a. Find the length of the midsegment of an equilateral triangle with side lengths of 12.5 cm.
b. Given that UT is the perpendicular bisector of line segment AB, where T is on AB, find the length of AT given AT = 3x + 6 and TB = 42 - x.
c. Given angle EFG has angle bisector FH, where EF = GF, find the value of y if EH = 5y + 10 and HG = 28 - y.
Answers
Answer:
a.the length of midsegment of an equilateral triangle with side lengths of 12.5 cm.=12.5/2=6.25cm
b.
sinceUT is the perpendicular bisector of line segment AB, where T is on AB, find the length of AT given AT = 3x + 6 and TB = 42 - x.
than AT=BT
3x+6=42-x
3x+x=42-6
x=36/4=9
AT=3×9+6=27+6=33
c.
since angle EFG has angle bisector FH, where EF = GF, find the value of y if EH = 5y + 10 and HG = 28 - y.
EH=GH
5y+10=28-y
6y=28-10
y=18/6=3
a. The length of the midsegment of an equilateral triangle is 6.25 cm
b. The length of AT is 33 units.
c. The value of y is 3.
What is an equilateral triangle?
"It is a triangle whose all sides are equal in length and all angles measure 60° "
What is perpendicular bisector?"It is a line that intersects another line perpendicularly and divides it into wo equal parts."
What is angle bisector?"It is a line that splits an angle into two equal angle."
What is an isosceles triangle?"It is a triangle that has two sides of equal length."
What is midsegment of the triangle?"It is the line segment connecting the midpoints of the two sides of a triangle."
What is midsegment formula?"midsegment = 0.5 × base of triangle"
a.
We have been given an equilateral triangle with side lengths of 12.5 cm.
We need to find the length of the midsegment of an equilateral triangle.
Using midsegment formula,
⇒ midsegment = 0.5 × 12.5
⇒ midsegment = 6.25 cm
Therefore, the length of the midsegment of an equilateral triangle is 6.25 cm
b.
UT is the perpendicular bisector of line segment AB, where T is on AB
We know that the perpendicular bisector divides the line segment into two equal parts.
⇒ AT = TB
⇒ 3x + 6 = 42 - x
⇒ 3x + x = 42 - 6
⇒ 4x = 36
⇒ x = 9
So, the length of AT would be,
⇒ AT = 3x + 6
⇒ AT = 3(9) + 6
⇒ AT = 33 units
Therefore, the length of AT is 33 units.
c.
An angle EFG has angle bisector FH, where EF = GF
From given data, we can say that for it must an isosceles triangle EFG with EF = GF and base is EG.
An angle EFG has angle bisector FH and point H is on the side EG.
We know that the angle bisector of isosceles triangle is also the perpendicular bisector of the base of an isosceles triangle.
⇒ EH = HG
⇒ 5y + 10 = 28 - y
⇒ 5y + y = 28 - 10
⇒ 6y = 18
⇒ y = 3
Therefore, the value of y is 3.
Learn more about the angle bisector and perpendicular bisector here:
https://brainly.com/question/12896755
#SPJ2
Related Questions
HELP ASAP
Keiko divided 5 cups of milk into 1/4 cup portions. How many 1/4 cup portions did Keiko have?
Answers
how do i sketch a graph of y=2x that passes through the origin
Answers
Step-by-step explanation:
Given
Equation of line is [tex]y=2x[/tex]
Equation of line with slope m and intercept c on Y-axis is
[tex]y=mx+c[/tex]
Comparing the given line with slope-intercept form
[tex]\Rightarrow m=2\ \text{and}\ c=0[/tex]
The slope is also equal to [tex]\tan \theta[/tex]
[tex]\Rightarrow \tan \theta =2\\\Rightarrow \theta =63.43^{\circ}[/tex]
To sketch the equation of [tex]y=2x[/tex]
Make a line that passes through the origin at an angle of [tex]63.43^{\circ}[/tex] with the x-axis.Find the perimeter of the figure
Answers
Answer:
82in
Step-by-step explanation:
brainliest?
Which of the following numbers Display the ration of 3/10?
Answers
Someone help and please make sure it’s right :)
Answers
Answer:
9
Step-by-step explanation:
[tex]11x + 1 + 7x + 17 = 180 \: \: \: \: 18x + 18 = 180 \: \: \: \: \: \: \: 18x = 180 - 18 \: \: \: \: \: \: \: \:18x = 162 \: \: \: \: \: \: \: \: \: \: 162 \div 18 = 9[/tex]
The daily fee for docking a boat at a marina in port Canaveral is proportional to the length of the boat. The table displays the fee for four different boat lengths. find the constant of proportionality and explain what it means in the context of this problem.
