The area of the white square is 64 square units. The diagonal of the square was extended to point A until the length of segment AB was double the length of the diagonal of the square. What is the area of the gray part?
Answers
Answer:
Area of the gray region = 64 square units
Step-by-step explanation:
Area of the white square = 64 square units
Length of a side of the given square = [tex]\sqrt{\text{Area}}[/tex]
= [tex]\sqrt{64}[/tex]
= 8 units
By Pythagoras theorem,
Length of diagonal DB = [tex]\sqrt{BC^2+CD^2}[/tex]
DB = [tex]\sqrt{8^2+8^2}[/tex]
= [tex]8\sqrt{2}[/tex]
AD = DB = [tex]8\sqrt{2}[/tex] [Given]
OD = OC = [tex]\frac{1}{2}(DB)[/tex]
= 4√2
Therefore, AO = AD + OD = 8√2 + 4√2
= 12√2
Area of ΔACD = Area of ΔAOC - Area of ΔCOD
= [tex]\frac{1}{2}(AO)(OC)-\frac{1}{2}(CO)(OD)[/tex]
= [tex]\frac{1}{2}[(12\sqrt{2}\times 4\sqrt{2})-(4\sqrt{2})^2][/tex]
= [tex]\frac{1}{2}[96-32][/tex]
= 32
Therefore, area of gray part = Area of ΔACD + Area of ΔAED
= 32 + 32
= 64 square units
Answer:
64 square units
Related Questions
Find the perimeter and area of the figure
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Answer:
Step-by-step explanation:
Perimeter = Add
Area= x
Use this solution to figure the area & Perimeter out.
Answer:
perimeter = 76 ft
area = 338 sq ft
Step-by-step explanation:
I need this solved please.
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Answer: 4 quizzes each week
Step-by-step explanation: all you have to do it divide the numbers like 12 divided by 3 would be 4
Just the answers please
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Angle F to angle S
Angle G to angle U
EF is TS
FG is SU
TU is GE
Hope it helps :)
3. What is slope of the line above?
4. What is slope of the line above?
help!
Answers
3.) -1/2
4.) 4/3
Find the total amount in Mr. G’s account, if he invests $9000 for 5 years at a 6% interest rate.
Answers
Answer:
20,000
Step-by-step explanation:
for 5 6% at those with division 20,000 together and they would have 20,000
what is the length of segment SA? show your work please I will give you brainliest
Answers
Answer:
SA=3
Step-by-step explanation:
9/11.7=10/x
9x=117
117/9=13
13-10=3
Answer:
3 ftStep-by-step explanation:
Use ratios:
SB/TB = SA/TC10/9 = SA/2.7SA = 10*2.7/9SA = 3 ftthe triangle Loom is made from wood strips shaped into a 45 45 90 triangle. pegs are placed every half inch along the hypotenuse and every quarter inch along each leg. suppose you make a loom with an 18 inch hypotenuse. approximately how many pegs will you need
Answers
Answer:
36 pegs (for the hypotenuse)
About 51 pegs (for the legs)
138 pegs (total)
Step-by-step explanation:
Along the hypotenuse, the pegs are placed every half-inch. That would make 2 pegs per inch. Multiply 2 x 18 to get 36.
The legs are each 9 sqrt 2. This is 12.7279220614. The pegs are placed at each quarter inch for the legs. This is 4 per inch. So multiply 12.7279220614 x 4 to get 50.9116882454. Round this to 51.
Add 51 + 51 for the legs total pegs. You get 102. Add 102 + 36 to get 138 pegs total.
Hope it helps!
17:3 and 15:60 Equivalent ratios
Answers
Answer:
Step-by-step explanation:
17:3 is already in lowest terms. 17:3 = 34:6, 51:9, etc.
15:60 = 1:4
1. What is the result when 3x2 - 4x + 5 is subtracted
from 3x3 – 13x + 4?
