² = 39.06π-6.13π=103.42

well, looking at the picture above, we can see that the diameters are 12.5 and 3.5 for those circles, that means the radii for them will be half that for each, namely 6.25 and 1.75 respectively.

let's get the whole area for containing circle, and then subtract the area of  the small ones, what's leftover is the shaded area.

[tex]\stackrel{large~one}{\textit{area of a circle}}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=6.25 \end{cases}\implies A=\pi 6.25^2 \\\\\\ \stackrel{small~one}{\textit{area of a circle}}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=1.75 \end{cases}\implies A=\pi 1.75^2 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE Areas}}{\stackrel{large}{\pi 6.25^2}~~ - ~~\stackrel{\textit{two small ones}}{2(\pi 1.75^2)}} ~~ \approx ~~ \text{\LARGE 103.48}[/tex]

Answer:

The two angles are [tex]75^{o}[/tex] ([tex]\frac{5\pi}{12}[/tex]radians) and [tex]15^{o}[/tex] ([tex]\frac{\pi}{12}[/tex]radians)

Step-by-step explanation:

Right angle = [tex]90^{o}[/tex] = [tex]\frac{\pi }{2}[/tex] radians
Let x = Lesser angle

     y = Greater angle

Angles in degrees:

Sum of angles in a right-angled triangle = [tex]180^{o}[/tex]

[tex]x^{o} + y^{o} + 90^{o} = 180^{o}[/tex]

[tex]= x + y = 180 - 90[/tex]

[tex]= x + y = 90[/tex]

[tex]= x = 90 - y[/tex] ——(equation i)

[tex]y^{o} -x^{o} =\frac{2}{3} (90^{o})[/tex]

[tex]= y - x = 60[/tex] ——(equation ii)

These two equations are linear simultaneous equations, which can be solved by substitution, elimination or graphical method:

Substitution method:

Substitute (equation i) into (equation ii) to solve for y:

Expand the brackets by applying the Distributive Law and bring all the like terms together:

[tex]= y - (90-y)= 60[/tex]

[tex]= y - 90 + y = 60[/tex]

[tex]= y + y = 60 + 90[/tex]

[tex]= 2y = 150[/tex]

[tex]= y = \frac{150}{2}[/tex]

[tex]= y = 75^{o}[/tex]

Substitute this calculated value in any of the equations to determine the value of x:

[tex]x = 90 - 75[/tex]

[tex]= x = 15^{o}[/tex]

Angles in Radians:

To convert an angle measured in degrees to radians, multiply by [tex]\frac{\pi }{180^{o} }[/tex]

[tex]= y = 75^{o} .\frac{\pi}{180^{o}}[/tex]

Divide both the numerator and denominator by the Highest Common Factor ‘15’:

[tex]= y = \frac{5\pi }{12}[/tex] radians

[tex]x = 15^{o}.\frac{\pi }{180^{o}}[/tex]

[tex]= x = \frac{\pi}{12}[/tex] radians

Step 1: Calculate the area of the room. To calculate the area of the room, multiply 12 feet by 15 feet, which gives us a total of 180 square feet.

Step 2: Calculate the area of one tile. To calculate the area of one tile, multiply 113 feet by 113 feet, which gives us a total of 1.369 square feet.

Step 3: Calculate the number of tiles needed. To calculate the number of tiles needed, divide the area of the room (180 square feet) by the area of one tile (1.369 square feet). This gives us a total of 131 tiles.

Therefore, 131 tiles are needed to cover the entire floor.

Start by multiplying the tile's length by its breadth in inches to determine the tile's square footage. Lastly, multiply the area of one tile by the determined size of the space. The outcome is the precise quantity of tiles needed for the space.

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Answer:

64.4 meters

Step-by-step explanation:

divide 7000 cm (7 metre) by 5 cm

you get 1400

multiply that by the smaller wingspan

Answer:

65.71

Step-by-step explanation:

According to the model's scale, which is 5 cm to 7 m, there are 7 m on the actual plane for every 5 cm on the model. By dividing the wingspan of the model by the scale factor and multiplying the result by the equivalent size in metres, we may determine the real plane's wingspan.

 With a model's wingspan of 46 cm, this means: (46 cm) * (7 m/5 cm) = 65.71 m (46 cm) / (5 cm/7 m) 

The actual airplane's wingspan is therefore roughly 65.71 metres.

Hope it helps! : )

The equivalent function in the form [tex]R(t) = ab^t[/tex] is: [tex]R(t) = 4001 * 0.9^t.[/tex]

What is an equivalent function?

The domain and range of an equivalent function are the same. In mathematics, the phrases equivalent and equal do not have the same meaning.

The equation R(t) = 4000(0.9)^t + 1 can be rewritten in the form [tex]R(t) = ab^t[/tex]by separating the constant factor and the exponential factor. We can do this by defining a = 4000 and b = 0.9:

 [tex]R(t) = 4000 * (0.9)^t + 1\\\\= 4000 * b^t + 1\\\\= (4000 + 1) * b^t\\\\= 4001 * b^t\\\\= ab^t[/tex]

where, a = 4001 and b = 0.9.

So, the equivalent function in the form [tex]R(t) = ab^t[/tex] is:

[tex]R(t) = 4001 * 0.9^t.[/tex]

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Answer:

16

Step-by-step explanation:

Any number to the power of 0 is 1

1/4^-2 -> 4^2 -> 16

Answer: 16

Step-by-step explanation:

-2^0 = 1

y^-2 => 1/y^2 => 1/4^2 = 1/16

1/ (1/16)

1 x 16/1 = 16

The balance at the end of three months is $652.

