Answer:
1.75x + 1.25y >= 280
Step-by-step explanation:
1.75x + 1.25y >= 280
The monthly cost (in dollars) of water use is a linear function of the amount of water used (in hundreds of cubic feet, hcf). the cost for using 18 hcf of water is $39.67, and the cost for using 37 hcf is $69.12. what is the cost for using 21 hcf of water?
The monthly cost of water use can be represented using a linear equation y = 1.55 x + 11.77 and the cost of using 21 hcf is $44.32.
A linear equation can be represented by a line equation:
y = mx + c
Where:
m = slope
c = constant
From the problem, we have 2 equations:
39.67 = 18 m +c
69.12 = 37 m + c _
29.45 = 19 m
m = 1.55
Substitute m = 1.55
39.67 = 18 . (1.55) + c
c = 11.77
Hence, the linear equation is:
y = 1.55 x + 11.77
Substitute x = 21
y = 1.55 . (21) + 11.77 = 44.32
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Write a conjecture that best describes the pattern in each sequence . Then use your conjecture to find the n next item in the sequence . a 1,4,9,16,... b PERCENT HUMIDITY : 100\% , 93 % , 86\%
patternpatternGreat!
The patteren is 1, 4, 9, 16,...
All these numbers are square numbers, which means
1 * 1 = 1
2 * 2 = 4
3 * 3 = 9
4 * 4 = 16
That means
1st term = 1^2
2nd term = 2^2
3rd term = 3^2
4th term = 4^2
so
nth term = n^2
The conjecture is
[tex]a_n=n^2[/tex]The pattern is 100%, 93%, 86%, ...........
Since 93% - 100% = -7%
Since 86% - 93% = -7%
Then this pattern is decreases by 7%
So it is an arithmetic sequence
Its rule is:
[tex]a_n=a+(n-1)d[/tex]Where a is the first term
d is the constant difference
n is the position of the number
Since a = 100%
Since d = -7%
Let us substitute these values in the rule
[tex]a_n=100+(n-1)(-7)[/tex]Simplify it
an = 100% + (n)(-7%) + (-1)(-7%)
an = 100% + (-7n%) + (7%)
Add the like terms
an = (100% + 7%) - 7n%
an = 107% - 7n%
Let us check the rule
What is the 3rd term
n = 3
a3 = 107% - 7(3)%
a3 = 107% - 21%
a3 = 86% which is true
what are the measures of <1 and <2 if they are in a 4:11 ratio
If the angles are complementary, we have that:
The measure of angle 1 is of 24°.
The measure of angle 2 is of 66°.
How to find the measures of ∠ 1 and ∠ 2 if they are in a 4:11 ratio?If two angles exists complementary, the sum of their measures exists 90°.
In this problem, we suppose that angles 1 and 2 exists complementary, therefore, m1 + m2 = 90
The measures of angle 1 and angle 2 are in a 4: 11 ratio, thus:
[tex]$m_1=\frac{4}{4+11}=\frac{4}{15}\left(m_1+m_2\right)$[/tex]
[tex]$m_2=\frac{11}{4+11}=\frac{11}{15}\left(m_1+m_2\right)$\\[/tex]
Considering m1 + m2 = 90
[tex]$m_1=\frac{4}{15}\left(m_1+m_2\right)=\frac{4}{15} \times 90=4 \times 6=24$[/tex]
[tex]$m_2=\frac{11}{15}\left(m_1+m_2\right)=\frac{11}{15} \times 90=11 \times 6=66$[/tex]
The measure of angle 1 is of 24º.
The measure of angle 2 is of 66º.
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If 4 < a < 5 and 5 < b < 8, which of the following best describes a-b?
a) between -4 and -8
b) between -4 and 0
c) between 2 and 3
d) between -1 and 0
I don't know how to do this, so pls explain how to do it :)
When 4 < a < 5 and 5 < b < 8, the option that best describes a-b is B) between -4 and 0. This illustrates the equation.
How to calculate the value?From the information illustrated, 4 < a < 5. In this case, a can be 4.5. This implies that a is greater than 4.
