If △ EFG ∼ △ ABC

, What value of x will make the two triangles similar?

u is the slope of the line passing through the points (1, -3) and (1, 0).

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We have to find the slope of the line passing through the points (1, -3) and (1, 0)

m=0-(-3)/1-1

=3/0

Undefined

Hence, the slope of the line passing through the points (1, -3) and (1, 0) is u.

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The volume of the parallelepiped formed by the adjacent edges u=i+j, v=j+k, and w=i+k is: 1.

The triple scalar product can be used to find the volume of the parallelepiped formed by three non-coplanar vectors u, v, and w. The triple scalar product is defined as:

where × represents the cross product and · represents the dot product.

Given that u=i+j, v=j+k, and w=i+k, we can first find the cross product of v and w as:

= i x (j+k) + k x (j+k)

= i x j + i x k + k x j + k x k

= -k + i -j

Next, we can find the dot product of u with the cross product of v and w as:

= i · (-k) + i · i + i · (-j) + j · (-k) + j · i + j · (-j)

= -ik + i^2 - ij - jk + ji - j^2

= i^2 - j^2 - k(i+j)

= 1 - 0 - (1+0)

= -1

The absolute value of this result gives the volume of the parallelepiped, so the volume is:

Therefore, the volume of the parallelepiped formed by the adjacent edges u=i+j, v=j+k, and w=i+k is 1.

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The equation of line in standard form is  y = -146x + 69.

A line equation is an algebraic way of representing a set of points that together form a line in a coordinate system. The various points that together form a line of axes can be represented as a set of (x,y) variables and form an algebraic equation, also called the line equation. You can use the straight line equation to determine if a given point lies on a straight line.

Each row of equations is a linear equation of degree 1. Read the entire article to learn about the different forms of linear equations and how to determine them. A line segment can be defined as a connection between two points. Any two points in a 2D geometry can be connected by a line segment or a simple straight line. The equation of a straight line can be obtained in three ways:

slope intercept method

point slope method

Standard method

Given two points lying on a given line, we usually follow the point-gradient method.

The equation for a straight line is y−y1=m(x−x1)

where y1 is the Y-axis coordinate, m is the tilt, x1 Coordinates on the x-axis.  m = y2-y1/x2-x1

eqn = y +4 = (-36/1/4)(x-1/2)

y +4 = -146x + 73

y = -146x + 69

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If y+3=-4/3(x-1) and y=-4/3x-1 are two lines then these are parallel.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The two equations are

y+3=-4/3(x-1)

y=-4/3x-1

When we compare both the equations to slope intercept form.

we get slope -4/3 for both the equations.

If the lines have same slope then the lines are parallel.

Hence, the two lines are parallel lines.

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Answer:

Jakaur7889 on inta

Step-by-step explanation:

Babahaja

Answer:

1 - 3i, 4

Step-by-step explanation:

The polynomial has real coefficients, so if it has a complex root, it must have at least two complex roots which are complex conjugates.

Since 1 + 3i is a root, then 1 - 3i is also a root.

Two of the factors of the polynomial are:

x - (1 + 3i) and x - (1 - 3i)

Simplify the factors above:

x - 1 - 3i and x - 1 + 3i

Find their product:

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

Rewrite them showing we have the product of  a sum and a difference.

= [(x - 1) - 3i][(x - 1) + 3i]

Multiply the factors above noticing they are a sum and a difference which follows the pattern (a + b)(a - b) = a² - b².

= (x - 1)² - (3i)²

= x² - 2x + 1 - 9(-1)

= x² - 2x + 10

Now we divide the original polynomial by the product we just found using long division.

                                        x - 4

                                  ------------------------------

         x² - 2x + 10      |    x³ - 6x² + 18x - 40

                                  -   x³ - 2x² + 10x

                                 ------------------------

                                            -4x² + 8x - 40

                                      -     -4x² + 8x - 40

                                     --------------------------

                                                0 +    0  + 0

Now we know that x³ - 6x² + 18x - 40 factors into (x² - 2x + 10)(x - 4).

(x² - 2x + 10)(x - 4) = 0

From x² - 2x + 10, we have roots x = 1 + 3i and x = 1 - 3i.

x - 4 = 0

x = 4

From x - 4, we have root x = 4.

Answer: 1 - 3i, 4

Answer:

You just want to find what 25% of 450 is. To do so, you can change 25% into a decimal, and then multiply:

25% as decimal is 0.25.

0.25 * 450 = 112.5

The discount is $112.50.

Step-by-step explanation:

Hope it helps! =D

Answer:

z = 50°

Step-by-step explanation:

We know that,

→ Sum of all sides of triangle is 180°.

Formula we use,

→ <A + <B + <C = 180°

Forming the equation,

→ 60° + 70° + z = 180°

Now the value of z will be,

→ 60° + 70° + z = 180°

→ 130° + z = 180°

→ z = 180° - 130°

→ [ z = 50° ]

Hence, the value of z is 50°.

The coordinates of the triangle when translated 2 units left are A'(-3, -1), B'(-3, -5) and C'(-1.5, -5).

Translation is a type of transformation of geometrical figures. After translation, the original figure is shifted from a place to another place without affecting it's size.

The given triangle has the coordinates A(-1, -1), B(-1, -5) and C(0.5, -5).

Translation is done 2 units left.

A(-1, -1) becomes A(-1 - 2, -1) = (-3, -1)

B(-1, -5) becomes B(-1 - 2, -5) = (-3, -5)

C(0.5, -5) becomes C(0.5 - 2, -5) = (-1.5, -5)

Hence the coordinates are A'(-3, -1), B'(-3, -5) and C'(-1.5, -5).

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"79 % of all students at the local university voted in the last election" the numerical value describes a population parameter.

Population Parameter is a quantity/measurement that can be used as material for follow-up on population management activities.

 Population is a generalized area consisting of: objects/subjects that have certain qualities and characteristics determined by the researcher to be studied and then drawn conclusions.

The population or universe is the total number of units or individuals whose characteristics are to be studied. And these units are called units of analysis, and can be people, institutions, things, etc.

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The total amount of cash collected is $10,418.6.

A percentage is expressed as a number or ratio that can be expressed as fraction of 100. It is denoted by % symbol.

The amount of cash collected at the time of making a cash sale of $9,220 worth of merchandise subject to 13 % HST is,

Rate of interest on the sales amount is 13%

13% of 9220 = [tex]\frac{13}{100}*9220=1198.6[/tex]

Here, sales price = $9,220

The total amount of cash collected = 1198.6+9220

                                                          = 10,418.6

Hence, the total amount of cash collected is $10,418.6.

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Answer:

= 11x + 20.

Step-by-step explanation:

2x + x + x+2x+3x+30+(2x-10)

= 2x+x+x+2x+3x+30+2x-10

=2x + x + x + 2x + 3x + 2x + 30 - 10

=11x + 20.

(a) The value of E(Y) will be = 0.8

(b)  The expected amount of the surcharge is $165.

(a) The expected value of Y is given by:

E(Y) = 0(0.5) + 1(0.25) + 2(0.2) + 3(0.05)

= 0.25 + 0.4 + 0.15

= 0.8

Therefore, the expected number of moving violations for which the individual was cited during the last 3 years is 0.8.

(b) The amount of the surcharge for an individual with Y violations is $110[tex]y^{2}[/tex]. The expected surcharge is given by:

E($110[tex]y^{2}[/tex]) = $110 * E([tex]y^{2}[/tex])

To calculate E([tex]y^{2}[/tex]), we use the formula:

E([tex]y^{2}[/tex]) = Σ [tex]y^{2}[/tex] p(y)

where the sum is taken over all possible values of Y.

E([tex]y^{2}[/tex]) = [tex]0^{2}[/tex](0.5) + [tex]1^{2}[/tex](0.25) + [tex]2^{2}[/tex](0.2) + [tex]3^{2}[/tex](0.05)

= 0 + 0.25 + 0.8 + 0.45

= 1.5

Therefore, the expected surcharge is:

E($110[tex]y^{2}[/tex]) = $110 * E([tex]y^{2}[/tex])

= $110 * 1.5

= $165

So, the expected amount of the surcharge for an individual with moving violations is $165.

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Answer:

The function g(x) is the derivative of the function sin(x). So, g(x) = cos(x).

Therefore, the instantaneous rate of change of g with respect to x at x = π/3 is cos(π/3), which is approximately equal to 0.5.

Step-by-step explanation:

np and pls mark brainlist:)

The fourth number ​is equal to -6.