If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, and it is left for T years for that simple interest, then the interest amount earned is given by:

[tex]I = \dfrac{P \times R \times T}{100}[/tex]

Given;

P=$630

R=0.14/12

= 0.01166

n=3

Interest rate = 14%

Using the formula;

A=P(1+r)^n

we can now insert the values

A=630(1+0.01166)^3

A=652.29

Therefore, the by interest of 14% the amount will be $652.29.

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Consequently, x = 12 is the value of x that equals the equations 2/3x Plus 2 and 4/3x - 6.

Depending about where it is in the number, each character has a different meaning, which is referred to as value. We figure it out by increasing the digit's place value by its face value. Location value plus face value equals value.

We can assign the equations 2/3x + 2 and 4/3x - 6 equal to one another and solve for x to determine the value of x at which they are equal:

2/3x + 2 = 4/3x - 6

First, by multiplying both sides by the least common multiple of the denominators, which is 3, we can reduce the expressions:

2x + 6 = 4x - 18

Next, we can simplify by subtracting 2x from both sides:

6 = 2x - 18

Adding 18 to both sides gives:

24 = 2x

Dividing both sides by 2 gives:

x = 12

Therefore, the value of x that makes the expressions 2/3x + 2 and 4/3x - 6 equal is x = 12.

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Answer:

3

Step-by-step explanation:

[tex]\displaystyle \frac{f(b)-f(a)}{b-a}\\ \\=\frac{f(1)-f(-1)}{1-(-1)}\\ \\=\frac{3-(-3)}{1+1}\\\\=\frac{3+3}{2}\\ \\=\frac{6}{2}\\ \\=3[/tex]

Answer:

The solution to the system of two linear equations is p = -6.

Step-by-step explanation:

First, we can isolate the variable p on one side of the equation. Subtract 8 from both sides to get 1/6p = -1/3p + 6.

Next, we can subtract -1/3p from both sides to get 4/6p = 6.

Finally, we can divide both sides by 4/6 to get p = -6.

The two quadrilaterals TUVW and EFGH are similar.

Those polygons look the same but are different in size.

And in similar polygons,

the corresponding sides are in constant proportion to each other and the corresponding angles are equal to each other.

Given:

TUVW and EFGH are the two quadrilaterals.

The sides of the polygon TUVW are equal.

And the sides of the polygon EFGH are equal.

That means the corresponding sides will have a constant ratio.

And corresponding angles are congruent.

So, the polygons are similar.

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Answer: $1486.01

Step-by-step explanation: 200*(1.2^(12-1))

Uniform distribution best describes the given shape of the distribution.

The uniform distribution is a probability distribution that has the same probability of occurrence across a defined interval. It is also sometimes referred to as a rectangular distribution or a flat distribution.

The uniform distribution is defined by two parameters, a and b, which represent the lower and upper bounds of the interval. For example, if a uniform distribution is defined between 0 and 1, the probability of any number between 0 and 1 occurring is equal and the same.

The uniform distribution has several properties, including:

The mean of the distribution is equal to the midpoint of the interval, (a + b) / 2.

The variance of the distribution is equal to (b - a)² / 12.

The distribution is symmetrical, meaning that it is equally likely for any value within the interval to occur.

Applications of the uniform distribution include modelling random processes such as coin flips, die rolls, and random sampling. It is also often used as a prior distribution in Bayesian statistics.

Hence, the correct answer is A.

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--The given question is incorrect; the correct question is

"Which BEST describes the shape of the distribution?

A) uniform

B) skewed right

C) skewed left

D) roughly symmetrical"--

It is unlikely for your height to be 70 inches exact because there are infinite number of possible ways.

Height is considered a continuous variable because it can take on any value within a certain range, including fractional values. Continuous variables are not limited to specific set of values, but can take on any value within a specified range. This is in contrast to discrete variables, which can only take on a specific, limited set of values. The continuous nature of height allows for precise measurement and calculation, as opposed to rounding to the nearest whole number.

When we talk about height, height is measure and hence it is a continuous variable. This means that it is possible for a person's height to be exactly 70 inches, but it is unlikely due to the vast number of possible values.

Hence, it is very unlikely for height to be specific.

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The value of a, A and C are 12.31 cm,44.07° and 34.68° respectively

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

To find C:

b/sinb = c/sinC

17.23/sin101.25 = 10/sinC

17.23 × sin C = sin101.25 × 10

17.23× sin C = 0.98 ×10

sinC = 9.8/17.23

sinC = 0.569

C = sin^-1(0.569)

C = 34.68°

The sum of angle in a triangle is 180

A = 180-(101.25+34.68)

A= 180-135.93

A = 44.07°

a/sinA = b/sin B

a/sin 44.07 = 17.23/sin101.25

a= sin 17.23 × sin 44.07/sin101.25

a =( 17.24× 0.70)/0.98

a = 12.31 cm

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A conclusion that the class can make is: there is no relationship between the number of books and the number of pens. The Option D is correct.

A relation is simply a link between two sets of data. When two values, x and y, are linked in an equation or inequality, they are related and thus represent a relation.

From the graph given, we can not draw any association or relationship between the number of books and the number of pens, rather, their quantity in the classroom is deducable.

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Answer:

Hope this help :)

Step-by-step explanation: