Triangle a b c has centroid g. lines are drawn from each point through the centroid to the midpoint of the opposite side to form line segments a f, b d, and c e. the length of line segment a g is 19 x 14 and the length of line segment d g is 9 x 2. g is the centroid of triangle abc. what is the length of gf? units

Factorization is the reverse process of expansion of mathematical expression to simple terms. The factorized term is: [tex]\frac{x + 14}{6}[/tex]

Factorization is a procedure in which a given number of terms of a mathematical expression is reduced by collecting common terms. It involves reducing a given mathematical expression to a simple form of terms.

Given that:

[tex]\frac{x^{2}+ 12x - 28}{6x^{2} }[/tex] ÷ [tex]\frac{x - 2 }{x^{2} }[/tex]

[tex]\frac{x^{2}+ 12x - 28}{6x^{2} }[/tex] x [tex]\frac{x^{2} }{x -2}[/tex]

[tex]\frac{x^{2} + 12x - 28}{6(x - 2)}[/tex]

Factorizing the numerator, we have;

[tex]x^{2} + 12x - 28[/tex] = (x - 2) (x + 14)

So that,

[tex]\frac{(x- 2) (x + 14)}{6(x - 2)}[/tex]

[tex]\frac{(x + 14)}{6}[/tex]

Thus the factorized form of the given question is [tex]\frac{1}{6}[/tex](x - 14).  

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These two triangles are congruent by angle angle side(AAS) congruency theorem.

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

From the given figure line segment AB is similar to line segment CD.

Angle E is congruent to angle D hence line segment AB is congruent to line segment BC.

So, These two triangles are congruent by angle angle side congruency theorem.

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The inequality represent the number of goals the team must score g ≥ 8.

An inequality show the relationship between two values in an algebraic equations that are probably not equal.

The statement about a game in which various teams are the playing:

It is given that To win that  game, the team must scores at least 8 goals.

The meaning of word at least is that , the team can score either 8 goals or more than the 8 goals.

So, we will write this situation in terms of the inequality as follows:

The value of g will be greater than or equal to 8.

= g ≥ 8.

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The equation of the parabola would be [tex]y = \frac{1}{4}(x + 1)^2 - 4[/tex].

What is a parabola?

A parabola is a curve that is shaped like a U or a mirror image of a U. It is a type of conic section, which is a curve that is formed by the intersection of a plane and a cone.

The equation of a parabola can be written in the form y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola and a is a coefficient that determines the shape of the curve.

To find the equation of the parabola described in the problem, we can first find the values of h and k and then substitute them into the equation.

We know that the vertex of the parabola is (-1, -4). Therefore, h = -1 and k = -4.

Substituting these values into the equation y = a(x - h)^2 + k, we get:

y = a(x - (-1))^2 + (-4)

= a(x + 1)^2 - 4

Now we can use the fact that the parabola passes through the points (-5, 0) and (3, 0) to find the value of a.

Substituting x = -5 into the equation, we get:

y = a((-5) + 1)^2 - 4

= a(4)^2 - 4

= 16a - 4

Since the point (-5, 0) lies on the parabola, y must equal 0 when x = -5. Therefore, we have the equation 16a - 4 = 0. Solving for a, we find that a = 1/4.

Substituting this value back into the equation for y, we get:

[tex]y = \frac{1}{4}(x + 1)^2 - 4[/tex]

Hence, the equation of the parabola would be [tex]y = \frac{1}{4}(x + 1)^2 - 4[/tex].

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The equation of the parabola would be [tex]y=\frac{1}{4}(x+1)^2-4[/tex].

What is a parabola?

A parabola is a curve that is shaped like a U or a mirror image of a U. It is a type of conic section, which is a curve that is formed by the intersection of a plane and a cone.

The equation of a parabola can be written in the form y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola and a is a coefficient that determines the shape of the curve.

To find the equation of the parabola described in the problem, we can first find the values of h and k and then substitute them into the equation.
We know that the vertex of the parabola is (-1, -4). Therefore, h = -1 and k = -4.
Substituting these values into the equation y = a(x - h)^2 + k, we get:
y = a(x - (-1))^2 + (-4)
= a(x + 1)^2 - 4
Now we can use the fact that the parabola passes through the points (-5, 0) and (3, 0) to find the value of a.
Substituting x = -5 into the equation, we get:
y = a((-5) + 1)^2 - 4
= a(4)^2 - 4
= 16a - 4
Since the point (-5, 0) lies on the parabola, y must equal 0 when x = -5. Therefore, we have the equation 16a - 4 = 0. Solving for a, we find that a = 1/4.
Substituting this value back into the equation for y, we get:

[tex]y=\frac{1}{4}(x+1)^2-4[/tex].
Hence, the equation of the parabola would be [tex]y=\frac{1}{4}(x+1)^2-4[/tex].

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The y-intercept of function f is 10 The x-intercept of function f is 20 but the y-intercept of function g is -12 but the x-intercept of function g is -3.