Mathematically, the arithmetic average for a given data set can be calculated by using this formula:

Average = [F(x)]/n

Next, we would calculate the arithmetic average for the four numbers (data set) as follows:

Let the fourth number be represented by the variable n.

Total numbers = 17 + 13 + 16 + n

Total numbers = 46 + n

10 = 46 + n/4

40 = 46 + n

n = 40 - 46

n = -6

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∫1.5 T(h) dh = 9.573, rounded to three decimal places. (a) To evaluate ∫1.5 T(h) dh, we need to integrate T(h) with respect to h from 0 to 1.5: ∫1.5 T(h) dh = ∫0.1.5 (9.43h^3 - 15.41h^2 + 17.34h - 9.83) dh

Using the power rule of integration, we can integrate each term of the polynomial: ∫0.1.5 (9.43h^3 - 15.41h^2 + 17.34h - 9.83) dh

= (9.43/4)h^4 - (15.41/3)h^3 + (17.34/2)h^2 - 9.83h |0.1.5

= [(9.43/4)(1.5)^4 - (15.41/3)(1.5)^3 + (17.34/2)(1.5)^2 - 9.83(1.5)] - [(9.43/4)(0)^4 - (15.41/3)(0)^3 + (17.34/2)(0)^2 - 9.83(0)] = 9.573

Therefore, ∫1.5 T(h) dh = 9.573, rounded to three decimal places.

(b) The answer to part (a) represents the total change in temperature during the hour and a half after the beginning of the thunderstorm. This means that the temperature increased by an average of 9.573 degrees per hour during this time period.

This integral gives us a measure of the total effect of the thunderstorm on the temperature, which is useful for predicting the weather and understanding the behavior of natural phenomena.

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By using fundamental theorem of calculus  The exact value of the definite integral [tex]\int {1}^{\pi}\left(3x^{-1} \sqrt{x}\right)\ dx[/tex] is 6(√(π) - 1).

First, we can find an antiderivative of the integrand by using the power rule and the constant multiple rule of integration:

∫(3x^(-1/2)) dx = 3 ∫(x^(-1/2)) dx = 3 (2x^(1/2)) + C = 6√(x) + C

where C is the constant of integration.

Now, we can use the fundamental theorem of calculus to evaluate the definite integral \int {1}^{\pi}\left(3x^{-1} \sqrt{x}\right)\ dx. The theorem states that if f(x) is continuous on the interval [a, b] and F(x) is an antiderivative of f(x), then

∫[a, b] f(x) dx = F(b) - F(a)

In this case, f(x) = 3x^(-1/2) and F(x) = 6√(x) + C. Therefore,

∫{1}^{π} (3x^(-1/2)) dx = F(π) - F(1) = 6√(π) + C - 6√(1) - C = 6√(π) - 6√(1) = 6(√(π) - 1)

So the exact value of the definite integral [tex]\int {1}^{\pi}\left(3x^{-1} \sqrt{x}\right)\ dx[/tex] is 6(√(π) - 1).

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The volume of the parallelepiped is 190.

The volume V of a parallelepiped with adjacent edges pq, pr, and ps can be found using the scalar triple product as:

V = |pq · (pr x ps)|

where · denotes the dot product and x denotes the cross product.

pq = q - p = (-1-3, 2-0, 5-1) = (-4, 2, 4)

pr = r - p = (5-3, 1-0, -1-1) = (2, 1, -2)

ps = s - p = (0-3, 4-0, 2-1) = (-3, 4, 1)

pr x ps = det([i, j, k; 2, 1, -2; -3, 4, 1]) = i(-4) - j(7) + k(10) = (-4, -7, 10)

V = |(-4, 2, 4) · (-4, -7, 10)| = 190

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Answer:

4 to the 4th power is 256

Explanation:

4 to the 4th power is a mathematical expression indicating that the number 4 is multiplied by itself four times. Mathematically, it is represented as 4^4.

To calculate 4^4, you would multiply 4 by itself four times: 4 x 4 x 4 x 4.

The result of this multiplication is 256, which means that 4 to the 4th power is equal to 256.

The number 4 to the 4th power is equal to 256.

When you raise a number to a power, it means multiplying that number by itself the specified number of times.

