All categories

3 years ago

Help me to prove the given below. Thank you in advance

Mathematics

1 answer:

sleet_krkn [62]3 years ago

8 0

Answer:

Construct MO, where O is the midpoint of CG. (As shown in the attached figure)

(1) LM = MG //given, CM is the median to the hypotenuse

(2) CO = OG // construction

(3) MO is a mid-segment //(1), (2) , Definition of a mid-segment

(4) MO // LC //triangle mid-segment theorem

(5) ∠MOG ≅ ∠LCO // corresponding angles in two parallel lines intersected by a transversal line (CG)

(6) m∠LCO=90° //given, ΔLCG is a right triangle

(7) m∠MOG=90° //(5), (6), definition of congruent angles

(8) m∠MOC=180° – 90° = 90° // linear pair

(9) ∠MOG ≅ ∠MOC //(7),(8), definition of congruent angles

(10) MO=MO //common side, reflexive property of equality

(11) ΔMCO ≅ ΔMGO //(2), (9), (10) Side-Angle-Side postulate

(12) MC = MG // Corresponding sides in congruent triangles (CPCTC)

(13) MG= ½LG // Given, CM is the median to the hypotenuse

(15) MC = ½LG //(12) , (13), substitution

You might be interested in

Eliza is two years younger than half her brother, Juan’s age. Write an equation to represent Eliza’s age. If Juan is 6 how old i

Natalka [10]

X = Juan's age
y = Eliza's age

Some key words/phrases we can use to help us make the equation are:

-is (whatever comes after this word usually equals the end result, or what it equals)
-two years younger
-than
-half her brother's age
.
just break it down :)

x/2 (half her brother's age) - 2 (two years younger) = y (Eliza is...)

| basically,
v

x/2 - 2 = y
So if Juan is 6, then we need to plug in 6 for x.

6/2 - 2 = y

3 - 2 = y

1 = y

ANSWER: Eliza is one year old.

6 0

3 years ago

What is the image of (6,-4) after a reflection over the y-axis?

kirill115 [55]

Answer:

(-6,-4)

Step-by-step explanation:

Hope this helps! (:

3 0

3 years ago

Find the solution of the given initial value problem in explicit form. y′=(1−5x)y2, y(0)=−12 Enclose numerators and denominators

Nata [24]

Answer:

The solution is $y=-\frac{12}{12x-30x^2+1}$ .

Step-by-step explanation:

A first order differential equation $y'=f(x,y)$ is called a separable equation if the function $f(x,y)$ can be factored into the product of two functions of $x$ and $y$ :

$f(x,y)=p(x)h(y)$

where $p(x)$ and $h(y)$ are continuous functions.

We have the following differential equation

$y'=(1-5x)y^2, \quad y(0)=-12$

In the given case $p(x)=1-5x$ and $h(y)=y^2$ .

We divide the equation by $h(y)$ and move $dx$ to the right side:

$\frac{1}{y^2}dy\:=(1-5x)dx$

Next, integrate both sides:

$\int \frac{1}{y^2}dy\:=\int(1-5x)dx\\\\-\frac{1}{y}=x-\frac{5x^2}{2}+C$

Now, we solve for $y$

$-\frac{1}{y}=x-\frac{5x^2}{2}+C\\-\frac{1}{y}\cdot \:2y=x\cdot \:2y-\frac{5x^2}{2}\cdot \:2y+C\cdot \:2y\\-2=2yx-5yx^2+2Cy\\y\left(2x-5x^2+2C\right)=-2\\\\y=-\frac{2}{2x-5x^2+2C}$

We use the initial condition $y(0)=-12$ to find the value of C.

$-12=-\frac{2}{2\left(0\right)-5\left(0\right)^2+2C}\\-12=-\frac{1}{c}\\c=\frac{1}{12}$

Therefore,

$y=-\frac{2}{2x-5x^2+2(\frac{1}{12})}\\y=-\frac{12}{12x-30x^2+1}$

4 0

3 years ago

Which graph represents the function over the interval [−3,3] ?<br><br> f(x)=⌈x+1⌉

CaHeK987 [17]

Answer: The correct graph is the bottom left graph.

Step-by-step explanation:

Given function is f(x)=ceil(x+1)

To plot graph of f(x) in interval of(-3,3) :

ceil(x+1) is ceiling function

The output of ceil(x) is least integer greater than x

for example ceil(5.5)=6

For an interval of (-3,-2):

Take x=(-2.4)

x+1=(-1.4)

y=f(x)=ceil(x+1)=(-1)

Similarly,

For an interval of (-2,-1):

Take x=(-1.4)

x+1=(-0.4)

y=f(x)=ceil(x+1)=(0)

For an interval of (-1,0)

y=f(x)=1

For an interval of (0,1)

y=f(x)=2

For an interval of (1,2)

y=f(x)=3

For an interval of (2,3)

y=f(x)=4

Thus, The correct graph is the bottom left graph.

4 0

3 years ago

You have $5 and earn $0.50 for each cup of orange juice you sell. Write an equation that represents the total amount $A$A (in d

hjlf

Answer: Your equation would be A(J)=.50j + 5

Step-by-step explanation:

6 0

2 years ago