Given:
The area of a sector = [tex]9\pi\text{cm}^2[/tex]
The sector cover [tex]\dfrac{1}{4}[/tex] of the entire circle.
To find:
The radius of the circle.
Solution:
Let r be the radius of the circle. Then, the area of the circle is:
[tex]A=\pi r^2[/tex]
It is given that the sector cover [tex]\dfrac{1}{4}[/tex] of the entire circle. So, the area of the sector is equal to [tex]\dfrac{1}{4}[/tex] of the area of the entire circle.
[tex]9\pi=\dfrac{1}{4}\times \pi r^2[/tex]
Multiply both sides by 4.
[tex]36\pi =\pi r^2[/tex]
Divide both sides by [tex]\pi[/tex].
[tex]36 =r^2[/tex]
Taking square root on both sides.
[tex]\pm \sqrt{36} =r[/tex]
[tex]\pm 6 =r[/tex]
Radius of a circle cannot be negative. So, [tex]r=6[/tex].
Therefore, the radius of the circle is 6 cm.
simplificar la expresion 3 ( - x - 2 ) me dicen cual es ? es para un examen
Answer:
-3x - 6
Step-by-step explanation:
3 × -x = -3x
3 × -2 = -6
-3x - 6 hope this helps
Answer:
Step-by-step explanation:
Factor
x^3+6x^2+2x+12
Answer:
(x + 6) (x^2 + 2)
Step-by-step explanation:
HELP PLEASE
solve the linear equation for x
-4.8(6.3x-4.18)=-58.56
Answer:
x = 81.6/30.24
Step-by-step explanation:
-4.8(6.3x - 4.18) = -58.56
-30.24x + 23.04 = -58.56
-30.24x = -81.6
x = 81.6/30.24
Write the slope-intercept form of the linear equation of a line with slope of
6 and a y-intercept of (0,-4).
Answer:
y = 6x -4
Step-by-step explanation:
help me out didifjdhfhfuf
help pls i can give brainliest?
Identify the solution to the system of equations.
Someone help me when this pls
Answer:
Distribute -9 to both numbers in the parenthesis
we have
(6^-4x-9 . 8^-7x-9)
When two negatives interact... They become positive
So we now have
(6^36 . 8^63)
Option C.
a regular sheet of letter (printing) paper measrues 8.5 inches by 11 inches. you want to cut out squares from each corner that it may be folded up to produce an open - top box. What are the dimensions of the square cut outs that will result in a box of maximum volume
Answer:
The dimensions of the square, that will result in a box of maximum volume is a square with side length of approximately 1.585 inches
Step-by-step explanation:
The given dimension of the steel sheet are;
The width = 8.5 inches
The length = 11 inches
Let 'x' represent the side length of the squares cut out, we have;
The length of the box formed, l = 11 - 2·x
The width of the box formed, w = 8.5 - 2·x
The height of the box, h = x
The volume of the box, V = (11 - 2·x) × (8.5 - 2·x) × (x) = 4·x³ - 39·x² + 93.5·x
The maximum or minimum volume is found from dV/dx = 0 at max. or min.
dV/dx = d(4·x³ - 39·x² + 93.5·x)/dx = 12·x² - 78·x + 93.5 = 0
Which gives;
x = (78 ± √((-78)² - 4×12×93.5))/(2 ×12)
x = 4.915 or 1.585
When x = 4.915, V = 4 × 4.915³ - 39 × 4.915² + 93.5 × 4.915 = -7.65
When x = 1.585, V = 4 × 1.585³ - 39 × 1.585² + 93.5 × 1.585 = 66.15
Therefore, the local maximum occurs at x ≈ 1.585
Therefore, the dimensions of the square, 'x' that will result in a box of maximum volume is x ≈ 1.585 inches.
which expression is equivalent to -1/2(1/4 x -3/8)
Answer:
-1/8x+3/16
Step-by-step explanation:
HEEEEEEEEELP!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Look at the image.
Step-by-step explanation:
(36 ÷ 4) - (36 ÷ 9)
9 - 4
5
(8 × 3) - 12 = 12
24 - 12
12
Find two consecutive odd numbers such that the difference of their square is 160.
how to solve the median
Answer:
1.) Set the data set in the ascending order
2.) Start cancelling out numbers each side, like if u cancel out the first number, then cancel out the last as well.
3.) Keep doing the step 2 until u reach the middle most number.
4.) Sometimes there are 2 middle numbers left, in that case find their average (add both numbers together and divide the sum by 2) which would be ur middle most number.
Hope this helps!
Something about this I don’t understand
Answer:
X >_-5
Step-by-step explanation:
>_ is greater than or equal to
The circumference of a circle is 23π ft. What is the area, in square feet? Express your answer in terms of \piπ
Answer:
A = 132.25π sq ft
Step-by-step explanation:
C = 2πr
23π = 2πr
r = 23/2 or 11.5
A = πr²
A = 11.5²π
A = 132.25π
Write 0.25 miles as a fraction in simplest form
Answer:
1/4 miles
Step-by-step explanation:
so let me explain it like this. a quarter is worth 25 cents. how many quarters in a dollar? 4. a dollar is 100 cents. its also called a quarter because it takes up 1/4th of a dollar. so 0.25 is a quarter of 100 and is 1/4 as a fraction.
Answer:
it's 1/4
Step-by-step explanation:
L 7.8.2 Test (CST): Area, Surface Area, and Volume Question 24 of 30 Find the area of the sector of the circle below. The radius of the circle is 6 cm. Use 3.14 for at 90" O A. 18.84 cm2 O B. 4.71 cm2 O C. 28.26 cm2 O D. 6.22 cm
Answer:
28.26 cm^2
Step-by-step explanation:
Mathematically, we have the area of a sector as;
theta/360 * pi * r^2
theta is the angle subtended at the center of the circle by the sector which is 90 degrees
r is the radius of the circle given as 6 cm
Substituting these values;
90/360 * 3.14 * 6^2 = 28.26 cm^2
a jug contains 2 gallons of water how many quarts of water does the jug contain
Answer:
8 quarts, in 2 gallons
Step-by-step explanation:
P- 24/n = 30/100
What’s N?
Z- n/4 = 18/72
What’s N?
Answer:
Z: n = 1 P: n =80
Step-by-step explanation:
cross multiple what you can and divide it by the last number left to find n
The perimeter of a parallelogram is 62cm. what is the length of the longest side if the equation of the sides are:-
*3x+5
*x+2
Given
perimeter is 62
Side 1 - 3x+5
Side 2 - x+2
Solution,
2(3x+5+x+2) = 62
4x+7 = 31
4X = 24
x = 6
Now substitute the value of x to get the sides
Side one - 3x+5 = 23cm
Side two - x+2 = 8cm
Answer- the length of the longest side is 23 cm
Sam saves $500 at a rate of 4%. What is the total amount of money she has after 20 years?
Answer:
$10,400
Step-by-step explanation:
A square is cut in half on the diagonal, creating two equal triangles. Each triangle has an area of's square units. What is the side length, in units, of the original square?
Answer:
5.656854249
Step-by-step explanation:
18 x 2 = 32 square units for the square's area
square root of 32 = approximately 5.65
Factor by grouping.
64p2 – 48p – 27
(8p – 9)(8p – 3)
(8p – 9)(8p + 3)
(8p + 9)(8p + 3)
(8p + 9)(8p – 3)
Answer:
B
Step-by-step explanation:
hope this helps with the work
Pete's Plainting charges $25 per room to paint, plus an additional $0.50 per square foot that they paint. If they charges me $201 to paint my kitchen, how many square feet did they paint?
Answer:
352 square feet
Step-by-step explanation:
thats the answer ( i dont know how to explain it sorry )
if a, b, c, and d represent positive real numbers, what is the inequality when solved for x?
The inequality equation is x ≥ ( by - c - d ) / a
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
by - d ≤ ax + c be equation (1)
On simplifying the equation , we get
Subtracting c on both sides of the equation , we get
by - d - c ≤ ax
And , ax ≥ by - d - c
Divide by a on both sides of the equation , we get
x ≥ ( by - c - d ) / 2
Hence , the inequality is x ≥ ( by - c - d ) / a
To learn more about inequality equations click :
https://brainly.com/question/11897796
#SPJ1
A data set is Normally distributed with a mean of 25 and a standard deviation of 8. If you calculate the standard score of every observation in this data set, the resulting scores will have a distribution that has
Answer:
The answer is "A mean of 0 and a standard deviation of 1".
Step-by-step explanation:
The standard answer of its following formula is calculated by:
[tex]\to z=\frac{X-\mu}{\sigma}[/tex]
Its standard score relates to the sampling distribution with the normal distribution average standard variation of 0 and 1, correspondingly. The mean for a standard scoring is 0, and the normal deviation is 1. that's why the mean=0, standard deviation=1.
if 5cosA =4 wat is CosA
Answer:
4/5
Step-by-step explanation:
5cosA=4
divide both sides by 5
cosA=4/5
x-1=-5-x if you know please
Answer:
X will be -2
Step-by-step explanation:
Divide each side by factors that don't contain the variable
Y’all mind helping thanks much love :) look at the picture
Answer:
[tex] S_8= 191.997071\approx 192[/tex]
Step-by-step explanation:
Given series is: 144, 36, 9,...
Here. 36/144 = 1/4, 9/36 = 1/4
Since, the ratio any two consecutive terms is same.
Therefore, it is a geometric progression.
So,
Common ratio (r) = 1/4= 0.25
First term (a) = 144
n = 8
To find: [tex] S_8[/tex]
[tex] \huge \because S_n= \frac{a(1-r^n)}{1-r}[/tex]
[tex] \huge \therefore S_8= \frac{144[1-(0.25)^8]}{1-0.25}[/tex]
[tex] \therefore S_8= \frac{144[1-0.00001525878]}{0.75}[/tex]
[tex] \therefore S_8= \frac{144[0.999984741]}{0.75}[/tex]
[tex]\huge \therefore S_8= \frac{143.997802734}{0.75}[/tex]
[tex]\huge \therefore S_8= 191.997071[/tex]
What else is true a little help
Answer:
This is a triangular prism.
The surface area is 105 square cm.
This is a square pyramid.
Write the equation of a line that goes through the points (4, 8) and (-8, 2)
show work i will appreciate it