Answer:
We know that the equation of the circle in standard form is equal to (x-h)² + (y-k)² = r² where (h,k) is the center of the circle and r is the radius of the circle.
We have x² + y² + 8x + 22y + 37 = 0, let's get to the standard form :
1 - We first group terms with the same variable :
(x²+8x) + (y²+22y) + 37 = 0
2 - We then move the constant to the opposite side of the equation (don't forget to change the sign !)
(x²+8x) + (y²+22y) = - 37
3 - Do you recall the quadratic identities ? (a+b)² = a² + 2ab + b². Now that's what we are trying to find. We call this process "completing the square".
x²+8x = (x²+8x + 4²) - 4² = (x+4)² - 4²
y²+22y = (y²+22y+11²)-11² = (y+11)²-11²
4 - We plug the new values inside our equation :
(x+4)² - 4² + (y+22)² - 11² = -37
(x+4)² + (y+22)² = -37+4²+11²
(x+4)²+(y+22)² = 100
5 - We re-write in standard form :
(x-(-4)²)² + (y - (-22))² = 10²
And now it is easy to identify h and k, h = -4 and k = - 22 and the radius r equal 10. You can now complete the sentence :)
Three consecutive integers have a sum of -42. Write and solve an equation to find the three integers.
x + ( x + 1 ) + ( x + 2 ) = -42
Opening the brackets and simplifying :
x + x + 1 + x + 2 = -42
3x + 3 = -42
Now , solving equation :
[tex]\bf \rightarrow \: \:3x \: + \: 3 \: = \: -42[/tex]
[tex]\bf \rightarrow \: \: 3x \: = \: -42 \: - 3[/tex]
[tex]\bf \rightarrow \:3x \: = \: -45 \: [/tex]
[tex]\bf \rightarrow \:x \: = \: \frac{ - 45}{ \: 3} \\ [/tex]
[tex]\bf \rightarrow \:x \: = \: \cancel\frac{ - 45}{ \: 3} \: \: ^{ - 15} \\ [/tex]
[tex]\bf \rightarrow \:x \: = \: - 15[/tex]
[tex]{\boxed{ \Large{ \red{ \rm{ \underline{ Now \: \: substitute}}}}}}[/tex]
[tex]\bf \implies \: \:x \: = \: - 15[/tex]
[tex]\bf \implies \: \:x \: + \: 1 \: = \: - 15 \: + \: 1 \: = \: - 14[/tex]
[tex]\bf \implies \: \:x \: + \:2 \: = \: - 15 \: + \: 2 \: = \: - 13[/tex]
-15 , -14 and -13 are the three consecutive integers.
Madison is thinking of a number. Sixty, decreased by four times the number, is the same as eight
times the number, increased by seventy-two. What is Madison's number?
Answer:
x = -1
Step-by-step explanation:
Let the mystery number be x
Equation:
60 - 4x = 8x + 72
Subtract 60 from both sides
-4x = 8x + 12
Subtract 8x from both sides
-12x = 12
x = -1
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
"The sum of two numbers is 17" <- that's our first equation. Sum means we're going to add. "two numbers" - well, we don't know what they are, so we can use x and y. (Note: x and y are just placeholders. You can use ANY placeholder as long as you keep it consistent with the second equations. x and y just mean "some number". We're going to work to find those numbers)
So for our first equation, we have two numbers being added together. So we can just write that as:
x+ y = 17
For the second equation:
"Three times one number increased by 5 is the same as twice the other number decreased by 4"
We have to work to process what is being asked. “Three times one number increased by 5”. So we know we are multiplying 3 to one of our numbers and increasing it (adding it) by 5.
So this part can be written as 3x+5
“Is the same as” just means “equal to”
“Twice the other number decreased by 4”. So twice, means two times and “decreased by four” just tells us to subtract four. So this part can be written as:
2y-4
Now we need to put this second equation together.
3x+5=2y-4.
So now we have our two equations:
x+y = 17
3x+5 = 2y-4
We have a few ways of solving this. We can use substitution, elimination, or graphing. I’m going to use substitution for this one.
So for substitution, we need to take one of two equations and solve for a single variable. So I’m going to take our first equation and solve for y.
x+y=17
-x. -x
y= -x+17
Now I’m going to put “-x+17” in for the “y” in the second equations.
3x+5=2y-4
3x+5 = 2 (-x+17) - 4. (Now distribute)
3x+5 = -2x + 34 - 4. (Now simplify)
3x+5 = - 2x + 30. (Now we need to get the x to one side)
+2x +2x
5x+5=30
-5. -5
5x = 25
X = 5
Now we can take the first equation and put 5 in for x to solve for y
x+y = 17
5 + y = 17
-5 -5
y= -12
So our x is 5 and our y is 12.