Answers
13.6.4 Quiz: The Quadratic Formula
Which two values of x are roots of the polynomial below?
x²-3x+5
O A. X=3--11
x3
O B. X=-3-17
I c. x= -3+
-3+ VTT
I D. X=
3-√23
Ex=
3+ -11
DEX=
3+29
Answers
Land's Beginning is a company that sells its merchandise through the mail. It is considering buying a list of addresses from a magazine. The magazine claims that at least 25% of its subscribers have high incomes (they define this to be household income in excess of $100,000). Land's Beginning would like to estimate the proportion of high-income people on the list. Checking income is very difficult and expensive but another company offers this service. Land's Beginning will pay to find incomes for an SRS of people on the magazine's list. They would like the margin of error of the 95% confidence interval for the proportion to be 0.05 or less. Use the guessed value p = 0.25 to find the required sample size.
Answers
Solution :
It is given that we use CI = 95%
Therefore, the value of z = 1.96 as the [tex]$P(-1.96 <z<1.96)=0.95$[/tex]
Also, here it is given that E = 0.05 and the value of p = 0.25
Thus from the formula of E, we can find n
[tex]$E= z \times \sqrt{\frac{pq}{n}}[/tex]
[tex]$n= \left(\frac{z}{E}\right)^2 \times p \times q$[/tex]
[tex]$n= \left(\frac{1.96}{0.05}\right)^2 \times 0.25 \times 0.75$[/tex]
= 288.12
= 289
Hello
Can anyone answer this
9+x=190
Answers
Answer:
9+x=190
Step-by-step explanation:
9+181=190
x=190-9
x=181
4.5=2c I need help plz
Answers
Answer:
[tex]c=2.25[/tex]
Step-by-step explanation:
[tex]4.5=2c\\2c=4.5\\c=4.5/2\\c=2.25[/tex]
What is a multiple of 1/7 I need a answer quickly. its due tonight please help
Answers
Answer:
2/7
Step-by-step explanation:
Hope that helps! (Brainliest please!)
Help, please it's due soon?
Answers
9514 1404 393
Answer:
398,765
Step-by-step explanation:
If s represents the number sold to date, the given relation is ...
0.081s = 32300
s = 32300/0.081 ≈ 398,765 . . . . . . divide by the coefficient of s
398,765 copies have been sold to date.
Rowena’s monthly gasoline bill dropped from $83.75 last month to $56.95 this month. Find the percent decrease.
Round your answer to the nearest percent.
Do NOT round until you have calculated the final answer.
Answers
Answer:
The percent decrease was of 32%.
Step-by-step explanation:
The percent decrease is the decrease multiplied by 100, and divided by the initial value.
Rowena’s monthly gasoline bill dropped from $83.75 last month to $56.95 this month.
So a decrease of 83.75 - 56.95 = $26.80
Percent decrease:
26.80*100/83.75 = 32%
The percent decrease was of 32%.
1. Write the standard form of the 6 in the numbel
. *
1 p
792,348,612
Answers
Answer:
600
Step-by-step explanation:
5&---------------------
21 = 7 + 4f what is f
Answers
Answer:
f= 3.5
Step-by-step explanation:
Look at attachment for further explanation
Hope this helps (:
please help me please i really need help please
Answers
Answer:
Step-by-step explanation:
(3x+3y)=63x + -3y = 6
3x + -3y = 6
3x + -3y + 3y = 6 + 3y
3x + 0 = 6 + 3y
3x = 6 + 3y
x = 2 + y
x = 2 + y
1) f(x)=2x+5
What is -2 [f(x)]-1?
Answers
Answer:
-4x - 11
Step-by-step explanation:
-2[f(x)] - 1
= -2[2x + 5] - 1
= -4x - 10 - 1
= -4x - 11
Quince menos que un numero
Answers
Answer:
14 xd xd xd
Step-by-step explanation:
xd xd xd
Answer:
fifteen less than a number.
The population of a school is 800 students and is increasing at a rate of 3% per year. How many students will be there in 6 years?
Answers
At a constant rate of 3% year over year their would be 955 students after 6 years
Through (4,-4) parallel to y=3
Answers
y = -4
Explanation:
The graph of y = 3 is horizontal.
The slope must be 0 for a line to be horizontal, and thus parallel to y=3.
In slope-intercept form (y = mx + b), “m” is the slope, “b” is the y-intercept.
