Given equation of the Circle is ,
[tex]\sf\implies x^2 + y^2 = 25 [/tex]
And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,
[tex]\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2[/tex]
Here we can say that ,
• Radius = 5 units
• Centre = (0,0)
Finding distance between the two points :-
[tex]\sf\implies Distance = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{20}\\\\\sf\implies\red{ Distance = 4.47 }[/tex]
Here we can see that the distance of point from centre is less than the radius.
Hence the point lies within the circle .
inside the circle
Step-by-step explanation:
we want to verify whether (-4,2) lies inside or outside or on the circle to do so recall that,
if [tex]\displaystyle (x-h)^2+(y-k)^2>r^2[/tex] then the given point lies outside the circleif [tex]\displaystyle (x-h)^2+(y-k)^2<r^2[/tex] then the given point lies inside the circleif [tex]\displaystyle (x-h)^2+(y-k)^2=r^2[/tex] then the given point lies on the circlestep-1: define h,k and r
the equation of circle given by
[tex] \displaystyle {(x - h)}^{2} + (y - k) ^2= {r}^{2} [/tex]
therefore from the question we obtain:
[tex] \displaystyle h= 0[/tex][tex] \displaystyle k= 0[/tex][tex] {r}^{2} = 25[/tex]step-2: verify
In this case we can consider the second formula
the given points (-4,2) means that x is -4 and y is 2 and we have already figured out h,k and r² therefore just substitute the value of x,y,h,k and r² to the second formula
[tex] \displaystyle {( - 4 - 0)}^{2} + (2 - 0 {)}^{2} \stackrel {?}{ < } 25[/tex]
simplify parentheses:
[tex] \displaystyle {( - 4 )}^{2} + (2 {)}^{2} \stackrel {?}{ < } 25[/tex]
simplify square:
[tex] \displaystyle 16 + 4\stackrel {?}{ < } 25[/tex]
simplify addition:
[tex] \displaystyle 20\stackrel { \checkmark}{ < } 25[/tex]
hence,
the point (-4, 2) lies inside the circle
If f(x) = k where k is a constant, and the points (6,1) and (8,1) lie on the graph of y = f(x), what is the value of f(0)?
I think the answer is 1 but not 100% sure.
Answer:
The value of f(0)=1
Step-by-step explanation:
We are given that
[tex]f(x)=k[/tex]
[tex]y=f(x)[/tex]
(6,1) and (8,1) lies on the graph of y=f(x)
We have to find the value of f(0).
[tex]f(6)=1[/tex]
[tex]f(8)=1[/tex]
[tex]f(x)=k[/tex]
By comparing ,we get
k=1
Therefore, [tex]y=f(x)=1[/tex]
Now, substitute x=0
[tex]f(0)=1[/tex]
Hence, the value of f(0)=1
Solve for x and y:
x – 3y = -8
3x + 2y = 31
Select one:
O a. (-11,-1)
O b. (11,1)
o c. (5,8)
O d. (7,5)
Answer:
O d. (7,5)
Step-by-step explanation:
x – 3y = -8 (1)
3x + 2y = 31 (2)
From (1)
x = -8 + 3y
Substitute x = -8 + 3y into (2)
3x + 2y = 31 (2)
3(-8 + 3y) + 2y = 31
-24 + 9y + 2y = 31
-24 + 11y = 31
11y = 31 + 24
11y = 55
y = 55/11
y = 5
Substitute y = 5 into (1)
x – 3y = -8 (1)
x - 3(5) = -8
x - 15 = -8
x = -8 + 15
x = 7
(x, y) = (7, 5)
If the price of a gallon of gas was $0.89 in 1984 and was $3.59 in 2014, what was the average rate of change in the price per gallon of gas?
Answer:
0.09
Step-by-step explanation:
avg rate of change is: change in y/ change in x
so it´d be 3.59 - 0.89 / 2014 - 1984
= 2.7/ 30
= 0.09
note:
The slope formula and the average rate of change formula are the same, just written a bit different, so you could also use:
y2 - y1 / x2 - x1
A new hospital tracked the number of births during its first 6 months of operation, as shown in the table.
A 2-column table with 6 rows. The first column is labeled month with entries 1, 2, 3, 4, 5, 6. The second column is labeled number of births with entries 137, 110, 93, 70, 65, 77.
Find a quadratic function that models the data. Round numerical values to the nearest whole number
Answer:
y = 4x² - 43x + 178
Step-by-step explanation:
Given that data:
1 __ 137
2 __ 110
3 __ 93
4 __ 70
5 __ 65
6 __ 77
Usibg technology, the quadratic regression equation obtained is written in the form:
Ax² + Bx + C
A = 4.34 = 4 ( nearest whole number)
B = - 43.46 = - 43 (nearest whole number)
C = 178.3 = 178 ( nearest whole number)
Hence, the quadratic model is
y = 4x² - 43x + 178
By rounding the coefficients to the nearest whole number, the quadratic function that models the data is[tex]f(x) = 5x^2 - 42x + 174[/tex]
How to Find a quadratic function that models the data.To find a quadratic function that models the data, use a quadratic equation of the form:
[tex]f(x) = ax^2 + bx + c[/tex]
Let's use the given data points to form a system of equations and solve for the coefficients a, b, and c.
Using the first data point (month 1 with 137 births):
[tex]f(1) = a(1)^2 + b(1) + c = 137[/tex]
a + b + c = 137 (Equation 1)
Using the second data point (month 2 with 110 births):
[tex]f(2) = a(2)^2 + b(2) + c = 110[/tex]
4a + 2b + c = 110 (Equation 2)
Using the third data point (month 3 with 93 births):
[tex]f(3) = a(3)^2 + b(3) + c = 93[/tex]
This simplifies to:
9a + 3b + c = 93 (Equation 3)
Solve this system of equations will give us the values of a, b, and c.
Subtract Equation 1 from Equation 2
3a + b = -27 (Equation 4)
Subtract Equation 1 from Equation 3
8a + 2b = -44 (Equation 5)
Now solve Equations 4 and 5 simultaneously.
Multiply Equation 4 by 2 and subtracting it from Equation 5:
8a + 2b - (6a + 2b) = -44 - (-54)
2a = 10
Divide both sides by 2:
a = 5
Now substitute the value of a back into Equation 4:
3(5) + b = -27
15 + b = -27
Subtract 15 from both sides:
b = -42
Finally, substitute the values of a and b into Equation 1
5 + (-42) + c = 137
-37 + c = 137
Add 37 to both sides:
c = 174
Therefore, the quadratic function that models the data is:
[tex]f(x) = 5x^2 - 42x + 174[/tex]
Rounding the coefficients to the nearest whole number, the quadratic function becomes:
[tex]f(x) = 5x^2 - 42x + 174[/tex]
Learn more on quadratic on https://brainly.com/question/1214333
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What is the y-intercept of the line 10x - 5y = 40
10x - 5y = 40
-5y = -10x + 40 || : (-5)
y = 2x - 8
help me solve this problem please
Step-by-step explanation:
nope guy but little you now
If 0 < f ≤ 90 and cos(22f − 1) = sin(7f + 4), what is the value of f?
Answer:
3
Step-by-step explanation:
We are going to be using cofunction identity cos(90-x)=sin(x).
Apply to either side but not both.
cos(22f − 1) = sin(7f + 4)
sin(90-[22f-1])=sin(7f+4)
90-[22f-1]=7f+4
Distribute
90-22f+1=7f+4
Combine like terms
91-22f=7f+4
Add 22f on both sides
91=29f+4
Subtract 4 on both sides
87=29f
Divide 29 on both sides
3=f
f=3 is between 0 and 90
Answer:
The answer is "3."
Step-by-step explanation:
Just submitted the test and got the answer correct!
1. Can cross multiplication be used to solve this problem? Why or why not?
HELP
Answer:
Step-by-step explanation:
Cross multiplication can be used but not in the beginning. First x should be isolated.
