Equilateral triangle ABC has a perimeter of 96 millimeters. A perpendicular bisector is drawn from angle A to side BC at point
M.
What is the length of MC?
16 mm
0 24 mm
O 32 mm
O 48 mm
Answer:
Correct option: First one -> 16 mm
Step-by-step explanation:
The equilateral triangle has its three sides with the same length.
So if the perimeter is 96 mm, we have:
[tex]Perimeter = 3*side[/tex]
[tex]3*side = 96[/tex]
[tex]side = 32 mm[/tex]
The segment MA is the height of the equilateral triangle, and its length can be calculated with the equation:
[tex]height = \frac{side * \sqrt{3}}{2}[/tex]
[tex]height = 16\sqrt{3}[/tex]
Using the Pythagoras' theorem in the triangle ACM, we have:
[tex]side^2 = MC^2 + height^2[/tex]
[tex]1024 = MC^2 + 768[/tex]
[tex]MC^2 = 256[/tex]
[tex]MC = 16\ mm[/tex]
Correct option: First one
Answer:
(A) 16mm
Step-by-step explanation:
Summer looked at the formula for the Pythagorean Theorem, a2 + b2 = c2, she said that it didn’t matter which sides of a right triangle were a, b, and c. Is she correct? A. Yes, she is correct. B. No, a must be the shortest side, then b, and c is the longest side. C. No, c must be the shortest side, then b, and a is the longest side. D. No, a and b are interchangable, and c is the longest side.
Answer: D. No, a and b are interchangeable, and C is the longest side.
Step-by-step explanation:
Either A and B which are the two legs can be greater than the hypotenuse which is C. They hypotenuse has to always be greater than the two legs and the two legs have the same lengths but it can't be greater than the hypotenuse.
For example let's say you have a right angle with side lengths 3,4 and 5.
5 in this case has to be always the hypotenuse.
A could be either 3 or 4 but not 5
And B could also be 3 or 4 but not 5
because A squared plus B squared is always equal to the hypotenuse which is 5.
3^2 + 4^2 = 5^2
9 + 16 = 25
25 = 25
Answer:
D. No, a and b are interchangeable, and C is the longest side.
Step-by-step explanation:
I WILL MARK YOU BRAINLIEST!!!!
Answer:
0; one real roots
* the answer is C
Explain what a direct line segment is and describe how you would find the coordinates of point P along a directed line segment AB that partitions segment AB so that the ratio of AP to PB is 3:1
Answer:
P = (A +3B)/4
Step-by-step explanation:
A "directed" line segment is one that has a "beginning" and an "end". The first letter of the line segment's name is the beginning; the last letter is the end.
Line segment AB begins at point A and ends at point B.
The problem statement tells you what it means to locate point P so the segment is divided in the ratio 3:1.
AP : PB = 3 : 1
(P -A) / (B -P) = 3 / 1
P -A = 3(B -P) . . . . . . . . multiply by (B-P)
P +3P = A +3B . . . . . . . add A+3P
P = (A +3B)/4
You can find point P by filling in the coordinate values in the formula just found.
_____
Comment on the general case
If you derive the formula for P dividing the segment in the ratio m : n, you find it is ...
P = (nA +mB)/(m+n) . . . length ratios are applied in reverse to the end points
What the answer to this
Answer:
(2 x + 5) (x - 1) (x + 7) thus the answer is D.)
Step-by-step explanation:
Factor the following:
2 x^3 + 17 x^2 + 16 x - 35
The possible rational roots of 2 x^3 + 17 x^2 + 16 x - 35 are x = ± 1/2, x = ± 5/2, x = ± 7/2, x = ± 35/2, x = ± 1, x = ± 5, x = ± 7, x = ± 35. Of these, x = -5/2, x = 1 and x = -7 are roots. This gives 2 x + 5, x - 1 and x + 7 as all factors:
Answer: (2 x + 5) (x - 1) (x + 7)
if cos =5\13 and 90°≤ø≤180,evaluate cotø,secø,cosø
Answer: [tex]\bold{\cot\theta=-\dfrac{5}{12}\qquad \sec\theta = \dfrac{13}{5}\qquad \cos\theta = \dfrac{5}{13}}[/tex]
Step-by-step explanation:
90° ≤ θ ≤ 180° means that it is in Quadrant II → x is + , y is -
[tex]\cos \theta = \dfrac{5}{13}\quad \rightarrow\quad x = 5, \ r = 13\\\\\\\text{Use Pythagorean Theorem to find y}:\\x^2+y^2=r^2\quad \rightarrow \quad 5^2+y^2=13^2\quad \rightarrow \quad y = -12\\\\\\\cot\theta=\dfrac{x}{y}\quad =\dfrac{5}{-12}\quad =\large\boxed{-\dfrac{5}{12}}\\\\\\\sec\theta=\dfrac{r}{x}\quad = \dfrac{13}{5}\quad = \large\boxed{\dfrac{13}{5}}\\\\\\\cos\theta =\dfrac{5}{13}\quad \text{(Given)}\\[/tex]
Corey and David both have lots of video games. The number of games Corey has can be represented by x . Ricky has 3 times as many games as Corey. The total number of games is 64 . What is x, the total number of games Corey has?
