Which equation represents the general form a circle with a center at (–2, –3) and a diameter of 8 units?
x2 + y2 + 4x + 6y – 51 = 0
x² + y² – 4x – 6y – 51 = 0
x2 + y2 + 4x + 6y – 3 = 0
x2 + y2 – 4x – 6y – 3 = 0
The equation for the given circle is:
[tex]x^2 + y^2 + 4x + 6y - 3 = 0[/tex]
How to get the equation of the circle?
Remember that for a circle whose center is (a, b) and has a radius r, the equation is:
[tex](x - a)^2 + (y - b)^2 = r^2[/tex]
In this case, the center is (-2, -3) and the diameter is 8 units, so the radius is r = 4.
Then the equation is:
[tex](x + 2)^2 + (y + 3)^2 = 4^2[/tex]
Expanding the squares we get:
[tex](x^2 + 2*2*x + 4) + (y^2 + 2*3*y + 3^2) = 16\\\\x^2 + y^2 + 4x + 6y + 4 + 9 - 16 = 0\\\\x^2 + y^2 + 4x + 6y - 3 = 0[/tex]
So the correct option is the third one.
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Line AB passes through points A (-6,6) and B(12,3). If the equation of the line is written in slope-intercept form, y=mx+b, the. m=-16. What is the value of b?
Answer:
You wrote the question wrong...
m is not -16 it is -1/6 (that is a big difference)
y=mx+b
y=-1/6x+b
3 = -1/6(12) + b
3 = -2 + b
b=5
Step-by-step explanation:
Please help I’ll give brainliest
Answer:
[tex]A=60m^2[/tex]
Step-by-step explanation:
formula for area of a parallelogram is [tex]A=bh[/tex] where [tex]b[/tex] stands for base and [tex]h[/tex] stands for height.
[tex]A=12(5)[/tex]
[tex]A=60[/tex]
If f (x) = 6x - 6, find f(-1).
Answer:
Step-by-step explanation:
1
Answer:
-12
Step-by-step explanation:
Hi Alyssa!,
For any x we multiply it by 6 and subtract 6 from it to get the F. The function tells us this. To find f(-1) it bassicly says what's f when x is -1. Well we know that. f is 6(-1)-6 whis is -12.
F is -12
JoeLouis2
Question 2
Find the equation of the line parallel to y = x - 2 that passes through the point (-3,2).
Answer:
The equation of the required line is y = x + 5
Step-by-step explanation:
The equation of the given line is y = x - 2
The required line = A line parallel to the given line
The point through which the required line passes = (-3, 2)
The general form of the equation of a straight line, is y = m·x + c
Where;
m = The slope of the line
By comparison, the slope of the given line, m = 1
When two lines are parallel, their slope are equal
Therefore, the slope of the required line = m = 1
The equation of the required line in point and slope form is therefore;
y - 2 = x - (-3) = x + 3
∴y = x + 3 + 2 = x + 5
The equation of the required line is therefore;
y = x + 5.
I need help understanding how to answer this question:
List the sides in order from the smallest to the largest.
A researcher wanted to know if there was a difference in fall and spring semester tuition at universities across the U.S. His study took a random sample of 200 universities, had a p-value of 0.013 and found that the tuition had increased by an average of $0.35 between fall and spring semester. What can be said about the results of this study
Answer:
The given parameters of the study are;
The number of people in the sample, n = 200
The p-value = 0.013
The average increase between fall and spring semester = $0.35
Therefore, we have;
Given that the p-value is less than 0.05, we reject the null hypothesis, and that there is significant statistical evidence to suggest that there is a difference between the fall and spring semester tuition at universities across the U.S.
Step-by-step explanation:
The result of the test hypothesis is incorrect or should be rejected.
What is P-value?Researchers frequently use P-values to determine if a trend they've seen is statistically significant. The p-value of a statistical test is small enough to reject the null hypothesis of the test, which is referred to as statistical significance.
What is the significance of the P-value?The likelihood that the null hypothesis is true is P > 0.05. The likelihood that the alternative hypothesis is correct is (1-P) the P-value. The test hypothesis is incorrect or should be rejected if the test result is statistically significant (P≤0.05). There was no effect if the P-value was bigger than 0.05.
We reject the null hypothesis since the p-value is less than 0.05, and there is strong statistical evidence to imply that there is a difference between autumn and spring semester tuition at institutions across the United States.
Hence, the result of the test hypothesis is incorrect or should be rejected.
