We have been given that Mrs. Culland is finding the center of a circle whose equation is [tex]x^2+y^2+6x+4y-3 = 0[/tex] by completing the square. We are asked to find the final step of her work.
Let us complete the square.
We know that to complete square, we need to add the half the square of coefficient of x and y term.
[tex]x^2+y^2+6x+4y-3+3 = 0+3[/tex]
[tex]x^2+6x+y^2+4y=3[/tex]
We can see that coefficient of x is 6 and coefficient of y is 4.
[tex](\frac{6}{2})^2=3^2=9[/tex]
[tex](\frac{4}{2})^2=2^2=4[/tex]
Now we will add 9 and 4 on both sides as:
[tex]x^2+6x+9+y^2+4y+4=3+9+4[/tex]
[tex](x^2+6x+9)+(y^2+4y+4)=16[/tex]
Now we will complete the square as:
[tex](x+3)^2+(y+2)^2=4^2[/tex]
We know that standard form of equation of a circle is in form [tex](x-h)^2+(y-k)^2=r^2[/tex], where point (h,k) represents center of circle and r represents radius of circle.
We can rewrite our equation as:
[tex](x-(-3))^2+(y-(-2))^2=4^2[/tex]
Now we can see that center is at point [tex](-3,-2)[/tex].
Therefore, the equation of the circle would be [tex](x+3)^2+(y+2)^2=4^2[/tex] with a center at point [tex](-3,-2)[/tex].
Answer:
d
Step-by-step explanation:
egd 2021
Which polynomial function has a leading coefficient of 1, roots -2 and 7 with multiplicity 1, and root 5 with multiplicity 27
O
f(x) = 2(x + 7)(x + 5)(x-2)
Rx) = 2(x - 7)(x - 5)(x + 2)
Rx) = (x + 7)(x + 5)(x + 5)(x - 2)
f(x) = (x - 7)(x - 5)(x - 5)(x + 2)
The polynomial function with a leading coefficient of 1 and the specified roots and multiplicities is f(x) = (x + 2)(x - 7)(x - 5)^27.
Explanation:The polynomial function you are looking for, which has a leading coefficient of 1, roots at -2 and 7 each with a multiplicity of 1, and a root at 5 with multiplicity 27, is given by the expression:
f(x) = (x + 2)(x - 7)(x - 5)^27
The given roots indicate the factors of the polynomial, and the multiplicity of each root shows how many times that factor is repeated. Hence, the root -2 becomes (x + 2), the root 7 becomes (x - 7), and the root 5 with multiplicity 27 becomes (x - 5)^27. The leading coefficient is 1, which means these factors are not multiplied by any other constant.
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1. Complete the inequality below to describe the
domain of the graph shown.
Domain
2. Complete the inequality below to describe the
range of the graph shown.
Range: <_y <5
Domain is the entire span left to right (on the x-axis) that the graph is on. Since the graph goes from x=-4 and ends at x=4, the domain would be from -4 to 4. The circle at -4 is open, so it does not include the point at -4, just everything leading up to it. So, the domain would be
[tex] - 4 < x \leqslant 4[/tex]
The range is similar, it is the entire span that the graph goes up and down (on the y-axis). The graph starts at the bottom at y=-2, and ends at y=5. The bottom point (4,-2) is closed, so the graph includes that point, and the top point (-4,5) is open and doesn't include the point. Therefore, the range would be
[tex] - 2 \leqslant x < 5[/tex]
Answer:
1) -4 2) -2
Step-by-step explanation:
i got it right
What is answer 6x+7-5x=10
Answer:
i think the answer is going to be 3
Step-by-step explanation:
Use the line plots to answer each question.
1) The line plot below shows the sizes of
different insects (in inches).
What is the difference in size between the
shortest and longest insect?
Andrea has a credit score of 895 and Ashley has a credit score of 768. Stutts National Bank has determined that both will receive a credit card; however, the borrower with the lower credit score will be charged a $50.00 fee the first time she makes a purchase. If both receive a credit card with $1,500.00 available credit, what will Ashley's remaining available credit be after she purchases a $425.00 Coach bag?
Answer:
Ashley's remaining available credit after her first purchase is $1025.00
Step-by-step explanation:
Here we are told that the borrower with the lower credit score will be charged $50.00 fee after the first purchase
Therefore, we have
Credit score Andrea = 895
Credit score for Ashley = 768
Therefore, Ashley has the lower credit score hence after her first purchase of a $425.00 Coach bag, we have
Available credit = Initial balance - Purchase - Charges
∴ Available credit = $1,500.00 - ($425.00 + $50.00) = $1025.00
Therefore, Ashley's remaining available credit after she purchases the $425.00 Coach bag = $1025.00.
