Answer:
x² + 4x + y² + 10y + 20 = 0
Step-by-step explanation:
Step 1: Expand (x + 2)²
x² + 2x + 2x + 4 + (y + 5)² = 9
Step 2: Combine like terms
x² + 4x + 4 + (y + 5)² = 9
Step 3: Expand (y + 5)²
x² + 4x + 4 + y² + 5y + 5y + 25 = 9
Step 4: Combine like terms
x² + 4x + 4 + y² + 10y + 25 = 9
Step 5: Move 9 over
x² + 4x + 4 + y² + 10y + 25 - 9 = 0
Step 6: Combine like terms
x² + 4x + y² + 10y + 20 = 0
Answer:
x^2+y^2+4x+10y+20=0
Step-by-step explanation:
(x+2)^2+(y+5)^2=9
x^2+4x+4+y^2+10y+25-9=0
general form: x^2+y^2+4x+10y+20=0
There are 30 students in a class. 10 students have a pet dog, 13 students have a pet cat, and 7 students have a pet fish. 4 students have both a pet dog and a pet cat, 6 students have a pet cat and a pet fish, 2 students have a pet dog and a pet fish. 1 student has all three. How many of the 30 students have pets?
Answer:
9 students have pets
Step-by-step explanation:
From the above question, we are given the following information
Total number of students = 30
Let Pet Dog = D
Pet Cat = C
Pet Fish = F
Number is students that have pet dog
(D) = 10 students
Number of students that have pet cat (C) = 13 students
Number of students that have pet fish (F) = 7 students
Number of students that have Pet dog and cat ( D and C) = 4 students
Number of students that have Pet cat and fish (C and F) = 6 students
Number of student that has pet dog and pet fish (D and F) = 2 students
1 student has all three = ( D and F and C)
Number of student that have a pet Dog only
= n(D) - [n( D and C) + n( D and F) - n(D and C and F)]
= 10 -( 4+ 2 -1)
= 10 - 5
= 5
Number of student that have Pet cat only
= n(C) -[ n( D and C) + n( C and F) - n( D and C and F)]
= 13 -( 4 + 6 - 1)
= 13 - 9
= 4
Number is student that have a pet fish only
= n(F) - [n (C and F) + n( D and F) - n( D and C and F)]
= 7 - [6 + 2 - 1]
= 7 - 7
= 0
The number of students that have pets is calculated as:
(Number of students that have dogs only + Number of student that have cats only + Number of students that have fish only)
= 5 + 4 + 0
= 9
Therefore only 9 students have pets.
Find the length of an earthworm 4 hours after its birth
Answer:
Maximum is 14 inches so maybe 5 inches?
Step-by-step explanation:
Tamara earns 2,050 every month. She spends 65% on the amount that she earns. The rest of the money is equally divided and deposited into two seperate accounts. How many months until tamara has deposited more than 2,500 in one of her accounts
Answer:
Tamara earns $2,050 each month.
She spends 65% of that, so the amount that she spends is:
S = (65%/100%)*$2,050 = 0.65*$2,050 = $1,332.50
Then the amount that she has left is:
R = $2,050 - $1,332.50 = $717.50
Now she divides that in half, and deposits those amounts in two separate accounts.
She deposits $717.50/2 = $358.75 in each acount.
Then she deposits $358.75 per month, so after x months she has:
x*$358.75 in each of those accounts, so one of the accounts will have more than $2,500 when:
x*$358.75 = $2,500
x = $2,500/$358.75 = 6.96
So after 6.96 moths she will have more than $2,500 in one of her accounts, we can round it to:
After 10 months Tamara has deposited more than 2,500 in one of her accounts.
simplify 4551 * 5541
Answer:
25,217,091
Step-by-step explanation:
4551 * 5541 = 25,217,091
Answer:
4551*5541=25217091
Step-by-step explanation:
identify the coefficient of x
1. 3xy³
2. xy
___
5
3. 3
___ x y
4
4. 3
___ x²y
4
Answer:
3
1/5
3/4
3/4
Step-by-step explanation:
Coefficient is a number that is always written in front of a term.
