2. ABCD is a square and P, Q are the midpoints of BC,CD respectively. If AP = a
and AQ = b. find in terms of a and b the directed line segments (i) AB (ii) AD
(iii) BD and (iv) AC.
Answers
Answer:
The answer is below
Step-by-step explanation:
A square is a quadrilateral (four sides and angles). All the sides and angles of a square are equal. Each angle of a square is 90° and the diagonals are equal.
In square ABCD:
AB = BC = CD = AC (all the sides of a square are equal)
Given that P is the midpoint of BC and Q is the midpoint of CD. AP = a and AQ = b.
a) Triangle APB is a right angled triangle:
BC = AB (all sides of a triangle are equal)
PB = 1/2 (BC) = 1/2(AB) = 0.5AB
Using Pythagoras theorem:
AB² + PB² = AP²
substituting:
AB² + (0.5AB)² = a²
AB² + 0.25AB² = a²
1.25AB² = a²
AB² = 0.8a²
AB = a√0.8
b) Triangle AQD is a right angled triangle:
AD = DC (all sides of a triangle are equal)
DQ = 1/2 (DC) = 1/2(AD) = 0.5AD
Using Pythagoras theorem:
AD² + DQ² = AQ²
substituting:
AD² + (0.5AD)² = b²
AD² + 0.25AD² = b²
1.25AD² = b²
AD² = 0.8b²
AD = b√0.8
c) In right triangle ADB, Using Pythagoras theorem:
AB² + AD² = BD²
But AB = AD
Substituting:
0.8a² + 0.8b² = BD²
BD = √(0.8a² + 0.8b²)
But AD = AB, hence 0.8a² = 0.8b²
BD = √(1.6a²)
BD = a√1.6
D) AC = AD (diagonals of a square are equal)
AC = √(0.8a² + 0.8b²)
AC = √(1.6b²) = b√1.6
Related Questions
The value of 2^0 ??
Answers
Answer:
1
Step-by-step explanation:
. It is read as 2 raised to zero. Now let see how to solve such problem For example 3^5 then it means 3×3×3×3×3 = 243 Now back to question Anything raised to zero is always 1 Hence 2^0= 1
Find the area of the circle. Use 3.14 for pi.
Question 1 options:
113.04 in2
56.52 in2
256.34 in2
1017.36 in2
Answers
Answer:
The answer is 254.34 in².
Step-by-step explanation:
Given that the diameter is 2 times the radius. So the radius will be 9 in. Next, you have to find the area of circle, A = π × r² :
A = π × r²
Let π = 3.14, r = 9,
A = 3.14 × 9²
A = 254.34 in²
One-seventh of a number, increased by twelve
Answers
Answer:
one seventh of 14 increased by 12 is 14
Step-by-step explanation:
so my example will use 14, so one seventh of 14 is 14 divided by 7 which is 2 then you just add 12 to 2 which gets you 14
An expression is defined as a set of numbers, variables, and mathematical operations. The given statement "One-seventh of a number, increased by twelve" is written as (x/7)+12.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given statement "One-seventh of a number, increased by twelve" can be written in the form of an expression as shown below.
One-seventh of a number → x × (1/7) = x/7One-seventh of a number, increased by twelve→ x/7 + 12Hence, The given statement "One-seventh of a number, increased by twelve" is written as (x/7)+12.
Learn more about Expression here:
https://brainly.com/question/13947055
#SPJ2
Write an expression equivalent to the one below
-2m-8+4(3m-9)
Answers
Answer:
Step-by-step explanation:
Distribute the 4 into the parentheses.
[tex]-2m-8+12m-36[/tex]
Combine like terms
[tex]10m-44[/tex]
Answer:
10m - 44
Step-by-step explanation:
Apply the distributed property: 12m - 36Re-write expression: -2m - 8 + 12m - 36-2m + 12m = 10m8 + 36 = 44Put them together: 10m - 44I hope this helps!
Select the correct answer.
What is the LCM of the numbers 3, 6, and 9?
A.
9
B.
18
C.
36
D.
54
Answers
Answer:
D
Because you have to find out what they could all equal up to
Answer:
d
Step-by-step explanation:
The circumference of a circle measures 11.277 ft.
What is the measure of the diameter of this circle?
Answers
Answer:
3.590ft
Step-by-step explanation:
We know what the circumference of the circle is, and we need to find its diameter. Therefore, we need to find an equation that links the two together.
Well, what comes to mind is the fact that the circumeference, [tex]c[/tex], is equal to [tex]\pi[/tex] multiplied by the diameter, [tex]d[/tex]. We can express this like so:
[tex]c = \pi d[/tex].
In this scenario, we know what [tex]c[/tex] is, so we need to rearrange the formula to make [tex]d[/tex] the subject. Dividing both sides by [tex]\pi[/tex] will accomplish this, and gives us:
[tex]\frac{c}{\pi} = d[/tex].
So if we divide the circumference by [tex]\pi[/tex], we will find the diamater. Well,
[tex]\frac{11.277}{\pi} = 3.58958...[/tex]
and so to 3 decimal places we get the answer
[tex]d = 3.590\text{ft}[/tex].
WILL GIVE BRAINLIEST GIVE CORRECT ANSWER
Answers
Answer:
everything u chose is right
Step-by-step explanation:
50 = 20 + 4h
-20. -20
30/4= 4h/4
7.5 = h
So 50 = 20 + 4(7.5)
50 = 30 + 20
50 = 50
Julie bought 12
packages of cucumber seeds. Each bag contains 42
seeds. If she plants half of the seeds, how many of the
seeds does she have left?
Answers
Answer:
12x42=504
504/2=252
252
Step-by-step explanation:
Please complete this question, the question is saying: write the correct integer in the blank
Is due please. I will give brainlest
Answers
Simplify completely
[tex] \frac{2x - 24}{8} [/tex]
A)
[tex] \frac{x - 24}{4} [/tex]
[tex] \frac{x - 12}{4} [/tex]
C) 2x-3
D) x-3
Answers
Answer: A) x-24/4
can someone please help me with this math problem thank you.
Answers
B). 5 (I think)
A garden table and a bench cost $903 combined. The garden table costs $53 more than the bench. What is the cost of the bench?
Answers
2x=850 divide by two
x=425
bench - $425
If f(x) = 9x-8, which of the following is the inverse of f(x)?
O A. f'(x) = *19
O B. f'(x) = x;
O c. f-'(x) = 48
X-9
O D. f-1(x) =
8
Answers
y = 9x+8
x = 8y + 9
x-9 = 8y
x-9
----- = y
8
f-¹ =
x-9
------
8
find the sample standard deviation
Answers
Answer:
Step 1: Calculate the mean of the data—this is xˉx, with, \bar, on top in the formula.
Step 2: Subtract the mean from each data point. ...
Step 3: Square each deviation to make it positive.
Step 4: Add the squared deviations together.
Step 5: Divide the sum by one less than the number of data points in the sample.
Step-by-step explanation:
Select the algebraic expression for the word expression.
24 less than h
24 - h
24 - h
h - 24
h - 24
24 ÷ h
24 ÷ h
h
Answers
Step-by-step explanation:
The Answer Is 24 - h
As, 24 Is Less Than "h"
What is the common ratio of 7, -14, 28, -56
Answers
Answer:
multiplied by -2 I believe
Step-by-step explanation:
Find the cos of angle T....
Answers
Answer:
C = 24/25
Step-by-step explanation:
Recall, CAH.
Thus:
Cos T = adjacent/hypotenuse
Reference angle = T
Adjacent = 24
Hypotenuse = 25
Therefore,
Cos T = 24/25
A submarine was situated 832 feet below sea level. If it descends 289 feet, what is its new position?
Answers
It's new position is 1121 feet below sea level.
(In this problem u are descending into a negative value so it made sense for me to add for some reason).
Hope this helps and have a good day.
Also, as proof I included my calculator showing the logic behind it. Sorry for bad Camera quality.
-R3TR0 Z3R0
13 as prime or composite
Answers
Answer:
prime
gggghfsssddfdfv ut b dc t
Answer:
the number 13 is a prime number
You bought some stock, and then the stock price went down by 17.2% from the purchase price. By what percentage would the price have to increase for the investment to be back to the original value?
Answers
Step-by-step explanation:
Let's pick some easy numbers for illustration.
Let x equal our initial stock purchase, and, say it was $100.
x = $100
The problem says it's value dropped by 17.2%. If x = 100 is 100% of our stock value the 17.2% less is
[tex]x - 0.172x = 0.828x[/tex]
So now our stock is worth 0.828(100) = $82.80.
Now how much of an increase do we need to get back to $100.
[tex]100 - 82.80 = 17.20[/tex]
So our base is $82.80 because our stock price dropped, we want to know what percent increase is $17.20 of $82.80
[tex]17.20 \div 82.80 = 0.2077[/tex]
Or 20.77% increase to get back to original price.
To make this generic, since $100 is not supplied information, substitute x for 100 and 0.828x for the amount of money dropped.
x = original stock value
[tex]x - 0.828x [/tex]
Is the amount of value lost, and to be regained in the second part of the question.
