Answer:
1. 2(x-2) = 2x -4 = -7 + 6x -4x +3
2. (x+14) - (8-2x) = 3x + 6 = 9x - 2(3x-3)
3. 3(x+5) = 3x + 15 = -2x + 9 + 5x + 6
4. -4(x+1) + 5x = x - 4 = (7-2x) + (3x -11)
5. (7 + 5x) + (-4x - 1) = 6 + x = -3x + 6 + 4x
Step by step:
For number 1:
2(x-2) = 2x - 4
-7 + 6x -4x + 3 = (-7 + 3) + (6x - 4x) = 2x - 4
For number 2:
(x+14) - (8-2x) = x + 14 - 8 + 2x = (14-8) + (2x + x) = 3x + 6
9x - 2(3x-3) = 9x - (6x - 6) = 9x - 6x +6 = 3x + 6
--
Have a nice day!!
Answer:
4
1
2
5
3
Step-by-step explanation:
we should simplify them first
we will keep the first column the same and call them by numbers 1-5 and the second column will be labled by letters A-E
1- 2(X-2)
2X-4
2- X+14-(8-2X)
X+14-8+2X
3X+6
3 - 3(x+5)
3x+15
4: -4(x+1)+5x
-4x-4+5x
x-4
5. (7+5x)+(-4x-1)
x+6
A: 7-2x+3x-11
x-4
A=4
B: -7+6x-4x+3
-7+2x+3
2x-4
B=1
C: 9x-6x+6
3x+6
c= 2
D: -3x+6+4x
x+6
D= 5
E-2x+9+5x+6
3x+15
E= 3
hopes this helps and im sorry for the mess i had to write a lot please mark brainliest
find the coordinates of the centroid of the triangle with the given vertices s(2,5) t(6,5) r(10,0)
Answer:
(6,[tex]\frac{10}{3}[/tex])
Step-by-step explanation:
[tex]\frac{2+6+10}{3}[/tex], [tex]\frac{5+5+0}{3}[/tex]
(6, [tex]\frac{10}{3}[/tex]) o r(6, 3 [tex]\frac{1}{3}[/tex])
The centroid of the triangle with the given vertices s(2, 5) t(6, 5) r(10, 0) is,
⇒ (6, 10/3)
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
Three vertices of the triangle are,
⇒ s(2, 5) t(6, 5) r(10, 0)
Now, We can find;
The centroid of the triangle with the given vertices s(2, 5) t(6, 5) r(10, 0) is,
⇒ (2 + 6 + 10) / 3, (5 + 5 + 0) / 3
⇒ (6, 10/3)
Thus, The centroid of the triangle = (6, 10/3)
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What is the first step to solving the equation -2(3x + 8) - 2 = 10 ?
Combine like terms.
Distribute the -2.
Add 3x + 8.
None of these choices are correct.
Simplify: -3x + 6-3x-24 + 2y
-6x + 2y - 18
2y - 18
6x + 2y - 30
None of these choices are correct.
Solve: 5x = 13
8
18
13
51
65
Solve: 6r-17r=-66
6
-6
-11
11
Solve: P = 2/+ 2w for w
P-21
4/w
P-4/w
None of these choices are correct.
Solve: 4(9y-5) = 10(3y +17) - 40
20
25
-10
10
Chicago's high temperature for a given month is 88 degrees Fahrenheit and the low temperature is 65 degrees Fahrenheit. Which inequality represents the model?
3x+5<2x-8 is:
x2 65 or x ≤ 88.
65 ≤ x ≤ 88.
88 ≤ x ≤ 65.
None of these choices are correct.
V= /wh when solved for his:
all values more than -13.
all values less than -13.
all values less than 3.
all values less than -3.
h=
V
lw
h=V-lw
h = V + lw
h = Vlw
Answer:
x = [tex]\frac{-14}{3}[/tex]
Step-by-step explanation:
-2(3x + 8) -2 = 10 Distribute the -2
-6x - 16 -2 = 10 Combine like terms
-6x - 18 = 10 Add 18 to both sides
-6x = 28 Divide both sides by -6
x = [tex]\frac{-28}{6}[/tex] = [tex]\frac{-14}{3}[/tex]
a salesperson receives a weekly salary of 600 , plus a 2.5% commission on sales. her total salary last week was 4720 . what were her sales that week?
With a total pay last week of $4720 and a 2.5% commission on sales, she made 275 in sales.
What is percent?In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.
Here,
The money earned by sales=2.5%*600
=$15
Let the total sales be x,
600+15x=4720
15x=4720-600
15x=4120
x=274.67
x=275 sales
Her last week sales was 275 as her total salary last week was $4720 and she receives 2.5% commission on sales.
