Based on the definition of a parallel line and the Midsegment Theorem the following are the right answers:
1. a.) BD║AE
b.) BF ║CE
c.) DF║CA
2. a.) YZ║RT
b.) RS ║XZ
c.) XY║TS
3. a.) FH = 24
b.) JL = 74
c.) KJ = 60
d.) FJ = 30
4. a.) AE = 26
b.) AN = 58
c.) CT = 21.5
d.) Perimeter of ΔAEN = 127
5. x = 15
6. x = 6
What are Parallel lines?Parallel lines coplanar straight lines that do not meet each other and are equal distance from each other.
The Triangle Midsegment TheoremA midsegment is a line that connects the midpoints of the two sides of a triangle together. Every triangle three midsegments.Based on the Midsegment Theorem of a triangle, the third side of a triangle is always parallel to the midsegment, and thus, the third side is twice the size of the midsegment. In order words, length of midsegment = ½(length of third side).Applying the definition of a parallel line and the Midsegment Theorem the following can be solved as shown below:
1. The pairs of parallel lines in ΔAEC (i.e. the midsegment is parallel to the third side) are:
a.) BD║AE
b.) BF ║CE
c.) DF║CA
2. The segment parallel to the given segments are:
a.) YZ║RT
b.) RS ║XZ
c.) XY║TS
3. Given:
FG = 37; KL = 48; GH = 30
a.) FH = ½(KL)
SubstituteFH = ½(48)
FH = 24
b.) JL = 2(FG)
SubstituteJL = 2(37)
JL = 74
c.) KJ = 2(GH)
SubstituteKJ = 2(30)
KJ = 60
d.) FJ = ½(KJ)
SubstituteFJ = ½(60)
FJ = 30
4. Given:
PT = 13
EN = 43
CP = 29
a.) AE = 2(PT)
SubstituteAE = 2(13)
AE = 26
b.) AN = 2(CP)
SubstituteAN = 2(29)
AN = 58
c.) CT = ½(EN)
SubstituteCT = ½(43)
CT = 21.5
d.) Perimeter of ΔAEN = EN + AN + AE
SubstitutePerimeter of ΔAEN = 43 + 58 + 26
Perimeter of ΔAEN = 127
5. 10x + 44 = 2(8x - 23) (midsegment theorem)
10x + 44 = 16x - 46
Add like terms together10x - 16x = -44 - 46
-6x = -90
Divide both sides by -6
x = 15
6. 19x - 28 = 2(6x + 7) (midsegment theorem)
19x - 28 = 12x + 14
Add like terms together19x - 12x = 28 + 14
7x = 42
Divide both sides by 7x = 6
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solve the following equation
Answer:
x=1 x=-11
Step-by-step explanation:
first you need to find what two numbers add together to make 10x and multiply together to make 25-
this would be 5
so we can rewrite it as (x+5)(x+5) = 36
which is the same thing as (x+5)^2 =36
then taking the root of both sides we get (x+5)= plus or minus 6
so x=-11 or x equals 1
Write an expression that is equivalent to 21h- 10h + 16 - 9 + 14h + 5
Answer:
25h+12
Step-by-step explanation:
Combine Like Terms:
21h+−10h+16+−9+14h+5
(21h+−10h+14h)+(16+−9+5)
25h+12
Same thing, no difference.
Hope this helped! :)
What is the area of this figure?
Answer:
84mm
Step-by-step explanation:
square = LxW = 6x6 =36
triangle = bxh/2 = 6x8/2 =24
add together 24x2+36=84
A drawing of a man is 4 inches high. The actual man is 64
inches tall. What is the scale factor for the drawing?
Answer:
Step-by-step explanation:
The scale factor is the ratio between the man's actual height and the height of the drawing.
Scale = 64/4 = 16
Answer:
1/16
Step-by-step explanation:
the actual man is 16 times bigger than drawing.