A fast food restaurant wants to know what types of toys to put in their kids meals, so they will survey their customers. What would be the BEST way to do this?
personally i would ask every one who orders a kids meal.
hope this helps
Answer:
the answer is c) Ask anyone who orders a kid's meals
Step-by-step explanation:
Look at the graph of the linear function.The rate of change between point A and point B is 2. What is the rate of change between point C and point D?
–2
Negative one-half
One-half
2
the answer is be like 20
Answer:
The answer is -1/2
Step-by-step explanation:
A line passes through the points (-1, 4) and (2, -2). What is the equation of this line?
Write your answer in the form y=mx+b.
I don't get it please help!
Answer:
y = -2x+2
Step-by-step explanation:
First we find the slope
m = (y2-y1)/(x2-x1)
= (-2-4)/(2--1)
= (-2-4)/(2+1)
-6/3
-2
We have the slope =-2
We can substitute it into the equation
y = mx+b where m is the slope and b is the y intercept
y =-2x+b
Use a point for x and y to solve for b
4 = -2(-1) +b
4 = 2+b
Subtract 2 from each side
4 -2 = -2+2+b
2 = b
We know m and b
y = -2x+2
Answer:
y = -2x + 2
Step-by-step explanation:
Slope: (-2-4)/(2--1) = -6/3 = -2
y - 4 = -2(x - -1)
y = -2x - 2 + 4
y = -2x + 2
When graphed, which parabola opens downward?
y = –3x2
y = (x – 3)2
y = one-third x squared
y = x2 – 3
The parabola that opens downward when graphed is y = –3x^2, as the negative coefficient of the x^2 term determines the downward opening direction.
The student has asked which parabola opens downward when graphed. The general form of a parabola is y = ax2 + bx + c. The direction in which the parabola opens is determined by the coefficient a of the x2 term. If a is negative, the parabola opens downward, and if a is positive, the parabola opens upward. Looking at the provided equations, we can identify the equation with a negative a value:
y = –3x2 (The coefficient of the x2 term is -3, so this parabola opens downward.)y = (x – 3)2 (The coefficient here is positive after expanding, so this parabola opens upward.)y = one-third x squared (The coefficient is positive 1/3, so this parabola opens upward.)y = x2 – 3 (The coefficient is positive 1, so this parabola opens upward.)Therefore, the equation of the parabola that opens downward when graphed is y = –3x2
PLZ HELP ON THIS QUESTION ASAP PLZ THANKS AND 5 STARS AND WHEN THERES OPTION FOR BRAINLEST ILL GIVE YOU BRAINLEST ASAP WITH ANSWER PLZ 15 POINTS
Answer:
£114
Let me know if it is incorrect so that I can review my answer and fix it! :)
Step-by-step explanation:
20% * £1200 = £240
£1200 + £240 = £1440
£1440 - £300 = £1140
£1140 / 10 = £114
Answer:
£114
Step-by-step explanation:
Total to be paid:
[1200 + (20% of 1200)] - 300
[1200 + (20/100 × 1200)] - 300
1200 + 240 - 300
1140
10 installments
Each:
1140/1
114
Write one digit on each side of 92 to make a four digit multiple of 45. How many different solutions does this problem have?
Answer:
Two solutions:
Adding 7 to the left and 0 to the right: 7920
Adding 2 to the left and 5 to the right: 2925
Step-by-step explanation:
The multiples of 45 always have as last digit 0 or 5, so the digit to the right of 92 has to be 0 or 5.
If we use 0 as the last digit, our options of multiples will be just 7920 (7920 = 45 * 176)
If we use 5 as the last digit, our option of multiples will be just 2925 (2925 = 45 * 65)
So we have just two solutions for this problem:
Adding 7 to the left and 0 to the right: 7920
Adding 2 to the left and 5 to the right: 2925
Which statement is true about the equation (x – 4)(x + 2) = 16?
The equation x - 4 = 16 can be used to solve for a solution of the given equation.
The standard form of the equation is x2 - 2x - 8 = 0.
The factored form of the equation is (x + 4)(x – 6) = 0.
One solution of the equation is x=-6.
Answer:
The factored from of the equation is (x+4)(x-6)=0.
Step-by-step explanation:
When solving this problem, we need to find the factored form of this problem. Remember that in factored form, the right-hand side of the equation must equal to 0.
We can simply convert the left-hand side to standard form first:
(x-4)(x+2)=16 --> x²-2x-8= 16.