Learn more about P-Value:
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If A and B are (-2,-2) and (2,-4). Find the coordinates P such that AP=3/7 AB and P lies on the line segment ab
Answer:
The coordinates of point P are [tex](-\frac{2}{7}, -\frac{20}{7})[/tex].
Step-by-step explanation:
Point P:
The coordinates of point P are (x,y).
AP=3/7 AB
So
[tex]P - A = \frac{3}{7}(B-A)[/tex]
We apply this both for coordinate x and coordinate y.
Coordinate x:
[tex]x - (-2) = \frac{3}{7}(2 - (-2))[/tex]
[tex]x + 2 = \frac{12}{7}[/tex]
[tex]x = \frac{12}{7} - 2 = \frac{12}{7} - \frac{14}{7} = -\frac{2}{7}[/tex]
Coordinate y:
[tex]y - (-2) = \frac{3}{7}(-4 - (-2))[/tex]
[tex]y + 2 = -\frac{6}{7}[/tex]
[tex]y = -\frac{6}{7} - 2 = -\frac{6}{7} - \frac{14}{7} = -\frac{20}{7}[/tex]
The coordinates of point P are [tex](-\frac{2}{7}, -\frac{20}{7})[/tex].
lus
A
B
С
D
If AC = 18 and CD = 5, AD = [?]
Enter
Answer:
hey,
18+5=23
so AD=23
this is the correct answer :)
please mark as brainliest
HELPPPPP
a) -3 x 4 - (-9) ÷3
b) 15 - 2(-8 +-7)
If Andrea traveled 300 miles in 5 hours at what rate was she driving?
Answer:
60
Step-by-step explanation:
[tex]\frac{300}{5}[/tex]
60
Hence, 60 is the answer
Answer:
60 mph
Step-by-step explanation:
For this problem, we are looking at the rate, miles per hour. We know that Andrea traveled 300 miles in 5 hours, but how many miles did she travel in one hour? Let's do the math:
[tex]300[/tex]÷[tex]5=60[/tex] miles.
So, in one hours, Andrea travels 60 miles. We get the rate, 60mph.
Andrea was driving at 60 mph.
I hope this helps! Please let me know if you have any questions :)
The tength of a picture frame is 12 cm more than twice the width. If the perimeter is 204cm, find the
dimensions (length and width) of the frame.
Answer:
30cm x 72 cm
Step-by-step explanation:
The perimeter is the measurements of all sides added together. Let's start by dividing the perimeter by 2, so we have the sum of the length and width. This gives us 102cm. Let's call the width x, and the length y. We know y is x times 2 plus 12. (2x + 12) So, we know [x + y = x + (2x + 12)]. So let's solve.
x + y = x + (2x + 12)
102 = x + (2x + 12)
102 = 3x + 12
102 - 12 = 3x + 12 - 12
90 = 3x
90/3 = 3x/3
30 = x
The width is 30cm.
How are exponents and roots related?
Step-by-step explanation:
sana po nakatulong sainyo thanks❤
a 25% tip was payed on a 30$ meal what is the amount of the tip
Answer:
$7.50
Step-by-step explanation:
30 x 0.25= 7.50
Bab needs help please!
Answer:
282.6 in³
Step-by-step explanation:
Volume = area circle * height
Area circle = πr²
Area circle = 3.14 * 9 = 28.26
28.26 * 10 = 282.6 in³
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
An isosceles triangle has an angle that measures 120°. Which other angles could be in that isosceles triangle? Choose all that apply. 75, 50, 30, 25
Answer:
30.
Step-by-step explanation:
The 120 degree has to be the vertex angle.
The other 2 angles in the triangle will be congruent as the triangle is isosceles.
These 2 are both = (180-120) / 2
= 60/2
= 30 degrees.
Find the circumference
Answer:
75.36 mi
Step-by-step explanation:
Given :-
Radius = 12 mi .We know :-
→ Circumference = 2 π r
→ C = 2 * 3.14 * 12 mi
→ C = 75.36 mi
Answer:
Step-by-step explanation:
circumference of a circle=2πr
=2*3.14*12
=24*3.14
=75.36 mi
Help me I don't know any
Answer:
25%
Step-by-step explanation:
(a)
We need to express in percent 8 as a percent of 32.
We have,
Numerator = 8
Denominator = 32
Percent,
[tex]P=\dfrac{8}{32}\times 100\\\\=25\%[/tex]
Hence, the required percentage is 25%.
What is the area of this cube 6 4 5
What is the value of f(3) in the function below? f(x) = 1/2 .2^x O A. 4 B. 2 O c. 133 3 2 D. 8
Answer:
B
Step-by-step explanation:
To evaluate f(3) substitute x = 3 into f(x) , that is
f(3) = [tex]\frac{1}{4}[/tex] × 2³ = [tex]\frac{1}{4}[/tex] × 8 = 2 → B
Answer:
2
Step-by-step explanation:
f(3)=1/4×2^3
f(3)=1/4×8
f(3)=8/4=2
[tex] {10}^x = 5[/tex]
What is x?
×= 5/log 10 ^10
x= In 5
x=log 10^5
x=1/2
Answer:
below
Step-by-step explanation:
10ˣ = 5
applying log to both sides
xlog 10 = log5
x = 0•699
Set X is made up of the possible ways five students, represented by A, B, C, D, and E, can be formed into groups of three. Set Y is made up of the possible ways five students can be formed into groups of three if student A must be in all possible groups. Which statements about the situation are true? Select three options.
I NEED THIS RIGHT AWAY
Set X has 10 possible groupings.
X Y
Set Y = {ABC, ABD, ABE, ACD, ACE, ADE}
If person E must be in each group, then there can be only one group.
There are three ways to form a group if persons A and C must be in it.
The answer is
A. Set X has 10 possible groupings.
C. Set Y = {ABC, ABD, ABE, ACD, ACE, ADE}
E. There are three ways to form a group if persons A and C must be in it.
Good luck :)
Answer:
It’s A,C,E
Step-by-step explanation:
i did the quiz friends
ur wlcm :)
hope i helped /made life easier
Solve for x. assume that lines which appear tangent are tangent. x=
Answer:
x = 8
Step-by-step explanation:
The product of the length of the exterior segment of a secant and the length of the secant is equal to the correpsonding operation with the other secant.
9(9 + 11) = 10(10 + x)
180 = 100 + 10x
10x = 80
x = 8
WHAT IS FOURTH OFR 17%
Im not sur eabout this but i think it mean that 17% is like0.98_08
Andres went out to a restaurant for dinner. His total bill before tax and tip was $27.30. He was charged an additional 9% tax and he also paid a 15% tip on the original bill.
Answer:
$25.66
Step-by-step explanation:
Given data
Total Bill before tax and tip= $27.30
Tax= 9%
Tip= 15%
Let us find the tax
=9/100*27.30
=0.09*27.30
=$2.457
Let us find the tip
=15/100*27.30
=0.15*27.30
=$4.095
Therefore his bill after tax and tip is
=27.30+2.457-4.095
=$25.66
marcus purchased a sail boat for $56,900. he anticipates each year the boat will decrease in value by 8.1% from the previous year.
enter numbers in the boxes to write an exponential function that models the value in dollars of the boat x years after Marcus's purchase.
Answer:
Results are below.
Step-by-step explanation:
Giving the following information:
Purchase price= $56,900
Decrease in value= 8.1% per year from the previous year
To calculate the value of the sailboat after x number of years, we need to use the following formula:
Future value= purchase price / (1 + decrease in value)^x
For 10 years:
FV= 56,900 / (1.081^10)
FV= $26,112.91
6. Using the distributive property, find the following products 1002 x 1518
Answer:
The best choice of answer answer is = 1521036
3) The triangles shown are congruent using ASA, but they arb not marked completely. Mark the corresponding parts in this drawing that must be congruent in order to apply the ASA. Then write the congruence statement in the spaces provided. (2 pts) CAB FDE ____=____
Answer:
angle A = Angle E
ΔCAB ≅ΔFED
Step-by-step explanation:
ASA means Angle side Angle Where the side is between the two angles
We have an angle C= F and a side AC = EF
We need angle A = Angle E
ΔCAB ≅ΔFED
the sum of two integers is 310. if one of them is - 52. find the other
Answer:
Integer = 362
Step-by-step explanation:
Let the two integers be x and y
Sum of two integers, x + y = 310 ------(1)
Given one of the integer, Let x = -52
Substitute x = -52 in (1) ,
-52 + y = 310
y = 310 + 52
y = 362
Given the equation 5x + 23 = − 2x − 12, which order of operations completely solves for x?
Step-by-step explanation:
5x+2x=-12 -23
7x=-35
which will give you 1 over 5writing your answer in a standard form it helps you to get the answer easy and quickAnswer:
-5
Step-by-step explanation:
5x+23=-2x-12
5x-(-2x)+23=-12
5x+2x=-12-23
7x=-35
x=-35/7
x=-5