3xy^3=3
xy/5=1/5
3/4xy=3/4
3/4x^2y=3/4
Hope this helps ;) ❤❤❤
The number of a two dollar bill i need to pay for a purchase is 9 more than the number of 5 dollar bills i need to pay for the same purchase what is the cost of the purchase?
Answer:
$60
Step-by-step explanation:
Let's say we need t $2 bills and v $5 bills.
We need 9 more $2 bills than $5 bills, so:
t = 9 + v
We also know that the amount of money in t $2 bills is 2 * t = 2t. The amount of money in v + 9 $5 bills is 5 * (v + 9) = 5v + 45. These amounts are equal:
5v + 45 = 2t
Plug v + 9 in for t in 5v = 2t + 18:
5v = 2t + 18
5v = 2 * (9 + v) + 18
5v = 18 + 2v + 18
3v = 36
v = 12
We have 12 $5 bills, so that total cost is 12 * 5 = $60.
~ an aesthetics lover
7 - 5x > 3x + 31
A.X2-3 (all numbers greater than or equal to -3 will satisfy the inequality)B.xs-3 (all numbers less than or equal to -3 will satisfy the inequality)
C.X26 (all numbers greater than or equal to 6 will satisfy the inequality)
D.xs 6 (all numbers less than or equal to 6 will satisfy the inequality)
Answer: B. (all numbers less than or equal to -3 will satisfy the inequality)
Step-by-step explanation:
Hi, to answer this question we have to solve the inequality for x:
7 - 5x > 3x + 31
7-31 > 3x +5x
-24 > 8x
-24/8 > x
-3 > x
x < -3
So, the correct option is:
B. (all numbers less than or equal to -3 will satisfy the inequality)
Feel free to ask for more if needed or if you did not understand something.
If (Fx) = Square root 4x+9+ 2, which inequality can be used to find the domain of f(x)?
A.Square root 4x is greater than or equal to zero
B.4x +9 is greater than or equal to 0
C. 4x is greater than or equal to 0
D.Square root 4x+9 +2 is greater than or equal to 0
Answer:
Third one 4x+9
Step-by-step explanation:
We khow that any any real number inside the root should be positive
Our root is [tex]\sqrt{4x+9}[/tex]4x+9 shoul be positive wich can be expressed mathematically by:
4x+9≥0
A scale drawing of Jimmy's living room is shown below:
If each 2 cm on the scale drawing equals 8 feet, what are the actual dimensions of the room?
Length = 8 feet, width = 6 feet
Length = 12 feet, width = 8 feet
Length = 18 feet, width = 16 feet
Length = 24 feet, width = 16 feet
Answer:
The answer is
Step-by-step explanation:
If 2cm is 8 feet on the drawing then since 4 is the double of 8,
16 would be the width
8·2=16
For the length, 4 is two less than 6 so, to find the width,
Add 16+2=18
Therefore,
The answer is C.
Length=18 Width=16
Answer:
Length = 24 ft, width = 16 ft
Step-by-step explanation:
The scale is 2 cm (drawing) = 8 ft (real).
The drawing length is 6 cm.
6 cm is 3 times 2 cm
Multiply both sides of the scale by 3.
3 * 2 cm = 3 * 8 ft
6 cm = 24 ft
The real length is 24 ft.
The drawing width is 4 cm.
4 cm is 2 times 2 cm
Multiply both sides of the scale by 2.
2 * 2 cm = 2 * 8 ft
4 cm = 16 ft
The real width is 16 ft.
Answer:
Length = 24 ft, width = 16 ft
What is the vertex of y=-3x^2+6x+15? Help is much appreciated.
Answer:
(1, 18)
Step-by-step explanation:
Rewrite the equation in vertex form by completing the square for -3x^2 + 6x + 15. This = -3(x - 1)^2 + 18.
