Given:
Coordinates of point A are (2,8).
Point M(-2,2) is the midpoint of AC.
To find:
The coordinates of C.
Solution:
Let the coordinates of point C are (a,b).
Formula for midpoint:
[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
Using the above formula, the midpoint of A(2,8) and C(a,b) is
[tex]M=\left(\dfrac{2+a}{2},\dfrac{8+b}{2}\right)[/tex]
[tex](-2,2)=\left(\dfrac{2+a}{2},\dfrac{8+b}{2}\right)[/tex]
On comparing both sides, we get
[tex]\dfrac{2+a}{2}=-2[/tex]
[tex]2+a=-4[/tex]
[tex]a=-4-2[/tex]
[tex]a=-6[/tex]
and,
[tex]\dfrac{8+b}{2}=2[/tex]
[tex]8+b=4[/tex]
[tex]b=4-8[/tex]
[tex]b=-4[/tex]
Therefore, the coordinates of point c are (-6,-4).
How do I solve this problem?
Please help me to prove this!
Answer: see proof below
Step-by-step explanation:
Given: A + B = C → A = C - B
→ B = C - A
Use the Double Angle Identity: cos 2A = 2 cos² A - 1
→ (cos 2A + 1)/2 = cos² A
Use Sum to Product Identity: cos A + cos B = 2 cos [(A + B)/2] · 2 cos [(A - B)/2]
Use Even/Odd Identity: cos (-A) = cos (A)
Proof LHS → RHS:
LHS: cos² A + cos² B + cos² C
[tex]\text{Double Angle:}\qquad \dfrac{\cos 2A+1}{2}+\dfrac{\cos 2B+1}{2}+\cos^2 C\\\\\\.\qquad \qquad \qquad =\dfrac{1}{2}\bigg(2+\cos 2A+\cos 2B\bigg)+\cos^2 C\\\\\\.\qquad \qquad \qquad =1+\dfrac{1}{2}\bigg(\cos 2A+\cos 2B\bigg)+\cos^2 C[/tex]
[tex]\text{Sum to Product:}\quad 1+\dfrac{1}{2}\bigg[2\cos \bigg(\dfrac{2A+2B}{2}\bigg)\cdot \cos \bigg(\dfrac{2A-2B}{2}\bigg)\bigg]+\cos^2 C\\\\\\.\qquad \qquad \qquad =1+\cos (A+B)\cdot \cos (A-B)+\cos^2 C[/tex]
[tex]\text{Given:}\qquad \qquad 1+\cos C\cdot \cos (A-B)+\cos^2C[/tex]
[tex]\text{Factor:}\qquad \qquad 1+\cos C[\cos (A-B)+\cos C][/tex]
[tex]\text{Sum to Product:}\quad 1+\cos C\bigg[2\cos \bigg(\dfrac{A-B+C}{2}\bigg)\cdot \cos \bigg(\dfrac{A-B-C}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =1+2\cos C\cdot \cos \bigg(\dfrac{A+(C-B)}{2}\bigg)\cdot \cos \bigg(\dfrac{-B-(C-A)}{2}\bigg)[/tex]
[tex]\text{Given:}\qquad \qquad =1+2\cos C\cdot \cos \bigg(\dfrac{A+A}{2}\bigg)\cdot \cos \bigg(\dfrac{-B-B}{2}\bigg)\\\\\\.\qquad \qquad \qquad =1+2\cos C \cdot \cos A\cdot \cos (-B)[/tex]
[tex]\text{Even/Odd:}\qquad \qquad 1+2\cos C \cdot \cos A\cdot \cos B\\\\\\.\qquad \qquad \qquad \quad =1+2\cos A \cdot \cos B\cdot \cos C[/tex]
LHS = RHS: 1 + 2 cos A · cos B · cos C = 1 + 2 cos A · cos B · cos C [tex]\checkmark[/tex]
I want to pull all nighter and stay awake for 36 hours. If I woke up at 12 PM, and if it's currently 11:22 PM right now, then how long have I been awake?
( I actually need to know I'm pulling an all nighter to reset my sleep schedule)
Answer:
11 hours and 22 minutes
Why are there two solutions for the equation |6 + y| = 2? Explain.
(there should be a solution and an explanation onto why there is two answers)
Answer:
Sample response: The absolute value symbol in the equation indicates two solutions because absolute value is the distance from a number to zero on a number line. Two different directions, to the right and to the left, will determine the
Step-by-step explanation:
The ratio of boys to girls in the lunch room was 4 to 3. If there were 84 students in the cafeteria, how many were girls?
Step-by-step explanation:
9868866858566586575765578
Use Similar triangles to calculate the height, h cm, of traingle ABE
Answer:
24 cm
Step-by-step explanation:
Since the triangles are similar, their dimensions are proportional. The base DC is half the base AE, so we know the ratio of triangle heights is 1 : 2.
Then the bottom height (h) ratio to the overall height is ...
h : 36 = 2 : (1+2) = 2 : 3 = 24 : 36
The height h is 24 cm.
The whole numbers are the set of what numbers and zero ?
Answer:
An integer number is one that can be written without using fractions or decimals, and it is an expression of ( 1.2.3..... ) and 0, and negative numbers (- 1-2-3...... )
Jillian solved the equation v + 4.3 = 7.05 using the work shown below. * v + 4.3 = 7.05 v + 4.3 − 4.3 = 7.05 + 4.3 v = 11.35 What error did Jillian make?
Answer:
Please check explanation
Step-by-step explanation:
Here, in this question, we are interested in identifying the error made by Jillian in his solution of the equation.
This error is traceable to the second step of his solution. Adding 4.3 to 7.05 and subtracting again is the same thing as not adding anything or just adding zero only.
What he should have done is to subtract the value of 4.3 from both sides of the equation. In that manner, he would have been able to isolate v on the left hand side of the equation
Sarah sold 12 boxes of girl scouts cookies. If Sarah sold three times as many boxes as Amiyah, how many boxes did Amiyah sell?
Answer:4
Step-by-step explanation:
What’s the absolute value of -6.5
Answer:
6.5
Step-by-step explanation:
|-6.5| = 6.5
Answer:
6.5
Step-by-step explanation:
Can someone help please
Answer:
[tex]x > \frac{16}{3} [/tex]
Step-by-step explanation:
[tex]4x - 8 > 24 - 2x \\ 4x + 2x > 24 + 8 \\ 6x > 32 \\ x > \frac{16}{3} [/tex]
In the bottom question what does X= to?
Answer:
The value of x is 29°...
When an angle is bisected, it is cut in half. We can assume that m<BAR = m<CAB and we know that m<CAR = m<CAB + m<BAR
88 = 2x - 14 + 2x - 14
Combine like terms
88 = 4x - 28
Add 28 to both sides
116 = 4x
Divide both sides by 4
29 = x
Why is thinking about the problem before you work important?
Answer: It's good to think about things before doing them because it is more thought out and you have a better chance of getting things correct whereas without thinking your most likely going to get it wrong. Without thinking through your options you are basically guessing the answer. I hope this helped you have a great day and god bless you :D
1.6.AP-9
A family is comparing different car seats. One car seat is designed for a child up to and including 25 lb. Another car seat is designed for a child between 16 lb and 35
Ib. A third car seat is designed for a child between 25 lb and 95 lb, inclusive. Model those ranges with compound inequalities. Which car seats are appropriate for a
33-lb child?
The inequality for a child up to and including 25 lb is
(Simplify your answer. Type a compound inequality using x as the variable.)
Answer:
a. i. x ≤ 25 ii. 16 < x < 35 iii. 25 < x ≤ 95
b. The second and third car seats are appropriate for a 35 lb child.
Step-by-step explanation:
a. Model those ranges with compound inequalities
Let x represent the car seat.
i. A car seat designed for a child weighing up to and including 25 lb is described by the inequality.
x ≤ 25
ii. A car seat designed for a child weighing between 16 lb and 35 lb is described by the inequality.
16 < x < 35
iii. A car seat designed for a child weighing between 25 lb and 95 lb inclusive is described by the inequality.
25 < x ≤ 95
b. Which car seats are appropriate for a 33-lb child?
Since 35 lb is included in the range of the inequalities for the second and third card seats, the second and third car seats are appropriate for a 35 lb child.
f(x)=18x+11, find f(5)
Answer:
[tex]\boxed {\tt f(5)=101}[/tex]
Step-by-step explanation:
We are given the function:
[tex]f(x)=18x+11[/tex]
and asked to find f(5). Therefore, we must substitute 5 in for each [tex]x[/tex].
[tex]f(5)=18(5)+11[/tex]
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
Multiply 18 and 5.
[tex]f(5)=90+11[/tex]
Add 90 and 11.
[tex]f(5)=101[/tex]
f(5) is equal to 101.
what would be equivalent to 32 ⋅ 35?
Step-by-step explanation:
35•32 or 1120 there you go
a profit of 9$ integer
Answer:
+ or - $9
Step-by-step explanation:
Mary Ellen has a white oak tree in her backyard.she observed that the tree had grown 2/3 foot in 3/4 year. What is the tree grownth rate in feet year? A.1/2 b.9/9 c1/1.8 d.2
Answer:
in 3/4 year tree had grown 2/3
in 1 year tree had grown (2/3)/0.75 =8/9 feet
Step-by-step explanation:
how do i solve this?