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Is 43 square root plus 5 rational or irrational?
Answer:
square root of 43 is irrational and thus square root of 43 + 5 is also irrational.
Step-by-step explanation:
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a boy throws a ball straight up. how fast must he have thrown it if he catches the ball in the same spot 3.5 seconds later?
The boy should throw the ball at a speed of 17.15 m/s.
Newton’s first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. This tendency to resist changes in a state of motion is inertia. If all the external forces cancel each other out, then there is no net force acting on the object. If there is no net force acting on the object, then the object will maintain a constant velocity. His second law defines a force to be equal to change in momentum (mass times velocity) per change in time. Momentum is defined to be the mass m of an object times its velocity V.
From Newton's equations of motion,
v = u + at
Here, v = 0 m/s
a = g = -9.8 m/s²
t = 3.5/2 = 1.75 s
Put these values in the above equation:
u = v - at
u = 0 - (-9.8)(1.75)
∴ u = 17.15 m/s
Thus, the boy should throw the ball at a speed of 17.15 m/s.
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A circular wheel makes 42 complete turns each minute.
How many degrees does it turn through in one second?
Answer:
252
Step-by-step explanation:
in each minute, the wheel makes 42 turns. That means it turns 42×360=15120 degrees in one minute (60 seconds). We want to find how many degrees it will turn in one second, not one minute, so we will divide the total degrees by 60.
15120÷60=252
So our answer is 252.
is 4+x=y proportional?
Answer:
yes
Step-by-step explanation:
Solve the following system of equations using an inverse matrix. You must also indicate the inverse matrix, A^−1, that was used to solve the system. You may optionally write the inverse matrix with a scalar coefficient.
x−6y=−1
−2x+9y=5
The solution to the system of equations is x = −7 and y = −1.
Step-by-step explanation:
To solve the given system of equations using an inverse matrix, we can represent the system in matrix form, Ax=B, then find the inverse of matrix A to solve for 'x'.
Given matrix:
[tex]\left\{\begin{array}{ccc}x-6y=-1\\-2x+9y=5\end{array}\right[/tex]
[tex]\hrulefill[/tex]
Step 1: Represent the System of Equations in Matrix Form[tex]\hrulefill[/tex]First, we rewrite the system of equations in matrix for, Ax=B:
[tex]A = \left[\begin{array}{cc}1&-6\\-2&9\\\end{array}\right], \ x = \left[\begin{array}{cc}x\\y\\\end{array}\right], \ B = \left[\begin{array}{cc}-1\\5\\\end{array}\right][/tex]
So, Ax=B can be written as:
[tex]\Longrightarrow \left[\begin{array}{cc}1&-6\\-2&9\\\end{array}\right] \left[\begin{array}{cc}x\\y\\\end{array}\right] = \left[\begin{array}{cc}-1\\5\\\end{array}\right][/tex]
[tex]\hrulefill[/tex]
Step 2: Find the Inverse of Matrix A[tex]\hrulefill[/tex][tex]\boxed{\left\begin{array}{ccc}\text{The inverse of a 2x2 matrix,} \ \left(\begin{array}{ccc}a&b\\c&d\end{array}\right), \ \text{is given by:}\\\\\\A^{-1}= \dfrac{1}{ad-bc}\left(\begin{array}{ccc}d&-b\\-c&a\end{array}\right)\end{array}\right}[/tex]
Here,
[tex]\Longrightarrow A = \left[\begin{array}{cc}1&-6\\-2&9\\\end{array}\right][/tex]
The determinant ∣A∣ is:
[tex]\Longrightarrow |A|=(1)(9)-(-6)(-2)=9-12\\\\\\\\\therefore |A|=-3[/tex]
Since the determinant is not zero, A has an inverse, which can be calculated as:
[tex]\Longrightarrow A^{-1}= \dfrac{1}{-3}\left(\begin{array}{ccc}9&6\\2&1\end{array}\right)\\\\\\\\\therefore A^{-1}=\left(\begin{array}{ccc}-3&-2\\-2/3&-1/3\end{array}\right)[/tex]
[tex]\hrulefill[/tex]
Step 3: Solve for 'x'[tex]\hrulefill[/tex]We can solve for 'x' using x=A⁻¹B:
[tex]\Longrightarrow x = \left(\begin{array}{ccc}-3&-2\\-2/3&-1/3\end{array}\right)\left(\begin{array}{cc}-1\\5\\\end{array}\right)[/tex]
Upon multiplication, we get:
[tex]\Longrightarrow x = \left(\begin{array}{cc}(-3)(-1)+(-2)(5)\\(-2/3)(-1)+(-1/3)(5)\\\end{array}\right)\\\\\\\\\Longrightarrow x = \left(\begin{array}{cc}3-10\\2/3-5/3\\\end{array}\right)\\\\\\\\\Longrightarrow x = \left(\begin{array}{cc}-7\\-3/3\\\end{array}\right)\\\\\\\\\therefore \boxed{\boxed{x=\left(\begin{array}{cc}-7\\-1\\\end{array}\right)}}[/tex]
Thus, the solution to the system of equations is x = −7 and y = −1.