Answers
Answer:
Constant of proportionality = 2.25
What this value means is that the ratio between the daily fee for docking a boat at a marina in port and the length of the boat is 2.25
Step-by-step explanation:
We are told that the daily fee for docking a boat at a marina in port Canaveral is proportional to the length of the boat.
Let D be represent the daily fee and let the lent be L.
D ∝ L
Let the constant of proportionality be k.
Thus;
D = kL
k = D/L
For length of 15 ft;
k = 33.75/15
k = 2.25
For length of 17 ft
k = 38.25/17
k = 2.25
For length of 20 ft
k = 45/20
k = 2.25
Foe length of 21 ft
k = 47.25/21
k = 2.25
This means the formula for the relationship between the daily fee and boat length is; D = 2.25L
Thus, D/L = 2.25
What this means is that the ratio between the daily fee for docking a boat at a marina in port and the length of the boat is 2.25
Can you answer this question?
Answers
Answer:
numerator is 1
denominator is 25
hope my ans helps
pls mark my ans as brainlist
be sure to follow me and I will follow u back
stay safe
Find the equation of the line by using y=mx+b
I tried to put the answer but it keeps asking for more
Answers
Answer:
Step-by-step explanation:
y=mx+b
m=(y2-y1)/(x2-x1), we have points (-3,6) and (9,-5)
m=(-5-6)/(9-(-3))
m=-11/12 so now we have
y=-11x/12+b, using point (9,-5) we can solve for b
-5=-11(9)/12+b
-5=-99/12+b
b=39/12
y=(-11x+39)/12
That is the line, m=-11/12 and b=39/12 or as a decimal b=3.25. You had b so not sure what the problem is. Though the question in the picture asks what the line is. The line is
y=-11x/12+13/4 so maybe they want the entire function instead of entering what b is.
I need help on this plz
Answers
Thomas drew a triangle which has one angle that measures more than
90° and two angles that each measure less than 90°. What kind of
triangle did he draw?
Answers
Answer:
obtuse triangle
Step-by-step explanation:
it is obtuse because it needs to have all 3 sides to be acute to be an acute angle and it doesn't have any 90° angles so it has to be obtuse. Also because to be an obtuse it has to have 2 acute angles and 1 obtuse angle. Hope this helps!!
Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle A?
Answers
Answer:
Step-by-step explanation:
21 because x= tend + lHk
Answer:
88
Step-by-step explanation:
X° + 116° = 180°(sum of opposite angle of a quadrilateral in circle is equal 180 °)
x°=180-116
x°=64°
therefore
A=(2(64)-40)
A=88°
tbh ik this is so easy but i’m too tired to do anything
Answers
Swimming Pool On a certain hot summer's day, 630 people used the public swimming pool. The
daily prices are $1.50 for children and $2.25 for adults. The receipts for admission totaled
$1170.00. How many children and how many adults swam at the public pool that day?
There were children at the public pool.
Enter your answer in the answer box and then click Check Answer.
1 pan
remaining
Clear All
CheART
Answers
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the linear equation in two variables.
So we have to form two equations to solve this.
Let the number of children be 'x' and number of adults be 'y'.
hence, we get as,
x+y = 630 ..... (1)
and also, to their total cost spending, we get as,
1.5x + 2.25y = 1170 ...... (2)
solving (1) and (2) we get as,
Number of children were = 330
and Number of Adults were = 300
(Solved in the attachment)
A tree is broken at a height of 7m from the ground and its top touches the ground at distance of 24m from the base of the tree. Find the original height of the tree. pls help with steps
Answers
then total height of tree=7+x
since it form a right angled triangle with base 24m and height 7m and hypotenuse be x
then by using Pythagoras theorem
(hypotenuse)^2=(base)^2+(height)^2
x^2=24^2+7^2
x^2=576+49
x^2=625
x=25
therefore height of tree =x+7=25+7=31
The weight of 25 folding chairs is 15 kg. How many
chairs can be loaded on a truck having a capacity of
carrying 2025 kg load?
Answers
Answer:
3,375 chairs
Step-by-step explanation:
The weight of 25 folding chairs is 15 kg
Number of folding chairs : weight
= 25 : 15
How many chairs can be loaded on a truck having a capacity of
carrying 2025 kg load?
Let number of folding chairs = x
Number of folding chairs : weight = x : 2025
Equate both ratios
25 : 15 = x : 2025
25/15 = x/2025
Cross product
25 * 2025 = 15 * x
50,625 = 15x
x = 50,625/15
x = 3,375
Number of folding chairs = 3,375 chairs
What does the standard form of a linear equation require?
A)No fractions
B)A must be negative
C)B must be positive
Answers
Answer:
the standard form of a linear equation required is B must be positive
what is the exponent for the expression 6x6x6x6x6x6x6?
