Answers
Answer:
The area of the shaded region is 11.606 square centimeters.
Step-by-step explanation:
The area of the shaded region is obtained by subtracting the area of the triangle from the area of the circular section. The area of the triangle ([tex]A_{t}[/tex]), in square centimeters, can be calculated by the Heron's formula:
[tex]A_{t} = \sqrt{s\cdot (s-a)\cdot (s-b)\cdot (s-c)}[/tex] (1)
[tex]s = \frac{a + b + c}{2}[/tex] (2)
Where:
[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Lengths of the sides of the triangle, in centimeters.
[tex]s[/tex] - Semiperimeter, in centimeters.
If we know that [tex]a = 10.50\,cm[/tex] and [tex]b = c = 9.28\,cm[/tex], then the area of the triangle is:
[tex]s = \frac{10.50\,cm + 2\cdot (9.28\,cm)}{2}[/tex]
[tex]s = 14.53\,cm[/tex]
[tex]A_{t} = \sqrt{(14.53\,cm)\cdot (14.53\,cm - 10.50\,cm)\cdot (14.53\,cm - 9.28\,cm)^{2}}[/tex]
[tex]A_{t} \approx 40.174\,cm^{2}[/tex]
And the area of the circular section ([tex]A_{c}[/tex]), in square centimeters, is determined by the following formula:
[tex]A_{c} = \left(\frac{\theta\cdot \pi}{360} \right)\cdot r^{2}[/tex] (3)
Where:
[tex]r[/tex] - Radius of the circle, in centimeters.
[tex]\theta[/tex] - Internal angle, in sexagesimal degrees.
If we know that [tex]r = 9.28\,cm[/tex] and [tex]\theta = 68.9^{\circ}[/tex], then the area of the circular section is:
[tex]A_{c} = \left(\frac{68.9}{360}\right)\cdot \pi\cdot (9.28\,cm)^{2}[/tex]
[tex]A_{c} \approx 51.780\,cm^{2}[/tex]
Finally, the area of the shaded region ([tex]A[/tex]), in square centimeters, is:
[tex]A = A_{c} - A_{t}[/tex] (4)
[tex]A = 51.780\,cm^{2}- 40.174\,cm^{2}[/tex]
[tex]A = 11.606\,cm^{2}[/tex]
The area of the shaded region is 11.606 square centimeters.
Related Questions
please help i’ll give brainliest!!! thanks
Answers
Find the zeros of the function.
Enter the solutions from least to greatest.
g(x) = 4x^2 – 484
lesser x =
greater x =
Answers
Answer:
11 and -11
Step-by-step explanation:
Mr. Wallace gives the cashier $120 to purchase 4 dress shirts. The cashier gives him
$11.84 in change. If each shirt costs the same amount, what is the cost in dollars and
cents for each dress shirt?
Answers
Answer:
27.04 per dress
Step-by-step explanation:
120 - 11.84 = 108.16
108.16 ÷ 4 = 27.04
A high school soccer team is going to Columbus to see a professional soccer game. A coordinate grid is superimposed on a highway map of Ohio. The high school is at point (3, 4) and the stadium in Columbus is at point (7, 1). The map shows a highway rest stop halfway between the cities. What are the coordinates of the rest stop? What is the approximate distance between the high school and the stadium? (One unit = 6.4 miles.)
Answers
Answer:
a) The coordinates of the rest stop is [tex]C(x,y) = \left(5, \frac{5}{2} \right)[/tex].
b) The approximate distance between the high school and the stadium is 32 miles.
Step-by-step explanation:
a) The rest stop is located in the midpoint of the line segment between the high school and the stadium. Vectorially speaking, we use the following formula:
[tex]C(x,y) = \frac{1}{2}\cdot A(x,y) + \frac{1}{2}\cdot B(x,y)[/tex] (1)
Where:
[tex]A(x,y)[/tex] - Coordinates of the high school.
[tex]B(x,y)[/tex] - Coordinates of the stadium.
[tex]C(x,y)[/tex] - Coordinates of the rest stop.
If we know that [tex]A(x,y) = (3, 4)[/tex] and [tex]B(x,y) = (7,1)[/tex], then the coordinates of the rest stop are, respectively:
[tex]C(x,y) = \frac{1}{2}\cdot (3, 4) + \frac{1}{2}\cdot (7, 1)[/tex]
[tex]C(x,y) = \left(\frac{3}{2}, 2 \right) + \left(\frac{7}{2}, \frac{1}{2} \right)[/tex]
[tex]C(x,y) = \left(5, \frac{5}{2} \right)[/tex]
The coordinates of the rest stop is [tex]C(x,y) = \left(5, \frac{5}{2} \right)[/tex].
b) The approximate distance between the high school and the stadium ([tex]d[/tex]), in miles, is the product of the Length Equation of the Line Segment and the scale factor:
[tex]d = r\cdot \sqrt{(\Delta x)^{2} + (\Delta y)^{2}}[/tex] (2)
Where:
[tex]r[/tex] - Scale factor, in miles.
[tex]\Delta x[/tex], [tex]\Delta y[/tex] - Horizontal and vertical distances between the high school and the stadium, no unit.
If we know that [tex]r = 6.4\,mi[/tex], [tex]\Delta x = 4[/tex] and [tex]\Delta y = -3[/tex], then the distance between the high school and the stadium is:
[tex]d = r\cdot \sqrt{(\Delta x)^{2} + (\Delta y)^{2}}[/tex]
[tex]d = (6.4\,mi)\cdot \sqrt{4^{2}+(-3)^{2}}[/tex]
[tex]d = 32\,mi[/tex]
The approximate distance between the high school and the stadium is 32 miles.
-3(8n+10)
distributive property
Answers
5/4 in factional form
HELPPPPPP how do you find the height of a right triangle
Answers
Answer:
The height of any right triangle is just simply the many units that are going up but it has to start from the right angle and upwards and that would be your height.
It may already give you a height so there is no need to worry if so.
Here, in this case the side on the very left is my height:
Answer:
Use Pythagorean Theorem
Step-by-step explanation:
a²+b²=c²
You need to find the height, which means you have a and c. You square a and c, subtract a from c, then find the square root of that difference. Now you have b.
EXAMPLE:
a=3, c=6
3²+b²=6²
9+b²=36
-9 -9
b²=27
sqrt of 27 is 5.2. So the side is 5.2
---
hope it helps
3 • 12 ÷ 2 • 3 ÷ 3
6
2
18
54
Answers
Answer:
18.
Step-by-step explanation:
3*12 = 36
36/2 = 18
18*3 = 54
54/3 = 18
Answer:
18
Step-by-step explanation:
3 x 12 is 36,
36 divided by 2 is 18,
18 x 3 is 54,
54 divided by 3 is 18
Write the equation in standard form for the circle with radius 6 centered at the origin.
Answers
Answer:
So, if the center is (0,0) and the radius is 6, an equation of the circle is: (x-0)2 + (y-0)2 = 62.
Step-by-step explanation:
please mark this answer as brainliest
The equation in standard form for the circle with radius 6 centered at the origin will be x² + y² = 36.
What is the equation of a circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
Let r be the radius of the circle and the location of the center of the circle be (h, k).
Then the equation of the circle is given as,
(x - h)² + (y - k)² = r²
The radius of the circle is 6 units and has a center at the origin. Then the equation is given as,
(x - 0)² + (y - 0)² = 6²
x² + y² = 36
The equation in standard form for the circle with radius 6 centered at the origin will be x² + y² = 36.
More about the equation of the circle link is given below.
https://brainly.com/question/10618691
#SPJ2
Which equation gives the rule for this table?
Answers
Answer:
C. y = x + 2
Step-by-step explanation:
2 is being added onto both sides
Find the volume of a pyramid with a square base, where the area of the base is 6.8m^2
and the height of the pyramid is 8.6. Round your answer to the nearest tenth of a cubic meter.
Answers
Answer:
[tex]19.5\:\mathrm{m^3}[/tex]
Step-by-step explanation:
The volume of a square pyramid is given by [tex]V=\frac{1}{3}\cdot s^2\cdot h[/tex], where [tex]s[/tex] is the base edge and [tex]h[/tex] is the height. Since the base area ([tex]s^2[/tex]) is already given to us, we can substitute directly in to our equation.
Solving for [tex]V[/tex]:
[tex]V=\frac{1}{3}\cdot 6.8\cdot 8.6\approx \boxed{19.5\:\mathrm{m^3}}[/tex]
The answer on deltamath is
19.5m^3
7x + 6y = -1 ; -x + 2y = 3 with elimination
Answers
Answer:
x= -1, y=1
Step-by-step explanation:
First label the 2 equations.
