The area of sector AOB whose radius OA 5 units is 19.6 sq. units.
What is the Sector?A sector is a portion of a circle which is enclosed between its two radii and the arc adjoining them. The most common sector of a circle is a semi-circle which represents half of a circle.
Here, Radius of Circle = 5 units
length of arc AB / circumference = 1/4
So, Area of Sector AOB = one fourth of area of circle
= 1/4 X π X r²
= 0.25 X 3.14 X 5²
= 0.25 X 3.14 X 25
= 19.625 sq. units
Thus, the area of sector AOB whose radius OA 5 units is 19.6 sq. units.
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Answer:
19.6
Step-by-step explanation:
What is the solution to this system of equations? negative 5.9 x minus 3.7 y = negative 2.1. 5.9 x 3.7 y = 2.1. (0, negative 2.1) (0, 2.1) infinitely many solutions no solution
The solution to this system of equations is infinitely many solutions
How to determine the solution?The system of equations is given as:
-5.9x -3.7y = -2.1.
5.9x + 3.7y = 2.1.
Add both equations to eliminate a variable
-5.9x + 5.9x - 3.7y + 3.7y = -2.1 + 2.1
Evaluate
0 +0 = 0
Evaluate the sum of zeros
0 = 0
Both sides of the equations are the same
Hence, the solution to this system of equations is infinitely many solutions
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Answer:
Option C is correct. The system of linear equation -5.9x - 3.7y = -2.1 and 5.9x +3.7y = 2.1 have infinitely many solutions.
What is system of linear equation?
The system of linear equations is "a set of two or more linear equations or variables is called system of linear equation".
What is infinitely many solutions?
An equation has infinitely many solutions only if "the two lines are coincident and having the same y-intercept".
According to the question,
The system of linear equation,
-5.9 x - 3.7y = -2.1 → (1)
5.9 x + 3.7y = 2.1 → (2)
The equation (1) is same as the equation (2) only the difference equation (1) is multiplied by (-1). Both equation give the same line. To check if above equations have same y-intercept, the equation can be written in slope intercept form y = m x +c where 'm' is the slope of the line, 'c' is the 'y-intercept'.
y = - (5.9/3.7) x + 2.1 [From equation (1)]
y = -(5.9/3.7) x + 2.1 [From equation (2)]
The both equation have same y-intercept. Therefore, the system of linear equations have infinitely many solution.
Hence, the system of linear equation -5.9x - 3.7y = -2.1 and 5.9x +3.7y = 2.1 have infinitely many solutions.
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Step-by-step explanation:
Find the slope of the line?
Answer:
Step-by-step explanation:
(-5, 3) and (-5, -3)
(-3 - 3)/(-5 + 5) = -6/0 = UNDEFINED
That is also the CORRECT ANSWER
Find the value of x.
7x-1
2x - 1
2. make sure you show all your work for full points. what is z?
Answer:
I don't understand what the means
What is the distance between these two points: (2, 3) and (- 5, 4)
Let's apply the distance formula:⇒d=√(x2−x1)²+(y2−y1)²⇒d=√(5−2+(−4−(−3))² ⇒d=√3²+(−7)²⇒d=√9+49 ⇒d=√58 Therefore, the distance between the two points (2,−3) and (5,−4) is √58 units.
Pls solve this for me
Answer:
141/1.95 km/hr, or 72.308 km/hr
Step-by-step explanation:
To find the average speed, we need to know the total distance traveled / time (hours).
The total distance is 72 km + 69 km = 141 km.
The total time is 48 minutes / 60 (because we want this in hours, not minutes) + 69/60 = 1.95 hours
141/1.95 = 72.3 km/hr
Quadrilateral abcd has the vertices a(-6,4) , b(-4,5) , c(-3,3) , d(-5,1) . determine if quadrilateral abcd is a rhombus
Answer:
No
Step-by-step explanation:
The defining property of a rhombus is that it has equal side lengths.
=============================================================
Finding all side lengths :
AB
⇒ √(-4 + 6)² + (5 - 4)²
⇒ √2² + 1²
⇒ √5 units
BC
⇒ √(-3 + 4)² + (3 - 5)²
⇒ √1² + (-2)²
⇒ √5 units
CD
⇒ √(-5 + 3)² + (1 - 3)²
⇒ √(-2)² + (-2)²
⇒ √8 units
DA
⇒ √(-6 + 5)² + (4 - 1)²
⇒ √(-1)² + 3²
⇒ √10 units
As all side lengths of the quadrilateral are not equal, ABCD is not a rhombus.
According to a poll conducted by the gallup corporation in march 2011, the metropolitan areas with the highest and lowest proportions of obese adults were evansville, in-ky, and boulder, co, respectively. in evansville, for every 311 people who were not obese, there were 189 who were. in boulder, for every 16 obese people, there were 109 who were not obese. at that time, the estimated populations were 358,676 for evansville and 303,482 for boulder. how many more obese people were there in evansville than in boulder
Using proportions, it is found that 96,734 more obese people were there in evansville than in boulder.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
For Evansville, the proportion of obese people is given by:
189/(311+189) = 189/500.
Hence, out of 358,676 people:
oE = 189/500 x 358676 = 135580.
For Boulder, the proportion is given by:
16/(16 + 109) = 16/125
Hence, out of 303,482 people:
oB = 16/125 x 303482 = 38846.
Hence the difference is given by:
135580 - 38846 = 96734
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What is the minimum of the data?
0
5
7
13
Answer:
b; [5]
Step-by-step explanation:
i took the quiz
how tall is a bridge if a 6-foot-tall person standing 100 feet away can see the top of the bridge at an angle of 30 degrees to the horizon
Answer:
R. 6+100 tan30∘=6+1003√3 feet tall.
Write an equation in
y = mx + b form for
the line graphed.
Answer:
y=2x-5
explanation
m is gradient so rise over run and b is the y intercept which is -5
Answer: y = 2x - 5
Step-by-step explanation:
Method I:
▪︎ Slope: m = (y2 - y1) / (x2 - x1)
▪︎ b is where the graph crosses the y-axis
▪︎ Points: (1, -3), (2, -1)
▪︎ m = (-1 - (-3)) / (2 - 1) = (3 - 1) / (1) = 2
▪︎ b = -5
▪︎ => y = 2x - 5
Method II:
▪︎ y = mx + b
▪︎ Points: (1, -3), (2, -1)
▪︎ System of equations:
-3 = m*1 + b,
-1 = m*2 + b
-3 = m + b,
-1 = 2m + b
m = -b - 3,
-1 = 2(-b - 3) + b
m = -b - 3,
-1 = -2b - 6 + b
m = -b - 3,
-1 + 6 = -2b + b
m = -b - 3,
5 = -b
m = -(-5) - 3,
b = -5
m = 2,
b = -5
▪︎ => y = 2x - 5
If f(x) = 2x+4, which of the following is the inverse of f(x)?
O A.r1(x) = 7(x+4)
2
OB. f¹(x) = 2(x+4
O C. f¹(x) = 2(x-4)
7
○ D. /¯¹(x) = 7(x-4)
)
2
By definition of inverse function,
[tex]f\left(f^{-1}(x)\right) = x[/tex]
Given that f(x) = 2x + 4, solve for the inverse of f :
[tex]f\left(f^{-1}(x)\right) = 2 f^{-1}(x) + 4 = x \implies f^{-1}(x) = \dfrac{x-4}2[/tex]
(I'm not entirely sure which answer that corresponds to from the choices provided...)
What is the distance between the two points (-48,23) and (15,23)
Answer:
63 units
Step-by-step explanation:
d = √(x2-x1)^2 + (y2-y1)^2
Meaning it would look like this
d = √(15+48)^2 + (23-23)^2
we changed the subtraction sign in the first one to an addition sign because it was a double negative
hope this helped
Which explains whether or not the graph represents a direct variation?
On a coordinate plane, a line goes through points (0, 0) and (1, 3).
The graph has a constant of variation of 3, so it represents a direct variation.
The graph has a slope of 3, so it represents a direct variation.
The graph has a positive slope, so it does not represent a direct variation.
The graph does not begin at the origin, so it does not represent a direct variation.
The line passes through the origin and if it has a constant of variation of 3, so it represents a direct variation , Option A is the correct answer.
What is Direct Variation ?When a quantity increases and the other quantity also increases , then those two quantities are said to be in direct variation.
It is asked in the question that which option depicts whether On a coordinate plane, a line goes through points (0, 0) and (1, 3) , represents a direct variation
As it is mentioned in the question that the line passes through the origin and if it has a constant of variation of 3, so it represents a direct variation.
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Answer:
a
Step-by-step explanation:
If point c lies on the tangent from part (a)
and segment ac was drawn such that mbca
is equal to 40 then what is the ratio of ab to bc to the nearest hundredth?
