Answer:
centre = (2, - 1), radius = 6
Step-by-step explanation:
Rearrange the equation by placing the x and y terms together and adding 31 to both sides
Given
x² + y² - 4x + 2y - 31 = 0, then
x² - 4x + y² + 2y = 31
Use the method of completing the square
add ( half the coefficient of the x/y term )² to both sides
x² + 2(- 2)x + 4 + y² + 2(1)y + 1 = 31 + 4 + 1
(x - 2)² + (y + 1)² = 36
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r the radius
compare to (x - 2)² + (y + 1)² = 36, then
centre = (2, - 1) and r = [tex]\sqrt{36}[/tex] = 6
The center of the circle is (2, - 1) and the radius is 6 units.
What are the types of equations of a circle?The equation for a circle has the generic form x² + y² + 2gx + 2fy + c = 0.
The standard equation of a circle is x² + y² = r².
The polar form of the equation of the circle is (rcosθ)² + (rsinθ)² = p².
Given, The equation of a circle is x² + y² - 4x + 2y - 31 = 0.
We know, In x² + y² + 2gx + 2fy + c = 0, The center of the circle is,
(- g, - f) and radius is [tex]\sqrt{g^2 + f^2 - c[/tex].
Therefore, 2gx = - 4x and 2fy = 2y.
2g = - 4 and 2f = 2.
g = - 2 and f = 1.
- g = 2 and - f = - 1.
So, The center is (2, - 1).
And the radius is, [tex]\sqrt{2^2 + -1^2 + 31[/tex].
= [tex]\sqrt{4 + 1 + 31[/tex].
= [tex]\sqrt{36[/tex].
= 6 units.
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What is the measure of a
Answer:
a = 70°
Step-by-step explanation:
a and 110 form a straight angle, thus
a + 110 = 180 ( subtract 110 from both sides )
a = 70°
Answer:
a =70
Step-by-step explanation:
Angle a and 110 are supplementary, which means they add to 180 degrees
a+ 110 = 180
Subtract 110 from each side
a+110-100=180-110
a = 70
The graph of y = 5x2 is the graph of y = x2.
Answer:
narrower than and opens in the same direction as
Step-by-step explanation:
Answer:
narrower than and opens in the same direction as
Step-by-step explanation:
The graph of y = 5x2 is narrower than and opens in the same direction as the graph of y = x2.
A square is increased by 4 inches on each side. If the new area is 36 in^2, what was the length of a side of the original square?.
Answer:
2in
Step-by-step explanation:
Let's call the original side "x". so x² (area of a square) is = x² (as we can't simplify it). Then we got a 4 added to each side. So now we redefine each side as "x+4". So now we can make an equation of the area of the square. x² + 4² = 36. Now you realize that 36 is 6² so you write it. x² + 4² = 6² . Since everything is now a square just square root everything (√) So Now x + 4 = 6. Now you have a 1st degree equation now solve simple math. x = 6 - 4 = 2. The side of original square is 2in
The drawing tip of a child’s marker is in the shape of a hemisphere. The diameter of the great circle of the hemisphere is 18 millimeters. What is the volume of the drawing tip? π cubic millimeters
Answer:
pi*486mm ^3
Step-by-step explanation:
The equation of a hemisphere is half of that of a sphere, therefore it is 2/3pi*radius^3
We must calculate radius, which is just diameter/2 so 18/2 or 9
We can remove pi, as you want this measured in pi cubic millimeters.
this leaves us with (2/3)*9^3 which is 486cm
Henceforth, the final answer is pi*486 cubic millimeters.
Answer:
Answer is C on Ed
Step-by-step explanation:
What expression gives the height, h, of the triangle?
Answer: Your answer is C.
Step-by-step explanation: I'm taking this test rn and it's C. K12 anyone?
Answer:
C.Step-by-step explanation:
In the given graph, we have an isosceles triangles, which height divides its side in two equal parts.
So, from the division, we have to equal right triangles, which on leg is 6, and its angle is 80°, being the height the other leg.
Now, to find the height, we have to use trigonometric reasons, specifically, the tangent reasons because involves a relation with both legs
[tex]tan80=\frac{h}{6}[/tex]
So, we isolate [tex]h[/tex] to find its expression
[tex]h=6(tan80)[/tex]
If we compare with given choices, you'll observe that option C is the right answer.
can someone please give me the answers to these 2 will add 40 points
Answer:
Q1. x = 17.1; y = 5.6Q2. x = 9.7; y = 24.1Step-by-step explanation:
Use sine and cosine.
[tex]sine=\dfrac{opposite}{hypotenuse}[/tex]
[tex]cosine=\dfrac{adjacent}{hypotenuse}[/tex]
Q8.
We have:
[tex]opposite=y\\\\adjacent=x\\\\hypotenuse=18\\\\\alpha=18^o\\\\\sin18^o\approx0.309\\\\\cos18^o\approx0.9511[/tex]
Substitute:
[tex]\dfrac{y}{18}=0.309[/tex] multiply both sides by 18
[tex]y=5.562\to y\approx5.6[/tex]
[tex]\dfrac{x}{0.9511}=18[/tex] multiply both sides by 0.9511
[tex]x=17.1198\to x\approx17.1[/tex]
Q9.
We have:
[tex]opposite=y\\\\adjacent=x\\\\hypotenuse=26\\\\\alpha=68^o\\\\\sin68^o\approx0.9272\\\\\cos68^o\approx0.3746[/tex]
Substitute:
[tex]\dfrac{y}{26}=0.9272[/tex] multiply both sides by 26
[tex]y=24.1072\to y\approx24.1[/tex]
[tex]\dfrac{x}{26}=0.3746[/tex] multiply both sides by 26
[tex]x=9.7396\to x\approx9.7[/tex]
What is the volume of a cube if the length is 3 mm, the width is 3 mm, and the height is 3 mm? A) 9 cubic millimeters B) 18 cubic millimeters C) 27 cubic millimeters D) 30 cubic millimeters
A nine cubic millimeters
The volume of a cube with each dimension being 3 mm is obtained by multiplying the length, width, and height which results in 27 cubic millimeters. So the correct answer is C) 27 cubic millimeters.
Explanation:To solve for the volume of a cube, the formula Volume = Length x Width x Height is used. In the case given, all three dimensions (length, width, and height) are 3 mm. This results in Volume = 3 mm x 3 mm x 3 mm which simplifies to 27 cubic millimeters.
Hence, the correct option is C) 27 cubic millimeters.
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Plz help me with this
Answer: Consistent
Step-by-step explanation:
When given a system of equations, the definitions of the solution are:
Consistent & Independent: exactly ONE solution (lines intersect)Consistent & Dependent: INFINITE solutions (same line)Inconsistent: NO solutions (parallel lines)In the given graph, the lines intersect and have exactly ONE solution --> The system is Consistent and Independent.
Identify each of the following numbers as rational or irrational.if the number is irrational,explain how you know?
Answer:
a) Irrational
b) Rational
c) Rational
d) Rational
e) Irrational
f) Irrational
Step-by-step explanation:
a) Not expressible as a ratio of two integers, and having an infinite and nonrecurring expansion when expressed as a decimal.
b) It is a terminating decimal
c) It is a fraction
d) It is a integer
e) Not expressible as a ratio of two integers, and having an infinite and nonrecurring expansion when expressed as a decimal
f) Not expressible as a ratio of two integers, and having an infinite and nonrecurring expansion when expressed as a decimal
HELP!!!
This Venn diagram shows sports played by 10 students .
Let event A = The students plays basketball .
Let event B = The student plays soccer .
What is P(A|B) ?
Answer:
the answer is c
Step-by-step explanation:
Probability is the ratio of the favorable event to the total number of events. Then P(A|B) is 0.40.
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen.
This Venn diagram shows sports played by 10 students.
Let event A = The students play basketball.
Let event B = The student plays soccer.
Then the probability of the will be
[tex]\rm P(A|B) = \dfrac{P(A \cap B)}{P(B)}\\\\\\P(A|B) = \dfrac{\dfrac{2}{10}}{\dfrac{5}{10}}\\\\\\P(A|B) = \dfrac{2}{5} = 0.40[/tex]
Thus, P(A|B) is 0.40.
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which graph below has a slope of -1/2
Where are your graph?
consider the inequality-5(x+7)<-10 write an inequality representing the solution for x
Answer:
x > -5
Step-by-step explanation:
-5(x+7)<-10
Divide each side by -5. Remember to flip the inequality
-5/-5(x+7)>-10/-5
x+7 > 2
Subtract 7 from each side
x+7-7>2-7
x > -5
john runs 15 miles in 3 hours.How many can he run per hour
Answer:
5 miles per hour
Step-by-step explanation:
You divide 15/3 and get 5.
Answer:
5 miles per hour
Step-by-step explanation:
To determine how fast he can run per hour, take the miles and divide by the number of hours
15 miles / 3 hours
5 miles per hour
Please help ASAP please
Answer:
in april
Step-by-step explanation:
Keep track of every 1, 2, 3, or 4 rolled in 30 rolls and repeat this process 100 times to represent the days the temperature is above 80°F in June.