Now, to set the right-hand side of the equation to 0, we must subtract -16 from both sides:
x²-2x-24=0.
Now, if we convert this to factored form, we will get:
(x+4)(x-6)= 0.
All of the other statements are false. This is the only true statement.
David is buying a cheese wheel priced at $650 before tax. The store charges 8%, percent sales tax.
What is the total price, including tax, David pays for the cheese wheel?
Answer:
Pretty sure it would end up being $702 including tax
Step-by-step explanation:
650 * 0.08 = 52
52 + 650 = 702
help please!! kinda confusing for me...
6
Step-by-step explanation:
-2^3=-8
-10+(-8)=-10-8=-18
-18÷-3=6
18,300 divided by 19.7%
Answer:
13,300 divided by 19.7 % is 92893.4010152
Step-by-step explanation:
The circumference of a circle measures 11.27π ft.What is the measure of the diameter of this Circle?
Find the volume of the figure
Answer:
see below
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
We know the diameter so we need the radius
r = d/2 =13/2 = 6.5
V = pi (6.5)^2 (19)
V = 802.75 pi mm^3
We can approximate pi by 3.14
V =2520.635 mm^3
or by using the pi button
V =2521.913503 mm^3
(11+i)^2
please help!
Answer:
121 + 22i - 1
Step-by-step explanation:
Expand:
(11 + i)² = (11 + i)(11 + i)
Note that:
i² = -1
Use FOIL method. Multiply first terms, outside terms, inside terms, then the last two terms:
(11)(11) = 121
(11)(i) = 11i
(i)(11) = 11i
(i)(i) = -1
Combine like terms:
121 + 11i + 11i - 1
121 + (11i + 11i) - 1
121 + 22i - 1
121 + 22i - 1 is your answer.
~
ANSWER FAST I NEED IT TO PASS Follow the steps to solve the equation using the algebra tiles.
−4x + 1 = x + (−4)
1. Add 4 positive x-tiles to both sides and create zero pairs.
2. Add 4 positive unit tiles to both sides and create zero pairs.
3. Divide the unit tiles evenly among the x-tiles.
x =
The solution to the equation -4x + 1 = x + (-4) using algebra tiles is x = 1
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation:
-4x + 1 = x + (-4)
Add 4 positive x-tiles to both sides and create zero pairs:
-4x + 1 + 4x = x + (-4) + 4x
1 = 5x - 4
Add 4 positive unit tiles to both sides and create zero pairs:
1 + 4 = 5x - 4 + 4
5x = 5
Divide the unit tiles evenly among the x-tiles:
5x/5 = 5/5
x = 1
The solution to the equation -4x + 1 = x + (-4) using algebra tiles is x = 1
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x = 1
Step-by-step explanation: did on edge
Determine the longest side in ΔDEF.
A) segment EF
B) segment DE
C) segment FE
D) segment DF
15 / x equals 50 / 4
Answer:
Step-by-step explanation:
Solve for x by cross multiplying.
Exact Form:
x=6/5
Decimal Form:
x=1.2
Mixed Number Form:
x=1 1/5
i hope its correct plz tell me if im wrong
Is 2 equal to 2 • 7? Explain.
Answer:
No, 2 is not 14
Step-by-step explanation:
Evaluate 2*7 you get 2*7 = 14
but 14 is not 2 so no.
Answer:
no
Step-by-step explanation:
No because, 2 times 7 is 14.
HELP WITH MY MATHS HOMEWORK, ITS A YEAR 7 QUESTION
The width of a swimming pool is 12 feet less than the pool's length. The area of the pool is 540 square feet. What are the dimensions of the pool?
Answer:
30 feet by 18 feet
Step-by-step explanation:
Area = length * width
A = x*w
w = x - 12
A = 540 sq. ft
540 = x * (x -12)
x*x - 12x - 540 = 0
x*x - 12x + 36 - 36 - 540 = 0
(x - 6)^2 - 576 = 0
x - 6 = 24
or x -6 = -24
x = 30 or x = -18
w = 30 - 12 = 18
30 ft by 18 ft
Which of the following scenarios represents an impulse purchase?
1) Tara goes to the pet store for fish food. She visits the pet adoption center and quickly decides to adopt a dog without considering all of the costs in caring for the dog.
2)Tara goes to the pet store for fish food. She visits the pet adoption center and decides to research the costs in caring for a dog before she adopts one.
3) Tara goes to the pet store for fish food. She visits the pet adoption center and decides to make an affordable donation towards the care of the animals waiting to be adopted.
Answer:
1
Step-by-step explanation:
Answer 1 is an impulse purchase. An impulse purchase is when someone does something just because they feel like it. She doesn't give herself time to think about the outcomes, how much it would cost, the type of dog, nada. She just buys it. Therefore, answer 1 is an example of impulse buying.
Find the HCF of 168 and 196.
Answer:
The HCF of 168 & 196 is 28
Step-by-step explanation:
The factors of 168 are: 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168
The factors of 196 are: 1, 2, 4, 7, 14, 28, 49, 98, 196
The highest factor that both 168 and 196 share is 28
Hope this helps :D
Answer:
28
Step-by-step explanation:
168 = 2³ × 3 × 7
196 = 2² × 7²
HCF(168 ; 196) = 2² × 7 = 4 × 7 = 28
Oil flows into a tank according to the rate F(t)=t^2+1/1+t , and at the same time empties out at the rate E(t)=ln(t+7)/t+2, with both F(t) and E(t) measured in gallons per minute. How much oil, to the nearest gallon, is in the tank at time t = 12 minutes. You must show your setup but can use your calculator for all evaluations. (10 points)
Answer:
573.95 gallons/minute
Step-by-step explanation:
To find the amount of oil after 12 minutes you take the difference between the amount of oil that flows into the tank minus the the oil that flows aout the tanks. Then you have:
[tex]T(t)=F(t)-E(t)\\\\F(t)=t^2+\frac{1}{t+1}\\\\E(t)=\frac{ln(t+7)}{t+2}[/tex]
Being F(t) the flow that goes into the tank per minute, and E(t) the amount of oil that flows outside the tank per minute.
To know the total amount of F and E for t=12 you integrate these function:
[tex]\int_0^{12}F(t)dt=\frac{t^3}{3}+ln(t+1)|_{0}^{12}=578.56\frac{gallons}{minute}\\\\\int_{0}^{12}E(t)dt=\int_0^{12}[\frac{ln(t+7)}{t+2}]dt=4.61\frac{gallons}{minute}\\\\\int_0^{12}T(t)dt=578.56-4.61=573.95\frac{gallons}{minute}[/tex]
573.95 gallons/minute
The grades on a history midterm at Almond are roughly symmetric with \mu = 85μ=85mu, equals, 85 and \sigma = 2.0σ=2.0sigma, equals, 2, point, 0. Michael scored 868686 on the exam. Find the z-score for Michael's exam grade. Round to two decimal places.
Answer:
0.50
Step-by-step explanation:
The z-score for Michael's exam grade is 0.5.
Explanation:To find the z-score for Michael's exam grade, we can use the formula: z = (x - µ) / σ, where x is the value of Michael's grade, µ is the mean, and σ is the standard deviation.
Plugging in the given values,
we get z = (86 - 85) / 2 = 0.5.
Therefore, the z-score for Michael's exam grade is 0.5.
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Which three-dimensional figures have lateral faces that are polygons? Check all that apply
Question:
Which three-dimensional figures have lateral faces that are polygons? check all that apply.
- cones
- cylinders
- hemispheres
- prisms
- pyramids
- spheres
Answer:
The correct choices are;
- prisms and
- pyramids
Step-by-step explanation:
A polygon is a figure closed or bounded with several straight line segments and polygons are named based on how many sides, side size and sizes of angles that they have present.
A three sided polygon for example is called a triangle
A lateral face are the faces of a prism except the base
Based on the definitions, we note that out of the options, only prisms, and pyramids have lateral faces that are made up entirely of straight line segments, hence polygons. Therefore, the correct choices are prisms and pyramids.
Answer:
Actually the correct is Cylinders, Prisms, and Pyramids. I just did it
Step-by-step explanation:
Suppose vanilla beans cost $600 per kilogram. Julie bought 9 grams of vanilla beans. Jacques bought 70 grams of vanilla beans. How much more did Jacques pay for his vanilla beans? $5.40 $12.00 $36.60 $42.00
Answer:
5.40
Step-by-step explanation:
Cost of 70 gram vanilla beans is $42, so Jacques pay $42 for his vanilla beans.
Cost based problem:What information do we have?
Cost of 1 kg vanilla beans = $600
Amount of vanilla beans bought by Jacque = 70 gram
Cost of 1 g vanilla beans = [600/1000]
Cost of 1 g vanilla beans = $0.6 per gram
Cost of 70 gram vanilla beans = 70 × Cost of 1 g vanilla beans
Cost of 70 gram vanilla beans = 70 × $0.6
Cost of 70 gram vanilla beans = $42
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