To find out what portion the decrease is of the new value
[tex] \frac{(x - 0.828x)}{0.828x} = \frac{0.172x}{0.828x} = 0.2077 [/tex]
Or 20.77%
-3m + 5>26
How to answer this question
Answers
9514 1404 393
Answer:
m < -7
Step-by-step explanation:
Maybe you want to find the value of m.
Subtract 5, then divide by -3.
-3m +5 > 26 . . . given
-3m > 21 . . . . . . subtract 5 from both sides
m < -7 . . . . . . . . divide by -3. Dividing by a negative number reverses the inequality.
VERY QUICK HELP!!!! A toy pyramid has the dimensions shown below. The base of the pyramid is an equilateral triangle. What is the surface area of this pyramid?
Answers
Answer: 102cm²
Step-by-step explanation:
Area of base = 6 × 7 ÷ 2 = 21
Area of lateral face = 6 × 9 ÷ 2 = 27
Since all of the sides of the base are equal, we can multiply the area of 1 lateral face by 3 to get the area of all the lateral faces.
27 × 3 = 81.
Now we add up the area of the base and the lateral faces.
21 + 81 = 102cm²
I am not a professional, simply using prior knowledge!
Note- It would mean the world to me if you could mark me brainliest!
The enrollment of students in evening classes at a local university decreased by 6% between two recent years. If the total number of students attending evening classes in both years was 13,925 , find how many students enrolled in evening classes in each of the years.
Answers
Answer:
First year: 13925; Second year: 13090
If our school has about 300 seventh graders, about how many would be expect to watch 4 to
8 hours of television weekly?
A. 55
B. 116
C. 138
D. 165
Answers
Answer:
55
Step-by-step explanation:
a. How many 1/3s are in 2 2/3?
Answers
Answer:
1 2/3 = (1•3+2)/3 = 5/3. Therefore, 5/3 ÷ 1/3. = 5.
Step-by-step explanation:
So the answer is 5.
Please answer these in a fraction form. Thank you have an AMAZING day!
1. 2/5 ÷ 3 1/10 = ?
2. 4 1/3 ÷ 4/7 = ?
3. 3 1/6 ÷ 9/10 = ?
4. 5/8 ÷ 2 7/12= ?
Answers
Answer:
use Photomath app to answer your question.
Please help me i am taking a test and i really need help
Answers
Answer:
31.4159in
Step-by-step explanation:
Answer:
31.4
Step-by-step explanation:
A prize was awarded to 24 women and 1010 men.
a. What fraction of the prize winners were women?
b. What fraction were men?
Answers
Answer:
[tex]W = \frac{12}{17}[/tex] -- Women
[tex]M = \frac{5}{17}[/tex] --- Men
Step-by-step explanation:
Given
[tex]Men = 10[/tex] --- not 1010
[tex]Women = 24[/tex]
Solving (a) Fraction of Women
This is calculated as:
[tex]W = \frac{Women}{Men + Women}[/tex]
Substitute values for Women and Men
[tex]W = \frac{24}{10+24}[/tex]
[tex]W = \frac{24}{34}[/tex]
Simplify fraction
[tex]W = \frac{12}{17}[/tex]
Solving (b) Fraction of Men
This is calculated as:
[tex]M = \frac{Men}{Men + Women}[/tex]
Substitute values for Women and Men
[tex]M = \frac{10}{10+24}[/tex]
[tex]M = \frac{10}{34}[/tex]
Simplify fraction
[tex]M = \frac{5}{17}[/tex]
Forty percent of all high school graduate work during the summer to earn money for college tuition for the upcoming fall term. Assuming a binomial distribution, if 6 graduates are selected at random, what is the probability that none of the graduates have a summer job
Answers
Answer:
[tex]0.0467[/tex] is the probability that none of the graduates have a summer job
Step-by-step explanation:
Here
P [tex]= 0.40[/tex] and n [tex]= 6[/tex]
Probability that none of the graduate gets job
this means that x = 0
P (x = 0) [tex]= ^6C_0 * (0.40)^0 * (0.60)^6[/tex]
P (x = 0) [tex]= 0.0467[/tex]
helppp!! For the given solid figure, find the value of the variable.
Answers
9514 1404 393
Answer:
10 cm
Step-by-step explanation:
The diameter of the cylinder is 6 cm, so the length designated 'c' is the hypotenuse of a right triangle with legs 6 cm and 8 cm.
The Pythagorean theorem tells you the hypotenuse is ...
c^2 = (6 cm)^2 + (8 cm)^2 = 100 cm^2
c = √(100 cm^2) = 10 cm
The value of c is 10 cm.
_____
You may recognize these numbers as double those of a 3-4-5 right triangle.