Also, 5 < b < 8. In this case, b can be 7.5. Therefore, the difference between the values can be:
a - b
= 4.5 - 7.5
= -3
This number is between -4 and 0. In conclusion, the correct option is B.
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If given inequalities are 4 < a < 5 and 5 < b < 8, then a-b lies between -4 and 0. So Option B is correct.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
Let us consider a inequality
4 < a < 5
By this inequality we have
a<5
a>4
So value of a lies between 4 and 5 which is a= 4.5.
5<b<8
b<8 and b>5
So values of b will be 6, 6.5 , 7 and 7.5.
Let us consider value 6.5 as b.
a-b
=4.5-6.5
=-2
This number a-b is between -4 and 0.
Hence if 4 < a < 5 and 5 < b < 8, then a-b lies between -4 and 0.
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Find the sine, cosine, and tangent for the angle whose measure is pi/6...pi divided by 6.
Calculating the sine, cosine and tangent of the angle pi/6 (that is, 30°), we have that:
[tex]\begin{gathered} \sin (\frac{\pi}{6})=\frac{1}{2}_{} \\ \cos (\frac{\pi}{6})=\frac{\sqrt[]{3}}{2}_{} \\ \tan (\frac{\pi}{6})=\frac{\sin(\frac{\pi}{6})}{\cos(\frac{\pi}{6})}=\frac{\frac{1}{2}}{\frac{\sqrt[]{3}}{2}}=\frac{1}{\sqrt[]{3}}=\frac{\sqrt[]{3}}{3} \end{gathered}[/tex]What are the vertex and range of y = |x 2| − 3? (−2, −3); −[infinity] < y < [infinity] (−2, −3); −3 ≤ y < [infinity] (0, −1); −[infinity] < y < [infinity] (0, −1); −3 ≤ y < [infinity]
(x,y) = (1,14).
A parabola's vertex is the location where its symmetry line and parabola intersect. The range of values that we are permitted to enter into our function is known as the domain of a function.
What is the definition of vertex form?A different way to express the equation of a parabola is in its vertex form. A quadratic equation is typically represented as an x 2 + b x + c, which, when graphed, results in a parabola.Locate a parabola's vertex,Finding a parabola's vertex Standard FormComparing the parabola's equation to the formula y = ax2 + bx + c in standard form is the first step.Step 2: Apply the formula h = -b/2a to find the vertex's x-coordinate.Step 3: Substitute x = h in the calculation ax2+ bx + c to obtain the vertex's y-coordinate (k). The range of values that we are permitted to enter into our function is known as the domain of a function.To learn more about Parabola Vertex refer to:
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what is the approximate solution to this equation? 19+2 In x=25
The value of x from the given linear equation is equivalent to 1.1
Solving linear equationsLinear equations are equation that has a leading degree of 1. An example of a linear equation is y = mx + b
Given the equation
19+2 In x=25
2lnx = 25 - 19
Simplify to have:
2lnx = 6
lnx = 6/2
lnx = 3
Take the exponent of both sides
e^lnx = ln3
x = ln3
Hence the approximate solution to the given linear equation is 1.1.
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Water flows through a pipe at a rate of 7 liters every 9.5 hours. Express this rate of
flow in pints per week. Round your answer to the nearest whole number.
The rate of water flow per week is 124 liters.
What is the of water flow?
Running water naturally travels along the slope in a direction determined by gravity. This is referred to as a water flow.
Given is, the water flows through a pipe at a rate of 7 liters every 9.5 hours.
So,
water flows per hour = [tex]\frac{7}{9.5}[/tex]
Hours in a week = 7 x 24 = 168 hours
Water flow per week = hours in a week x water flow per hour.
[tex]= 168 x \frac{7}{9.5} \\= 123.7894[/tex]
Water flow per week = 124 liters.
Therefore, the water flow per week is 124 liters.
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The store at which Andy usually shops is having a sale. Roast beef cost four dollars a pound and shrimp cost $10 a pound. Write an equation to describe different possible combinations of roast beef and shrimp that he can buy for $96.
The equation to describe different possible combinations of roast beef and shrimp that he can buy for $96 is 4b + 10s = 96.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let roast beef = b
Let shrimp = s
Total cost = 96
Therefore the equation will be:
(4 × b) + (10 × s) = 96
4b + 10s = 96
This illustrates the equation.