HELP!!Mark the figure to illustrate the givens.(Show work) ~will make brainliest
Refer to the attachment for solution.
In geometry a
is a location. It has no size. It is
represented by a dot.
Points play a crucial role in defining distances, angles, and relationships between different geometric objects, providing a foundation for the study of geometry.
In geometry, a point is a fundamental concept that represents a precise location in space. It is a basic building block from which geometric figures and shapes are constructed. A point has no size, shape, or dimensions. It is often denoted by a dot or a small letter, such as point A (A). Points are used to describe the positions of other geometric elements, such as lines, curves, and polygons. They serve as reference markers and can be connected to form line segments and rays.
To know more about distances here
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Solve for x. 20 points and I give brainliest
Pls provide work. Due in an hour
Answer:
[tex]x=5[/tex]
Step-by-step explanation:
To solve for x, we can use the Exterior Angle Theorem.
The Exterior Angle Theorem states that the exterior angle is equivalent to the sum of the two opposite, interior angles.
So, we can write the following equation:
[tex](6+25x)=(44)+(18x-3)[/tex]
Now, we just have to solve for x.
On the right, let's subtract. So:
[tex]6+25x=18x+41[/tex]
Now, let's subtract 18x from both sides. This gives:
[tex]6+7x=41[/tex]
Now, let's subtract 6 from both sides. This will yield:
[tex]7x=35[/tex]
And, finally, let's divide both sides by 7, giving us:
[tex]x=5[/tex]
And we're done!
We can use the Exterior Angle Theorem.
6 + 25x = 44 + 18x - 3
6 + 25x = 18x + 41
25x = 18x + 35
7x = 35
x = 5
Best of Luck!
x[8x + (-4)x]² - (4)-(-6)x
A line segment has the endpoints P(-7, 6) and Q(-3, 9). Find the coordinates of its
midpoint M
Write the coordinates as decimals or integers.
Answer:
[tex]MP= (-5,7.5 )[/tex]
Step-by-step explanation:
[tex]MP= (\frac{x_1+x_2}{2} )(\frac{y_1+y_2}{2} )[/tex]
[tex]MP= (\frac{-7+-3}{2} )(\frac{6+9}{2} )[/tex] -7+-3= -10 6+9=15
[tex]MP= (\frac{-10}{2} )(\frac{15}{2} )[/tex] -10/2=-5 15/2=7.5
[tex]MP= (-5,7.5)[/tex]
yes I am so certainly brainly right now
What is that supposed to mean
write two inequaltities to compare -5 and -3
-5 < -3 and the second inequality is -3 > -5
5. Solve for x:
| 5x – 4 =16
Answer:
x=4
Step-by-step explanation:
Answer:
x=4
Step-by-step explanation:
Let x= -11/8 and y= -11/4
Which expression has a negative value?
x + y
x — у
х.у
х/y
Answer:
x + y
Step-by-step explanation:
In these examples, a and b are positive numbers.
- a + ( - b) = - (a+ b)
- a - ( - b) = - a + b
- a * - b = a * b
- a / -b = a/b
Hope this helps understanding.
what is 210 divided by 2 1/2
Answer:
210 divided 2 1/2= 84....
The 210 divided by 2 1/2 is 84.
To calculate 210 divided by 2 1/2, first, we need to convert the mixed number 2 1/2 to an improper fraction. The improper fraction for 2 1/2 is (2 * 2 + 1) / 2 = 5/2.
Now, we can perform the division:
210 ÷ 5/2
To divide by a fraction, we multiply by its reciprocal:
210 * 2/5
Now, perform the multiplication:
(210 * 2) / 5 = 420 / 5
Next, simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD), which is 5:
420 ÷ 5 = 84
The result of 210 divided by 2 1/2 is 84. So, 210 ÷ 2 1/2 = 84.
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What equation can Janet use to calculate the principal amount? (and please don't just answer try to solve it someone ripped me off, the last time i asked by just typing)
Answer:
t = [tex]\frac{l}{pr}[/tex]
Step-by-step explanation:
Formula or literal equation used to calculate the simple interest is,
l = prt
where 'l' = Simple interest
p = principle amount invested
r = rate of interest
t = time or duration of the investment
If we have to calculate the time of investment form the given formula,
l = prt
By the division property of equality,
[tex]\frac{l}{pr}=\frac{prt}{pr}[/tex]
[tex]t=\frac{l}{pr}[/tex]
Therefore, formula to be used is, [tex]t=\frac{l}{pr}[/tex]