Find the missing length the triangles are similar.
Answer:
Step-by-step explanation:
The missing length is 13 because,
Lets say the top triangle is A and the bottom triangle is B.
Triangle A gives us the side GF, and Triangle B gives us the sides TU and ST. Since the triangles are similar(as stated in the problem), we can pair 2 sides GF(A) and TU(B) which is 11:22.(one way I usually figure which sides are similar is by first- matching the hypotenuse, then checking which of the remaining two is longer.. if that made any sense). You can see that their relationship is x2 or /2 (In another word, from A to B is multiplication- ex: 11 * 2 is 22, and from B to A is division- ex 22/2 is 11.) Since the missing number is the hypotenuse of triangle A and you know the Hypotenuse of triangle B all you have to do is divide side TS by 2 to get side SF. So the missing side is 13.
Answer: 13
A basketball team won 8 games and lost 7 games. Based on these results what is the probability of winning a game
the probability is made of the desired outcome divided by the total outcome.
desired = wins = 8
total = wins and losses = 15
8/15 is the probability (approx. 53%)
hope it helps :)
Last year, Mary opened an investment account with $5400. At the end of the year, the amount in the account
had decreased by 6%.
PLS HELP MEE
1st equation: a^2 + b^2 = c^2
2nd equation: a^2 + b^2 = n^2
Since the equations for both triangles have a^2 + b^2, you can think of the two equations for c^2 and n^2 as a system of equations. Substitute what a^2 + b^2 equals in the first equation for a^2 + b^2 in the second equation. After you substitute, what equation do
you get?
Answer:
c² = n²
Step-by-step explanation:
Given the 2 equations
a² + b² = c² → (1)
a² + b² = n² → (2)
Substitute a² + b² = c² into (2)
c² = n²
For his long distance phone service, tony pays $3 monthly fees plus 11 cents per minute. Last month, Tony's long distance bill was $22.03. For how many minutes was tony billed
Answer:
11+11= 22 answer is $ 22.03
The population of a large U.S. city is 2,707,210. Which of the following best expresses this population?
A 2.7 × 106 C 2.707 × 106
B 2.7 × 107 D 27.07 × 106
Answer:
2.707 * 10^6
i think it is the best expression
the first three terms of an arithmetic progression are m,12 and n . Find the value of m+n
===========================================
Explanation:
There are a few approaches. Here's one way to solve.
Let d be the common difference between the terms.
We add d to each term of this arithmetic sequence to get the next term.
First term = mSecond term = 12 = m+dThird term = n = (m+d)+d = m+2dFocusing on the second equation, we can solve for d like so
m+d = 12
d = 12-m
This is then plugged into the third equation
n = m+2d
n = m+2(12-m)
n = m+24-2m
n = 24-m
Therefore,
m+n = m+(24-m) = 24
It turns out that it doesn't matter what m and n are because m+n is always equal to 24 in this case.
-----------------
A more concrete example:
Let's say m = 2. We won't set up n just yet but we'll be able to compute it fairly soon.
Since m = 2, this means d = 12-m = 12-2 = 10. This is the gap between adjacent or neighboring terms.
If d = 10, then the third term must be n = 12+d = 12+10 = 22
We can then see that m+n = 2+22 = 24
-----------------
I'll do another example:
m = 5
d = 12-m = 12-5 = 7
n = 12+d = 7 = 19
m+n = 5+19 = 24
Whenever in doubt, or if you get stuck, it helps to come up with actual numeric values to hopefully clear things up.
-----------------
An alternative way to get the answer:
Let's try to determine what m+n is actually saying. We have 12 right in the middle of the first term (m) and third term (n). Because the gap between the numbers is the same (that being d), we know that 12 is the midpoint of m and n. It might help to draw out a number line to see what's going on.
The midpoint of m and n is (m+n)/2
Set this equal to 12 and isolate the "m+n"
(firstTerm+thirdTerm)/2 = second term
(m+n)/2 = 12
m+n = 2*12
m+n = 24
So in general, if the first three terms of the arithmetic sequence are m, k, n, then m+n = 2k.
If A = {2,4,6,8,}, write the set A by description method
Step-by-step explanation:
Set-builder notation is a notation for describing a set by indicating the properties that its members must satisfy.