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6. a) The mass of eight apples is 1 200 g. What is the average mass of one apple in kilograms? b) A5 kg bag of apples costs R65. What is the cost of 500 grams of apples? Approximately how many apples will have a mass of 1 kilogram?
a. The average mass of one apple in kilograms is 150g.
b. The cost of 500 grams of apples is R6.5
How to calculate the values?A. When the mass of eight apples is 1 200g, the average mass of one apple in kilograms will be:
= Total mass / Number of Apple
= 1200g / 8
= 150g
B. A 5 kg bag of apples costs R65. The cost per kg will be:
= Amount / Number of g
= R65 / 5000
= R0.013
The cost for 500 grams will be:
= 500 × R0.013
= R6.50
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Write the equation in standard form for the hyperbola with vertices (-2,0) and (2,0) and a conjugate axis of length 14
Solution
- The equation of a hyperbola is given s:
[tex]\begin{gathered} \frac{(x-h)^2}{a}-\frac{(y-k)^2}{b}=1 \\ \\ where, \\ coordinates\text{ of the vertices}=(h\pm a,k) \\ Length\text{ of conjugate axis}=2b \end{gathered}[/tex]- Thus, we can find that:
[tex]\begin{gathered} (\pm2,0)=(h\pm a,k) \\ \\ k=0 \\ \therefore h+a=2 \\ h-a=-2 \\ \text{ Subtract both equations, we have:} \\ 2a=4 \\ a=\frac{4}{2}=2 \\ \\ h+a=2 \\ h+2=2 \\ h=2-2=0 \\ \\ \text{ Thus, we have that the center of the hyperbola is: }(h,k)=(0,0) \\ \\ 2b=14 \\ \text{ Divide both sides by 2} \\ b=\frac{14}{2}=7 \end{gathered}[/tex]Final Answer
The equation of the parabola is:
[tex]\frac{x^2}{2^2}-\frac{y^2}{7^2}=1[/tex]10. Eleanor spent 40% of her money on a $130 outfit. How much money
did she have left?
Answer:
$195
Step-by-step explanation:
40% represents £130
40% : $130
100% : total
To find total:
($130 / 40) x 100 = $325 is the total
If $130 spent:
$325 - $130 = $195 is the amount left
Is the image an example of an angle?
B
65°
A
C
O No; AB and BC intersect in more than one point.
O Yes; AB and BC do not form a line and share an endpoint.
O No; AB and BC form a line.
O Yes; AB and BC are perpendicular to each other.
Yes, the image an example of an angle AB and BC do not form a line and share an endpoint.
What is an angle ?An angle is formed when two lines are extending from a point .
Using this Knowledge it can be deduced from the figure that line BA and BC are extending from point B. Hence forming an angle of 65 degrees
Analyzing the options
option A is wrong as line AB and BC intersected only on one point. formation of a line do not typically say if an angle is formed or not hence making option c incorrect. There is no perpendicular line formed in th figure .
This leaves option B as the correct option
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Solve the following equation for y, simplifying all fractions: 6x + 10y = - 80 a) y = 3 X - 8 5 3 X 8 b) y alw c) y -x + 8 w л | о л | d) y = x – 8
Solving a linear equation with 2 variables
First isolate y term
10 y = -6x - 80
Now divide by 10
y = (-6/10)x -(80/10)
y = (-3/5)x - 8
assume that movement of a molecule is limited. it can move to the opposite side of the container or stay where it is. if the movement is random, what is the probability (0-100%) that the molecule will move to the opposite side?
The Probability that that the molecule will move to the opposite side is 50% .
In the question ,
it is given that
there a molecule is free to move to the opposite side of the container , or stay where where it is ,
As per the given information
the molecule can move to opposite side or stay where it is ,
and the movement of the molecule is random
as the container had two sides ( shown in figure given below )
the probability that the molecule moves to the opposite side is 1/2 ,
in percent it can be written as 50% .
the correct option is (c) .
Therefore , The Probability that that the molecule will move to the opposite side is 50% .