In the case of 4⁴, you are multiplying 4 by itself four times:

4⁴ = 4 × 4 × 4 × 4

When you perform the multiplication, you get:

4 × 4 = 16

16 × 4 = 64

64 × 4 = 256

Therefore, 4 to the 4th power is equal to 256.

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The proof method to show that the statement "The average of any three odd integers is an odd integer" is true is "Prove true by direct proof."

To prove that the statement is true by direct proof, we can assume that the three odd integers are a, b, and c, where a = 2k + 1, b = 2m + 1, and c = 2n + 1 for some integers k, m, and n. Then, the average of these three odd integers is:

(a + b + c)/3 = (2k + 1 + 2m + 1 + 2n + 1)/3

= (2k + 2m + 2n + 3)/3

= 2(k + m + n) + 1

Since k, m, and n are integers, k + m + n is also an integer. Therefore, the average of any three odd integers is of the form 2x + 1, where x is an integer, which is an odd integer.

The reason the attempted proof of the statement "The difference between any odd integer and any even integer is odd" is not correct is "The proof violates the parity property." The student incorrectly subtracted an even integer from an odd integer and concluded that the result is odd. However, the difference between an odd integer and an even integer is always odd, which can be proven directly as follows:

Let n be any odd integer and m be any even integer. Then, by definition, n = 2k + 1 and m = 2j for some integers k and j. The difference between n and m is:

n - m = (2k + 1) - 2j

= 2k - 2j + 1

= 2(k - j) + 1

Since k and j are integers, k - j is also an integer. Therefore, the difference between any odd integer and any even integer is of the form 2x + 1, where x is an integer, which is an odd integer.

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The rod's linear density at 1 metre from the left end and a point x meters to the right is 8 x 3 kg is = 8(1)2 = 8 kg/m.

We can start by using the definition of linear density, which is the mass per unit length of a rod or wire. Let's assume that the linear density of the rod at a distance of 1 meter from the left end is ρ kg/m.

Then, the mass of the part of the rod that lies between 0 meters and 1 meter to the right is:

m1 = ρ * 1 kg

Similarly, the mass of the part of the rod that lies between 0 meters and x meters to the right is:

m2 = 8x^3 kg

The mass of the part of the rod that lies between 1 meter and x meters to the right is:

m2 - m1 = (8x^3 - ρ) kg

Since we know that this mass is equal to ρ times the length of the rod segment, which is (x-1) meters, we can write:

ρ * (x-1) = 8x^3 - ρ

By condensing this solution, we obtain:

ρ * (x-1+1) = 8x^3

ρ * x = 8x^3

ρ = 8x^2 kg/m

As a result, the rod's linear density at 1 metre from the left end is = 8(1)2 = 8 kg/m.

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Answer:

120

Step-by-step explanation:

18 = .15x  Divide both sides by .15 (15% as a decimal is .15)

[tex]\frac{18}{.15}[/tex] = [tex]\frac{.15x}{.15\\}[/tex]

120 = x

In accordance with Side-Angle-Side theorem of congruence, the triangles seen in choices A and C are congruent.

In this problem we need to determine what triangles are congruent, that is, two triangles whose sides and angles are the same in measure and distribution. We can prove congruence by means of Side-Angle-Side theorem, where given angle is between two given sides.

Then, by direct inspection, the triangles from choices A and C are congruent, because sides and in-between angle are the same in measure and distribution.

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The triangles that are certainly congruent in the diagram are triangle A and triangle C.

Congruent triangles are triangles that have the same size and shape, such that the lengths of the three sides in one triangle are equivalent or have same length as the lengths of the three sides of the other triangle.

The congruent triangles can be obtained by using the congruence rules, or conditions for congruence, which includes; ASA, SAA, SSS, SAS

Where;

ASA is an acronym for Angle-Side-Angle

SAA is an acronym for Side-Angle-Angle

SSS is an acronym for Side-Side-Side

SAS is an acronym for Side-Angle-Side

The lengths of two sides and the measure of the included angle in triangle A are congruent to the length of two sides and the measure of the included side between the two sides in triangle C.

Therefore, the triangle in option A is congruent to the triangle in option C by the Side-Angle-Side, SAS, congruency rule.

The angle 62° is the non included angle to the 14 m and 10 m long side in option B and D, while the 14 m long side is the adjacent side to the 62° angle in option B. In option D the 10 m long side is adjacent to the 62° angle, which the orientation of triangles B and D to be different

The only two congruent triangles are triangles in option A and option C

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we can conclude that the value of n for which [tex]t_n[/tex] = 0.3325 is between 3 and 4 and the value of n for which [tex]S_n[/tex]= -6 is 6.

A) To find the value of n for which [tex]t_n[/tex] = 0.3325, we can use trial and error method.

Starting with n=1, we have:

[tex]t_1 = (1^2 - 1)/(3 * 1^2) = 0[/tex]

For n=2, we have:

[tex]t_2 = (2^2 - 1)/(3 * 2^2) = (3)/(12) = 0.25[/tex]

For n=3, we have:

[tex]t_3 = (3^2 - 1)/(3 * 3^2) = (8)/(27) = 0.296296...[/tex]

Continuing in this way, we find that t_3 < 0.3325 < t_4, where

[tex]t_4 = (4^2 - 1)/(3 * 4^2) = (15)/(48) = 0.3125[/tex]

Thus, we can conclude that the value of n for which [tex]t_n[/tex] = 0.3325 is between 3 and 4, and it can be found more accurately by using numerical methods such as bisection or Newton's method.

B) To find the sum of the arithmetic series 16 + 13 + 10 + ..., we can use the formula for the sum of an arithmetic series:

[tex]S_n = n/2 * (a_1 + a_n),[/tex]

where n is the number of terms in the series, [tex]a_1[/tex] is the first term (16 in this case), and a_n is the nth term.

Let's assume that the nth term is represented by [tex]a_n = 16 - 3 * (n - 1),[/tex] so that a_1 = 16 and a_n = 16 - 3 * (n - 1).

Then, we have:

S_n = n/2 * (16 + 16 - 3 * (n - 1)) = n/2 * (16 + 16 - 3n + 3) = n/2 * (16 + 16 - 3n + 3) = n/2 * (32 - 3n + 3) = 16n - (3/2)n^2 + (3/2)n

We want to find the value of n for which S_n = -6, so we can substitute the value of S_n into the equation and solve for n:

[tex]S_n = n/2 * (16 + 16 - 3 * (n - 1)) = n/2 * (16 + 16 - 3n + 3) = n/2 * (16 + 16 - 3n + 3) = n/2 * (32 - 3n + 3) = 16n - (3/2)n^2 + (3/2)n[/tex]

[tex]-6 = 16n - (3/2)n^2 + (3/2)n[/tex]

Expanding the equation and solving for n, we find that n = 6.

Thus, the value of n for which [tex]S_n[/tex]= -6 is 6.

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The difference of  8/3x+5 -2x/3x+5 is (8 - 2x) / (3x+ 5).

The correct option is (A).

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

We have the Expression as:

8/3x+5 -2x/3x+5

Now, Simplifying the expression as:

=  8/3x+5 -2x/3x+5

= (8 - 2x) / (3x+ 5)

= 8/(3x+ 5) - 2x/ (3x+ 5)

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The cost for each person is $12.

So, each person paid $12 for a movie ticket.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

The cost of going to the movie theater for Elissa and 11 of her friends is $144.

The total cost is divided equally among each person.

The number of total people is 12.

So, the cost of each person,

= total cost/ the number of total people

= 144/12

= 12

Therefore, 12 is the required value.

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a) The factors that impact a person's credit score and history include:

b) To raise or improve a credit score and history, you must undertake the following actions:

A credit score is a numerical rating or expression of an individual's credit history to determine their creditworthiness.

Credit scores are presented on credit reports, which are regularly prepared by credit bureaus.

On the other hand, a credit history is an official record of an individual's credit management.

Thus, one must understand the credit history and meet payment obligations to improve a person's credit score.

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Answer:

13.3 miles

Step-by-step explanation:

Picture a right triangle with legs of 3 and 13.  The hypotenuse is the straight line distance back to the starting point.  Use the Pythagorean theorem to find the hypotenuse (c):

c² = 13² + 3² = 178

c = √178 = 13.3 miles

Answer:

Robin.

Step-by-step explanation:

Clinton scored 24% of his attempts which means 24/100.

Then Katniss scored 6/25 of his attempts which means 24/100.

After that Robin scored 0.26 of his attempts which means 26/100.

Finally William scored 1/5 of his attempts which means 20/100.

Therefore, Robin has the highest score and wins the competition.