Answer:
21.3333333
Step-by-step explanation:
64/3=x
64/3=21.3333333
Sorry if its wrong.
What is the equation of the following line? Be sure to scroll down first to see all answer options.
Answer:
C
Step-by-step explanation:
Since the graph hits 0 at x = 0, your y intercept is 0.
The graph is decreasing which means you have a negative slope.
They gave you a coordinate so use it to find the slope.
[tex]\frac{1-0}{-3-0} = \frac{-1}{3}[/tex]
That's your slope.
C is the correct answer.
y=-1/3x
mark brianliest if my answer suits ur question.
What represents the inverse of the function f(x)=4x?
Answer:
Dear user,
Answer to your query is provided below
The inverse of the function f(x)=4x is y=(x/4)
Step-by-step explanation:
To find the inverse function, swap x and y, and solve the resulting equation for x.
If the initial function is not one-to-one, then there will be more than one inverse.
So, swap the variables: y=4x becomes x=4y.
Now, solve the equation x=4y for y.
y=(x/4)
a plane flies 1640 miles in 4 hours. what is the average speed of the plane?
Answer:
Speed = 410 miles/hour
Step-by-step explanation:
Speed = Distance / Time
Distance = 1640 miles, Time = 4 hours
Speed = 1640/4
Speed = 410 miles/hour
Expand and simplify
n(6 + n) =
Answer:
n²+6n
Step-by-step explanation:
n(6 + n) = 6n+n²= n²+6n
Answer the following Questions
Which of the following points lie on the x-axis?
A(1, 1), B (1.0). c (0,1)D (0,0), E (-1,0), F (0-1), G (4,0), H (0,7)
Answer:
B, D, E and G lies on X axis
There is a bag filled with 3 blue and 5 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is not replaced.
Another marble is taken at random.
What is the probability of getting exactly 1 red?
Answer:
4/6 chance
One is taken at random, we do not know the colour so we just take away 1 from both colours, this leaves us with 4/6 chance.
When 10b=5 is solved for c, one equation is c=(2b-2)^2
Answer:
b= 1/2
c = 1
Step-by-step explanation:
10b = 5
You want to leave the variable b on it's own so you divide both sides by 10
10b/10 = 5/10 --> b = 5/10 or 1/2
Since you have the value of b now, plug it in to solve for the value of c
c = (2 (1/2) - 2)^2
= (1 - 2)^2 Half of 2 is 1, of course
= (-1)^2 (-1 * -1)
c = 1 (a negative times a negative is a positive
So the value of be is 1/2 and c is 1
Hope this helps!
What is the slope of the line shown?
Answer:1/2 slope
Step-by-step explanation:
Answer: -2
Step-by-step explanation: Using rise/run, take two points of the line. I took the points (3,1) (2,3). I then went down 2 (run) and then I went 1 to the right(run). Since the graph goes by 2, the equation is -4/2 resulting in the answer -2.
What is the slope of the line that contains the points (-23, -16) and (13, -16)?
Answer:
Use the slope formula to find the slope . m = 0
Step-by-step explanation:
Ans:
3/2. your welcome
Step-by-step explanation:
7. Diana took 2 hours to cycle from town X to town Y. Her average speed was 10 kilometers per
hour.
a) Find the distance between the two towns. (2 marks)
b) If her average speed was increased by 2 kilometers per hour, how much time would she take
for the journey? (2 marks)
Answer:
a.) 20 kilometers
b.)1.67 hours
Step-by-step explanation:
a.) formula= speed =distance/time
Speed= 10km/hr
Distance=unknown
Time=2hrs
Therefore from formula, distance=speed x time
10 x 2
20 kilometers
b.) If average speed is increased by 2km/hr then
total speed= 2+10=12km/hr
Distance remains constant therefore distance= 20km
Therefore time =distance/speed
20/12
= 1.67 hours
Please help!
there were 6000 people at a football match
10% of them left 2 minutes before the end of the game to avoid traffic
50% of the rest left as soon as the match ended
a) how many people in total had left the football match when it ended?
b) what percentage of the original crowd was still there?
10%+50%=60%
60% of 6000=3600
a)3600 people had left the match when it ended
b)6000-3600=2400
40% of the crowd was still there
Select all that apply.
Which of the following name a line in the drawings
Answer:
DB
It's the only line that is not a segment.
Step-by-step explanation:
Help me please I need help!!!!
Answer:
Answer B (proportional)
Step-by-step explanation:
The variable y and x are related by the constant of proportionality "6" in the expression
y = 6 x
Such means that if x adopts whatever value, y is always proportional to that x-value, by the multiplicative factor 6.
y is proportional to x via the proportionality constant (it has to be always a multiplicative constant) "6"
Find the distance between the points.