When the slope, m = 0, the equation becomes y = b.
Point (4,-4) is written (x, y).
y = -4
Since y = b, b = -4.
Therefore, the equation is y = -4.
Answer:
y = -4
Step-by-step explanation:
Because y = b, b = -4, the equation would be written as y = -4.
(a) Write the ratio 32 : 80 in its simplest form
Answers
Answer:
Therefore, 32/80 simplified to lowest terms is 2/5.
A fair dice has six sides, numbered 1 to 6
After it is rolled, five of the numbers can be seen.
a) Write down the probability that one of these five numbers is 3
b) Work out the least possible sum of the five numbers
Answers
(a). The probability that one of these five numbers is 3 is [tex]\frac{5}{6}[/tex].
(b). The least possible sum of the five numbers is 15
Probability:Probability is the ratio of number of favourable outcomes to the total number of outcomes.
When a fair dice has six sides, numbered 1 to 6 ,After it is rolled, five of the numbers can be seen.
The probability that one of these five numbers is 3 is computed as,
[tex]P(E)=\frac{5}{6}[/tex]
The least possible sum of the five numbers, when the number 6 is hidden.
Least sum = 1 + 2 + 3 + 4 + 5 = 15
Learn more about the probability here:
https://brainly.com/question/24756209
6. Red carpet tiles need to go on the dance floor for the
valentine's dance. The floor has a length of 9m and a width
of 8m. What is the area of the dance floor?
7. Use information from Q6 above
Each tile is 25cm by 25cm.
How many tiles do you need for the dance floor?
Answers
Answer:
6. 72 m²
7. 1152 tiles
Step-by-step explanation:
6. Determination of the area of the dance floor.
Length (L) = 9 m
Width (W) = 8 m
Area (A) =?
Area of the floor (rectangle) = L × W
A = 9 × 8
A = 72 m²
Therefore, the area of the dance floor is 72 m²
7. Determination of the number of tiles needed for the dance floor.
We'll begin by converting the dimension of the tile to metre (m). This can be obtained as follow:
100 cm = 1 m
Therefore,
25 cm = 25 cm × 1 m / 100 cm
25 cm = 0.25 m
Thus, the dimension of the tile is 0.25 m by 0.25 m
Next, we shall determine the area of the tile. This can be obtained as follow:
Dimension of tile = 0.25 m by 0.25 m
Area of tile = 0.25 × 0.25
Area of tile = 0.0625 m²
Finally, we shall determine the number of tile needed. This can be obtained as follow:
Area of the floor (Aₔ) = 72 m²
Area of tile (Aₜ) = 0.0625 m²
Number of tile (n) =?
n = Aₔ / Aₜ
n = 72 / 0.0625
n = 1152 tiles
Therefore, the number of tiles needed for the dance floor is 1152 tiles
which expression is equivalent to 5* 5 * 5?
Answers
Answer:
three one
Step-by-step explanation:
5*5*5
Help person right gets brainlist
Answers
brainliest?
If its mixed number
P=3.60714285
If its need to be decimal
Just copy the answer from the pic
Why doesn't the SSA triplet guarantee triangle congruence?
Answers
Answer: Because Knowing only side-side-angle (SSA) does not work because the unknown side could be located in two different places. Knowing only angle-angle-angle (AAA) does not work because it can produce similar but not congruent triangles.The AS.S Postulate does not exist because an angle and two sides does not guarantee that two triangles are congruent. If two triangles have two congruent sides and a congruent non included angle, then triangles are NOT NECESSARILY congruent. And The SSA (or AS.S) combination deals with two sides and the non-included angle. This combination is humorously referred to as the "Donkey Theorem". SS.A (or AS.S) is NOT a universal method to prove triangles congruent since it cannot guarantee that the shapes of the triangles formed will always be the same.
Step-by-step explanation:
hope this helps have a great night ❤️❤️❤️❤️
ILL GIVE BRAINLIEST! PLEASE ANSWER IF YOU SEE THIS!!! David has a container filled with quarters and nickels. He has 29 coins which add up to $5.85. How many quarters does he have?
Answers
Answer:
23 of the coins will be quarters
Step-by-step explanation: