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
The step function g(x) is defined as shown.
-3, X < 0
g(x) = 2 0 < x < 4
5, 4 < x < 10
What is the range of g(x)?
0 -3 = g(x) 5
Os g(x) = 10
O {-3, 2, 5)
{0, 4, 10}
The 3rd option is correct.
The range refers to the y-values so the multiple choice answer is restricted to the 1st and 3rd options. The range of the step function is not continuous, it is only the discrete values {-3, 2, 5}.
use an algebraic equation to find the measures of the two angles described below. begin by letting x represent the degree measure of the angles supplement.
the measure of the angle is twenty-nine times greater than its supplement
Which of the following planets has the strongest winds in the solar system?
O Jupiter
O Mars
O Neptune
O Venus
Answer: The answer is Neptune ^-^
Step-by-step explanation:
Got it correct on the test :]
find the missing side lengths
Answer:
x= 4 square root 3 y=4
Step-by-step explanation:
Its 30 60 90 triangle
Hope this helps <3
Find an explicit rule for the nth term of the arithmetic sequence.
-9, -4, 1, 6, ...
Answer:
hope it's helpful
Step-by-step explanation:
glad to help
Tommy stands on a diving bored that is 4 feet above the pool’s surface. He dives and touches the bottom of the pool, which is 12 feet below the pool’s surface. What is the total length of Tommy’s dive?
Answer:t below the pool’s surface. What is the total length of Tommy’s dive?
7 feet
Step-by-step explanation:
What is the volume of the regular pyramid?
576m
96 m
480 m
240 m
Answer:
volume is 576
Step-by-step explanation:
all you do to find volume is multiply LxWxH which will give you volume so just take 18m x 4m x 8m = 576m hopefully its a simply and direct explanation make me brainlist please !!!
The volume of a pyramid is 720 m³.
What is a pyramid?A pyramid is a structure where outer surfaces are triangular and converge to a point at the top.
The volume of a pyramid with a square base is given as:
Volume = 1/3 x base area x height
We have,
Base area:
A = (1/2) x apothem x perimeter
where the perimeter is the total length of all five sides of the pentagon.
So,
= 1/2 x 4 x (5 x 8)
= 2 x 40
= 80 m²
Height.
= 18 m
Now,
The volume of a pyramid.
= 1/2 x 80 x 18
= 80 x 9
= 720 m³
Thus,
The volume of a pyramid is 720 m³.
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A function w satisfies w(1) = 5 and w(4) = 1. A
function z satisfies z(3) = 4 and z(4) = 5. What is
the value of w(z(3)) ?
A) 1
B) 2
C) 4.
D) 5
ce A
Answer: A) 1
Since z(3) = 4, w(z(3)) = w(4)Since w(4) = 1, w(z(3)) = w(4) = 1the question is in the picture
Answer:
∠CBA
Step-by-step explanation:
Answer:
<CBA
Step-by-step explanation:
The vertex has to be in the middle
<CBA
<ABC
or we can name it with just the vertex
<B
PLEASE HURRY I HAVE 3 mins left Which relationship could be the one shown on the graph?
10fx
9
8+
7
6
5
4.
3
2+
1
1 2 3 4 5 6 7 8 9 X
Option A
Must click thanks and mark brainliest
Sorry if i am wrong
It's estimated that 330 billion photographs are taken each year. If there are 6.9
billion people in the world, how many photos on average is that per person?
Find the missing term and the missing coefficient.
(6a −_)5a =_a2 − 35a
Answer:
[tex](6a-7)5a=30a^2-35a[/tex]
Step-by-step explanation:
Message if you want a detailed explanation.
hannah has $345 in her savings account she wants to icrease that number by 20%
Answer:
345 × 20%
= $69 (20% increase)
345 +69
= $414 (final amount with 20% increase)
Translate into an alegbraic expression and simplify if possible.
I have a total of 10 gigabytes of data on my computer, x gigabytes are movies and the rest is music. how many gigabytes of music is stored on my computer?
Answer:
(10-x)GB
Step-by-step explanation:
Music=10-x, simple arithmetic
what is 5cd
when c = 3
and d = 4
Answer:
60
Step-by-step explanation:
5*3*4
evaluate 7-3s for s= -3
Answer:
16
Step-by-step explanation:
Substitute s = - 3 into the expression
7 - 3(- 3) = 7 + 9 = 16
I need help, can someone help me. please
Answer:
y = - 1/3x
Step-by-step explanation:
So the equation of a line can be written in the form y= mx+ c
Here y is the value of y in the y axis, x is the value of x in the x axis, m is the gradient ad c is the co-efficient.
We need to find the gradient of the line which is - 1/3.
That makes our equation y = - 1/3x
HOPE THIS HELPED
Order each set of numbers from least to greatest
1.[tex]\sqrt{200}[/tex], 14, [tex]\frac{41}{3}[/tex]
Answer:
41/3, 14, square root of 200
Step-by-step explanation:
41/3 = 13.66
14 is just 14
and square root of 200 is 14.14
Help this needs to be answered
The equation of the linear function in slope-intercept form is [tex]f(x) = \frac{1}{2}x - 5[/tex]
The equation of a linear function can be written in the slope intercept form as:
f(x) = mx + b,
where,
m represents the slope of the linear function
b represents the point on the y-axis where the line intercepts the y-axis. (at this point, x = 0)
we need to find the value of m and b to be able to write the equation of the linear function.
Find slope (m):
From the image attached, the red line represents the rise (3 units) while the blue line represents the run (6 units).
Slope (m) = rise/run
Substitute:
Slope (m) = 3/6
m = 1/2
Find the y-intercept (b):
From the graph, the line cuts the y-axis at y = -5.
Therefore,
b = -5
Next is to substitute m = 1/2 and b = -5 into f(x) = mx + b. Thus:
[tex]f(x) = \frac{1}{2}x - 5[/tex]
The equation of the linear function is: [tex]f(x) = \frac{1}{2}x - 5[/tex]
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Store employees are handing out coupons. Every 5th customer gets a free bagel coupon. Every 9th customer gets a free drink coupon.
Which customer is the first to receive both coupons?
Answer:
the 45th customer.
Step-by-step explanation:
9•1= 9 9•2=18 9•3=27 9•4=36 9•5=45
5 doesn't go into any other number except for 45.
The first customer to receive both a free bagel coupon and a free drink coupon is the 45th customer.
To find the first customer who receives both coupons (a free bagel coupon and a free drink coupon), we need to determine the least common multiple (LCM) of 5 and 9, which represents the point at which both coupon distributions coincide.
The LCM of 5 and 9 is 45.
This means that the first customer to receive both coupons will be the 45th customer. On the 45th customer, both the 5th customer and the 9th customer coincide, so this customer will receive both a free bagel coupon and a free drink coupon.
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geometry: follow directions below for each figure. Show steps. Circle answers. find the area of each figure.
HELP ASAP!!!!
THANK YOUUUUU
Answer:
575sq. ft
Step-by-step explanation:
The diagram given can be divided into two rectangles.
Area of a rectangle = length * width
Area of the larger rectangle = 15 * (45 - 10)
Area of the larger rectangle = 15 * 35
Area of the larger rectangle = 525sq. ft
Area of the smaller rectangle = 5 * 10
Area of the smaller rectangle = 50 sq. ft
Area of the room = 525 + 50
Area of the room = 575sq. ft
A P E X fasted answer is getting 30 points please hurry.
suppose a normal distribution has a mean of 98 and a standard deviation of 6. what is p(x ≥ 92)
Answer:
Step-by-step explanation:
If the mean is 98 and standard deviation is 6, then 92 is one standard deviation to the left of the mean; that means that 34% + 34% + 13.5% + 2.35% + .15% of the data is included in this area. Add those up and you get, as a percentage, 84%.
Answer:
0.84
Step-by-step explanation:
yee its right
if you can travel 25 miles in 35 minutes, how long should it take you to travel 12 miles?
Answer:
It's going to take you 17 min to travel 12 miles
assuming you are going with mph
Step-by-step explanation:
I looked at a speed calculator and calculated that to go 25 miles in 35 min, you were going 42 mph. so I changed the imput to 12 miles and I got my answer.
A bag contains 4 purple beads and 3 green beads. A bead is drawn and then replaced before drawing the second bead. Find the probability both beads drawn are green.
A) 16/49
B) 6/7
C) 6/49
D) 9/49
Answer:
9/49
Step-by-step explanation:
4 purple beads and 3 green beads= 7 beads
P( green) = green = total = 3/7
Replace the bead
4 purple beads and 3 green beads= 7 beads
P( green) = green = total = 3/7
P( green , replace, green) = 3/7 * 3/7 = 9/49
Find the line of symmetry for the parabola whose equation is y = 2x^2 - 4x + 1.
wrong answers = reported
ty<3
Answer:
y = 2 x^2 - 4 x + 1
parábola
Step-by-step explanation:
(|5 - 3x | - 1) - ( 1 - 3x ) = 0
(| 5 - 3x | - 1) - (1 - 3x) = 0
|5 - 3x| - 1 - 1 + 3x = 0
|5 - 3x| - 2 + 3x = 0
1) (5 - 3x) - 2 + 3x = 0, if 5 - 3x >= 0
3 = 0. has no solutions
2) -(5 - 3x) - 2 + 3x = 0, if 5 - 3x < 0
-5 + 3x - 2 + 3x = 0
6x = 7
x = 7/6
5 - 3x < 0
-3x < -5
x > 5/3.
has no solutions
What are the solutions to the equation f(x)=g(x)?
A) x= -3, 4
B) x= -4, 2.5
C) x= -0.8, 2.5
D) x= 8, -8
Answer:
B
Step-by-step explanation:
The points where f(x) intersects g(x) are - 4 and 2.5. These points are the solution of the equation f(x)=g(x)
Answer:
(-4,8) and ( 2.5, -8)
Step-by-step explanation:
The solutions are where the two graphs intersect
They intersect at x = -4 and y = 8 and at x = 2.5 and y = -8
(-4,8) and ( 2.5, -8)
Determine the value of y, if x is -5.
y = |x| – 6
Answer:
The value of y = -1 , if x is -5.
Step-by-step explanation:
y = |x| – 6
y = |-5| – 6
|-x| = x ---> this is the rule of absolute value, so let's apply this to our equation.
y = 5 – 6 --------------> -5 becomes 5
y = -1
Pls help ASAP will give brainliest
Answer:
hope it help you.........
Answer:
[tex]\boxed {\boxed {\sf y= -1.2 }}[/tex]
Step-by-step explanation:
We are asked to solve the following equation for y.
[tex]-2y-4.2= 1.8 + 3y[/tex]
To solve for y, we have to isolate the variable by performing the inverse operations. First, move all the terms without a variable or the constants to one side, and the terms with a variable to the other side.
4.2 is being subtracted and the inverse operation of subtraction is addition. Add 4.2 to both sides.
[tex]-2y-4.2 +4.2= 1.8 + 3y+ 4.2[/tex]
[tex]-2y=1.8 + 4.2 + 3y[/tex]
[tex]-2y= 6 + 3y[/tex]
3y is being added and the inverse operation of addition is subtraction. Subtract 3y from both sides.
[tex]-2y-3y= 6+ 3y -3y[/tex]
[tex]-2y-3y= 6[/tex]
[tex]-5y=6[/tex]
y is being multiplied by -5. The inverse operation of multiplication is division. Divide both sides by -5.
[tex]\frac {-5y}{-5}= \frac{6}{-5}[/tex]
[tex]y=- 1.2[/tex]
Check the answer by substituting -1.2 back into the original equation.
[tex]-2 (-1.2)-4.2 = 1.8 + 3(-1.2)[/tex]
[tex]2.4-4.2=1.8 + - 3.6[/tex]
[tex]-1.8 = -1.8[/tex]
This checks out, so we know our answer is correct.
16-32)
What is the equation of the line that is perpendicular to
the given line and passes through the point (3, 0)?
O 3x + 5y = -9
O 3x + 5y = 9
O 5x - 3y = -15
O 5x - 3y = 15
Answer:
the fourth option : 5x - 3y = 15
Step-by-step explanation:
the slope of the original line is given by the coordinate differences between the 2 points on the line.
remember, the slope is the factor of x in the line equation and is the ratio y/x indicating how many units y is changing, when x changes a certain number of units.
so, to go from (-3. 2) to (2, -1) x changes 5 units and y -3 units.
therefore, the slope is -3/5.
the slope of a perpendicular line simply switched x and y. and the sign of the slope.
therefore the slope of the perpendicular line is 5/3.
and the line equation is
y = (5/3)x + c
to get c we need the point on the line (3, 0).
0 = (5/3)×3 + c = 5 + c
c = -5
y = (5/3)x - 5
3y = 5x - 15
3y - 5x = -15 or (after multiplying both sides by -1)
5x - 3y = 15