Set y equal to the new right side.
y = -3(x - 1)
Use the vertex form, y = a(x - h)^2 + k, to determine the values of a, h, and k.
a = -3
h = 1
k = 18
Vertex = (h, k) / (1, 18)
please help!!!!!!!!!!!
Answer:
The x value of the point 1/4 the distance from point C to point D is -0.25
Step-by-step explanation:
The given information are;
The location of point C = (1, 2)
The location of point D = (-4, -2)
The point 1/4 from point C to point D is the point 3/4 from point D to point C
Which gives;
The coordinate at point D + 3/4× The difference between the coordinates of point C and point D
Which is (-4 + 3/4×(1 - (-4), - 2 + 3/4×(2 - (-2))
Which gives;
(-4 + 3.75, -2 + 3) and (-0.25, 1)
The coordinates of the point 1/4 the distance from point C to point D is (-0.25, 1)
Therefore, the x value of the point 1/4 the distance from point C to point D = -0.25.
What the answer fast
Answer: 60 degrees
Step-by-step explanation:
This triangle is a 30-60-90 right triangle because the hypotenuse is double the shortest side. Because this is a 30-60-90 right triangle, Angle C, which opens up to the x√3 side, is 60 degrees.
Hope it helps <3
Answer:
angle C=60 degrees
Step-by-step explanation:
cos C=adj/hyp
cos C=√11/2√11
cos C=1/2 ( convert to degrees)
angle C=60 degrees
A survey devices eyepiece is 6 feet off the ground. The device is placed 60 feet from a tree, the eyepiece must be elevated upwards at a 33 angle to see the top of the tree. How tall is the tree?
Greetings from Brasil...
Pure application of trigonometry - tangent
see the attachment
H = X + 6
and
TG 33 = X/60
X = 60.TG 33
X ≈ 39
H = X + 6
H = 39 + 6
H = 45The tee for the fourth hole on a golf course is 300 yards from the tee. On that hole, Marsha hooked her ball to the left, as sketched below. Find the distance between Marsha’s ball and the hole to the nearest tenth of a yard.
A. 195.4 yd
B. 123.7 yd
C. 97.5 yd
D. 105.1 yd
Answer:
97.5
Step-by-step explanation:
Which pairs of events describe independent events?
Answer:last one is the correct ans...
Step-by-step explanation:
Pleased to help u....
vertical stretch of the graph f(x)= x² by a factor of 5
PLEASE HELP!!
Answer:
f(x) = 5x^2
Step-by-step explanation:
A vertical stretch is in the y direction
y = Cf(x) C > 1 stretches it in the y-direction
f(x) = 5x^2
What is the equation of the function in vertex form?
Answer:
Your correct answer is -b/2a
Step-by-step explanation:
What you need to do is find the coordinates of the vertex from the equation itself, using this formula: x = -b/2a
How many solutions does the equation 3x + 6 =- 1 - 3 + 4x have?
TWO
Zero
One
Infinitely many
Answer:
one solution
Step-by-step explanation:
3x + 6 =- 1 - 3 + 4x
Subtract 3x from each side
3x-3x + 6 =- 1 - 3 + 4x -3x
6 = -4+x
Add 4 to each side
6+4 = -4+4+x
10 =x
One solution
Answer:
The answer is one solution. Graph the line, and you will see that it is an infinite vertical line that goes through the x-axis at x=10. It only goes through the x-axis once, at x=10, so the answer is one solution.
Step-by-step explanation:
The answer is one solution. Graph the line, and you will see that it is an infinite vertical line that goes through the x-axis at x=10. It only goes through the x-axis once, at x=10, so the answer is one solution.
Which account has the highest effective annual interest rate? Account 1: Interest is compounded quarterly at an annual rate of 4.20%. Account 2: Interest is compounded monthly at an annual rate of 4.15%. Account 3: Interest is compounded semiannually at an annual rate of 4.10% Account 4: Interest is compounded annually at a rate of 4.25%.