The ratio of ab to bc to the nearest hundredth is gotten as; 0.84
How to Solve Circle Geometry?From the attached image showing the circle geometry, we will first connect point A to point B.
After connecting point A to point B, we will draw a perpendicular line to AB through B to terminate at C.
Thus, we can have the ratio of trigonometry at;
tan ∠ABC = AB/BC
Thus;
AB/BC = tan 40
AB/BC = 0.84
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can i have help with this
Answer:
2nd option
Step-by-step explanation:
(5x² - 4x - 1) - (- 4x² - 4)
remove first set of parenthesis and distribute second set by - 1
= 5x² - 4x - 1 + 4x² + 4 ← collect like terms
= 9x² - 4x + 3
ABC is shown on the coordinate plane below
What is the perimeter of △ABC? If necessary, round your answer to the nearest tenth.
Using the distance formula, the perimeter of triangle ABC is approximately 40.5 units.
What is the Perimeter of a Triangle?Perimeter = sum of all three sides.
Use the distance formula, [tex]d = \sqrt{(y_2 - y_1)^2 - (x_2 - x_1)^2}[/tex] to find the distance between each of the vertices of the triangle.
The given vertices are:
A = (-6, 4)B = (8, -1)C = (0, -9)AB = √[(8−(−6))² + (−1−4)²]
AB = √221
AB ≈ 14.9 units
BC = √[(8−0)² + (−1−(−9))²]
BC = √128
BC ≈ 11.3 units
AC = √[(−6−0)² + (4−(−9))²
AC = √205
AC ≈ 14.3 units
Perimeter of △ABC = 14.9 + 11.3 + 14.3
Perimeter of △ABC ≈ 40.5 units
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Need help with Trigonometry
Answer:
29
Step-by-step explanation:
using Pythagorean theory.
equate it to the hypotenus.
thus- hyp sq=adjacent sq +opposite sq
Here are four digit cards 6 5 5 7
arrange the cards to give the greatest possible answer to the calculation
Answer:
7 6 5 5
Step-by-step explanation:
the highest numbers should go in the leftmost digits place, as these are worth more
here, we put 7 in the thousands place, which is 2 thousand higher than if we put 5 in the thousands place
Kofi brought 6 books and 10 pencils from a store ama brought 3 books and 20 pencils of the same kind from the store if each of them paid $ 17000.00 from the items find the cost of each pencil each book two books and 4 pencils
Answer:
Answer by josgarithmetic(37226) (Show Source): You can put this solution on YOUR website!
system%2810b%2B6p=17000%2C3b%2B20p=17000%29
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let +a+ = the cost of 1 pencil
Let +b+ = the cost of 1 book
---------------------------
(1) +6b+%2B+10a+=+17000+
(2) +3b+%2B+22a+=+17000+
----------------------
Multiply both sides of (2) by +2+
and subtract (1) from (2)
(2) +6b+%2B+44a+=+34000+
(1) +-6b+-+10a+=+-17000+
-------------------------
+34a+=+17000+
+a+=+500+
and
(1) +6b+%2B+10a+=+17000+
(1) +3b+%2B+5a+=+8500+
(1) +3b+%2B+5%2A500+=+8500+
(1) +3b+=+8500+-+2500+
(1) +3b+=+6000+
(1) +b+=+2000+
------------------
Step-by-step explanation:
IT,LL
HELP
Please answer correctly.
Answer:
same thing for the rest, you just change the value of the radius according to the question
Step-by-step explanation:
area = pi * radius²
1)
a = pi * 10²
a = ~3.14 * 100
a = 314 mi²
A line passes through the point(1,6) and is parallel to y=4x+6. what is the value of b?
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]y= \stackrel{\stackrel{m}{\downarrow }}{4}x+6\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we're really looking for the equation of a line whose slope is 4 and passes through (1 , 6)
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{4}(x-\stackrel{x_1}{1})[/tex]
[tex]y-6=4x-4\implies y=4x\underset{\stackrel{\uparrow }{b}}{+2}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
please solve quickly
total no of marbles = 10
no. of marbles which are not yellow = 9
9/10
hope it helps...!!!
Answers to the questions?
Based on the relationship of special angles, the values of x are:
1. x = 34
2. x = 9
3. x = 6
What are The Relationship of Angles Formed by a Transversal and Parallel Lines?Alternate interior angles are equals and corresponding angles are also equal.
Linear pair angles are supplementary.
1. Angles j and a are linear pair angles, therefore:
3x + 15 + 2x - 5 = 180
5x + 10 = 180
5x = 180 - 10
5x = 170
x = 170/5
x = 34
2. Angles m and g are corresponding angles, therefore:
4x + 12 = 2x + 30
4x - 2x = -12 + 30
2x = 18
x = 9
3. Angles c and v are alternate interior angles, therefore:
6x + 9 = 3x + 27
6x - 3x = -9 + 27
3x = 18
x = 6
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Today, Isaac needs to walk his dog, water the garden, and feed his fish. DDD is the number of minutes it takes to walk his dog, GGG is the number of minutes it takes to water the garden, and FFF is the number of minutes it takes to feed his fish.
The expression G+(D+F)G+(D+F)G, plus, left parenthesis, D, plus, F, right parenthesis describes the total number of minutes it takes Isaac to do all three tasks. We can also use the expression (G+D)+F(G+D)+Fleft parenthesis, G, plus, D, right parenthesis, plus, F to represent the same quantity.
Match each amount in the situation with the expression that represents it.
For reference:
The dog is an animal, and he needs to go outside to walk.
The garden is a bunch of plants (not an animal), and it is outside.
The fish is an animal, and she lives in a water tank inside.
The correct matching of each amount in the situation with the expression that represents it is:
The total Minutes of the tasks involving animals.-D+F (Dog and fish)The total Minutes of the tasks not involving animals.-G (Garden)The total Minutes of the Inside tasks.-F (Fish)The total Minutes of the Outside tasks.-G+D (Garden and Dog)Explanations of the expressionsGiven that:
D = number of minutes it takes to walk his dogG = number of minutes it takes to water the garden; andF = number of minutes it takes to feed his fishWe have the situations and expressions that need to be matched such that:
D+FG+DGFTherefore, considering the situation,
The total Minutes of the Inside tasks.The total Minutes of the Outside tasks.The total Minutes of the tasks involving animals.The total Minutes of the tasks not involving animals.The correct matching is given as:
The total Minutes of the tasks involving animals.-D+F (Dog and fish)The total Minutes of the tasks not involving animals.-G (Garden)The total Minutes of the Inside tasks.-F (Fish)The total Minutes of the Outside tasks.-G+D (Garden and Dog)Read more about mathematical expressions here:
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Match the tan R, cos R and sin R to the correct ratios
Three coins are tossed up in the air, one at a time. What is the probability that the first two will land heads up and the third will land tails up?
In a bag, there are red and blue cubes in the ratio 4 : 7
red blue
4;7
I add 10 more red cubes to the bag.
Now there are red and blue cubes in the ratio 6 : 7
red blue
6;7
How many blue cubes are in the bag?
The number of the blue cubes is 35 and the number of the red cubes is 20.
What is the ratio?The ratio is defined as the representation of the one number with respect to the other number. or one number is how many times the other number.
Given that:-
In a bag, there are red and blue cubes in the ratio of 4: 7I add 10 more red cubes to the bag. Now there are red and blue cubes in the ratio of 6: 7The number of the blue cubes are calculated as:-
The two equations will be formed by the given data in the question.
[tex]\dfrac{r}{b}=\dfrac{4}{7}[/tex]
7r = 4b
[tex]\dfrac{r+10}{b}=\dfrac{6}{7}[/tex]
7r + 70 = 6b
Solving the above equation we will get the value of b.
4b + 70 = 6b
6b - 4b = 70
2b = 70
b = 35
7r = 4b
7r = 4 x 35
r = 20
Therefore the number of the blue cubes is 35 and the number of the red cubes is 20.
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Line k is parallel to y= -2x - 1 and passes through the point (4,3). What is the y intercept of line k?
A. (0,1)
B. (0,7)
C. (0,10)
D. 0,11)
Ok, so I have a math assignment that is due on Monday (so in 2 days), but I don't understand it. Here are the instructions:
You buy a pair of jeans at a department store.
Jeans_____ $39.99
Discount___ -10.00
Subtotal____ 29.99
Sales Tax___ 31.94
I have the first two questions done for this question, and I just need help on the last one. Here it is:
The price of the jeans includes a 60% markup. After the discount, what is the percent of markup to the nearest percent?
The percent of markup is __%.
Can anyone please help me?
Thanks!