Which equation represents a linear function that is proportional? Answer A y=13x B y=x2 C y=x−2 D y=2x+11
Answer:
Step-by-step explanation:
No it is not
y = 13x ,y = x - 2 and y = 2x + 11 represents a straight line which is proportional to x i.e. a linear function .
Define proportionality of the equation?The proportional relation equation is y = kx .
The letters y and x are the variables, which can change, and the letter k is the constant of proportionality.
According to the question ,
Given: y = 13x
since y ∝ x,
Therefore the equation is said to be proportional .
Given: y = x²
Since the term y is proportional to the square of square ,so we can't say say that the equation is proportional .
Given: y = x - 2
Since ,y is in the form of the equation y = mx + c and y is proportional to x as well ,therefore we say that x is proportional to x .
Given : y = 2x + 11
Since y is in the form of y = mx + c and y is proportional to x
As the given expression represents a straight line , so its proportional to x .
Hence, all the given expressions are proportional to x except the second option which is proportional to square of x and is not forming a linear equation that is a straight line.
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Suppose a binomial trial has a probability of success of 0.2, and 75 trials are
performed. What is the standard deviation of the possible outcomes? Round
your answer to two decimal places.
A. 3.97
B. 4.24
C. 3.46
D. 4.33
The standard deviation of a binomial distribution is C. 3.46
What is standard deviation?Standard deviation is the measure of spread of a set of data.
Since a binomial trial has a probability of success of 0.2, and 75 trials are performed. To find the standard deviation, we use the formula for standard deviation of a binomial distribution.
What is the standard deviation of a binomial distribution?The standard deviation of a binomial distribution is given by σ = √(npq) where
n = number of possible outcomes, p = probability of successes and q = probability of failures = 1 - pGiven that for our binomial trial
n = 75p = 0.2 andq = 1 - p = 1 - 0.2 = 0.8So, substituting the values of the variables into the equation, we have that
σ = √(npq)
σ = √(75 × 0.2 × 0.8)
σ = √(75 × 0.16)
σ = √12
σ = 3.464
σ ≅ 3.46
So, the standard deviation is C. 3.46
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Which ordered pairs is in the solution set of y>1/3 x+4
The ordered pair for the given solution set should be (-1, 6) when the graph solution set for the given inequality function is involved.
What is inequality function?
Since an inequality is merely a particular kind of relation, we can graph it just like we would any other relation. When dealing with inequalities, the trick is to shade large portions of the graph rather than using lines to connect the dots. But you could use some cover.
The given inequality function be like
y > 1 ÷ 3x + 4
The ordered pair refer to the solution set that provided by plotting the graph of the inequality, that expressed the inequality where an equation, plotting the graph along with a solid line, and shading the sides should be above the line of the graph to show the greater than or equal to sign.
Hence, the ordered pair for the given solution set should be (-1,6).
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Matthew Westhoven deposited $925 in a new regular savings account that earns 5.5% interest compounded semiannually for 1 year. What is the compound interest?
Matthew Westhoven deposited $925 in a new regular savings account that earns 5.5% interest compounded semiannually for 1 year. 51.09 is the compound interest.
What is compound interest?The interest you earn on interest is known as compound interest. Simple math may be used to demonstrate this: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year. You will wind up with $110.25 at the conclusion of the second year.
Given that,
principal amount (P) = $925
number of times interest applied per time period (n) = semiannually = 6
number of time periods (t) = 1 year
Thus, formula becomes:
[tex]I = P (1 + r/n)^{nt} - P[/tex]
or, [tex]I = 925 (1 + 5.5/6*100)^{1*6} - 925[/tex]
or, [tex]I = 925 (1.009)^6 -925[/tex]
or, [tex]I = 925 *(1.055) -925[/tex]
or, [tex]I = 976.09 -925[/tex]
or, [tex]I = 51.09[/tex]
Thus, the compound interest becomes 51.09
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One of the legs of a right triangle measures 10 cm and the other leg measures 14 cm.
Find the measure of the hypotenuse
If (x₁9) is a solution to the
equations -4x=y-21
What is x
The value of x = 3 for y = 9 is a solution of the linear equation -4x = y - 21.
What is a Linear Equation ?If an equation is written in the form ax + 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 equalises the two sides of the equation.
A specific point on the graph represents the solution of a linear equation in two variables, ax+by = c, where the total of these two values will equal c when the x-coordinate is multiplied by a and the y-coordinate by b.
Basically, there are infinitely many solutions to a linear equation with two variables.
The solution of the equation (x,9).
For the equation -4x = y -21
here, y = 9
-4x = 9 - 21
⇒ -4x = -12
⇒ x = 3.
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If you chose the letters D and H for 20 turns, how many times are you most likely to win?
A. 1
B. 2
C. 3
D. 4
E. 5
edmentum
If you chose the letters D and H for 20 turns, the number of times you are most likely to win is; Option C: 3
What are the number of ways of winning?We are given the probability of winning for each letter as;
A = 5%
B = 10%
C = 15%
D = 5%
E = 5%
F = 25%
G = 10%
H = 10%
I = 10%
J = 5%
Now, we want to find the number of times you can win If you chose the letters D and H for 20 turns.
Thus;
Number of times you can win if you chose Letter D = 5% * 20 = 1 time
Number of times you can win if you chose Letter H = 10% * 20 = 2 times
Thus;
Total number of ways of winning = 1 + 2 = 3 times
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Karen i putting together a mall bookhelf to go in the pace between her two bedroom window. The width of the bookhelf i 2. 5 feet. The pace i 3. 25 feet wide. How much pace will be left on each ide of the bookhelf if he place it directly in the middle?
After fitting a bookcase with a height of 2.5 feet into a space with a width of 3.25 feet, 0.375 feet will be left on each side.
What is arithmetic operation?A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
Here,
Width of bookshelf=2.5 feet
Space to keep the bookshelf=3.25 feet
Total difference for the remaining space near bookshelf,
=3.25-2.5
=0.75 feet
Space remaining on either side of bookshelf,
=0.75/2
=0.375 feet
A space of 0.375 feet will be remaining on each side after keeping a bookshelf of size 2.5 feet in a space of 3.25 feet.
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What is the slope of this line?
Enter your answer as a whole number or a fraction in simplest form in the box.
Answer:
-1
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}[/tex]
Define two points on the line:
Let (x₁, y₁) = (-2, 0)Let (x₂, y₂) = (0, -2)Substitute the defined points into the slope formula:
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-2-0}{0-(-2)}=\dfrac{-2}{2}=-1[/tex]
Therefore, the slope of the line is -1.
parallelogram fghj was dilated and translated to form similar parallelogram f'g'h'j'. what is the scale factor of the dilation? 4 8
The scale factor of the dilation is s = 4 units .
Given :
parallelogram fghj was dilated and translated to form similar parallelogram f'g'h'j'.
To find scale factor between figures, find two corresponding sides and write the ratio of the two sides.
The value of y is same through the distance of F to G.
So, FG = change in x coordinates
FG = -2 - ( -4 )
= -2 + 4
= 2
F'G' = 3 - ( - 5 )
= 3 + 5
= 8
Let s be the scale factor
s = F'G' / FG
= 8 / 2
= 4
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4) A line has a slope of 3 and passes through the point (1, 1). What is its equation in
slope-intercept form?
Answer:
Step-by-step explanation:
You want it to be in y=mx+b form.
B= y intercept
mx= slope (3x)
Y=3x+-2
A 29.2-ounce bottle costs $5.37. what is the unit price?
would 3x+2>-4 be a
open circle —->
open circle <——
closed circle—->
closed circle<—-
the discriminant of a quadratic function is 64 and its vertex is in quadrant III. Identify and explain 3 things you know about the function and /or its graph
Help PLEASE this due tommorow
Answer:
Step-by-step explanation:
If the discriminant of a quadratic function is 64 and its vertex is in quadrant III, here are three things you can know about the function and/or its graph:
The function has two distinct real roots. The discriminant of a quadratic function is the value under the square root in the quadratic formula:
x = (-b +/- √(b^2 - 4ac)) / 2a
If the discriminant is positive, it means that there are two real roots (values of x that make the equation equal to zero). If the discriminant is negative, it means that there are no real roots (the equation has no solutions). If the discriminant is zero, it means that there is only one real root (the equation has one solution). Therefore, if the discriminant is 64, it means that the function has two distinct real roots.