Answer:
Account 1 has the highest effective annual interest rate (0.042666142)
Step-by-step explanation:
Hi, to answer this question we have to apply the Effective Annual Interest Rate formula:
EAIR = [(1+r/n)^n ]-1
Where:
r = nominal interest rate
n = number of periods
If interest is compounded annually, then n = 1; if semi-annually, then n = 2; quarterly, then n = 4; monthly, then n = 12
SO:
Account 1: Interest is compounded quarterly at an annual rate of 4.20%.
EAIR = [(1+r/n)^n ]-1 = [(1+(4.20/100)/4)^4 ]-1 = 0.042666142
Account 2: Interest is compounded monthly at an annual rate of 4.15%.
EAIR = [(1+r/n)^n ]-1 = [(1+(4.15/100)/12)^12 ]-1 =0.042298535
Account 3: Interest is compounded semiannually at an annual rate of 4.10%
EAIR = [(1+r/n)^n ]-1 = [(1+(4.10/100)/2)^2]-1 = 0.04142025
Account 4: Interest is compounded annually at a rate of 4.25%.
EAIR = [(1+r/n)^n ]-1 = [(1+(4.25/100)/1)^1 ]-1 = 0.0425
Since:
0.042666142 (1) < 0.0425 (4) < 0.042298535(2) <0.041420258(3)
Account 1 has the highest effective annual interest rate 0.042666142
Which ordered pair is a solution of the equation? y = 7 x − 3 y=7x−3
Answer:
(1,4)
Step-by-step explanation:
Which ordered pair is a solution of the equation? y = 7 x − 3
a. (1,4) b. (-1,-4) c. both d. neither
Solution
y=7x-3
Solve by trying each ordered pair
a. (1,4)
x=1, y=4
Substituting the value of x and y into the equation
y=7x-3
4=7(1)-3
4=7-3
4=4
This is a true statement
b. (-1,-4)
x=-1, y=-4
Substitute the value into the equation
y=7x-3
-4=7(-1)-3
-4= -7-3
-4= -11
This is not a true statement
This true statement is when x=1 and y=4
So, the ordered pair (1, 4) is the solution
Suppose your soccer coach is ordering duffel bags online for your team. The online store charges $16.49 per bag plus $10.50
for shipping and handling of the order. Suppose x is the number of bags ordered and go is the total cost of the bags. Select
the function that models the relationship. Then select the cost of buying 12 bags.
Answer: g(x)=16.49x+10.50
Total cost of 12 bags
$208.38
Answer:
g(x) = $16.49x + $10.50
$208.38
Step-by-step explanation:
Given the following:
Cost per bag = $16.49
Shipping and handling fee = $10.50
Number of bags ordered = x
If g(x) = total cost of bags
Bag cost = cost per bag × number of bags ordered
Bag Cost = $16.49 * x = $16.49x
Shipping and handling fee = $10.50
Total cost of bags = Bag cost + shipping and handling fee
g(x) = $16.49x + $10.50
Where x is the number of bags ordered.
Therefore, total cost of 12 bags equals ;
g(12) = $16.49(12) + $10.50
g(12) = $197.88 + $10.50
g(12) = $208.38
Answer:
g(x)=16.49x+10.50
$208.38
Step-by-step explanation:
let the cost of x bags = g(x)
cost of one bag = $16.49
cost of x bags = $16.49x
shipping and handling charges = $10.50
total cost of x bags = 16.49x + 10.50
g(x) = 16.49x + 10.50
To determine the cost of 12 bags, substitute x with 12 and simplify:
g(12) = 16.49(12) + 10.50
= 208.38
(PLEASE HELP) Match each hypotenuse length with the leg lengths that will create a right triangle.
Answer:
Step-by-step explanation:
(√2)^2 + (√5)^2 =
2 + 5 = 7
But that equals the hypotenuse squared. The actual value will be √7
======================
(√3)^2 + 4^2 =
3 + 16
19 But this equals the hypotenuse squared, so the answer is actually (√19 ) which isn't there. It might be a right triangle, but none of the answers match this one.