The places where a function or equation's graph crosses or "touches" the x-axis of the Cartesian Plane are known as the x-intercepts. This may be compared to a point with a y-value of zero. The locations where a function or equation's graph crosses or "touches" the y-axis of the Cartesian Plane are known as the y-intercepts. This may be compared to a point with a zero x-value.

Given two functions f(x) = -1/2 x + 10 and g(x) = -4x - 12

For function f(x)

Y-intercept of f(x) = -1/2 * 0 + 10 = 10

X-intercept of f(x) =>  -1/2x  + 10 = 0

X-intercept of f(x) => x = 20

For function g(x)

Y-intercept of g(x) = -4*0 - 12 = -12

X-intercept of g(x) =>  -4x -12 = 0

X-intercept of g(x) => x = -3

Therefore, Function f's y-intercept is 10 Function f's x-intercept is 20, but the function g's y-intercept is -12 and its x-intercept is -3.

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The statement 5 less than three times a number x is expressed as an expression to 3x - 5

An algebraic expression can be described as an expression made up of coefficients, terms, factors, variables and constants.These expressions are also composed of some mathematical and arithmetic operations.

They include;

Addition

Division

Multiplication

Subtraction

Parentheses

Bracket, etc

From the information given, we have that; The number is x. The number is 5 times lesser than three times the value of xThis can be represented as; 3x - 5

Hence, the expression represented is 3x - 5

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Answer:

4

Step-by-step explanation:

Constant of proportionality is the same as slope in the context of a linear function, which is defined as Δy / Δx. We can find this by taking two points and finding the difference in their x- and y-coordinates.

I'll use (1, 4) and (2, 8).

[tex]\textrm{slope}=\dfrac{8-4}{2-1} = \dfrac{4}{1} = 4[/tex]

By using simultaneous linear equation, it can be calculated that

Xochitl has 8 nickels and 16 dimes

What is simultaneous linear equation?

At first it is important to know about linear equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.

Let the number of nickel Xochitl has be x and the number of dimes Xochitl has be y

She has a total of 24 nickels and dimes altogether

x  + y = 24 .... (1)

Xochitl has $2 worth of nickels and dimes

0.05x + 0.1y = 2

5x + 10y = 200

x + 2y = 40 ..... (2)

From the graph, it is clear that the two simultaneous linear equation intersects at (8, 16)

So x = 8, y = 16

Xochitl has 8 nickels and 16 dimes

The graph has been attached

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Answer:

x≤−10

Step-by-step explanation:

x−(−11)≤1

Step 1: Simplify both sides of the inequality.

x+11≤1

Step 2: Subtract 11 from both sides.

x+11−11≤1−11

x≤−10

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By using the concept of function, it can be seen that the given graph represents a function.

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here the values on the x axis represents the domain and the values on the y axis represents the Range.

From the graph it can be seen that

Every point of the domain maps to unique point on the range.

So this is a function

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Answer:

z = 0.9

Step-by-step explanation:

1/3(6z + 7.2) = 0.5 (8z + 2) - 0.4

Step 1) (2z +2.4)=(4z+1) - 0.4

Step 2) (2z +2.4)=(4z+0.6)

Step 3) 1.8 = 2z

Step 4) 1.8/2 = z

Step 5) 0.9 = z

Answer:

.9

Step-by-step explanation:

it is 0.9 i did this assignment with my teacher

Observing the nature of the graph and the pattern it develops relating time and distance covered by Manuel, The graph explains the nature of distance covered in bike with respect to time.

A representation of the relationship between two variables, often measured along one of two right-angled axes each.

Different types of graphs are:

Manuel drives away from house for 2 units of time and stayed at a place for another 2 units of time. He start to bike towards the house for 2 units of time and again started to travel away for a single unit of time. He stayed at a place for 2 unit of time and bike back to the house in 5 units of time.

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Answer:

Step-by-step explanation:

4.2430

Answer:

It's going to take 32.7 years

1. Given

2. Alternate interior angles theorem

3. Given

4. Vertical angles

5. ASA

Answer:

H=5

Step-by-step explanation:

25=1/2h(2+8)

25=1/2h(10)

25=10*h/2

what is dividend by 2 equals 25?

50

what times 10 equals 50?

5

The linear inequality that is represented by the graph is; y ≤ One-halfx + 2

The general form of equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Now, from the inequality graph attached, we can see that we can calculate the slope from;

m = (y2 - y1)/(x2 - x1)

m = (3 - 2)/(2 - 0)

m = 1/2

We can also see that the y-intercept which is the point where the line crosses the y-axis is; y = 2.

The line is a solid line and not dotted and the shaded part is beneath the line and as such;

The inequality is; y ≤ One-halfx + 2

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The surface area of the composite figure is 1856.53cm²(nearest hundredth)

A composite shape can be defines as a shape created with two or more basic shapes. We often refer to composite shapes as compound and complex shapes.

The figure has two shapes; a cylinder and an hemisphere.

Therefore the total surface area of the composite figure = surface area of cylinder + surface area of hemisphere.

The surface area of cylinder= 2πr(r+h)

= 2× 3.14 × 5.5( 5.5+40)= 1571.57cm²

The surface area of hemisphere= 3πr²

= 3×3.14×5.5²

= 284.96cm²

Therefore the surface area of the composite figure is 1571.57cm² + 284.96cm²= 1856.53cm²(nearest hundredth)

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Answer:

Not a function

Step-by-step explanation:

If we use the vertical line test, we can get an answer quite easily. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function.

If we were to move a vertical line across the above graph, it would touch two places, so therefore it is not a function.

The dates the survey was conducted are not crucial to the findings, so the researcher is not required to report them. It is "false" to say that.

This information is thorough data that was acquired from the a target audience regarding a particular subject to perform research.

Thus, it is "false" to say that the dates the survey was conducted are not crucial to the findings, so the researcher is not required to report them.

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Answer:

if m/1 +m/5=234°, find m26=

m26 = 234° - (1 + 5)m = 234° - 6m

m26 = 234° - 6(26)

m26 = 234° - 156°

m26 = 78°

Answer:

The tail of a 1-mile long train exits a tunnel exactly 3 minutes after the front of the train entered the tunnel. If the train is moving 60 miles per hour, how long is the tunnel? Hint : How far does the front of the train move in 3 minutes?

Explanation

The front of the train moves 3 miles in 3 minutes. Therefore, the tunnel must be 1 mile long.

Answer:

2 miles long

Step-by-step :

The tail of the train starts one mile from the mouth of the tunnel and it must travel that distance plus the length of the tunnel in 3 minutes.

Let t = tunnel length

t + 1  = distance the tail must travel in 3 minutes.

3 minutes = 1/20 hr

(t+1) miles  /  60 m/hr  = 1/20 hr

t + 1 = 60/20

t+1 = 3

Subtract 1 from each side:

t = 2

The tunnel is 2 miles long.

x = 36

Step-by-step explanation:

First find the difference of size for the two givens sides on figure A and figure B. On figure A we have the given side 45, and Figure B the given size 27. Subtract the two to get 18. So the difference of scale is 18 for the two figures. So in order to find x just add the 18 to the 18 in figure B, and you get 36.

The value of x in the linear inequality 5/8x - 1 ≥ 9 is x ≥ 16

Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, ‘<’, ‘>’, ‘≤’ or ‘≥’. These values could be numerical or algebraic or a combination of both.

An inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠).

In the problem given;

5/8x - 1 ≥ 9

Solving for x in the inequality;

x ≥ 16 which can be represented using an interval notation as [16, ∞)

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Answer:

The answer is 81.85%

Step-by-step explanation:

The z score is used to determine by how many standard deviations the raw score is above or below the mean.

The z score is given by:

z = x - μ/σ

where,

For x = 88

z = 88 - 116/14

z = (-2)

For x = 130

z = 130 - 116/14

z = (1)

Thus,

P(88 < x < 130) = P(-2 < z < 1)

= P(z < 1) - P(z < -2)

= 0.8413 - 0.0228 = 81.85%

Thus, 81.85% of the population would be between 88 and 130.

After solving the linear equation in two variables we get the value of x=13 and y =-24/5

What is linear equation in two variable?

If an equation is written in the form axe + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero, then it is said to be a linear equation in two variables.

Examples of two-variable linear equations are 10x+4y = 3 and -x+5y = 2.

Such an equation has a pair of numbers as its solution, one for x and one for y, which further equalizes the two sides of the equation.

A system of linear equations in two variables can be solved using one of five techniques. These techniques are described below:

2x+5y=2 multiply this equation by 2

we get,

4x+10y=4

And the other equation is :-

5x+10y=17

Subtracting both the equation we get :-

4x+10y=4

5x+10y=17

-    -        -

________

-x =-13

x=13

y=2-26/5

y=-4.8 or -24/5

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Answer:

Below

Step-by-step explanation:

The line has negative slope and y-axis intercept = 2  from inspection

 two points on the line are needed to calculate the slope

    find two easy to work-with points

          like   (-3,4)  and  (4,-1)

           slope = (y1-y2) / ( x1-x2)  = (4 - -1) / ( -3-4) =  -5/7

Slope intercept form   y = mx +b     m is slope   b is intercept of y-axis

                               soooo   ...   y = -5/7 x + 2

The graph is rather fuzzy:

I looked a little longer and decided points   (-4,5) and (4,-1) may be more accurate:

 slope =  5--1 / -4-4 =- 6/8      so then the answer would be  y = -3/4x + 2

Answer: K^15

Step-by-step explanation:

The equation is (k^5)^3

To simplify this, we take the square root of 5-time square root 3 equal square root of 15

So the answer is k^15

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