C={2,4,6,8}
C={2×1,2×2,2×3,2×4}
thus set builder form is:
{x:x=2n,n∈N} and this set is also call even number set in description mathod
[tex]\frac{1}{3} d +4=28[/tex]
Answer:
d = 72
Step-by-step explanation:
1/3 d + 4 = 28
Subtract 4 from each side
1/3d +4-4 = 28-4
1/3d = 24
Multiply each side by 3
3 * 1/3d = 3 * 24
d = 72
Writing equations in standard form:
(1,-6) and (-7,2)
How would I write this in standard form? I already tried but I keep getting x+y=7 and it says it’s wrong so could someone help?
Answer:
[tex]x + y = - 5[/tex]
Step-by-step explanation:
hopefully it is clear and makes sense
:)
after allowing a 15% discount on the Marked price of a radio becomes rupees 1997 find the Marked price of the radio
Answer:
after discount sales price is rs 1997 which is 85 % of market price the market price = 1997/85×100 = 2350 ans.
Plz help me out with this ;)
[tex]\sqrt{\\\frac{9+\sqrt{17} }{2}[/tex]
[tex]\huge\underline\pink{✏ANSWER}[/tex]
Hello and sorry but it's a Gatheted Question Can you fix it Can you?Sorry for answering a nonsense
#BrainliestBunch
3b of 9
The ordered pair (5, – 3) is a solution to which of the following inequalities?
o 4y + 2x < -1
oy > - 2x + 8
O-2y < 3x - 9
Oy - 2x > 5
Answer:
4y+2x ≤ -1
(5,-3)
4x(-3)+2×(5) ≤ -1
-12+10≤ -1
-2 ≤ -1
A) 4y+2x ≤ -1
~OAmalOHopeO
I have done it more than 10 times i still cant find the answer
Question:
Answer:
there may be mistake in the question
The speed of a car as a function of time is shown in the figure(attached up) . Find the distance travelled by the car in 8 seconds and its acceleration .
______________________________
[tex]\sf\bold{The\:above\:graph\:says:}[/tex]
$\sf\bold\red{a=slope\:of\:v-t\:graph}$$\space$
$\sf\bold{here:}$
$\sf\bold\red{a=acceleration}$$\space$
$\sf\bold{Find\:acceleration\:by\:v-t\:graph:}$
$\mapsto$ $\sf\small{TanØ =}$ $\sf\dfrac{slope\:of\:y}{slope\:of\:x}$= $\sf\dfrac{20}{8}$ $\sf{m/s^2}$
$\space$
$\mapsto$ [tex]\sf\underline\bold\purple{a=2.5m/s^2}[/tex]$\space$
$\sf\bold{Now,calculate\:the\:distance:}$
$\sf\bold{By\:equation\:of\:motion.}$$\sf{s=}$ $\sf{ut+}$ $\sf\dfrac{1}{2}$ $\sf{at^2}$$\space$
$\sf\bold{Given\:parameters:}$
$\sf\bold{u=0}$$\sf\bold{a=5/8}$$\sf\bold{t=8}$$\space$
$\sf\bold{Substituting \: the\:values:}$
$\mapsto$ $\sf\small{s=0+}$ $\sf\dfrac{1}{2}$ $\times$ $\sf\dfrac{5}{8}$ $\sf\small{8^2}$
$\space$
$\longmapsto$ $\sf\underline\bold\purple{S=80m}$
$\space$
❍Therefore , the acceleration is $\sf\bold{2.5m/s^2}$ and the distance traveled by car is $\sf\bold{80m.}$
_______________________________
80 m is distance ! Please mark as brainliest
find the measure of the missing angles in the kite
Answer:
x = y = 104°
Step-by-step explanation:
The sum of the interior angles = 360°
The opposite angles x and y are congruent , that is y = x , then
92 + 60 + x + x = 360
152 + 2x = 360 ( subtract 152 from both sides )
2x = 208 ( divide both sides by 2 )
x = 104
Then
x = y = 104°
State the leading coefficient of -7x+10x^3-9x^5+3x^2+3?
Answer:
-9
Step-by-step explanation:
-7x+10x^3-9x^5+3x^2+3
We need to write the terms from highest power to smallest power
-9x^5+10x^3+3x^2-7x+3
The leading coefficient is the number in front of the highest power
-9
A father's age now is three times the age that his son was 4 years ago. In 12 years, the father will be twice as old as his son. find their ages now.
Answer:
the dad is 60 im not sure about the son
Step-by-step explanation:
What is the area of the circle?
Diameter = radius x 2
So, the radius is half of the denominator.
10 / 2 = 5
A = pi x r^2
A = pi x 5^2
A = 3 x 25
A = 75 ft^2
Hope this helps!
Problem
Write the slope of the line containing each pair of points.
1. (3,4) and (5,7)
Answer:
3/2
Step-by-step explanation:
the slope is the ratio y/x indicating how many units y changes, when x changes a certain amount of units.
so, when we have 2 points, we can look at the difference of the x and y coordinates. y difference / x difference is the slope.
going from (3, 4) to (5, 7) changes x by +2 and y by +3.
so, the slope of the line is 3/2
Emília ganhou 350 reais de sua avó. Com esse dinheiro, ela comprou um sapato, e uma roupa que custou o dobro do preço do sapato. Os 200 reais que sobraram foram depositados por Emília em sua conta poupança.
Qual é a equação eu permite determinar o preço x, em reais, que Emília pagou por esse sapato?
A) x + 2× = 350
B) x + 2× 200 = 350
C) x + (x + 2) + 200 = 350
D) x + ײ + 200 = 350
Is the equation below written in standard form? If not, select which explanation best applies to why the equation
is not written in standard form.
12 = 2x + 4y
A. the requirement that A 20 is not satisfied
B. the requirement that A and B are not both zero is not satisfied
C. A, B, and C do not have a greatest common factor of 1
D. the equation is written in standard form
Answer:
D
Step-by-step explanation:
The equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers
12 = 2x + 4y , that is
2x + 4y = 12 ← is in standard form
The population of valleytown is also 5,000 with an annual increase of 1,000. Can the expected population for Valleytown be modeled with an exponential growth fu nction ? Explan
Answer:
An annual increase of 1000 means that the number by which the population increases is constant, which means that the population cannot be modeled with an exponential growth function, it is modeled by a linear growth function.
Step-by-step explanation:
Linear growth:
The number by which it increases is constant.
Exponential growth:
The rate which it increases is constant, that is, a proportion of population.
Annual increase of 1,000.
An annual increase of 1000 means that the number by which the population increases is constant, which means that the population cannot be modeled with an exponential growth function, it is modeled by a linear growth function.
In parallelogram ABCD, m∠B = 105°.
What is the value of x. (Round your answer to the nearest tenth, if necessary.)
Answer:
x=52.5
Step-by-step explanation:
Since ABCD is a parallelogram, B= ADC. So angle ADC is 105. Next since ED=AD, angle EAD=angle AED=x and ADE=75. So 2x+75=180, 2x=105, x=105/2
In parallelogram ABCD, m∠B = 105° then the value of x = 52.5
What is a parallelogram?That quadrilateral in which opposite sides are parallel is called a parallelogram.
Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
Since ED ≈ AD,
∆AED is an isosceles triangle where ∠EAD and ∠AED has the same angle measurement
Now, ∠B = 105°, since ABCD is a parallelogram,
∠B = ∠D
∠ADC = 105°
∠ADE = 180°-105° = 75°
Now, ∠EAD + ∠AED+ ∠ADE = 180°
∠AED+∠AED+∠ADE = 180°
x+x+75°=180°
2x=180+75°
2x = 105°
x = 52.5°
Learn more about parallelogram;
https://brainly.com/question/1563728
#SPJ2
Triangle ABC with vertices A(-4, 2), B(4,7), and
C(5, 1) in the x-axis.
A’
B’
C’
D’
9514 1404 393
Answer:
A'(-4, -2), B'(4, -7), C'(5, -1)
Step-by-step explanation:
Reflection in the x-axis changes the sign of each y-coordinate.
(x, y) ⇒ (x, -y)
A(-4, 2) ⇒ A'(-4, -2)
B(4, 7) ⇒ B'(4, -7)
C(5, 1) ⇒ C'(5, -1)
Amy bakes and sells cupcakes out of her home. She uses baking pans that hold 12 cupcakes and 36 cupcakes to fill her orders. Amy needs to fill her biggest order of 504 cupcakes for a special event.
a. Write an equation to represent the number of 12-cup and 36-cup baking pans for her
order.
b. Amy needs to use a combination of the 12-cup and 36-cup baking pans to fill the order. With only eighteen 12-cup baking pans in her shop, how many of the 36-cup baking pans does she need to complete the order?
Answer:
Below
Step-by-step explanation:
a) let's say that x represents the number of 12 pan cupcakes and y represent the number of 36 pan cupcakes. For her larger order she needs 504 cupcakes so that is the total. This can be demonstrated by the equation below!
12x + 36y = 504
b) here we know that x = 18, so...
12(18) + 36y = 504
216 + 36y = 504
36y = 288
Divide both sides by 36
y = 8
Amy needs 8 of the 36 cup baking pans in order to complete her order.
Hope this helps! Best of luck <3
here is another question i need help