(4,6),(9,6)
Answer:
5
Step-by-step explanation:
Find the difference between coordinates:
(x²-x1) = (9 - 4) = 5
(y²-y1) = (6 - 6) = 0
Square the results and sum them up:
(5)² + (0)² = 25 + 0 = 25
Now Find the square root
Sum of the ages of a father and the son is 40 years. If father's age is 3 times that of his son, then father's age is ________ * 2 points 35 40 30 45
Answer:
30
Step-by-step explanation:
Sum of ages= 40
Let the sons age be x
Fathers age = 3 times x or ,3x
So 3x+x=40
4x= 40
x= 40/4
= 10
Therefore the fathers age = 3x
= 3*10
= 30
A quadratic function g(x) passes through the points (-8, 33), (2, 1), and (8, 1).
Which statement correctly describes g(x)?
1. The line x = -5 is an axis of symmetry, and the vertex is a minimum because the y-values increase as the graph moves away from that function.
2. The line x = -5 is an axis of symmetry, and the vertex is a maximum because the y-values increase as the graph moves away from that function.
3. The line x = 5 is an axis of symmetry, and the vertex is a minimum because the y-values increase as the graph moves away from that function.
4. The line x = 5 is an axis of symmetry, and the vertex is a maximum because the y-values increase as the graph moves away from that function.
Answer:
Correct option: 3
Step-by-step explanation:
The points (2,1) and (8,1) have the same y-coordinate, so to find the vertex of the quadratic function (where the axis of symmetry will be located), we just need to find the average of their x-coordinate:
x_vertex = (2 + 8) / 2 = 5
The points (2, 1) and (-8, 33) show that when the graph moves away from the axis of symmetry (from x = 2 to x = -8), the y value increases (from 1 to 33), so the vertex is a minimum.
Correct option: 3
Answer:
3
Step-by-step explanation:
I had this question and got it right on a test
If GF = 3.2 ft, which is a possible measure of T5?
1.6 ft
3.0 ft
3.2 ft
4.0 ft
Complete Question:
In the triangles, TR= GE and SR=FE. If GF= 3.2 ft, which is a possible measure of TS?
Answer:
3.2ft
Step-by-step Explanation:
From the given information of the question, we can draft out the diagram of the triangles being depicted here. See attached picture showing triangles RST and EFG.
Since we are told that TR= GE, and SR = FE, it means both triangles are isosceles triangle a having 2 equal sides, and triangles RST and EFG are similar.
Also, given that the measure of the 3rd side (GF) of triangle EFG is 3.2ft, therefore, TS = 3.2ft
Answer:
c
Step-by-step explanation:
The Expression3(x-9) equivalent to
Answer:
3x - 27
Step-by-step explanation:
3(x-9)
Distribute
3x * -3*9
3x - 27
Answer:
Brainliest!
Step-by-step explanation:
it is equivialent to 3x-27
just simplify the equatoin
2⁄6 + 4⁄8 + 3⁄4 = is what?
Answer:
2/6+4/8+3/4=19/12
(Decimal: 1.583333)
hope i helped
-lvr
Answer:
1 7/12
Step-by-step explanation:
2/6 + 4/8+3/4
Simplify the fractions
1/3 + 1/2 +3/4
The common denominator is 12
1/3*4/4 + 1/2 *6/6+ 3/4*3/3
4/12 + 6/12 +9/12
19/12
12/12 + 7/12
1 7/12
a parabola has its vertex at 1,1 and passes through the point -2,-2. Find the equation of this parabola
Answer:
Step-by-step explanation:1/2 of answer is zero
Answer:
y=1/3x^2+4/3 x -2/3
Step-by-step explanation:
y=1/3x^2+4/3 x -2/3
Find median of the data. 14, 18, 16, 122, 22, 19, 12
Answer:
18
Step-by-step explanation:
The order from least to greatest is 12,14,16,18,19,22,122.
The middle number is 18 because there is 3 numbers next to 18 on the right which is 19,22,122 and 3 numbers on the left which is 12,14,16. A median would be easier to find if there is an odd amount of numbers.
After reading 7/9 of a book , 40 pages are left .How many pages are there in the book
Answer:
180 pages
Step-by-step explanation:
Answer: 180 pages
Step-by-step explanation:
Let the equation be
x - 7/9x = 40
9x - 7x = 360
x = 360 / 2 = 180
The book has total 180 pages
Means he has read (180 - 40) = 140 pages
please help me with question b) and please explain!!
look at the attached image
Answer:
17
Step-by-step explanation:
let x be the number of boxes to be shaded to make it 80%
x = 80% of total number
= 80/100 of 25
= 80/4
= 20
So 20 need to be shaded to fill 80%
Now, 13 of the grids are already shared so the amount of more squares that need to be shaded = 20-13
= 17 squares