===========================
2^2 + (√5)^2 = 4 + 5 = 9
This is the square of the hypotenuse. √9 = 3 which is the last one.
===========================
(2)^2 + (2)^2 = 4 + 4 = 8
But the hypotenuse will be √8
==========================
1^2 + 2^2 = 1 + 4 = 5
The hypotenuse is √5
Answer:
√8 ==> 2 units, 2 units
√7 ==> √5 units, √2 units
√5 ==> 1 unit, 2 units
3 ==> >2 units, √5 units
Step-by-step explanation:
Find an equation of the line through the point (3,2) with a slope of −2.
It takes Peter 4 hours to walk 12 miles.If he continues to walk at the same rate, how long will it take him to walk:
a) 7miles. b)11miles?
Answer:
a]2.3 hrs
b]3.6hrs
Step-by-step explanation:
4hrs = 12 miles
x = 7miles
4 x 7=28/12=2.3
4 x 11=44/12=3.6hrs
Answer:
Below in bold.
Step-by-step explanation:
His rate of walking = 12/4 = 3 miles per hour.
So the times for 7 and 11 miles are
(a) 7/3 = 2 1/3 hours.
(b) 11/3 = 3 2/3 hours.
Which was one of the goals for some advocates of the Progressive movement?
A: conservation
B: laissez-faire economy
C: welfare
D: establishment of a national bank
Answer:
d
Step-by-step explanation:
The altitude of an object, d, can be modeled using the equation below. d=-16t^2+vh+h.where v is the initial velocity and h is the initial height.A catapult launches a stone with an initial velocity of 48 feet per second and an initial height of 0 feet. How long will the stone be in flight?
Answer:
The stone will be in flight for 3 seconds
Step-by-step explanation:
Given the equation;
d = -16t^2 + vt + h
Where;
v = the initial velocity
h = the initial height
Given;
v = 48 ft/s
h = 0
Substituting into function d;
d = -16t^2 + 48t + 0
d = -16t^2 + 48t
At the point of launch and the point of landing d = 0.
We need to calculate the values of t for d to be equal to zero.
d = -16t^2 + 48t = 0
-16t^2 + 48t = 0
Factorising, we have;
16(-t+3)t = 0
So,
t = 0 or -t+3 = 0
t= 0 or t =3
Change in t is;
∆t = t2 - t1 = 3 - 0
∆t = 3 seconds.
The stone will be in flight for 3 seconds.
By visual inspection, determine the best-fitting regression model for the
scatterplot.
A. no pattern
B. Exponential
C. Quadratic
D. Linear
Answer: C
I just took the test
A city has a population of 220,000 people. Suppose that each year the population grows by 7.25%. What will the population be after 13 years?
Answer:
427,350
Step-by-step explanation:
so you do 7.25×13=94.25
and then you do 94.25%×220,000=207,350
So you can now do 207,250+220,000 (which) =427,350
A plumber wishes to cut a piece of pipe
32 inches long into two parts so that the
larger part is 4 inches less than three
times the smaller part. What are the
lengths of the two parts of the pipe?
Answer:
9 and 23
Step-by-step explanation:
Let x be smaller length in inches.
x+3x-4=32
4x=36
x=9
9*3-4=23
So they're 9 and 23 inches long.
The lengths of the two parts of the pipe are 9 and 23 inches long.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Let x be the smaller length in inches.
x + 3x - 4 = 32
4x = 36
x =9
Now substitute;
9*3 - 4 = 23
Hence, the lengths of the two parts of the pipe are 9 and 23 inches long.
Learn more about the unitary method;
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Can someone help me with this plz? Will give brainliest
Answer:
∆ABC=∆DBC
Step-by-step explanation:
The angle of ABC, which is 90° is the same as the angle DBC which is also 90°