The graph of the function is a parabola that opens downward. The direction in which a parabola opens (upward or downward) is determined by the coefficient of the x^2 term (a). If a is positive, the parabola opens upward. If a is negative, the parabola opens downward. In this case, the vertex of the parabola is in quadrant III.
Please helpp
(That’s a i not a L)
Solve for A in the terms I and P
I = A - P
A =
Answer:
A= I + P
for real? And why is high-school question
The value of x when g(x) = 3
After solving the given equation at g(x) = 3 the value obtained is 3.
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the information given in the question,
The given equation is,
g(x) = -2x + 9
Then,
g(3) = -2(3) + 9
= -6 + 9
g(3) = 3
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Your question seems incomplete, the complete question may be:
If g(x) = -2x + 9, what is the value of x
when g(x) = 3?
What is the order from least to greatest of the following: 0.8, −0.1, 1.1, and −1.5?
Answer:
I think -1.5 -0.1 0.8 1.1
Answer:
-1.5 || -0.1 || 0.8 || 1.1
Explanation:
Since it is from least to greatest, let's compare the 2 negative numbers -1.5 and -0.1.
-1.5 has a 1 in its first place while -0.1 has a 0. This means that -1.5 is smaller because the further a number is on the negative number line the smaller it is.
So, -1.5 is the smallest, then -0.1.
-1.5 || -0.1
Now we compare the 2 positive numbers 0.8 and 1.1.
0.8 has a 0 in its first place and 1.1 has a 1 in its first place. Because the numbers are positive, the number with the biggest digit in in front of the decimal is greater.
So, in this case 1.1 is greater than 0.8.
0.8 || 1.1
In order it is:
-1.5 || -0.1 || 0.8 || 1.1
and his friends decided to have a water fight on a hot summer day. They filled a bunch of water balloons and started the fight at 1:00 P.M. The water balloons lasted for 1 hour. When all the water balloons were gone, they sprayed water with hoses for 30 minutes, until Rudy's dad showed up with ice cream. What time was it when the water fight ended?
Answer:
the water fight ended at 2:30pm
Step-by-step explanation:
the balloons lasted an hour bringing it to 2pm then they used the hoses for 30 min bringing it to 2:30pm
the sum of the ages of a father and his son is 38 years. if the father is 22 years older than his son , find their present ages
If the father is 22 years older than his son, and the sum of their ages is 38 years, we can set up the following equations to represent this information:
Copy code
father + son = 38
father = son + 22
We can solve for the father's and son's ages by substituting the second equation into the first equation:
Copy code
(son + 22) + son = 38
2 * son + 22 = 38
2 * son = 16
son = 8
Therefore, the son's age is 8 years, and the father's age is 8 + 22 = <<8+22=30>>30 years.
Answer:
16
Step-by-step explanation:
son=38-22
son=16
hope am correct
Help me please I don’t really understand how to do these types of problems
to get the slope of any straight line, we simply need two points off of it, let's use those in the picture above.
[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-5)}}} \implies \cfrac{-3 +4}{1 +5} \implies {\Large \begin{array}{llll} \cfrac{ 1 }{ 6 } \end{array}}[/tex]
What is the greatest common factor of 15n^{5}15n 5 15, n, start superscript, 5, end superscript, 30n^{3}30n 3 30, n, cubed, and 45n^{2}45n 2 45, n, squared?.
The greatest common factor of 15n^5, 30n^3, and 45n^2 is 15n^2
In this question we need to find the greatest common factor of 15n^5, 30n^3, and 45n^2.
we know that the greatest common factor of given numbers is nothing but the highest number that divides given numbers.
If we look at the variable part of given monomials, then the highest power of n that divide given monomials is n^2.
And the greatest common factor os (15, 30, 45) is 15
So, we get a monomial 15n^2
Therefore, the greatest common factor is 15n^2
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if AB= 7.2 m, what is C?
Based on the triangle midsegment theorem, the length of CZ is calculated as: 7.2 m.
How to Apply the Triangle Midsegment Theorem?The triangle midsegment theorem states that when two sides of a triangle are joined together by a line segment at their midpoint, the line segment is called the midsegment, and it is parallel to the third side whose measure is twice its length.
This implies that, AB is a midsegment in the image shown for triangle XYZ. It is parallel to YZ.
Therefore:
AB = 1/2(the length of YZ)
Substitute the value of AB into the equation:
7.2 = 1/2(YZ)
2(7.2) = YZ
YZ = 14.4 m.
The length of CZ = 1/2(the length of YZ) [this is because YC = CZ]
CZ = 1/2(14.4)
CZ = 7.2 m.
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