Eight squared plus B squared equals 14 squared
[tex]8^2 +B^2 = 14^2\\\\\implies B^2 = 14^2 -8^2 \\\\\implies B^2 = 132\\\\\implies B=\pm\sqrt{132} = \pm 2\sqrt{33}[/tex]
what number is the square root of 13 between
A 2 and 3
B 5 and 6
C 4 and 5
D 3 and 4
Answer:
D
Step-by-step explanation:
3:
12
4:
16
Therefore 13 is in between 12 and 16
ASAP HELPPPPPPPPP PLEASE!!!!
Answer:
1. y=3/5x +1
2. x = -3
3. y = 4
4. y = -1/3x + 4
5. y=5x + 4
6. y= 3/4 x + 1
7. y = 9/4x - 1/2
8. y = 5/3x
9. y = -5x +5
10. y = 2x - 5
11. y = -4x - 4
12. y = 1/4x - 4
Step-by-step explanation:
math lol
Why are there certain question where you multiply to a power and some you don't. Like tree diagrams. This is for probability of compound events.
Compound probabilities that required AND use multiplication
How to determine the reason?The probability of compound events is of two types
The one that require ANDThe one that require ORAs a general rule, the AND probability require products
Take for instance
P(A and B) = P(A) and P(B)
This gives
P(A and B) = P(A) * P(B)
So, compound probabilities that required AND use multiplication
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#SPJ1
In a recent year, 21% of all college students were enrolled part-time. If 7.6 million college students were enrolled part-time that year, what was the total number of college students?
Answer:
36.19047619 million
or 36,190,476 students
Step-by-step explanation:
7.6 million / all students = 21% / 100%
7.6 * 100 / 21 = 36.19047619
36.19047619 million
or 36,190,476 students
A functionf(x) is graphed on the coordinate plane. What is the function rule in slope-intercept form? Enter your answer in the box. F(x)=.
Linear functions are used to represented straight lines.
The linear function is [tex]y = -\frac 12x + 1[/tex]
The points on the graph are: (2,0) and (0,1)
Start by calculating the slope (m) using:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
Substitute values for x and y
[tex]m = \frac{1 - 0}{ 0 -2}[/tex]
[tex]m = \frac{1 }{ -2}[/tex]
Rewrite as:
[tex]m = -\frac{1 }{2}[/tex]
The equation is then calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
This gives
[tex]y = -\frac 12(x -0) + 1[/tex]
[tex]y = -\frac 12(x) + 1[/tex]
Open bracket
[tex]y = -\frac 12x + 1[/tex]
Hence, the linear function is [tex]y = -\frac 12x + 1[/tex]
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in 2020 the attendance at kennedy school's spring festival was 210. in 2021 the attendance was 168. What was tge percent change in the attendance from 2020 to 2022 tound to nearest whole percent
Step-by-step explanation:
Total change in number of student = (210 - 168)
=> 42
% change = Change/Original no. of students × 100
=> 42/210 × 100
=> 42/21 × 10
=> 20%
F(x) = the integral from 0 to x cos(t^2)dt. Use your calculator to find F’(1)
By the fundamental theorem of calculus,
[tex]\displaystyle F(x) = \int_0^x \cos(t^2) \, dt \implies F'(x) = \cos(x^2)[/tex]
and so F'(1) = cos(1).
PLEASE HELP GIVING POINTS
Answer: You are correct, the slope 2, is the slope of the present line displayed on the graph.
Step-by-step explanation:
To find slope, you use the formula/term; [tex]\frac{rise}{run}[/tex].
This means to rise up ___ amount of numbers and run __ amount of numbers.
Rise is moving along y, and x is moving along x.
-Additional info:
positive slope (when lines go uphill from left to right) negative slope (when lines go downhill from left to right) zero slope (when lines are horizontal) undefined slope (when lines are vertical)-------------
#TeamTrees #TeamSeas #PAW #Spread_Positivity
I hope this helps,
-Oceanbreeze24
5. A quarter is tossed in the air 300 times.
About how many times would you expect the quarter to land on heads?
A 50
E 200
B 110
C 150
D 180
Answer:
C
Step-by-step explanation:
The probability of getting heads or tails is 50%.
300*50% = 150
Answer:
C. 150 times
Step-by-step explanation:
Because a coin only has tails and heads, you can say that the probability would be half. Because it was tossed 300 times, you can say: 300*0.5=150
What’s the Pythagorean therorimm
Answer:
38.29 i think
Step-by-step explanation:
my Christmas present to you
Answer:
Is this a points post or something? If so, thank you!
For what values of x: Is the binomial 7x+1 equal to the trinomial 3x2−2x+1?
Answer:
x = 0 , x = 3
Step-by-step explanation:
Equate the 2 expressions and solve for x
3x² - 2x + 1 = 7x + 1 ( subtract 7x + 1 from both sides )
3x² - 9x = 0 ← factor out 3x from each term
3x(x - 3) = 0
Equate each factor to zero and solve for x
3x = 0 ⇒ x = 0
x - 3 = 0 ⇒ x = 3
5 1/28=1/2p+5 4/7
Please help!!
Answer:
p = (-15)/14
Step-by-step explanation:
Solve for p:
5 + 1/28 = p/2 + 4/7 + 5
Put 5 + 1/28 over the common denominator 28. 5 + 1/28 = (28×5)/28 + 1/28:
((28×5)/28 + 1/28) = p/2 + 4/7 + 5
28×5 = 140:
140/28 + 1/28 = p/2 + 4/7 + 5
140/28 + 1/28 = (140 + 1)/28:
((140 + 1)/28) = p/2 + 4/7 + 5
140 + 1 = 141:
141/28 = p/2 + 4/7 + 5
Put each term in p/2 + 4/7 + 5 over the common denominator 14: p/2 + 4/7 + 5 = (7 p)/14 + 8/14 + 70/14:
141/28 = ((7 p)/14 + 8/14 + 70/14)
(7 p)/14 + 8/14 + 70/14 = (7 p + 8 + 70)/14:
141/28 = ((7 p + 8 + 70)/14)
Grouping like terms, 7 p + 8 + 70 = 7 p + (70 + 8):
141/28 = (7 p + (70 + 8))/14
70 + 8 = 78:
141/28 = (7 p + 78)/14
141/28 = (7 p + 78)/14 is equivalent to (7 p + 78)/14 = 141/28:
(7 p + 78)/14 = 141/28
Multiply both sides of (7 p + 78)/14 = 141/28 by 14:
(14 (7 p + 78))/14 = (14×141)/28
(14 (7 p + 78))/14 = 14/14×(7 p + 78) = 7 p + 78:
(7 p + 78) = (14×141)/28
14/28 = 14/(14×2) = 1/2:
7 p + 78 = 141/2
Subtract 78 from both sides:
7 p + (78 - 78) = 141/2 - 78
78 - 78 = 0:
7 p = 141/2 - 78
Put 141/2 - 78 over the common denominator 2. 141/2 - 78 = 141/2 + (2 (-78))/2:
7 p = (141/2 - (78×2)/2)
2 (-78) = -156:
7 p = 141/2 + (-156)/2
141/2 - 156/2 = (141 - 156)/2:
7 p = ((141 - 156)/2)
141 - 156 = -15:
7 p = (-15)/2
Divide both sides by 7:
p = ((-15)/7)/2
2×7 = 14:
Answer: p = (-15)/14
3х + 9 = 2х + 5
is it no solutions, all real numbers, or does x equal something?
Answer:
x = -4Step-by-step explanation:
Given Equation:3x + 9 = 2x + 5Question:Whether x has one solution or infinite solutions or no solutions?Solution:=> 3x + 9 = 2x + 5
(On shifting like terms to one side we get)=> 3x - 2x = 5 - 9
(On subtracting)=> x = - 4
Result:Hence, x has only one solution that is, x = -4 (Ans)
Topic : Linear equations in one variable
Given :
3х + 9 = 2х + 5Solution :
[tex]\qquad \sf \: { \dashrightarrow 3x + 9 = 2x + 5}[/tex]
Transposing variables on one side and constant terms on the other side, we get :
[tex]\qquad \sf \: { \dashrightarrow 3x - 2x = 5 - 9}[/tex]
[tex]\qquad \sf \: { \dashrightarrow x = - 4}[/tex]
Hence, the x is equal to something which is (– 4)1. A roll of wire holds 3 meters of wire.
About how many inches of wire does
the roll hold ?
Answer:
Step-by-step explanation:
1 meter = 39.3701, by definition.
3 meters = 3*(39.3701)
3 meters of wire = 118 inches
Answer:
3 meters ≈ 118 inches
Step-by-step explanation:
1 meter = 3.28084 feet
1 foot = 12 inches
3 · 3.28084 = 9.84252
9.84252 · 12 = 118.11024
What is the perimeter of triangle ABC with coordinates of A(3,4), B(3,11), C(27,4)
Answer:
Is there supposed to be a picture or no?
Step-by-step explanation:
A forest covers 54,000 acres. A survey finds that 0.6% of the forest is old-growth trees. How many
acres of old-growth trees are there?
Answer:
324
Step-by-step explanation:
A line passes through (3,7) and (5,9). Write the equation of the
line in slope-intercept form.
Answer:
y = x+4
Step-by-step explanation:
First, we find the slope
m = (y2-y1)/(x2-x1)
m = ( 9-7)/(5-3)
= 2/2
=1
Slope intercept form of a line is y = mx+b where m is the slope and b is the y intercept
y = 1x+b
Using one of the points
7 = 1*3+b
7 = 3+b
4=b
y = x+4
The number of blogs has grown rapidly. Assuming that two new blogs are created each second,
how many blogs will be set up in one month (30 days)?
O 5.27 x 105
O 6.17 x 105
O 5.27 x 106
O 6.17 x 106
2. Felicia took out a simple interest loan at 12 percent interest for 6 months. Her previous balance is $2,460,
What is the final payment if the loan is paid off with the next payment?
Answer:
Answer:
28+66+86=180
180=180
Step-by-step explanation:
Since there is a triangle and the 3 measures from the angles we can find the value of x using the hint given that the sum of the interior angles must be 180°
Write the equation
\begin{gathered}x+(2x+10)+(3x+2)=180\\\end{gathered}
x+(2x+10)+(3x+2)=180
Simplify left side of the equation
\begin{gathered}6x+12=180\\\end{gathered}
6x+12=180
Solve equation for x
\begin{gathered}6x=180-12\\6x=168\\x=28\end{gathered}
6x=180−12
6x=168
x=28
Replace x into the 3 angles and find their respectives values
\begin{gathered}A=x\\A=28\\\\B=2x+10\\B=2*28+10\\B=56+10\\B=66\\\\C=3x+2\\C=84+2\\C=86\end{gathered}
A=x
A=28
B=2x+10
B=2∗28+10
B=56+10
B=66
C=3x+2
C=84+2
C=86
Check if the answers are correct
\begin{gathered}28+66+86=180\\180=180\end{gathered}
28+66+86=180
180=180
PLEASE MARK ME AS BRAINLIEST
Someone plz help me :(
Answer:
c
Step-by-step explanation:
when we add 0 to x ,it remains x.
x+0=x
0 is additive identity.
Answer:
C
Step-by-step explanation:
Are these lines parallel explain?
The follow through is where you "pause" and hold the bow still for a few seconds after releasing the arrow.
True or false
True-... i think because like i am not sure-
pls help me with this:((
Answer:
9. A. One - to - One Correspondence
10. D. None of the above
9.) one to one correspondence
10.)one to many correspondence
Step-by-step explanation:
in 9 it shows that 1-4 are connected to different number
in 10 it shows that a is connected to 2 different numbers
How i can answer this question, NO LINKS, if you answer correctly i will give u brainliest!
Answer:
10
Step-by-step explanation:
Equation=5*2^3/2^2