The BEST way to perform the simulation in this scenario would be to keep track of every 1, 2, 3, or 4 rolled in 30 rolls, as these represent the number of days the temperature is above 80°F in June. Repeat this process 100 times.
By simulating the number of days the temperature is above 80°F in June for 30 rolls and repeating it 100 times, you will obtain a larger sample size and a more accurate estimate of the probability. This approach allows for more data points and reduces the impact of random variations that can occur in smaller sample sizes.
Therefore, option 3 is the best way to perform the simulation: Keep track of every 1, 2, 3, or 4 rolled in 30 rolls and repeat this process 100 times to represent the days the temperature is above 80°F in June.
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Simplify to create an equivalent expression.
4(6r+3) + 2(r + 2)
plsss i need helppp
To simplify 4(6r+3) + 2(r + 2), distribute the coefficients, combine like terms, resulting in the simplified expression 26r + 16.
To simplify the expression 4(6r+3) + 2(r + 2), we need to distribute the multiplication over the addition inside the parentheses and then combine like terms.
Distribute the 4 into the first set of parentheses: 4 × 6r = 24r and 4 × 3 = 12.
Do the same with the 2 into the second set of parentheses: 2 × r = 2r and 2 × 2 = 4.
Now, combine the individual terms: The expression becomes 24r + 12 + 2r + 4.
Combine like terms (24r and 2r) and constants (12 and 4): 24r + 2r = 26r and 12 + 4 = 16.
The simplified expression is therefore 26r + 16.
Can someone help me with 8 , 9 , and 10?
which best describes the range of a function
Answer:
The range of a function is the set of all possible output values.
Answer: any numbers along the x axis
Step-by-step explanation:
One American flamingo has a mass of about 2 kg. What is the mass of 40American flamingos that each have a mass of about 2kg?
They have a total mass of about 80kg
Answer: 80kg
Step-by-step explanation: 40 flamingos X 2kg = 80 kg
y=4x + 45
x = 4y
Solve the system of equation algebraically.
Answer:
x= -12,y= -3
Step-by-step explanation:
Answer:
hey this is the answer
Step-by-step explanation:
x= -12,y= -3
The surface area of a jumbo size Rubik’s cube is 294in2. Find the lateral edge
Answer:
The lateral edge is [tex]7\ in[/tex]
Step-by-step explanation:
we know that
The surface area of a cube is equal to
[tex]SA=6b^{2}[/tex]
where
b is the length side of the cube
we have
[tex]SA=294\ in^{2}[/tex]
substitute in the formula and solve for b
[tex]294=6b^{2}[/tex]
[tex]b^{2}=294/6[/tex]
[tex]b^{2}=49[/tex]
[tex]b=7\ in[/tex]
Answer:
7
Step-by-step explanation:
294/6 = 49
square root of 49 is 7
Which ratios are all equivalent to 1:5 2/9,2/10,6:30,5 to 20, 3/20, 8 to 40
2:10 6:30 8:40 has a ratio of 1:5. How I did it was to divide the first number by the second number to get 1:5
Mrs. Smith had 4/6 of a carton of eggs. she dropped a fourth of the eggs. how many eggs was left
First, let's get out common denominators.
8/12 and 3/12.
We then minus the 8 and 3 = 5/12.
We have 5/12.
That's your answer.
4. Which relation is a function?
O {(3, 4), (2, 4), (5, 1), (3,5)}
O {(3, 4), (3, 3), (1, 2), (1,5)}
{(1,4), (1, 3), (1, 2), (1, 1);
{(1, 3), (2, 6), (3,9), (4, 12)}
Answer:
The last option choice [(1,3), (2,6), (3,9), (4,12)
Step-by-step explanation:
The key idea to understand in a function/relation is that each input can only have one output. Inputs are your x-variables and outputs are your y-variables.
In the first relation, you see the two points (3,4) and (3,5). 3 is your input [since its x] , however, it gives you two outputs [y's], 4 and 5. So you can cross out the first option.
In the second relation, look at the points (3,4) and (3,3). Again, both have the same input 3, but different outputs, 4 and 3. So you can cross out the second option.
In the third relation, look at all of the points. They all share a common input, 1, but different outputs, 2, 3, 4, and 5. So you can cross out the third option too.
Lastly, look at the last relation. They all have different inputs but the key thing to look at here is that each input only has one corresponding output. Thus, this is the right answer.
I hope this helps!
Samuel is looking at the floor plan of his house to determine how much carpet he needs to buy for his basement. Based on the floor plan of his basement, how can he decompose the measurements into expressions find the area? A) First, find two areas using (4m + 10m = 14m2) and (8m + 3m = 11m2). Next, add (14m2 + 11m2 = 25m2). B) First, find two areas using (4m x 10m = 40m2) and (8m x 3m = 24m2). Next, add (40m2 + 24m2 = 64m2). C) First, find two areas using (4m x 10m = 40m2) and (8m x 3m = 24m2). Next, subtract (40m2 - 24m2 = 16m2). D) First, add all the labeled sides using (4m + 10m + 12m + 3m = 29m2). Next, add the remaining sides (8m + 7m = 15m2).
Answer:
B) First, find two areas using (4m x 10m = 40m2) and (8m x 3m = 24m2). Next, add (40m2 + 24m2 = 64m2).
Step-by-step explanation:
Samuel should is looking to find the area of his basement in order to cover it with carpet.
An area is calculated by multiplying two dimensions (so answers A and D are not it).
Best solution is to divide the area into two large rectangles then ADD them together to get the total area.
The only scenario where he could have subtracted something based on his plan is if he would have multiplied the 10m by the 12m then subtracted the area that is not part of his basement (7mx8m). He would have achieved the same result of course, but by going a different way.
students were asked to write a trinomial that could not be factored using integers. which students followed the given directions.
pat x2 + 3x- 10
sam x2+x-12
mel x2+2x-1
lee x2+2x-3
ANSWER
Mel followed the right direction.
EXPLANATION
Pat's trinomial is;
[tex] {x}^{2} + 3x - 10[/tex]
There are factors of -10 that sums up to 3.
[tex]5 + - 2 = 3[/tex]
Hence this trinomial could be factored into (x-2)(x+5)
Sam's trinomial:
[tex] {x}^{2} + x - 12[/tex]
There are factors of -12 that sums up to 1.
4+-3=1
[tex] {x}^{2} + x - 12 = (x + 4)(x - 3)[/tex]
Mel's trinomial:
[tex] {x}^{2} + 2x - 1[/tex]
There are no factors of -1 that sums to 2.
This trinomial cannot be factored.
Lee's trinomial:
[tex] {x}^{2} + 2x - 3[/tex]
There are factors of -3 that sums up to 2
3+-1=2
[tex] {x}^{2} + 2x + 3 = (x + 3)(x - 1)[/tex]
Please help with this Math work.
Answer:
12
Step-by-step explanation:
12 is the lowest common denominator here. Both 4 and 6 divide evenly into 12 with no remainder.
Help with sectors of circles
Answer:
Step-by-step explanation:
The perimeter is the arc length plus the two radius lines.
Arc length is:
s = (θ/360) 2πr
So the perimeter is:
P = (θ/360) 2πr + 2r
Given that θ=135 and r = 11:
P = (135/360) 2π(11) + 2(11)
P = 8.25π + 22
P ≈ 47.9
So the perimeter is greater than 47.5 cm.
WHAT IS THIS PLS HELP
Answer:
x = -10
Step-by-step explanation:
-3/4 (x+2) = 6
Multiply each side of the equation by -4/3 to clear the fraction
-4/3 *-3/4 (x+2) = 6*-4/3
(x+2) = 2*-4
x+2 = -8
Subtract 2 from each side
x+2-2 = -8-2
x=-10
use a protractor to find the measure of each angle. Write each angle and its measure in a box ordered by the measure of the angles from least to greatest.
Answer:
Part 1) and Part 2) in the procedure
Step-by-step explanation:
step 1
Find the measures of angles
we know that
The sum of the angles A, B and C must be equal to 360 degrees
Using a protractor
The measures of angles are
∠A=140°
∠B=100°
∠C=120°
step 2
Ordered the measures of the angles from least to greatest
1) ∠B=100°
2) ∠C=120°
3) ∠A=140°
which expression is equivalent to sin7pi/6?
A. sinpi/6
B. sin5pi/6
C. sin5pi/3
D. sin11pi/6
The answer choice is D because sin7pi/6 which it’s exact form is -1/2 the only answer choice which the same exact form is D.
For this case we must find an expression equivalent to:
[tex]Sin (\frac {7 \pi} {6})[/tex]
According to the unit circle, [tex]\frac {7 \pi} {6}[/tex] is in the third quadrant and equals 210 degrees.
Then, we must find an expression equivalent to:
[tex]Sin (210) = - \frac {1} {2} = - 0.5[/tex]
We have to:
[tex]\frac{11 \pi} {6}[/tex]
It is in the fourth quadrant and is equivalent to 330 degrees, according to the unit circle.
[tex]Sin (330) = - \frac {1} {2} = - 0.5[/tex]
Answer:
Option D