7x +6y= -1 -----(1)
-x +2y= 3 -----(2)
Then choose which term you would like to eliminate. To eliminate the y term, multiply equation (2) by 3 such that the coefficient of y is 6.
(2) ×3:
-3x +6y= 9 -----(3)
Since the coefficient of y is positive 6 in both equations, subtract one equation from the other.
(3) -(1):
-3x +6y -(7x +6y)= 9 -(-1)
Expand:
-3x +6y -7x -6y= 9 +1
-10x= 10
x= 10 ÷(-10)
x= -1
Substitute x= -1 into (2):
-(-1) +2y= 3
1 +2y= 3
2y= 3 -1
2y= 2
y= 2 ÷2
y= 1
------------------------------------------------------------
2nd method: eliminating the x term
(2) ×7:
-7x +14y= 21 -----(3)
Since the coefficient of y in equation (1) is a positive 7, while that in equation (3) is a negative 7, add the 2 equations together to eliminate the x term.
(1) +(3):
7x +6y -7x +14y= -1 +21
20y= 20
y= 20 ÷20
y= 1
Substitute y= 1 into (2):
-x +2(1)= 3
-x +2= 3
-x= 3 -2
-x= 1
x= -1
Why does the equation 5(3x-4)-6x=3(3x-4) have no solutions?
Bureause when you subtract from both sides of the equation and simplify you get 20-20
Berise when you add to both sides of the equation and simplify you get = -12
Because when you add to both sides of the equation and simplify you get 2020
Because when you add-to both sides of the equation and simple you get 20-12
Answers
What is the value of x. Please help out. This is due today!
Answers
Answer:
70°
Step-by-step explanation:
In the context it says that Franklin St. is parallel to Washington St.
The 110° formed by Franklin St. and Mulberry St. is a supplementary angle to Angle x.
Supplementary angles are angles that add up to each other to make 180°
So lets subtract:
180 - 110 = 70°
Angle x = 70°
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
What is the area of the triangle shown below?
Answers
...................
..........
10 TIMES 10 = 100
100 TIMES 12 = 1,200
So there for , the answer is 1,200
Choose the law and the formula that would be used to solve the triangle.
Answers
Answer: A^2
Step-by-step explanation:
Angle C + Angle B = Angle A
Which expression is equivalent to 3^-1⋅3^0?
A) 1/3
B) 1/9
C) 9
D) 3
Answers
pls helpppp lol :/ I’d really appreciate it !!
Answers
Step-by-step explanation:
60+5x+5=180 (being angle of straight line)
5x+65=180
5x=180-65
5x=115
x=23
Can someone help me out my grads are bad
Answers
Answer:
10 across and 6 down
Step-by-step explanation:
multiply sides by 2
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Please Help ASAP
Jorge has a swimming pool that is rectangular in shape. The length and width of the pool are 24 feet and 14 feet. He also knows that the pool has a consistent depth of 5 feet. He needs to add 4 drops of chlorine for every 50 cubic feet in his pool. How many drops of chlorine should Jorge use to chlorinate his pool properly?
Answers
Answer:
140 drops
Step-by-step explanation:
Length of the pool = 24 feet
Width of the pool = 14 feet
Depth of the pool = 5 feet
Volume of the pool = length × width × depth
= 24 ft * 14 ft * 5 ft
= 1,750 ft³
Volume of the pool = 1,750 ft³
He needs to add 4 drops of chlorine for every 50 cubic feet in his pool.
Number of 50 cubic feet in the volume of the pool = Volume of the pool / 50 ft³
= 1,750 ft³ / 50 ft³
= 35
Number of 50 cubic feet in the volume of the pool = 35
How many drops of chlorine should Jorge use to chlorinate his pool properly?
Number of drops of chlorine Jorge should use = number of drops per 50 ft³ × Number of 50 cubic feet in the volume of the pool
= 4 × 35
= 140 drops
Number of drops of chlorine Jorge should use = 140 drops
!DUE SOON!
You estimate that a kitten weighs 8 pounds. The actual weight of th kitten is 6 pounds. Find the percent error. Round your answer to the nearest tenth of a percent.
Answers
Answer:
you have 33.3% percent error
Step-by-step explanation:
Can someone plz help me on this plz I beg u plz
Answers
==========================================================
Explanation:
He starts off with 200 cards. Then he adds on 25w more cards for each week (w). Overall, he'll have 200+25w cards
We can think of it like this:
After 1 week, he adds on 25*1 = 25 cardsAfter 2 weeks, he adds on 25*2 = 50 cards totalAfter 3 weeks, he adds on 25*3 = 75 cards totalAfter 4 weeks, he adds on 25*4 = 100 cards total, and so on.After w weeks, he adds on 25w cards totalSo that's another way to see where the 25w comes from.
The expression 200+25w is the same as 25w+200. This is because we can add two numbers in any order.
------------
Since he wants to know when he'll have more than 750 cards, this means we set 25w+200 greater than 750.
That's how we get to the answer of 25w+200 > 750
Notice how there isn't a line under the inequality sign. We aren't using the "greater than or equal to" symbol here. We want to know when the cards gets over 750, but we don't want to know when it's equal to 750.
Amelia randomly selects two cards, with replacement, from a normal deck of cards. Calculate the probability that: the first card is a 9 of Clubs and the second card is a 10 of Clubs.
Answers
Answer:
1 / 2704
Step-by-step explanation:
Number of cards in a deck = 52
9 of clubs in a deck = 1
10 of clubs in a deck = 1
Probability = required outcome / Total possible outcomes
P(9 of club) = 1 / 52
With replacement ;
Then ;
P(10 of club) = 1 / 52
Hence,
P(9 of club, then 10 of club) = 1/52 * 1/52 = 1 / 2704
I am a two digit number divisible my 19 the sum of my digits is 14
Answers
Answer:
95
Step-by-step explanation:
9+5=14
95÷19=5
this is the answer (I'm just typing so brainly let's me post)
PLEASE HELP ME I'M SO CONFUSED!!!!
Answers
Answer: C is the answer for first picture
F is the answer for second picture
C is the answer for number one on 3rd picture
F is the answer for number 2 on 3rd picture
Step-by-step explanation:
Answer:
look below
Step-by-step explanation:
for the first picture, the answer to the first problem is C
for the first picture, the answer to the second problem is G
for the second picture, the answer is F
for the third picture, the answer to the first problem is C
for the third picture, the answer to the second problem is G
have a nice day!
what percentage would this be?
Answers
Answer:
50%
Step-by-step explanation:
Simplify 2/5 (40x – 75)
which one ?? help plsss
100x - 187.5
80x/5 - 150/5
80x - 150
16x-30
Answers
Answer:
16x-30
Step-by-step explanation:
distribute 2/5 by 40x and then 75
2/5(40x) - 2/5(75)
16x - 30
Three-dimensional objects are measured by their length, width and what
Answers
Answer:
height
Step-by-step explanation:
you can just look these questions up
So it would be length x width x height
Find a formula for the nth term of the geometric sequence. Assume the n begins with 1. a1=18, a2=9
Answers
Answer:
Option E
Step-by-step explanation:
Explicit formula of a geometric sequence is,
[tex]T_n=a_1(r)^{n-1}[/tex]
Here, [tex]a_1=[/tex] First term
[tex]r=[/tex] common ratio
[tex]n=[/tex] number of terms
If, [tex]a_1=18[/tex] and [tex]a_2=9[/tex]
Common ratio of the sequence [tex]r=\frac{a_2}{a_1}[/tex]
[tex]r=\frac{9}{18}[/tex]
[tex]r=\frac{1}{2}[/tex]
By substituting these values in the formula,
[tex]T_n=18(\frac{1}{2} )^{n-1}[/tex]
Therefore, Option E is the answer.
factor each polynomial
Answers
ok so
leave y^2 alone
so you need to get 2 factors that when added equal 11 so 9x2=18
and 9+2=11
so it would be (y+9)(y+2)
hope this helps
Answer:
Step-by-step explanation:
(x + 9 ) ( x + 2 )
:Renita's Bike Ride
Renita is riding her bike to school. It takes her 5 minutes to
travel half of a mile.
Answers
Answer:
Okay well if you need to find mph she is going 10 mph
Step-by-step explanation:
1/2+1/2= 1 mile in 10 min, multiply both sides by 6 and you get 1 mile = 60min