[tex]3 +\frac{5}{x}=\frac{7}{x}\\\\[/tex]
Now subtract [tex]\frac{5}{x}[/tex] from both sides
[tex]3 = \frac{7}{x}-\frac{5}{x}\\\\3=\frac{7-5}{x}\\\\3=\frac{2}{x}[/tex]
In this stage, cross multiplication can be used.
[tex]\frac{3}{1}=\frac{2}{x}\\\\3*x=2*1\\\\x = \frac{2}{3}[/tex]
Answer:
x =0 and x =2/3
Step-by-step explanation:
as is no
but if you put an x under the 3 to make 3x/x
then you'd have 3x+5/x = 7/x
to make
3x^2 + 5x = 7x
this makes
3x^2 -2x =0
using the quadratic formula
answers
x =0 and x =2/3
15. ABCD is a cyclic quadrilateral in which
AB = BC and ABC = 70°.
AD produced meets BC produced at the
point P, where APB = 30°.
Calculate
a) ADB
b) ABD
Answer:
a) ∠ADB is 55°
b) ∠ABD is 45°
Step-by-step explanation:
a) In the cyclic quadrilateral ABCD, we have;
Segment AB = Segment BC
∠ABC = 70°
Therefore, ∠ADC = 180° - 70° = 110° (Opposite angles are supplementary)
∠ADC + ∠CDP = 180° (Sum of angles on a straight line)
∴ ∠CDP = 180° - ∠ADC
∠CDP = 180° - 110° = 70°
∠DCP = 180° - 70° - 30° = 80°, (Angle sum property)
Similar to ∠DCP = ∠DAB = 80° (Exterior angle of a cyclic quadrilateral)
∠CAB = ∠ACB = (180° - 70°)/2 = 55° (Base angles of isosceles triangle ΔABC)
∠ADB = ∠ACB = 55° (Inscribed angle of a circle subtended by the same chord)
∠ADB = 55°
b) ∠ABD = 180° - ∠DAB - ∠ADB
∴ ∠ABD = 180° - 55° - 80° = 45°
∠ABD = 45°
Multiply by using suitable rearrangement: 2 × 4 × 8 × 50 × 125. I need this answer. Quick. Ok, How about I give 15 points? Yeah cool just answer.
Answer:
[tex]2 \times 4 \times 8 \times 50 \times 125 \\ \\ = 400000[/tex]
plss answer someone the bottom question qracias
0.6(180) is the same as asking the question - What is 60% of 180?
To find that answer, we can multiply 0.6 by 180. We use the decimal 0.6 because that is the decimal form of 60%.
0.6 x 180 = 108
Another way we can find this answer is to find 1/10 of 180 and multiply this answer by 6 because 60/100 is the same thing as 6/10.
1/10 of 180 = 18
18 x 6 = 108
Hope this helps!
Please help me here. I've tried this one over and over and I'm unable to get the answer that was given. How do I find the area of this triangle?
Answer:
jjdjdjdj and technology and technology and technology and technology and technology
You have job were you are paid (p) $1,000 a month plus $15.00 for every hour (h) you work. You work 150 hrs (h), how much money did you make?
Answer:
15 x 150 = 2250
2250 + 1000 = 3250
you make $3250,00
Which of these is an example of a literal equation?
A. 4x + 7 = 22
B. 5+ 20 = 52
C. ax - by = k
D. 2x + 7y
Let u = <-7, -2>. Find 4u.
Answer:
<-28, -8>
Step-by-step explanation:
you multiply the values by 4 because that's what the question tells you to do.
if <-7,-2>=u and it's asking for 4u, then the answer is the solution to the equation 4(<-7,-2>)
15 years from now Renu will be four times her present age. What is Renu's present age?
Answer:
5 years
Step-by-step explanation:
(x+15)=4x
15=4x-x
15=3x
5=x
please help I will give brainliest
Answer:
the second one I think it is the second one
What is the product of 3/5 and 25. Is the product more or less than 14? Explain your answer in complete sentences.
(3/5 is a fraction Not Disvison )
Answer:
15, The answer is greater than 14 because when you multiply the 2 fractions you get a number that is greater than 15
Step 1: Set up equation
[tex]\frac{25}{1}*\frac{3}{5}[/tex]
Step 2: Cross reduce
you can cross reduce 25 and 5 because they are both share a common divisor
[tex]\frac{5}{1} *\frac{3}{1}[/tex]
Step 3: Multiply numerator and denominator together
[tex]\frac{15}{1}[/tex]
Final Answer:
15
The answer is greater than 14 because when you multiply the 2 fractions you get a number that is greater than 15
in need help
Relationships in Triangles
Answer: x = 17
Step-by-step explanation: Since ray SQ bisects <TSR, we know
that the m<TSQ ≅ m<QSR by the definition of an angle bisector.
So we can setup the equation (3x - 9) + (3x - 9) = 84
using the angle addition postulate.
Simplifying on the left gives us 6x - 18 = 84.
Now add 18 to both sides to get 6x = 102.
Now divide both sides by 6 so x = 17.
Please help asap, how do I find the missing variables? (Trigonometry)
Answer:
x = 5.333 , y= 9.620764575
Step-by-step explanation:
sin(29)/x = sin(90)/11
x = 11* sin(29)/sin(90)
x = 5.333
(5.333)^2 + y^2 = 121
y^2 = 121 - (5.333)^2
y= 9.620764575
plzzzz help me outttt!!!! asap thank you!
Answer:
a
Step-by-step explanation:
answer is a + c
find the sum of the series
√2 - 2 + 2√2 +__+64√2.
Step-by-step explanation:
The question is not clear to me
What is the measure of angle ABC of a circle
Answer:
the angle <ABC is equal to 65°
Solve 2(1 – x) > 2x.
x < 2
x > 0.5
x < 0.5
x > 2
Answer:
x < 0.5
Step-by-step explanation:
Given
2(1 - x) > 2x ( divide both sides by 2 )
1 - x > x ( add x to both sides )
1 > 2x ( divide both sides by 2 )
[tex]\frac{1}{2}[/tex] > x , that is
x < [tex]\frac{1}{2}[/tex] OR x < 0.5
help.........................
Answer:
solution
here,
Step-by-step explanation:
f={(2,1/2), ( 3, 1/3) , (4, 1/4)}
Range = { / (\ frac 12\) , \ (\ frac 13\) ,
\( \ frac 14\ )}
Inverse function ( f-^1 ) = {( 1/2, 2) ,( 1/3 ,3) , 1/4, 4 )} is the required answer
Question
The quotient of a number and 5 has a result of 2. What is the number
Answer:
Probably 10
Step-by-step explanation:
10/5=2
O(Q0) A(2,0), B(3, 2) and C(1, 2) are the vertices of quadrilateral OABC. Translate quadrilateral by translation vector [0,2]
Answer:
A'(2,2) B'(3,4) C'(1,4) O'(Q,2)
PLZ I NEED ANSWER ILL GIVE BRAINLIEST
Answer:
2
Step-by-step explanation:
Every 24 hours, Earth makes a full rotation around its axis. Earth's speed of rotation at the equator is 1.670 km per hour. What is the
circumference of Earth's equator?
(Hint. Earth's circumference at the equator is equal to the distance that Earth rotates around the equator).
Answer:
The circumference of Earth's equator is 40,080 km.
Step-by-step explanation:
Given that every 24 hours, Earth makes a full rotation around its axis, and Earth's speed of rotation at the equator is 1,670 km per hour, to determine what is the circumference of Earth's equator the following calculation must be performed:
24 x 1,670 = X
40,080 = X
Therefore, the circumference of Earth's equator is 40,080 km.
Question 12 (5 points)
Determine the value of x
0.28 units
0.98 units
3.58 units
1.12 units
Answer:
1.12 Units
Step-by-step explanation:
1. Use cos(56°) = x/2
Make sure your calculator mode is in deg (degree) not rad(radians)
2. 2(cos(56°)) = x
3. x = 1.118385807
4. Round up to get 1.12 Units