Answers
Answer:7 is the exponent
Step-by-step explanation:
Answer:
[tex]6^7[/tex]
Step-by-step explanation:
Exponents can be expressed through repeated multiplication, meaning that the amount of times one number is being repeated, would be the same amount as put in an exponent. Therefore :
6 * 6 * 6 * 6 * 6 * 6 * 6
6 is being repeated, therefore it's the constant.
6 is repeated 7 times, therefore the exponent is 7.
[tex]6^7[/tex]
round 1.19!!!! PLEASE
Answers
Answer:
1.2
Step-by-step explanation:
I am just writing this sentence to get the required amount of characters.
Find the selling price of a $10 item after a 40% markup
Answers
Answer:
Revenue: $14
Profit: $4
Step-by-step explanation:
Hope this helps!
A brainlist would be appreciated! I'm almost an expert!
Guys, please help me, I need to pass my Finals In math!! please answer these two questions with the definitions! Please please please I will mark the brainiest!!!
Answers
Answer:
Q1) The actual distance is 2400 km.
Q2) 1:5000000
please help me, u have no clue what to do. all it says is find the slope of the line that passes through the given two points using ratio method.
Answers
Answer:
Triangle y = 7
Triangle x = -3
Slope = - 7/3
Step-by-step explanation:
Formula:
slope (or m) = (y2 - y1)/(x2 - x1)
Plug numbers into formula
m = 8 - 1 / 4 - 7
m = 7 / -3
Cannot be simplified further
Slope = - 7/3
The triangle before y is asking for the difference, meaning what number do you get after taking y2 (8 in this problem) and subtracting y1 (1 in this problem) from it.
8 - 1 = 7 which forms the numerator for our slope
The same goes for the triangle before x. Find the difference
x2 - x1 = 4 - 7 = -3. This forms the denominator of our slope
Find all the missing sides and angles of this triangle.
А
7
B
70°
Show your work for full credit. You are finding the measure of angle A, side length of AC and side
Show Your Work
I
Answers
Answer:
A = 20°
AC = 6.6
BC = 2.4
Step-by-step explanation:
Given:
B = 70°
C = right angle = 90°
AB = 7
Required:
A, AC, and BC
Solution:
✔️A = 180 - (90 + 70) (sum of triangle)
A = 20°
✔️Use trigonometric function to find AC:
Refernce angle = 70°
Opp = AC
Hypotenuse = 7
Apply SOH,
sin 70 = Opp/Hyp
sin 70 = AC/7
7 * sin 70 = AC
6.57784835 = AC
AC = 6.6 (nearest tenth)
✔️Use trigonometric function to find Bc:
Refernce angle = 70°
Adj = BC
Hypotenuse = 7
Apply CAH,
cos 70 = Adj/Hyp
cos 70 = BC/7
7 * cos 70 = BC
2.394141 = BC
BC = 2.4 (nearest tenth)
I will brainlist you please help me i need this
Answers
Answer:
[tex]q = 16\sqrt{2}, r = 16[/tex]
Step-by-step explanation:
Use proportions for 45-45-90 triangle.
Answer:
Step-by-step explanation:
Use proportions for 45-45-90 triangle.
Work out the length of AC.
Give your answer to 3 significant figures.
A
29 cm
23°
ch
B
Answers
Answer:
AC ≈ 11.3 cm
Step-by-step explanation:
Using the sine ratio in the right triangle
sin23° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{AC}{29}[/tex] ( multiply both sides by 29 )
29 × sin23° = AC , then
AC ≈ 11.3 cm ( to 3 significant figures )
Determine how far the vehicle travels in 3 hours.
A helicopter travels 240 miles every 2 hours.
Answers
Answer:
360 miles
Step-by-step explanation:
The unit rate here is (240 miles) / (2 hours), or 120 mph.
In 3 hours the vehicle travels (120 mph)(3 hrs) = 360 miles
Answer:
360
Step-by-step explanation:
240/2 =120 So, you want to add 120 to 240 to get 360.
Does any one know how to to do Determining the GFC
Answers
What is the area of this figure?
Answers
Answer:
You split it into two parts then add them
Step-by-step explanation:
Find the value of x.
93
2x + 12
Answers
ill mark brainlist plss help
Answers
Answer:
18.5
Step-by-step explanation:
74% of 25 = 18.5
Hope this helps!
Solving systems of equations by graphing. how do you do this
Answers
Answer:
Solve systems of equations by graphing
A system of linear equations contains two or more equations e.g. y=0.5x+2 and y=x-2. The solution of such a system is the ordered pair that is a solution to both equations. To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.
Example
[tex]\left \{ {{y=2x+2} \atop {y=x-1}} \right.[/tex]
Graph the equations in a coordinate plane
The two lines intersect in (-3, -4) which is the solution to this system of equations.
Step-by-step explanation: