In △ABC, BM is a median, △BMC is equilateral and MC = 3cm. Through M is drawn line l∥AB that intersects CB at point N. Find:
- m∠ABC
- The distance from C to AB
- The distance from l to AB
Answer:
m∠ABC = 60°
The distance from C to AB = 3 cm
The distance from l to AB = 1.5 cm
Step-by-step explanation:
The median of ΔABC = BM
The length of MC = 3 cm
Type of triangle given as ΔBMC = Equilateral triangle
Line MN is parallel to AB and passes through M intersecting CB at N
Given that BM is a median, we have;
MC = AM = 3 cm
BM = MC = CB = 3 cm, from ΔBMC = Equilateral triangle
CN = NB by midpoint theorem
∴ CB = CN + NB = 2·CN = 3 cm
The distance from C to AB = CB = 3 cm
The distance from C to AB = 3 cm
CN = 3/2 = 1.5
CN = NB = 1.5
The distance from l to AB = CN = 1.5 cm
The distance from l to AB = 1.5 cm
m∠ABC = m∠BMC = m∠MBC = 60° Interior angles of an equilateral triangle.
m∠ABC = 60°
Two forces of 17.3 pounds and 42.5 pounds act on a body with an angle of 21.9 degrees between them. The force of 42.5 pounds acts on the body in the horizontal direction. Choose the correct approximation for the direction angle the resultant vector makes with the horizontal force.
a. 6.3
b. 21.9
c. 15.7
d. 10.9
The resultant vector makes a 6.3-degree angle with the horizontal force, the correct option is A.
What is the formula for determination of angle of the resultant vector ?The resultant angle between the vectors is given by
[tex]\rm \theta = tan^{-1} \dfrac{B sin\theta}{A +B cos\theta}[/tex]
The two forces have magnitude of 17.3 and 42.5 pounds.
The angle of the resultant vector is
[tex]\rm \rm \theta = tan^{-1} \dfrac{17.3\; sin\; 21.9}{42.5 +17.3 cos\;21.9}[/tex]
[tex]\rm \theta = tan^{-1}[/tex] (6.453/58.55)
[tex]\rm \theta[/tex] = 6.2886 degree = 6.3 degree.
Therefore, the resultant vector makes a 6.3-degree angle with the horizontal force.
To know more about Resultant vector angle
https://brainly.com/question/18794275?referrer=searchResults
#SPJ2
Answer:
6.3 on edge
Step-by-step explanation:
how to turn a fraction into a decimal, help
A fraction is really just another way to write a division problem without dividing. So all you have to do is divide, then round to whichever decimal place your teacher wants.
What is (0.2 + -5) x (4.1) ?
Answer:
-19.68
Step-by-step explanation:
(0.2 + (-5) × (4.1)
-4.8 × (4.1)
-19.68
Answer:
-19.68
Step-by-step explanation:
(0.2 + (-5)) * (4.1)
(-4.8) * (4.1)
-19.68
When given the equation where you have to add a negative, it's similar to subtraction. Where the positive number will be subtracted from the negative number.
What is the unit rate for each size of peanut butter?
Regular: $ ____ per ounce
Family Size: $ _____ per ounce.
Which one is a better buy (claim)?
How do you know (reasoning)?
Answer:
It would be better to buy the regular size
Step-by-step explanation:
For regular size You would divide
16/3.36 = 4.7619
For family size you would divide
40/7.60 = 5.2631
As you can see with the regular size you would pay about $4.75 cents for every ounce but if you buy the family size then you would be paying about $5.26 for every ounce
The local newspaper has letters to the editor from 50 people. If this number represents 2% of all of the newspaper's readers, how many readers does the newspaper have?
Answer: The newspaper has 2500 readers.
Step-by-step explanation:
Given: The local newspaper has letters to the editor from 50 people.
This is the 2% of all newspaper readers.
Let x be the number of all newspaper readers.
Then. 2% of x= 50
[tex]\Rightarrow\ 0.02x=50\ \ [\text{To remove }\% \text{we divide number by 100}]\\\\\Rightarrow\ x=\dfrac{50}{0.02}=\dfrac{5000}{2}=2500\\\\\Rightarrow x=2500[/tex]
Hence, the newspaper has 2500 readers.
Which statement about rigid transformations is true?
A.
A rigid transformation preserves only the side lengths of a polygon.
B.
A rigid transformation preserves only the angle measures of a polygon.
C.
A rigid transformation preserves both the side lengths and the angle measures of a polygon.
D.
A rigid transformation preserves neither the side l
Answer:
The answer is B because it is only the measure of the polygon
BRAINLIEST!!! Correct and fastest answer!
Answer:
whats the question?????
Step-by-step explanation:
7. Estimote the following percentages of 60.
10% =
25% =
50% =
20% =
Answer:
10% of 60 = 6
25% of 60 = 15
50% of 60 = 30
20% of 60 = 12
Step-by-step explanation:
Answer:
10% = 6
25% = 15
50% = 30
20% = 12
Step-by-step explanation:
10 % just drop the 0 from 60. 1/10 of 60 is 6
25% is 1/4. Divide: 60/4 =15
50% is half. Divide 60/2 = 30
20% is 1/5 Divide 60/5 =12
Simplify (-56) ÷ 7.
A. 9
B. -9
C. 8
D. -8
Write an equation in slope-intercept form of the line that passes through (3,8) and (1,-2)
Step-by-step explanation:
let eqn be y = mx + b.
m = (-2 - 8)/(1 - 3) = 5
sub (3, 8):
8 = 5(3) + b
b = -7
therefore equation of the line is y = 5x - 7
Topic: coordinate geometry
If you like to venture further, feel free to check out my insta (learntionary). I'll be constantly posting math tips and notes! Thanks!
Answer:y = 5x - 7
Step-by-step explanation: /
What is 37% out of 87%?
!!20 POINTS!! BRAINLIEST TO CORRECT ANSWER!!
Select the correct answer.
Which ratio is equal to 27:81?
А.1:9
B.2:9
C.3:9
D. 3:27
E.9:12
Answer:
3:9
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
27:81
= 27/81
=3/9
=3:9
it could be reduced to 1:3 but because the alternatives does not include, it 3: 9
please reward me by marking me as the brainliest.
The cheerleading squad sold 480 spirit ribbons, collecting a total of $360.00. What was the cost of each ribbon?
Answer:
1.33
Step-by-step explanation:
480 divided by 360 gets you 1.33
Answer:
Each ribbon costs $0.75.
Step-by-step explanation:
All you need to do solve the problem is divide 360/480 = 0.75.
To check your answer, multiply 0.75 by the number of ribbons sold:
0.75 x 480 = 360
I hope this helped! If it did, please consider rating my answer and pressing thanks. Have a fantastic day!
I give Brainliest!
Determine whether the following statements are sometimes, always or never true.
Equilateral triangles are also right triangles.
All angles of an equilateral triangle are congruent.
Answer: Equilateral triangles are also right triangles sometimes. All angles of an equilateral are congruet sometimes.
10
10
5
-10
0
10
-10
0
10
10
1.5
10
10
-10
Answer:
???????................ .mm
Answer:
???????................ .mm
Step-by-step explanation:
a scale drawing of a rectangular room measures 3 1/2 inches by 11/2 inches the scale is 1/4 inches the scale 1/4 inch = 2 feet carpeting cost $10 per square foot how much will it cost to buy enough carpenter to cover the floor of this room
Answer:
$1540
Step-by-step explanation:
3/2 x 11/2 = 19 1/4
19 times 4 to find how many 1/4s fit in 19 = 76
Add 1/4 = 77
77 x 2 = 154 feet
154 x 10 = $1540
Answer:
1,120
Step-by-step explanation:
I don’t really know but it’s 1,120
Ms. Sakai rode her bike 7.25 miles on Friday. She then rode 12.3 miles on Saturday and then 7.3 miles on Sunday. How many total miles did she ride over those three days?
Answer:26.85 miles
Step-by-step explanation: 7.25+12.3+7.3=26.85
What fraction is 20 min of 3 hours? Answer in simplest form
Answer:
1/9
Step-by-step explanation:
You are checking in a customer’s bag for a flight out of the country. There is a 50-pound weight limit per bag. The customer’s bag weighs 47 pounds. The country the customer is flying to needs the weight of the bag in kilograms to determine compliance.
Answer:
21.3188kg or 21.3kg
Step-by-step explanation:
As one kilogram is equal to 2.20462 pounds we can calculate the weight in kilograms by taking 2.20462 / 47 and we get 21.3188kg
HELP PLEASE 12 POINTS
Answer:
Step-by-step explanation:
5^2=3^2+a^2
25=9+a^2
16=a^2
take the square root of both
4=a
3/4 divided by what equals 12
Answer:
0.05357142
Step-by-step explanation:
Which pair of triangles can be proven congruent by SAS?
identify the TWO sets of ordered pairs that represent a function
A).(1,-1),(-2,-7),(0,1),(-1,-1)
B).(1,-3),(-2,-8),(0,-1),(1,-2)
C).(2,-3),(-3,6),(-2,-2),(2,3)
D).(-3,2),(1,6),(2,2),(1,3)
E).(-5,2),(2,6),(3,2),(4,-5)
Answer:
A and E
Step-by-step explanation:
(1, −1), (−2, −7), (0, 1), (−1, −1) and (−5, 2), (2, 6), (3, 2), (4, −5) are functions because each x value corresponds to exactly one y value. a function must have only one output value for each input value.
A baker in 70 minutes iced 40 cupcakes and in 49 minutes he iced 28 cupcakes what is the constant of proportionality? express your awnser in decimal form.
Answer:
1 cupcake is made in 1.75 minutes.
1.75 minutes
Step-by-step explanation:
Divide 70 by 40 = 1.75.
49/28=1.75
The constant of proportionality of the given data is 0.57.
What is constant of proportionality?The constant of proportionality is the ratio of two proportional values at a constant value.
Now it is given that,
Time taken for icing 40 cupcakes = 70 minutes
∴ Icing of cupcakes in 1 minute = 40/70
= 0.57
Time taken for icing 28 cupcakes = 49 minutes
∴ Icing of cupcakes in 1 minute = 28/49
= 0.57
⇒ constant of proportionality = 0.57
Thus, the constant of proportionality of the given data is 0.57.
To learn more about constant of proportionality:
https://brainly.com/question/10159347
#SPJ6
Complete the steps to find the value of x.
Answer:
Step-by-step explanation:
72+7x+24=180
7x+96=180
7x=84
x=12
help please please
If i just knew the answer i would tell you buti dont know sorrry
Answer:
1. A. 9
B. - 51
2. A. (-3,2)
B. (5,-2)
3. A. (11,-3) B. (11,1) C. They have the same x
What is the solution to this equation?
X-15
5
O A. x=3
O B. x = 10
O C. x= 20
O D. x = 75
2x + 5 = 2x - 3 how many solutions ??
Answer:
-8
Step-by-step explanation:
Subtract 5 from both sides of the equation:
2+5=2−3
2+5−5=2−3−5
Simplify:
2=2−8
Subtract 2 from both sides of the equation:
2=2−8
2−2=2−8−2
Simplify:
0=−8
The solution to the algebraic expression has no solutions.
What is an algebraic expression?An algebraic expression comprises numbers, variables, and arithmetic operations with the aim of determining and finding a solution to the variables.
From the given expression, we have:
2x + 5 = 2x - 3
subtract 2x from both sides, we have:
2x -2x + 5 = 2x -2x - 3
5 = -3
Therefore, the solution algebraic equation has no solution since we don't have a variable to solve.
Learn more about algebraic expressions here:
https://brainly.com/question/2164351
#SPJ2
( use elimination) on 3x+5y=12 and x-3y=4
Answer:
x=4 y=0
Step-by-step explanation:
3x+5y=12
-(x-3y=4)
3x+5y=12
3(-x+3y=-4)
3x+5y=12
-3x+9y=-12
14y=0
y=0
Then, substitute the y into the equation to find x
x-3(0)=4
x=4