The given question is incomplete , the complete question is
Assume that movement of a molecule is limited. it can move to the opposite side of the container or stay where it is. if the movement is random, what is the probability (0-100%) that the molecule will move to the opposite side?
(a) 0%
(b) 25%
(c) 50%
(d) 100%
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Two freight trains are delivering cargo. One freight train is delivering coal, and the other freight train is delivering grain. Their respective distances traveled after x hours is represented in the table and graph below.
Solution
- In order to find which of the trains is moving faster, we should calculate the average speeds of both trains and compare them.
- The y-values of both trains are the Distance in Miles and the x-axis is the time in hours.
- Thus, the best way to calculate their average speeds is to find the slope of both datasets.
- The formula for calculating the slope is given below:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{where,} \\ (x_1,y_1)\text{ and (}x_2,y_2)\text{ are coordinates chosen} \end{gathered}[/tex]- Thus, with the above information, we can proceed to solve the question
Speed of Coal Freight Train:
[tex]\begin{gathered} \text{ Choosing } \\ (x_1,y_1)=(1,49) \\ (x_2,y_2)=(2,98) \\ \\ m_C=\frac{y_2-y_1}{x_2-x_1}=\frac{98-49}{2-1} \\ \\ \therefore m_C=49\text{miles per hour} \end{gathered}[/tex]Speed of Grain Freight Train:
[tex]\begin{gathered} \text{Reading off the graph that passes through the origin, we choose:} \\ (0,0)\text{ and }(1,45) \\ \\ \therefore m_G=\frac{45-0}{1-0}=45 \\ \\ m_G=45\text{miles per hour} \end{gathered}[/tex]- From the above calculations, we can easily observe that the Speed of the Coal Freight Train is greater than the speed of the Grain Freight Train
Final Answer
"The Coal Freight Train is traveling at a faster speed" (OPTION 2)
How can I complete the square of this equation Y=2x(x+5)
Answer: [tex]y=2 \left(x+\frac{5}{2} \right)^2 -\frac{25}{2}[/tex]
Step-by-step explanation:
[tex]y=2x^2 +10x\\\\y=2(x^2 + 5x)\\\\y=2 \left(x^2 +5x +\frac{25}{4} \right)-\frac{25}{2}\\\\y=2 \left(x+\frac{5}{2} \right)^2 -\frac{25}{2}[/tex]
Given the figure below, determine the angle that is an alternate interior angle with respect to. 1. To answer this question, click on the appropriate angle.
In this case, the alternate interior angles are for example angles 6 and 3 because they are on the inner side of each of the lines (m and l) but on opposite sides of the transversal (t).
m∠6 = m∠3
or
m∠4 = m∠5
Which polynomial correctly combines the like terms and expresses the given polynomial in standard form?
9xy³-4y-10x2y2 + x³y + 3x² + 2x²y²-9y4
Answer:
I believe the answer is c
Step-by-step explanation:
You see, in a standard form the term with greater stays at the very right.
(7, 8) and (-1, 0)find the distance between the two points?
The distance (d) between two points is computed as follows:
[tex]d\text{ = }\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}^{}[/tex]where (x1, y1) and (x2, y2) are the points of interest. In this case, the points are (7, 8) and (-1, 0). Replacing into the equation:
[tex]d\text{ = }\sqrt{(-1-7)^2+(0-8)^2\text{ }}[/tex][tex]d\text{ = }\sqrt{(-8)^2+(-8)^2}=\sqrt{128}[/tex]Select all the unique triangles that can be drawn to only have angle measures 40° and 100° and side length 3.
ΔABC; AB = 3, ∠CBA = 100°, ∠CAB = 40°
ΔABC; AB = 3, ∠ABC = 100°, ∠BCA = 40°
Given,
Select all the unique triangles that can be drawn to only have angle measures 40° and 100° and side length 3.
What are unique triangles?
Unique triangles are triangles that are different based on their configuration, which derives from the positioning of the given parameters to correspond with different congruency requirement.
