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 (has four sides and four angles) in which all the sides are equal. Also all the angle of a square are equal and measure 90°. The diagonals of a square are equal.
In square ABCD:
AB = BC = CD = AC
Given that P, Q are the midpoints of BC, CD respectively. If AP = a and AQ = b.
a) In triangle ABP:
BC = AB (all sides of a triangle are equal)
BP = 1/2 (BC) = 1/2(AB) = 0.5AB
Using Pythagoras theorem:
AB² + BP² = AP²
substituting:
AB² + (0.5AB)² = a²
AB² + 0.25AB² = a²
1.25AB² = a²
AB² = a² / 1.25
AB² = 0.8a²
AB = √(0.8a²)
AB = a√0.8
b) In triangle ADQ:
AD = CD (all sides of a triangle are equal)
DQ = 1/2 (CD) = 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 = b² / 1.25
AD² = 0.8b²
AD = √(0.8b²)
AD = b√0.8
c) In triangle ABD, Using Pythagoras theorem:
AB² + AD² = BD²
Substituting:
0.8a² + 0.8b² = BD²
But AB = AD (all sides of a triangle are equal). Hence AB = AD = 0.8a² = 0.8b²
BD = √(0.8a² + 0.8b²)
BD = √(1.6a²) 0.8a² = 0.8b²
BD = a√1.6
D) AC = AD (diagonal are equal)
AC = √(0.8a² + 0.8b²)
AC = √(1.6b²) 0.8a² = 0.8b²
AC = b√1.6
Related Questions
If the cost of 10 tables is $750. Find the number of tables that can be purchased with $8250.
Answers
Team A scored the following points per game 20,17,25,25,13,25,12,25,25 and 23 team B scored the following points per game 25,25,9,10,25,11,25,15,10 and 25 what is the mean of team A and team B
Answers
Answer:
Mean of team A = 21
Mean of team B = 18
Step-by-step explanation:
Formula:
Mean = Sum of values / Number of values
Calculations:
[tex]A = \frac{20+17+25+25+13+25+12+25+25+23}{10} = \frac{210}{10} = 21[/tex]
[tex]B = \frac{25+25+9+10+25+11+25+15+10+25}{10} =\frac{180}{10} =18[/tex]
Mean of team A = 21
Mean of team B = 18
Plsss help I suck at math and I’m sure one of you are super smart ♀️
Answers
Answer:
3
Step-by-step explanation:
-14x - 7 + 5y - x = -14x - x - 7 + 5y
= -15x - 7 + 5y
Answer:
Step-by-step explanation:
3
A scientist wants to measure out .62liters of a liquid, but she can only find a beaker that measures volume in milliliters. How many milliliters should she measure to equal .62liters?
Answers
Answer:
620 milliliters
Step-by-step explanation:
1 milliliter= 0.001 liters
0.62L= move the decimal point 3 places to the left
0.62
06.2
062.
0620.
620 milliliters
What is the purpose of having like terms on each side
of the equation?
Answers
Answer:
A frequently-used procedure in algebra is the process of combining like terms. This is a way to "clean-up" an equation and make it much easier to solve. In case you've forgotten, a term is each single part of an expression. For example, in the expression 4x+3+7y 4 x + 3 + 7 y , there are three terms: 4x , 3 , and 7y .
How do I do 2 and 3
Answers
Answer:
y=52
x=46
questions 3
x=84
y=84
Step-by-step explanation:
Answer:
#2: x = 64 y = 32[tex]\sqrt{3}[/tex]
#3: x = 6[tex]\sqrt{2}[/tex] y = 6[tex]\sqrt{2}[/tex]
Or, if you are supposed to write your answers in decimal form instead:
#2: x = 64 y = 55.43
#3: x = 8.49 y = 8.49
Step-by-step explanation:
Special right triangles have specific angle measurements that tell you the lengths of each side. I attached an image that explains the rules of different special right triangles in case you need it :)
#2 is a 30-60-90 triangle. This means that x (the side opposite the 90° angle) is two times the length of the shortest side (32×2), and y is equal to 32[tex]\sqrt{3}[/tex].
#3 is a 45-45-90 triangle. This means that x (the side opposite the 45° angle) is equal to y (the side opposite the other 45° angle). The hypotenuse, 12, is x[tex]\sqrt{2}[/tex] (or y[tex]\sqrt{2}[/tex], since x = y). This means 12 = x[tex]\sqrt{2}[/tex]
If m∠4 = 101.9°, find each of the following in degrees.
(a) m∠5
(b) m∠8
Answers
Answer:
m<5=101.9 m<8=101.9
Step-by-step explanation:
alternate interior and vertical angles
Answer:
(a) m∠5=<4[alternate angle]=101.9°,
(b) m∠8=<5[vertically opposite angle]=101.9°,
I have a big question what is 720 x 0.1
Answers
Answer:
72
Step-by-step explanation:
Answer:
72
Step-by-step explanation:
I hope this helps :)
s - k + x; when s = 7, k = 4, x = 6
what does this mean someone help quick
Answers
Answer:
you just plug in those numbers... 7-4+6 = 9
f(x) = x? – x3
Select the value of f(-2)
4
-12
12
A
B
C D
Answers
Step-by-step explanation:
f(x) = x² - x³
f(-2) = (-2)² - (-2)³
= 4 - (-8)
= 4 + 8 = 12
3.) The ratio of dogs to cats at the animal shelter is 4:1. If there are a total of 85 dogs and cats
at the shelter, how many dogs are at the shelter?
Answers
Answer:
Step-by-step explanation:
The ratio of dogs to cats is
quantities relative to each other. There are two cats and one dog. This means there are twice as many cats as dogs, or half as many dogs as cats.
...
Equivalence.
cats : dogs
8 : 4
Answer:
d
Step-by-step explanation:
yes
If 11 times a number is added to twice the number, the result is 78.
Answers
Answer:
x = 6
Step-by-step explanation:
if you guess what 81 ➗ 918 =
ill give brainiest
Answers
Answer:
918 ➗ 81
Step-by-step explanation:
Answer:
It's about 0.088.
If y= cx" and dy/dx =
4/root x
what are the values of c and n?
Answers
Answer:
c = 8
n = 1/2
Step-by-step explanation:
Since dy/dx is the derivative form, we can integrate the answer to get the value of y.
The values of c and n are obtained by forming the equations as 1/2 and 8 respectively.
What is differentiation?The differentiation of a function is defined as rate of change of its value at a point. It can be written as f'(x) = (f(x + h) - f(x)) /(x + h - x).
It can be stated in terms of geometry as the slope of tangent of the function at a given point.
It is given as y = cxⁿ and dy/dx = 4/√x.
Take the derivative of y = cxⁿ with respect to x as,
dy/dx = cd(xⁿ)/dx
⇒ nc × xⁿ⁻¹
Compare the obtained derivative with 4/√x to obtain,
nc = 4 and n - 1 = -1/2
⇒ n = 1/2 and c = 8
Hence, the values of c and n are 1/2 and 8 respectively.
To know more about differentiation click on,
https://brainly.com/question/24898810
#SPJ2
factor the expression-15x +39
Answers
Answer:
3(5−13)
Step-by-step explanation:
..............
Answer:
-3(5x-13)
Step-by-step explanation:
The greatest common factor is 3 and you want the # with the variable to be positive, usually, so just factor -3 out and that's what you get.
If 210 people said football was their favorite sport to watch, how many people were surveyed? 42% said football.
Answers
Answer:
500 people surveyed
Step-by-step explanation:
210 / 42 = 5
5 x 100 = 500
Answer:
500 people were surveyed
Step-by-step explanation:
Let the total number of people surveyed be x
42% said football was their favorite sport to watch
=> 42/100 x = 210
=> x = (210 × 100) / 42
=> x = 21000 / 42
=> x = 500
Therefore, 500 people were surveyed.
Hope it helps :)
Please mark my answer as the brainliest
Jack is going to make treat bags to hand out on
Halloween. He is going to put a variety of candy in each
bag. To make 4 treat bags he will need 24 candies. How
many candies will he need to make 10 treat bags?
Answers
Answer:
60 candies
Step-by-step explanation:
Explanation:
Since there are 24 candies for 4 treat bags, you divide the amount of candies into the 4 bags. This gives you 6 candies per bag. Multiply 6 by 10(number of treat bags) to get 60.;)
Find the missing side. Round
to the nearest tenth.
Х
141
43°
у
X=[?]
Answers
Answer:
x = 206.7
Step-by-step explanation:
law of sines:
sin 90° / x = sin 43° / 141
sin 43° · x = 141
x = 141 / sin 43°
The measure of the length of the hypotenuse is 206.75 and the measure of the length of the base is 151.20 units.
What is a right-angle triangle?It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.
The perpendicular is 141 and the angle opposite to the perpendicular is 43 degrees. Then the value of the base and hypotenuse will be
The length of the base will be
[tex]\rm \dfrac{141}{y} = \tan 43^o\\\\y\ \ \ = \dfrac{141}{ \tan 43^o}\\\\y \ \ \ = 151.20[/tex]
Then the length of the hypotenuse will be
[tex]\rm x = \dfrac{141}{\sin 43^o}\\\\x = 206.75[/tex]
More about the right-angle triangle link is given below.
https://brainly.com/question/3770177
#SPJ2
Please write these in a fraction form, thank you have an AMAZING day!
1. 2/5 ÷ 1/3= ?
2. 3/4 ÷ 1/2= ?
Answers
Answer:
1 = 1 1/5
2=1 1/2
Step-by-step explanation:
The model below is shaded to represent 7 3/10
Answers
Answer:
blue 7.3
Step-by-step explanation:
Answer:
7.3
Step-by-step explanation:
There are 7 groups with 10 parts in each, 7 complete rows are filled in. 3 are left in the last row. This means that there are 7 wholes with 3 left over. 7.3
If the turning point is lower than the nearby point it's called a
Answers
Answer:
Step-by-step explanation:
Local minimum. It would be the minimum value of the function not including the end points. If you are including the end points, its an absolute minimum
Find the y intercept and x intercept of the line below.
Answers
Y intercept is -2
Hope this helps
HELP HELPOPPPP-EWOPW0E HELP PLSSSSS
Answers
Answer:
6 more girls than boys
Step-by-step explanation:
5 out of 12 are boys (multiply both sides of equation by 3 because 3x12 = 36)
7 out of 12 are girls (multiply both sides of equation by 3 because 3x12 = 36)
so: 15 out of 36 are boys
so: 21 out of 36 are girls
21-15 = 6 more girls than boys
Answer: There are 6 more girls than boys
Step-by-step explanation:
To find how many more girls there are we need to find what one block equals to.
We use this equation to find it.
36 = ( 5 + 7 )x
36 = 12x
3 = x
or
x = 3 (same thing)
So each block represents 3 girls/boys
The girls have 2 more meaning there are 6 more girls than boys.
I don’t know what to do please help
Answers
Answer:
d i think can u give me a bainliest
Step-by-step explanation:
What is 2(x -3) in simplest form?
Answers
Answer:
2x-6 is the right answer
Step-by-step explanation:
I'm very good at math
Research has shown that approximately 1 woman in 600 carries a mutation of a particular gene. About66 % of women with this mutation develop cancer. Find the probability that a randomly selected woman will carry the mutation of this gene and will develop cancer.
Answers
Answer:
add otherwise I don't know sorry im on that question
Step-by-step explanation:
Which side lengths form a right triangle?
Choose all answers that apply:
A
3.4.5
B
7.8.9
3.9.95
Answers
Answer:
A. 3.4.5
Step-by-step explanation:
I looked it up and it forms a right angle.
Can anyone help me pweeezzzz
Answers
Answer:
17
Step-by-step explanation:
ABC, which is 9z - 1, and CBD, which is 6z + 58, make up ABD, which is a total of 87 degrees.
in order to find the measurement of ABC, you first need to solve for z.
since ABC and CBD make up ABD, add those measurements and set them equal to 87, which is the measure of ABD.
9z - 1 + 6z + 58 = 87
combine like terms starting with the z terms. (it doesn't matter which like terms you combine first)
9z - 1 + 6z + 58 = 87 ⇒ 15z - 1 + 58 = 87
combine the next set of like terms.
15z - 1 + 58 = 87 ⇒ 15z + 57 = 87
subtract 57 from both sides of the equation. it'll cancel itself out on the left, leaving you with 15z = 30 after subtracting 57 from 87.
divide both sides of the equation by 15.
15z/15 = 30/15 ⇒ z = 2
now, plug in 2 for z in each of your equations for the measurements of ABC and CBD.
ABC = 9z - 1 ⇒ 9(2) - 1 ⇒ 18 - 1 ⇒ 17
CBD = 6z + 58 ⇒ 6(2) + 58 ⇒ 12 + 58 ⇒ 70
now, your measurements are
ABD: 87
ABC: 17
CBD: 70
check your work by adding the measurements of ABC and CBD and setting them equal to ABD, or 87.
17 + 70 = 87
87 = 87
since both sides of the equation are equal to 87, you know that your measurements are correct.
therefore, the measure of ABC is 17 degrees.
find the product (a + 3)(a - 2)
Answers
Answer:
a2 + a − 6
Step-by-step explanation:
the a with the 2 beside of it is to the power of
PLEASE PLEASE HELP ASAP 30 POINTS AND WILL GIVE BRAINIEST
what is the measure of angle ABC
What is the measure of angle CBE
what is the measure of angle DBE
What is the measure of angle ABD
Answers
Answer:
hope this is what u want
and don't mind my handwriting I wrote it as fast as I could