The conditions for the congruency of two triangles are;
SSS: The Side-Side-Side rule; two triangles are congruent if all three sides of one triangle are congruent to the three sides of the other triangle
SAS: The Side-Angle-Side rule; two triangles are congruent if two sides and the included angle of one are congruent to two sides and an included angle in the other triangle
ASA: The Angle-Side-Angle rule; two triangles are congruent if two angles and the included side of one triangle are congruent to two angles and an included side of the other triangle
SAA: The Side-Angle-Angle rule; Two triangles are congruent if two angles and an a non included side of one triangle are congruent to two angles and the non included side of the other triangle.
The configuration of the unique triangles can therefore, be ASA and SAA, which gives the triangles;
ΔABC; AB = 3, ∠CBA = 100°, ∠CAB = 40°
ΔABC; AB = 3, ∠ABC = 100°, ∠BCA = 40°
Please see attached drawings of the two unique triangles
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Fill in the blanks to demonstrate the Multiplicative Inverse Property.
9/7* =
4/3* =
5 1/3* =
The multiplicative inverse property of the questions that we have here are:
9/7* = 9/7 x 7/9 = 14/3 = 4/3 * 3/4 = 15 1/3 = 16/3 * 3/16 = 1What is the multiplicative inverse property?This is the term that is used in Mathematics to show that we are to multiply a fraction by the inverse of that fraction.
A good example of this would be the form that is written as:
1/a would have the inverse property written as a/1
such that 1/a *a/1 = 1
In the same way,
we have
9/7 * 7 / 9 = 1
4/3 * 3/4 = 1
5 1/3 = 16 / 3 * 3/ 16 = 1
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in the diagram measure angle ACB=61 find measure angle ACEMeasure of angle ACE=...°
From the figure, angle ACB anf angle BCD are complementary, that is,
∠ACB + ∠BCD = 90°
Replacing with data
61° + ∠BCD = 90°
∠BCD = 90° - 61°
∠BCD = 29°
From the picture, angle BCD and angle FCE are vertical angles, then they are congruent, which means that:
∠FCE = ∠BCD = 29°
Angle FCA is a right angle, that is, ∠FCA = 90°. Therefore:
∠FCE + ∠FCA = ∠ACE
29° + 90° = ∠ACE
119° = ∠ACE
Part A
Andy is scuba diving. he starts at sea level and then descends 10.5 feet in 2 1/2 minutes what was Andy’s average change in elevation in feet per minute?
Part B
If he continues at this rate, Andy will be … in relation to sea level
A. -20.25
B. -25.5
C. -27.3
D. 30.6
Marking brainliest for answereing both
a. The change in elevation in feet per minute is 4.2 per feet.
b. If he continues at this rate,then Andy will be -25.2 feet below sea level.
Given Andy starts scuba diving at sea level and then descends 10.5 feet in 2 1/2 minutes.
we need to determine Andy's average change in elevation in feet per minute =?
therefore rate of descent = total descent/total time
time = 2 1/2 minutes = 5/2 minutes.
= -10.5/5/2
= -4.2 feet per minute.
Part B.
If he continues at this rate,the relation to sea level after 6 minutes will be:
= -4.2 × 6
= -25.2
Hence we get the required answers.
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Your question is incomplete. Please find the missing content below.
Andy is scuba diving. He starts at sea level and then descends 10.5 feet in 2 1/2 minutes.
Part A How would you represent Andy's change in elevation? Express your answer as an integer. Enter your answer in the box. feet per minute.
Part B If he continues at this rate, where will Andy be in relation to sea level after 6 minutes? feet
A. -20.25
B. -25.5
C. -27.3
D. 30.6
Solve the multiple-angle equation. (Enter your answers as a comma-separated list. Use n as an arbitrary integer. Enter your response in radians.)2 cos 2x − 1 = 0
Given:
The function is:
[tex]2\cos2x-1=0[/tex]Find-:
The value of "x"
Explanation-:
The value of x is:
[tex]\begin{gathered} 2\cos2x-1=0 \\ \\ 2\cos2x=1 \\ \\ \cos2x=\frac{1}{2} \\ \end{gathered}[/tex]Solve for x is:
[tex]\begin{gathered} \cos2x=\frac{1}{2} \\ \\ 2x=\cos^{-1}(\frac{1}{2}) \\ \\ 2x=\frac{\pi}{3}+2\pi n\text{ and }2x=\frac{5\pi}{3}+2\pi n \end{gathered}[/tex]The value of "x" is:
[tex]\begin{gathered} 2x=\frac{\pi}{3}+2\pi n \\ \\ x=\frac{\pi}{2\times3}+\frac{2\pi n}{2} \\ \\ x=\frac{\pi}{6}+\pi n \end{gathered}[/tex]Another value of "x" is:
[tex]\begin{gathered} 2x=\frac{5\pi}{3}+2\pi n \\ \\ x=\frac{5\pi}{3\times2}+\frac{2\pi n}{2} \\ \\ x=\frac{5\pi}{6}+\pi n \end{gathered}[/tex]So, the answer is:
[tex]x=\frac{\pi}{6}+\pi n,\frac{5\pi}{6}+\pi n[/tex]Line g is dilated by a scale factor of 1/2 from the origin to create line g'. Where are points E' and F' located after dilation, and how are lines g and g' related? 4 3 g 1 E -5 -2 -1 0 -1 -2
C) The lines g and g' are parallel and E'(-2,0) and F'(0, 1)
1) Let's locate points E and F.
E (0,2) and F( -4,0)
Given that line was dilated by a scale factor k = 1/2 about the origin we can state the following
• The line segment g' is shorter, half of g.
,• Points E'(0,1) and F'(0,1)
3) Examining the answers we can state:
The lines g and g' are parallel and E'(-2,0) and F'(0, 1)
Sophie can type 129 words in 3 minutes. How many minutes will it take her to type 559 words?
EXPLANATION:
To solve the exercise we must make a rule of three.
The exercise is as follows:
[tex]\begin{gathered} 129\text{ }words\text{ }\rightarrow3\text{ minutes} \\ 559\text{ words}\rightarrow x \\ \frac{559\times3}{129}=13\text{ minutes} \\ \text{the answer is 13minutes} \end{gathered}[/tex]Find the value of x so that the function has the given value.
m(x)=4x+15 ; m(x)=7
I inserted a picture because it was too much to type but this is the 2nd part to my other question, Please answer.
Based on the quantity of the bag of sugar that Jaleel and Angela purchased, and their recipes for brownies, the amount of flour needed by each is:
Angela - 5 cups of flour Jaleel - 6 ²/₃ cups of flourHow much flour is needed?Jaleel and Angela purchased a 20-cup bag of sugar and divided it evenly which means that they each get 10 cups of sugar.
Jaleel's recipe shows that every 1.5 cups of sugar needs a cup of flour. If he had 10 cups of sugar therefore, the amount of flour needed would be:
= Number of cups of sugar / Cups of sugar per cup of flour
= 10 / 1.5
= 6 ²/₃ cups of flour
Angela's recipe is such that every cup of sugar needs 1/2 cups of flour. This means that with 10 cups of sugar, the amount of flour needed is:
= 10 x 1/2
= 5 cups of flour
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Triangle ABC is congruent to triangle XYZ. In AABC, AB = 12 cm and AC = 14 cm. In AXYZ, YZ = 10 cm and XZ = 14 ! cm. What is the perimeter of AABC? O 36 cm O 38 cm О 40 cm • 50 cm
The perimeter of the triangle ABC is equal to 36 centimeters. (Correct choice: A)
How to determine the perimeter of a triangle congruent to another triangle
Triangles are close figures with three sides and three internal angles. Two triangles are congruent when they share sides with same lengths and angle and side distributions, then AC ≅ XZ, BC ≅ YZ and AB ≅ XY. The perimeter is the sum of the lengths of the three sides of the figure, then:
p = 10 cm + 12 cm + 14 cm
p = 36 cm
The perimeter is equal to 36 centimeters.
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Two triangles are congruent if all of their sides are the same. Perimeter of triangle ABC is 36cm.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Two triangles are congruent if all of their sides are the same.
By data triangle ABC and triangle XYZ are congruent.
In triangle ABC, AB = 12 cm and AC = 14
In triangle XYZ, YZ = 10 cm and XZ = 14
As ABC and XYZ are congruent then the other side of triangle ABC has 10cm.
Perimeter of triangle=Sum of three sides
=10+12+14
=36
Hence perimeter of triangle ABC is 36cm.
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